Supersymmetric giant graviton solutions in AdS3

International Nuclear Information System (INIS)

Mandal, Gautam; Raju, Suvrat; Smedbaeck, Mikael

2008-01-01

We parametrize all classical probe brane configurations that preserve four supersymmetries in (a) the extremal D1-D5 geometry, (b) the extremal D1-D5-P geometry, (c) the smooth D1-D5 solutions proposed by Lunin and Mathur, and (d) global AdS 3 xS 3 xT 4 /K3. These configurations consist of D1 branes, D5 branes, and bound states of D5 and D1 branes with the property that a particular Killing vector is tangent to the brane world volume at each point. We show that the supersymmetric sector of the D5-brane world volume theory may be analyzed in an effective 1+1 dimensional framework that places it on the same footing as D1 branes. In global AdS and the corresponding Lunin-Mathur solution, the solutions we describe are ''bound'' to the center of AdS for generic parameters and cannot escape to infinity. We show that these probes only exist on the submanifold of moduli space where the background B NS field and theta angle vanish. We quantize these probes in the near-horizon region of the extremal D1-D5 geometry and obtain the theory of long strings discussed by Seiberg and Witten

Asymptotically AdS spacetimes with a timelike Kasner singularity

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Ren, Jie [Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel)

2016-07-21

Exact solutions to Einstein’s equations for holographic models are presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz) singularity, and the UV is asymptotically AdS. This solution describes a holographic RG flow between them. The solution’s appearance is an interpolation between the planar AdS black hole and the AdS soliton. The causality constraint is always satisfied. The entanglement entropy and Wilson loops are discussed. The boundary condition for the current-current correlation function and the Laplacian in the IR is examined. There is no infalling wave in the IR, but instead, there is a normalizable solution in the IR. In a special case, a hyperscaling-violating geometry is obtained after a dimensional reduction.

From free fields to AdS space: Thermal case

International Nuclear Information System (INIS)

Furuuchi, Kazuyuki

2005-01-01

We analyze the reorganization of free field theory correlators to closed string amplitudes investigated in previous papers in the case of Euclidean thermal field theory and study how the dual bulk geometry is encoded on them. The expectation value of Polyakov loop, which is an order parameter for confinement-deconfinement transition, is directly reflected on the dual bulk geometry. The dual geometry of the confined phase is found to be AdS space periodically identified in Euclidean time direction. The gluing of Schwinger parameters, which is a key step for the reorganization of field theory correlators, works in the same way as in the nonthermal case. In the deconfined phase the gluing is made possible only by taking the dual geometry correctly. The dual geometry for the deconfined phase does not have a noncontractable circle in the Euclidean time direction

On thermodynamics of AdS black holes in M-theory

International Nuclear Information System (INIS)

Belhaj, A.; Chabab, M.; Masmar, K.; El Moumni, H.; Sedra, M.B.

2016-01-01

Motivated by recent work on asymptotically AdS 4 black holes in M-theory, we investigate the thermodynamics and thermodynamical geometry of AdS black holes from M2- and M5-branes. Concretely, we consider AdS black holes in AdS p+2 x S 11-p-2 , where p = 2,5 by interpreting the number of M2- (and M5-branes) as a thermodynamical variable. More precisely, we study the corresponding phase transition to examine their stabilities by calculating and discussing various thermodynamical quantities including the chemical potential. Then we compute the thermodynamical curvatures from the Quevedo metric for M2- and M5-branes geometries to reconsider the stability of such black holes. The Quevedo metric singularities recover similar stability results provided by the phase-transition program. It has been shown that similar behaviors are also present in the limit of large N. (orig.)

On thermodynamics of AdS black holes in M-theory

Energy Technology Data Exchange (ETDEWEB)

Belhaj, A. [Universite Sultan Moulay Slimane, Departement de Physique, LIRST, Faculte Polydisciplinaire, Beni Mellal (Morocco); Cadi Ayyad University, High Energy Physics and Astrophysics Laboratory, FSSM, Marrakesh (Morocco); Chabab, M.; Masmar, K. [Cadi Ayyad University, High Energy Physics and Astrophysics Laboratory, FSSM, Marrakesh (Morocco); El Moumni, H. [Cadi Ayyad University, High Energy Physics and Astrophysics Laboratory, FSSM, Marrakesh (Morocco); Universite Ibn Zohr, Departement de Physique, Faculte des Sciences, Agadir (Morocco); Sedra, M.B. [Universite Ibn Tofail, Departement de Physique, LASIMO, Faculte des Sciences, Kenitra (Morocco)

2016-02-15

Motivated by recent work on asymptotically AdS{sub 4} black holes in M-theory, we investigate the thermodynamics and thermodynamical geometry of AdS black holes from M2- and M5-branes. Concretely, we consider AdS black holes in AdS{sub p+2} x S{sup 11-p-2}, where p = 2,5 by interpreting the number of M2- (and M5-branes) as a thermodynamical variable. More precisely, we study the corresponding phase transition to examine their stabilities by calculating and discussing various thermodynamical quantities including the chemical potential. Then we compute the thermodynamical curvatures from the Quevedo metric for M2- and M5-branes geometries to reconsider the stability of such black holes. The Quevedo metric singularities recover similar stability results provided by the phase-transition program. It has been shown that similar behaviors are also present in the limit of large N. (orig.)

Fermions in nonrelativistic AdS/CFT correspondence

International Nuclear Information System (INIS)

Akhavan, Amin; Alishahiha, Mohsen; Davody, Ali; Vahedi, Ali

2009-01-01

We extend the nonrelativistic AdS/CFT correspondence to the fermionic fields. In particular, we study the two point function of a fermionic operator in nonrelativistic CFTs by making use of a massive fermion propagating in geometries with Schroedinger group isometry. Although the boundary of the geometries with Schroedinger group isometry differ from that in AdS geometries where the dictionary of AdS/CFT is established, using the general procedure of AdS/CFT correspondence, we see that the resultant two point function has the expected form for fermionic operators in nonrelativistic CFTs, though a nontrivial regularization may be needed.

AdS3: the NHEK generation

International Nuclear Information System (INIS)

Bena, Iosif; Heurtier, Lucien; Puhm, Andrea

2016-01-01

It was argued in http://dx.doi.org/10.1007/JHEP03(2013)028 that the five-dimensional near-horizon extremal Kerr (NHEK) geometry can be embedded in String Theory as the infrared region of an infinite family of non-supersymmetric geometries that have D1, D5, momentum and KK monopole charges. We show that there exists a method to embed these geometries into asymptotically-AdS 3 ×S 3 /ℤ N solutions, and hence to obtain infinite families of flows whose infrared is NHEK. This indicates that the CFT dual to the NHEK geometry is the IR fixed point of a Renormalization Group flow from a known local UV CFT and opens the door to its explicit construction.

Near-horizon limit of the charged BTZ black hole and AdS2 quantum gravity

International Nuclear Information System (INIS)

Cadoni, Mariano; Setare, Mohammad R.

2008-01-01

We show that the 3D charged Banados-Teitelboim-Zanelli (BTZ) black hole solution interpolates between two different 2D AdS spacetimes: a near-extremal, near-horizon AdS 2 geometry with constant dilaton and U(1) field and an asymptotic AdS 2 geometry with a linear dilaton. Thus, the charged BTZ black hole can be considered as interpolating between the two different formulations proposed until now for AdS 2 quantum gravity. In both cases the theory is the chiral half of a 2D CFT and describes, respectively, Brown-Hennaux-like boundary deformations and near-horizon excitations. The central charge c as of the asymptotic CFT is determined by 3D Newton constant G and the AdS length l, c as = 3l/G, whereas that of the near-horizon CFT also depends on the U(1) charge Q, c nh ∝lQ/√G.

Arithmetic noncommutative geometry

CERN Document Server

Marcolli, Matilde

2005-01-01

Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...

Generalised structures for N=1 AdS backgrounds

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Coimbra, André [Institut für Theoretische Physik & Center for Quantum Engineering and Spacetime Research,Leibniz Universität Hannover,Appelstraße 2, 30167 Hannover (Germany); Strickland-Constable, Charles [Institut de physique théorique, Université Paris Saclay, CEA, CNRS, Orme des Merisiers, F-91191 Gif-sur-Yvette (France)

2016-11-16

We expand upon a claim made in a recent paper [http://arxiv.org/abs/1411.5721] that generic minimally supersymmetric AdS backgrounds of warped flux compactifications of Type II and M theory can be understood as satisfying a straightforward weak integrability condition in the language of E{sub d(d)}×ℝ{sup +} generalised geometry. Namely, they are spaces admitting a generalised G-structure set by the Killing spinor and with constant singlet generalised intrinsic torsion.

AdS Black Hole with Phantom Scalar Field

Directory of Open Access Journals (Sweden)

Limei Zhang

2017-01-01

Full Text Available We present an AdS black hole solution with Ricci flat horizon in Einstein-phantom scalar theory. The phantom scalar fields just depend on the transverse coordinates x and y, which are parameterized by the parameter α. We study the thermodynamics of the AdS phantom black hole. Although its horizon is a Ricci flat Euclidean space, we find that the thermodynamical properties of the black hole solution are qualitatively the same as those of AdS Schwarzschild black hole. Namely, there exists a minimal temperature and the large black hole is thermodynamically stable, while the smaller one is unstable, so there is a so-called Hawking-Page phase transition between the large black hole and the thermal gas solution in the AdS space-time in Poincare coordinates. We also calculate the entanglement entropy for a strip geometry dual to the AdS phantom black holes and find that the behavior of the entanglement entropy is qualitatively the same as that of the black hole thermodynamical entropy.

Three theorems on near horizon extremal vanishing horizon geometries

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S. Sadeghian

2016-02-01

Full Text Available EVH black holes are Extremal black holes with Vanishing Horizon area, where vanishing of horizon area is a result of having a vanishing one-cycle on the horizon. We prove three theorems regarding near horizon geometry of EVH black hole solutions to generic Einstein gravity theories in diverse dimensions. These generic gravity theories are Einstein–Maxwell-dilaton-Λ theories, and gauged or ungauged supergravity theories with U(1 Maxwell fields. Our three theorems are: (1 The near horizon geometry of any EVH black hole has a three dimensional maximally symmetric subspace. (2 If the energy momentum tensor of the theory satisfies strong energy condition either this 3d part is an AdS3, or the solution is a direct product of a locally 3d flat space and a d−3 dimensional part. (3 These results extend to the near horizon geometry of near-EVH black holes, for which the AdS3 part is replaced with BTZ geometry.

Warped AdS3 black holes

International Nuclear Information System (INIS)

Anninos, Dionysios; Li Wei; Padi, Megha; Song Wei; Strominger, Andrew

2009-01-01

Three dimensional topologically massive gravity (TMG) with a negative cosmological constant -l -2 and positive Newton constant G admits an AdS 3 vacuum solution for any value of the graviton mass μ. These are all known to be perturbatively unstable except at the recently explored chiral point μl = 1. However we show herein that for every value of μl ≠ 3 there are two other (potentially stable) vacuum solutions given by SL(2,R) x U(1)-invariant warped AdS 3 geometries, with a timelike or spacelike U(1) isometry. Critical behavior occurs at μl = 3, where the warping transitions from a stretching to a squashing, and there are a pair of warped solutions with a null U(1) isometry. For μl > 3, there are known warped black hole solutions which are asymptotic to warped AdS 3 . We show that these black holes are discrete quotients of warped AdS 3 just as BTZ black holes are discrete quotients of ordinary AdS 3 . Moreover new solutions of this type, relevant to any theory with warped AdS 3 solutions, are exhibited. Finally we note that the black hole thermodynamics is consistent with the hypothesis that, for μl > 3, the warped AdS 3 ground state of TMG is holographically dual to a 2D boundary CFT with central charges c R -formula and c L -formula.

Flow equation, conformal symmetry, and anti-de Sitter geometry

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Aoki, Sinya; Yokoyama, Shuichi

2018-03-01

We argue that the anti-de Sitter (AdS) geometry in d+1 dimensions naturally emerges from an arbitrary conformal field theory in d dimensions using the free flow equation. We first show that an induced metric defined from the flowed field generally corresponds to the quantum information metric, called the Bures or Helstrom metric, if the flowed field is normalized appropriately. We next verify that the induced metric computed explicitly with the free flow equation always becomes the AdS metric when the theory is conformal. We finally prove that the conformal symmetry in d dimensions converts to the AdS isometry in d+1 dimensions after d-dimensional quantum averaging. This guarantees the emergence of AdS geometry without explicit calculation.

Machine learning spatial geometry from entanglement features

Science.gov (United States)

You, Yi-Zhuang; Yang, Zhao; Qi, Xiao-Liang

2018-02-01

Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network holography. We show that each RTN can be mapped to a Boltzmann machine, trained by the entanglement entropies over all subregions of a given quantum many-body state. The goal is to construct the optimal RTN that best reproduce the entanglement feature. The RTN geometry can then be interpreted as the emergent holographic geometry. We demonstrate the EFL algorithm on a 1D free fermion system and observe the emergence of the hyperbolic geometry (AdS3 spatial geometry) as we tune the fermion system towards the gapless critical point (CFT2 point).

AdS strings with torsion: Noncomplex heterotic compactifications

International Nuclear Information System (INIS)

Frey, Andrew R.; Lippert, Matthew

2005-01-01

Combining the effects of fluxes and gaugino condensation in heterotic supergravity, we use a ten-dimensional approach to find a new class of four-dimensional supersymmetric AdS 4 compactifications on almost-Hermitian manifolds of SU(3) structure. Computation of the torsion allows a classification of the internal geometry, which for a particular combination of fluxes and condensate, is nearly Kaehler. We argue that all moduli are fixed, and we show that the Kaehler potential and superpotential proposed in the literature yield the correct AdS 4 radius. In the nearly Kaehler case, we are able to solve the H Bianchi identity using a nonstandard embedding. Finally, we point out subtleties in deriving the effective superpotential and understanding the heterotic supergravity in the presence of a gaugino condensate

Comments on AdS2 solutions of D = 11 supergravity

International Nuclear Information System (INIS)

Kim, Nakwoo; Park, Jong-Dae

2006-01-01

We study the supersymmetric solutions of 11-dimensional supergravity with a factor of AdS 2 made of M2-branes. Such solutions can provide gravity duals of superconformal quantum mechanics, or through double Wick rotation, the generic bubbling geometry of M-theory which are 1/16-BPS. We show that, when the internal manifold is compact, it should take the form of a warped U(1)-fibration over an 8-dimensional Kaehler space

Thermal geometry from CFT at finite temperature

Directory of Open Access Journals (Sweden)

Wen-Cong Gan

2016-09-01

Full Text Available We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.

Thermal geometry from CFT at finite temperature

Energy Technology Data Exchange (ETDEWEB)

Gan, Wen-Cong, E-mail: ganwencong@gmail.com [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China); Shu, Fu-Wen, E-mail: shufuwen@ncu.edu.cn [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China); Wu, Meng-He, E-mail: menghewu.physik@gmail.com [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China)

2016-09-10

We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.

Null infinity and extremal horizons in AdS-CFT

International Nuclear Information System (INIS)

Hickling, Andrew; Wiseman, Toby; Lucietti, James

2015-01-01

We consider AdS gravity duals to CFT on background spacetimes with a null infinity. Null infinity on the conformal boundary may extend to an extremal horizon in the bulk. For example it does so for Poincaré–AdS, although does not for planar Schwarzschild–AdS. If null infinity does extend into an extremal horizon in the bulk, we show that the bulk near-horizon geometry is determined by the geometry of the boundary null infinity. Hence the ‘infra-red’ geometry of the bulk is fixed by the large scale behaviour of the CFT spacetime. In addition the boundary stress tensor must have a particular decay at null infinity. As an application, we argue that for CFT on asymptotically flat backgrounds, any static bulk dual containing an extremal horizon extending from the boundary null infinity, must have the near-horizon geometry of Poincaré–AdS. We also discuss a class of boundary null infinity that cannot extend to a bulk extremal horizon, although we give evidence that they can extend to an analogous null surface in the bulk which possesses an associated scale-invariant ‘near-geometry’. (paper)

Critical gravity on AdS2 spacetimes

International Nuclear Information System (INIS)

Myung, Yun Soo; Kim, Yong-Wan; Park, Young-Jai

2011-01-01

We study the critical gravity in two-dimensional anti-de Sitter (AdS 2 ) spacetimes, which was obtained from the cosmological topologically massive gravity (TMG Λ ) in three dimensions by using the Kaluza-Klein dimensional reduction. We perform the perturbation analysis around AdS 2 , which may correspond to the near-horizon geometry of the extremal Banados, Teitelboim, and Zanelli (BTZ) black hole obtained from the TMG Λ with identification upon uplifting three dimensions. A massive propagating scalar mode δF satisfies the second-order differential equation away from the critical point of K=l, whose solution is given by the Bessel functions. On the other hand, δF satisfies the fourth-order equation at the critical point. We exactly solve the fourth-order equation, and compare it with the log gravity in two dimensions. Consequently, the critical gravity in two dimensions could not be described by a massless scalar δF ml and its logarithmic partner δF log 4th .

Topology and geometry of six-dimensional (1, 0) supergravity black hole horizons

International Nuclear Information System (INIS)

Akyol, M; Papadopoulos, G

2012-01-01

We show that the supersymmetric near horizon black hole geometries of six-dimensional supergravity coupled to any number of scalar and tensor multiplets are either locally AdS 3 x Σ 3 , where Σ 3 is a homology 3-sphere, or R 1,1 )xS 4 , where S 4 is a 4-manifold whose geometry depends on the hypermultiplet scalars. In both cases, we find that the tensorini multiplet scalars are constant and the associated 3-form field strengths vanish. We also demonstrate that the AdS 3 x Σ 3 horizons preserve two, four and eight supersymmetries. For horizons with four supersymmetries, Σ 3 is in addition a non-trivial circle fibration over a topological 2-sphere. The near horizon geometries preserving eight supersymmetries are locally isometric to either AdS 3 x S 3 or R 1, 1 x T 4 . Moreover, we show that the R 1,1 xS horizons preserve one, two and four supersymmetries and the geometry of S is Riemann, Kaehler and hyper-Kaehler, respectively. (paper)

Network geometry with flavor: From complexity to quantum geometry

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Bianconi, Ginestra; Rahmede, Christoph

2016-03-01

Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but

On thermodynamics of charged AdS black holes in extended phases space via M2-branes background

International Nuclear Information System (INIS)

Chabab, M.; Masmar, K.; El Moumni, H.

2016-01-01

Motivated by a recent work on asymptotically AdS 4 black holes in M-theory, we investigate both thermodynamics and the thermodynamical geometry of Reissner-Nordstrom-AdS black holes from M2-branes. More precisely, we study AdS black holes in AdS 4 x S 7 , with the number of M2-branes interpreted as a thermodynamical variable. In this context, we calculate various thermodynamical quantities including the chemical potential, and examine their phase transitions along with the corresponding stability behaviors. In addition, we also evaluate the thermodynamical curvatures of the Weinhold, Ruppeiner, and Quevedo metrics for M2-branes geometry to study the stability of such a black object. We show that the singularities of these scalar curvature's metrics reproduce similar stability results to those obtained by the phase transition diagram via the heat capacities in different ensembles either when the number of the M2 branes or the charge is held fixed. Also, we note that all results derived in Belhaj et al. (Eur Phys J C 76(2):73, 2016) are recovered in the limit of the vanishing charge. (orig.)

Near horizon geometry of rotating black holes in five dimensions

International Nuclear Information System (INIS)

Cvetic, M.; Larsen, F.

1998-01-01

We interpret the general rotating black holes in five dimensions as rotating black strings in six dimensions. In the near-horizon limit the geometry is locally AdS 3 x S 3 , as in the non-rotating case. However, the global structure couples the AdS 3 and the S 3 , giving angular velocity to the S 3 . The asymptotic geometry is exploited to count the microstates and recover the precise value of the Bekenstein-Hawking entropy, with rotation taken properly into account. We discuss the perturbation spectrum of the rotating black hole, and its relation to the underlying conformal field theory. (orig.)

Emergent Geometry from Entropy and Causality

Science.gov (United States)

Engelhardt, Netta

In this thesis, we investigate the connections between the geometry of spacetime and aspects of quantum field theory such as entanglement entropy and causality. This work is motivated by the idea that spacetime geometry is an emergent phenomenon in quantum gravity, and that the physics responsible for this emergence is fundamental to quantum field theory. Part I of this thesis is focused on the interplay between spacetime and entropy, with a special emphasis on entropy due to entanglement. In general spacetimes, there exist locally-defined surfaces sensitive to the geometry that may act as local black hole boundaries or cosmological horizons; these surfaces, known as holographic screens, are argued to have a connection with the second law of thermodynamics. Holographic screens obey an area law, suggestive of an association with entropy; they are also distinguished surfaces from the perspective of the covariant entropy bound, a bound on the total entropy of a slice of the spacetime. This construction is shown to be quite general, and is formulated in both classical and perturbatively quantum theories of gravity. The remainder of Part I uses the Anti-de Sitter/ Conformal Field Theory (AdS/CFT) correspondence to both expand and constrain the connection between entanglement entropy and geometry. The AdS/CFT correspondence posits an equivalence between string theory in the "bulk" with AdS boundary conditions and certain quantum field theories. In the limit where the string theory is simply classical General Relativity, the Ryu-Takayanagi and more generally, the Hubeny-Rangamani-Takayanagi (HRT) formulae provide a way of relating the geometry of surfaces to entanglement entropy. A first-order bulk quantum correction to HRT was derived by Faulkner, Lewkowycz and Maldacena. This formula is generalized to include perturbative quantum corrections in the bulk at any (finite) order. Hurdles to spacetime emergence from entanglement entropy as described by HRT and its quantum

Wilson lines for AdS5 black strings

International Nuclear Information System (INIS)

Hristov, Kiril; Katmadas, Stefanos

2015-01-01

We describe a simple method of extending AdS 5 black string solutions of 5d gauged supergravity in a supersymmetric way by addition of Wilson lines along a circular direction in space. When this direction is chosen along the string, and due to the specific form of 5d supergravity that features Chern-Simons terms, the existence of magnetic charges automatically generates conserved electric charges in a 5d analogue of the Witten effect. Therefore we find a rather generic, model-independent way of adding electric charges to already existing solutions with no backreaction from the geometry or breaking of any symmetry. We use this method to explicitly write down more general versions of the Benini-Bobev black strings (http://dx.doi.org/10.1103/PhysRevLett.110.061601, http://dx.doi.org/10.1007/JHEP06(2013)005) and comment on the implications for the dual field theory and the similarities with generalizations of the Cacciatori-Klemm black holes (http://dx.doi.org/10.1007/JHEP01(2010)085) in AdS 4 .

Zooming in on AdS3/CFT2 near a BPS bound

Science.gov (United States)

Hartong, Jelle; Lei, Yang; Obers, Niels; Oling, Gerben

2018-05-01

Any ( d + 1)-dimensional CFT with a U(1) flavor symmetry, a BPS bound and an exactly marginal coupling admits a decoupling limit in which one zooms in on the spectrum close to the bound. This limit is an Inönü-Wigner contraction of so(2 , d+1)⊕ u(1) that leads to a relativistic algebra with a scaling generator but no conformal generators. In 2D CFTs, Lorentz boosts are abelian and by adding a second u(1) we find a contraction of two copies of sl(2, ℝ) ⊕ u(1) to two copies of P 2 c , the 2-dimensional centrally extended Poincaré algebra. We show that the bulk is described by a novel non-Lorentzian geometry that we refer to as pseudo-Newton-Cartan geometry. Both the Chern-Simons action on sl(2, ℝ) ⊕ u(1) and the entire phase space of asymptotically AdS3 spacetimes are well-behaved in the corresponding limit if we fix the radial component for the u(1) connection. With this choice, the resulting Newton-Cartan foliation structure is now associated not with time, but with the emerging holographic direction. Since the leaves of this foliation do not mix, the emergence of the holographic direction is much simpler than in AdS3 holography. Furthermore, we show that the asymptotic symmetry algebra of the limit theory consists of a left- and a right-moving warped Virasoro algebra.

Supersymmetric AdS6 solutions of type IIB supergravity

International Nuclear Information System (INIS)

Kim, Hyojoong; Kim, Nakwoo; Suh, Minwoo

2015-01-01

We study the general requirement for supersymmetric AdS 6 solutions in type IIB supergravity. We employ the Killing spinor technique and study the differential and algebraic relations among various Killing spinor bilinears to find the canonical form of the solutions. Our result agrees precisely with the work of Apruzzi et al. (JHEP 1411:099, 2014), which used the pure spinor technique. Hoping to identify the geometry of the problem, we also computed four-dimensional theory through the dimensional reduction of type IIB supergravity on AdS 6 . This effective action is essentially a non-linear sigma model with five scalar fields parametrizing SL(3,ℝ)/SO(2,1), modified by a scalar potential and coupled to Einstein gravity in Euclidean signature. We argue that the scalar potential can be explained by a subgroup CSO(1,1,1) ⊂SL(3,ℝ) in a way analogous to gauged supergravity

Bubbling AdS3

International Nuclear Information System (INIS)

Martelli, Dario; Morales, Jose Francisco

2005-01-01

In the light of the recent Lin, Lunin, Maldacena (LLM) results, we investigate 1/2-BPS geometries in minimal (and next to minimal) supergravity in D = 6 dimensions. In the case of minimal supergravity, solutions are given by fibrations of a two-torus T 2 specified by two harmonic functions. For a rectangular torus the two functions are related by a non-linear equation with rare solutions: AdS 3 x S 3 , the pp-wave and the multi-center string. 'Bubbling', i.e. superpositions of droplets, is accommodated by allowing the complex structure of the T 2 to vary over the base. The analysis is repeated in the presence of a tensor multiplet and similar conclusions are reached, with generic solutions describing D1D5 (or their dual fundamental string-momentum) systems. In this framework, the profile of the dual fundamental string-momentum system is identified with the boundaries of the droplets in a two-dimensional plane. (author)

Dayside merging and cusp geometry

International Nuclear Information System (INIS)

Crooker, N.U.

1979-01-01

Geometrical considerations are presented to show that dayside magnetic merging when constrained to act only where the fields are antiparallel results in lines of merging that converge at the polar cusps. An important consequence of this geometry is that no accelerated flows are predicted across the dayside magnetopause. Acceleration owing to merging acts in opposition to the magnetosheath flow at the merging point and produces the variably directed, slower-than-magnetosheath flows observed in the entry layer. Another consequence of the merging geometry is that much of the time closed field lines constitute the subsolar region of the magnetopause. The manner in which the polar cap convection patterns predicted by the proposed geometry change as the interplanetary field is rotated through 360 0 provides a unifying description of how the observed single circular vortex and the crescent-shaped double vortex patterns mutually evolve under the influence of a single operating principle

A requiem for AdS4×C P3 fermionic self-T duality

Science.gov (United States)

O'Colgáin, E.; Pittelli, A.

2016-11-01

Strong evidence for dual superconformal symmetry in N =6 superconformal Chern-Simons theory has fueled expectations that the AdS /CFT dual geometry AdS4×C P3 is self-dual under T duality. We revisit the problem to identify commuting bosonic and fermionic isometries in a systematic fashion and show that fermionic T duality, a symmetry originally proposed by Berkovits and Maldacena, inevitably leads to a singularity in the dilaton transformation. We show that TsT deformations commute with fermionic T duality and comment on T duality in the corresponding sigma model. Our results rule out self-duality based on fermionic T duality for AdS4×C P3 or its TsT deformations but leave the door open for new possibilities.

On supersymmetric AdS6 solutions in 10 and 11 dimensions

Science.gov (United States)

Gutowski, J.; Papadopoulos, G.

2017-12-01

We prove a non-existence theorem for smooth, supersymmetric, warped AdS 6 solutions with connected, compact without boundary internal space in D = 11 and (massive) IIA supergravities. In IIB supergravity we show that if such AdS 6 solutions exist, then the NSNS and RR 3-form fluxes must be linearly independent and certain spinor bilinears must be appropriately restricted. Moreover we demonstrate that the internal space admits an so(3) action which leaves all the fields invariant and for smooth solutions the principal orbits must have co-dimension two. We also describe the topology and geometry of internal spaces that admit such a so(3) action and show that there are no solutions for which the internal space has topology F × S 2, where F is an oriented surface.

Electric/magnetic deformations of S3 and AdS3, and geometric cosets

International Nuclear Information System (INIS)

Israel, D.; Kounnas, C.; Marios Petropoulos, P.; Orlando, D.

2005-01-01

We analyze asymmetric marginal deformations of SU(2) k and SL(2,R) k WZW models. These appear in heterotic string backgrounds with non-vanishing Neveu-Schwarz three-forms plus electric or magnetic fields, depending on whether the deformation is elliptic, hyperbolic or parabolic. Asymmetric deformations create new families of exact string vacua. The geometries which are generated in this way, deformed S 3 or AdS 3 , include in particular geometric cosets such as S 2 , AdS 2 or H 2 . Hence, the latter are consistent, exact conformal sigma models, with electric or magnetic backgrounds. We discuss various geometric and symmetry properties of the deformations at hand as well as their spectra and partition functions, with special attention to the supersymmetric AdS 2 x S 2 background. We also comment on potential holographic applications. (Abstract Copyright [2005], Wiley Periodicals, Inc.)

A rotating hairy AdS3 black hole with the metric having only one Killing vector field

International Nuclear Information System (INIS)

Iizuka, Norihiro; Ishibashi, Akihiro; Maeda, Kengo

2015-01-01

We perturbatively construct a three-dimensional rotating AdS black hole with a real scalar hair. We choose the mass of a scalar field slightly above the Breitenlohner-Freedman bound and impose a general boundary condition for the bulk scalar field at AdS infinity. We first show that rotating BTZ black holes are unstable against scalar field perturbations under our more general boundary condition. Next we construct a rotating hairy black hole perturbatively with respect to a small amplitude ϵ of the scalar field, up to O(ϵ 4 ). Our hairy black hole is stationary and exhibits no dissipation, but the lumps of the non-linearly perturbed geometry break axial symmetry, thus providing the first example of a rotating black hole whose metric admits only one Killing vector field. Furthermore, we numerically show that the entropy of our hairy black hole is larger than that of the BTZ black hole with the same energy and the angular momentum. We briefly discuss if our rotating hairy black hole in lumpy geometry could be the endpoint of the instability.

Holographic free energy and thermodynamic geometry

Science.gov (United States)

Ghorai, Debabrata; Gangopadhyay, Sunandan

2016-12-01

We obtain the free energy and thermodynamic geometry of holographic superconductors in 2+1 dimensions. The gravitational theory in the bulk dual to this 2+1-dimensional strongly coupled theory lives in the 3+1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method.

Holographic free energy and thermodynamic geometry

International Nuclear Information System (INIS)

Ghorai, Debabrata; Gangopadhyay, Sunandan

2016-01-01

We obtain the free energy and thermodynamic geometry of holographic superconductors in 2 + 1 dimensions. The gravitational theory in the bulk dual to this 2 + 1-dimensional strongly coupled theory lives in the 3 + 1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method. (orig.)

Holographic free energy and thermodynamic geometry

Energy Technology Data Exchange (ETDEWEB)

Ghorai, Debabrata [S.N. Bose National Centre for Basic Sciences, Kolkata (India); Gangopadhyay, Sunandan [Indian Institute of Science Education and Research, Kolkata, Nadia (India); West Bengal State University, Department of Physics, Barasat (India); Inter University Centre for Astronomy and Astrophysics, Pune (India)

2016-12-15

We obtain the free energy and thermodynamic geometry of holographic superconductors in 2 + 1 dimensions. The gravitational theory in the bulk dual to this 2 + 1-dimensional strongly coupled theory lives in the 3 + 1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method. (orig.)

Closed string tachyons on AdS orbifolds and dual Yang-Mills instantons

Energy Technology Data Exchange (ETDEWEB)

Hikida, Y. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Iizuka, N. [California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics

2007-06-15

We study the condensation of localized closed string tachyons on AdS orbifolds both from the bulk and boundary theory viewpoints. We first extend the known results for AdS{sub 5}/Z{sub k} to AdS{sub 3}/Z{sub k} case, and we proposed that the AdS{sub 3}/Z{sub k} decays into AdS{sub 3}/Z{sub k'} with k{sup '} < k. From the bulk viewpoint, we obtain a time-dependent gravity solution describing the decay of AdS orbifold numerically. From the dual gauge theory viewpoint, we calculated the Casimir energies of gauge theory vacua and it is found that their values are exactly the same as the masses of dual geometries, even though they are in different parameter regimes of 't Hooft coupling. We also consider AdS{sub 5} orbifold. The decay of AdS{sub 5}/Z{sub k} is dual to the transition between the vacua of dual gauge theory on R{sub t} x S{sup 3}/Z{sub k}. We constructed the instanton solutions describing the transitions by making use of instanton solutions on R{sub t} x S{sup 2}. (orig.)

Geometry, packing, and evolutionary paths to increased multicellular size

Science.gov (United States)

Jacobeen, Shane; Graba, Elyes C.; Brandys, Colin G.; Day, Thomas C.; Ratcliff, William C.; Yunker, Peter J.

2018-05-01

The evolutionary transition to multicellularity transformed life on earth, heralding the evolution of large, complex organisms. Recent experiments demonstrated that laboratory-evolved multicellular "snowflake yeast" readily overcome the physical barriers that limit cluster size by modifying cellular geometry [Jacobeen et al., Nat. Phys. 14, 286 (2018), 10.1038/s41567-017-0002-y]. However, it is unclear why this route to large size is observed, rather than an evolved increase in intercellular bond strength. Here, we use a geometric model of the snowflake yeast growth form to examine the geometric efficiency of increasing size by modifying geometry and bond strength. We find that changing geometry is a far more efficient route to large size than evolving increased intercellular adhesion. In fact, increasing cellular aspect ratio is on average ˜13 times more effective than increasing bond strength at increasing the number of cells in a cluster. Modifying other geometric parameters, such as the geometric arrangement of mother and daughter cells, also had larger effects on cluster size than increasing bond strength. Simulations reveal that as cells reproduce, internal stress in the cluster increases rapidly; thus, increasing bond strength provides diminishing returns in cluster size. Conversely, as cells become more elongated, cellular packing density within the cluster decreases, which substantially decreases the rate of internal stress accumulation. This suggests that geometrically imposed physical constraints may have been a key early selective force guiding the emergence of multicellular complexity.

Closed-String Tachyons and the Hagedorn Transition in AdS Space

CERN Document Server

Barbón, José L F

2002-01-01

We discuss some aspects of the behaviour of a string gas at the Hagedorn temperature from a Euclidean point of view. Using AdS space as an infrared regulator, the Hagedorn tachyon can be effectively quasi-localized and its dynamics controled by a finite energetic balance. We propose that the off-shell RG flow matches to an Euclidean AdS black hole geometry in a generalization of the string/black-hole correspondence principle. The final stage of the RG flow can be interpreted semiclassically as the growth of a cool black hole in a hotter radiation bath. The end-point of the condensation is the large Euclidan AdS black hole, and the part of spacetime behind the horizon has been removed. In the flat-space limit, holography is manifest by the system creating its own transverse screen at infinity. This leads to an argument, based on the energetics of the system, explaining why the non-supersymmetric type 0A string theory decays into the supersymmetric type IIB vacuum. We also suggest a notion of `boundary entropy'...

Holography beyond conformal invariance and AdS isometry?

CERN Document Server

Barvinsky, A.O.

2015-01-01

We suggest that the principle of holographic duality can be extended beyond conformal invariance and AdS isometry. Such an extension is based on a special relation between functional determinants of the operators acting in the bulk and on its boundary, provided that the boundary operator represents the inverse propagators of the theory induced on the boundary by the Dirichlet boundary value problem from the bulk spacetime. This relation holds for operators of general spin-tensor structure on generic manifolds with boundaries irrespective of their background geometry and conformal invariance, and it apparently underlies numerous $O(N^0)$ tests of AdS/CFT correspondence, based on direct calculation of the bulk and boundary partition functions, Casimir energies and conformal anomalies. The generalized holographic duality is discussed within the concept of the "double-trace" deformation of the boundary theory, which is responsible in the case of large $N$ CFT coupled to the tower of higher spin gauge fields for t...

The Systems Biology Research Tool: evolvable open-source software

Directory of Open Access Journals (Sweden)

Wright Jeremiah

2008-06-01

Full Text Available Abstract Background Research in the field of systems biology requires software for a variety of purposes. Software must be used to store, retrieve, analyze, and sometimes even to collect the data obtained from system-level (often high-throughput experiments. Software must also be used to implement mathematical models and algorithms required for simulation and theoretical predictions on the system-level. Results We introduce a free, easy-to-use, open-source, integrated software platform called the Systems Biology Research Tool (SBRT to facilitate the computational aspects of systems biology. The SBRT currently performs 35 methods for analyzing stoichiometric networks and 16 methods from fields such as graph theory, geometry, algebra, and combinatorics. New computational techniques can be added to the SBRT via process plug-ins, providing a high degree of evolvability and a unifying framework for software development in systems biology. Conclusion The Systems Biology Research Tool represents a technological advance for systems biology. This software can be used to make sophisticated computational techniques accessible to everyone (including those with no programming ability, to facilitate cooperation among researchers, and to expedite progress in the field of systems biology.

Bulk Fields and Supersymmetry in a Slice of AdS

CERN Document Server

Gherghetta, Tony; Gherghetta, Tony; Pomarol, Alex

2000-01-01

Five-dimensional models where the bulk is a slice of AdS have the virtue of solving the hierarchy problem. The electroweak scale is generated by a ``warp'' factor of the induced metric on the brane where the standard model fields live. However, it is not necessary to confine the standard model fields on the brane and we analyze the possibility of having the fields actually living in the slice of AdS. Specifically, we study the behaviour of fermions, gauge bosons and scalars in this geometry and their implications on electroweak physics. These scenarios can provide an explanation of the fermion mass hierarchy by warp factors. We also consider the case of supersymmetry in the bulk, and analyze the conditions on the mass spectrum. Finally, a model is proposed where the warp factor generates a small (TeV) supersymmetry-breaking scale, with the gauge interactions mediating the breaking to the scalar sector.

Multilevel geometry optimization

Science.gov (United States)

Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.

2000-02-01

Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.

Inflation in AdS/CFT

Energy Technology Data Exchange (ETDEWEB)

Freivogel, Ben; /Stanford U., Phys. Dept. /LBL, Berkeley; Hubeny, Veronika E.; /LBL, Berkeley /Durham U., Dept. of Math.; Maloney, Alexander; /Stanford U., Phys. Dept.; Myers, Rob; /Perimeter Inst. Theor. Phys. /Waterloo U.; Rangamani, Mukund; /LBL, Berkeley /Durham U., Dept. of Math.; Shenker, Stephen; /Stanford U., Phys. Dept.

2005-10-07

We study the realization of inflation within the AdS/CFT correspondence. We assume the existence of a string landscape containing at least one stable AdS vacuum and a (nearby) metastable de Sitter state. Standard arguments imply that the bulk physics in the vicinity of the AdS minimum is described by a boundary CFT. We argue that large enough bubbles of the dS phase, including those able to inflate, are described by mixed states in the CFT. Inflating degrees of freedom are traced over and do not appear explicitly in the boundary description. They nevertheless leave a distinct imprint on the mixed state. Analytic continuation allows us, in principle, to recover a large amount of nonperturbatively defined information about the inflating regime. Our work also shows that no scattering process can create an inflating region, even by quantum tunneling, since a pure state can never evolve into a mixed state under unitary evolution.We study the realization of inflation within the AdS/CFT correspondence. We assume the existence of a string landscape containing at least one stable AdS vacuum and a (nearby) metastable de Sitter state. Standard arguments imply that the bulk physics in the vicinity of the AdS minimum is described by a boundary CFT. We argue that large enough bubbles of the dS phase, including those able to inflate, are described by mixed states in the CFT. Inflating degrees of freedom are traced over and do not appear explicitly in the boundary description. They nevertheless leave a distinct imprint on the mixed state. Analytic continuation allows us, in principle, to recover a large amount of nonperturbatively defined information about the inflating regime. Our work also shows that no scattering process can create an inflating region, even by quantum tunneling, since a pure state can never evolve into a mixed state under unitary evolution.

Dualities in D=5, N=2 supergravity, black hole entropy, and AdS central charges

International Nuclear Information System (INIS)

Klemm, D.

2001-01-01

The issue of microstate counting for general black holes in D=5, N=2 supergravity coupled to vector multiplets is discussed from various viewpoints. The statistical entropy is computed for the near-extremal case by using the central charge appearing in the asymptotic symmetry algebra of AdS 2 . Furthermore, we show that the considered supergravity theory enjoys a duality invariance which connects electrically charged black holes and magnetically charged black strings. The near-horizon geometry of the latter turns out to be AdS 3 x S 2 , which allows a microscopic calculation of their entropy using the Brown-Hennaux central charges in Cardy's formula. In both approaches we find perfect agreement between statistical and thermodynamical entropy. (orig.)

Multilevel geometry optimization

Energy Technology Data Exchange (ETDEWEB)

Rodgers, Jocelyn M. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Fast, Patton L. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Truhlar, Donald G. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)

2000-02-15

Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol. (c) 2000 American Institute of Physics.

Boundary stress tensor and asymptotically AdS3 non-Einstein spaces at the chiral point

International Nuclear Information System (INIS)

Giribet, Gaston; Goya, Andres; Leston, Mauricio

2011-01-01

Chiral gravity admits asymptotically AdS 3 solutions that are not locally equivalent to AdS 3 ; meaning that solutions do exist which, while obeying the strong boundary conditions usually imposed in general relativity, happen not to be Einstein spaces. In topologically massive gravity (TMG), the existence of non-Einstein solutions is particularly connected to the question about the role played by complex saddle points in the Euclidean path integral. Consequently, studying (the existence of) nonlocally AdS 3 solutions to chiral gravity is relevant to understanding the quantum theory. Here, we discuss a special family of nonlocally AdS 3 solutions to chiral gravity. In particular, we show that such solutions persist when one deforms the theory by adding the higher-curvature terms of the so-called new massive gravity. Moreover, the addition of higher-curvature terms to the gravity action introduces new nonlocally AdS 3 solutions that have no analogues in TMG. Both stationary and time-dependent, axially symmetric solutions that asymptote AdS 3 space without being locally equivalent to it appear. Defining the boundary stress tensor for the full theory, we show that these non-Einstein geometries have associated vanishing conserved charges.

