Correlation Functions of the Energy Momentum Tensor on Spaces of Constant Curvature

CERN Document Server

Osborn, H

2000-01-01

An analysis of one and two point functions of the energy momentum tensor on homogeneous spaces of constant curvature is undertaken. The possibility of proving a c-theorem in this framework is discussed, in particular in relation to the coefficients c,a, which appear in the energy momentum tensor trace on general curved backgrounds in four dimensions. Ward identities relating the correlation functions are derived and explicit expressions are obtained for free scalar, spinor field theories in general dimensions and also free vector fields in dimension four. A natural geometric formalism which is independent of any choice of coordinates is used and the role of conformal symmetries on such constant curvature spaces is analysed. The results are shown to be constrained by the operator product expansion. For negative curvature the spectral representation, involving unitary positive energy representations of $O(d-1,2)$, for two point functions of vector currents is derived in detail and extended to the energy momentu...

The Explicit Construction of Einstein Finsler Metrics with Non-Constant Flag Curvature

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Enli Guo

2009-04-01

Full Text Available By using the Hawking Taub-NUT metric, this note gives an explicit construction of a 3-parameter family of Einstein Finsler metrics of non-constant flag curvature in terms of navigation representation.

The geometry of plane waves in spaces of constant curvature

International Nuclear Information System (INIS)

Tran, H.V.

1988-01-01

We examined the geometry of possible plane wave fronts in spaces of constant curvature for three cases in which the cosmological constant is positive, zero, or negative. The cosmological constant and a second-order invariant determined by a congruence of null rays were used in the investigation. We embedded the spaces under investigation in a flat five-dimensional space, and studied the null hyperplanes passing through the origin of the flat five-dimensional space. The embedded spaces are represented by quadrics in the five-dimensional space. The plane wave fronts are represented by the intersection of the quadric with null hyperplanes passing through the origin of the five-dimensional space. We concluded that in Minkowski spaces (zero cosmological constant), the plane-fronted waves will intersect if and only if the second-order invariant mentioned above is non-zero. For deSitter spaces (positive cosmological constant), plane-fronted waves will always intersect. For anti-deSitter spaces (negative cosmological constant), plane-fronted waves may but need not intersect

The Spatial Structure of Planform Migration - Curvature Relation of Meandering Rivers

Science.gov (United States)

Guneralp, I.; Rhoads, B. L.

2005-12-01

Planform dynamics of meandering rivers have been of fundamental interest to fluvial geomorphologists and engineers because of the intriguing complexity of these dynamics, the role of planform change in floodplain development and landscape evolution, and the economic and social consequences of bank erosion and channel migration. Improved understanding of the complex spatial structure of planform change and capacity to predict these changes are important for effective stream management, engineering and restoration. The planform characteristics of a meandering river channel are integral to its planform dynamics. Active meandering rivers continually change their positions and shapes as a consequence of hydraulic forces exerted on the channel banks and bed, but as the banks and bed change through sediment transport, so do the hydraulic forces. Thus far, this complex feedback between form and process is incompletely understood, despite the fact that the characteristics and the dynamics of meandering rivers have been studied extensively. Current theoretical models aimed at predicting planform dynamics relate rates of meander migration to local and upstream planform curvature where weighting of the influence of curvature on migration rate decays exponentially over distance. This theoretical relation, however, has not been rigorously evaluated empirically. Furthermore, although models based on exponential-weighting of curvature effects yield fairly realistic predictions of meander migration, such models are incapable of reproducing complex forms of bend development, such as double heading or compound looping. This study presents the development of a new methodology based on parametric cubic spline interpolation for the characterization of channel planform and the planform curvature of meandering rivers. The use of continuous mathematical functions overcomes the reliance on bend-averaged values or piece-wise discrete approximations of planform curvature - a major limitation

Cosmological backreaction within the Szekeres model and emergence of spatial curvature

Energy Technology Data Exchange (ETDEWEB)

Bolejko, Krzysztof, E-mail: krzysztof.bolejko@sydney.edu.au [Sydney Institute for Astronomy, School of Physics A28, The University of Sydney, Sydney, NSW, 2006 (Australia)