Exploring the bulk in AdS /CFT : A covariant approach

Science.gov (United States)

Engelhardt, Netta

2017-03-01

I propose a general, covariant way of defining when one region is "deeper in the bulk" than another. This definition is formulated outside of an event horizon (or in the absence thereof) in generic geometries; it may be applied to both points and surfaces, and it may be used to compare the depth of bulk points or surfaces relative to a particular boundary subregion or relative to the entire boundary. Using the recently proposed "light-cone cut" formalism, the comparative depth between two bulk points can be determined from the singularity structure of Lorentzian correlators in the dual field theory. I prove that, by this definition, causal wedges of progressively larger regions probe monotonically deeper in the bulk. The definition furthermore matches expectations in pure AdS and in static AdS black holes with isotropic spatial slices, where a well-defined holographic coordinate exists. In terms of holographic renormalization group flow, this new definition of bulk depth makes contact with coarse graining over both large distances and long time scales.

Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals

CERN Document Server

Martelli, D; Martelli, Dario; Sparks, James

2006-01-01

Recently an infinite family of explicit Sasaki-Einstein metrics Y^{p,q} on S^2 x S^3 has been discovered, where p and q are two coprime positive integers, with qgeometry, we show that these are Kahler quotients C^4//U(1), namely the vacua of gauged linear sigma models with charges (p,p,-p+q,-p-q), thereby generalising the conifold, which is p=1,q=0. We present the corresponding toric diagrams and show that these may be embedded in the toric diagram for the orbifold C^3/Z_{p+1}xZ_{p+1} for all q

AdS/CFT dual to an infinite class of N=1 superconformal field theories arising as infra-red (IR) fixed points of toric quiver gauge theories with gauge group SU(N)^{2p}. As a non-trivial example, we show that Y^{2,1} is an explicit irregular Sasaki-Einstein metric on the horizon of the complex cone over the first del Pezz...

Thermodynamics of charged Lovelock: AdS black holes

International Nuclear Information System (INIS)

Prasobh, C.B.; Suresh, Jishnu; Kuriakose, V.C.

2016-01-01

We investigate the thermodynamic behavior of maximally symmetric charged, asymptotically AdS black hole solutions of Lovelock gravity. We explore the thermodynamic stability of such solutions by the ordinary method of calculating the specific heat of the black holes and investigating its divergences which signal second-order phase transitions between black hole states. We then utilize the methods of thermodynamic geometry of black hole spacetimes in order to explain the origin of these points of divergence. We calculate the curvature scalar corresponding to a Legendre-invariant thermodynamic metric of these spacetimes and find that the divergences in the black hole specific heat correspond to singularities in the thermodynamic phase space. We also calculate the area spectrum for large black holes in the model by applying the Bohr-Sommerfeld quantization to the adiabatic invariant calculated for the spacetime. (orig.)

Thermodynamics of charged Lovelock: AdS black holes

Science.gov (United States)

Prasobh, C. B.; Suresh, Jishnu; Kuriakose, V. C.

2016-04-01

We investigate the thermodynamic behavior of maximally symmetric charged, asymptotically AdS black hole solutions of Lovelock gravity. We explore the thermodynamic stability of such solutions by the ordinary method of calculating the specific heat of the black holes and investigating its divergences which signal second-order phase transitions between black hole states. We then utilize the methods of thermodynamic geometry of black hole spacetimes in order to explain the origin of these points of divergence. We calculate the curvature scalar corresponding to a Legendre-invariant thermodynamic metric of these spacetimes and find that the divergences in the black hole specific heat correspond to singularities in the thermodynamic phase space. We also calculate the area spectrum for large black holes in the model by applying the Bohr-Sommerfeld quantization to the adiabatic invariant calculated for the spacetime.

Complexity of the AdS soliton

Science.gov (United States)

Reynolds, Alan P.; Ross, Simon F.

2018-05-01

We consider the holographic complexity conjectures in the context of the AdS soliton, which is the holographic dual of the ground state of a field theory on a torus with antiperiodic boundary conditions for fermions on one cycle. The complexity is a non-trivial function of the size of the circle with antiperiodic boundary conditions, which sets an IR scale in the dual geometry. We find qualitative differences between the calculations of complexity from spatial volume and action (CV and CA). In the CV calculation, the complexity for antiperiodic boundary conditions is smaller than for periodic, and decreases monotonically with increasing IR scale. In the CA calculation, the complexity for antiperiodic boundary conditions is larger than for periodic, and initially increases with increasing IR scale, eventually decreasing to zero as the IR scale becomes of order the UV cutoff. We compare these results to a simple calculation for free fermions on a lattice, where we find the complexity for antiperiodic boundary conditions is larger than for periodic.

Young children’s understanding of angles in a dynamic geometry environment

OpenAIRE

Kaur, Harpreet

2017-01-01

Angle is an important topic in geometry. It is a concept that children find challenging to learn, in part because of its multifaceted nature. The purpose of this study is to understand how children’s thinking about angles evolves as they participate in a classroom setting featuring the use of a dynamic geometry environment (DGE) in which the concept of angle as turn was privileged, a concept that does not require a quantitative dimension. Three research questions were proposed for the study, ...

Spinning geometry = Twisted geometry

International Nuclear Information System (INIS)

Freidel, Laurent; Ziprick, Jonathan

2014-01-01

It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)

Supersymmetric AdS{sub 2} x Σ{sub 2} solutions from tri-sasakian truncation

Energy Technology Data Exchange (ETDEWEB)

Karndumri, Parinya [Chulalongkorn University, String Theory and Supergravity Group, Department of Physics, Faculty of Science, Bangkok (Thailand)

2017-10-15

A class of AdS{sub 2} x Σ{sub 2}, with Σ{sub 2} being a two-sphere or a hyperbolic space, solutions within four-dimensional N = 4 gauged supergravity coupled to three-vector multiplets with dyonic gauging is identified. The gauged supergravity has a non-semisimple SO(3) x (T{sup 3}, T{sup 3}) gauge group and can be obtained from a consistent truncation of 11-dimensional supergravity on a tri-sasakian manifold. The maximally symmetric vacua contain AdS{sub 4} geometries with N = 1, 3 supersymmetry corresponding to N = 1 and N = 3 superconformal field theories (SCFTs) in three dimensions. We find supersymmetric solutions of the form AdS{sub 2} x Σ{sub 2} preserving two supercharges. These solutions describe twisted compactifications of the dual N = 1 and N = 3 SCFTs and should arise as near horizon geometries of dyonic black holes in asymptotically AdS{sub 4} space-time. Most solutions AdS{sub 2} x Σ{sub 2} geometries with known M-theory origin. (orig.)

D = 4 Yang-Mills correlators from NSR strings on AdS5 x S5

International Nuclear Information System (INIS)

Polyakov, D.

1999-07-01

In our previous work (hep-th/9812044) we have proposed the sigma-model action, conjectured to be the NSR analogue of superstring theory on AdS 5 x S 5 . This sigma-model is the NSR superstring action with potential term corresponding to the exotic 5-form vertex operator (branelike state). This 5-form potential plays the role of cosmological term, effectively curving the flat space-time geometry to that of AdS 5 x S 5 . In this paper we study this ansatz in more detail and provide the derivation of the correlators of the four-dimensional super Yang-Mills theory from the above mentioned sigma-model. In particular, we show that the correlation function of two dilaton vertex operators in such a model reproduces the well-known result for the two-point function in N = 4 four-dimensional super Yang-Mills theory. (author)

4d quantum geometry from 3d supersymmetric gauge theory and holomorphic block

International Nuclear Information System (INIS)

Han, Muxin

2016-01-01

A class of 3d N=2 supersymmetric gauge theories are constructed and shown to encode the simplicial geometries in 4-dimensions. The gauge theories are defined by applying the Dimofte-Gaiotto-Gukov construction http://dx.doi.org/10.1007/s00220-013-1863-2 in 3d-3d correspondence to certain graph complement 3-manifolds. Given a gauge theory in this class, the massive supersymmetric vacua of the theory contain the classical geometries on a 4d simplicial complex. The corresponding 4d simplicial geometries are locally constant curvature (either dS or AdS), in the sense that they are made by gluing geometrical 4-simplices of the same constant curvature. When the simplicial complex is sufficiently refined, the simplicial geometries can approximate all possible smooth geometries on 4-manifold. At the quantum level, we propose that a class of holomorphic blocks defined in http://dx.doi.org/10.1007/JHEP12(2014)177 from the 3d N=2 gauge theories are wave functions of quantum 4d simplicial geometries. In the semiclassical limit, the asymptotic behavior of holomorphic block reproduces the classical action of 4d Einstein-Hilbert gravity in the simplicial context.

c-Extremization from toric geometry

Science.gov (United States)

Amariti, Antonio; Cassia, Luca; Penati, Silvia

2018-04-01

We derive a geometric formulation of the 2d central charge cr from infinite families of 4d N = 1 superconformal field theories topologically twisted on constant curvature Riemann surfaces. They correspond to toric quiver gauge theories and are associated to D3 branes probing five dimensional Sasaki-Einstein geometries in the AdS/CFT correspondence. We show that cr can be expressed in terms of the areas of the toric diagram describing the moduli space of the 4d theory, both for toric geometries with smooth and singular horizons. We also study the relation between a-maximization in 4d and c-extremization in 2d, giving further evidences of the mixing of the baryonic symmetries with the exact R-current in two dimensions.

Evolvable Neural Software System

Science.gov (United States)

Curtis, Steven A.

2009-01-01

The Evolvable Neural Software System (ENSS) is composed of sets of Neural Basis Functions (NBFs), which can be totally autonomously created and removed according to the changing needs and requirements of the software system. The resulting structure is both hierarchical and self-similar in that a given set of NBFs may have a ruler NBF, which in turn communicates with other sets of NBFs. These sets of NBFs may function as nodes to a ruler node, which are also NBF constructs. In this manner, the synthetic neural system can exhibit the complexity, three-dimensional connectivity, and adaptability of biological neural systems. An added advantage of ENSS over a natural neural system is its ability to modify its core genetic code in response to environmental changes as reflected in needs and requirements. The neural system is fully adaptive and evolvable and is trainable before release. It continues to rewire itself while on the job. The NBF is a unique, bilevel intelligence neural system composed of a higher-level heuristic neural system (HNS) and a lower-level, autonomic neural system (ANS). Taken together, the HNS and the ANS give each NBF the complete capabilities of a biological neural system to match sensory inputs to actions. Another feature of the NBF is the Evolvable Neural Interface (ENI), which links the HNS and ANS. The ENI solves the interface problem between these two systems by actively adapting and evolving from a primitive initial state (a Neural Thread) to a complicated, operational ENI and successfully adapting to a training sequence of sensory input. This simulates the adaptation of a biological neural system in a developmental phase. Within the greater multi-NBF and multi-node ENSS, self-similar ENI s provide the basis for inter-NBF and inter-node connectivity.

Geometric Monte Carlo and black Janus geometries

Energy Technology Data Exchange (ETDEWEB)

Bak, Dongsu, E-mail: dsbak@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); B.W. Lee Center for Fields, Gravity & Strings, Institute for Basic Sciences, Daejeon 34047 (Korea, Republic of); Kim, Chanju, E-mail: cjkim@ewha.ac.kr [Department of Physics, Ewha Womans University, Seoul 03760 (Korea, Republic of); Kim, Kyung Kiu, E-mail: kimkyungkiu@gmail.com [Department of Physics, Sejong University, Seoul 05006 (Korea, Republic of); Department of Physics, College of Science, Yonsei University, Seoul 03722 (Korea, Republic of); Min, Hyunsoo, E-mail: hsmin@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); Song, Jeong-Pil, E-mail: jeong_pil_song@brown.edu [Department of Chemistry, Brown University, Providence, RI 02912 (United States)

2017-04-10

We describe an application of the Monte Carlo method to the Janus deformation of the black brane background. We present numerical results for three and five dimensional black Janus geometries with planar and spherical interfaces. In particular, we argue that the 5D geometry with a spherical interface has an application in understanding the finite temperature bag-like QCD model via the AdS/CFT correspondence. The accuracy and convergence of the algorithm are evaluated with respect to the grid spacing. The systematic errors of the method are determined using an exact solution of 3D black Janus. This numerical approach for solving linear problems is unaffected initial guess of a trial solution and can handle an arbitrary geometry under various boundary conditions in the presence of source fields.

Degree distribution of a new model for evolving networks

Indian Academy of Sciences (India)

on intuitive but realistic consideration that nodes are added to the network with both preferential and random attachments. The degree distribution of the model is between a power-law and an exponential decay. Motivated by the features of network evolution, we introduce a new model of evolving networks, incorporating the ...

F-theory and AdS3/CFT2 (2, 0)

Science.gov (United States)

Couzens, Christopher; Martelli, Dario; Schäfer-Nameki, Sakura

2018-06-01

We continue to develop the program initiated in [1] of studying supersymmetric AdS3 backgrounds of F-theory and their holographic dual 2d superconformal field theories, which are dimensional reductions of theories with varying coupling. Imposing 2d N=(0,2) supersymmetry,wederivethegeneralconditionsonthegeometryforTypeIIB AdS3 solutions with varying axio-dilaton and five-form flux. Locally the compact part of spacetime takes the form of a circle fibration over an eight-fold Y_8^{τ } , which is elliptically fibered over a base \\tilde{M}_6 . We construct two classes of solutions given in terms of a product ansatz \\tilde{M}_6}=Σ × {M}_4 , where Σ is a complex curve and \\tilde{M}_4 is locally a Kähler surface. In the first class \\tilde{M}_4 is globally a Kähler surface and we take the elliptic fibration to vary non-trivially over either of these two factors, where in both cases the metrics on the total space of the elliptic fibrations are not Ricci-flat. In the second class the metric on the total space of the elliptic fibration over either curve or surface are Ricci-flat. This results in solutions of the type AdS3 × K3 × ℳ 5 τ , dual to 2d (0, 2) SCFTs, and AdS3 × S 3/Γ × CY 3, dual to 2d (0, 4) SCFTs, respectively. In all cases we compute the charges for the dual field theories with varying coupling and find agreement with the holographic results. We also show that solutions with enhanced 2d N=(2,2) supersymmetry must have constant axio-dilaton. Allowing the internal geometry to be non-compact leads to the most general class of Type IIB AdS5 solutions with varying axio-dilaton, i.e. F-theoretic solutions, that are dual to 4d N=1 SCFTs.

Trak Investigation of Focusing Electrode Geometries for the DARHT Axis-I Diode

Energy Technology Data Exchange (ETDEWEB)

Kallas, Nicholas Dimitrious [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2017-05-15

An investigation was carried out on the effects of different cathode shroud geometries of the DARHT Axis-1 diode using the Trak ray tracing software. Pierce angles of 20, 30, 45, 60, and 67.5 degrees were investigated. For each geometry the current density with respect to radial position will be presented as it evolves in the longitudinal direction. In addition the emittances for each geometry are compared and this information is used to determine the optimal geometry from the selected angles. These results are compared to the baseline geometry currently employed at DARHT of a simple 2.5mm recessed velvet cathode. Of the selected angles it was found that 45 degrees produced the lowest normalized emittance value, whereas 60 degrees produced the most uniform current density profile at 1cm away from the emission surface. For the purpose of this investigation the effects of the bucking coil and solenoid around the hollow anode of the DARHT Axis I injector are neglected.

General Geometry and Geometry of Electromagnetism

OpenAIRE

Shahverdiyev, Shervgi S.

2002-01-01

It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...

Q ‑ Φ criticality and microstructure of charged AdS black holes in f(R) gravity

Science.gov (United States)

Deng, Gao-Ming; Huang, Yong-Chang

2017-12-01

The phase transition and critical behaviors of charged AdS black holes in f(R) gravity with a conformally invariant Maxwell (CIM) source and constant curvature are further investigated. As a highlight, this research is carried out by employing new state parameters (T,Q, Φ) and contributes to deeper understanding of the thermodynamics and phase structure of black holes. Our analyses manifest that the charged f(R)-CIM AdS black hole undergoes a first-order small-large black hole phase transition, and the critical behaviors qualitatively behave like a Van der Waals liquid-vapor system. However, differing from the case in Einstein’s gravity, phase structures of the black holes in f(R) theory exhibit an interesting dependence on gravity modification parameters. Moreover, we adopt the thermodynamic geometry to probe the black hole microscopic properties. The results show that, on the one hand, both the Ruppeiner curvature and heat capacity diverge exactly at the critical point, on the other hand, the f(R)-CIM AdS black hole possesses the property as ideal Fermi gases. Of special interest, we discover a microscopic similarity between the black holes and a Van der Waals liquid-vapor system.

Instability in near-horizon geometries of even-dimensional Myers–Perry black holes

International Nuclear Information System (INIS)

Tanahashi, Norihiro; Murata, Keiju

2012-01-01

We study the gravitational, electromagnetic and scalar field perturbations on the near-horizon geometries of the even-dimensional extremal Myers–Perry black holes. By dimensional reduction, the perturbation equations are reduced to effective equations of motion in AdS 2 . We find that some modes in the gravitational perturbations violate the Breitenlöhner–Freedman bound in AdS 2 . This result suggests that the even-dimensional (near-)extremal Myers–Perry black holes are unstable against gravitational perturbations. We also discuss implications of our results to the Kerr–CFT correspondence. (paper)

AdS5 solutions from M5-branes on Riemann surface and D6-branes sources

Energy Technology Data Exchange (ETDEWEB)

Bah, Ibrahima [Department of Physics and Astronomy, University of Southern California,Los Angeles, CA 90089 (United States); Institut de Physique Théorique, CEA/Saclay,91191 Gif-sur-Yvette (France)

2015-09-24

We describe the gravity duals of four-dimensional N=1 superconformal field theories obtained by wrapping M5-branes on a punctured Riemann surface. The internal geometry, normal to the AdS{sub 5} factor, generically preserves two U(1)s, with generators (J{sup +},J{sup −}), that are fibered over the Riemann surface. The metric is governed by a single potential that satisfies a version of the Monge-Ampère equation. The spectrum of N=1 punctures is given by the set of supersymmetric sources of the potential that are localized on the Riemann surface and lead to regular metrics near a puncture. We use this system to study a class of punctures where the geometry near the sources corresponds to M-theory description of D6-branes. These carry a natural (p,q) label associated to the circle dual to the killing vector pJ{sup +}+qJ{sup −} which shrinks near the source. In the generic case the world volume of the D6-branes is AdS{sub 5}×S{sup 2} and they locally preserve N=2 supersymmetry. When p=−q, the shrinking circle is dual to a flavor U(1). The metric in this case is non-degenerate only when there are co-dimension one sources obtained by smearing M5-branes that wrap the AdS{sub 5} factor and the circle dual the superconformal R-symmetry. The D6-branes are extended along the AdS{sub 5} and on cups that end on the co-dimension one branes. In the special case when the shrinking circle is dual to the R-symmetry, the D6-branes are extended along the AdS{sub 5} and wrap an auxiliary Riemann surface with an arbitrary genus. When the Riemann surface is compact with constant curvature, the system is governed by a Monge-Ampère equation.

Generalized geometry and partial supersymmetry breaking

Energy Technology Data Exchange (ETDEWEB)

Triendl, Hagen Mathias

2010-08-15

This thesis consists of two parts. In the first part we use the formalism of (exceptional) generalized geometry to derive the scalar field space of SU(2) x SU(2)-structure compactifications. We show that in contrast to SU(3) x SU(3) structures, there is no dynamical SU(2) x SU(2) structure interpolating between an SU(2) structure and an identity structure. Furthermore, we derive the scalar manifold of the low-energy effective action for consistent Kaluza-Klein truncations as expected from N = 4 supergravity. In the second part we then determine the general conditions for the existence of stable Minkowski and AdS N = 1 vacua in spontaneously broken gauged N = 2 supergravities and construct the general solution under the assumption that two appropriate commuting isometries exist in the hypermultiplet sector. Furthermore, we derive the low-energy effective action below the scale of partial supersymmetry breaking and show that it satisfies the constraints of N = 1 supergravity. We then apply the discussion to special quaternionic-Kaehler geometries which appear in the low-energy limit of SU(3) x SU(3)-structure compactifications and construct Killing vectors with the right properties. Finally we discuss the string theory realizations for these solutions. (orig.)

Generalized geometry and partial supersymmetry breaking

International Nuclear Information System (INIS)

Triendl, Hagen Mathias

2010-08-01

This thesis consists of two parts. In the first part we use the formalism of (exceptional) generalized geometry to derive the scalar field space of SU(2) x SU(2)-structure compactifications. We show that in contrast to SU(3) x SU(3) structures, there is no dynamical SU(2) x SU(2) structure interpolating between an SU(2) structure and an identity structure. Furthermore, we derive the scalar manifold of the low-energy effective action for consistent Kaluza-Klein truncations as expected from N = 4 supergravity. In the second part we then determine the general conditions for the existence of stable Minkowski and AdS N = 1 vacua in spontaneously broken gauged N = 2 supergravities and construct the general solution under the assumption that two appropriate commuting isometries exist in the hypermultiplet sector. Furthermore, we derive the low-energy effective action below the scale of partial supersymmetry breaking and show that it satisfies the constraints of N = 1 supergravity. We then apply the discussion to special quaternionic-Kaehler geometries which appear in the low-energy limit of SU(3) x SU(3)-structure compactifications and construct Killing vectors with the right properties. Finally we discuss the string theory realizations for these solutions. (orig.)

Vacuum currents in braneworlds on AdS bulk with compact dimensions

Science.gov (United States)

Bellucci, S.; Saharian, A. A.; Vardanyan, V.

2015-11-01

The two-point function and the vacuum expectation value (VEV) of the current density are investigated for a massive charged scalar field with arbitrary curvature coupling in the geometry of a brane on the background of AdS spacetime with partial toroidal compactification. The presence of a gauge field flux, enclosed by compact dimensions, is assumed. On the brane the field obeys Robin boundary condition and along compact dimensions periodicity conditions with general phases are imposed. There is a range in the space of the values for the coefficient in the boundary condition where the Poincaré vacuum is unstable. This range depends on the location of the brane and is different for the regions between the brane and AdS boundary and between the brane and the horizon. In models with compact dimensions the stability condition is less restrictive than that for the AdS bulk with trivial topology. The vacuum charge density and the components of the current along non-compact dimensions vanish. The VEV of the current density along compact dimensions is a periodic function of the gauge field flux with the period equal to the flux quantum. It is decomposed into the boundary-free and brane-induced contributions. The asymptotic behavior of the latter is investigated near the brane, near the AdS boundary and near the horizon. It is shown that, in contrast to the VEVs of the field squared an denergy-momentum tensor, the current density is finite on the brane and vanishes for the special case of Dirichlet boundary condition. Both the boundary-free and brane-induced contributions vanish on the AdS boundary. The brane-induced contribution vanishes on the horizon and for points near the horizon the current is dominated by the boundary-free part. In the near-horizon limit, the latter is connected to the corresponding quantity for a massless field in the Minkowski bulk by a simple conformal relation. Depending on the value of the Robin coefficient, the presence of the brane can either

Geometries

CERN Document Server

Sossinsky, A B

2012-01-01

The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...

D-brane potentials from multi-trace deformations in AdS/CFT

International Nuclear Information System (INIS)

Bernamonti, Alice; Craps, Ben

2009-01-01

It is known that certain AdS boundary conditions allow smooth initial data to evolve into a big crunch. To study this type of cosmological singularity, one can use the dual quantum field theory, where the non-standard boundary conditions are reflected by the presence of a multi-trace potential unbounded below. For specific AdS 4 and AdS 5 models, we provide a D-brane (or M-brane) interpretation of the unbounded potential. Using probe brane computations, we show that the AdS boundary conditions of interest cause spherical branes to be pushed to the boundary of AdS in finite time, and that the corresponding potential agrees with the multi-trace deformation of the dual field theory. Systems with expanding spherical D3-branes are related to big crunch supergravity solutions by a phenomenon similar to geometric transition.

RG flow and thermodynamics of causal horizons in higher-derivative AdS gravity

International Nuclear Information System (INIS)

Banerjee, Shamik; Bhattacharyya, Arpan

2016-01-01

In http://arxiv.org/abs/1508.01343 [hep-th], one of the authors proposed that in AdS/CFT the gravity dual of the boundary c-theorem is the second law of thermodynamics satisfied by causal horizons in AdS and this was verified for Einstein gravity in the bulk. In this paper we verify this for higher derivative theories. We pick up theories for which an entropy expression satisfying the second law exists and show that the entropy density evaluated on the causal horizon in a RG flow geometry is a holographic c-function. We also prove that given a theory of gravity described by a local covariant action in the bulk a sufficient condition to ensure holographic c-theorem is that the second law of causal horizon thermodynamics be satisfied by the theory. This allows us to explicitly construct holographic c-function in a theory where there is curvature coupling between gravity and matter and standard null energy condition cannot be defined although second law is known to hold. Based on the duality between c-theorem and the second law of causal horizon thermodynamics proposed in http://arxiv.org/abs/1508.01343 [hep-th] and the supporting calculations of this paper we conjecture that every Unitary higher derivative theory of gravity in AdS satisfies the second law of causal horizon thermodynamics. If this is not true then c-theorem will be violated in a unitary Lorentz invariant field theory.

Geometric Transformations in Engineering Geometry

Directory of Open Access Journals (Sweden)

I. F. Borovikov

2015-01-01

Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry

Geometry

CERN Document Server

Prasolov, V V

2015-01-01

This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.

Gravitational perturbation of the BTZ black hole induced by test particles and weak cosmic censorship in AdS spacetime

International Nuclear Information System (INIS)

Rocha, Jorge V.; Cardoso, Vitor

2011-01-01

We analyze the gravitational perturbations induced by particles falling into a three dimensional, asymptotically AdS black hole geometry. More specifically, we solve the linearized perturbation equations obtained from the geodesic motion of a ringlike distribution of test particles in the BTZ background. This setup ensures that the U(1) symmetry of the background is preserved. The nonasymptotic flatness of the background raises difficulties in attributing the significance of energy and angular momentum to the conserved quantities of the test particles. This issue is well known but, to the best of our knowledge, has never been addressed in the literature. We confirm that the naive expressions for energy and angular momentum are the correct definitions. Finally, we put an asymptotically AdS version of the weak cosmic censorship to a test: by attempting to overspin the BTZ black hole with test particles it is found that the black hole cannot be spun-up past its extremal limit.

Extrinsic and intrinsic curvatures in thermodynamic geometry

Energy Technology Data Exchange (ETDEWEB)

Hosseini Mansoori, Seyed Ali, E-mail: shossein@bu.edu [Department of Physics, Boston University, 590 Commonwealth Ave., Boston, MA 02215 (United States); Department of Physics, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of); Mirza, Behrouz, E-mail: b.mirza@cc.iut.ac.ir [Department of Physics, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of); Sharifian, Elham, E-mail: e.sharifian@ph.iut.ac.ir [Department of Physics, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of)

2016-08-10

We investigate the intrinsic and extrinsic curvatures of a certain hypersurface in thermodynamic geometry of a physical system and show that they contain useful thermodynamic information. For an anti-Reissner–Nordström-(A)de Sitter black hole (Phantom), the extrinsic curvature of a constant Q hypersurface has the same sign as the heat capacity around the phase transition points. The intrinsic curvature of the hypersurface can also be divergent at the critical points but has no information about the sign of the heat capacity. Our study explains the consistent relationship holding between the thermodynamic geometry of the KN-AdS black holes and those of the RN (J-zero hypersurface) and Kerr black holes (Q-zero hypersurface) ones [1]. This approach can easily be generalized to an arbitrary thermodynamic system.

Extrinsic and intrinsic curvatures in thermodynamic geometry

International Nuclear Information System (INIS)

Hosseini Mansoori, Seyed Ali; Mirza, Behrouz; Sharifian, Elham

2016-01-01

We investigate the intrinsic and extrinsic curvatures of a certain hypersurface in thermodynamic geometry of a physical system and show that they contain useful thermodynamic information. For an anti-Reissner–Nordström-(A)de Sitter black hole (Phantom), the extrinsic curvature of a constant Q hypersurface has the same sign as the heat capacity around the phase transition points. The intrinsic curvature of the hypersurface can also be divergent at the critical points but has no information about the sign of the heat capacity. Our study explains the consistent relationship holding between the thermodynamic geometry of the KN-AdS black holes and those of the RN (J-zero hypersurface) and Kerr black holes (Q-zero hypersurface) ones [1]. This approach can easily be generalized to an arbitrary thermodynamic system.

Parameterized combinatorial geometry modeling in Moritz

International Nuclear Information System (INIS)

Van Riper, K.A.

2005-01-01

We describe the use of named variables as surface and solid body coefficients in the Moritz geometry editing program. Variables can also be used as material numbers, cell densities, and transformation values. A variable is defined as a constant or an arithmetic combination of constants and other variables. A variable reference, such as in a surface coefficient, can be a single variable or an expression containing variables and constants. Moritz can read and write geometry models in MCNP and ITS ACCEPT format; support for other codes will be added. The geometry can be saved with either the variables in place, for modifying the models in Moritz, or with the variables evaluated for use in the transport codes. A program window shows a list of variables and provides fields for editing them. Surface coefficients and other values that use a variable reference are shown in a distinctive style on object property dialogs; associated buttons show fields for editing the reference. We discuss our use of variables in defining geometry models for shielding studies in PET clinics. When a model is parameterized through the use of variables, changes such as room dimensions, shielding layer widths, and cell compositions can be quickly achieved by changing a few numbers without requiring knowledge of the input syntax for the transport code or the tedious and error prone work of recalculating many surface or solid body coefficients. (author)

Engineering graphics theoretical foundations of engineering geometry for design

CERN Document Server

Brailov, Aleksandr Yurievich

2016-01-01

This professional treatise on engineering graphics emphasizes engineering geometry as the theoretical foundation for communication of design ideas with real world structures and products. It considers each theoretical notion of engineering geometry as a complex solution of direct- and inverse-problems of descriptive geometry and each solution of basic engineering problems presented is accompanied by construction of biunique two- and three-dimension models of geometrical images. The book explains the universal structure of formal algorithms of the solutions of positional, metric, and axonometric problems, as well as the solutions of problems of construction in developing a curvilinear surface. The book further characterizes and explains the added laws of projective connections to facilitate construction of geometrical images in any of eight octants. Laws of projective connections allow constructing the complex drawing of a geometrical image in the American system of measurement and the European system of measu...

Critical geometry of a thermal big bang

Science.gov (United States)

Afshordi, Niayesh; Magueijo, João

2016-11-01

We explore the space of scalar-tensor theories containing two nonconformal metrics, and find a discontinuity pointing to a "critical" cosmological solution. Due to the different maximal speeds of propagation for matter and gravity, the cosmological fluctuations start off inside the horizon even without inflation, and will more naturally have a thermal origin (since there is never vacuum domination). The critical model makes an unambiguous, nontuned prediction for the spectral index of the scalar fluctuations: nS=0.96478 (64 ) . Considering also that no gravitational waves are produced, we have unveiled the most predictive model on offer. The model has a simple geometrical interpretation as a probe 3-brane embedded in an E AdS2×E3 geometry.

Bubbling 1/2 BPS geometries and Penrose limits

International Nuclear Information System (INIS)

Takayama, Yastoshi; Yoshida, Kentaroh

2005-01-01

We discuss how to take a Penrose limit in bubbling 1/2 Bogomol'nyi-Prasad-Sommerfield geometries at the stage of a single function z(x 1 ,x 2 ,y). By starting from the z of the AdS 5 xS 5 , we can directly derive that of the pp wave via the Penrose limit. In the course of the calculation, the function z for the pp wave with 1/R 2 corrections is obtained. We see that it surely reproduces the pp wave with 1/R 2 terms. We also investigate the pp wave with higher-order 1/R 2 corrections. In addition, the Penrose limit in the configuration of the concentric rings is considered

Probing emergent geometry through phase transitions in free vector and matrix models

Energy Technology Data Exchange (ETDEWEB)

Amado, Irene; Sundborg, Bo [The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University,AlbaNova, 106 91 Stockholm (Sweden); Thorlacius, Larus [The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University,AlbaNova, 106 91 Stockholm (Sweden); Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavik (Iceland); Wintergerst, Nico [The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University,AlbaNova, 106 91 Stockholm (Sweden)

2017-02-01

Boundary correlation functions provide insight into the emergence of an effective geometry in higher spin gravity duals of O(N) or U(N) symmetric field theories. On a compact manifold, the singlet constraint leads to nontrivial dynamics at finite temperature and large N phase transitions even at vanishing ’t Hooft coupling. At low temperature, the leading behavior of boundary two-point functions is consistent with propagation through a bulk thermal anti de Sitter space. Above the phase transition, the two-point function shows significant departure from thermal AdS space and the emergence of localized black hole like objects in the bulk. In adjoint models, these objects appear at length scales of order of the AdS radius, consistent with a Hawking-Page transition, but in vector models they are parametrically larger than the AdS scale. In low dimensions, we find another crossover at large distances beyond which the correlation function again takes a thermal AdS form, albeit with a temperature dependent normalization factor.

Evolvability Search: Directly Selecting for Evolvability in order to Study and Produce It

DEFF Research Database (Denmark)

Mengistu, Henok; Lehman, Joel Anthony; Clune, Jeff

2016-01-01

of evolvable digital phenotypes. Although some types of selection in evolutionary computation indirectly encourage evolvability, one unexplored possibility is to directly select for evolvability. To do so, we estimate an individual's future potential for diversity by calculating the behavioral diversity of its...... immediate offspring, and select organisms with increased offspring variation. While the technique is computationally expensive, we hypothesized that direct selection would better encourage evolvability than indirect methods. Experiments in two evolutionary robotics domains confirm this hypothesis: in both...... domains, such Evolvability Search produces solutions with higher evolvability than those produced with Novelty Search or traditional objective-based search algorithms. Further experiments demonstrate that the higher evolvability produced by Evolvability Search in a training environment also generalizes...

Geometry and Optics of the Electrostatic ELENA Transfer Lines

CERN Document Server

Vanbavinckhove, G; Barna, D; Bartmann, W; Butin, F; Choisnet, O; Yamada, H

2013-01-01

The future ELENA ring at CERN will decelerate the AD anti-proton beam further from 5.3 MeV to 100 keV kinetic energy, to increase the efficiency of anti-proton trapping. At present there are four experiments in the AD hall which will be complemented with the installation of ELENA by additional three experiments and an additional source for commissioning. This paper describes the optimization of the transfer line geometry, ring rotation and source position. The optics of the transfer lines and error studies to define field and alignment tolerances are shown, and the optics particularities of electrostatic elements and their optimization highlighted.

Instanton strings and hyper-Kaehler geometry

International Nuclear Information System (INIS)

Dijkgraaf, Robbert

1999-01-01

We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces. These N = (4, 4) superconformal field theories describe the near-horizon dynamics of the D1-D5-brane system and are dual to string theory on AdS 3 . We derive a precise map relating the moduli of the K3 type 1113 string compactification to the moduli of these conformal field theories and the corresponding classical hyper-Kahler geometry. We conclude that in the absence of background gauge fields, the metric on the instanton moduli spaces degenerates exactly to the orbifold symmetric product of K3. Turning on a self-dual NS B-field deforms this symmetric product to a manifold that is diffeomorphic to the Hilbert scheme. We also comment on the mathematical applications of string duality to the global issues of deformations of hyper-Kaehler manifolds

Optical geometry

International Nuclear Information System (INIS)

Robinson, I.; Trautman, A.

1988-01-01

The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem

Tensor analysis and elementary differential geometry for physicists and engineers

CERN Document Server

Nguyen-Schäfer, Hung

2017-01-01

This book comprehensively presents topics, such as Dirac notation, tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. Additionally, two new chapters of Cartan differential forms and Dirac and tensor notations in quantum mechanics are added to this second edition. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors, differential geometry, and differential forms; and to apply them to the physical and engineering world. Many methods and applications are given in CFD, continuum mechanics, electrodynamics in special relativity, cosmology in the Minkowski four-dimensional spacetime, and relativistic and non-relativistic quantum mechanics. Tensors, differential geometry, differential forms, and Dirac notation are very useful advanced mathematical tools in many fields of modern physics and computational engineering. They are involved in special and general relativity physics, quantum m...

Introducing geometry concept based on history of Islamic geometry

Science.gov (United States)

Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.

2018-01-01

Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.

Evolvable synthetic neural system

Science.gov (United States)

Curtis, Steven A. (Inventor)

2009-01-01

An evolvable synthetic neural system includes an evolvable neural interface operably coupled to at least one neural basis function. Each neural basis function includes an evolvable neural interface operably coupled to a heuristic neural system to perform high-level functions and an autonomic neural system to perform low-level functions. In some embodiments, the evolvable synthetic neural system is operably coupled to one or more evolvable synthetic neural systems in a hierarchy.

Evolving RBF neural networks for adaptive soft-sensor design.

Science.gov (United States)

Alexandridis, Alex

2013-12-01

This work presents an adaptive framework for building soft-sensors based on radial basis function (RBF) neural network models. The adaptive fuzzy means algorithm is utilized in order to evolve an RBF network, which approximates the unknown system based on input-output data from it. The methodology gradually builds the RBF network model, based on two separate levels of adaptation: On the first level, the structure of the hidden layer is modified by adding or deleting RBF centers, while on the second level, the synaptic weights are adjusted with the recursive least squares with exponential forgetting algorithm. The proposed approach is tested on two different systems, namely a simulated nonlinear DC Motor and a real industrial reactor. The results show that the produced soft-sensors can be successfully applied to model the two nonlinear systems. A comparison with two different adaptive modeling techniques, namely a dynamic evolving neural-fuzzy inference system (DENFIS) and neural networks trained with online backpropagation, highlights the advantages of the proposed methodology.

Flexible intuitions of Euclidean geometry in an Amazonian indigene group

Science.gov (United States)

Izard, Véronique; Pica, Pierre; Spelke, Elizabeth S.; Dehaene, Stanislas

2011-01-01

Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ∼180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics. PMID:21606377

Quantum criticality and duality in the Sachdev-Ye-Kitaev/AdS2 chain

Science.gov (United States)

Jian, Shao-Kai; Xian, Zhuo-Yu; Yao, Hong

2018-05-01

We show that the quantum critical point (QCP) between a diffusive metal and ferromagnetic (or antiferromagnetic) phases in the SYK chain has a gravitational description corresponding to the double-trace deformation in an AdS2 chain. Specifically, by studying a double-trace deformation of a Z2 scalar in an AdS2 chain where the Z2 scalar is dual to the order parameter in the SYK chain, we find that the susceptibility and renormalization group equation describing the QCP in the SYK chain can be exactly reproduced in the holographic model. Our results suggest that the infrared geometry in the gravity theory dual to the diffusive metal of the SYK chain is also an AdS2 chain. We further show that the transition in SYK model captures universal information about double-trace deformation in generic black holes with near horizon AdS2 space-time.

Supersymmetric AdS3, AdS2 and bubble solutions

International Nuclear Information System (INIS)

Gauntlett, Jerome P.; Waldram, Daniel; Kim, Nakwoo

2007-01-01

We present new supersymmetric AdS 3 solutions of type IIB supergravity and AdS 2 solutions of D = 11 supergravity. The former are dual to conformal field theories in two dimensions with N = (0, 2) supersymmetry while the latter are dual to conformal quantum mechanics with two supercharges. Our construction also includes AdS 2 solutions of D = 11 supergravity that have non-compact internal spaces which are dual to three-dimensional N = 2 superconformal field theories coupled to point-like defects. We also present some new bubble-type solutions, corresponding to BPS states in conformal theories, that preserve four supersymmetries

Geometry through history Euclidean, hyperbolic, and projective geometries

CERN Document Server

Dillon, Meighan I

2018-01-01

Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...

Free-energy analysis of spin models on hyperbolic lattice geometries.

Science.gov (United States)

Serina, Marcel; Genzor, Jozef; Lee, Yoju; Gendiar, Andrej

2016-04-01

We investigate relations between spatial properties of the free energy and the radius of Gaussian curvature of the underlying curved lattice geometries. For this purpose we derive recurrence relations for the analysis of the free energy normalized per lattice site of various multistate spin models in the thermal equilibrium on distinct non-Euclidean surface lattices of the infinite sizes. Whereas the free energy is calculated numerically by means of the corner transfer matrix renormalization group algorithm, the radius of curvature has an analytic expression. Two tasks are considered in this work. First, we search for such a lattice geometry, which minimizes the free energy per site. We conjecture that the only Euclidean flat geometry results in the minimal free energy per site regardless of the spin model. Second, the relations among the free energy, the radius of curvature, and the phase transition temperatures are analyzed. We found out that both the free energy and the phase transition temperature inherit the structure of the lattice geometry and asymptotically approach the profile of the Gaussian radius of curvature. This achievement opens new perspectives in the AdS-CFT correspondence theories.

Architectural geometry

KAUST Repository

Pottmann, Helmut

2014-11-26

Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

Architectural geometry

KAUST Repository

Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes

2014-01-01

Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

The inside outs of AdS{sub 3}/CFT{sub 2}: exact AdS wormholes with entangled CFT duals

Energy Technology Data Exchange (ETDEWEB)

Mandal, Gautam; Sinha, Ritam; Sorokhaibam, Nilakash [Department of Theoretical Physics, Tata Institute of Fundamental Research,Mumbai 400005 (India)

2015-01-09

We present the complete family of solutions of 3D gravity (Λ<0) with two asymptotically AdS exterior regions. The solutions are constructed from data at the two boundaries, which correspond to two independent and arbitrary stress tensors T{sub R},T-bar{sub R}, and T{sub L},T-bar{sub L}. The two exteriors are smoothly joined on to an interior region through a regular horizon. We find CFT duals of these geometries which are entangled states of two CFT’s. We compute correlators between general operators at the two boundaries and find perfect agreement between CFT and bulk calculations. We calculate and match the CFT entanglement entropy (EE) with the holographic EE which involves geodesics passing through the wormhole. We also compute a holographic, non-equilibrium entropy for the CFT using properties of the regular horizon. The construction of the bulk solutions here uses an exact version of Brown-Henneaux type diffeomorphisms which are asymptotically nontrivial and transform the CFT states by two independent unitary operators on the two sides. Our solutions provide an infinite family of explicit examples of the ER=EPR relation of Maldacena and Susskind http://dx.doi.org/10.1002/prop.201300020.

Two lectures on D-geometry and noncommutative geometry

International Nuclear Information System (INIS)

Douglas, M.R.

1999-01-01

This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)

Evolving colon injury management: a review.

Science.gov (United States)

Greer, Lauren T; Gillern, Suzanne M; Vertrees, Amy E

2013-02-01

The colon is the second most commonly injured intra-abdominal organ in penetrating trauma. Management of traumatic colon injuries has evolved significantly over the past 200 years. Traumatic colon injuries can have a wide spectrum of severity, presentation, and management options. There is strong evidence that most non-destructive colon injuries can be successfully managed with primary repair or primary anastomosis. The management of destructive colon injuries remains controversial with most favoring resection with primary anastomosis and others favor colonic diversion in specific circumstances. The historical management of traumatic colon injuries, common mechanisms of injury, demographics, presentation, assessment, diagnosis, management, and complications of traumatic colon injuries both in civilian and military practice are reviewed. The damage control revolution has added another layer of complexity to management with continued controversy.

Twistor geometry

NARCIS (Netherlands)

van den Broek, P.M.

1984-01-01

The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.

Tetrahydropentalenyl-phosphazene constrained geometry complexes of rare-earth metal alkyls.

Science.gov (United States)

Hangaly, Noa K; Petrov, Alexander R; Elfferding, Michael; Harms, Klaus; Sundermeyer, Jörg

2014-05-21

Reactions of Cp™HPPh2 (1, diphenyl(4,4,6,6-tetramethyl-1,4,5,6-tetrahydropentalen-2-yl)phosphane) with the organic azides AdN3 and DipN3 (Ad = 1-adamantyl; Dip = 2,6-di-iso-propylphenyl) led to the formation of two novel CpPN ligands: P-amino-cyclopentadienylidene-phosphorane (Cp™PPh2NHAd; L(Ad)H) and P-cyclopentadienyl-iminophosphorane (Cp™HPPh2NDip; L(Dip)H). Both were characterized by NMR spectroscopy and X-ray structure analysis. For both compounds only one isomer was observed. Neither possesses any detectable prototropic or elementotropic isomers. Reactions of these ligands with [Lu(CH2SiMe3)3(thf)2] or with rare-earth metal halides and three equivalents of LiCH2SiMe3 produced the desired bis(alkyl) Cp™PN complexes: [{Cp™PN}M(CH2SiMe3)2] (M = Sc (1(Ad), 1(Dip)), Lu (2(Ad), 2(Dip)), Y (3(Ad), 3(Dip)), Sm (4(Ad)), Nd (5(Ad)), Pr (6(Ad)), Yb (7(Ad))). These complexes were characterized by extensive NMR studies for the diamagnetic and the paramagnetic complexes with full signal assignment. An almost mirror inverted order of the paramagnetic shifts has been observed for ytterbium complex 7(Ad) compared to 4(Ad), 5(Ad) and 6(Ad). For the assignment of the NMR signals [{η(1) : η(5)-C5Me4PMe2NAd}Yb(CH2SiMe3)2] 7 was synthesized, characterized and the (1)H NMR signals were compared to 7(Ad) and to other paramagnetic lanthanide complexes with the same ligand. 1(Ad), 2(Ad), 2(Dip), 3(Ad) and 3(Dip) were characterized by X-ray structure analysis revealing a sterically congested constrained geometry structure.

Geometry

Indian Academy of Sciences (India)

. In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...

Critical behavior and microscopic structure of charged AdS black holes via an alternative phase space

Directory of Open Access Journals (Sweden)

Amin Dehyadegari

2017-05-01

Full Text Available It has been argued that charged Anti-de Sitter (AdS black holes have similar thermodynamic behavior as the Van der Waals fluid system, provided one treats the cosmological constant as a thermodynamic variable (pressure in an extended phase space. In this paper, we disclose the deep connection between charged AdS black holes and Van der Waals fluid system from an alternative point of view. We consider the mass of an AdS black hole as a function of square of the charge Q2 instead of the standard Q, i.e. M=M(S,Q2,P. We first justify such a change of view mathematically and then ask if a phase transition can occur as a function of Q2 for fixed P. Therefore, we write the equation of state as Q2=Q2(T,Ψ where Ψ (conjugate of Q2 is the inverse of the specific volume, Ψ=1/v. This allows us to complete the analogy of charged AdS black holes with Van der Waals fluid system and derive the phase transition as well as critical exponents of the system. We identify a thermodynamic instability in this new picture with real analogy to Van der Waals fluid with physically relevant Maxwell construction. We therefore study the critical behavior of isotherms in Q2–Ψ diagram and deduce all the critical exponents of the system and determine that the system exhibits a small–large black hole phase transition at the critical point (Tc,Qc2,Ψc. This alternative view is important as one can imagine such a change for a given single black hole i.e. acquiring charge which induces the phase transition. Finally, we disclose the microscopic properties of charged AdS black holes by using thermodynamic geometry. Interestingly, we find that scalar curvature has a gap between small and large black holes, and this gap becomes exceedingly large as one moves away from the critical point along the transition line. Therefore, we are able to attribute the sudden enlargement of the black hole to the strong repulsive nature of the internal constituents at the phase transition.

Static BPS black holes in AdS{sub 4} with general dyonic charges

Energy Technology Data Exchange (ETDEWEB)

Halmagyi, Nick [Sorbonne Universités, UPMC Paris 06, UMR 7589, LPTHE,75005, Paris (France); CNRS, UMR 7589, LPTHE,75005, Paris (France)

2015-03-06

We complete the study of static BPS, asymptotically AdS{sub 4} black holes within N=2 FI-gauged supergravity and where the scalar manifold is a symmetric very special Kähler manifold. We find the analytic form for the general solution to the BPS equations, the horizon appears as a double root of a particular quartic polynomial whereas in previous work this quartic polynomial further factored into a pair of double roots. A new and distinguishing feature of our solutions is that the phase of the supersymmetry parameter varies throughout the black hole. The general solution has 2n{sub v} independent parameters; there are two algebraic constraints on 2n{sub v}+2 charges, matching our previous analysis on BPS solutions of the form AdS{sub 2}×Σ{sub g}. As a consequence we have proved that every BPS geometry of this form can arise as the horizon geometry of a BPS AdS{sub 4} black hole. When specialized to the STU-model our solutions uplift to M-theory and describe a stack of M2-branes wrapped on a Riemman surface in a Calabi-Yau fivefold with internal angular momentum.

Molecular geometry

CERN Document Server

Rodger, Alison

1995-01-01

Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and trans

Large N phase transitions and the fate of small Schwarzschild-AdS black holes

Science.gov (United States)

Yaffe, Laurence G.

2018-01-01

Sufficiently small Schwarzschild-AdS black holes in asymptotically global AdS5×S5 spacetime are known to become dynamically unstable toward deformation of the internal S5 geometry. The resulting evolution of such an unstable black hole is related, via holography, to the dynamics of supercooled plasma which has reached the limit of metastability in maximally supersymmetric large-N Yang-Mills theory on R ×S3. Puzzles related to the resulting dynamical evolution are discussed, with a key issue involving differences between the large-N limit in the dual field theory and typical large volume thermodynamic limits.

Effects of viewing- and illumination geometry on settlement type classification of quickbird images

CSIR Research Space (South Africa)

Van den Bergh, F

2011-07-01

Full Text Available of classifiers based on such texture features, since the illumination geometry has a direct impact on both the amount and direction of shadowing within a scene. 2. METHODOLOGY A good image feature is one that is designed to have a repre- sentation... purpose of the study, though, was to quantify the influence of spurious differences on the generalization per- formance of classifiers using texture features as input, repre- sented directly by the Ad1*) Ad2and Bd1*) Bd2classes. Here, the GLCM features...

Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology & Symplectic Geometry, Noncommutative Geometry and Physics

CERN Document Server

Eliashberg, Yakov; Maeda, Yoshiaki; Symplectic, Poisson, and Noncommutative geometry

2014-01-01

Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously unpublished results and ...

An alternative path to the boundary: The CFT as the Fourier space of AdS

Science.gov (United States)

Tolfree, Ian M.

2009-12-01

In this thesis we shed new light on the conjectured duality between an n + 1 dimensional theory of gravity in anti de Sitter space (AdS) and an n dimensional conformal field theory (CFT) by showing that the CFT can be interpreted as the Fourier space of AdS. We then make use of this to gain insight into the nature of black hole entropy. In the first part of this thesis, we give an introduction to the ideas of and review the basics of the AdS/CFT. In the next section we make use of well known integral geometry techniques to derive the Fourier transformation of a function on AdS and see it is a function with compact support on the boundary. Comparing this to the literature, we find that the Green's functions from the literature are actually the Fourier weights of the transformation and that the boundary values of fields appearing in the correspondence are the Fourier coefficients of the transformation. One is thus left to interpret the CFT as the quantized version of a classical theory in AdS and the dual operator as the Fourier coefficients. Group theoretic considerations are discussed in relation to the transformation and its potential use in constructing QCD like theories. In the last section, we then build upon this to study the BTZ black hole. Named after its authors, Banados, Teitelboim and Zanelli, the BTZ black hole is a three dimensional (two space plus one time dimension) black hole in anti de Sitter space. Following standard procedures for modifying Fourier Transformations to accommodate quotient spaces we arrive at a mapping in a black hole background consistent with known results that yields the exact micro-states of a scalar field in a black hole background. We find that the micro-states are the Fourier coefficients on the boundary, which transform under the principal series representation of SL(2, R). Using the knowledge of how to represent a bulk scalar field in the CFT, and knowing how a black hole interacts with a scalar field, we deduce the

A Maxwell-vector p-wave holographic superconductor in a particular background AdS black hole metric

Directory of Open Access Journals (Sweden)

Dan Wen

2018-05-01

Full Text Available We study the p-wave holographic superconductor for AdS black holes with planar event horizon topology for a particular Lovelock gravity, in which the action is characterized by a self-interacting scalar field nonminimally coupled to the gravity theory which is labeled by an integer k. As the Lovelock theory of gravity is the most general metric theory of gravity based on the fundamental assumptions of general relativity, it is a desirable theory to describe the higher dimensional spacetime geometry. The present work is devoted to studying the properties of the p-wave holographic superconductor by including a Maxwell field which nonminimally couples to a complex vector field in a higher dimensional background metric. In the probe limit, we find that the critical temperature decreases with the increase of the index k of the background black hole metric, which shows that a larger k makes it harder for the condensation to form. We also observe that the index k affects the conductivity and the gap frequency of the holographic superconductors.

A Maxwell-vector p-wave holographic superconductor in a particular background AdS black hole metric

Science.gov (United States)

Wen, Dan; Yu, Hongwei; Pan, Qiyuan; Lin, Kai; Qian, Wei-Liang

2018-05-01

We study the p-wave holographic superconductor for AdS black holes with planar event horizon topology for a particular Lovelock gravity, in which the action is characterized by a self-interacting scalar field nonminimally coupled to the gravity theory which is labeled by an integer k. As the Lovelock theory of gravity is the most general metric theory of gravity based on the fundamental assumptions of general relativity, it is a desirable theory to describe the higher dimensional spacetime geometry. The present work is devoted to studying the properties of the p-wave holographic superconductor by including a Maxwell field which nonminimally couples to a complex vector field in a higher dimensional background metric. In the probe limit, we find that the critical temperature decreases with the increase of the index k of the background black hole metric, which shows that a larger k makes it harder for the condensation to form. We also observe that the index k affects the conductivity and the gap frequency of the holographic superconductors.

Morphology and stratal geometry of the Antarctic continental shelf: Insights from models

Science.gov (United States)

Cooper, Alan K.; Barker, Peter F.; Brancolini, Giuliano

1997-01-01

Reconstruction of past ice-sheet fluctuations from the stratigraphy of glaciated continental shelves requires understanding of the relationships among the stratal geometry, glacial and marine sedimentary processes, and ice dynamics. We investigate the formation of the morphology and the broad stratal geometry of topsets on the Antarctic continental shelf with numerical models. Our models assume that the stratal geometry and morphology are principally the results of time-integrated effects of glacial erosion and sedimentation related to the location of the seaward edge of the grounded ice. The location of the grounding line varies with time almost randomly across the shelf. With these simple assumptions, the models can successfully mimic salient features of the morphology and the stratal geometry. The models suggest that the current shelf has gradually evolved to its present geometry by many glacial advances and retreats of the grounding line to different locations across the shelf. The locations of the grounding line do not appear to be linearly correlated with either fluctuations in the 5 l s O record (which presumably represents changes in the global ice volume) or with the global sea-level curve, suggesting that either a more complex relationship exists or local effects dominate. The models suggest that erosion of preglacial sediments is confined to the inner shelf, and erosion decreases and deposition increases toward the shelf edge. Some of the deposited glacial sediments must be derived from continental erosion. The sediments probably undergo extensive transport and reworking obliterating much of the evidence for their original depositional environment. The flexural rigidity and the tectonic subsidence of the underlying lithosphere modify the bathymetry of the shelf, but probably have little effect on the stratal geometry. Our models provide several guidelines for the interpretation of unconformities, the nature of preserved topset deposits, and the

Network Analysis of Earth's Co-Evolving Geosphere and Biosphere

Science.gov (United States)

Hazen, R. M.; Eleish, A.; Liu, C.; Morrison, S. M.; Meyer, M.; Consortium, K. D.

2017-12-01

A fundamental goal of Earth science is the deep understanding of Earth's dynamic, co-evolving geosphere and biosphere through deep time. Network analysis of geo- and bio- `big data' provides an interactive, quantitative, and predictive visualization framework to explore complex and otherwise hidden high-dimension features of diversity, distribution, and change in the evolution of Earth's geochemistry, mineralogy, paleobiology, and biochemistry [1]. Networks also facilitate quantitative comparison of different geological time periods, tectonic settings, and geographical regions, as well as different planets and moons, through network metrics, including density, centralization, diameter, and transitivity.We render networks by employing data related to geographical, paragenetic, environmental, or structural relationships among minerals, fossils, proteins, and microbial taxa. An important recent finding is that the topography of many networks reflects parameters not explicitly incorporated in constructing the network. For example, networks for minerals, fossils, and protein structures reveal embedded qualitative time axes, with additional network geometries possibly related to extinction and/or other punctuation events (see Figure). Other axes related to chemical activities and volatile fugacities, as well as pressure and/or depth of formation, may also emerge from network analysis. These patterns provide new insights into the way planets evolve, especially Earth's co-evolving geosphere and biosphere. 1. Morrison, S.M. et al. (2017) Network analysis of mineralogical systems. American Mineralogist 102, in press. Figure Caption: A network of Phanerozoic Era fossil animals from the past 540 million years includes blue, red, and black circles (nodes) representing family-level taxa and grey lines (links) between coexisting families. Age information was not used in the construction of this network; nevertheless an intrinsic timeline is embedded in the network topology. In

Higher geometry an introduction to advanced methods in analytic geometry

CERN Document Server

Woods, Frederick S

2005-01-01

For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study

Supergravity one-loop corrections on AdS7 and AdS3, higher spins and AdS/CFT

Directory of Open Access Journals (Sweden)

Matteo Beccaria

2015-03-01

Full Text Available As was shown earlier, the one-loop correction in 10d supergravity on AdS5×S5 corresponds to the contributions to the vacuum energy and 4d boundary conformal anomaly which are minus the values for one N=4 Maxwell supermultiplet, thus reproducing the subleading term in the N2−1 coefficient in the dual SU(N SYM theory. We perform similar one-loop computations in 11d supergravity on AdS7×S4 and 10d supergravity on AdS3×S3×T4. In the AdS7 case we find that the corrections to the 6d conformal anomaly a-coefficient and the vacuum energy are again minus the ones for one (2,0 tensor multiplet, suggesting that the total a-anomaly coefficient for the dual (2,0 theory is 4N3−9/4N−7/4 and thus vanishes for N=1. In the AdS3 case the one-loop correction to the vacuum energy or 2d central charge turns out to be equal to that of one free (4,4 scalar multiplet, i.e. is c=+6. This reproduces the subleading term in the central charge c=6(Q1Q5+1 of the dual 2d CFT describing decoupling limit of D5–D1 system. We also present the expressions for the 6d a-anomaly coefficient and vacuum energy contributions of general-symmetry higher spin field in AdS7 and consider their application to tests of vectorial AdS/CFT with the boundary conformal 6d theory represented by free scalars, spinors or rank-2 antisymmetric tensors.

Non-Riemannian geometry

CERN Document Server

Eisenhart, Luther Pfahler

2005-01-01

This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.

Evolving Capabilities for Virtual Globes

Science.gov (United States)

Glennon, A.

2006-12-01

Though thin-client spatial visualization software like Google Earth and NASA World Wind enjoy widespread popularity, a common criticism is their general lack of analytical functionality. This concern, however, is rapidly being addressed; standard and advanced geographic information system (GIS) capabilities are being developed for virtual globes--though not centralized into a single implementation or software package. The innovation is mostly originating from the user community. Three such capabilities relevant to the earth science, education, and emergency management communities are modeling dynamic spatial phenomena, real-time data collection and visualization, and multi-input collaborative databases. Modeling dynamic spatial phenomena has been facilitated through joining virtual globe geometry definitions--like KML--to relational databases. Real-time data collection uses short scripts to transform user-contributed data into a format usable by virtual globe software. Similarly, collaborative data collection for virtual globes has become possible by dynamically referencing online, multi-person spreadsheets. Examples of these functions include mapping flows within a karst watershed, real-time disaster assessment and visualization, and a collaborative geyser eruption spatial decision support system. Virtual globe applications will continue to evolve further analytical capabilities, more temporal data handling, and from nano to intergalactic scales. This progression opens education and research avenues in all scientific disciplines.

Robustness to Faults Promotes Evolvability: Insights from Evolving Digital Circuits.

Science.gov (United States)

Milano, Nicola; Nolfi, Stefano

2016-01-01

We demonstrate how the need to cope with operational faults enables evolving circuits to find more fit solutions. The analysis of the results obtained in different experimental conditions indicates that, in absence of faults, evolution tends to select circuits that are small and have low phenotypic variability and evolvability. The need to face operation faults, instead, drives evolution toward the selection of larger circuits that are truly robust with respect to genetic variations and that have a greater level of phenotypic variability and evolvability. Overall our results indicate that the need to cope with operation faults leads to the selection of circuits that have a greater probability to generate better circuits as a result of genetic variation with respect to a control condition in which circuits are not subjected to faults.

The Geometry Conference

CERN Document Server

Bárány, Imre; Vilcu, Costin

2016-01-01

This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.

Hyperbolic geometry

CERN Document Server

Iversen, Birger

1992-01-01

Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics

Geometry of the Universe

International Nuclear Information System (INIS)

Gurevich, L.Eh.; Gliner, Eh.B.

1978-01-01

Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding

Preface: evolving rotifers, evolving science: Proceedings of the XIV International Rotifer Symposium

Czech Academy of Sciences Publication Activity Database

Devetter, Miloslav; Fontaneto, D.; Jersabek, Ch.D.; Welch, D.B.M.; May, L.; Walsh, E.J.

2017-01-01

Roč. 796, č. 1 (2017), s. 1-6 ISSN 0018-8158 Institutional support: RVO:60077344 Keywords : evolving rotifers * 14th International Rotifer Symposium * evolving science Subject RIV: EG - Zoology OBOR OECD: Zoology Impact factor: 2.056, year: 2016

Hairy AdS solitons

International Nuclear Information System (INIS)

Anabalón, Andrés; Astefanesei, Dumitru; Choque, David

2016-01-01

We construct exact hairy AdS soliton solutions in Einstein-dilaton gravity theory. We examine their thermodynamic properties and discuss the role of these solutions for the existence of first order phase transitions for hairy black holes. The negative energy density associated to hairy AdS solitons can be interpreted as the Casimir energy that is generated in the dual filed theory when the fermions are antiperiodic on the compact coordinate.

Hairy AdS solitons

Energy Technology Data Exchange (ETDEWEB)

Anabalón, Andrés, E-mail: andres.anabalon@uai.cl [Departamento de Ciencias, Facultad de Artes Liberales and Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar (Chile); Astefanesei, Dumitru, E-mail: dumitru.astefanesei@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Choque, David, E-mail: brst1010123@gmail.com [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso (Chile)

2016-11-10

We construct exact hairy AdS soliton solutions in Einstein-dilaton gravity theory. We examine their thermodynamic properties and discuss the role of these solutions for the existence of first order phase transitions for hairy black holes. The negative energy density associated to hairy AdS solitons can be interpreted as the Casimir energy that is generated in the dual filed theory when the fermions are antiperiodic on the compact coordinate.

Quantum mechanics in an evolving Hilbert space

Science.gov (United States)

Artacho, Emilio; O'Regan, David D.

2017-03-01

Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives in the context of differential geometry, thereby obtaining a more transparent formalization, and a geometrical perspective for better understanding the resulting equations. The effect of the evolution of the basis set within the spanned Hilbert space separates explicitly from the effect of the turning of the space itself when moving in parameter space, as the tangent space turns when moving in a curved space. New insights are obtained using familiar concepts in that context such as the Riemann curvature. The differential geometry is not strictly that for curved spaces as in general relativity, a more adequate mathematical framework being provided by fiber bundles. The language used here, however, will be restricted to tensors and basic quantum mechanics. The local gauge implied by a smoothly varying basis set readily connects with Berry's formalism for geometric phases. Generalized expressions for the Berry connection and curvature are obtained for a parameter-dependent occupied Hilbert space spanned by nonorthogonal Wannier functions. The formalism is applicable to basis sets made of atomic-like orbitals and also more adaptative moving basis functions (such as in methods using Wannier functions as intermediate or support bases), but should also apply to other situations in which nonorthogonal functions or related projectors should arise. The formalism is applied to the time-dependent quantum evolution of electrons for moving atoms. The geometric insights provided here allow us to propose new finite-difference time integrators, and also better understand those already proposed.

On organizing principles of discrete differential geometry. Geometry of spheres

International Nuclear Information System (INIS)

Bobenko, Alexander I; Suris, Yury B

2007-01-01

Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.

AdS solutions through transgression

International Nuclear Information System (INIS)

Donos, Aristomenis; Gauntlett, Jerome P.; Kim, Nakwoo

2008-01-01

We present new classes of explicit supersymmetric AdS 3 solutions of type IIB supergravity with non-vanishing five-form flux and AdS 2 solutions of D = 11 supergravity with electric four-form flux. The former are dual to two-dimensional SCFTs with (0,2) supersymmetry and the latter to supersymmetric quantum mechanics with two supercharges. We also investigate more general classes of AdS 3 solutions of type IIB supergravity and AdS 2 solutions of D = 11 supergravity which in addition have non-vanishing three-form flux and magnetic four-form flux, respectively. The construction of these more general solutions makes essential use of the Chern-Simons or 'transgression' terms in the Bianchi identity or the equation of motion of the field strengths in the supergravity theories. We construct infinite new classes of explicit examples and for some of the type IIB solutions determine the central charge of the dual SCFTs. The type IIB solutions with non-vanishing three-form flux that we construct include a two-torus, and after two T-dualities and an S-duality, we obtain new AdS 3 solutions with only the NS fields being non-trivial.

Nuclear data sensitivity/uncertainty analysis for XT-ADS

International Nuclear Information System (INIS)

Sugawara, Takanori; Sarotto, Massimo; Stankovskiy, Alexey; Van den Eynde, Gert

2011-01-01

Highlights: → The sensitivity and uncertainty analyses were performed to comprehend the reliability of the XT-ADS neutronic design. → The uncertainties deduced from the covariance data for the XT-ADS criticality were 0.94%, 1.9% and 1.1% by the SCALE 44-group, TENDL-2009 and JENDL-3.3 data, respectively. → When the target accuracy of 0.3%Δk for the criticality was considered, the uncertainties did not satisfy it. → To achieve this accuracy, the uncertainties should be improved by experiments under an adequate condition. - Abstract: The XT-ADS, an accelerator-driven system for an experimental demonstration, has been investigated in the framework of IP EUROTRANS FP6 project. In this study, the sensitivity and uncertainty analyses were performed to comprehend the reliability of the XT-ADS neutronic design. For the sensitivity analysis, it was found that the sensitivity coefficients were significantly different by changing the geometry models and calculation codes. For the uncertainty analysis, it was confirmed that the uncertainties deduced from the covariance data varied significantly by changing them. The uncertainties deduced from the covariance data for the XT-ADS criticality were 0.94%, 1.9% and 1.1% by the SCALE 44-group, TENDL-2009 and JENDL-3.3 data, respectively. When the target accuracy of 0.3%Δk for the criticality was considered, the uncertainties did not satisfy it. To achieve this accuracy, the uncertainties should be improved by experiments under an adequate condition.

Geometry and its applications

CERN Document Server

Meyer, Walter J

2006-01-01

Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...

Beautiful geometry

CERN Document Server

Maor, Eli

2014-01-01

If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur

A local-world evolving hypernetwork model

International Nuclear Information System (INIS)

Yang Guang-Yong; Liu Jian-Guo

2014-01-01

Complex hypernetworks are ubiquitous in the real system. It is very important to investigate the evolution mechanisms. In this paper, we present a local-world evolving hypernetwork model by taking into account the hyperedge growth and local-world hyperedge preferential attachment mechanisms. At each time step, a newly added hyperedge encircles a new coming node and a number of nodes from a randomly selected local world. The number of the selected nodes from the local world obeys the uniform distribution and its mean value is m. The analytical and simulation results show that the hyperdegree approximately obeys the power-law form and the exponent of hyperdegree distribution is γ = 2 + 1/m. Furthermore, we numerically investigate the node degree, hyperedge degree, clustering coefficient, as well as the average distance, and find that the hypernetwork model shares the scale-free and small-world properties, which shed some light for deeply understanding the evolution mechanism of the real systems. (interdisciplinary physics and related areas of science and technology)

Revolutions of Geometry

CERN Document Server

O'Leary, Michael

2010-01-01

Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull

Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry

Science.gov (United States)

Mammana, M. F.; Micale, B.; Pennisi, M.

2012-01-01

We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…

Information geometry

CERN Document Server

Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz

2017-01-01

The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...

Twistor methods for AdS{sub 5}

Energy Technology Data Exchange (ETDEWEB)

Adamo, Tim; Skinner, David; Williams, Jack [Department of Applied Mathematics & Theoretical Physics, University of Cambridge,Wilberforce Road, Cambridge, CB3 0WA United Kingdom (United Kingdom)

2016-08-30

We consider the application of twistor theory to five-dimensional anti-de Sitter space. The twistor space of AdS{sub 5} is the same as the ambitwistor space of the four-dimensional conformal boundary; the geometry of this correspondence is reviewed for both the bulk and boundary. A Penrose transform allows us to describe free bulk fields, with or without mass, in terms of data on twistor space. Explicit representatives for the bulk-to-boundary propagators of scalars and spinors are constructed, along with twistor action functionals for the free theories. Evaluating these twistor actions on bulk-to-boundary propagators is shown to produce the correct two-point functions.

Euclid's window the story of geometry from parallel lines to hyperspace

CERN Document Server

Mlodinow, Leonard

2002-01-01

In "Euclid's Window", Leonard Mlondinow takes us on a brilliantly entertaining journey through 3,000 years of genius and geometry, introducing the people who revolutionized the way we see the world around us. Ever since Pythagoras hatched a 'little scheme' to invent a set of rules describing the entire universe, scientists and mathematicians have tried to seek order in the cosmos: Euclid, who in 300BC defined the nature of space; Descartes, a fourteenth-century gambler and idler who invented the graph; Gauss, the fifteen-year-old genius who discovered that space is curved; Einstein, who added time to the equation; and Witten, who ushered in today's weird new world of extra, twisted dimensions. They all show how geometry is the key to understanding the universe. Once you have viewed life through "Euclid's Window", it will never be the same again...

Differential geometry of group lattices

International Nuclear Information System (INIS)

Dimakis, Aristophanes; Mueller-Hoissen, Folkert

2003-01-01

In a series of publications we developed ''differential geometry'' on discrete sets based on concepts of noncommutative geometry. In particular, it turned out that first-order differential calculi (over the algebra of functions) on a discrete set are in bijective correspondence with digraph structures where the vertices are given by the elements of the set. A particular class of digraphs are Cayley graphs, also known as group lattices. They are determined by a discrete group G and a finite subset S. There is a distinguished subclass of ''bicovariant'' Cayley graphs with the property ad(S)S subset of S. We explore the properties of differential calculi which arise from Cayley graphs via the above correspondence. The first-order calculi extend to higher orders and then allow us to introduce further differential geometric structures. Furthermore, we explore the properties of ''discrete'' vector fields which describe deterministic flows on group lattices. A Lie derivative with respect to a discrete vector field and an inner product with forms is defined. The Lie-Cartan identity then holds on all forms for a certain subclass of discrete vector fields. We develop elements of gauge theory and construct an analog of the lattice gauge theory (Yang-Mills) action on an arbitrary group lattice. Also linear connections are considered and a simple geometric interpretation of the torsion is established. By taking a quotient with respect to some subgroup of the discrete group, generalized differential calculi associated with so-called Schreier diagrams are obtained

Hawking radiation from AdS black holes

International Nuclear Information System (INIS)

Hubeny, Veronika E; Rangamani, Mukund; Marolf, Donald

2010-01-01

We study Hartle-Hawking-like states of quantum field theories on asymptotically AdS black hole backgrounds, with particular regard to the phase structure of interacting theories. By a suitable analytic continuation we show that the equilibrium dynamics of field theories on large asymptotically AdS black holes can be related to the low-temperature states of the same field theory on the AdS soliton (or pure AdS) background. This allows us to gain insight into Hartle-Hawking-like states on large-radius Schwarzschild- or rotating-AdS black holes. Furthermore, we exploit the AdS/CFT correspondence to explore the physics of strongly coupled large N theories on asymptotically AdS black holes. In particular, we exhibit a plausibly complete set of phases for the M2-brane world-volume superconformal field theory on a BTZ black hole background. Our analysis partially resolves puzzles previously raised in connection with Hawking radiation on large AdS black holes.

Geometry and quadratic nonlinearity of charge transfer complexes in solution: A theoretical study

International Nuclear Information System (INIS)

Mukhopadhyay, S.; Ramasesha, S.; Pandey, Ravindra; Das, Puspendu K.

2011-01-01

In this paper, we have computed the quadratic nonlinear optical (NLO) properties of a class of weak charge transfer (CT) complexes. These weak complexes are formed when the methyl substituted benzenes (donors) are added to strong acceptors like chloranil (CHL) or di-chloro-di-cyano benzoquinone (DDQ) in chloroform or in dichloromethane. The formation of such complexes is manifested by the presence of a broad absorption maximum in the visible range of the spectrum where neither the donor nor the acceptor absorbs. The appearance of this visible band is due to CT interactions, which result in strong NLO responses. We have employed the semiempirical intermediate neglect of differential overlap (INDO/S) Hamiltonian to calculate the energy levels of these CT complexes using single and double configuration interaction (SDCI). The solvent effects are taken into account by using the self-consistent reaction field (SCRF) scheme. The geometry of the complex is obtained by exploring different relative molecular geometries by rotating the acceptor with respect to the fixed donor about three different axes. The theoretical geometry that best fits the experimental energy gaps, β HRS and macroscopic depolarization ratios is taken to be the most probable geometry of the complex. Our studies show that the most probable geometry of these complexes in solution is the parallel displaced structure with a significant twist in some cases.

Geometry essentials for dummies

CERN Document Server

Ryan, Mark

2011-01-01

Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque

Stationary and nonstationary properties of evolving networks with preferential linkage

International Nuclear Information System (INIS)

Jezewski, W.

2002-01-01

Networks evolving by preferential attachment of both external and internal links are investigated. The rate of adding an external link is assumed to depend linearly on the degree of a preexisting node to which a new node is connected. The process of creating an internal link, between a pair of existing vertices, is assumed to be controlled entirely by the vertex that has more links than the other vertex in the pair, and the rate of creation of such a link is assumed to be, in general, nonlinear in the degree of the more strongly connected vertex. It is shown that degree distributions of networks evolving only by creating internal links display for large degrees a nonstationary power-law decay with a time-dependent scaling exponent. Nonstationary power-law behaviors are numerically shown to persist even when the number of nodes is not fixed and both external and internal connections are introduced, provided that the rate of preferential attachment of internal connections is nonlinear. It is argued that nonstationary effects are not unlikely in real networks, although these effects may not be apparent, especially in networks with a slowly varying mean degree

Complex analysis and geometry

CERN Document Server

Silva, Alessandro

1993-01-01

The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.

Natural selection promotes antigenic evolvability.

Science.gov (United States)

Graves, Christopher J; Ros, Vera I D; Stevenson, Brian; Sniegowski, Paul D; Brisson, Dustin

2013-01-01

The hypothesis that evolvability - the capacity to evolve by natural selection - is itself the object of natural selection is highly intriguing but remains controversial due in large part to a paucity of direct experimental evidence. The antigenic variation mechanisms of microbial pathogens provide an experimentally tractable system to test whether natural selection has favored mechanisms that increase evolvability. Many antigenic variation systems consist of paralogous unexpressed 'cassettes' that recombine into an expression site to rapidly alter the expressed protein. Importantly, the magnitude of antigenic change is a function of the genetic diversity among the unexpressed cassettes. Thus, evidence that selection favors among-cassette diversity is direct evidence that natural selection promotes antigenic evolvability. We used the Lyme disease bacterium, Borrelia burgdorferi, as a model to test the prediction that natural selection favors amino acid diversity among unexpressed vls cassettes and thereby promotes evolvability in a primary surface antigen, VlsE. The hypothesis that diversity among vls cassettes is favored by natural selection was supported in each B. burgdorferi strain analyzed using both classical (dN/dS ratios) and Bayesian population genetic analyses of genetic sequence data. This hypothesis was also supported by the conservation of highly mutable tandem-repeat structures across B. burgdorferi strains despite a near complete absence of sequence conservation. Diversification among vls cassettes due to natural selection and mutable repeat structures promotes long-term antigenic evolvability of VlsE. These findings provide a direct demonstration that molecular mechanisms that enhance evolvability of surface antigens are an evolutionary adaptation. The molecular evolutionary processes identified here can serve as a model for the evolution of antigenic evolvability in many pathogens which utilize similar strategies to establish chronic infections.

Natural selection promotes antigenic evolvability.

Directory of Open Access Journals (Sweden)

Christopher J Graves

Full Text Available The hypothesis that evolvability - the capacity to evolve by natural selection - is itself the object of natural selection is highly intriguing but remains controversial due in large part to a paucity of direct experimental evidence. The antigenic variation mechanisms of microbial pathogens provide an experimentally tractable system to test whether natural selection has favored mechanisms that increase evolvability. Many antigenic variation systems consist of paralogous unexpressed 'cassettes' that recombine into an expression site to rapidly alter the expressed protein. Importantly, the magnitude of antigenic change is a function of the genetic diversity among the unexpressed cassettes. Thus, evidence that selection favors among-cassette diversity is direct evidence that natural selection promotes antigenic evolvability. We used the Lyme disease bacterium, Borrelia burgdorferi, as a model to test the prediction that natural selection favors amino acid diversity among unexpressed vls cassettes and thereby promotes evolvability in a primary surface antigen, VlsE. The hypothesis that diversity among vls cassettes is favored by natural selection was supported in each B. burgdorferi strain analyzed using both classical (dN/dS ratios and Bayesian population genetic analyses of genetic sequence data. This hypothesis was also supported by the conservation of highly mutable tandem-repeat structures across B. burgdorferi strains despite a near complete absence of sequence conservation. Diversification among vls cassettes due to natural selection and mutable repeat structures promotes long-term antigenic evolvability of VlsE. These findings provide a direct demonstration that molecular mechanisms that enhance evolvability of surface antigens are an evolutionary adaptation. The molecular evolutionary processes identified here can serve as a model for the evolution of antigenic evolvability in many pathogens which utilize similar strategies to establish

String Theory on AdS Spaces

NARCIS (Netherlands)

de Boer, J.

2000-01-01

In these notes we discuss various aspects of string theory in AdS spaces. We briefly review the formulation in terms of Green-Schwarz, NSR, and Berkovits variables, as well as the construction of exact conformal field theories with AdS backgrounds. Based on lectures given at the Kyoto YITP Workshop

Algebraically special solutions in AdS/CFT

International Nuclear Information System (INIS)

Freitas, Gabriel Bernardi de; Reall, Harvey S.

2014-01-01

We investigate the AdS/CFT interpretation of the class of algebraically special solutions of Einstein gravity with a negative cosmological constant. Such solutions describe a CFT living in a 2+1 dimensional time-dependent geometry that, generically, has no isometries. The algebraically special condition implies that the expectation value of the CFT energy-momentum tensor is a local function of the boundary metric. When such a spacetime is slowly varying, the fluid/gravity approximation is valid and one can read off the values of certain higher order transport coefficients. To do this, we introduce a formalism for studying conformal, relativistic fluids in 2+1 dimensions that reduces everything to the manipulation of scalar quantities.

Algebraically special solutions in AdS/CFT

Energy Technology Data Exchange (ETDEWEB)

Freitas, Gabriel Bernardi de; Reall, Harvey S. [Department of Applied Mathematics and Theoretical Physics, University of Cambridge,Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)

2014-06-26

We investigate the AdS/CFT interpretation of the class of algebraically special solutions of Einstein gravity with a negative cosmological constant. Such solutions describe a CFT living in a 2+1 dimensional time-dependent geometry that, generically, has no isometries. The algebraically special condition implies that the expectation value of the CFT energy-momentum tensor is a local function of the boundary metric. When such a spacetime is slowly varying, the fluid/gravity approximation is valid and one can read off the values of certain higher order transport coefficients. To do this, we introduce a formalism for studying conformal, relativistic fluids in 2+1 dimensions that reduces everything to the manipulation of scalar quantities.

Open strings on AdS2 branes

International Nuclear Information System (INIS)

Lee, Peter; Ooguri, Hirosi.; Park, Jongwon; Tannenhauser, Jonathan

2001-01-01

We study the spectrum of open strings on AdS 2 branes in AdS 3 in an NS-NS background, using the SL(2,R) WZW model. When the brane carries no fundamental string charge, the open string spectrum is the holomorphic square root of the spectrum of closed strings in AdS 3 . It contains short and long strings, and is invariant under spectral flow. When the brane carries fundamental string charge, the open string spectrum again contains short and long strings in all winding sectors. However, branes with fundamental string charge break half the spectral flow symmetry. This has different implications for short and long strings. As the fundamental string charge increases, the brane approaches the boundary of AdS 3 . In this limit, the induced electric field on the worldvolume reaches its critical value, producing noncommutative open string theory on AdS 2

Simulations and Experiments of Dynamic Granular Compaction in Non-ideal Geometries

Science.gov (United States)

Homel, Michael; Herbold, Eric; Lind, John; Crum, Ryan; Hurley, Ryan; Akin, Minta; Pagan, Darren; LLNL Team

2017-06-01

Accurately describing the dynamic compaction of granular materials is a persistent challenge in computational mechanics. Using a synchrotron x-ray source we have obtained detailed imaging of the evolving compaction front in synthetic olivine powder impacted at 300 - 600 m / s . To facilitate imaging, a non-traditional sample geometry is used, producing multiple load paths within the sample. We demonstrate that (i) commonly used models for porous compaction may produce inaccurate results for complex loading, even if the 1 - D , uniaxial-strain compaction response is reasonable, and (ii) the experimental results can be used along with simulations to determine parameters for sophisticated constitutive models that more accurately describe the strength, softening, bulking, and poroelastic response. Effects of experimental geometry and alternative configurations are discussed. Our understanding of the material response is further enhanced using mesoscale simulations that allow us to relate the mechanisms of grain fracture, contact, and comminution to the macroscale continuum response. Numerical considerations in both continuum and mesoscale simulations are described. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LDRD#16-ERD-010. LLNL-ABS-725113.

Conical singularities in AdS space time

International Nuclear Information System (INIS)

Ferreira, Cristine Nunes

2011-01-01

Full text: In recent years, the study of conformal gauge theories from 10-D has been motivated by the AdS d+1 /CFT d correspondence, first conjectured by J. Maldacena. The aim of this work is to consider the d = 4 case by analysing the configuration of the N coincident D3 branes. In this context, the work shows that there is a duality between type IIB string theory in AdS 5 x S 5 and N = 4 SU(N) Super Yang-Mills Theory in the IR. The AdS 5 /CFT 4 correspondence brought also new approaches to the strong coupling problem in QCD. Nowadays, there is a whole line of works that focus on the low dimensional correspondence AdS 4 /CFT 3 , like the application to graphene and topological insulators, and the AdS 3 /CFT 2 correspondence, related with the entanglement entropy. In this work, we consider the vortex configuration solution to the AdS 4 and AdS 3 space-time. The most important motivation is to discuss the boundary theory resulting from these solutions. We have examined a straightforward approach to a holographic computation of the graphene and entanglement entropy in the presence of the conical singularity. After this analysis, we consider the scalar field in the bulk in the presence of this metrics and work out the compactification modes. Taking the holographic point of view, we study and discuss the resulting Green function. (author)

Geometry

CERN Document Server

Pedoe, Dan

1988-01-01

""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he

Einstein black holes, free scalars, and AdS/CFT correspondence

International Nuclear Information System (INIS)

Louko, Jorma; Wisniewski, Jacek

2004-01-01

We investigate AdS/CFT correspondence for two families of Einstein black holes in d≥4 dimensions, modeling the boundary conformal field theory by a free conformal scalar field and evaluating the boundary two-point function in the bulk geodesic approximation. For the d≥4 counterpart of the nonrotating Banados-Teitelboim-Zanelli hole and for its Z 2 quotient, the boundary state is thermal in the expected sense, and its stress-energy reflects the properties of the bulk geometry and suggests a novel definition for the mass of the hole. For the generalized Schwarzschild-AdS hole with a flat horizon of topology R d-2 , the boundary stress-energy has a thermal form with energy density proportional to the hole Arnowitt-Deser-Misner mass, but stress-energy corrections from compactified horizon dimensions cannot be consistently included at least for d=5

Complex algebraic geometry

CERN Document Server

Kollár, János

1997-01-01

This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.

CMS geometry through 2020

International Nuclear Information System (INIS)

Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J

2014-01-01

CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.

Globally regular instability of AdS_3

OpenAIRE

Bizon, P.; Jałmużna, J.

2013-01-01

We consider three-dimensional AdS gravity minimally coupled to a massless scalar field and study numerically the evolution of small smooth circularly symmetric perturbations of the $AdS_3$ spacetime. As in higher dimensions, for a large class of perturbations, we observe a turbulent cascade of energy to high frequencies which entails instability of $AdS_3$. However, in contrast to higher dimensions, the cascade cannot be terminated by black hole formation because small perturbations have ener...

Analisis Keterampilan Geometri Siswa Dalam Memecahkan Masalah Geometri Berdasarkan Tingkat Berpikir Van Hiele

OpenAIRE

Muhassanah, Nuraini; Sujadi, Imam; Riyadi, Riyadi

2014-01-01

The objective of this research was to describe the VIII grade students geometry skills atSMP N 16 Surakarta in the level 0 (visualization), level 1 (analysis), and level 2 (informaldeduction) van Hiele level of thinking in solving the geometry problem. This research was aqualitative research in the form of case study analyzing deeply the students geometry skill insolving the geometry problem based on van Hiele level of thingking. The subject of this researchwas nine students of VIII grade at ...