2017-06-01

This paper discusses the phenomenon of backreaction within the Szekeres model. Cosmological backreaction describes how the mean global evolution of the Universe deviates from the Friedmannian evolution. The analysis is based on models of a single cosmological environment and the global ensemble of the Szekeres models (of the Swiss-Cheese-type and Styrofoam-type). The obtained results show that non-linear growth of cosmic structures is associated with the growth of the spatial curvature Ω{sub R} (in the FLRW limit Ω{sub R} → Ω {sub k} ). If averaged over global scales the result depends on the assumed global model of the Universe. Within the Swiss-Cheese model, which does have a fixed background, the volume average follows the evolution of the background, and the global spatial curvature averages out to zero (the background model is the ΛCDM model, which is spatially flat). In the Styrofoam-type model, which does not have a fixed background, the mean evolution deviates from the spatially flat ΛCDM model, and the mean spatial curvature evolves from Ω{sub R} =0 at the CMB to Ω{sub R} ∼ 0.1 at 0 z =. If the Styrofoam-type model correctly captures evolutionary features of the real Universe then one should expect that in our Universe, the spatial curvature should build up (local growth of cosmic structures) and its mean global average should deviate from zero (backreaction). As a result, this paper predicts that the low-redshift Universe should not be spatially flat (i.e. Ω {sub k} ≠ 0, even if in the early Universe Ω {sub k} = 0) and therefore when analysing low- z cosmological data one should keep Ω {sub k} as a free parameter and independent from the CMB constraints.

Hawking temperature of constant curvature black holes

International Nuclear Information System (INIS)

Cai Ronggen; Myung, Yun Soo

2011-01-01

The constant curvature (CC) black holes are higher dimensional generalizations of Banados-Teitelboim-Zanelli black holes. It is known that these black holes have the unusual topology of M D-1 xS 1 , where D is the spacetime dimension and M D-1 stands for a conformal Minkowski spacetime in D-1 dimensions. The unusual topology and time-dependence for the exterior of these black holes cause some difficulties to derive their thermodynamic quantities. In this work, by using a globally embedding approach, we obtain the Hawking temperature of the CC black holes. We find that the Hawking temperature takes the same form when using both the static and global coordinates. Also, it is identical to the Gibbons-Hawking temperature of the boundary de Sitter spaces of these CC black holes.

Correlation functions of the energy-momentum tensor on spaces of constant curvature

International Nuclear Information System (INIS)

Osborn, H.; Shore, G.M.

2000-01-01

An analysis of one- and two-point functions of the energy-momentum tensor on homogeneous spaces of constant curvature is undertaken. The possibility of proving a c-theorem in this framework is discussed, in particular in relation to the coefficients c,a, which appear in the energy-momentum tensor trace on general curved backgrounds in four dimensions. Ward identities relating the correlation functions are derived and explicit expressions are obtained for free scalar, spinor field theories in general dimensions and also free vector fields in dimension four. A natural geometric formalism which is independent of any choice of coordinates is used and the role of conformal symmetries on such constant curvature spaces is analysed. The results are shown to be constrained by the operator product expansion. For negative curvature the spectral representation, involving unitary positive energy representations of O(d-1,2), for two-point functions of vector currents is derived in detail and extended to the energy-momentum tensor by analogy. It is demonstrated that, at non-coincident points, the two-point functions are not related to a in any direct fashion and there is no straightforward demonstration obtainable in this framework of irreversibility under renormalisation group flow of any function of the couplings for four-dimensional field theories which reduces to a at fixed points

The motion of a vortex on a closed surface of constant negative curvature.

Science.gov (United States)

Ragazzo, C Grotta

2017-10-01

The purpose of this work is to present an algorithm to determine the motion of a single hydrodynamic vortex on a closed surface of constant curvature and of genus greater than one. The algorithm is based on a relation between the Laplace-Beltrami Green function and the heat kernel. The algorithm is used to compute the motion of a vortex on the Bolza surface. This is the first determination of the orbits of a vortex on a closed surface of genus greater than one. The numerical results show that all the 46 vortex equilibria can be explicitly computed using the symmetries of the Bolza surface. Some of these equilibria allow for the construction of the first two examples of infinite vortex crystals on the hyperbolic disc. The following theorem is proved: 'a Weierstrass point of a hyperellitic surface of constant curvature is always a vortex equilibrium'.