Manifestly T-dual formulation of AdS space

International Nuclear Information System (INIS)

Hatsuda, Machiko; Kamimura, Kiyoshi; Siegel, Warren

2017-01-01

We present a manifestly T-dual formulation of curved spaces such as an AdS space. For group manifolds related by the orthogonal vielbein fields the three form H=dB in the doubled space is universal at least locally. We construct an affine nondegenerate doubled bosonic AdS algebra to define the AdS space with the Ramond-Ramond flux. The non-zero commutator of the left and right momenta leads to that the left momentum is in an AdS space while the right momentum is in a dS space. Dimensional reduction constraints and the physical AdS algebra are shown to preserve all the doubled coordinates.

Manifestly T-dual formulation of AdS space

Energy Technology Data Exchange (ETDEWEB)

Hatsuda, Machiko [Physics Division, Faculty of Medicine, Juntendo University,Chiba 270-1695 (Japan); KEK Theory Center, High Energy Accelerator Research Organization,Tsukuba, Ibaraki 305-0801 (Japan); Kamimura, Kiyoshi [Physics Division, Faculty of Medicine, Juntendo University,Chiba 270-1695 (Japan); Siegel, Warren [C.N. Yang Institute for Theoretical Physics, Stony Brook University,Stony Brook, NY 11794-3840 (United States)

2017-05-12

We present a manifestly T-dual formulation of curved spaces such as an AdS space. For group manifolds related by the orthogonal vielbein fields the three form H=dB in the doubled space is universal at least locally. We construct an affine nondegenerate doubled bosonic AdS algebra to define the AdS space with the Ramond-Ramond flux. The non-zero commutator of the left and right momenta leads to that the left momentum is in an AdS space while the right momentum is in a dS space. Dimensional reduction constraints and the physical AdS algebra are shown to preserve all the doubled coordinates.

Geometry of the TJ-II in Astra 6.0

International Nuclear Information System (INIS)

Lopez-Bruna, D.; Romero, J.A.; Castejon, F.

2006-01-01

One of the most exploited features of the TJ-II Heliac, a facility in the Laboratorio Nacional de Fusion (CIEMAT, Madrid), is its ability to explore plasmas in different magnetic configurations. For this reason, there are available libraries that provide the metrics and associated magnitudes for many among all possible configurations. On the other hand, the transport codes that can normally be used to perform transport calculations cannot dea properly with these geometries, which is especially delicate when there are induced plasma currents. In the present work we adopt ASTRA, a transport analysis shell, to study the approximations performed when calculations that impose axi-symmetry (as ASTRA does) are performed on magnetic configurations that are not really axi-symmetric. After describing how we obtain those TJ-II metric averages that must be set in ASTRA, we perform two comparisons: (i) we obtain the vacuum rotational transform as deduced from the metric coefficients but imposing axisymmetry, and compare the results with the rotational transform yielded by the existing libraries; and (ii) we build a ID transport code with TJ-II metrics so its results can be compared with those of ASTRA. In both cases, the differences found indicate that evaluating the evolution of the rotational transform under ohmic induction and transport evolution is acceptable assuming that the geometry itself does not evolve. (Author) 11 refs

Fractal geometry in an expanding, one-dimensional, Newtonian universe.

Science.gov (United States)

Miller, Bruce N; Rouet, Jean-Louis; Le Guirriec, Emmanuel

2007-09-01

Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with new, larger, sample sizes from recent surveys, it is difficult to extract information concerning fractal properties with confidence. Similarly, three-dimensional N-body simulations with a billion particles only provide a thousand particles per dimension, far too small for accurate conclusions. With one-dimensional models these limitations can be overcome by carrying out simulations with on the order of a quarter of a million particles without compromising the computation of the gravitational force. Here the multifractal properties of two of these models that incorporate different features of the dynamical equations governing the evolution of a matter dominated universe are compared. For each model at least two scaling regions are identified. By employing criteria from dynamical systems theory it is shown that only one of them can be geometrically significant. The results share important similarities with galaxy observations, such as hierarchical clustering and apparent bifractal geometry. They also provide insights concerning possible constraints on length and time scales for fractal structure. They clearly demonstrate that fractal geometry evolves in the mu (position, velocity) space. The observed patterns are simply a shadow (projection) of higher-dimensional structure.

Slab2 - Updated Subduction Zone Geometries and Modeling Tools

Science.gov (United States)

Moore, G.; Hayes, G. P.; Portner, D. E.; Furtney, M.; Flamme, H. E.; Hearne, M. G.

2017-12-01

The U.S. Geological Survey database of global subduction zone geometries (Slab1.0), is a highly utilized dataset that has been applied to a wide range of geophysical problems. In 2017, these models have been improved and expanded upon as part of the Slab2 modeling effort. With a new data driven approach that can be applied to a broader range of tectonic settings and geophysical data sets, we have generated a model set that will serve as a more comprehensive, reliable, and reproducible resource for three-dimensional slab geometries at all of the world's convergent margins. The newly developed framework of Slab2 is guided by: (1) a large integrated dataset, consisting of a variety of geophysical sources (e.g., earthquake hypocenters, moment tensors, active-source seismic survey images of the shallow slab, tomography models, receiver functions, bathymetry, trench ages, and sediment thickness information); (2) a dynamic filtering scheme aimed at constraining incorporated seismicity to only slab related events; (3) a 3-D data interpolation approach which captures both high resolution shallow geometries and instances of slab rollback and overlap at depth; and (4) an algorithm which incorporates uncertainties of contributing datasets to identify the most probable surface depth over the extent of each subduction zone. Further layers will also be added to the base geometry dataset, such as historic moment release, earthquake tectonic providence, and interface coupling. Along with access to several queryable data formats, all components have been wrapped into an open source library in Python, such that suites of updated models can be released as further data becomes available. This presentation will discuss the extent of Slab2 development, as well as the current availability of the model and modeling tools.

Algorithms in Algebraic Geometry

CERN Document Server

Dickenstein, Alicia; Sommese, Andrew J

2008-01-01

In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its

Non-Euclidean geometry

CERN Document Server

Kulczycki, Stefan

2008-01-01

This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff

Fake gaps in AdS{sub 3}/CFT{sub 2}

Energy Technology Data Exchange (ETDEWEB)

Belin, Alexandre [Department of Physics, Stanford University,Stanford, CA 94305-4060 (United States); Castro, Alejandra [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, Postbus 94485, 1090 GL Amsterdam (Netherlands); Hung, Ling-Yan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Collaborative Innovation Center of Advanced Microstructures, Fudan University,220 Handan Road, 200433 Shanghai (China)

2015-11-23

We discuss properties of interpolating geometries in three dimensional gravity in the presence of a chiral anomaly. This anomaly, which introduces an unbalance between left and right central charges, is protected under RG flows. For this simple reason it is impossible to gap a system with such an anomaly. Our goal is to discuss how holography captures this basic and robust feature. We demonstrate the absence of a mass gap by analysing the linearized spectrum and holographic entanglement entropy of these backgrounds in the context of AdS{sub 3}/CFT{sub 2}.

Geometry on the space of geometries

International Nuclear Information System (INIS)

Christodoulakis, T.; Zanelli, J.

1988-06-01

We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs

A Lorentzian quantum geometry

Energy Technology Data Exchange (ETDEWEB)

Grotz, Andreas

2011-10-07

In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

A Lorentzian quantum geometry

International Nuclear Information System (INIS)

Grotz, Andreas

2011-01-01

In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

Mixed-symmetry fields in AdS(5), conformal fields, and AdS/CFT

Energy Technology Data Exchange (ETDEWEB)

Metsaev, R.R. [Department of Theoretical Physics, P.N. Lebedev Physical Institute,Leninsky prospect 53, Moscow 119991 (Russian Federation)

2015-01-15

Mixed-symmetry arbitrary spin massive, massless, and self-dual massive fields in AdS(5) are studied. Light-cone gauge actions for such fields leading to decoupled equations of motion are constructed. Light-cone gauge formulation of mixed-symmetry anomalous conformal currents and shadows in 4d flat space is also developed. AdS/CFT correspondence for normalizable and non-normalizable modes of mixed-symmetry AdS fields and the respective boundary mixed-symmetry anomalous conformal currents and shadows is studied. We demonstrate that the light-cone gauge action for massive mixed-symmetry AdS field evaluated on solution of the Dirichlet problem amounts to the light-cone gauge 2-point vertex of mixed-symmetry anomalous shadow. Also we show that UV divergence of the action for mixed-symmetry massive AdS field with some particular value of mass parameter evaluated on the Dirichlet problem amounts to the action of long mixed-symmetry conformal field, while UV divergence of the action for mixed-symmetry massless AdS field evaluated on the Dirichlet problem amounts to the action of short mixed-symmetry conformal field. We speculate on string theory interpretation of a model which involves short low-spin conformal fields and long higher-spin conformal fields.

Security enhancement of hand geometry scanners using optical blood flow detection

Science.gov (United States)

Crihalmeanu, Musat C.; Jerabek, Mark A.; Meehan, Kathleen

2004-08-01

In today's security conscious society the efficiency of biometric systems has an increasing tendency to replace the classic but less effective keys and passwords. Hand geometry readers are popular biometrics used for acces control and time and attendance applications. One of their weaknesses is vulnerability to spoofing using fake hands (latex, play-doh or dead-hands). The object of this paper is to design a feature to be added to the hand geometry scanner in order to detect vitality in the hand, reducing the possibilities for spoofing. This paper demonstrates how the hand reader was successfully spoofed and shows the implementation of the vitality detection feature through an inexpensive but efficient electronic design. The method used for detection is photo-plethysmography. The Reflectance Sensor built is of original conception. After amplifying, filtering and processing the sensor's signal, a message is shown via an LCD display, concerning the liveness of the hand and the pulse rate.

Mass, angular momentum and thermodynamics in four-dimensional Kerr-AdS black holes

Energy Technology Data Exchange (ETDEWEB)

Olea, Rodrigo [Departamento de Fisica, Pontificia Universidad Catolica de Chile, Casilla 306, Santiago 22 (Chile)

2005-06-01

In this paper, the connection between the Lorentz-covariant counterterms that regularize the four-dimensional AdS gravity action and topological invariants is explored. It is shown that demanding the spacetime to have a negative constant curvature in the asymptotic region permits the explicit construction of such series of boundary terms. The orthonormal frame is adapted to appropriately describe the boundary geometry and, as a result, the boundary term can be expressed as a functional of the boundary metric, extrinsic curvature and intrinsic curvature. This choice also allows to write down the background-independent Noether charges associated to asymptotic symmetries in standard tensorial formalism. The absence of the Gibbons-Hawking term is a consequence of an action principle based on a boundary condition different than Dirichlet on the metric. This argument makes plausible the idea of regarding this approach as an alternative regularization scheme for AdS gravity in all even dimensions, different than the standard counterterms prescription. As an illustration of the finiteness of the charges and the euclidean action in this framework, the conserved quantities and black hole entropy for four-dimensional Kerr-AdS are computed.

Nonlinear realization of supersymmetric AdS space isometries

International Nuclear Information System (INIS)

Clark, T. E.; Love, S. T.

2006-01-01

The isometries of AdS 5 space and supersymmetric AdS 5 xS 1 space are nonlinearly realized on four-dimensional Minkowski space. The resultant effective actions in terms of the Nambu-Goldstone modes are constructed. The dilatonic mode governing the motion of the Minkowski space probe brane into the covolume of supersymmetric AdS 5 space is found to be unstable and the bulk of the AdS 5 space is unable to sustain the brane. No such instability appears in the nonsupersymmetric case

Bidirectional holographic codes and sub-AdS locality

Energy Technology Data Exchange (ETDEWEB)

Yang, Zhao; Hayden, Patrick; Qi, Xiao-Liang [Stanford Institute for Theoretical Physics,Physics Department, Stanford University, CA 94304-4060 (United States)

2016-01-28

Tensor networks implementing quantum error correcting codes have recently been used to construct toy models of holographic duality explicitly realizing some of the more puzzling features of the AdS/CFT correspondence. These models reproduce the Ryu-Takayanagi entropy formula for boundary intervals, and allow bulk operators to be mapped to the boundary in a redundant fashion. These exactly solvable, explicit models have provided valuable insight but nonetheless suffer from many deficiencies, some of which we attempt to address in this article. We propose a new class of tensor network models that subsume the earlier advances and, in addition, incorporate additional features of holographic duality, including: (1) a holographic interpretation of all boundary states, not just those in a “code” subspace, (2) a set of bulk states playing the role of “classical geometries” which reproduce the Ryu-Takayanagi formula for boundary intervals, (3) a bulk gauge symmetry analogous to diffeomorphism invariance in gravitational theories, (4) emergent bulk locality for sufficiently sparse excitations, and (5) the ability to describe geometry at sub-AdS resolutions or even flat space.

Geometry and Combinatorics

DEFF Research Database (Denmark)

Kokkendorff, Simon Lyngby

2002-01-01

The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...

Geometry and billiards

CERN Document Server

Tabachnikov, Serge

2005-01-01

Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...

Evolvability Is an Evolved Ability: The Coding Concept as the Arch-Unit of Natural Selection.

Science.gov (United States)

Janković, Srdja; Ćirković, Milan M

2016-03-01

Physical processes that characterize living matter are qualitatively distinct in that they involve encoding and transfer of specific types of information. Such information plays an active part in the control of events that are ultimately linked to the capacity of the system to persist and multiply. This algorithmicity of life is a key prerequisite for its Darwinian evolution, driven by natural selection acting upon stochastically arising variations of the encoded information. The concept of evolvability attempts to define the total capacity of a system to evolve new encoded traits under appropriate conditions, i.e., the accessible section of total morphological space. Since this is dependent on previously evolved regulatory networks that govern information flow in the system, evolvability itself may be regarded as an evolved ability. The way information is physically written, read and modified in living cells (the "coding concept") has not changed substantially during the whole history of the Earth's biosphere. This biosphere, be it alone or one of many, is, accordingly, itself a product of natural selection, since the overall evolvability conferred by its coding concept (nucleic acids as information carriers with the "rulebook of meanings" provided by codons, as well as all the subsystems that regulate various conditional information-reading modes) certainly played a key role in enabling this biosphere to survive up to the present, through alterations of planetary conditions, including at least five catastrophic events linked to major mass extinctions. We submit that, whatever the actual prebiotic physical and chemical processes may have been on our home planet, or may, in principle, occur at some time and place in the Universe, a particular coding concept, with its respective potential to give rise to a biosphere, or class of biospheres, of a certain evolvability, may itself be regarded as a unit (indeed the arch-unit) of natural selection.

Non-relativistic AdS branes and Newton-Hooke superalgebra

International Nuclear Information System (INIS)

Sakaguchi, Makoto; Yoshida, Kentaroh

2006-01-01

We examine a non-relativistic limit of D-branes in AdS 5 x S 5 and M-branes in AdS 4/7 x S 7/4 . First, Newton-Hooke superalgebras for the AdS branes are derived from AdS x S superalgebras as Inoenue-Wigner contractions. It is shown that the directions along which the AdS-brane worldvolume extends are restricted by requiring that the isometry on the AdS-brane worldvolume and the Lorentz symmetry in the transverse space naturally extend to the super-isometry. We also derive Newton-Hooke superalgebras for pp-wave branes and show that the directions along which a brane worldvolume extends are restricted. Then the Wess-Zumino terms of the AdS branes are derived by using the Chevalley-Eilenberg cohomology on the super-AdS x S algebra, and the non-relativistic limit of the AdS-brane actions is considered. We show that the consistent limit is possible for the following branes: Dp (even,even) for p = 1 mod 4 and Dp (odd,odd) for p = 3 mod 4 in AdS 5 x S 5 , and M2 (0,3), M2 (2,1), M5 (1,5) and M5 (3,3) in AdS 4 x S 7 and S 4 x AdS 7 . We furthermore present non-relativistic actions for the AdS branes

Drawing Dynamic Geometry Figures Online with Natural Language for Junior High School Geometry

Science.gov (United States)

Wong, Wing-Kwong; Yin, Sheng-Kai; Yang, Chang-Zhe

2012-01-01

This paper presents a tool for drawing dynamic geometric figures by understanding the texts of geometry problems. With the tool, teachers and students can construct dynamic geometric figures on a web page by inputting a geometry problem in natural language. First we need to build the knowledge base for understanding geometry problems. With the…

Natural selection promotes antigenic evolvability

NARCIS (Netherlands)

Graves, C.J.; Ros, V.I.D.; Stevenson, B.; Sniegowski, P.D.; Brisson, D.

2013-01-01

The hypothesis that evolvability - the capacity to evolve by natural selection - is itself the object of natural selection is highly intriguing but remains controversial due in large part to a paucity of direct experimental evidence. The antigenic variation mechanisms of microbial pathogens provide

KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI

Directory of Open Access Journals (Sweden)

Irkham Ulil Albab

2014-10-01

Full Text Available Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research, HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews

A closer look at two AdS4 branes in an AdS5 bulk

International Nuclear Information System (INIS)

Thambyahpillai, Shiyamala

2005-01-01

We investigate a scenario with two AdS 4 branes in an AdS 5 bulk. In this scenario there are two gravitons and we investigate the role played by each of them for different positions of the second brane. We show that both gravitons play a significant role only when the turn-around point in the warp factor is approximately equidistant from both branes. We find that the ultralight mode becomes heavy as the second brane approaches the turn-around point, and the physics begins to resemble that of the RS model. Thus we demonstrate the crucial role played by the turn-around in the warp factor in enabling the presence of both gravitons. (author)

Software Geometry in Simulations

Science.gov (United States)

Alion, Tyler; Viren, Brett; Junk, Tom

2015-04-01

The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).

Methods of information geometry

CERN Document Server

Amari, Shun-Ichi

2000-01-01

Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...

Exploiting Mobile Ad Hoc Networking and Knowledge Generation to Achieve Ambient Intelligence

Directory of Open Access Journals (Sweden)

Anna Lekova

2012-01-01

Full Text Available Ambient Intelligence (AmI joins together the fields of ubiquitous computing and communications, context awareness, and intelligent user interfaces. Energy, fault-tolerance, and mobility are newly added dimensions of AmI. Within the context of AmI the concept of mobile ad hoc networks (MANETs for “anytime and anywhere” is likely to play larger roles in the future in which people are surrounded and supported by small context-aware, cooperative, and nonobtrusive devices that will aid our everyday life. The connection between knowledge generation and communication ad hoc networking is symbiotic—knowledge generation utilizes ad hoc networking to perform their communication needs, and MANETs will utilize the knowledge generation to enhance their network services. The contribution of the present study is a distributed evolving fuzzy modeling framework (EFMF to observe and categorize relationships and activities in the user and application level and based on that social context to take intelligent decisions about MANETs service management. EFMF employs unsupervised online one-pass fuzzy clustering method to recognize nodes' mobility context from social scenario traces and ubiquitously learn “friends” and “strangers” indirectly and anonymously.

Developments in special geometry

International Nuclear Information System (INIS)

Mohaupt, Thomas; Vaughan, Owen

2012-01-01

We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.

Evaporation of large black holes in AdS

International Nuclear Information System (INIS)

Rocha, Jorge V

2010-01-01

The AdS/CFT correspondence offers a new perspective on the long-standing black hole information paradox. However, to be able to use the available gauge/gravity machinery one is forced to consider so-called 'large' black holes in AdS, and these objects are thermodynamically stable - they do not evaporate. We describe a simple toy model that allows large AdS black holes to decay, by coupling the emitted radiation to an external scalar field propagating in an auxiliary space. This effectively changes the properties of the boundary of AdS, making it partly absorbing. We demonstrate that the evaporation process never ceases by explicitly presenting (a) the transmission coefficient for a wave scattering from the bulk into auxiliary space and (b) the greybody factor for a black 3-brane in an AdS background. Therefore, the model provides an interesting framework to address the information paradox using AdS/CFT techniques.

Disgust: Evolved function and structure

NARCIS (Netherlands)

Tybur, J.M.; Lieberman, D.; Kurzban, R.; DeScioli, P.

2013-01-01

Interest in and research on disgust has surged over the past few decades. The field, however, still lacks a coherent theoretical framework for understanding the evolved function or functions of disgust. Here we present such a framework, emphasizing 2 levels of analysis: that of evolved function and

The design of geometry teaching: learning from the geometry textbooks of Godfrey and Siddons

OpenAIRE

Fujita, Taro; Jones, Keith

2002-01-01

Deciding how to teach geometry remains a demanding task with one of major arguments being about how to combine the intuitive and deductive aspects of geometry into an effective teaching design. In order to try to obtain an insight into tackling this issue, this paper reports an analysis of innovative geometry textbooks which were published in the early part of the 20th Century, a time when significant efforts were being made to improve the teaching and learning of geometry. The analysis sugge...

Direct simulation Monte Carlo method for gas flows in micro-channels with bends with added curvature

Directory of Open Access Journals (Sweden)

Tisovský Tomáš

2017-01-01

Full Text Available Gas flows in micro-channels are simulated using an open source Direct Simulation Monte Carlo (DSMC code dsmcFOAM for general application to rarefied gas flow written within the framework of the open source C++ toolbox called OpenFOAM. Aim of this paper is to investigate the flow in micro-channel with bend with added curvature. Results are compared with flows in channel without added curvature and equivalent straight channel. Effects of micro-channel bend was already thoroughly investigated by White et al. Geometry proposed by White is also used here for refference.

Sources of hyperbolic geometry

CERN Document Server

Stillwell, John

1996-01-01

This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...

Universal regularization prescription for Lovelock AdS gravity

International Nuclear Information System (INIS)

Kofinas, Georgios; Olea, Rodrigo

2007-01-01

A definite form for the boundary term that produces the finiteness of both the conserved quantities and Euclidean action for any Lovelock gravity with AdS asymptotics is presented. This prescription merely tells even from odd bulk dimensions, regardless the particular theory considered, what is valid even for Einstein-Hilbert and Einstein-Gauss-Bonnet AdS gravity. The boundary term is a given polynomial of the boundary extrinsic and intrinsic curvatures (also referred to as Kounterterms series). Only the coupling constant of the boundary term changes accordingly, such that it always preserves a well-posed variational principle for boundary conditions suitable for asymptotically AdS spaces. The background-independent conserved charges associated to asymptotic symmetries are found. In odd bulk dimensions, this regularization produces a generalized formula for the vacuum energy in Lovelock AdS gravity. The standard entropy for asymptotically AdS black holes is recovered directly from the regularization of the Euclidean action, and not only from the first law of thermodynamics associated to the conserved quantities

The geometry of elementary particles

International Nuclear Information System (INIS)

Lov, T.R.

1987-01-01

A new model of elementary particles based on the geometry of Quantum deSitter space QdS = SU (3,2)/(SU(3,1) x U(1)) is introduced and studied. QdS is a complexification of quantization of anti-de Sitter space, AdS = SO(3,2)/SO(3,1), which in recent years had played a pivotal role in supergravity. The nontrival principle fiber bundle has total space SU(3,2), fiber SU(3,1) x U(1) and base QdS. In this setting, the standard recipes for Yang-Mills fields don't work. These require connections and the associated covariant derivatives. Here it is shown that the Lie derivatives, not the covariant derivatives are important in quantization. In this setting, the no-go theorems are not valid. This new quantum mechanics leads to a model of elementary particles as vertical vector fields in the bundle with interaction via the Lie bracket. There are five physical interactions modelled by the bracket interaction. The quantum numbers are identified as the roots of su(3,2) and are preserved under the bracket interaction. The model explains conservation of charge, baryon number, lepton number, parity and the heirarchy problem. Since the bracket is the curvature of a homogeneous space, particles are then the curvature of QdS. This model for particles is consistent with the requirements of General Relativity. Furthermore, since the curvature tensor is built from the quantized wave functions, the curvature tensor is quantized and this is quantum theory of gravity

AdS Branes from Partial Breaking of Superconformal Symmetries

International Nuclear Information System (INIS)

Ivanov, E.A.

2005-01-01

It is shown how the static-gauge world-volume superfield actions of diverse superbranes on the AdS d+1 superbackgrounds can be systematically derived from nonlinear realizations of the appropriate AdS supersymmetries. The latter are treated as superconformal symmetries of flat Minkowski superspaces of the bosonic dimension d. Examples include the N = 1 AdS 4 supermembrane, which is associated with the 1/2 partial breaking of the OSp(1|4) supersymmetry down to the N = 1, d = 3 Poincare supersymmetry, and the T-duality related L3-brane on AdS 5 and scalar 3-brane on AdS 5 x S 1 , which are associated with two different patterns of 1/2 breaking of the SU(2, 2|1) supersymmetry. Another (closely related) topic is the AdS/CFT equivalence transformation. It maps the world-volume actions of the codimension-one AdS d+1 (super)branes onto the actions of the appropriate Minkowski (super)conformal field theories in the dimension d

The geometry description markup language

International Nuclear Information System (INIS)

Chytracek, R.

2001-01-01

Currently, a lot of effort is being put on designing complex detectors. A number of simulation and reconstruction frameworks and applications have been developed with the aim to make this job easier. A very important role in this activity is played by the geometry description of the detector apparatus layout and its working environment. However, no real common approach to represent geometry data is available and such data can be found in various forms starting from custom semi-structured text files, source code (C/C++/FORTRAN), to XML and database solutions. The XML (Extensible Markup Language) has proven to provide an interesting approach for describing detector geometries, with several different but incompatible XML-based solutions existing. Therefore, interoperability and geometry data exchange among different frameworks is not possible at present. The author introduces a markup language for geometry descriptions. Its aim is to define a common approach for sharing and exchanging of geometry description data. Its requirements and design have been driven by experience and user feedback from existing projects which have their geometry description in XML

Complex analysis and CR geometry

CERN Document Server

Zampieri, Giuseppe

2008-01-01

Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the \\bar\\partial-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometry requires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting to graduate students who wish to learn it. However, the present book does not aim at introducing all the topics of current interest in CR geometry. Instead, an attempt is made to be friendly to the novice by moving, in a fairly relaxed way, f...

Global aspects of complex geometry

CERN Document Server

Catanese, Fabrizio; Huckleberry, Alan T

2006-01-01

Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.

The value added of accountancy programs: a study in the Southeast of Brazil

Directory of Open Access Journals (Sweden)

Silvana Cristina dos Santos

2015-03-01

Full Text Available In recent years, the accounting profession has gone through different changes. The role of accountants in society has evolved, making their function more sophisticated and turning their academic background fundamental to execute tasks in companies. In that context, this paper aims to identify the factors that explain the Value Added of higher education institutions to Accountancy students. Therefore, the results of the specific knowledge test, part of the National Student Performance Examination (Enade 2009, were used, based on a sample of 251 Accountancy programs from the Southeast. In the empirical analysis of the data, descriptive statistics and the linear regression model were used. Based on the valued added method, the Production Function theory was applied, controlling for the students’ individual and socioeconomic characteristics. The results suggest that the main determinants of the Value Added are as follows: the existence of a teaching plan, the number of students receiving grants and the size of the student group.

AdS2 models in an embedding superspace

International Nuclear Information System (INIS)

McKeon, D.G.C.; Sherry, T.N.

2003-01-01

An embedding superspace, whose bosonic part is the flat (2+1)-dimensional embedding space for AdS 2 , is introduced. Superfields and several supersymmetric models are examined in the embedded AdS 2 superspace

Analytic geometry

CERN Document Server

Burdette, A C

1971-01-01

Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st

Vector geometry

CERN Document Server

Robinson, Gilbert de B

2011-01-01

This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom

Roles of Imperial women in the Later Roman Empire (AD 306-455)

OpenAIRE

Washington, Belinda Charlotte

2016-01-01

This thesis examines the roles of imperial women in the later Roman Empire, with a central focus on the period from Constantine I to Valentinian III (306-455 AD). In this period the emperor’s role evolved from a military leader presiding over an itinerant court to a court-based figure, often a child, who was reliant on ceremonial presentation to display imperial prestige. In my analysis, I explore how the roles of imperial women developed alongside this evolution of the emperor...

Physics- and engineering knowledge-based geometry repair system for robust parametric CAD geometries

OpenAIRE

Li, Dong

2012-01-01

In modern multi-objective design optimisation, an effective geometry engine is becoming an essential tool and its performance has a significant impact on the entire process. Building a parametric geometry requires difficult compromises between the conflicting goals of robustness and flexibility. The work presents a solution for improving the robustness of parametric geometry models by capturing and modelling relative engineering knowledge into a surrogate model, and deploying it automatically...

AdS. Klein-Gordon equation

OpenAIRE

Bel, Ll.

2014-01-01

I propose a generalization of the Klein-Gordon equation in the framework of AdS space-time and exhibit a four parameter family of solutions among which there is a two parameter family of time-dependent bound states.

Baby Skyrmions in AdS

Energy Technology Data Exchange (ETDEWEB)

Elliot-Ripley, Matthew; Winyard, Thomas [Department of Mathematical Sciences, Durham University,South Rd, Durham (United Kingdom)

2015-09-01

We study the baby Skyrme model in a pure AdS background without a mass term. The tail decays and scalings of massless radial solutions are demonstrated to take a similar form to those of the massive flat space model, with the AdS curvature playing a similar role to the flat space pion mass. We also numerically find minimal energy solutions for a range of higher topological charges and find that they form concentric ring-like solutions. Popcorn transitions (named in analogy with studies of toy models of holographic QCD) from an n layer to an n+1-layer configuration are observed at topological charges 9 and 27 and further popcorn transitions for higher charges are predicted. Finally, a point-particle approximation for the model is derived and used to successfully predict the ring structures and popcorn transitions for higher charge solitons.

The Cardy-Verlinde formula and topological AdS-Schwarzschild black holes

International Nuclear Information System (INIS)

Youm, Donam

2001-05-01

We consider the brane universe in the background of the topological AdS-Schwarzschild black holes. The induced geometry of the brane is that of a flat or an open radiation dominated FRW-universe. Just like the case of a closed radiation dominated FRW-universe, the temperature and entropy are simply expressed in terms of the Hubble parameter and its time derivative when the brane crosses the black hole horizon. We propose the modified Cardy-Verlinde formula which is valid for any values of the curvature parameter k in the Friedmann equations. (author)

Wess-Zumino terms for AdS D-branes

International Nuclear Information System (INIS)

Hatsuda, Machiko; Kamimura, Kiyoshi

2004-01-01

We show that Wess-Zumino terms for Dp branes with p>0 in the anti-de Sitter (AdS) space are given in terms of 'left-invariant' currents on the super-AdS group or the 'expanded' super-AdS group. As a result there is no topological extension of the super-AdS algebra. In the flat limit the global Lorentz rotational charges of the AdS space turn out to be brane charges of the supertranslation algebra representing the BPS mass. We also show that a D-instanton is described by the GL(1) degree of freedom in the Roiban-Siegel formalism based on the GL(4 vertical bar 4)/[Sp(4)xGL(1)]2 coset

Noncommutative geometry

CERN Document Server

Connes, Alain

1994-01-01

This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat

Geometry Revealed

CERN Document Server

Berger, Marcel

2010-01-01

Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,

Discrete differential geometry. Consistency as integrability

OpenAIRE

Bobenko, Alexander I.; Suris, Yuri B.

2005-01-01

A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...

Spinorial Geometry and Branes

International Nuclear Information System (INIS)

Sloane, Peter

2007-01-01

We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

The group approach to AdS space propagators

International Nuclear Information System (INIS)

Leonhardt, Thorsten; Manvelyan, Ruben; Ruehl, Werner

2003-01-01

We show that AdS two-point functions can be obtained by connecting two points in the interior of AdS space with one point on its boundary by a dual pair of Dobrev's boundary-to-bulk intertwiners and integrating over the boundary point

An introduction to incidence geometry

CERN Document Server

De Bruyn, Bart

2016-01-01

This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end...

Spinorial Geometry and Branes

Energy Technology Data Exchange (ETDEWEB)

Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)

2007-09-15

We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

Introduction to non-Euclidean geometry

CERN Document Server

Wolfe, Harold E

2012-01-01

One of the first college-level texts for elementary courses in non-Euclidean geometry, this concise, readable volume is geared toward students familiar with calculus. A full treatment of the historical background explores the centuries-long efforts to prove Euclid's parallel postulate and their triumphant conclusion. Numerous original exercises form an integral part of the book.Topics include hyperbolic plane geometry and hyperbolic plane trigonometry, applications of calculus to the solutions of some problems in hyperbolic geometry, elliptic plane geometry and trigonometry, and the consistenc

Optical geometry across the horizon

International Nuclear Information System (INIS)

Jonsson, Rickard

2006-01-01

In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework

Efek Tegangan Searah pada Aliran Ionik dan Geometri Pelepah dan Daun Kelapa Sawit

Directory of Open Access Journals (Sweden)

Toto Saktioto

2018-04-01

Full Text Available Productivity of palm tree grown are generally measured in months periods, but in a shorter time scale is particularly less measured by the plant maintenance of palm tree. Consideration of the general productivity in time is how to produce good fruit fertilizer (chemical aspect, healthy plants, fast growing and evolving (agricultural aspect and genetic type of palm that grows (biological aspect. However, the growth and production on the physical aspect is still less attention. Through physical treatment, the growth of palm tree can be optimized, as it has been proven in advanced countries on the plant Aloe Vera, Avocado and Pine trees. This paper proposes a treatment of direct current voltage to palm tree that can accelerate the flow of ions to grow and develop nutrients with the increment of geometry and sturcture of leaf and midrib. The palm tree samples are aged 1 to 5 years corresponding to the provision of various current voltage. Identification of samples before and after treatment by electricity determined is based on the geometry of leaves and midrib and ions effect. This identification can support the productivity of palm trees.

THE ANALYSIS OF THE EVOLUTION OF THE FUNCTIONAL GEOMETRY OF THE TOOL AT THE LATHING WITH A TRANSVERSE ADVANCE

Directory of Open Access Journals (Sweden)

Dan DOBROTĂ

2017-12-01

Full Text Available The role of processing by machining is to generate surfaces that have to meet the requirements imposed by the designer through the execution drawing of the piece. The study aims to analyze how the functional geometry of the tool evolves when lathing with a transverse advance. The technological process of lathing with transverse advance is realized with a variable machining speed, and this also causes a variation of the functional geomtry of the tool. Thus, in the paper was established the optimal construction geometry of a lathe knife that can be used for lathing a piece of a certain diameter. Under these conditions, a correlation was established between the values of the geometrical constructive parameters of the knife used for the transverse lathing and the diameter of the workpiece which can be processed in optimal conditions

Holographic description of AdS2 black holes

International Nuclear Information System (INIS)

Castro, Alejandra; Larsen, Finn; Grumiller, Daniel; McNees, Robert

2008-01-01

We develop the holographic renormalization of AdS 2 gravity systematically. We find that a bulk Maxwell term necessitates a boundary mass term for the gauge field and verify that this unusual term is invariant under gauge transformations that preserve the boundary conditions. We determine the energy-momentum tensor and the central charge, recovering recent results by Hartman and Strominger. We show that our expressions are consistent with dimensional reduction of the AdS 3 energy-momentum tensor and the Brown-Henneaux central charge. As an application of our results we interpret the entropy of AdS 2 black holes as the ground state entropy of a dual CFT.

Convection in Slab and Spheroidal Geometries

Science.gov (United States)

Porter, David H.; Woodward, Paul R.; Jacobs, Michael L.

2000-01-01

Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.

Complex and symplectic geometry

CERN Document Server

Medori, Costantino; Tomassini, Adriano

2017-01-01

This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.

Initiation to global Finslerian geometry

CERN Document Server

Akbar-Zadeh, Hassan

2006-01-01

After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p

Light-cone AdS/CFT-adapted approach to AdS fields/currents, shadows, and conformal fields

Energy Technology Data Exchange (ETDEWEB)

Metsaev, R.R. [Department of Theoretical Physics, P.N. Lebedev Physical Institute, Leninsky prospect 53, Moscow 119991 (Russian Federation)

2015-10-16

Light-cone gauge formulation of fields in AdS space and conformal field theory in flat space adapted for the study of AdS/CFT correspondence is developed. Arbitrary spin mixed-symmetry fields in AdS space and arbitrary spin mixed-symmetry currents, shadows, and conformal fields in flat space are considered on an equal footing. For the massless and massive fields in AdS and the conformal fields in flat space, simple light-cone gauge actions leading to decoupled equations of motion are found. For the currents and shadows, simple expressions for all 2-point functions are also found. We demonstrate that representation of conformal algebra generators on space of currents, shadows, and conformal fields can be built in terms of spin operators entering the light-cone gauge formulation of AdS fields. This considerably simplifies the study of AdS/CFT correspondence. Light-cone gauge actions for totally symmetric arbitrary spin long conformal fields in flat space are presented. We apply our approach to the study of totally antisymmetric (one-column) and mixed-symmetry (two-column) fields in AdS space and currents, shadows, and conformal fields in flat space.

The evolving history of influenza viruses and influenza vaccines.

Science.gov (United States)

Hannoun, Claude

2013-09-01

The isolation of influenza virus 80 years ago in 1933 very quickly led to the development of the first generation of live-attenuated vaccines. The first inactivated influenza vaccine was monovalent (influenza A). In 1942, a bivalent vaccine was produced after the discovery of influenza B. It was later discovered that influenza viruses mutated leading to antigenic changes. Since 1973, the WHO has issued annual recommendations for the composition of the influenza vaccine based on results from surveillance systems that identify currently circulating strains. In 1978, the first trivalent vaccine included two influenza A strains and one influenza B strain. Currently, there are two influenza B lineages circulating; in the latest WHO recommendations, it is suggested that a second B strain could be added to give a quadrivalent vaccine. The history of influenza vaccine and the associated technology shows how the vaccine has evolved to match the evolution of influenza viruses.

A neighbourhood evolving network model

International Nuclear Information System (INIS)

Cao, Y.J.; Wang, G.Z.; Jiang, Q.Y.; Han, Z.X.

2006-01-01

Many social, technological, biological and economical systems are best described by evolved network models. In this short Letter, we propose and study a new evolving network model. The model is based on the new concept of neighbourhood connectivity, which exists in many physical complex networks. The statistical properties and dynamics of the proposed model is analytically studied and compared with those of Barabasi-Albert scale-free model. Numerical simulations indicate that this network model yields a transition between power-law and exponential scaling, while the Barabasi-Albert scale-free model is only one of its special (limiting) cases. Particularly, this model can be used to enhance the evolving mechanism of complex networks in the real world, such as some social networks development

Planetary Image Geometry Library

Science.gov (United States)

Deen, Robert C.; Pariser, Oleg

2010-01-01

The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A

Algebraic geometry in India

Indian Academy of Sciences (India)

algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.

Generalizing optical geometry

International Nuclear Information System (INIS)

Jonsson, Rickard; Westman, Hans

2006-01-01

We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity

Introduction to combinatorial geometry

International Nuclear Information System (INIS)

Gabriel, T.A.; Emmett, M.B.

1985-01-01

The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity

Central charge for AdS2 quantum gravity

International Nuclear Information System (INIS)

Hartman, Thomas; Strominger, Andrew

2009-01-01

Two-dimensional Maxwell-dilaton quantum gravity on AdS 2 with radius l and a constant electric field E is studied. In conformal gauge, this is equivalent to a CFT on a strip. In order to maintain consistent boundary conditions, the usual conformal diffeomorphisms must be accompanied by a certain U(1) gauge transformation. The resulting conformal transformations are generated by a twisted stress tensor, which has a central charge c = 3kE 2 l 4 /4 where k is the level of the U(1) current. This is an AdS 2 analog of the Brown-Henneaux formula c = 3l/2G for the central charge of quantum gravity on AdS 3 .

On the Critical Role of Divergent Selection in Evolvability

Directory of Open Access Journals (Sweden)

Joel Lehman

2016-08-01

Full Text Available An ambitious goal in evolutionary robotics is to evolve increasingly complex robotic behaviors with minimal human design effort. Reaching this goal requires evolutionary algorithms that can unlock from genetic encodings their latent potential for evolvability. One issue clouding this goal is conceptual confusion about evolvability, which often obscures the aspects of evolvability that are important or desirable. The danger from such confusion is that it may establish unrealistic goals for evolvability that prove unproductive in practice. An important issue separate from conceptual confusion is the common misalignment between selection and evolvability in evolutionary robotics. While more expressive encodings can represent higher-level adaptations (e.g. sexual reproduction or developmental systems that increase long-term evolutionary potential (i.e. evolvability, realizing such potential requires gradients of fitness and evolvability to align. In other words, selection is often a critical factor limiting increasing evolvability. Thus, drawing from a series of recent papers, this article seeks to both (1 clarify and focus the ways in which the term evolvability is used within artificial evolution, and (2 argue for the importance of one type of selection, i.e. divergent selection, for enabling evolvability. The main argument is that there is a fundamental connection between divergent selection and evolvability (on both the individual and population level that does not hold for typical goal-oriented selection. The conclusion is that selection pressure plays a critical role in realizing the potential for evolvability, and that divergent selection in particular provides a principled mechanism for encouraging evolvability in artificial evolution.

Evolved H II regions

International Nuclear Information System (INIS)

Churchwell, E.

1975-01-01

A probable evolutionary sequence of H II regions based on six distinct types of observed objects is suggested. Two examples which may deviate from this idealized sequence, are discussed. Even though a size-mean density relation of H II regions can be used as a rough indication of whether a nebula is very young or evolved, it is argued that such a relation is not likely to be useful for the quantitative assignment of ages to H II regions. Evolved H II regions appear to fit into one of four structural types: rings, core-halos, smooth structures, and irregular or filamentary structures. Examples of each type are given with their derived physical parameters. The energy balance in these nebulae is considered. The mass of ionized gas in evolved H II regions is in general too large to trace the nebula back to single compact H II regions. Finally, the morphological type of the Galaxy is considered from its H II region content. 2 tables, 2 figs., 29 refs

AdS5 black holes with fermionic hair

International Nuclear Information System (INIS)

Burrington, Benjamin A.; Liu, James T.; Sabra, W. A.