Influence of spatial curvature of a liquid jet on the rainbow positions: Ray tracing and experimental study

Science.gov (United States)

Duan, Qingwei; Zhong, Ruliang; Han, Xiang'e.; Ren, Kuan Fang

2017-07-01

Rainbow refractometry is largely used in optical metrology of particles thanks to its advantages of being non-intrusive, precise and fast. Many authors have contributed to its development and the application in the characterization of liquid jets/droplets. The researches reported in the literature are mainly for the spherical droplets or the liquid jets which can be considered as a cylinder of constant section. However, the section of a real liquid jet, even in the simplest configuration, varies with distance from the exit. The influence of the spatial curvature of the jets must, therefore, be taken into account. In this paper, we report experimental measurements of the shifts of the rainbow positions in the horizontal and vertical directions of a liquid jet and the theoretical investigation with the vectorial complex ray model. It is shown that the shifts of rainbow positions are very sensitive to the spatial curvature of the jets. This work is hoped to provide a new approach to characterizing the structure and the instability of liquid jets.

New solution to the problem of the tension between the high-redshift and low-redshift measurements of the Hubble constant

Science.gov (United States)

Bolejko, Krzysztof

2018-01-01

During my talk I will present results suggesting that the phenomenon of emerging spatial curvature could resolve the conflict between Planck's (high-redshift) and Riess et al. (low-redshift) measurements of the Hubble constant. The phenomenon of emerging spatial curvature is absent in the Standard Cosmological Model, which has a flat and fixed spatial curvature (small perturbations are considered in the Standard Cosmological Model but their global average vanishes, leading to spatial flatness at all times).In my talk I will show that with the nonlinear growth of cosmic structures the global average deviates from zero. As a result, the spatial curvature evolves from spatial flatness of the early universe to a negatively curved universe at the present day, with Omega_K ~ 0.1. Consequently, the present day expansion rate, as measured by the Hubble constant, is a few percent higher compared to the high-redshift constraints. This provides an explanation why there is a tension between high-redshift (Planck) and low-redshift (Riess et al.) measurements of the Hubble constant. In the presence of emerging spatial curvature these two measurements should in fact be different: high redshift measurements should be slightly lower than the Hubble constant inferred from the low-redshift data.The presentation will be based on the results described in arXiv:1707.01800 and arXiv:1708.09143 (which discuss the phenomenon of emerging spatial curvature) and on a paper that is still work in progress but is expected to be posted on arxiv by the AAS meeting (this paper uses mock low-redshift data to show that starting from the Planck's cosmological models (in the early universe) but with the emerging spatial curvature taken into account, the low-redshift Hubble constant should be 72.4 km/s/Mpc.

Constant curvature black holes in Einstein AdS gravity: Euclidean action and thermodynamics

Science.gov (United States)

Guilleminot, Pablo; Olea, Rodrigo; Petrov, Alexander N.

2018-03-01

We compute the Euclidean action for constant curvature black holes (CCBHs), as an attempt to associate thermodynamic quantities to these solutions of Einstein anti-de Sitter (AdS) gravity. CCBHs are gravitational configurations obtained by identifications along isometries of a D -dimensional globally AdS space, such that the Riemann tensor remains constant. Here, these solutions are interpreted as extended objects, which contain a (D -2 )-dimensional de-Sitter brane as a subspace. Nevertheless, the computation of the free energy for these solutions shows that they do not obey standard thermodynamic relations.

On the quantum field theory in the momentum space with the constant curvature

International Nuclear Information System (INIS)

Gadzhiev, S.A.; Petrosyan, V.A.

1981-01-01

Model of polarization operator in the approximation of ''opalescent'' diagrams in the momentum space of constant curvature is investigated. Integral equation for an absorptive part of the hadron polarization operator has been obtained in stereographic parametrization of the de Sitter space. Integral equation for the case of zero mass of an exchange particle has been solved, cross section and mean multiplicity of hadron production in the e + e - annihilation have been calculated. Infrared divergences arising during exact summation of the considered diagram class are separated to a multiplicative constant of renormalization [ru

Bonnesen-style inequality for the first eigenvalue on a complete surface of constant curvature

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Niufa Fang

2017-08-01

Full Text Available Abstract By Cheeger’s isoperimetric constants, some lower bounds and upper bounds of λ 1 $\\lambda_{1}$ , the first eigenvalue on a complete surface of constant curvature, are given. Some Bonnesen-style inequalities and reverse Bonnesen-style inequalities for the first eigenvalue are obtained. Those Bonnesen-style inequalities obtained are stronger than the well-known Osserman’s results and the upper bound is stronger than Osserman’s results (Osserman in Proceedings of the International Congress of Mathematicians, Helsinki, 1978.

Imprint of spatial curvature on inflation power spectrum

International Nuclear Information System (INIS)

Masso, Eduard; Zsembinszki, Gabriel; Mohanty, Subhendra; Nautiyal, Akhilesh

2008-01-01

If the Universe had a large curvature before inflation there is a deviation from the scale invariant perturbations of the inflaton at the beginning of inflation. This may have some effect on the cosmic microwave background anisotropy at large angular scales. We calculate the density perturbations for both open and closed universe cases using the Bunch-Davies vacuum condition on the initial state. We use our power spectrum to calculate the temperature anisotropy spectrum and compare the results with the Wilkinson microwave anisotropy map five year data. We find that our power spectrum gives a lower quadrupole anisotropy when Ω-1>0, but matches the temperature anisotropy calculated from the standard Ratra-Peebles power spectrum at large l. The determination of spatial curvature from temperature anisotropy data is not much affected by the different power spectra which arise from the choice of different boundary conditions for the inflaton perturbation.

On a curvature-statistics theorem

International Nuclear Information System (INIS)

Calixto, M; Aldaya, V

2008-01-01

The spin-statistics theorem in quantum field theory relates the spin of a particle to the statistics obeyed by that particle. Here we investigate an interesting correspondence or connection between curvature (κ = ±1) and quantum statistics (Fermi-Dirac and Bose-Einstein, respectively). The interrelation between both concepts is established through vacuum coherent configurations of zero modes in quantum field theory on the compact O(3) and noncompact O(2; 1) (spatial) isometry subgroups of de Sitter and Anti de Sitter spaces, respectively. The high frequency limit, is retrieved as a (zero curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the physical significance of the vacuum energy density and the cosmological constant problem.

On a curvature-statistics theorem

Energy Technology Data Exchange (ETDEWEB)

Calixto, M [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain); Aldaya, V [Instituto de Astrofisica de Andalucia, Apartado Postal 3004, 18080 Granada (Spain)], E-mail: Manuel.Calixto@upct.es

2008-08-15

The spin-statistics theorem in quantum field theory relates the spin of a particle to the statistics obeyed by that particle. Here we investigate an interesting correspondence or connection between curvature ({kappa} = {+-}1) and quantum statistics (Fermi-Dirac and Bose-Einstein, respectively). The interrelation between both concepts is established through vacuum coherent configurations of zero modes in quantum field theory on the compact O(3) and noncompact O(2; 1) (spatial) isometry subgroups of de Sitter and Anti de Sitter spaces, respectively. The high frequency limit, is retrieved as a (zero curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the physical significance of the vacuum energy density and the cosmological constant problem.

Sinh-Gordon, cosh-Gordon, and Liouville equations for strings and multistrings in constant curvature spacetimes

International Nuclear Information System (INIS)

Larsen, A.L.; Sanchez, N.

1996-01-01

We find that the fundamental quadratic form of classical string propagation in (2+1)-dimensional constant curvature spacetimes solves the sinh-Gordon equation, the cosh-Gordon equation, or the Liouville equation. We show that in both de Sitter and anti endash de Sitter spacetimes (as well as in the 2+1 black hole anti endash de Sitter spacetime), all three equations must be included to cover the generic string dynamics. The generic properties of the string dynamics are directly extracted from the properties of these three equations and their associated potentials (irrespective of any solution). These results complete and generalize earlier discussions on this topic (until now, only the sinh-Gordon sector in de Sitter spacetime was known). We also construct new classes of multistring solutions, in terms of elliptic functions, to all three equations in both de Sitter and anti endash de Sitter spacetimes. Our results can be straightforwardly generalized to constant curvature spacetimes of arbitrary dimension, by replacing the sinh-Gordon equation, the cosh-Gordon equation, and the Liouville equation by their higher dimensional generalizations. copyright 1996 The American Physical Society

Singularities of spacelike constant mean curvature surfaces in Lorentz-Minkowski space

DEFF Research Database (Denmark)

Brander, David

2011-01-01

We study singularities of spacelike, constant (non-zero) mean curvature (CMC) surfaces in the Lorentz-Minkowski 3-space L-3. We show how to solve the singular Bjorling problem for such surfaces, which is stated as follows: given a real analytic null-curve f(0)(x), and a real analytic null vector...... field v(x) parallel to the tangent field of f(0), find a conformally parameterized (generalized) CMC H surface in L-3 which contains this curve as a singular set and such that the partial derivatives f(x) and f(y) are given by df(0)/dx and v along the curve. Within the class of generalized surfaces...