2005-01-01

The study of new Bogomol'nyi-Prasad-Sommerfield (BPS) objects in AdS 5 has led to a deeper understanding of AdS/CFT. To help complete this picture, and to fully explore the consequences of the supersymmetry algebra, it is also important to obtain new solutions with bulk fermions turned on. In this paper we construct superpartners of the 1/2 BPS black hole in AdS 5 using a natural set of fermion zero modes. We demonstrate that these superpartners, carrying fermionic hair, have conserved charges differing from the original bosonic counterpart. To do so, we find the R-charge and dipole moment of the new system, as well as the mass and angular momentum, defined through the boundary stress tensor. The complete set of superpartners fits nicely into a chiral representation of AdS 5 supersymmetry, and the spinning solutions have the expected gyromagnetic ratio, g=1

Phases of global AdS black holes

International Nuclear Information System (INIS)

Basu, Pallab; Krishnan, Chethan; Subramanian, P.N. Bala

2016-01-01

We study the phases of gravity coupled to a charged scalar and gauge field in an asymptotically Anti-de Sitter spacetime (AdS_4) in the grand canonical ensemble. For the conformally coupled scalar, an intricate phase diagram is charted out between the four relevant solutions: global AdS, boson star, Reissner-Nordstrom black hole and the hairy black hole. The nature of the phase diagram undergoes qualitative changes as the charge of the scalar is changed, which we discuss. We also discuss the new features that arise in the extremal limit.

Graded geometry and Poisson reduction

OpenAIRE

Cattaneo, A S; Zambon, M

2009-01-01

The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics

Geometry of multihadron production

Energy Technology Data Exchange (ETDEWEB)

Bjorken, J.D.

1994-10-01

This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.

Geometry of multihadron production

International Nuclear Information System (INIS)

Bjorken, J.D.

1994-10-01

This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions

Geometry of higher-dimensional black hole thermodynamics

International Nuclear Information System (INIS)

Aaman, Jan E.; Pidokrajt, Narit

2006-01-01

We investigate thermodynamic curvatures of the Kerr and Reissner-Nordstroem (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in four-dimensional spacetime. The thermodynamic geometries are the Ruppeiner geometry and the conformally related Weinhold geometry. The Ruppeiner geometry for a d=5 Kerr black hole is curved and divergent in the extremal limit. For a d≥6 Kerr black hole there is no extremality but the Ruppeiner curvature diverges where one suspects that the black hole becomes unstable. The Weinhold geometry of the Kerr black hole in arbitrary dimension is a flat geometry. For the RN black hole the Ruppeiner geometry is flat in all spacetime dimensions, whereas its Weinhold geometry is curved. In d≥5 the Kerr black hole can possess more than one angular momentum. Finally we discuss the Ruppeiner geometry for the Kerr black hole in d=5 with double angular momenta

New Massive Gravity and AdS4 Counterterms

International Nuclear Information System (INIS)

Jatkar, Dileep P.; Sinha, Aninda

2011-01-01

We show that the recently proposed Dirac-Born-Infeld extension of new massive gravity emerges naturally as a counterterm in four-dimensional anti-de Sitter space (AdS 4 ). The resulting on-shell Euclidean action is independent of the cutoff at zero temperature. We also find that the same choice of counterterm gives the usual area law for the AdS 4 Schwarzschild black hole entropy in a cutoff-independent manner. The parameter values of the resulting counterterm action correspond to a c=0 theory in the context of the duality between AdS 3 gravity and two-dimensional conformal field theory. We rewrite this theory in terms of the gauge field that is used to recast 3D gravity as a Chern-Simons theory.

Classical geometry to quantum behavior correspondence in a virtual extra dimension

International Nuclear Information System (INIS)

Dolce, Donatello

2012-01-01

In the Lorentz invariant formalism of compact space–time dimensions the assumption of periodic boundary conditions represents a consistent semi-classical quantization condition for relativistic fields. In Dolce (2011) we have shown, for instance, that the ordinary Feynman path integral is obtained from the interference between the classical paths with different winding numbers associated with the cyclic dynamics of the field solutions. By means of the boundary conditions, the kinematical information of interactions can be encoded on the relativistic geometrodynamics of the boundary, see Dolce (2012) . Furthermore, such a purely four-dimensional theory is manifestly dual to an extra-dimensional field theory. The resulting correspondence between extra-dimensional geometrodynamics and ordinary quantum behavior can be interpreted in terms of AdS/CFT correspondence. By applying this approach to a simple Quark–Gluon–Plasma freeze-out model we obtain fundamental analogies with basic aspects of AdS/QCD phenomenology. - Highlights: ► Quantum behavior is related to the intrinsic periodicity of isolated systems. ► A periodic phenomenon can be parameterized by a virtual extra dimension. ► KK modes are used to describe the quantum excitations. ► 5D classical geometry encodes 4D quantum behavior. ► Geometrodynamical description of AdS/QCD as modulation of space–time periodicity.

Antismoking Ads at the Point of Sale: The Influence of Ad Type and Context on Ad Reactions.

Science.gov (United States)

Kim, Annice; Nonnemaker, James; Guillory, Jamie; Shafer, Paul; Parvanta, Sarah; Holloway, John; Farrelly, Matthew

2017-06-01

Efforts are underway to educate consumers about the dangers of smoking at the point of sale (POS). Research is limited about the efficacy of POS antismoking ads to guide campaign development. This study experimentally tests whether the type of antismoking ad and the context in which ads are viewed influence people's reactions to the ads. A national convenience sample of 7,812 adult current smokers and recent quitters was randomized to 1 of 39 conditions. Participants viewed one of the four types of antismoking ads (negative health consequences-graphic, negative social consequences-intended emotive, benefits of quitting-informational, benefits of quitting-graphic) in one of the three contexts (alone, next to a cigarette ad, POS tobacco display). We assessed participants' reactions to the ads, including perceived effectiveness, negative emotion, affective dissonance, and motivational reaction. Graphic ads elicited more negative emotion and affective dissonance than benefits of quitting ads. Graphic ads elicited higher perceived effectiveness and more affective dissonance than intended emotive ads. Antismoking ads fared best when viewed alone, and graphic ads were least influenced by the context in which they were viewed. These results suggest that in developing POS campaigns, it is important to consider the competitive pro-tobacco context in which antismoking ads will be viewed.

The impact of galaxy geometry and mass evolution on the survival of star clusters

International Nuclear Information System (INIS)

Madrid, Juan P.; Hurley, Jarrod R.; Martig, Marie

2014-01-01

Direct N-body simulations of globular clusters in a realistic Milky-Way-like potential are carried out using the code NBODY6 to determine the impact of the host galaxy disk mass and geometry on the survival of star clusters. A relation between disk mass and star-cluster dissolution timescale is derived. These N-body models show that doubling the mass of the disk from 5 × 10 10 M ☉ to 10 × 10 10 M ☉ halves the dissolution time of a satellite star cluster orbiting the host galaxy at 6 kpc from the galactic center. Different geometries in a disk of identical mass can determine either the survival or dissolution of a star cluster orbiting within the inner 6 kpc of the galactic center. Furthermore, disk geometry has measurable effects on the mass loss of star clusters up to 15 kpc from the galactic center. N-body simulations performed with a fine output time step show that at each disk crossing the outer layers of star clusters experiences an increase in velocity dispersion of ∼5% of the average velocity dispersion in the outer section of star clusters. This leads to an enhancement of mass loss—a clearly discernable effect of disk shocking. By running models with different inclinations, we determine that star clusters with an orbit that is perpendicular to the Galactic plane have larger mass loss rates than do clusters that evolve in the Galactic plane or in an inclined orbit.

Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake

International Nuclear Information System (INIS)

Kotschenreuther, Mike; Valanju, Prashant; Covele, Brent; Mahajan, Swadesh

2013-01-01

Advanced divertors are magnetic geometries where a second X-point is added in the divertor region to address the serious challenges of burning plasma power exhaust. Invoking physical arguments, numerical work, and detailed model magnetic field analysis, we investigate the magnetic field structure of advanced divertors in the physically relevant region for power exhaust—the scrape-off layer. A primary result of our analysis is the emergence of a physical “metric,” the Divertor Index DI, which quantifies the flux expansion increase as one goes from the main X-point to the strike point. It clearly separates three geometries with distinct consequences for divertor physics—the Standard Divertor (DI = 1), and two advanced geometries—the X-Divertor (XD, DI > 1) and the Snowflake (DI < 1). The XD, therefore, cannot be classified as one variant of the Snowflake. By this measure, recent National Spherical Torus Experiment and DIIID experiments are X-Divertors, not Snowflakes

Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake

Energy Technology Data Exchange (ETDEWEB)

Kotschenreuther, Mike; Valanju, Prashant; Covele, Brent; Mahajan, Swadesh [Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)

2013-10-15

Advanced divertors are magnetic geometries where a second X-point is added in the divertor region to address the serious challenges of burning plasma power exhaust. Invoking physical arguments, numerical work, and detailed model magnetic field analysis, we investigate the magnetic field structure of advanced divertors in the physically relevant region for power exhaust—the scrape-off layer. A primary result of our analysis is the emergence of a physical “metric,” the Divertor Index DI, which quantifies the flux expansion increase as one goes from the main X-point to the strike point. It clearly separates three geometries with distinct consequences for divertor physics—the Standard Divertor (DI = 1), and two advanced geometries—the X-Divertor (XD, DI > 1) and the Snowflake (DI < 1). The XD, therefore, cannot be classified as one variant of the Snowflake. By this measure, recent National Spherical Torus Experiment and DIIID experiments are X-Divertors, not Snowflakes.

Lectures on Symplectic Geometry

CERN Document Server

Silva, Ana Cannas

2001-01-01

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...

Complex differential geometry

CERN Document Server

Zheng, Fangyang

2002-01-01

The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...

Computational synthetic geometry

CERN Document Server

Bokowski, Jürgen

1989-01-01

Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...

Designs and finite geometries

CERN Document Server

1996-01-01

Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.

Toward the AdS/CFT gravity dual for high energy collisions. III. Gravitationally collapsing shell and quasiequilibrium

International Nuclear Information System (INIS)

Lin, Shu; Shuryak, Edward

2008-01-01

The equilibration of matter and onset of hydrodynamics can be understood in the AdS/CFT context as a gravitational collapse process, in which 'collision debris' create a horizon. In this paper we consider the simplest geometry possible, a flat shell (or membrane) falling in the holographic direction toward the horizon. The metric is a combination of two well-known solutions: thermal AdS above the shell and pure AdS below, while motion of the shell is given by the Israel junction condition. Furthermore, when the shell motion can be considered slow, we were able to solve for two-point functions of all boundary stress tensors and found that an observer on the boundary sees a very peculiar quasiequilibrium: while the average stress tensor μν> contains the equilibrium plasma energy and pressure at all times, the spectral densities of the correlators (related with occupation probabilities of the modes) reveal additional oscillating terms absent in equilibrium. This is explained by the echo phenomenon, a partial return of the field coherence at certain echo times.

d-geometries revisited

CERN Document Server

Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio

2013-01-01

We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.

Current status of AdS instability

CERN Multimedia

CERN. Geneva

2016-01-01

arXiv:1403.6471 and thoroughly developed in arXiv:1407.6273. On the other hand the negative cosmological constant allows for the existence of stable, time-periodic, asymptotically AdS solutions of Einstein equations [arXiv:1303.3186].

Geometry success in 20 minutes a day

CERN Document Server

LLC, LearningExpress

2014-01-01

Whether you're new to geometry or just looking for a refresher, Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day: Covers all vital geometry skills, from the basic building blocks of geometry to ratio, proportion, and similarity to trigonometry and beyond Provides hundreds of practice exercises in test format Applies geometr

Loops in AdS from conformal field theory

Science.gov (United States)

Aharony, Ofer; Alday, Luis F.; Bissi, Agnese; Perlmutter, Eric

2017-07-01

We propose and demonstrate a new use for conformal field theory (CFT) crossing equations in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. Loops in AdS are largely unexplored, mostly due to technical difficulties in direct calculations. We revisit this problem, and the dual 1 /N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1 /N 2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. Our second approach involves Mellin space. We show how the polar part of the four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order data. The anomalous dimensions computed with both methods agree. In the case of ϕ 4 theory in AdS, our crossing solution reproduces a previous computation of the one-loop bubble diagram. We can go further, deriving the four-point scalar triangle diagram in AdS, which had never been computed. In the process, we show how to analytically derive anomalous dimensions from Mellin amplitudes with an infinite series of poles, and discuss applications to more complicated cases such as the N = 4 super-Yang-Mills theory.

Supersymmetric warped AdS in extended topologically massive supergravity

International Nuclear Information System (INIS)

Deger, N.S.; Kaya, A.; Samtleben, H.; Sezgin, E.

2014-01-01

We determine the most general form of off-shell N=(1,1) supergravity field configurations in three dimensions by requiring that at least one off-shell Killing spinor exists. We then impose the field equations of the topologically massive off-shell supergravity and find a class of solutions whose properties crucially depend on the norm of the auxiliary vector field. These are spacelike-squashed and timelike-stretched AdS 3 for the spacelike and timelike norms, respectively. At the transition point where the norm vanishes, the solution is null warped AdS 3 . This occurs when the coefficient of the Lorentz–Chern–Simons term is related to the AdS radius by μℓ=2. We find that the spacelike-squashed AdS 3 can be modded out by a suitable discrete subgroup of the isometry group, yielding an extremal black hole solution which avoids closed timelike curves

New supersymmetric AdS4 type II vacua

International Nuclear Information System (INIS)

Tsimpis, D.

2010-01-01

We review the supersymmetric AdS 4 x w M 6 backgrounds of type IIA/IIB supergravity constructed in[1]. In type IIA the supersymmetry is N=2, and the six-dimensional internal space is locally an S 2 bundle over a four-dimensional Kaehler-Einstein base; in IIB the internal space is the direct product of a circle and a five-dimensional squashed Sasaki-Einstein manifold. These backgrounds do not contain any sources, all fluxes (including the Romans mass in IIA) are generally non-zero, and the dilaton and warp factor are non-constant. The IIA solutions include the massive deformations of the IIA reduction of the eleven-dimensional AdS 4 x Y p,q solutions, and had been predicted to exist on the basis of the AdS 4 /CFT 3 correspondence. (Abstract Copyright [2010], Wiley Periodicals, Inc.)

Instantons from geodesics in AdS moduli spaces

Science.gov (United States)

Ruggeri, Daniele; Trigiante, Mario; Van Riet, Thomas

2018-03-01

We investigate supergravity instantons in Euclidean AdS5 × S5/ℤk. These solutions are expected to be dual to instantons of N = 2 quiver gauge theories. On the supergravity side the (extremal) instanton solutions are neatly described by the (lightlike) geodesics on the AdS moduli space for which we find the explicit expression and compute the on-shell actions in terms of the quantised charges. The lightlike geodesics fall into two categories depending on the degree of nilpotency of the Noether charge matrix carried by the geodesic: for degree 2 the instantons preserve 8 supercharges and for degree 3 they are non-SUSY. We expect that these findings should apply to more general situations in the sense that there is a map between geodesics on moduli-spaces of Euclidean AdS vacua and instantons with holographic counterparts.

Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes

International Nuclear Information System (INIS)

Durkee, Mark N.; Reall, Harvey S.

2011-01-01

It is shown that the equations governing linearized gravitational (or electromagnetic) perturbations of the near-horizon geometry of any known extreme vacuum black hole (allowing for a cosmological constant) can be Kaluza-Klein reduced to give the equation of motion of a charged scalar field in AdS 2 with an electric field. One can define an effective Breitenloehner-Freedman bound for such a field. We conjecture that if a perturbation preserves certain symmetries then a violation of this bound should imply an instability of the full black hole solution. Evidence in favor of this conjecture is provided by the extreme Kerr solution and extreme cohomogeneity-1 Myers-Perry solution. In the latter case, we predict an instability in seven or more dimensions and, in five dimensions, we present results for operator conformal weights assuming the existence of a conformal field theory dual. We sketch a proof of our conjecture for scalar field perturbations.

Lectures on coarse geometry

CERN Document Server

Roe, John

2003-01-01

Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...

Introduction to tropical geometry

CERN Document Server

Maclagan, Diane

2015-01-01

Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...

Geometry Euclid and beyond

CERN Document Server

Hartshorne, Robin

2000-01-01

In recent years, I have been teaching a junior-senior-level course on the classi­ cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa­ rately. The remainder of the book is an exploration of questions that arise natu­ rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...

Evolving Evidence for the Value of Neuroimaging Methods and Biological Markers in Subjects Categorized with Subjective Cognitive Decline.

Science.gov (United States)

Lista, Simone; Molinuevo, Jose L; Cavedo, Enrica; Rami, Lorena; Amouyel, Philippe; Teipel, Stefan J; Garaci, Francesco; Toschi, Nicola; Habert, Marie-Odile; Blennow, Kaj; Zetterberg, Henrik; O'Bryant, Sid E; Johnson, Leigh; Galluzzi, Samantha; Bokde, Arun L W; Broich, Karl; Herholz, Karl; Bakardjian, Hovagim; Dubois, Bruno; Jessen, Frank; Carrillo, Maria C; Aisen, Paul S; Hampel, Harald

2015-09-24

There is evolving evidence that individuals categorized with subjective cognitive decline (SCD) are potentially at higher risk for developing objective and progressive cognitive impairment compared to cognitively healthy individuals without apparent subjective complaints. Interestingly, SCD, during advancing preclinical Alzheimer's disease (AD), may denote very early, subtle cognitive decline that cannot be identified using established standardized tests of cognitive performance. The substantial heterogeneity of existing SCD-related research data has led the Subjective Cognitive Decline Initiative (SCD-I) to accomplish an international consensus on the definition of a conceptual research framework on SCD in preclinical AD. In the area of biological markers, the cerebrospinal fluid signature of AD has been reported to be more prevalent in subjects with SCD compared to healthy controls; moreover, there is a pronounced atrophy, as demonstrated by magnetic resonance imaging, and an increased hypometabolism, as revealed by positron emission tomography, in characteristic brain regions affected by AD. In addition, SCD individuals carrying an apolipoprotein ɛ4 allele are more likely to display AD-phenotypic alterations. The urgent requirement to detect and diagnose AD as early as possible has led to the critical examination of the diagnostic power of biological markers, neurophysiology, and neuroimaging methods for AD-related risk and clinical progression in individuals defined with SCD. Observational studies on the predictive value of SCD for developing AD may potentially be of practical value, and an evidence-based, validated, qualified, and fully operationalized concept may inform clinical diagnostic practice and guide earlier designs in future therapy trials.

Evolving Technologies: A View to Tomorrow

Science.gov (United States)

Tamarkin, Molly; Rodrigo, Shelley

2011-01-01

Technology leaders must participate in strategy creation as well as operational delivery within higher education institutions. The future of higher education--the view to tomorrow--is irrevocably integrated and intertwined with evolving technologies. This article focuses on two specific evolving technologies: (1) alternative IT sourcing; and (2)…

Basic algebraic geometry, v.2

CERN Document Server

Shafarevich, Igor Rostislavovich

1994-01-01

Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of al...

Pseudo-Coherence-Based MVDR Beamformer for Speech Enhancement with Ad Hoc Microphone Arrays

DEFF Research Database (Denmark)

Tavakoli, Vincent Mohammad; Jensen, Jesper Rindom; Christensen, Mads Græsbøll

2015-01-01

Speech enhancement with distributed arrays has been met with various methods. On the one hand, data independent methods require information about the position of sensors, so they are not suitable for dynamic geometries. On the other hand, Wiener-based methods cannot assure a distortionless output....... This paper proposes minimum variance distortionless response filtering based on multichannel pseudo-coherence for speech enhancement with ad hoc microphone arrays. This method requires neither position information nor control of the trade-off used in the distortion weighted methods. Furthermore, certain...

Canonical differential geometry of string backgrounds

International Nuclear Information System (INIS)

Schuller, Frederic P.; Wohlfarth, Mattias N.R.

2006-01-01

String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field. While an area metric does not determine a connection, we identify the appropriate differential geometric structure which is of relevance for the minimal surface equation in such a generalized geometry. In particular the notion of a derivative action of areas on areas emerges naturally. Area metric geometry provides new tools in differential geometry, which promise to play a role in the description of gravitational dynamics on D-branes

Constrained supermanifolds for AdS M-theory backgrounds

International Nuclear Information System (INIS)

Fre, Pietro; Grassi, Pietro Antonio

2008-01-01

A long standing problem is the supergauge completion of AdS 4 x ({G/H}) 7 or AdS 5 x ({G/H}) 5 backgrounds which preserve less then maximal supersymmetry. In parallel with the supersolvable realization of the AdS 4 x S 7 background based on κ-symmetry, we develop a technique which amounts to solving the above-mentioned problem in a way useful for pure spinor quantization for supermembranes and superstrings. Instead of gauge fixing some of the superspace coordinates using κ-symmetry, we impose an additional constraint on them reproducing the simplifications of the supersolvable representations. The constraints are quadratic, homogeneous, Sp(4,R)-covariant, and consistent from the quantum point of view in the pure spinor approach. Here we provide the geometrical solution which, in a subsequent work, will be applied to the membrane and the superstring sigma models

Intercept Algorithm for Maneuvering Targets Based on Differential Geometry and Lyapunov Theory

Directory of Open Access Journals (Sweden)

Yunes Sh. ALQUDSI

2018-03-01

Full Text Available Nowadays, the homing guidance is utilized in the existed and under development air defense systems (ADS to effectively intercept the targets. The targets became smarter and capable to fly and maneuver professionally and the tendency to design missile with a small warhead became greater, then there is a pressure to produce a more precise and accurate missile guidance system based on intelligent algorithms to ensure effective interception of highly maneuverable targets. The aim of this paper is to present an intelligent guidance algorithm that effectively and precisely intercept the maneuverable and smart targets by virtue of the differential geometry (DG concepts. The intercept geometry and engagement kinematics, in addition to the direct intercept condition are developed and expressed in DG terms. The guidance algorithm is then developed by virtue of DG and Lyapunov theory. The study terminates with 2D engagement simulation with illustrative examples, to demonstrate that, the derived DG guidance algorithm is a generalized guidance approach and the well-known proportional navigation (PN guidance law is a subset of this approach.

Superradiant instabilities in the Kerr-mirror and Kerr-AdS black holes with Robin boundary conditions

Science.gov (United States)

Ferreira, Hugo R. C.; Herdeiro, Carlos A. R.

2018-04-01

It has been recently observed that a scalar field with Robin boundary conditions (RBCs) can trigger both a superradiant and a bulk instability for a Bañados-Teitelboim-Zanelli (BTZ) black hole (BH) [1]. To understand the generality and scrutinize the origin of this behavior, we consider here the superradiant instability of a Kerr BH confined either in a mirrorlike cavity or in anti-de Sitter (AdS) space, triggered also by a scalar field with RBCs. These boundary conditions are the most general ones that ensure the cavity/AdS space is an isolated system and include, as a particular case, the commonly considered Dirichlet boundary conditions (DBCs). Whereas the superradiant modes for some RBCs differ only mildly from the ones with DBCs, in both cases, we find that as we vary the RBCs the imaginary part of the frequency may attain arbitrarily large positive values. We interpret this growth as being sourced by a bulk instability of both confined geometries when certain RBCs are imposed to either the mirrorlike cavity or the AdS boundary, rather than by energy extraction from the BH, in analogy with the BTZ behavior.

The Beauty of Geometry

Science.gov (United States)

Morris, Barbara H.

2004-01-01

This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…

Spacetimes containing slowly evolving horizons

International Nuclear Information System (INIS)

Kavanagh, William; Booth, Ivan

2006-01-01

Slowly evolving horizons are trapping horizons that are ''almost'' isolated horizons. This paper reviews their definition and discusses several spacetimes containing such structures. These include certain Vaidya and Tolman-Bondi solutions as well as (perturbatively) tidally distorted black holes. Taking into account the mass scales and orders of magnitude that arise in these calculations, we conjecture that slowly evolving horizons are the norm rather than the exception in astrophysical processes that involve stellar-scale black holes

Teaching Spatial Geometry in a Virtual World

DEFF Research Database (Denmark)

Förster, Klaus-Tycho

2017-01-01

Spatial geometry is one of the fundamental mathematical building blocks of any engineering education. However, it is overshadowed by planar geometry in the curriculum between playful early primary education and later analytical geometry, leaving a multi-year gap where spatial geometry is absent...

Trends and developments in computational geometry

NARCIS (Netherlands)

Berg, de M.

1997-01-01

This paper discusses some trends and achievements in computational geometry during the past five years, with emphasis on problems related to computer graphics. Furthermore, a direction of research in computational geometry is discussed that could help in bringing the fields of computational geometry

Noncommutative D-branes from covariant AdS superstring

International Nuclear Information System (INIS)

Sakaguchi, Makoto; Yoshida, Kentaroh

2008-01-01

We study noncommutative (NC) D-branes on AdS 5 xS 5 from κ-invariance of covariant Green-Schwarz action of an open string with a non-trivial world-volume flux. Finding boundary conditions to ensure the κ-invariance, we can see possible configurations of the NC D-branes. With this method 1/4 BPS NC D-branes are discussed. The resulting NC Dp-branes are 1/4 BPS at arbitrary position other than the p=1 case. The exceptional D-string is 1/2 BPS at the origin and 1/4 BPS outside the origin. Those are reduced to possible 1/4 BPS or 1/2 BPS AdS D-branes in the commutative limit. The same analysis is applied to an open superstring in a pp-wave and leads to 1/4 BPS configurations of NC D-branes. These D-branes are consistently obtained from AdS D-branes via the Penrose limit

Integrability and black-hole microstate geometries

Science.gov (United States)

Bena, Iosif; Turton, David; Walker, Robert; Warner, Nicholas P.

2017-11-01

We examine some recently-constructed families of asymptotically-AdS3 × S^3 supergravity solutions that have the same charges and mass as supersymmetric D1-D5- P black holes, but that cap off smoothly with no horizon. These solutions, known as superstrata, are quite complicated, however we show that, for an infinite family of solutions, the null geodesic problem is completely integrable, due to the existence of a non-trivial conformal Killing tensor that provides a quadratic conservation law for null geodesics. This implies that the massless scalar wave equation is separable. For another infinite family of solutions, we find that there is a non-trivial conformal Killing tensor only when the left-moving angular momentum of the massless scalar is zero. We also show that, for both these families, the metric degrees of freedom have the form they would take if they arose from a consistent truncation on S^3 down to a (2 + 1)-dimensional space-time. We discuss some of the broader consequences of these special properties for the physics of these black-hole microstate geometries.

Decoupling limit and throat geometry of non-susy D3 brane

Energy Technology Data Exchange (ETDEWEB)

Nayek, Kuntal, E-mail: kuntal.nayek@saha.ac.in; Roy, Shibaji, E-mail: shibaji.roy@saha.ac.in

2017-03-10

Recently it has been shown by us that, like BPS Dp branes, bulk gravity gets decoupled from the brane even for the non-susy Dp branes of type II string theories indicating a possible extension of AdS/CFT correspondence for the non-supersymmetric case. In that work, the decoupling of gravity on the non-susy Dp branes has been shown numerically for the general case as well as analytically for some special case. Here we discuss the decoupling limit and the throat geometry of the non-susy D3 brane when the charge associated with the brane is very large. We show that in the decoupling limit the throat geometry of the non-susy D3 brane, under appropriate coordinate change, reduces to the Constable–Myers solution and thus confirming that this solution is indeed the holographic dual of a (non-gravitational) gauge theory discussed there. We also show that when one of the parameters of the solution takes a specific value, it reduces, under another coordinate change, to the five-dimensional solution obtained by Csaki and Reece, again confirming its gauge theory interpretation.

Exactly marginal deformations from exceptional generalised geometry

Energy Technology Data Exchange (ETDEWEB)

Ashmore, Anthony [Merton College, University of Oxford,Merton Street, Oxford, OX1 4JD (United Kingdom); Mathematical Institute, University of Oxford,Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG (United Kingdom); Gabella, Maxime [Institute for Advanced Study,Einstein Drive, Princeton, NJ 08540 (United States); Graña, Mariana [Institut de Physique Théorique, CEA/Saclay,91191 Gif-sur-Yvette (France); Petrini, Michela [Sorbonne Université, UPMC Paris 05, UMR 7589, LPTHE,75005 Paris (France); Waldram, Daniel [Department of Physics, Imperial College London,Prince Consort Road, London, SW7 2AZ (United Kingdom)

2017-01-27

We apply exceptional generalised geometry to the study of exactly marginal deformations of N=1 SCFTs that are dual to generic AdS{sub 5} flux backgrounds in type IIB or eleven-dimensional supergravity. In the gauge theory, marginal deformations are parametrised by the space of chiral primary operators of conformal dimension three, while exactly marginal deformations correspond to quotienting this space by the complexified global symmetry group. We show how the supergravity analysis gives a geometric interpretation of the gauge theory results. The marginal deformations arise from deformations of generalised structures that solve moment maps for the generalised diffeomorphism group and have the correct charge under the generalised Reeb vector, generating the R-symmetry. If this is the only symmetry of the background, all marginal deformations are exactly marginal. If the background possesses extra isometries, there are obstructions that come from fixed points of the moment maps. The exactly marginal deformations are then given by a further quotient by these extra isometries. Our analysis holds for any N=2 AdS{sub 5} flux background. Focussing on the particular case of type IIB Sasaki-Einstein backgrounds we recover the result that marginal deformations correspond to perturbing the solution by three-form flux at first order. In various explicit examples, we show that our expression for the three-form flux matches those in the literature and the obstruction conditions match the one-loop beta functions of the dual SCFT.

An approach for management of geometry data

Science.gov (United States)

Dube, R. P.; Herron, G. J.; Schweitzer, J. E.; Warkentine, E. R.

1980-01-01

The strategies for managing Integrated Programs for Aerospace Design (IPAD) computer-based geometry are described. The computer model of geometry is the basis for communication, manipulation, and analysis of shape information. IPAD's data base system makes this information available to all authorized departments in a company. A discussion of the data structures and algorithms required to support geometry in IPIP (IPAD's data base management system) is presented. Through the use of IPIP's data definition language, the structure of the geometry components is defined. The data manipulation language is the vehicle by which a user defines an instance of the geometry. The manipulation language also allows a user to edit, query, and manage the geometry. The selection of canonical forms is a very important part of the IPAD geometry. IPAD has a canonical form for each entity and provides transformations to alternate forms; in particular, IPAD will provide a transformation to the ANSI standard. The DBMS schemas required to support IPAD geometry are explained.

Holographic description of Kerr-Bolt-AdS-dS spacetimes

International Nuclear Information System (INIS)

Chen, B.; Ghezelbash, A.M.; Kamali, V.; Setare, M.R.

2011-01-01

We show that there exists a holographic 2D CFT description of a Kerr-Bolt-AdS-dS spacetime. We first consider the wave equation of a massless scalar field propagating in extremal Kerr-Bolt-AdS-dS spacetimes and find in the 'near region', the wave equation in extremal limit could be written in terms of the SL(2,R) quadratic Casimir. This suggests that there exist dual CFT descriptions of these black holes. In the probe limit, we compute the scattering amplitudes of the scalar off the extremal black holes and find perfect agreement with the CFT prediction. Furthermore we study the holographic description of the generic four-dimensional non-extremal Kerr-Bolt-AdS-dS black holes. We find that if focusing on the near-horizon region, for the massless scalar scattering in the low-frequency limit, the radial equation could still be rewritten as the SL(2,R) quadratic Casimir, suggesting the existence of dual 2D description. We read the temperatures of the dual CFT from the conformal coordinates and obtain the central charges by studying the near-horizon geometry of near-extremal black holes. We recover the macroscopic entropy from the microscopic counting. We also show that for the super-radiant scattering, the retarded Green's functions and the corresponding absorption cross sections are in perfect match with CFT prediction.

"WGL," a Web Laboratory for Geometry

Science.gov (United States)

Quaresma, Pedro; Santos, Vanda; Maric, Milena

2018-01-01

The role of information and communication technologies (ICT) in education is nowadays well recognised. The "Web Geometry Laboratory," is an e-learning, collaborative and adaptive, Web environment for geometry, integrating a well known dynamic geometry system. In a collaborative session, teachers and students, engaged in solving…

Twistor description of spinning particles in AdS

Science.gov (United States)

Arvanitakis, Alex S.; Barns-Graham, Alec E.; Townsend, Paul K.

2018-01-01

The two-twistor formulation of particle mechanics in D-dimensional anti-de Sitter space for D = 4 , 5 , 7, which linearises invariance under the AdS isometry group Sp(4; K ) for K=R,C,H, is generalized to the massless N -extended "spinning particle". The twistor variables are gauge invariant with respect to the initial N local worldline supersymmetries; this simplifies aspects of the quantum theory such as implications of global gauge anomalies. We also give details of the two-supertwistor form of the superparticle, in particular the massive superparticle on AdS5.

Holography in Lovelock Chern-Simons AdS gravity

Science.gov (United States)

Cvetković, Branislav; Miskovic, Olivera; Simić, Dejan

2017-08-01

We analyze holographic field theory dual to Lovelock Chern-Simons anti-de Sitter (AdS) gravity in higher dimensions using first order formalism. We first find asymptotic symmetries in the AdS sector showing that they consist of local translations, local Lorentz rotations, dilatations and non-Abelian gauge transformations. Then, we compute 1-point functions of energy-momentum and spin currents in a dual conformal field theory and write Ward identities. We find that the holographic theory possesses Weyl anomaly and also breaks non-Abelian gauge symmetry at the quantum level.

Estimating added sugars in US consumer packaged goods: An application to beverages in 2007-08.

Science.gov (United States)

Ng, Shu Wen; Bricker, Gregory; Li, Kuo-Ping; Yoon, Emily Ford; Kang, Jiyoung; Westrich, Brian

2015-11-01

This study developed a method to estimate added sugar content in consumer packaged goods (CPG) that can keep pace with the dynamic food system. A team including registered dietitians, a food scientist and programmers developed a batch-mode ingredient matching and linear programming (LP) approach to estimate the amount of each ingredient needed in a given product to produce a nutrient profile similar to that reported on its nutrition facts label (NFL). Added sugar content was estimated for 7021 products available in 2007-08 that contain sugar from ten beverage categories. Of these, flavored waters had the lowest added sugar amounts (4.3g/100g), while sweetened dairy and dairy alternative beverages had the smallest percentage of added sugars (65.6% of Total Sugars; 33.8% of Calories). Estimation validity was determined by comparing LP estimated values to NFL values, as well as in a small validation study. LP estimates appeared reasonable compared to NFL values for calories, carbohydrates and total sugars, and performed well in the validation test; however, further work is needed to obtain more definitive conclusions on the accuracy of added sugar estimates in CPGs. As nutrition labeling regulations evolve, this approach can be adapted to test for potential product-specific, category-level, and population-level implications.

Analytische Geometrie

Science.gov (United States)

Kemnitz, Arnfried

Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.

Connections between algebra, combinatorics, and geometry

CERN Document Server

Sather-Wagstaff, Sean

2014-01-01

Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics, and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University, February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resou...

Evolving phenotypic networks in silico.

Science.gov (United States)

François, Paul

2014-11-01

Evolved gene networks are constrained by natural selection. Their structures and functions are consequently far from being random, as exemplified by the multiple instances of parallel/convergent evolution. One can thus ask if features of actual gene networks can be recovered from evolutionary first principles. I review a method for in silico evolution of small models of gene networks aiming at performing predefined biological functions. I summarize the current implementation of the algorithm, insisting on the construction of a proper "fitness" function. I illustrate the approach on three examples: biochemical adaptation, ligand discrimination and vertebrate segmentation (somitogenesis). While the structure of the evolved networks is variable, dynamics of our evolved networks are usually constrained and present many similar features to actual gene networks, including properties that were not explicitly selected for. In silico evolution can thus be used to predict biological behaviours without a detailed knowledge of the mapping between genotype and phenotype. Copyright © 2014 The Author. Published by Elsevier Ltd.. All rights reserved.

Non-Abelian T-duality and the AdS/CFT correspondence: New N=1 backgrounds

Energy Technology Data Exchange (ETDEWEB)

Itsios, Georgios, E-mail: gitsios@upatras.gr [Department of Engineering Sciences, University of Patras, 26110 Patras (Greece); Department of Mathematics, University of Surrey, Guildford GU2 7XH (United Kingdom); Núñez, Carlos, E-mail: c.nunez@swansea.ac.uk [Swansea University, School of Physical Sciences, Singleton Park, Swansea SA2 8PP (United Kingdom); Sfetsos, Konstadinos, E-mail: k.sfetsos@surrey.ac.uk [Department of Mathematics, University of Surrey, Guildford GU2 7XH (United Kingdom); Department of Engineering Sciences, University of Patras, 26110 Patras (Greece); Thompson, Daniel C., E-mail: dthompson@tena4.vub.ac.be [Theoretische Natuurkunde, Vrije Universiteit Brussel (Belgium); International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium)

2013-08-01

We consider non-Abelian T-duality on N=1 supergravity backgrounds possessing well understood field theory duals. For the case of D3-branes at the tip of the conifold, we dualise along an SU(2) isometry. The result is a type-IIA geometry whose lift to M-theory is of the type recently proposed by Bah et al. as the dual to certain N=1 SCFT quivers produced by M5-branes wrapping a Riemann surface. In the non-conformal cases we find smooth duals in massive IIA supergravity with a Romans mass naturally quantised. We initiate the interpretation of these geometries in the context of AdS/CFT correspondence. We show that the central charge and the entanglement entropy are left invariant by this dualisation. The backgrounds suggest a form of Seiberg duality in the dual field theories which also exhibit domain walls and confinement in the infrared.

Exploring AdS waves via nonminimal coupling

International Nuclear Information System (INIS)

Ayon-Beato, Eloy; Hassaiene, Mokhtar

2006-01-01

We consider nonminimally coupled scalar fields to explore the Siklos spacetimes in three dimensions. Their interpretation as exact gravitational waves propagating on AdS space restrict the source to behave as a pure radiation field. We show that the related pure radiation constraints single out a unique self-interaction potential depending on one coupling constant. For a vanishing coupling constant, this potential reduces to a mass term with a mass fixed in terms of the nonminimal-coupling parameter. This mass dependence allows the existence of several free cases including massless and tachyonic sources. There even exists a particular value of the nonminimal-coupling parameter for which the corresponding mass exactly compensates the contribution generated by the negative scalar curvature, producing a genuinely massless field in this curved background. The self-interacting case is studied in detail for the conformal coupling. The resulting gravitational wave is formed by the superposition of the free and the self-interaction contributions, except for a critical value of the coupling constant where a nonperturbative effect relating the strong and weak regimes of the source appears. We establish a correspondence between the scalar source supporting an AdS wave and a pp wave by showing that their respective pure radiation constraints are conformally related, while their involved backgrounds are not. Finally, we consider the AdS waves for topologically massive gravity and its limit to conformal gravity

Algebraic Geometry and Number Theory Summer School

CERN Document Server

Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk

2017-01-01

This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

Applications of Affine and Weyl geometry

CERN Document Server

García-Río, Eduardo; Nikcevic, Stana

2013-01-01

Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannia

canEvolve: a web portal for integrative oncogenomics.

Directory of Open Access Journals (Sweden)

Mehmet Kemal Samur

Full Text Available BACKGROUND & OBJECTIVE: Genome-wide profiles of tumors obtained using functional genomics platforms are being deposited to the public repositories at an astronomical scale, as a result of focused efforts by individual laboratories and large projects such as the Cancer Genome Atlas (TCGA and the International Cancer Genome Consortium. Consequently, there is an urgent need for reliable tools that integrate and interpret these data in light of current knowledge and disseminate results to biomedical researchers in a user-friendly manner. We have built the canEvolve web portal to meet this need. RESULTS: canEvolve query functionalities are designed to fulfill most frequent analysis needs of cancer researchers with a view to generate novel hypotheses. canEvolve stores gene, microRNA (miRNA and protein expression profiles, copy number alterations for multiple cancer types, and protein-protein interaction information. canEvolve allows querying of results of primary analysis, integrative analysis and network analysis of oncogenomics data. The querying for primary analysis includes differential gene and miRNA expression as well as changes in gene copy number measured with SNP microarrays. canEvolve provides results of integrative analysis of gene expression profiles with copy number alterations and with miRNA profiles as well as generalized integrative analysis using gene set enrichment analysis. The network analysis capability includes storage and visualization of gene co-expression, inferred gene regulatory networks and protein-protein interaction information. Finally, canEvolve provides correlations between gene expression and clinical outcomes in terms of univariate survival analysis. CONCLUSION: At present canEvolve provides different types of information extracted from 90 cancer genomics studies comprising of more than 10,000 patients. The presence of multiple data types, novel integrative analysis for identifying regulators of oncogenesis, network

The Idea of Order at Geometry Class.

Science.gov (United States)

Rishel, Thomas

The idea of order in geometry is explored using the experience of assignments given to undergraduates in a college geometry course "From Space to Geometry." Discussed are the definition of geometry, and earth measurement using architecture, art, and common experience. This discussion concludes with a consideration of the question of whether…

Spike-adding in parabolic bursters: The role of folded-saddle canards

Science.gov (United States)

Desroches, Mathieu; Krupa, Martin; Rodrigues, Serafim

2016-09-01

The present work develops a new approach to studying parabolic bursting, and also proposes a novel four-dimensional canonical and polynomial-based parabolic burster. In addition to this new polynomial system, we also consider the conductance-based model of the Aplysia R15 neuron known as the Plant model, and a reduction of this prototypical biophysical parabolic burster to three variables, including one phase variable, namely the Baer-Rinzel-Carillo (BRC) phase model. Revisiting these models from the perspective of slow-fast dynamics reveals that the number of spikes per burst may vary upon parameter changes, however the spike-adding process occurs in an explosive fashion that involves special solutions called canards. This spike-adding canard explosion phenomenon is analysed by using tools from geometric singular perturbation theory in tandem with numerical bifurcation techniques. We find that the bifurcation structure persists across all considered systems, that is, spikes within the burst are incremented via the crossing of an excitability threshold given by a particular type of canard orbit, namely the true canard of a folded-saddle singularity. However there can be a difference in the spike-adding transitions in parameter space from one case to another, according to whether the process is continuous or discontinuous, which depends upon the geometry of the folded-saddle canard. Using these findings, we construct a new polynomial approximation of the Plant model, which retains all the key elements for parabolic bursting, including the spike-adding transitions mediated by folded-saddle canards. Finally, we briefly investigate the presence of spike-adding via canards in planar phase models of parabolic bursting, namely the theta model by Ermentrout and Kopell.

Special geometry

International Nuclear Information System (INIS)

Strominger, A.

1990-01-01

A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)

Using Dynamic Geometry Software to Improve Eight Grade Students' Understanding of Transformation Geometry

Science.gov (United States)

Guven, Bulent

2012-01-01

This study examines the effect of dynamic geometry software (DGS) on students' learning of transformation geometry. A pre- and post-test quasi-experimental design was used. Participants in the study were 68 eighth grade students (36 in the experimental group and 32 in the control group). While the experimental group students were studying the…

Disformal transformation in Newton-Cartan geometry

Energy Technology Data Exchange (ETDEWEB)

Huang, Peng [Zhejiang Chinese Medical University, Department of Information, Hangzhou (China); Sun Yat-Sen University, School of Physics and Astronomy, Guangzhou (China); Yuan, Fang-Fang [Nankai University, School of Physics, Tianjin (China)

2016-08-15

Newton-Cartan geometry has played a central role in recent discussions of the non-relativistic holography and condensed matter systems. Although the conformal transformation in non-relativistic holography can easily be rephrased in terms of Newton-Cartan geometry, we show that it requires a nontrivial procedure to arrive at the consistent form of anisotropic disformal transformation in this geometry. Furthermore, as an application of the newly obtained transformation, we use it to induce a geometric structure which may be seen as a particular non-relativistic version of the Weyl integrable geometry. (orig.)

Geometry and symmetry

CERN Document Server

Yale, Paul B

2012-01-01

This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi

Stochastic Geometry Analysis of Ultra Dense Network and TRSC Green Communication Strategy

Directory of Open Access Journals (Sweden)

Guoqiang Wang

2017-12-01

Full Text Available In recent years, with the rapid development of wireless communication, the traditional cellular with isomorphic and regular structure has been unable to meet the increasing number of users and business needs involving data of big volume. The trend is evolving into Ultra Dense Network (UDN architecture which is covered by cellular of irregular complex structure. In UDN, the spatial distribution of the base station plays an important role in the interference and performance evaluation of the whole cellular network, and the concept of green communication has also been put on agenda. In this paper, stochastic geometry theory is used to model UDN and to analyze the key performance of interference and wireless network. Moreover, a green communication strategy called TRSC is proposed, which is aimed at saving energy and reducing the signal interference among cells to a certain extent.

Optimizing solar-cell grid geometry

Science.gov (United States)

Crossley, A. P.

1969-01-01

Trade-off analysis and mathematical expressions calculate optimum grid geometry in terms of various cell parameters. Determination of the grid geometry provides proper balance between grid resistance and cell output to optimize the energy conversion process.

A Grassmann path from AdS3 to flat space

International Nuclear Information System (INIS)

Krishnan, Chethan; Raju, Avinash; Roy, Shubho

2014-01-01

We show that interpreting the inverse AdS 3 radius 1/l as a Grassmann variable results in a formal map from gravity in AdS 3 to gravity in flat space. The underlying reason for this is the fact that ISO(2,1) is the Inonu-Wigner contraction of SO(2,2). We show how this works for the Chern-Simons actions, demonstrate how the general (Banados) solution in AdS 3 maps to the general flat space solution, and how the Killing vectors, charges and the Virasoro algebra in the Brown-Henneaux case map to the corresponding quantities in the BMS 3 case. Our results straightforwardly generalize to the higher spin case: the recently constructed flat space higher spin theories emerge automatically in this approach from their AdS counterparts. We conclude with a discussion of singularity resolution in the BMS gauge as an application

Geometry and Cloaking Devices

Science.gov (United States)

Ochiai, T.; Nacher, J. C.

2011-09-01

Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.

A first course in geometry

CERN Document Server

Walsh, Edward T

2014-01-01

This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The extensive treatment can be easily adapted to accommodate shorter courses. Starting with the language of mathematics as expressed in the algebra of logic and sets, the text covers geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, space geometry, and coordinate geometry. Each chapter incl

Reducing workpieces to their base geometry for multi-step incremental forming using manifold harmonics

Science.gov (United States)

Carette, Yannick; Vanhove, Hans; Duflou, Joost

2018-05-01

Single Point Incremental Forming is a flexible process that is well-suited for small batch production and rapid prototyping of complex sheet metal parts. The distributed nature of the deformation process and the unsupported sheet imply that controlling the final accuracy of the workpiece is challenging. To improve the process limits and the accuracy of SPIF, the use of multiple forming passes has been proposed and discussed by a number of authors. Most methods use multiple intermediate models, where the previous one is strictly smaller than the next one, while gradually increasing the workpieces' wall angles. Another method that can be used is the manufacture of a smoothed-out "base geometry" in the first pass, after which more detailed features can be added in subsequent passes. In both methods, the selection of these intermediate shapes is freely decided by the user. However, their practical implementation in the production of complex freeform parts is not straightforward. The original CAD model can be manually adjusted or completely new CAD models can be created. This paper discusses an automatic method that is able to extract the base geometry from a full STL-based CAD model in an analytical way. Harmonic decomposition is used to express the final geometry as the sum of individual surface harmonics. It is then possible to filter these harmonic contributions to obtain a new CAD model with a desired level of geometric detail. This paper explains the technique and its implementation, as well as its use in the automatic generation of multi-step geometries.

Global affine differential geometry of hypersurfaces

CERN Document Server

Li, An-Min; Zhao, Guosong; Hu, Zejun

2015-01-01

This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry- as differential geometry in general- has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces.

Spectral dimension of quantum geometries

International Nuclear Information System (INIS)

Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes

2014-01-01

The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. (paper)

Algebraic geometry

CERN Document Server

Lefschetz, Solomon

2005-01-01

An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

On the Benefits of Divergent Search for Evolved Representations

DEFF Research Database (Denmark)

Lehman, Joel; Risi, Sebastian; Stanley, Kenneth O

2012-01-01

Evolved representations in evolutionary computation are often fragile, which can impede representation-dependent mechanisms such as self-adaptation. In contrast, evolved representations in nature are robust, evolvable, and creatively exploit available representational features. This paper provide...

A geometry calibration method for rotation translation trajectory

International Nuclear Information System (INIS)

Zhang Jun; Yan Bin; Li Lei; Lu Lizhong; Zhang Feng

2013-01-01

In cone-beam CT imaging system, it is difficult to directly measure the geometry parameters. In this paper, a geometry calibration method for rotation translation trajectory is proposed. Intrinsic parameters are solved from the relationship built on geometry parameter of the system and projection trajectory of calibration object. Parameters of rotation axis are extrapolated from the unified intrinsic parameter, and geometry parameters of the idle trajectory are acquired too. The calibration geometry can be analytically determined using explicit formulae, it can avoid getting into local optimum in iterative way. Simulation experiments are carried out on misaligned geometry, experiment results indicate that geometry artifacts due to misaligned geometry are effectively depressed by the proposed method, and the image quality is enhanced. (authors)

Vacuum degeneracy and Conformal Mass in Lovelock AdS gravity

Science.gov (United States)

Arenas-Henriquez, Gabriel; Miskovic, Olivera; Olea, Rodrigo

2017-11-01

It is shown that the notion of Conformal Mass can be defined within a given anti-de Sitter (AdS) branch of a Lovelock gravity theory as long as the corresponding vacuum is not degenerate. Indeed, conserved charges obtained by the addition of Kounterterms to the bulk action turn out to be proportional to the electric part of the Weyl tensor, when the fall-off of a generic solution in that AdS branch is considered. The factor of proportionality is the degeneracy condition for the vacua in the particular Lovelock AdS theory under study. This last feature explains the obstruction to define Conformal Mass in the degenerate case.

Perturbative and non-perturbative approaches to string sigma-models in AdS/CFT

Energy Technology Data Exchange (ETDEWEB)

Vescovi, Edoardo

2016-10-05

This thesis discusses quantum aspects of type II superstring theories in AdS{sub 5} x S{sup 5} and AdS{sub 4} x CP{sup 3} backgrounds relevant for the AdS/CFT correspondence, using perturbative methods at large string tension and lattice field theory techniques inspired by a work of Roiban and McKeown. We review the construction of the supercoset sigma-model for strings in the AdS{sub 5} x S{sup 5} background, whereas the general quantum dynamics of the superstring in AdS{sub 4} x CP{sup 3} is described by a double dimensional reduction of the supermembrane action in AdS{sub 4} x S{sup 7}. We present a manifestly covariant formalism for semiclassical quantization of strings around arbitrary minimal-area surfaces in AdS{sub 5} x S{sup 5}, expressing the fluctuation operators in terms of intrinsic and extrinsic invariants of the background geometry. We exactly solve the spectral problem for a fourth-order generalization of the Lame differential equation with doubly periodic coefficients in a complex variable. This calculates the one-loop energy of the (J{sub 1},J{sub 2})-string in the SU(2) sector in the limit described by a quantum Landau-Lifshitz model and the bosonic contribution to the energy of the (S,J)-string rotating in AdS{sub 5} and S{sup 5}. Similar techniques calculate the 1/4-BPS latitude Wilson loops in N=4 SYM theory at one loop, normalized to the 1/2-BPS circular loop. Our regularization scheme reproduces the next-to-leading order predicted by supersymmetric localization, up to a remainder function that we discuss upon. We also study the AdS{sub 4} x CP{sup 3} string action expanded around the null cusp background and compute the cusp anomaly up to two loops. This agrees with an all-loop conjectured expression of the ABJM interpolating function. We finally discretize the AdS{sub 5} x S{sup 5} superstring theory in the AdS light-cone gauge and perform lattice simulations at finite coupling with a Monte Carlo algorithm. We measure the string action

Geometry modeling for SAM-CE Monte Carlo calculations

International Nuclear Information System (INIS)

Steinberg, H.A.; Troubetzkoy, E.S.

1980-01-01

Three geometry packages have been developed and incorporated into SAM-CE, for representing in three dimensions the transport medium. These are combinatorial geometry - a general (non-lattice) system, complex combinatorial geometry - a very general system with lattice capability, and special reactor geometry - a special purpose system for light water reactor geometries. Their different attributes are described

The genotype-phenotype map of an evolving digital organism

OpenAIRE

Fortuna, Miguel A.; Zaman, Luis; Ofria, Charles; Wagner, Andreas

2017-01-01

To understand how evolving systems bring forth novel and useful phenotypes, it is essential to understand the relationship between genotypic and phenotypic change. Artificial evolving systems can help us understand whether the genotype-phenotype maps of natural evolving systems are highly unusual, and it may help create evolvable artificial systems. Here we characterize the genotype-phenotype map of digital organisms in Avida, a platform for digital evolution. We consider digital organisms fr...

Perturbative entanglement thermodynamics for AdS spacetime: renormalization

International Nuclear Information System (INIS)

Mishra, Rohit; Singh, Harvendra

2015-01-01

We study the effect of charged excitations in the AdS spacetime on the first law of entanglement thermodynamics. It is found that ‘boosted’ AdS black holes give rise to a more general form of first law which includes chemical potential and charge density. To obtain this result we have to resort to a second order perturbative calculation of entanglement entropy for small size subsystems. At first order the form of entanglement law remains unchanged even in the presence of charged excitations. But the thermodynamic quantities have to be appropriately ‘renormalized’ at the second order due to the corrections. We work in the perturbative regime where T thermal ≪T E .

Estimating added sugars in US consumer packaged goods: An application to beverages in 2007–08

Science.gov (United States)

Ng, Shu Wen; Bricker, Gregory; Li, Kuo-ping; Yoon, Emily Ford; Kang, Jiyoung; Westrich, Brian

2015-01-01

This study developed a method to estimate added sugar content in consumer packaged goods (CPG) that can keep pace with the dynamic food system. A team including registered dietitians, a food scientist and programmers developed a batch-mode ingredient matching and linear programming (LP) approach to estimate the amount of each ingredient needed in a given product to produce a nutrient profile similar to that reported on its nutrition facts label (NFL). Added sugar content was estimated for 7021 products available in 2007–08 that contain sugar from ten beverage categories. Of these, flavored waters had the lowest added sugar amounts (4.3g/100g), while sweetened dairy and dairy alternative beverages had the smallest percentage of added sugars (65.6% of Total Sugars; 33.8% of Calories). Estimation validity was determined by comparing LP estimated values to NFL values, as well as in a small validation study. LP estimates appeared reasonable compared to NFL values for calories, carbohydrates and total sugars, and performed well in the validation test; however, further work is needed to obtain more definitive conclusions on the accuracy of added sugar estimates in CPGs. As nutrition labeling regulations evolve, this approach can be adapted to test for potential product-specific, category-level, and population-level implications. PMID:26273127

EVOLVE

CERN Document Server

Deutz, André; Schütze, Oliver; Legrand, Pierrick; Tantar, Emilia; Tantar, Alexandru-Adrian

2017-01-01

This book comprises nine selected works on numerical and computational methods for solving multiobjective optimization, game theory, and machine learning problems. It provides extended versions of selected papers from various fields of science such as computer science, mathematics and engineering that were presented at EVOLVE 2013 held in July 2013 at Leiden University in the Netherlands. The internationally peer-reviewed papers include original work on important topics in both theory and applications, such as the role of diversity in optimization, statistical approaches to combinatorial optimization, computational game theory, and cell mapping techniques for numerical landscape exploration. Applications focus on aspects including robustness, handling multiple objectives, and complex search spaces in engineering design and computational biology.

Molecular motion in restricted geometries

Indian Academy of Sciences (India)

Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...

Heavy ion collisions in AdS5

International Nuclear Information System (INIS)

Kovchegov, Yuri V.

2011-01-01

We study heavy ion collisions at strong 't Hooft coupling using AdS/CFT correspondence. Heavy ion collisions correspond to gravitational shock wave collisions in AdS 5 . We construct the metric in the forward light cone after the collision perturbatively through expansion of Einstein equations in graviton exchanges. We obtain an analytic expression for the metric including all-order graviton exchanges with one shock wave, while keeping the exchanges with another shock wave at the lowest order. We read off the corresponding energy-momentum tensor of the produced medium. Unfortunately this energy-momentum tensor does not correspond to ideal hydrodynamics, indicating that higher order graviton exchanges are needed to construct the full solution of the problem. We also show that shock waves must completely stop almost immediately after the collision in AdS 5 , which, on the field theory side, corresponds to complete nuclear stopping due to strong coupling effects, likely leading to Landau hydrodynamics. Finally, we perform trapped surface analysis of the shock wave collisions demonstrating that a bulk black hole, corresponding to ideal hydrodynamics on the boundary, has to be created in such collisions, thus constructing a proof of thermalization in heavy ion collisions at strong coupling.

Advances in discrete differential geometry

CERN Document Server

2016-01-01

This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...

Analytical study on holographic superfluid in AdS soliton background

International Nuclear Information System (INIS)

Lai, Chuyu; Pan, Qiyuan; Jing, Jiliang; Wang, Yongjiu

2016-01-01

We analytically study the holographic superfluid phase transition in the AdS soliton background by using the variational method for the Sturm–Liouville eigenvalue problem. By investigating the holographic s-wave and p-wave superfluid models in the probe limit, we observe that the spatial component of the gauge field will hinder the phase transition. Moreover, we note that, different from the AdS black hole spacetime, in the AdS soliton background the holographic superfluid phase transition always belongs to the second order and the critical exponent of the system takes the mean-field value in both s-wave and p-wave models. Our analytical results are found to be in good agreement with the numerical findings.

Quality improvement of pyrolysis oil from waste rubber by adding sawdust

International Nuclear Information System (INIS)

Wang, Wen-liang; Chang, Jian-min; Cai, Li-ping; Shi, Sheldon Q.

2014-01-01

Highlights: • Rubber-pyrolysis oil is difficult to be fuel due to high proportion of PAHs. • The efficiency of pyrolysis was increased as the percentage of sawdust increased. • The adding of sawdust improved pyrolysis oil quality by reducing the PAHs content. • Adding sawdust reduced nitrogen/sulfur in oil and was easier to convert to diesel. - Abstract: This work was aimed at improving the pyrolysis oil quality of waste rubber by adding larch sawdust. Using a 1 kg/h stainless pyrolysis reactor, the contents of sawdust in rubber were gradually increased from 0%, 50%, 100% and 200% (wt%) during the pyrolysis process. Using a thermo-gravimetric (TG) analyzer coupled with Fourier transform infrared (FTIR) analysis of evolving products (TG–FTIR), the weight loss characteristics of the heat under different mixtures of sawdust/rubber were observed. Using the pyrolysis–gas chromatography (GC)–mass spectrometry (Py–GC/MS), the vapors from the pyrolysis processes were collected and the compositions of the vapors were examined. During the pyrolysis process, the recovery of the pyrolysis gas and its composition were measured in-situ at a reaction temperature of 450 °C and a retaining time of 1.2 s. The results indicated that the efficiency of pyrolysis was increased and the residual carbon was reduced as the percentage of sawdust increased. The adding of sawdust significantly improved the pyrolysis oil quality by reducing the polycyclic aromatic hydrocarbons (PAHs) and nitrogen and sulfur compounds contents, resulting in an improvement in the combustion efficiency of the pyrolysis oil

Quality improvement of pyrolysis oil from waste rubber by adding sawdust

Energy Technology Data Exchange (ETDEWEB)

Wang, Wen-liang [MOE Key Laboratory of Wooden Material Science and Application, College of Material Science and Technology, Wood Science and Technology, Beijing Forestry University, 100083 Beijing (China); Chang, Jian-min, E-mail: cjianmin@bjfu.edu.cn [MOE Key Laboratory of Wooden Material Science and Application, College of Material Science and Technology, Wood Science and Technology, Beijing Forestry University, 100083 Beijing (China); Cai, Li-ping [Mechanical and Energy Engineering Department, University of North Texas, 3940 N. Elm, Denton 72076, TX (United States); Shi, Sheldon Q., E-mail: Sheldon.Shi@unt.edu [Mechanical and Energy Engineering Department, University of North Texas, 3940 N. Elm, Denton 72076, TX (United States)

2014-12-15

Highlights: • Rubber-pyrolysis oil is difficult to be fuel due to high proportion of PAHs. • The efficiency of pyrolysis was increased as the percentage of sawdust increased. • The adding of sawdust improved pyrolysis oil quality by reducing the PAHs content. • Adding sawdust reduced nitrogen/sulfur in oil and was easier to convert to diesel. - Abstract: This work was aimed at improving the pyrolysis oil quality of waste rubber by adding larch sawdust. Using a 1 kg/h stainless pyrolysis reactor, the contents of sawdust in rubber were gradually increased from 0%, 50%, 100% and 200% (wt%) during the pyrolysis process. Using a thermo-gravimetric (TG) analyzer coupled with Fourier transform infrared (FTIR) analysis of evolving products (TG–FTIR), the weight loss characteristics of the heat under different mixtures of sawdust/rubber were observed. Using the pyrolysis–gas chromatography (GC)–mass spectrometry (Py–GC/MS), the vapors from the pyrolysis processes were collected and the compositions of the vapors were examined. During the pyrolysis process, the recovery of the pyrolysis gas and its composition were measured in-situ at a reaction temperature of 450 °C and a retaining time of 1.2 s. The results indicated that the efficiency of pyrolysis was increased and the residual carbon was reduced as the percentage of sawdust increased. The adding of sawdust significantly improved the pyrolysis oil quality by reducing the polycyclic aromatic hydrocarbons (PAHs) and nitrogen and sulfur compounds contents, resulting in an improvement in the combustion efficiency of the pyrolysis oil.

Joule-Thomson expansion of the charged AdS black holes

International Nuclear Information System (INIS)

Oekcue, Oezguer; Aydiner, Ekrem

2017-01-01

In this paper, we study Joule-Thomson effects for charged AdS black holes. We obtain inversion temperatures and curves. We investigate similarities and differences between van der Waals fluids and charged AdS black holes for the expansion. We obtain isenthalpic curves for both systems in the T-P plane and determine the cooling-heating regions. (orig.)

Joule-Thomson expansion of the charged AdS black holes

Energy Technology Data Exchange (ETDEWEB)

Oekcue, Oezguer; Aydiner, Ekrem [Istanbul University, Department of Physics, Faculty of Science, Vezneciler, Istanbul (Turkey)

2017-01-15

In this paper, we study Joule-Thomson effects for charged AdS black holes. We obtain inversion temperatures and curves. We investigate similarities and differences between van der Waals fluids and charged AdS black holes for the expansion. We obtain isenthalpic curves for both systems in the T-P plane and determine the cooling-heating regions. (orig.)

An Investigation into Conversion from Non-Uniform Rational B-Spline Boundary Representation Geometry to Constructive Solid Geometry

Science.gov (United States)

2015-12-01

ARL-SR-0347 ● DEC 2015 US Army Research Laboratory An Investigation into Conversion from Non-Uniform Rational B-Spline Boundary...US Army Research Laboratory An Investigation into Conversion from Non-Uniform Rational B-Spline Boundary Representation Geometry to...from Non-Uniform Rational B-Spline Boundary Representation Geometry to Constructive Solid Geometry 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c

W-geometry

International Nuclear Information System (INIS)

Hull, C.M.

1993-01-01

The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)

Revisiting Robustness and Evolvability: Evolution in Weighted Genotype Spaces

Science.gov (United States)

Partha, Raghavendran; Raman, Karthik

2014-01-01

Robustness and evolvability are highly intertwined properties of biological systems. The relationship between these properties determines how biological systems are able to withstand mutations and show variation in response to them. Computational studies have explored the relationship between these two properties using neutral networks of RNA sequences (genotype) and their secondary structures (phenotype) as a model system. However, these studies have assumed every mutation to a sequence to be equally likely; the differences in the likelihood of the occurrence of various mutations, and the consequence of probabilistic nature of the mutations in such a system have previously been ignored. Associating probabilities to mutations essentially results in the weighting of genotype space. We here perform a comparative analysis of weighted and unweighted neutral networks of RNA sequences, and subsequently explore the relationship between robustness and evolvability. We show that assuming an equal likelihood for all mutations (as in an unweighted network), underestimates robustness and overestimates evolvability of a system. In spite of discarding this assumption, we observe that a negative correlation between sequence (genotype) robustness and sequence evolvability persists, and also that structure (phenotype) robustness promotes structure evolvability, as observed in earlier studies using unweighted networks. We also study the effects of base composition bias on robustness and evolvability. Particularly, we explore the association between robustness and evolvability in a sequence space that is AU-rich – sequences with an AU content of 80% or higher, compared to a normal (unbiased) sequence space. We find that evolvability of both sequences and structures in an AU-rich space is lesser compared to the normal space, and robustness higher. We also observe that AU-rich populations evolving on neutral networks of phenotypes, can access less phenotypic variation compared to

Ad gist : Ad communication in a single eye fixation

NARCIS (Netherlands)

Pieters, R.; Wedel, M.

2012-01-01

Most ads in practice receive no more than a single eye fixation. This study investigates the limits of what ads can communicate under such adverse exposure conditions. We find that consumers already know at maximum levels of accuracy and with high degree of certainty whether something is an ad or is

Head First 2D Geometry

CERN Document Server

Fallow), Stray

2009-01-01

Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and

Factorized tree-level scattering in AdS4 x CP3

International Nuclear Information System (INIS)

Kalousios, Chrysostomos; Vergu, C.; Volovich, Anastasia

2009-01-01

AdS 4 /CFT 3 duality relating IIA string theory on AdS 4 x CP 3 to N = 6 superconformal Chern-Simons theory provides an arena for studying aspects of integrability in a new potentially exactly solvable system. In this paper we explore the tree-level worldsheet scattering for strings on AdS 4 x CP 3 . We compute all bosonic four-, five- and six-point amplitudes in the gauge-fixed action and demonstrate the absence of particle production.

Numerically robust geometry engine for compound solid geometries

International Nuclear Information System (INIS)

Vlachoudis, V.; Sinuela-Pastor, D.

2013-01-01

Monte Carlo programs heavily rely on a fast and numerically robust solid geometry engines. However the success of solid modeling, depends on facilities for specifying and editing parameterized models through a user-friendly graphical front-end. Such a user interface has to be fast enough in order to be interactive for 2D and/or 3D displays, but at the same time numerically robust in order to display possible modeling errors at real time that could be critical for the simulation. The graphical user interface Flair for FLUKA currently employs such an engine where special emphasis has been given on being fast and numerically robust. The numerically robustness is achieved by a novel method of estimating the floating precision of the operations, which dynamically adapts all the decision operations accordingly. Moreover a predictive caching mechanism is ensuring that logical errors in the geometry description are found online, without compromising the processing time by checking all regions. (authors)

Competitive Advantage and its Sources in an Evolving Market

Science.gov (United States)

Zaridis, Apostolos D.

2009-08-01

In a continuously altered and evolving Market, as is the food manufacturing market, the main and long-lasting objective of firm that is the maximization of its wealth and consequently the continuous remaining in profit regions, appears that it is possible to be achieved via the obtainment and maintenance of diachronically long-term competitive advantage, which it will render the firm unique or leader force in a inexorable competition that is continuously extended in a globalized market. Various definitions and different regards are developed in regard to the competitive advantage and the way with which a firm it is possible, acquiring it, to star in the market in which it is activated. As result of sustainable competitive advantage in a firm comes the above the average performance. Abundance of resources and competences that are proposed as sources of competitive advantage in the resource-based view literature exists, while they are added continuously new based on empiric studies. In any case, it appears to suffer hierarchy of sources of competitive advantage, with regard to sustainability of these.

Quantification of Porcine Vocal Fold Geometry.

Science.gov (United States)

Stevens, Kimberly A; Thomson, Scott L; Jetté, Marie E; Thibeault, Susan L

2016-07-01

The aim of this study was to quantify porcine vocal fold medial surface geometry and three-dimensional geometric distortion induced by freezing the larynx, especially in the region of the vocal folds. The medial surface geometries of five excised porcine larynges were quantified and reported. Five porcine larynges were imaged in a micro-CT scanner, frozen, and rescanned. Segmentations and three-dimensional reconstructions were used to quantify and characterize geometric features. Comparisons were made with geometry data previously obtained using canine and human vocal folds as well as geometries of selected synthetic vocal fold models. Freezing induced an overall expansion of approximately 5% in the transverse plane and comparable levels of nonuniform distortion in sagittal and coronal planes. The medial surface of the porcine vocal folds was found to compare reasonably well with other geometries, although the compared geometries exhibited a notable discrepancy with one set of published human female vocal fold geometry. Porcine vocal folds are qualitatively geometrically similar to data available for canine and human vocal folds, as well as commonly used models. Freezing of tissue in the larynx causes distortion of around 5%. The data can provide direction in estimating uncertainty due to bulk distortion of tissue caused by freezing, as well as quantitative geometric data that can be directly used in developing vocal fold models. Copyright © 2016 The Voice Foundation. Published by Elsevier Inc. All rights reserved.

Holographic description of Kerr-Bolt-AdS-dS spacetimes

Energy Technology Data Exchange (ETDEWEB)

Chen, B., E-mail: bchen01@pku.edu.c [Department of Physics, and State Key Laboratory of Nuclear Physics and Technology, and Center for High Energy Physics, Peking University, Beijing 100871 (China); Ghezelbash, A.M., E-mail: masoud.ghezelbash@usask.c [Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E2 (Canada); Kamali, V., E-mail: vkamali1362@gmail.co [Department of Campus of Bijar, Kurdistan University, Bijar (Iran, Islamic Republic of); Setare, M.R., E-mail: rezakord@ipm.i [Department of Campus of Bijar, Kurdistan University, Bijar (Iran, Islamic Republic of)

2011-07-01

We show that there exists a holographic 2D CFT description of a Kerr-Bolt-AdS-dS spacetime. We first consider the wave equation of a massless scalar field propagating in extremal Kerr-Bolt-AdS-dS spacetimes and find in the 'near region', the wave equation in extremal limit could be written in terms of the SL(2,R) quadratic Casimir. This suggests that there exist dual CFT descriptions of these black holes. In the probe limit, we compute the scattering amplitudes of the scalar off the extremal black holes and find perfect agreement with the CFT prediction. Furthermore we study the holographic description of the generic four-dimensional non-extremal Kerr-Bolt-AdS-dS black holes. We find that if focusing on the near-horizon region, for the massless scalar scattering in the low-frequency limit, the radial equation could still be rewritten as the SL(2,R) quadratic Casimir, suggesting the existence of dual 2D description. We read the temperatures of the dual CFT from the conformal coordinates and obtain the central charges by studying the near-horizon geometry of near-extremal black holes. We recover the macroscopic entropy from the microscopic counting. We also show that for the super-radiant scattering, the retarded Green's functions and the corresponding absorption cross sections are in perfect match with CFT prediction.

Lectures on discrete geometry

CERN Document Server

2002-01-01

Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...

Discrete and computational geometry

CERN Document Server

Devadoss, Satyan L

2011-01-01

Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...

A prediction for bubbling geometries

OpenAIRE

Okuda, Takuya

2007-01-01

We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.

Geometry -----------~--------------RESONANCE

Indian Academy of Sciences (India)

Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.

Financial and health literacy predict incident AD dementia and AD pathology

Science.gov (United States)

Yu, Lei; Wilson, Robert S.; Schneider, Julie A.; Bennett, David A.; Boyle, Patricia A.

2017-01-01

Background Domain specific literacy is a multidimensional construct that requires multiple resources including cognitive and non-cognitive factors. Objective We test the hypothesis that domain specific literacy is associated with AD dementia and AD pathology after controlling for cognition. Methods Participants were community based older persons who completed a baseline literacy assessment, underwent annual clinical evaluations for up to 8 years and agreed to organ donation after death. Financial and health literacy was measured using 32 questions and cognition was measured using 19 tests. Annual diagnosis of AD dementia followed standard criteria. AD pathology was examined post-mortem by quantifying plaques and tangles. Cox models examined the association of literacy with incident AD dementia. Performance of model prediction for incident AD dementia was assessed using indices for integrated discrimination improvement and continuous net reclassification improvement. Linear regression models examined the independent association of literacy with AD pathology in autopsied participants. Results All 805 participants were free of dementia at baseline and 102 (12.7%) developed AD dementia during the follow-up. Lower literacy was associated with higher risk for incident AD dementia (pliteracy measure had better predictive performance than the one with demographics and cognition only. Lower literacy also was associated with higher burden of AD pathology after controlling for cognition (β=0.07, p=0.035). Conclusion Literacy predicts incident AD dementia and AD pathology in community-dwelling older persons, and the association is independent of traditional measures of cognition. PMID:28157101

Enthalpy and the mechanics of AdS black holes

International Nuclear Information System (INIS)

Kastor, David; Traschen, Jennie; Ray, Sourya

2009-01-01

We present geometric derivations of the Smarr formula for static AdS black holes and an expanded first law that includes variations in the cosmological constant. These two results are further related by a scaling argument based on Euler's theorem. The key new ingredient in the constructions is a two-form potential for the static Killing field. Surface integrals of the Killing potential determine the coefficient of the variation of Λ in the first law. This coefficient is proportional to a finite, effective volume for the region outside the AdS black hole horizon, which can also be interpreted as minus the volume excluded from a spatial slice by the black hole horizon. This effective volume also contributes to the Smarr formula. Since Λ is naturally thought of as a pressure, the new term in the first law has the form of effective volume times change in pressure that arises in the variation of the enthalpy in classical thermodynamics. This and related arguments suggest that the mass of an AdS black hole should be interpreted as the enthalpy of the spacetime.

Intermediate algebra & analytic geometry

CERN Document Server

Gondin, William R

1967-01-01

Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system

Thermodynamic and classical instability of AdS black holes in fourth-order gravity

International Nuclear Information System (INIS)

Myung, Yun Soo; Moon, Taeyoon

2014-01-01

We study thermodynamic and classical instability of AdS black holes in fourth-order gravity. These include the BTZ black hole in new massive gravity, Schwarzschild-AdS black hole, and higher-dimensional AdS black holes in fourth-order gravity. All thermodynamic quantities which are computed using the Abbot-Deser-Tekin method are used to study thermodynamic instability of AdS black holes. On the other hand, we investigate the s-mode Gregory-Laflamme instability of the massive graviton propagating around the AdS black holes. We establish the connection between the thermodynamic instability and the GL instability of AdS black holes in fourth-order gravity. This shows that the Gubser-Mitra conjecture holds for AdS black holes found from fourth-order gravity

Geometry The Language of Space and Form (Revised Edition)

CERN Document Server

Tabak, John

2011-01-01

Geometry, Revised Edition describes geometry in antiquity. Beginning with a brief description of some of the geometry that preceded the geometry of the Greeks, it takes up the story of geometry during the European Renaissance as well as the significant mathematical progress in other areas of the world. It also discusses the analytic geometry of Ren Descartes and Pierre Fermat, the alternative coordinate systems invented by Isaac Newton, and the solid geometry of Leonhard Euler. Also included is an overview of the geometry of one of the most successful mathematicians of the 19th century, Bernha

Winding strings and AdS3 black holes

International Nuclear Information System (INIS)

Troost, Jan

2002-01-01

We start a systematic study of string theory in AdS 3 black hole backgrounds. Firstly, we analyse in detail the geodesic structure of the BTZ black hole, including spacelike geodesics. Secondly, we study the spectrum for massive and massless scalar fields, paying particular attention to the connection between Sl(2,R) subgroups, the theory of special functions and global properties of the BTZ black holes. We construct classical strings that wind the black holes. Finally, we apply the general formalism to the vacuum black hole background, and formulate the boundary spacetime Virasoro algebra in terms of worldsheet operators. We moreover establish the link between a proposal for a ghost free spectrum for Sl(2,R) string propagation and the massless black hole background, thereby claryfing aspects of the AdS 3 /CFT correspondence. (author)

Contextual advertising using Google AdWords and Google AdSense

OpenAIRE

Mihok, Radovan

2008-01-01

The thesis introduces contextual advertising on internet using Google AdWords. The paper describes individual steps of an ad campaign (product choosing, ad types, keywords), its management and success evaluation (calculation of ROI and modified ROI).

Maintaining evolvability.

Science.gov (United States)

Crow, James F

2008-12-01

Although molecular methods, such as QTL mapping, have revealed a number of loci with large effects, it is still likely that the bulk of quantitative variability is due to multiple factors, each with small effect. Typically, these have a large additive component. Conventional wisdom argues that selection, natural or artificial, uses up additive variance and thus depletes its supply. Over time, the variance should be reduced, and at equilibrium be near zero. This is especially expected for fitness and traits highly correlated with it. Yet, populations typically have a great deal of additive variance, and do not seem to run out of genetic variability even after many generations of directional selection. Long-term selection experiments show that populations continue to retain seemingly undiminished additive variance despite large changes in the mean value. I propose that there are several reasons for this. (i) The environment is continually changing so that what was formerly most fit no longer is. (ii) There is an input of genetic variance from mutation, and sometimes from migration. (iii) As intermediate-frequency alleles increase in frequency towards one, producing less variance (as p --> 1, p(1 - p) --> 0), others that were originally near zero become more common and increase the variance. Thus, a roughly constant variance is maintained. (iv) There is always selection for fitness and for characters closely related to it. To the extent that the trait is heritable, later generations inherit a disproportionate number of genes acting additively on the trait, thus increasing genetic variance. For these reasons a selected population retains its ability to evolve. Of course, genes with large effect are also important. Conspicuous examples are the small number of loci that changed teosinte to maize, and major phylogenetic changes in the animal kingdom. The relative importance of these along with duplications, chromosome rearrangements, horizontal transmission and polyploidy

From geometry to algebra and vice versa: Realistic mathematics education principles for analyzing geometry tasks

Science.gov (United States)

Jupri, Al

2017-04-01

In this article we address how Realistic Mathematics Education (RME) principles, including the intertwinement and the reality principles, are used to analyze geometry tasks. To do so, we carried out three phases of a small-scale study. First we analyzed four geometry problems - considered as tasks inviting the use of problem solving and reasoning skills - theoretically in the light of the RME principles. Second, we tested two problems to 31 undergraduate students of mathematics education program and other two problems to 16 master students of primary mathematics education program. Finally, we analyzed student written work and compared these empirical to the theoretical results. We found that there are discrepancies between what we expected theoretically and what occurred empirically in terms of mathematization and of intertwinement of mathematical concepts from geometry to algebra and vice versa. We conclude that the RME principles provide a fruitful framework for analyzing geometry tasks that, for instance, are intended for assessing student problem solving and reasoning skills.

The genotype-phenotype map of an evolving digital organism.

Directory of Open Access Journals (Sweden)

Miguel A Fortuna

2017-02-01

Full Text Available To understand how evolving systems bring forth novel and useful phenotypes, it is essential to understand the relationship between genotypic and phenotypic change. Artificial evolving systems can help us understand whether the genotype-phenotype maps of natural evolving systems are highly unusual, and it may help create evolvable artificial systems. Here we characterize the genotype-phenotype map of digital organisms in Avida, a platform for digital evolution. We consider digital organisms from a vast space of 10141 genotypes (instruction sequences, which can form 512 different phenotypes. These phenotypes are distinguished by different Boolean logic functions they can compute, as well as by the complexity of these functions. We observe several properties with parallels in natural systems, such as connected genotype networks and asymmetric phenotypic transitions. The likely common cause is robustness to genotypic change. We describe an intriguing tension between phenotypic complexity and evolvability that may have implications for biological evolution. On the one hand, genotypic change is more likely to yield novel phenotypes in more complex organisms. On the other hand, the total number of novel phenotypes reachable through genotypic change is highest for organisms with simple phenotypes. Artificial evolving systems can help us study aspects of biological evolvability that are not accessible in vastly more complex natural systems. They can also help identify properties, such as robustness, that are required for both human-designed artificial systems and synthetic biological systems to be evolvable.

The genotype-phenotype map of an evolving digital organism.

Science.gov (United States)

Fortuna, Miguel A; Zaman, Luis; Ofria, Charles; Wagner, Andreas

2017-02-01

To understand how evolving systems bring forth novel and useful phenotypes, it is essential to understand the relationship between genotypic and phenotypic change. Artificial evolving systems can help us understand whether the genotype-phenotype maps of natural evolving systems are highly unusual, and it may help create evolvable artificial systems. Here we characterize the genotype-phenotype map of digital organisms in Avida, a platform for digital evolution. We consider digital organisms from a vast space of 10141 genotypes (instruction sequences), which can form 512 different phenotypes. These phenotypes are distinguished by different Boolean logic functions they can compute, as well as by the complexity of these functions. We observe several properties with parallels in natural systems, such as connected genotype networks and asymmetric phenotypic transitions. The likely common cause is robustness to genotypic change. We describe an intriguing tension between phenotypic complexity and evolvability that may have implications for biological evolution. On the one hand, genotypic change is more likely to yield novel phenotypes in more complex organisms. On the other hand, the total number of novel phenotypes reachable through genotypic change is highest for organisms with simple phenotypes. Artificial evolving systems can help us study aspects of biological evolvability that are not accessible in vastly more complex natural systems. They can also help identify properties, such as robustness, that are required for both human-designed artificial systems and synthetic biological systems to be evolvable.

Differential geometry curves, surfaces, manifolds

CERN Document Server

Kohnel, Wolfgang

2002-01-01

This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra.

Projective Geometry

Indian Academy of Sciences (India)

mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.

Google Advertising Tools Cashing in with AdSense and AdWords

CERN Document Server

Davis, Harold

2010-01-01

With this book, you'll learn how to take full advantage of Google AdWords and AdSense, the sophisticated online advertising tools used by thousands of large and small businesses. This new edition provides a substantially updated guide to advertising on the Web, including how it works in general, and how Google's advertising programs in particular help you make money. You'll find everything you need to work with AdWords, which lets you generate text ads to accompany specific search term results, and AdSense, which automatically delivers precisely targeted text and image ads to your website.

U.S. Army Armament Research, Development and Engineering Center Grain Evaluation Software to Numerically Predict Linear Burn Regression for Solid Propellant Grain Geometries

Science.gov (United States)

2017-10-01

ENGINEERING CENTER GRAIN EVALUATION SOFTWARE TO NUMERICALLY PREDICT LINEAR BURN REGRESSION FOR SOLID PROPELLANT GRAIN GEOMETRIES Brian...distribution is unlimited. AD U.S. ARMY ARMAMENT RESEARCH, DEVELOPMENT AND ENGINEERING CENTER Munitions Engineering Technology Center Picatinny...U.S. ARMY ARMAMENT RESEARCH, DEVELOPMENT AND ENGINEERING CENTER GRAIN EVALUATION SOFTWARE TO NUMERICALLY PREDICT LINEAR BURN REGRESSION FOR SOLID

Evolvability as a Quality Attribute of Software Architectures

NARCIS (Netherlands)

Ciraci, S.; van den Broek, P.M.; Duchien, Laurence; D'Hondt, Maja; Mens, Tom

We review the definition of evolvability as it appears on the literature. In particular, the concept of software evolvability is compared with other system quality attributes, such as adaptability, maintainability and modifiability.

Second International workshop Geometry and Symbolic Computation

CERN Document Server

Walczak, Paweł; Geometry and its Applications

2014-01-01

This volume has been divided into two parts: Geometry and Applications. The geometry portion of the book relates primarily to geometric flows, laminations, integral formulae, geometry of vector fields on Lie groups, and osculation; the articles in the applications portion concern some particular problems of the theory of dynamical systems, including mathematical problems of liquid flows and a study of cycles for non-dynamical systems. This Work is based on the second international workshop entitled "Geometry and Symbolic Computations," held on May 15-18, 2013 at the University of Haifa and is dedicated to modeling (using symbolic calculations) in differential geometry and its applications in fields such as computer science, tomography, and mechanics. It is intended to create a forum for students and researchers in pure and applied geometry to promote discussion of modern state-of-the-art in geometric modeling using symbolic programs such as Maple™ and Mathematica®, as well as presentation of new results. ...

Light-cone gauge formulation for AdS4 x CP3

International Nuclear Information System (INIS)

Uvarov, D.V.

2011-01-01

We review the Type IIA superstring on the AdS 4 x CP 3 background in the k-symmetry light-cone gauge characterized by the choice of the lightlike directions from the D = 3 Minkowski boundary of AdS 4 both in the Lagrangian and Hamiltonian formulations

Penrose inequality for asymptotically AdS spaces

International Nuclear Information System (INIS)

Itkin, Igor; Oz, Yaron

2012-01-01

In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background. If the inequality is violated by an initial Cauchy data, it suggests a creation of a naked singularity, thus providing means to consider the cosmic censorship hypothesis. We propose a general form of Penrose inequality for asymptotically locally AdS spaces.

Penrose inequality for asymptotically AdS spaces

Energy Technology Data Exchange (ETDEWEB)

Itkin, Igor [Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978 (Israel); Oz, Yaron, E-mail: yaronoz@post.tau.ac.il [Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978 (Israel)

2012-02-28

In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background. If the inequality is violated by an initial Cauchy data, it suggests a creation of a naked singularity, thus providing means to consider the cosmic censorship hypothesis. We propose a general form of Penrose inequality for asymptotically locally AdS spaces.

Minimal surfaces in AdS space and integrable systems

Science.gov (United States)

Burrington, Benjamin A.; Gao, Peng

2010-04-01

We consider the Pohlmeyer reduction for spacelike minimal area worldsheets in AdS5. The Lax pair for the reduced theory is found, and written entirely in terms of the A3 = D3 root system, generalizing the B2 affine Toda system which appears for the AdS4 string. For the B2 affine Toda system, we show that the area of the worlsheet is obtainable from the moduli space Kähler potential of a related Hitchin system. We also explore the Saveliev-Leznov construction for solutions of the B2 affine Toda system, and recover the rotationally symmetric solution associated to Painleve transcendent.