Contribution to the establishment and resolution of the Schroedinger equation in a Riemannian manifold with constant curvature

International Nuclear Information System (INIS)

Rasolofoson, N.G.

2014-01-01

The properties of a physical system may vary significantly due to the presence of matter or energy. This change can be defined by the deformation of the space which is described as the variation of its curvature. In order to describe this law of physics, we have used differential geometry and studied especially a Schroedinger equation which describes a system evolving with time on a Riemannian manifold of constant curvature. Therefore, we have established and solved the Schroedinger equation using appropriate mathematics tools. As perspective, the study of string theory may be considered. [fr

Path integral approach for superintegrable potentials on spaces of non-constant curvature. Pt. 1. Darboux spaces D{sub I} and D{sub II}

Energy Technology Data Exchange (ETDEWEB)

Grosche, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Pogosyan, G.S. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics]|[Guadalajara Univ., Jalisco (Mexico). Dept. de Matematicas CUCEI; Sissakian, A.N. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics

2006-07-15

In this paper the Feynman path integral technique is applied for superintegrable potentials on two-dimensional spaces of non-constant curvature: these spaces are Darboux spaces D{sub I} and D{sub II}, respectively. On D{sub I} there are three and on D{sub II} foru such potentials, respectively. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is either determined by a transcendental equation involving parabolic cylinder functions (Darboux space I), or by a higher order polynomial equation. The solutions on D{sub I} in particular show that superintegrable systems are not necessarily degenerate. We can also show how the limiting cases of flat space (Constant curvature zero) and the two-dimensional hyperboloid (constant negative curvature) emerge. (Orig.)

Quantum field theory with a momentum space of constant curvature (perturbation theory)

International Nuclear Information System (INIS)

Mir-Kasimov, R.M.

1978-01-01

In the framework of the field-theoretical approach in which the off-the-mass shell extension proceeds in the p-space of constant curvature, the perburbation theory is developed. The configurational representation of the de Sitter space is introduced with the help of the Fourier transformation of the group of motions. On the basis of a natural generalization of the Bogolyubov causality condition to the case of the new configurational representation a perturbation theory is constructed with the local in xi space Lagrangian density fucntion. The obtained S matrix obeys the reguirement of translation invariance. The S matrix elements are given by convergent expressions

Holomorphic representation of constant mean curvature surfaces in Minkowski space: Consequences of non-compactness in loop group methods

DEFF Research Database (Denmark)

Brander, David; Rossman, Wayne; Schmitt, Nicholas

2010-01-01

We give an infinite dimensional generalized Weierstrass representation for spacelike constant mean curvature (CMC) surfaces in Minkowski 3-space $\\R^{2,1}$. The formulation is analogous to that given by Dorfmeister, Pedit and Wu for CMC surfaces in Euclidean space, replacing the group $SU_2$ with...

Isotropic oscillator in the space of constant positive curvature. Interbasis expansions

International Nuclear Information System (INIS)

Akopyan, E.M.; Pogosyan, G.S.; Sisakyan, A.N.; Vinitskij, S.I.

1997-01-01

The Schroedinger equation is thoroughly analysed for the isotropic oscillator in the three-dimensional space of constant positive curvature in the spherical and cylindrical systems of coordinates. The expansion coefficients between the spherical and cylindrical bases of the oscillator are calculated. It is shown that the relevant coefficients are expressed through the generalised hypergeometric functions 4 F 3 of the unit argument or 6j Racah symbols extended over their indices to the region of real values. Limiting transitions to a free motion and flat space are considered in detail. Elliptic bases of the oscillator are constructed in the form of expansion over the spherical and cylindrical bases. The corresponding expansion coefficients are shown to obey the three-term recurrence relations expansion coefficients are shown to obey the three-term recurrence relations

Quantum maps of geodesic flows on surfaces of constant negative curvature

International Nuclear Information System (INIS)

Bogomolny, E.B.; Carioli, M.