AdS5 magnetized solutions in minimal gauged supergravity

Directory of Open Access Journals (Sweden)

Jose Luis Blázquez-Salcedo

2017-08-01

Full Text Available We construct a generalization of the AdS charged rotating black holes with two equal magnitude angular momenta in five-dimensional minimal gauged supergravity. In addition to the mass, electric charge and angular momentum, the new solutions possess an extra-parameter associated with a non-zero magnitude of the magnetic potential at infinity. In contrast with the known cases, these new black holes possess a non-trivial zero-horizon size limit which describes a one parameter family of spinning charged solitons. All configurations reported in this work approach asymptotically an AdS5 spacetime in global coordinates and are free of pathologies.

A new evolutionary system for evolving artificial neural networks.

Science.gov (United States)

Yao, X; Liu, Y

1997-01-01

This paper presents a new evolutionary system, i.e., EPNet, for evolving artificial neural networks (ANNs). The evolutionary algorithm used in EPNet is based on Fogel's evolutionary programming (EP). Unlike most previous studies on evolving ANN's, this paper puts its emphasis on evolving ANN's behaviors. Five mutation operators proposed in EPNet reflect such an emphasis on evolving behaviors. Close behavioral links between parents and their offspring are maintained by various mutations, such as partial training and node splitting. EPNet evolves ANN's architectures and connection weights (including biases) simultaneously in order to reduce the noise in fitness evaluation. The parsimony of evolved ANN's is encouraged by preferring node/connection deletion to addition. EPNet has been tested on a number of benchmark problems in machine learning and ANNs, such as the parity problem, the medical diagnosis problems, the Australian credit card assessment problem, and the Mackey-Glass time series prediction problem. The experimental results show that EPNet can produce very compact ANNs with good generalization ability in comparison with other algorithms.

The Persistification of the ATLAS Geometry

CERN Document Server

AUTHOR|(INSPIRE)INSPIRE-00068562; The ATLAS collaboration; Bianchi, Riccardo-Maria

2016-01-01

The complex geometry of the whole detector of the ATLAS experiment at LHC is currently stored only in custom online databases, from which it is built on-the- y on request. Accessing the online geometry guarantees accessing the latest version of the detector description, but requires the setup of the full ATLAS so ware framework “Athena”, which provides the online services and the tools to retrieve the data from the database. is operation is cumbersome and slows down the applications that need to access the geometry. Moreover, all applications that need to access the detector geom- etry need to be built and run on the same platform as the ATLAS framework, preventing the usage of the actual detector geometry in stand-alone applications. Here we propose a new mechanism to persistify and serve the geometry of HEP experiments. e new mechanism is composed by a new le format and a REST API. e new le format allows to store the whole detector description locally in a at le, and it is especially optimized to descri...

Folded three-spin string solutions in AdS5 x S5

International Nuclear Information System (INIS)

Ryang Shijong

2004-01-01

We construct a spinning closed string solution in AdS 5 x S 5 which is folded in the radial direction and has two equal spins in AdS 5 and a spin in S 5 . The energy expression of the three-spin solution specified by the folding and winding numbers for the small S 5 spin shows a logarithmic behavior and a one-third power behavior of the large total AdS 5 spin, in the long string and in the short string located near the boundary of AdS 5 respectively. It exhibits the non-regular expansion in the 't Hooft coupling constant, while it takes the regular one when the S 5 spin becomes large. (author)

Invariant differential operators and characters of the AdS4 algebra

International Nuclear Information System (INIS)

Dobrev, V K

2006-01-01

The aim of this paper is to apply systematically to AdS 4 some modern tools in the representation theory of Lie algebras which are easily generalized to the supersymmetric and quantum group settings and necessary for applications to string theory and integrable models. Here we introduce the necessary representations of the AdS 4 algebra and group. We give explicitly all singular (null) vectors of the reducible AdS 4 Verma modules. These are used to obtain the AdS 4 invariant differential operators. Using this we display a new structure-a diagram involving four partially equivalent reducible representations one of which contains all finite-dimensional irreps of the AdS 4 algebra. We study in more detail the cases involving UIRs, in particular, the Di and the Rac singletons, and the massless UIRs. In the massless case, we discover the structure of sets of 2s 0 - 1 conserved currents for each spin s 0 UIR, s 0 = 1, 3/2,.... All massless cases are contained in a one-parameter subfamily of the quartet diagrams mentioned above, the parameter being the spin s 0 . Further we give the classification of the so(5,C) irreps presented in a diagrammatic way which makes easy the derivation of all character formulae. The paper concludes with a speculation on the possible applications of the character formulae to integrable models

Implosions and hypertoric geometry

DEFF Research Database (Denmark)

Dancer, A.; Kirwan, F.; Swann, A.

2013-01-01

The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....

Granular flows in constrained geometries

Science.gov (United States)

Murthy, Tejas; Viswanathan, Koushik

Confined geometries are widespread in granular processing applications. The deformation and flow fields in such a geometry, with non-trivial boundary conditions, determine the resultant mechanical properties of the material (local porosity, density, residual stresses etc.). We present experimental studies of deformation and plastic flow of a prototypical granular medium in different nontrivial geometries- flat-punch compression, Couette-shear flow and a rigid body sliding past a granular half-space. These geometries represent simplified scaled-down versions of common industrial configurations such as compaction and dredging. The corresponding granular flows show a rich variety of flow features, representing the entire gamut of material types, from elastic solids (beam buckling) to fluids (vortex-formation, boundary layers) and even plastically deforming metals (dead material zone, pile-up). The effect of changing particle-level properties (e.g., shape, size, density) on the observed flows is also explicitly demonstrated. Non-smooth contact dynamics particle simulations are shown to reproduce some of the observed flow features quantitatively. These results showcase some central challenges facing continuum-scale constitutive theories for dynamic granular flows.

EVOLVE 2014 International Conference

CERN Document Server

Tantar, Emilia; Sun, Jian-Qiao; Zhang, Wei; Ding, Qian; Schütze, Oliver; Emmerich, Michael; Legrand, Pierrick; Moral, Pierre; Coello, Carlos

2014-01-01

This volume encloses research articles that were presented at the EVOLVE 2014 International Conference in Beijing, China, July 1–4, 2014.The book gathers contributions that emerged from the conference tracks, ranging from probability to set oriented numerics and evolutionary computation; all complemented by the bridging purpose of the conference, e.g. Complex Networks and Landscape Analysis, or by the more application oriented perspective. The novelty of the volume, when considering the EVOLVE series, comes from targeting also the practitioner’s view. This is supported by the Machine Learning Applied to Networks and Practical Aspects of Evolutionary Algorithms tracks, providing surveys on new application areas, as in the networking area and useful insights in the development of evolutionary techniques, from a practitioner’s perspective. Complementary to these directions, the conference tracks supporting the volume, follow on the individual advancements of the subareas constituting the scope of the confe...

An AdS3 dual for minimal model CFTs

International Nuclear Information System (INIS)

Gaberdiel, Matthias R.; Gopakumar, Rajesh

2011-01-01

We propose a duality between the 2d W N minimal models in the large N't Hooft limit, and a family of higher spin theories on AdS 3 . The 2d conformal field theories (CFTs) can be described as Wess-Zumino-Witten coset models, and include, for N=2, the usual Virasoro unitary series. The dual bulk theory contains, in addition to the massless higher spin fields, two complex scalars (of equal mass). The mass is directly related to the 't Hooft coupling constant of the dual CFT. We give convincing evidence that the spectra of the two theories match precisely for all values of the 't Hooft coupling. We also show that the renormalization group flows in the 2d CFT agree exactly with the usual AdS/CFT prediction of the gravity theory. Our proposal is in many ways analogous to the Klebanov-Polyakov conjecture for an AdS 4 dual for the singlet sector of large N vector models.

AdS pure spinor superstring in constant backgrounds

International Nuclear Information System (INIS)

Chandia, Osvaldo; Bevilaqua, L. Ibiapina; Vallilo, Brenno Carlini

2014-01-01

In this paper we study the pure spinor formulation of the superstring in AdS_5×S"5 around point particle solutions of the classical equations of motion. As a particular example we quantize the pure spinor string in the BMN background

A vector space approach to geometry

CERN Document Server

Hausner, Melvin

2010-01-01

The effects of geometry and linear algebra on each other receive close attention in this examination of geometry's correlation with other branches of math and science. In-depth discussions include a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.

Integral geometry and valuations

CERN Document Server

Solanes, Gil

2014-01-01

Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...

CBM RICH geometry optimization

Energy Technology Data Exchange (ETDEWEB)

Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration

2016-07-01

The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.

Smoothed transitions in higher spin AdS gravity

International Nuclear Information System (INIS)

Banerjee, Shamik; Shenker, Stephen; Castro, Alejandra; Hellerman, Simeon; Hijano, Eliot; Lepage-Jutier, Arnaud; Maloney, Alexander

2013-01-01

We consider CFTs conjectured to be dual to higher spin theories of gravity in AdS 3 and AdS 4 . Two-dimensional CFTs with W N symmetry are considered in the λ = 0 (k → ∞) limit where they are conjectured to be described by continuous orbifolds. The torus partition function is computed, using reasonable assumptions, and equals that of a free-field theory. We find no phase transition at temperatures of order 1; the usual Hawking–Page phase transition is removed by the highly degenerate light states associated with conical defect states in the bulk. Three-dimensional Chern–Simons matter CFTs with vector-like matter are considered on T 3 , where the dynamics is described by an effective theory for the eigenvalues of the holonomies. Likewise, we find no evidence for a Hawking–Page phase transition at a large level k. (paper)

Riemannian geometry

CERN Document Server

Petersen, Peter

2016-01-01

Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...

Kaehler geometry and SUSY mechanics

International Nuclear Information System (INIS)

Bellucci, Stefano; Nersessian, Armen

2001-01-01

We present two examples of SUSY mechanics related with Kaehler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kaehler manifold. The relation of these models with antisymplectic geometry is discussed

GPS: Geometry, Probability, and Statistics

Science.gov (United States)

Field, Mike

2012-01-01

It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…

FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS

Energy Technology Data Exchange (ETDEWEB)

Singer, Isadore M.

2008-03-04

The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.

Final Report: Geometry And Elementary Particle Physics

International Nuclear Information System (INIS)

Singer, Isadore M.

2008-01-01

The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.

Shock wave collisions and thermalization in AdS5

International Nuclear Information System (INIS)

Kovchegov, Yuri V.

2011-01-01

We study heavy ion collisions at strong 't Hooft coupling using AdS/CFT correspondence. According to the AdS/CFT dictionary heavy ion collisions correspond to gravitational shock wave collisions in AdS 5 . We construct the metric in the forward light cone after the collision perturbatively through expansion of Einstein equations in graviton exchanges. We obtain an analytic expression for the metric including all-order graviton exchanges with one shock wave, while keeping the exchanges with another shock wave at the lowest order. We read off the corresponding energy-momentum tensor of the produced medium. Unfortunately this energy-momentum tensor does not correspond to ideal hydrodynamics, indicating that higher order graviton exchanges are needed to construct the full solution of the problem. We also show that shock waves must completely stop almost immediately after the collision in AdS 5 , which, on the field theory side, corresponds to complete nuclear stopping due to strong coupling effects, likely leading to Landau hydrodynamics. Finally, we perform trapped surface analysis of the shock wave collisions demonstrating that a bulk black hole, corresponding to ideal hydrodynamics on the boundary, has to be created in such collisions, thus constructing a proof of thermalization in heavy ion collisions at strong coupling. (author)

Discrete quantum geometries and their effective dimension

International Nuclear Information System (INIS)

Thuerigen, Johannes

2015-01-01

In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension d on low energy scales to a real number between 0 and d on high energy scales. In the particular case of 1 these results allow to understand the quantum geometry as effectively fractal.

Mentoring: An Evolving Relationship.

Science.gov (United States)

Block, Michelle; Florczak, Kristine L

2017-04-01

The column concerns itself with mentoring as an evolving relationship between mentor and mentee. The collegiate mentoring model, the transformational transcendence model, and the humanbecoming mentoring model are considered in light of a dialogue with mentors at a Midwest university and conclusions are drawn.

Nonsynonymous substitution rate (Ka is a relatively consistent parameter for defining fast-evolving and slow-evolving protein-coding genes

Directory of Open Access Journals (Sweden)

Wang Lei

2011-02-01

Full Text Available Abstract Background Mammalian genome sequence data are being acquired in large quantities and at enormous speeds. We now have a tremendous opportunity to better understand which genes are the most variable or conserved, and what their particular functions and evolutionary dynamics are, through comparative genomics. Results We chose human and eleven other high-coverage mammalian genome data–as well as an avian genome as an outgroup–to analyze orthologous protein-coding genes using nonsynonymous (Ka and synonymous (Ks substitution rates. After evaluating eight commonly-used methods of Ka and Ks calculation, we observed that these methods yielded a nearly uniform result when estimating Ka, but not Ks (or Ka/Ks. When sorting genes based on Ka, we noticed that fast-evolving and slow-evolving genes often belonged to different functional classes, with respect to species-specificity and lineage-specificity. In particular, we identified two functional classes of genes in the acquired immune system. Fast-evolving genes coded for signal-transducing proteins, such as receptors, ligands, cytokines, and CDs (cluster of differentiation, mostly surface proteins, whereas the slow-evolving genes were for function-modulating proteins, such as kinases and adaptor proteins. In addition, among slow-evolving genes that had functions related to the central nervous system, neurodegenerative disease-related pathways were enriched significantly in most mammalian species. We also confirmed that gene expression was negatively correlated with evolution rate, i.e. slow-evolving genes were expressed at higher levels than fast-evolving genes. Our results indicated that the functional specializations of the three major mammalian clades were: sensory perception and oncogenesis in primates, reproduction and hormone regulation in large mammals, and immunity and angiotensin in rodents. Conclusion Our study suggests that Ka calculation, which is less biased compared to Ks and Ka

Interactively Evolving Compositional Sound Synthesis Networks

DEFF Research Database (Denmark)

Jónsson, Björn Þór; Hoover, Amy K.; Risi, Sebastian

2015-01-01

the space of potential sounds that can be generated through such compositional sound synthesis networks (CSSNs). To study the effect of evolution on subjective appreciation, participants in a listener study ranked evolved timbres by personal preference, resulting in preferences skewed toward the first......While the success of electronic music often relies on the uniqueness and quality of selected timbres, many musicians struggle with complicated and expensive equipment and techniques to create their desired sounds. Instead, this paper presents a technique for producing novel timbres that are evolved...

Evolving effective incremental SAT solvers with GP

OpenAIRE

Bader, Mohamed; Poli, R.

2008-01-01

Hyper-Heuristics could simply be defined as heuristics to choose other heuristics, and it is a way of combining existing heuristics to generate new ones. In a Hyper-Heuristic framework, the framework is used for evolving effective incremental (Inc*) solvers for SAT. We test the evolved heuristics (IncHH) against other known local search heuristics on a variety of benchmark SAT problems.

Introduction into integral geometry and stereology

DEFF Research Database (Denmark)

Kiderlen, Markus

Statistics and Random Fields and is a self-containing introduction into integral geometry and its applications in stereology. The most important integral geometric tools for stereological applications are kinematic formulas and results of Blaschke-Petkantschin type. Therefore, Crofton's formula......This text is the extended version of two talks held at the Summer Academy Stochastic Geometry, Spatial Statistics and Random Fields in the Soellerhaus, Germany, in September 2009. It forms (with slight modifications) a chapter of the Springer lecture notes Lectures on Stochastic Geometry, Spatial...

AdS3/CFT2, finite-gap equations and massless modes

International Nuclear Information System (INIS)

Lloyd, Thomas; Stefański, Bogdan Jr.

2014-01-01

It is known that string theory on AdS 3 ×M 7 backgrounds, where M 7 =S 3 ×S 3 ×S 1 or S 3 ×T 4 , is classically integrable. This integrability has been previously used to write down a set of integral equations, known as the finite-gap equations. These equations can be solved for the closed string spectrum of the theory. However, it has been known for some time that the finite-gap equations on these AdS 3 ×M 7 backgrounds do not capture the dynamics of the massless modes of the closed string theory. In this paper we re-examine the derivation of the AdS 3 ×M 7 finite-gap system. We find that the conditions that had previously been imposed on these integral equations in order to implement the Virasoro constraints are too strict, and are in fact not required. We identify the correct implementation of the Virasoro constraints on finite-gap equations and show that this new, less restrictive condition captures the complete closed string spectrum on AdS 3 ×M 7

Surrogate Modeling for Geometry Optimization

DEFF Research Database (Denmark)

Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie

2009-01-01

A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....

Winding strings in AdS3

International Nuclear Information System (INIS)

Herscovich, Estanislao; Minces, Pablo; Nunez, Carmen

2006-01-01

Correlation functions of one-unit spectral flowed states in string theory on AdS 3 are considered. We present the modified Knizhnik-Zamolodchikov and null vector equations to be satisfied by amplitudes containing states in winding sector one and study their solution corresponding to the four point function including one w = 1 field. We compute the three point function involving two one-unit spectral flowed operators and find expressions for amplitudes of three w = 1 states satisfying certain particular relations among the spins of the fields. Several consistency checks are performed

Geometric control theory and sub-Riemannian geometry

CERN Document Server

Boscain, Ugo; Gauthier, Jean-Paul; Sarychev, Andrey; Sigalotti, Mario

2014-01-01

This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as  sub-Riemannian, Finslerian  geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods  has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group  of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.

Special metrics and group actions in geometry

CERN Document Server

Fino, Anna; Musso, Emilio; Podestà, Fabio; Vezzoni, Luigi

2017-01-01

The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.

January: IBM 7094 programme for the resolution of cell problems in planar, spherical and cylindrical geometry using the double P{sub n} approximation; Janvier: programme de resolution sur IBM 7094 des problemes de cellules en geometrie plane, spherique et cylindrique dans l'approximation double P{sub n}

Energy Technology Data Exchange (ETDEWEB)

Amouyal, A; Tariel, H [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1966-07-01

Code name: January 1{sup st} SCEA 011S. 2) Computer: IBM 7094; Programme system: Fortran II, 2{sup nd} version. 3) Nature of the problem: resolution of cell problems with one space variable (planar, spherical and cylindrical geometries) and with one energy group, with isotropic sources in the double P{sub n} approximation (DP 1 and DP 3 approximation in planar and spherical geometries, DP 1 and DP 2 in cylindrical geometry). 4) Method used: the differential equations with limiting conditions are transformed into differential system with initial conditions which are integrated by a separate-step method. 5) Restrictions: number of physical media < 100, number of geometrical regions < 100, number of points < 1000. 6) Physical approximations: limiting conditions for reflection, black body or grey body (restrictions for spherical and cylindrical geometries). The diffusion can include an isotropy term in cylindrical geometry, 2 terms in the other geometries. Taking into account of macroscopic data. 7) Duration: calculation time for a network of 100 points: planar and spherical geometry: double P 1 1 second, D P 3 = 4 seconds; cylindrical geometry: double P 1 2 seconds, D P 2 = 4 seconds. To these times should be added the 3 seconds required for the output. 8) State of the programme under production. (authors) [French] 1) Nom du Code: Janvier 1 SCEA 011S. 2) Calculateur: IBM 7094; Systeme de programmation: Fortran II version-2. 3) Nature du probleme: resolution des problemes de cellule a une variable d'espace (geometries plane, spherique et cylindrique) et un groupe d'energie, avec sources isotropes, dans l'approxirnation double P{sub n} (Approximations DP 1 et DP 3 en geometrie plane et spherique, approximations DP 1 et DP 2 en geometrie cylindrique). Methode employee: les equations differentielles avec conditions aux limites sont transformees en systemes differentiels avec conditions initiales que l'on integre par une methode a pas separes. 5) Restrictions: nombre de

Guide to Computational Geometry Processing

DEFF Research Database (Denmark)

Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François

be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction...... to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages. Topics and features: Presents an overview of the underlying mathematical theory, covering vector spaces......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...

A Whirlwind Tour of Computational Geometry.

Science.gov (United States)

Graham, Ron; Yao, Frances

1990-01-01

Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)

Black hole formation in AdS Einstein-Gauss-Bonnet gravity

Energy Technology Data Exchange (ETDEWEB)

Deppe, Nils [Cornell Center for Astrophysics and Planetary Science andDepartment of Physics, Cornell University,122 Sciences Drive, Ithaca, New York 14853 (United States); Kolly, Allison [Department of Atmospheric and Oceanic Sciences, McGill University,805 Sherbrooke Street West, Montréal, Québec H3A 0B9 (Canada); Frey, Andrew R.; Kunstatter, Gabor [Department of Physics and Winnipeg Institute for Theoretical Physics, University of Winnipeg,515 Portage Avenue, Winnipeg, Manitoba R3B 2E9 (Canada)

2016-10-17

AdS spacetime has been shown numerically to be unstable against a large class of arbitrarily small perturbations. In http://dx.doi.org/10.1103/PhysRevLett.114.071102, the authors presented a preliminary study of the effects on stability of changing the local dynamics by adding a Gauss-Bonnet term to the Einstein action. Here we provide further details as well as new results with improved numerical methods. In particular, we elucidate new structure in Choptuik scaling plots. We also provide evidence of chaotic behavior at the transition between immediate horizon formation and horizon formation after the matter pulse reflects from the AdS conformal boundary. Finally, we present data suggesting the formation of naked singularities in spacetimes with ADM mass below the algebraic bound for black hole formation.

Internet Advertising. Google AdWords versus Facebook Ads

OpenAIRE

Paul PAŞCU

2014-01-01

This article describes how to use the applications for Internet advertising, Google AdWords and Facebook Ads. Our attempt is to present the advantages and disadvantages of each of them, the costs and benefits, a useful aspect for companies that plan to start advertising campaigns on the Internet.

Monte Carlo simulation of fully Markovian stochastic geometries

International Nuclear Information System (INIS)

Lepage, Thibaut; Delaby, Lucie; Malvagi, Fausto; Mazzolo, Alain

2010-01-01

The interest in resolving the equation of transport in stochastic media has continued to increase these last years. For binary stochastic media it is often assumed that the geometry is Markovian, which is never the case in usual environments. In the present paper, based on rigorous mathematical theorems, we construct fully two-dimensional Markovian stochastic geometries and we study their main properties. In particular, we determine a percolation threshold p c , equal to 0.586 ± 0.0015 for such geometries. Finally, Monte Carlo simulations are performed through these geometries and the results compared to homogeneous geometries. (author)

Tidal stresses and energy gaps in microstate geometries

Science.gov (United States)

Tyukov, Alexander; Walker, Robert; Warner, Nicholas P.

2018-02-01

We compute energy gaps and study infalling massive geodesic probes in the new families of scaling, microstate geometries that have been constructed recently and for which the holographic duals are known. We find that in the deepest geometries, which have the lowest energy gaps, the geodesic deviation shows that the stress reaches the Planck scale long before the probe reaches the cap of the geometry. Such probes must therefore undergo a stringy transition as they fall into microstate geometry. We discuss the scales associated with this transition and comment on the implications for scrambling in microstate geometries.

VIII International Meeting on Lorentzian Geometry

CERN Document Server

Flores, José; Palomo, Francisco; GeLoMa 2016; Lorentzian geometry and related topics

2017-01-01

This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime. In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathem...

Transformational plane geometry

CERN Document Server

Umble, Ronald N

2014-01-01

Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...

Fractal geometry mathematical foundations and applications

CERN Document Server

Falconer, Kenneth

2013-01-01

The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals.  The book introduces and develops the general theory and applica

Evolving Intelligent Systems Methodology and Applications

CERN Document Server

Angelov, Plamen; Kasabov, Nik

2010-01-01

From theory to techniques, the first all-in-one resource for EIS. There is a clear demand in advanced process industries, defense, and Internet and communication (VoIP) applications for intelligent yet adaptive/evolving systems. Evolving Intelligent Systems is the first self- contained volume that covers this newly established concept in its entirety, from a systematic methodology to case studies to industrial applications. Featuring chapters written by leading world experts, it addresses the progress, trends, and major achievements in this emerging research field, with a strong emphasis on th

Stability of warped AdS3 vacua of topologically massive gravity

International Nuclear Information System (INIS)

Anninos, Dionysios; Esole, Mboyo; Guica, Monica

2009-01-01

AdS 3 vacua of topologically massive gravity (TMG) have been shown to be perturbatively unstable for all values of the coupling constant except the chiral point μl = 1. We study the possibility that the warped vacua of TMG, which exist for all values of μ, are stable under linearized perturbations. In this paper, we show that spacelike warped AdS 3 vacua with Compere-Detournay boundary conditions are indeed stable in the range μl>3. This is precisely the range in which black hole solutions arise as discrete identifications of the warped AdS 3 vacuum. The situation somewhat resembles chiral gravity: although negative energy modes do exist, they are all excluded by the boundary conditions, and the perturbative spectrum solely consists of boundary (pure large gauge) gravitons.

Planning for Evolution in a Production Environment: Migration from a Legacy Geometry Code to an Abstract Geometry Modeling Language in STAR

Science.gov (United States)

Webb, Jason C.; Lauret, Jerome; Perevoztchikov, Victor

2012-12-01

Increasingly detailed descriptions of complex detector geometries are required for the simulation and analysis of today's high-energy and nuclear physics experiments. As new tools for the representation of geometry models become available during the course of an experiment, a fundamental challenge arises: how best to migrate from legacy geometry codes developed over many runs to the new technologies, such as the ROOT/TGeo [1] framework, without losing touch with years of development, tuning and validation. One approach, which has been discussed within the community for a number of years, is to represent the geometry model in a higher-level language independent of the concrete implementation of the geometry. The STAR experiment has used this approach to successfully migrate its legacy GEANT 3-era geometry to an Abstract geometry Modelling Language (AgML), which allows us to create both native GEANT 3 and ROOT/TGeo implementations. The language is supported by parsers and a C++ class library which enables the automated conversion of the original source code to AgML, supports export back to the original AgSTAR[5] representation, and creates the concrete ROOT/TGeo geometry implementation used by our track reconstruction software. In this paper we present our approach, design and experience and will demonstrate physical consistency between the original AgSTAR and new AgML geometry representations.

Three dimensional modeling of depositional geometries. A case study from Tofane Group (Dolomites, Italy).

Science.gov (United States)

Gattolin, G.; Franceschi, M.; Breda, A.; Teza, G.; Preto, N.

2012-04-01

At the end of the Early Carnian, the Carnian Pluvial Event (CPE) resulted in a major crisis of carbonate factories. The sharp change in carbonate production lead to a dramatic modifications in depositional geometries. Steep clinoforms of the high-relief pre-crisis carbonate platforms were replaced by low-angle ramps. Spatial characters of depositional geometries can be decisive in identifying the genesis of geological bodies. We here show how 3D modeling techniques can be applied to help in quantifying and highlighting their variations. As case study we considered two outcrops in the Tofane Group (Dolomites, Italy). The first outcrop (bottom of southern walls of Tofana di Rozes) exposes a platform-to-basin transect of pre- and post-crisis platforms, the second (Dibona hut) a clinostratified carbonate body deposited during the Carnian crisis. Outcrop conditions at both sites, with vertical and hardly accessible walls, make the field tracing of depositional geometries particularly challenging. Line drawing on high resolution pictures can help (e.g. for clinoforms), but its use for quantification is hampered by perspective deformation. Three dimensional acquisition and modeling allow to retrieve the true spatial characters of sedimentary bodies in these outcrops. The geometry of the carbonate body at Dibona (~ 15000 sqm) was acquired with terrestrial LiDAR, while for Tofana photogrammetric techniques were applied because of the extension of the outcrop itself (~ 240000 sqm) and the lack of suitable points of view for terrestrial laser scanning. At Tofana, field observations reveal the presence of tens-hundreds m large carbonate mounds grown on a pre-existing inclined surface, intercalated with skeletal carbonates and siltites-arenites. This system rapidly evolves into a carbonate-clastic ramp. Photogrammetric topography acquisition permitted to place and visualize geological features in a three dimensional frame, thus obtaining a conceptual sedimentological model. A 3

Internet Advertising. Google AdWords versus Facebook Ads

Directory of Open Access Journals (Sweden)

Paul PAŞCU

2014-05-01

Full Text Available This article describes how to use the applications for Internet advertising, Google AdWords and Facebook Ads. Our attempt is to present the advantages and disadvantages of each of them, the costs and benefits, a useful aspect for companies that plan to start advertising campaigns on the Internet.

MIFT: GIFT Combinatorial Geometry Input to VCS Code

Science.gov (United States)

1977-03-01

r-w w-^ H ^ß0318is CQ BRL °RCUMr REPORT NO. 1967 —-S: ... MIFT: GIFT COMBINATORIAL GEOMETRY INPUT TO VCS CODE Albert E...TITLE (and Subtitle) MIFT: GIFT Combinatorial Geometry Input to VCS Code S. TYPE OF REPORT & PERIOD COVERED FINAL 6. PERFORMING ORG. REPORT NUMBER...Vehicle Code System (VCS) called MORSE was modified to accept the GIFT combinatorial geometry package. GIFT , as opposed to the geometry package

Methods Evolved by Observation

Science.gov (United States)

Montessori, Maria

2016-01-01

Montessori's idea of the child's nature and the teacher's perceptiveness begins with amazing simplicity, and when she speaks of "methods evolved," she is unveiling a methodological system for observation. She begins with the early childhood explosion into writing, which is a familiar child phenomenon that Montessori has written about…

Physical meaning of the optical reference geometry

International Nuclear Information System (INIS)

Abramowicz, M.A.

1990-09-01

I show that contrary to a popular misconception the optical reference geometry, introduced a few years ago as a formally possible metric of a 3-space corresponding to a static spacetime, is quite satisfactory also from the physical point of view. The optical reference geometry has a clear physical meaning, as it may be constructed experimentally by measuring light round travel time between static observers. Distances and directions in the optical reference geometry are more strongly connected to experiment than distances and directions in the widely used directly projected metric (discussed e.g. in Landau and Lifshitz textbook. In addition, the optical reference geometry is more natural and convenient than the directly projected one in application to dynamics. In the optical geometry dynamical behaviour of matter is described by concepts and formulae identical to those well known in Newtonian dynamics on a given two dimensional (curved) surface. (author). 22 refs

What's the point? Hole-ography in Poincare AdS

International Nuclear Information System (INIS)

Espindola, Ricardo; Gueijosa, Alberto; Landetta, Alberto; Pedraza, Juan F.

2018-01-01

In the context of the AdS/CFT correspondence, we study bulk reconstruction of the Poincare wedge of AdS 3 via hole-ography, i.e., in terms of differential entropy of the dual CFT 2 . Previous work had considered the reconstruction of closed or open spacelike curves in global AdS, and of infinitely extended spacelike curves in Poincare AdS that are subject to a periodicity condition at infinity. Working first at constant time, we find that a closed curve in Poincare is described in the CFT by a family of intervals that covers the spatial axis at least twice. We also show how to reconstruct open curves, points and distances, and obtain a CFT action whose extremization leads to bulk points. We then generalize all of these results to the case of curves that vary in time, and discover that generic curves have segments that cannot be reconstructed using the standard hole-ographic construction. This happens because, for the nonreconstructible segments, the tangent geodesics fail to be fully contained within the Poincare wedge. We show that a previously discovered variant of the hole-ographic method allows us to overcome this challenge, by reorienting the geodesics touching the bulk curve to ensure that they all remain within the wedge. Our conclusion is that all spacelike curves in Poincare AdS can be completely reconstructed with CFT data, and each curve has in fact an infinite number of representations within the CFT. (orig.)

Recommendations by NACP for accurate treatment geometry specification

International Nuclear Information System (INIS)

Aaltonen, P.

1995-01-01

An investigation among the Nordic radiotherapy centres in 1991 confirmed that inconsistent use of dose and volume concepts is jeopardizing the high standard of radiation therapy. A Nordic working group was set up by NACP to standardize the concepts and quantities used throughout the whole radiation process. Now the draft report 'Specification of Dose Delivery in Radiation Therapy' is discussed with the radiotherapy community. The recent ICRU 50 report is the first step towards a uniform terminology and procedure at all radiotherapy centres. The new NACP report will be an important and more detailed addition for level 2-3 radiotherapy clinics and it will be specially adopted to the situation at the Nordic centres as well as other well equipped centres. The aim has been to recommend the use of concepts based on recent scientific development in the field of radiation therapy which are needed for the development of daily clinical practice. The terms and concepts for treatment geometry have been chosen by separating the concepts of tissues and volumes inside a patient. The tissues can be fixed in the coordinate system of the patient by adding a margin around them. This margin accounts for the movements of the tissues of interest inside the patient. The outer boundary of this margin is then encompassing the Strict Target Volume or Organ at Risk Volume which are fixed in the patient coordinate system. The set-up uncertainties of the patient in relation to the beams are considered during treatment planning by adding set-up margins to the beams

Transformasi Geometri Rotasi Berbantuan Software Geogebra

Directory of Open Access Journals (Sweden)

Muhamad Hanafi

2018-02-01

Full Text Available Penelitian  ini bertujuan untuk membantu visualisasi dan menemukan konsep pada Transformasi geometri Rotasi di titik Pusat  dengan menggunakan software GeoGebra. Penelitian ini mengulas tentang Koordinat Kartesius dan Polar, dan selanjutntya Transformasi geometri Rotasi di titik Pusat .

Algebra, Geometry and Mathematical Physics Conference

CERN Document Server

Paal, Eugen; Silvestrov, Sergei; Stolin, Alexander

2014-01-01

This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers a...

Homological mirror symmetry and tropical geometry

CERN Document Server

Catanese, Fabrizio; Kontsevich, Maxim; Pantev, Tony; Soibelman, Yan; Zharkov, Ilia

2014-01-01

The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory, and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Ge...

Use of information technologies in teaching course "Analytical geometry" in higher schools on example of software "ANALYTICAL GEOMETRY"

OpenAIRE

V. B. Grigorieva

2009-01-01

In article are considered the methodical questions of using of computer technologies, for example, the software "Analytical geometry", in process of teaching course of analytical geometry in the higher school.

Evolving artificial metalloenzymes via random mutagenesis

Science.gov (United States)

Yang, Hao; Swartz, Alan M.; Park, Hyun June; Srivastava, Poonam; Ellis-Guardiola, Ken; Upp, David M.; Lee, Gihoon; Belsare, Ketaki; Gu, Yifan; Zhang, Chen; Moellering, Raymond E.; Lewis, Jared C.

2018-03-01

Random mutagenesis has the potential to optimize the efficiency and selectivity of protein catalysts without requiring detailed knowledge of protein structure; however, introducing synthetic metal cofactors complicates the expression and screening of enzyme libraries, and activity arising from free cofactor must be eliminated. Here we report an efficient platform to create and screen libraries of artificial metalloenzymes (ArMs) via random mutagenesis, which we use to evolve highly selective dirhodium cyclopropanases. Error-prone PCR and combinatorial codon mutagenesis enabled multiplexed analysis of random mutations, including at sites distal to the putative ArM active site that are difficult to identify using targeted mutagenesis approaches. Variants that exhibited significantly improved selectivity for each of the cyclopropane product enantiomers were identified, and higher activity than previously reported ArM cyclopropanases obtained via targeted mutagenesis was also observed. This improved selectivity carried over to other dirhodium-catalysed transformations, including N-H, S-H and Si-H insertion, demonstrating that ArMs evolved for one reaction can serve as starting points to evolve catalysts for others.

Variable geometry Darrieus wind machine

Science.gov (United States)

Pytlinski, J. T.; Serrano, D.

1983-08-01

A variable geometry Darrieus wind machine is proposed. The lower attachment of the blades to the rotor can move freely up and down the axle allowing the blades of change shape during rotation. Experimental data for a 17 m. diameter Darrieus rotor and a theoretical model for multiple streamtube performance prediction were used to develop a computer simulation program for studying parameters that affect the machine's performance. This new variable geometry concept is described and interrelated with multiple streamtube theory through aerodynamic parameters. The computer simulation study shows that governor behavior of a Darrieus turbine can not be attained by a standard turbine operating within normally occurring rotational velocity limits. A second generation variable geometry Darrieus wind turbine which uses a telescopic blade is proposed as a potential improvement on the studied concept.

Flux compactifications and generalized geometries

International Nuclear Information System (INIS)

Grana, Mariana

2006-01-01

Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T 6 /(Z 3 x Z 3 ) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry

Flux compactifications and generalized geometries

Energy Technology Data Exchange (ETDEWEB)

Grana, Mariana [Service de Physique Theorique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex (France)

2006-11-07

Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T{sup 6} /(Z{sub 3} x Z{sub 3}) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry.

Predicting AD conversion

DEFF Research Database (Denmark)

Liu, Yawu; Mattila, Jussi; Ruiz, Miguel �ngel Mu�oz

2013-01-01

To compare the accuracies of predicting AD conversion by using a decision support system (PredictAD tool) and current research criteria of prodromal AD as identified by combinations of episodic memory impairment of hippocampal type and visual assessment of medial temporal lobe atrophy (MTA) on MRI...

Rehme correlation for spacer pressure drop compared to XT-ADS rod bundle simulations and water experiment

International Nuclear Information System (INIS)

Batta, A.; Class, A.; Litfin, K.; Wetzel, T.

2011-01-01

The Rehme correlation is the most common formula to estimate the pressure drop of spacers in the design phase of new bundle geometries. It is based on considerations of momentum losses and takes into account the obstruction of the flow cross section but it ignores the geometric details of the spacer design. Within the framework of accelerator driven sub-critical reactor systems (ADS), heavy-liquid-metal (HLM) cooled fuel assemblies are considered. At the KArlsruhe Liquid metal LAboratory (KALLA) of the Karlsruhe Institute of Technology a series of experiments to quantify both pressure losses and heat transfer in HLM-cooled rod bundles are performed. The present study compares simulation results obtained with the commercial CFD code Star-CCM to experiments and the Rehme correlation. It can be shown that the Rehme correlation, simulations and experiments all yield similar trends, but quantitative predictions can only be delivered by the CFD which takes into account the full geometric details of the spacer geometry. (orig.)

Holographic dual of de Sitter universe with AdS bubbles

International Nuclear Information System (INIS)

Kanno, Sugumi; Sasaki, Misao; Soda, Jiro

2012-01-01

We study the proposal that a de Sitter (dS) universe with an Anti-de Sitter (AdS) bubble can be replaced by a dS universe with a boundary CFT. To explore this duality, we consider incident gravitons coming from the dS universe through the bubble wall into the AdS bubble in the original picture. In the dual picture, this process has to be identified with the absorption of gravitons by CFT matter. We have obtained a general formula for the absorption probability in general d+1 spacetime dimensions. The result shows the different behavior depending on whether spacetime dimensions are even or odd. We find that the absorption process of gravitons from the dS universe by CFT matter is controlled by localized gravitons (massive bound state modes in the Kaluza-Klein decomposition) in the dS universe. The absorption probability is determined by the effective degrees of freedom of the CFT matter and the effective gravitational coupling constant which encodes information of localized gravitons. We speculate that the dual of (d+1)-dimensional dS universe with an AdS bubble is also dual to a d-dimensional dS universe with CFT matter.

The evolution of resource adaptation: how generalist and specialist consumers evolve.

Science.gov (United States)

Ma, Junling; Levin, Simon A

2006-07-01

Why and how specialist and generalist strategies evolve are important questions in evolutionary ecology. In this paper, with the method of adaptive dynamics and evolutionary branching, we identify conditions that select for specialist and generalist strategies. Generally, generalist strategies evolve if there is a switching benefit; specialists evolve if there is a switching cost. If the switching cost is large, specialists always evolve. If the switching cost is small, even though the consumer will first evolve toward a generalist strategy, it will eventually branch into two specialists.

Curvature tensor copies in affine geometry

International Nuclear Information System (INIS)

Srivastava, P.P.

1981-01-01

The sets of space-time and spin-connections which give rise to the same curvature tensor are constructed. The corresponding geometries are compared. Results are illustrated by an explicit calculation and comment on the copies in Einstein-Cartan and Weyl-Cartan geometries. (Author) [pt

Poisson geometry from a Dirac perspective

Science.gov (United States)

Meinrenken, Eckhard

2018-03-01

We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop Quantum Groups and Gravity at the University of Waterloo, April 2016.

Ranking in evolving complex networks

Science.gov (United States)

Liao, Hao; Mariani, Manuel Sebastian; Medo, Matúš; Zhang, Yi-Cheng; Zhou, Ming-Yang

2017-05-01

Complex networks have emerged as a simple yet powerful framework to represent and analyze a wide range of complex systems. The problem of ranking the nodes and the edges in complex networks is critical for a broad range of real-world problems because it affects how we access online information and products, how success and talent are evaluated in human activities, and how scarce resources are allocated by companies and policymakers, among others. This calls for a deep understanding of how existing ranking algorithms perform, and which are their possible biases that may impair their effectiveness. Many popular ranking algorithms (such as Google's PageRank) are static in nature and, as a consequence, they exhibit important shortcomings when applied to real networks that rapidly evolve in time. At the same time, recent advances in the understanding and modeling of evolving networks have enabled the development of a wide and diverse range of ranking algorithms that take the temporal dimension into account. The aim of this review is to survey the existing ranking algorithms, both static and time-aware, and their applications to evolving networks. We emphasize both the impact of network evolution on well-established static algorithms and the benefits from including the temporal dimension for tasks such as prediction of network traffic, prediction of future links, and identification of significant nodes.

Development of the geometry database for the CBM experiment

Science.gov (United States)

Akishina, E. P.; Alexandrov, E. I.; Alexandrov, I. N.; Filozova, I. A.; Friese, V.; Ivanov, V. V.

2018-01-01

The paper describes the current state of the Geometry Database (Geometry DB) for the CBM experiment. The main purpose of this database is to provide convenient tools for: (1) managing the geometry modules; (2) assembling various versions of the CBM setup as a combination of geometry modules and additional files. The CBM users of the Geometry DB may use both GUI (Graphical User Interface) and API (Application Programming Interface) tools for working with it.

SABRINA, Geometry Plot Program for MCNP

International Nuclear Information System (INIS)

SEIDL, Marcus

2003-01-01

1 - Description of program or function: SABRINA is an interactive, three-dimensional, geometry-modeling code system, primarily for use with CCC-200/MCNP. SABRINA's capabilities include creation, visualization, and verification of three-dimensional geometries specified by either surface- or body-base combinatorial geometry; display of particle tracks are calculated by MCNP; and volume fraction generation. 2 - Method of solution: Rendering is performed by ray tracing or an edge and intersection algorithm. Volume fraction calculations are made by ray tracing. 3 - Restrictions on the complexity of the problem: A graphics display with X Window capability is required

Differential geometry and topology of curves

CERN Document Server

Animov, Yu

2001-01-01

Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates problems for special classes of curves and gives the working method used to obtain the conditions for closed polygonal curves. The proof of the Bakel-Werner theorem in conditions of boundedness for curves with periodic curvature and torsion is also presented. This volume also highlights the contributions made by great geometers. past and present, to differential geometry and the topology of curves.

The Mixed Phase of Charged AdS Black Holes

Directory of Open Access Journals (Sweden)

Piyabut Burikham

2016-01-01

Full Text Available We study the mixed phase of charged AdS black hole and radiation when the total energy is fixed below the threshold to produce a stable charged black hole branch. The coexistence conditions for the charged AdS black hole and radiation are derived for the generic case when radiation particles carry charge. The phase diagram of the mixed phase is demonstrated for both fixed potential and charge ensemble. In the dual gauge picture, they correspond to the mixed phase of quark-gluon plasma (QGP and hadron gas in the fixed chemical potential and density ensemble, respectively. In the nuclei and heavy-ion collisions at intermediate energies, the mixed phase of exotic QGP and hadron gas could be produced. The mixed phase will condense and evaporate into the hadron gas as the fireball expands.

Geometry of surfaces a practical guide for mechanical engineers

CERN Document Server

Radzevich, Stephen P

2012-01-01

Presents an in-depth analysis of geometry of part surfaces and provides the tools for solving complex engineering problems Geometry of Surfaces: A Practical Guide for Mechanical Engineers is a comprehensive guide to applied geometry of surfaces with focus on practical applications in various areas of mechanical engineering. The book is divided into three parts on Part Surfaces, Geometry of Contact of Part Surfaces and Mapping of the Contacting Part Surfaces. Geometry of Surfaces: A Practical Guide for Mechanical Engineers combines differential geometry and gearing theory and presents new developments in the elementary theory of enveloping surfaces. Written by a leading expert of the field, this book also provides the reader with the tools for solving complex engineering problems in the field of mechanical engineering. Presents an in-depth analysis of geometry of part surfaces Provides tools for solving complex engineering problems in the field of mechanical engineering Combines differential geometry an...

Adaptation of Escherichia coli to glucose promotes evolvability in lactose.

Science.gov (United States)

Phillips, Kelly N; Castillo, Gerardo; Wünsche, Andrea; Cooper, Tim F

2016-02-01

The selective history of a population can influence its subsequent evolution, an effect known as historical contingency. We previously observed that five of six replicate populations that were evolved in a glucose-limited environment for 2000 generations, then switched to lactose for 1000 generations, had higher fitness increases in lactose than populations started directly from the ancestor. To test if selection in glucose systematically increased lactose evolvability, we started 12 replay populations--six from a population subsample and six from a single randomly selected clone--from each of the six glucose-evolved founder populations. These replay populations and 18 ancestral populations were evolved for 1000 generations in a lactose-limited environment. We found that replay populations were initially slightly less fit in lactose than the ancestor, but were more evolvable, in that they increased in fitness at a faster rate and to higher levels. This result indicates that evolution in the glucose environment resulted in genetic changes that increased the potential of genotypes to adapt to lactose. Genome sequencing identified four genes--iclR, nadR, spoT, and rbs--that were mutated in most glucose-evolved clones and are candidates for mediating increased evolvability. Our results demonstrate that short-term selective costs during selection in one environment can lead to changes in evolvability that confer longer term benefits. © 2016 The Author(s). Evolution © 2016 The Society for the Study of Evolution.

GEOMETRY – AN IMPORTANT MEANS OF EDUCATION IN THE CIVILISATION SCOPE

OpenAIRE

Liliana TOCARIU, PhD

2017-01-01

Geometry (from the Greek: γεωμετρία; geo = earth, metria = measure) is a genuine science, rooted in mathematics, which studies the plane and spatial forms of bodies from the objective or conceptual reality and the nature of the relationship that exists between them. Due to its complexity, geometry is divided into: Euclidian geometry, analytical geometry, descriptive geometry, projective geometry, kinematic geometry, surface and curve differential geometry, axiomatic geometry,...

Geometry Effect Investigation on a Conical Chamber with Porous Media Boundary Condition Using Computational Fluid Dynamic (CFD Technique

Directory of Open Access Journals (Sweden)

Yazid Bindar

2009-11-01

Full Text Available The present study is an attempt to introduce the method for optimizing the geometry of the unit process. The comprehensive unit process performances are generated by a CFD engine. The CFD engine can simulate the unit process performances at what ever conditions. Both design geometry and operating variables weree used on the CFD simulation. The burden on a simplified process was taken out from CFD simulation. A complex geometry of a unit process is represented by a secondary reformer. A secondary reformer has a conical volume as a space to undergo the combustion reaction before entering the catalyst bed. This complexity is added by the boundary of the porous solid surface as the top surface of catalyst bed. The spread angle affect the flow pattern in side the conical volume having a porous solid surface as a base. The spread angle above 65o results the disappearing of the recirculation flow. The inlet distance from the porous solid surface also can exhibit different characteristics of recirculation flow. The closer the distance to the porous solid surface, the stronger the recirculation is. The inlet velocity values have no significant effect on the flow pattern. The introduction of a solid volume inside the geometry creates the distortion of the flow pattern. In the application, the inserted solid volume is equivalent to a burner. It means that the use of the burner inherently produces some problems of the flow distribution

Evolving fuzzy rules for relaxed-criteria negotiation.

Science.gov (United States)

Sim, Kwang Mong

2008-12-01

In the literature on automated negotiation, very few negotiation agents are designed with the flexibility to slightly relax their negotiation criteria to reach a consensus more rapidly and with more certainty. Furthermore, these relaxed-criteria negotiation agents were not equipped with the ability to enhance their performance by learning and evolving their relaxed-criteria negotiation rules. The impetus of this work is designing market-driven negotiation agents (MDAs) that not only have the flexibility of relaxing bargaining criteria using fuzzy rules, but can also evolve their structures by learning new relaxed-criteria fuzzy rules to improve their negotiation outcomes as they participate in negotiations in more e-markets. To this end, an evolutionary algorithm for adapting and evolving relaxed-criteria fuzzy rules was developed. Implementing the idea in a testbed, two kinds of experiments for evaluating and comparing EvEMDAs (MDAs with relaxed-criteria rules that are evolved using the evolutionary algorithm) and EMDAs (MDAs with relaxed-criteria rules that are manually constructed) were carried out through stochastic simulations. Empirical results show that: 1) EvEMDAs generally outperformed EMDAs in different types of e-markets and 2) the negotiation outcomes of EvEMDAs generally improved as they negotiated in more e-markets.

Random geometry and Yang-Mills theory

International Nuclear Information System (INIS)

Froehlich, J.

1981-01-01

The author states various problems and discusses a very few preliminary rigorous results in a branch of mathematics and mathematical physics which one might call random (or stochastic) geometry. Furthermore, he points out why random geometry is important in the quantization of Yang-Mills theory. (Auth.)

Quantification of variability in bedform geometry

NARCIS (Netherlands)

van der Mark, C.F.; Blom, Astrid; Hulscher, Suzanne J.M.H.

2008-01-01

We analyze the variability in bedform geometry in laboratory and field studies. Even under controlled steady flow conditions in laboratory flumes, bedforms are irregular in size, shape, and spacing, also in case of well-sorted sediment. Our purpose is to quantify the variability in bedform geometry.

Gauge theories from toric geometry and brane tilings

International Nuclear Information System (INIS)

Franco, Sebastian; Hanany, Amihay; Martelli, Dario; Sparks, James; Vegh, David; Wecht, Brian

2006-01-01

We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi-Yau singularity. Our method combines information from the geometry and topology of Sasaki-Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quantum numbers, and superpotential of a superconformal gauge theory on D3-branes probing a toric Calabi-Yau singularity can be deduced. The infinite family of toric singularities with known horizon Sasaki-Einstein manifolds L a,b,c is used to illustrate these ideas. We construct the corresponding quiver gauge theories, which may be fully specified by giving a tiling of the plane by hexagons with certain gluing rules. As checks of this construction, we perform a-maximisation as well as Z-minimisation to compute the exact R-charges of an arbitrary such quiver. We also examine a number of examples in detail, including the infinite subfamily L a,b,a , whose smallest member is the Suspended Pinch Point

DrawCompileEvolve: Sparking interactive evolutionary art with human creations

DEFF Research Database (Denmark)

Zhang, Jinhong; Taarnby, Rasmus; Liapis, Antonios

2015-01-01

This paper presents DrawCompileEvolve, a web-based drawing tool which allows users to draw simple primitive shapes, group them together or define patterns in their groupings (e.g. symmetry, repetition). The user’s vector drawing is then compiled into an indirectly encoded genetic representation......, which can be evolved interactively, allowing the user to change the image’s colors, patterns and ultimately transform it. The human artist has direct control while drawing the initial seed of an evolutionary run and indirect control while interactively evolving it, thus making DrawCompileEvolve a mixed...

10th China-Japan Geometry Conference

CERN Document Server

Miyaoka, Reiko; Tang, Zizhou; Zhang, Weiping

2016-01-01

Since the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincaré conjecture, the Yau–Tian–Donaldson conjecture, and the Willmore conjecture. There are still many important and challenging unsolved problems including, among others, the Strominger–Yau–Zaslow conjecture on mirror symmetry, the relative Yau–Tian–Donaldson conjecture in Kähler geometry, the Hopf conjecture, and the Yau conjecture on the first eigenvalue of an embedded minimal hypersurface of the sphere. For the younger generation to approach such problems and obtain the required techniques, it is of the utmost importance to provide them with up-to-date information from leading specialists. The geometry conference for the friendship of China and Japan has achieved this purpose during the past 10 years. Their talks deal with problems at the highest level, often accompanied with solutions and ideas, which extend across various fields in Riemannian geometry, sympl...

COMPETITIVE ACCRETION IN A SHEET GEOMETRY AND THE STELLAR IMF

International Nuclear Information System (INIS)

Hsu, Wen-Hsin; Hartmann, Lee; Heitsch, Fabian; Gomez, Gilberto C.

2010-01-01

We report a set of numerical experiments aimed at addressing the applicability of competitive accretion to explain the high-mass end of the stellar initial mass function in a sheet geometry with shallow gravitational potential, in contrast to most previous simulations which have assumed formation in a cluster gravitational potential. Our flat cloud geometry is motivated by models of molecular cloud formation due to large-scale flows in the interstellar medium. The experiments consisted of smoothed particle hydrodynamics simulations of gas accretion onto sink particles formed rapidly from Jeans-unstable dense clumps placed randomly in the finite sheet. These simplifications allow us to study accretion with a minimum of free parameters and to develop better statistics on the resulting mass spectra. We considered both clumps of equal mass and Gaussian distributions of masses and either uniform or spatially varying gas densities. In all cases, the sink mass function develops a power-law tail at high masses, with dN/dlog M ∝ M -Γ . The accretion rates of individual sinks follow M-dot ∝M 2 at high masses; this results in a continual flattening of the slope of the mass function toward an asymptotic form Γ ∼ 1 (where the Salpeter slope is Γ = 1.35). The asymptotic limit is most rapidly reached when starting from a relatively broad distribution of initial sink masses. In general, the resulting upper mass slope is correlated with the maximum sink mass; higher sink masses are found in simulations with flatter upper mass slopes. Although these simulations are of a highly idealized situation, the results suggest that competitive accretion may be relevant in a wider variety of environments than previously considered, and in particular that the upper mass distribution may generally evolve toward a limiting value of Γ ∼ 1.

Neutronics and shielding issues of ADS

International Nuclear Information System (INIS)

Abderrahim, H. A.; Aoust, T.; Haeck, W.; Malambu, E.; Van den Eynde, G.; Gonzalez, E.; Vicente, C.; Martinez-Val, J. M.; Romanets, Y.; Vaz, P.

2007-01-01

implementation and deployment have in common the fact that they raise cutting edge scientific and technological problems, associated to the operation of the high-intensity proton accelerator, the high-power (in the multi-MegaWatt range) delivered to the target and the material damage in the target and surrounding structures. The thermal power in the core, the thermal-hydraulic aspects associated to the heat removal in steady state and also in transient mode, the subcriticality level of the system and the efficiency of the transmutation process, is particularly sensitive to the core design (geometry, number of subassemblies, fuel composition, among many other aspects). Neutronic and shielding issues and the computation and mapping of neutron fluxes and doses are important throughout all stages of design of these systems. In this paper, i) the main characteristics and parameters of the ADS systems previously alluded to will be reviewed ii) the neutronics and shielding calculations of relevance for the design of the ADS systems, for radiation damage and for radiation protection purposes will be extensively described

AdS2 holographic dictionary

International Nuclear Information System (INIS)

Cvetič, Mirjam; Papadimitriou, Ioannis

2016-01-01

We construct the holographic dictionary for both running and constant dilaton solutions of the two dimensional Einstein-Maxwell-Dilaton theory that is obtained by a circle reduction from Einstein-Hilbert gravity with negative cosmological constant in three dimensions. This specific model ensures that the dual theory has a well defined ultraviolet completion in terms of a two dimensional conformal field theory, but our results apply qualitatively to a wider class of two dimensional dilaton gravity theories. For each type of solutions we perform holographic renormalization, compute the exact renormalized one-point functions in the presence of arbitrary sources, and derive the asymptotic symmetries and the corresponding conserved charges. In both cases we find that the scalar operator dual to the dilaton plays a crucial role in the description of the dynamics. Its source gives rise to a matter conformal anomaly for the running dilaton solutions, while its expectation value is the only non trivial observable for constant dilaton solutions. The role of this operator has been largely overlooked in the literature. We further show that the only non trivial conserved charges for running dilaton solutions are the mass and the electric charge, while for constant dilaton solutions only the electric charge is non zero. However, by uplifting the solutions to three dimensions we show that constant dilaton solutions can support non trivial extended symmetry algebras, including the one found by Compère, Song and Strominger http://dx.doi.org/10.1007/JHEP05(2013)152, in agreement with the results of Castro and Song http://arxiv.org/abs/1411.1948. Finally, we demonstrate that any solution of this specific dilaton gravity model can be uplifted to a family of asymptotically AdS 2 ×S 2 or conformally AdS 2 ×S 2 solutions of the STU model in four dimensions, including non extremal black holes. The four dimensional solutions obtained by uplifting the running dilaton solutions coincide

Crystal manyfold universes in /AdS space

Science.gov (United States)

Kaloper, N.

2000-02-01

We derive crystal braneworld solutions, comprising of intersecting families of parallel /n+2-branes in a /4+n-dimensional /AdS space. Each family consists of alternating positive and negative tension branes. In the simplest case of exactly orthogonal families, there arise different crystals with unbroken /4D Poincaré invariance on the intersections, where our world can reside. A crystal can be finite along some direction, either because that direction is compact, or because it ends on a segment of /AdS bulk, or infinite, where the branes continue forever. If the crystal is interlaced by connected /3-branes directed both along the intersections and orthogonal to them, it can be viewed as an example of a Manyfold universe proposed recently by Arkani-Hamed, Dimopoulos, Dvali and the author. There are new ways for generating hierarchies, since the bulk volume of the crystal and the lattice spacing affect the /4D Planck mass. The low energy physics is sensitive to the boundary conditions in the bulk, and has to satisfy the same constraints discussed in the Manyfold universe. Phenomenological considerations favor either finite crystals, or crystals which are infinite but have broken translational invariance in the bulk. The most distinctive signature of the bulk structure is that the bulk gravitons are Bloch waves, with a band spectrum, which we explicitly construct in the case of a /5-dimensional theory.

DOGBONE GEOMETRY FOR RECIRCULATING ACCELERATORS

International Nuclear Information System (INIS)

BERG, J.S.; JOHNSTONE, C.; SUMMERS, D.

2001-01-01

Most scenarios for accelerating muons require recirculating acceleration. A racetrack shape for the accelerator requires particles with lower energy in early passes to traverse almost the same length of arc as particles with the highest energy. This extra arc length may lead to excess decays and excess cost. Changing the geometry to a dogbone shape, where there is a single linac and the beam turns completely around at the end of the linac, returning to the same end of the linac from which it exited, addresses this problem. In this design, the arc lengths can be proportional to the particle's momentum. This paper proposes an approximate cost model for a recirculating accelerator, attempts to make cost-optimized designs for both racetrack and dogbone geometries, and demonstrates that the dogbone geometry does appear to be more cost effective

Renormalization, averaging, conservation laws and AdS (in)stability

International Nuclear Information System (INIS)

Craps, Ben; Evnin, Oleg; Vanhoof, Joris

2015-01-01

We continue our analytic investigations of non-linear spherically symmetric perturbations around the anti-de Sitter background in gravity-scalar field systems, and focus on conservation laws restricting the (perturbatively) slow drift of energy between the different normal modes due to non-linearities. We discover two conservation laws in addition to the energy conservation previously discussed in relation to AdS instability. A similar set of three conservation laws was previously noted for a self-interacting scalar field in a non-dynamical AdS background, and we highlight the similarities of this system to the fully dynamical case of gravitational instability. The nature of these conservation laws is best understood through an appeal to averaging methods which allow one to derive an effective Lagrangian or Hamiltonian description of the slow energy transfer between the normal modes. The conservation laws in question then follow from explicit symmetries of this averaged effective theory.

Increasing insightful thinking in analytic geometry

NARCIS (Netherlands)

Timmer, Mark; Verhoef, Neeltje Cornelia

Elsewhere in this issue Ferdinand Verhulst described the discussion of the interaction of analysis and geometry in the 19th century. In modern times such discussions come up again and again. As of 2014, synthetic geometry will not be part of the Dutch 'vwo - mathematics B' programme anymore.

Development and application of CATIA-GDML geometry builder

International Nuclear Information System (INIS)

Belogurov, S; Chernogorov, A; Ovcharenko, E; Schetinin, V; Berchun, Yu; Malzacher, P

2014-01-01

Due to conceptual difference between geometry descriptions in Computer-Aided Design (CAD) systems and particle transport Monte Carlo (MC) codes direct conversion of detector geometry in either direction is not feasible. The paper presents an update on functionality and application practice of the CATIA-GDML geometry builder first introduced at CHEP2010. This set of CATIAv5 tools has been developed for building a MC optimized GEANT4/ROOT compatible geometry based on the existing CAD model. The model can be exported via Geometry Description Markup Language (GDML). The builder allows also import and visualization of GEANT4/ROOT geometries in CATIA. The structure of a GDML file, including replicated volumes, volume assemblies and variables, is mapped into a part specification tree. A dedicated file template, a wide range of primitives, tools for measurement and implicit calculation of parameters, different types of multiple volume instantiation, mirroring, positioning and quality check have been implemented. Several use cases are discussed.

Foundations of the AdS5 x S5 superstring: I

International Nuclear Information System (INIS)

Arutyunov, Gleb; Frolov, Sergey

2009-01-01

We review the recent advances towards finding the spectrum of the AdS 5 x S 5 superstring. We thoroughly explain the theoretical techniques which should be useful for the ultimate solution of the spectral problem. In certain cases our exposition is original and cannot be found in the existing literature. The present part I deals with foundations of classical string theory in AdS 5 x S 5 , light-cone perturbative quantization and the derivation of the exact light-cone world-sheet scattering matrix

Integrable systems from membranes on AdS4 x S7

International Nuclear Information System (INIS)

Bozhilov, P.

2008-01-01

We describe how Neumann and Neumann-Rosochatius type integrable systems, as well as the continuous limit of the SU(2) integrable spin chain, can be obtained from membranes on AdS 4 x S 7 background, in the framework of AdS/CFT correspondence. (Abstract Copyright [2008], Wiley Periodicals, Inc.)

What's the point? Hole-ography in Poincare AdS

Energy Technology Data Exchange (ETDEWEB)

Espindola, Ricardo [Universidad Nacional Autonoma de Mexico, Departamento de Fisica de Altas Energias, Instituto de Ciencias Nucleares, Mexico City (Mexico); University of Southampton, Mathematical Sciences and STAG Research Centre, Southampton (United Kingdom); Gueijosa, Alberto; Landetta, Alberto [Universidad Nacional Autonoma de Mexico, Departamento de Fisica de Altas Energias, Instituto de Ciencias Nucleares, Mexico City (Mexico); Pedraza, Juan F. [University of Amsterdam, Institute for Theoretical Physics, Amsterdam (Netherlands)

2018-01-15

In the context of the AdS/CFT correspondence, we study bulk reconstruction of the Poincare wedge of AdS{sub 3} via hole-ography, i.e., in terms of differential entropy of the dual CFT{sub 2}. Previous work had considered the reconstruction of closed or open spacelike curves in global AdS, and of infinitely extended spacelike curves in Poincare AdS that are subject to a periodicity condition at infinity. Working first at constant time, we find that a closed curve in Poincare is described in the CFT by a family of intervals that covers the spatial axis at least twice. We also show how to reconstruct open curves, points and distances, and obtain a CFT action whose extremization leads to bulk points. We then generalize all of these results to the case of curves that vary in time, and discover that generic curves have segments that cannot be reconstructed using the standard hole-ographic construction. This happens because, for the nonreconstructible segments, the tangent geodesics fail to be fully contained within the Poincare wedge. We show that a previously discovered variant of the hole-ographic method allows us to overcome this challenge, by reorienting the geodesics touching the bulk curve to ensure that they all remain within the wedge. Our conclusion is that all spacelike curves in Poincare AdS can be completely reconstructed with CFT data, and each curve has in fact an infinite number of representations within the CFT. (orig.)

Remarks on Hamiltonian structures in G2-geometry

International Nuclear Information System (INIS)

Cho, Hyunjoo; Salur, Sema; Todd, A. J.

2013-01-01

In this article, we treat G 2 -geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G 2 -structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G 2 -structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry

Smooth causal patches for AdS black holes

Science.gov (United States)

Raju, Suvrat

2017-06-01

We review the paradox of low energy excitations of a black hole in anti-de Sitter space (AdS). An appropriately chosen unitary operator in the boundary theory can create a locally strong excitation near the black hole horizon, whose global energy is small as a result of the gravitational redshift. The paradox is that this seems to violate a general rule of statistical mechanics, which states that an operator with energy parametrically smaller than k T cannot create a significant excitation in a thermal system. When we carefully examine the position dependence of the boundary unitary operator that produces the excitation and the bulk observable necessary to detect the anomalously large effect, we find that they do not both fit in a single causal patch. This follows from a remarkable property of position-space AdS correlators that we establish explicitly and resolves the paradox in a generic state of the system, since no combination of observers can both create the excitation and observe its effect. As a special case of our analysis, we show how this resolves the "Born rule" paradox of Marolf and Polchinski [J. High Energy Phys. 01 (2016) 008, 10.1007/JHEP01(2016)008] and we verify our solution using an independent calculation. We then consider boundary states that are finely tuned to display a spontaneous excitation outside the causal patch of the infalling observer, and we propose a version of causal patch complementarity in AdS/CFT that resolves the paradox for such states as well.

Classical geometry Euclidean, transformational, inversive, and projective

CERN Document Server

Leonard, I E; Liu, A C F; Tokarsky, G W

2014-01-01

Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which p

MOCUM: A two-dimensional method of characteristics code based on constructive solid geometry and unstructured meshing for general geometries

International Nuclear Information System (INIS)

Yang Xue; Satvat, Nader

2012-01-01

Highlight: ► A two-dimensional numerical code based on the method of characteristics is developed. ► The complex arbitrary geometries are represented by constructive solid geometry and decomposed by unstructured meshing. ► Excellent agreement between Monte Carlo and the developed code is observed. ► High efficiency is achieved by parallel computing. - Abstract: A transport theory code MOCUM based on the method of characteristics as the flux solver with an advanced general geometry processor has been developed for two-dimensional rectangular and hexagonal lattice and full core neutronics modeling. In the code, the core structure is represented by the constructive solid geometry that uses regularized Boolean operations to build complex geometries from simple polygons. Arbitrary-precision arithmetic is also used in the process of building geometry objects to eliminate the round-off error from the commonly used double precision numbers. Then, the constructed core frame will be decomposed and refined into a Conforming Delaunay Triangulation to ensure the quality of the meshes. The code is fully parallelized using OpenMP and is verified and validated by various benchmarks representing rectangular, hexagonal, plate type and CANDU reactor geometries. Compared with Monte Carlo and deterministic reference solution, MOCUM results are highly accurate. The mentioned characteristics of the MOCUM make it a perfect tool for high fidelity full core calculation for current and GenIV reactor core designs. The detailed representation of reactor physics parameters can enhance the safety margins with acceptable confidence levels, which lead to more economically optimized designs.

Evolving Procurement Organizations

DEFF Research Database (Denmark)

Bals, Lydia; Laine, Jari; Mugurusi, Godfrey

Procurement has to find further levers and advance its contribution to corporate goals continuously. This places pressure on its organization in order to facilitate its performance. Therefore, procurement organizations constantly have to evolve in order to match these demands. A conceptual model...... and external contingency factors and having a more detailed look at the structural dimensions chosen, beyond the well-known characteristics of centralization, formalization, participation, specialization, standardization and size. From a theoretical perspective, it opens up insights that can be leveraged...

Position space analysis of the AdS (in)stability problem

Science.gov (United States)

Dimitrakopoulos, Fotios V.; Freivogel, Ben; Lippert, Matthew; Yang, I.-Sheng

2015-08-01

We investigate whether arbitrarily small perturbations in global AdS space are generically unstable and collapse into black holes on the time scale set by gravitational interactions. We argue that current evidence, combined with our analysis, strongly suggests that a set of nonzero measure in the space of initial conditions does not collapse on this time scale. We perform an analysis in position space to study this puzzle, and our formalism allows us to directly study the vanishing-amplitude limit. We show that gravitational self-interaction leads to tidal deformations which are equally likely to focus or defocus energy, and we sketch the phase diagram accordingly. We also clarify the connection between gravitational evolution in global AdS and holographic thermalization.

Position space analysis of the AdS (in)stability problem

Energy Technology Data Exchange (ETDEWEB)

Dimitrakopoulos, Fotios V.; Freivogel, Ben; Lippert, Matthew; Yang, I-Sheng [ITFA and GRAPPA, Universiteit van Amsterdam,Science Park 904, 1090 GL Amsterdam (Netherlands)

2015-08-17

We investigate whether arbitrarily small perturbations in global AdS space are generically unstable and collapse into black holes on the time scale set by gravitational interactions. We argue that current evidence, combined with our analysis, strongly suggests that a set of nonzero measure in the space of initial conditions does not collapse on this time scale. We perform an analysis in position space to study this puzzle, and our formalism allows us to directly study the vanishing-amplitude limit. We show that gravitational self-interaction leads to tidal deformations which are equally likely to focus or defocus energy, and we sketch the phase diagram accordingly. We also clarify the connection between gravitational evolution in global AdS and holographic thermalization.

Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.

Science.gov (United States)

Shang, Yilun

2015-01-01

Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices.

State Operator Correspondence and Entanglement in AdS2/CFT1

Directory of Open Access Journals (Sweden)

Ashoke Sen

2011-07-01

Full Text Available Since Euclidean global AdS2 space represented as a strip has two boundaries, the state-operator correspondence in the dual CFT1 reduces to the standard map from the operators acting on a single copy of the Hilbert space to states in the tensor product of two copies of the Hilbert space. Using this picture we argue that the corresponding states in the dual string theory living on AdS2 × K are described by the twisted version of the Hartle–Hawking states, the twists being generated by a large unitary group of symmetries that this string theory must possess. This formalism makes natural the dual interpretation of the black hole entropy—as the logarithm of the degeneracy of ground states of the quantum mechanics describing the low energy dynamics of the black hole, and also as an entanglement entropy between the two copies of the same quantum theory living on the two boundaries of global AdS2 separated by the event horizon.

Electrodynamics and Spacetime Geometry: Foundations

Science.gov (United States)

Cabral, Francisco; Lobo, Francisco S. N.

2017-02-01

We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.

Quantum spectral curve for the η-deformed AdS5 × S5 superstring

Science.gov (United States)

Klabbers, Rob; van Tongeren, Stijn J.

2017-12-01

The spectral problem for the AdS5 ×S5 superstring and its dual planar maximally supersymmetric Yang-Mills theory can be efficiently solved through a set of functional equations known as the quantum spectral curve. We discuss how the same concepts apply to the η-deformed AdS5 ×S5 superstring, an integrable deformation of the AdS5 ×S5 superstring with quantum group symmetry. This model can be viewed as a trigonometric version of the AdS5 ×S5 superstring, like the relation between the XXZ and XXX spin chains, or the sausage and the S2 sigma models for instance. We derive the quantum spectral curve for the η-deformed string by reformulating the corresponding ground-state thermodynamic Bethe ansatz equations as an analytic Y system, and map this to an analytic T system which upon suitable gauge fixing leads to a Pμ system - the quantum spectral curve. We then discuss constraints on the asymptotics of this system to single out particular excited states. At the spectral level the η-deformed string and its quantum spectral curve interpolate between the AdS5 ×S5 superstring and a superstring on "mirror" AdS5 ×S5, reflecting a more general relationship between the spectral and thermodynamic data of the η-deformed string. In particular, the spectral problem of the mirror AdS5 ×S5 string, and the thermodynamics of the undeformed AdS5 ×S5 string, are described by a second rational limit of our trigonometric quantum spectral curve, distinct from the regular undeformed limit.

Partition functions in even dimensional AdS via quasinormal mode methods

International Nuclear Information System (INIS)

Keeler, Cynthia; Ng, Gim Seng

2014-01-01

In this note, we calculate the one-loop determinant for a massive scalar (with conformal dimension Δ) in even-dimensional AdS d+1 space, using the quasinormal mode method developed in http://dx.doi.org/10.1088/0264-9381/27/12/125001 by Denef, Hartnoll, and Sachdev. Working first in two dimensions on the related Euclidean hyperbolic plane H 2 , we find a series of zero modes for negative real values of Δ whose presence indicates a series of poles in the one-loop partition function Z(Δ) in the Δ complex plane; these poles contribute temperature-independent terms to the thermal AdS partition function computed in http://dx.doi.org/10.1088/0264-9381/27/12/125001. Our results match those in a series of papers by Camporesi and Higuchi, as well as Gopakumar et al. http://dx.doi.org/10.1007/JHEP11(2011)010 and Banerjee et al. http://dx.doi.org/10.1007/JHEP03(2011)147. We additionally examine the meaning of these zero modes, finding that they Wick-rotate to quasinormal modes of the AdS 2 black hole. They are also interpretable as matrix elements of the discrete series representations of SO(2,1) in the space of smooth functions on S 1 . We generalize our results to general even dimensional AdS 2n , again finding a series of zero modes which are related to discrete series representations of SO(2n,1), the motion group of H 2n .

Investigating pyroclast ejection dynamics using shock-tube experiments: temperature, grain size and vent geometry effects.

Science.gov (United States)

Cigala, V.; Kueppers, U.; Dingwell, D. B.

2015-12-01

Explosive volcanic eruptions eject large quantities of gas and particles into the atmosphere. The portion directly above the vent commonly shows characteristics of underexpanded jets. Understanding the factors that influence the initial pyroclast ejection dynamics is necessary in order to better assess the resulting near- and far-field hazards. Field observations are often insufficient for the characterization of volcanic explosions due to lack of safe access to such environments. Fortunately, their dynamics can be simulated in the laboratory where experiments are performed under controlled conditions. We ejected loose natural particles from a shock-tube while controlling temperature (25˚ and 500˚C), overpressure (15MPa), starting grain size distribution (1-2 mm, 0.5-1 mm and 0.125-0.250 mm), sample-to-vent distance and vent geometry. For each explosion we quantified the velocity of individual particles, the jet spreading angle and the production of fines. Further, we varied the setup to allow for different sample-to-gas ratios and deployed four different vent geometries: 1) cylindrical, 2) funnel with a flaring of 30˚, 3) funnel with a flaring of 15˚ and 4) nozzle. The results showed maximum particle velocities up to 296 m/s, gas spreading angles varying from 21˚ to 37˚ and particle spreading angles from 3˚ to 40˚. Moreover we observed dynamically evolving ejection characteristics and variations in the production of fines during the course of individual experiments. Our experiments mechanistically mimic the process of pyroclast ejection. Thus the capability for constraining the effects of input parameters (fragmentation conditions) and conduit/vent geometry on ballistic pyroclastic plumes has been clearly established. These data obtained in the presence of well-documented conduit and vent conditions, should greatly enhance our ability to numerically model explosive ejecta in nature.

Small AdS black holes from SYM

International Nuclear Information System (INIS)

Asplund, Curtis; Berenstein, David

2009-01-01

We provide a characterization of the set of configurations in N=4 SYM theory that are dual to small AdS black holes. Our construction shows that the black hole dual states are approximately thermal on a SU(M) subset of degrees of freedom of a SU(N) gauge theory. M is determined dynamically and the black hole degrees of freedom are dynamically insulated from the rest. These states are localized on the S 5 and have dynamical processes that correspond to matter absorption that make them behave as black objects

Digital and discrete geometry theory and algorithms

CERN Document Server

Chen, Li

2014-01-01

This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences. It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData.The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms. The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and a

Time-dependent AdS backgrounds from S-branes

Energy Technology Data Exchange (ETDEWEB)

Deger, Nihat Sadik, E-mail: sadik.deger@boun.edu.tr [Department of Mathematics, Bogazici University, Bebek, 34342, Istanbul (Turkey); Feza Gursey Center for Physics and Mathematics, Bogazici University, Kandilli, 34684, Istanbul (Turkey)

2016-11-10

We construct time and radial dependent solutions that describe p-branes in chargeless S-brane backgrounds. In particular, there are some new M5- and D3-branes among our solutions which have AdS limits and contain a cosmological singularity as well. We also find a time-dependent version of the dyonic membrane configuration in 11-dimensions by applying a Lunin–Maldacena deformation to our new M5-brane solution.

Attitudes of High School Students towards Geometry

Directory of Open Access Journals (Sweden)

Esat Avcı

2014-12-01

Full Text Available In this research, attitudes of high school students towards geometry were investigated in terms of gender, grade, types of the field and school. Population of research includes students who were studying at high school in five distincs of Mersin in 2013-2014 academical year. Sample of research includes 935 students from twelve high schools. Attitude scale which was developed by Su-Özenir (2008 was used for data collection. For data analysis, mean, standart deviation, t test and ANOVA were used. A meaningful difference between students’ attitudes towards geometry and variance of gender and grade level wasn’t observed, on the other hand a meaningful difference according to field and school type is observed.Key Words:    Attitudes towards geometry, high school geometry lesson, attitude scale

A 4-m evolvable space telescope configured for NASA's HabEx Mission: the initial stage of LUVOIR

Science.gov (United States)

Lillie, Charles F.; MacEwen, Howard A.; Polidan, Ronald S.; Breckinridge, James B.

2017-09-01

Previous papers have described our concept for a large telescope that would be assembled in space in several stages (in different configurations) over a period of fifteen to 20 years. Spreading the telescope development, launch and operations cost over 20 years would minimize the impact on NASA's annual budget and drastically shorten the time between program start and "first light" for this space observatory. The first Stage of this Evolvable Space Telescope (EST) would consist of an instrument module located at the prime focus of three 4-meter hexagonal mirrors arranged in a semi-circle to form one-half of a 12-m segmented mirror. After several years three additional 4-m mirrors would be added to create a 12-m filled aperture. Later, twelve more 4-m mirrors will be added to this Stage 2 telescope to create a 20-m filled aperture space telescope. At each stage the telescope would have an unparalleled capability for UVOIR observations, and the results of these observations will guide the evolution of the telescope and its instruments. In this paper we describe our design concept for an initial configuration of our Evolvable Space Telescope that can meet the requirements of the 4-m version of the HabEx spacecraft currently under consideration by NASA's Habitable Exoplanet Science and Technology Definition Team. This "Stage Zero" configuration will have only one 4-m mirror segment with the same 30-m focal length and a prime focus coronagraph with normal incidence optics to minimize polarization effects. After assembly and checkout in cis-lunar space, the telescope would transfer to a Sun-Earth L2 halo orbit and obtain high sensitivity, high resolution, high contrast UVOIR observations that address the scientific objectives of the Habitable-Exoplanet Imaging Missions.

Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.

Directory of Open Access Journals (Sweden)

Yilun Shang

Full Text Available Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices.

Commutative and Non-commutative Parallelogram Geometry: an Experimental Approach

OpenAIRE

Bertram, Wolfgang

2013-01-01

By "parallelogram geometry" we mean the elementary, "commutative", geometry corresponding to vector addition, and by "trapezoid geometry" a certain "non-commutative deformation" of the former. This text presents an elementary approach via exercises using dynamical software (such as geogebra), hopefully accessible to a wide mathematical audience, from undergraduate students and high school teachers to researchers, proceeding in three steps: (1) experimental geometry, (2) algebra (linear algebr...

A Study of Geometry Content Knowledge of Elementary Preservice Teachers

Directory of Open Access Journals (Sweden)

Fatma ASLAN-TUTAK

2015-06-01

Full Text Available The purpose of this research is to examine preservice elementary school teachers’ geometry learning as investigated by both qualitative and quantitative methods. For the qualitative investigation, narrative analysis and thematic analysis methods were used. The findings of narrative analysis indicated two main kinds of stories: as a learner and as a beginning teacher. The thematic analysis findings yield to three themes: history of learning geometry, perceptions about geometry, effective geometry instructional practices. The findings informed the quantitative investigation on geometry content knowledge for the case of quadrilaterals. During the second phase of the study, 102 participants who enrolled in the methods course completed pre and post test of teachers’ geometry content knowledge. Treatment group participants (n=54 received series of activities (geometry activities and student work analysis focusing on quadrilaterals, and control group participants (n=48 received traditional instruction. Repeated measures ANOVA results showed a significant change in treatment group participants’ geometry content knowledge. The mixed ANOVA results indicated a significant main effect of knowledge but no significant interaction between geometry content knowledge and grouping. Even though treatment group participants’ geometry content knowledge growth was significant, the difference between treatment group and control group participants’ growth in geometry content knowledge was not significant. This study informs mathematics teacher education in three important areas; limited knowledge of preservice teachers’ geometry content knowledge, integrating mathematics content and the context of teaching into methods course, and use of student work with preservice teachers.

A study of geometry content knowledge of elementary preservice teachers

Directory of Open Access Journals (Sweden)

Fatma Aslan Tutak

2015-06-01

Full Text Available The purpose of this research is to examine preservice elementary school teachers’ geometry learning as investigated by both qualitative and quantitative methods. For the qualitative investigation, narrative analysis and thematic analysis methods were used. The findings of narrative analysis indicated two main kinds of stories: as a learner and as a beginning teacher. The thematic analysis findings yield to three themes: history of learning geometry, perceptions about geometry, effective geometry instructional practices. The findings informed the quantitative investigation on geometry content knowledge for the case of quadrilaterals. During the second phase of the study, 102 participants who enrolled in the methods course completed pre and post test of teachers’ geometry content knowledge. Treatment group participants (n=54 received series of activities (geometry activities and student work analysis focusing on quadrilaterals, and control group participants (n=48 received traditional instruction. Repeated measures ANOVA results showed a significant change in treatment group participants’ geometry content knowledge. The mixed ANOVA results indicated a significant main effect of knowledge but no significant interaction between geometry content knowledge and grouping. Even though treatment group participants’ geometry content knowledge growth was significant, the difference between treatment group and control group participants’ growth in geometry content knowledge was not significant. This study informs mathematics teacher education in three important areas; limited knowledge of preservice teachers’ geometry content knowledge, integrating mathematics content and the context of teaching into methods course, and use of student work with preservice teachers.

Combinatorial geometry in the plane

CERN Document Server

Hadwiger, Hugo; Klee, Victor

2014-01-01

Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research.The two-part treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second pa

Topology and geometry for physicists

CERN Document Server

Nash, Charles

1983-01-01

Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr

Quality improvement of pyrolysis oil from waste rubber by adding sawdust.

Science.gov (United States)

Wang, Wen-liang; Chang, Jian-min; Cai, Li-ping; Shi, Sheldon Q

2014-12-01

This work was aimed at improving the pyrolysis oil quality of waste rubber by adding larch sawdust. Using a 1 kg/h stainless pyrolysis reactor, the contents of sawdust in rubber were gradually increased from 0%, 50%, 100% and 200% (wt%) during the pyrolysis process. Using a thermo-gravimetric (TG) analyzer coupled with Fourier transform infrared (FTIR) analysis of evolving products (TG-FTIR), the weight loss characteristics of the heat under different mixtures of sawdust/rubber were observed. Using the pyrolysis-gas chromatography (GC)-mass spectrometry (Py-GC/MS), the vapors from the pyrolysis processes were collected and the compositions of the vapors were examined. During the pyrolysis process, the recovery of the pyrolysis gas and its composition were measured in-situ at a reaction temperature of 450 °C and a retaining time of 1.2s. The results indicated that the efficiency of pyrolysis was increased and the residual carbon was reduced as the percentage of sawdust increased. The adding of sawdust significantly improved the pyrolysis oil quality by reducing the polycyclic aromatic hydrocarbons (PAHs) and nitrogen and sulfur compounds contents, resulting in an improvement in the combustion efficiency of the pyrolysis oil. Copyright © 2014 Elsevier Ltd. All rights reserved.

Duplex geometry: an example from the Moine Thrust Belt

Science.gov (United States)

Bowler, S.

1987-04-01

The geometry and microstructure of a small duplex formed in one bed from the Moine Thrust Belt of northwest Scotland is reported. The structure is seen in oblique section, within the Cambrian Pipe-rock, in an area of low strain. A range of movement direction indicators are present in the structure. An early grain shape fabric developed close to the roof thrust is taken as the best estimate of the overall movement direction towards 287°. Slickensides in the gouge developed on movement planes within the duplex show varied orientations on a given plane, and are not considered useful indicators of thrust transport direction. Branch lines exposed converge and diverge, suggesting little lateral continuity of the exposed structure. The microstructures present within the structure indicate an increase in localised deformation, and in cataclastic behavior as the duplex evolved. Early layer parallel shear is ubiquitous, giving rise to an elongate grain shape fabric close to bedding surfaces. In early formed horses, a layer-parallel, oblate grain shape fabric, which shows localised slip zones, is overprinted by gouge formation. Later formed horses show only fracturing and gouge development. This sequence is attributed to stick-slip behavior in the propagation or displacement of the original fault, now the floor thrust.

Hindmarsh–Rose model: Close and far to the singular limit