1992-01-01

The Selberg zeta function Z(s) yields an exact relationship between the periodic orbits of a fully chaotic Hamiltonian system (the geodesic flow on surfaces of constant negative curvature) and the corresponding quantum system (the spectrum of the Laplace-Beltrami operator on the same manifold). It was found that for certain manifolds Z(s) can be exactly rewritten as the Fredholm determinant det(1-T s ), where T s is the generalization of the Ruelle-Perron-Frobenius transfer operator. An alternative derivation of this result is presented, yielding a method to find not only the spectrum but also the eigenvalues of the Laplace-Beltrami operator in terms of eigenfunctions of T s . Various properties of the transfer operator are investigated both analytically and numerically. (author) 15 refs., 10 figs

Path integral approach for quantum motion on spaces of non-constant curvature according to Koenigs - Three dimensions

International Nuclear Information System (INIS)

Grosche, C.

2007-08-01

In this contribution a path integral approach for the quantum motion on three-dimensional spaces according to Koenigs, for short''Koenigs-Spaces'', is discussed. Their construction is simple: One takes a Hamiltonian from three-dimensional flat space and divides it by a three-dimensional superintegrable potential. Such superintegrable potentials will be the isotropic singular oscillator, the Holt-potential, the Coulomb potential, or two centrifugal potentials, respectively. In all cases a non-trivial space of non-constant curvature is generated. In order to obtain a proper quantum theory a curvature term has to be incorporated into the quantum Hamiltonian. For possible bound-state solutions we find equations up to twelfth order in the energy E. (orig.)

Cosmic curvature tested directly from observations

Science.gov (United States)

Denissenya, Mikhail; Linder, Eric V.; Shafieloo, Arman

2018-03-01

Cosmic spatial curvature is a fundamental geometric quantity of the Universe. We investigate a model independent, geometric approach to measure spatial curvature directly from observations, without any derivatives of data. This employs strong lensing time delays and supernova distance measurements to measure the curvature itself, rather than just testing consistency with flatness. We define two curvature estimators, with differing error propagation characteristics, that can crosscheck each other, and also show how they can be used to map the curvature in redshift slices, to test constancy of curvature as required by the Robertson-Walker metric. Simulating realizations of redshift distributions and distance measurements of lenses and sources, we estimate uncertainties on the curvature enabled by next generation measurements. The results indicate that the model independent methods, using only geometry without assuming forms for the energy density constituents, can determine the curvature at the ~6×10‑3 level.

A curvature theory for discrete surfaces based on mesh parallelity

KAUST Repository

Bobenko, Alexander Ivanovich

2009-12-18

We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces\\' areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discrete isothermic minimal surfaces and surfaces of constant mean curvature. We discuss various types of natural Gauss images, the existence of principal curvatures, constant curvature surfaces, Christoffel duality, Koenigs nets, contact element nets, s-isothermic nets, and interesting special cases such as discrete Delaunay surfaces derived from elliptic billiards. © 2009 Springer-Verlag.

Curvature force and dark energy

International Nuclear Information System (INIS)

Balakin, Alexander B; Pavon, Diego; Schwarz, Dominik J; Zimdahl, Winfried

2003-01-01

A curvature self-interaction of the cosmic gas is shown to mimic a cosmological constant or other forms of dark energy, such as a rolling tachyon condensate or a Chaplygin gas. Any given Hubble rate and deceleration parameter can be traced back to the action of an effective curvature force on the gas particles. This force self-consistently reacts back on the cosmological dynamics. The links between an imperfect fluid description, a kinetic description with effective antifriction forces and curvature forces, which represent a non-minimal coupling of gravity to matter, are established

Parametrised Constants and Replication for Spatial Mobility

DEFF Research Database (Denmark)

Hüttel, Hans; Haagensen, Bjørn

2009-01-01

Parametrised replication and replication are common ways of expressing infinite computation in process calculi. While parametrised constants can be encoded using replication in the π-calculus, this changes in the presence of spatial mobility as found in e.g. the distributed π- calculus...... of the distributed π-calculus with parametrised constants and replication are incomparable. On the other hand, we shall see that there exists a simple encoding of recursion in mobile ambients....

Balancing anisotropic curvature with gauge fields in a class of shear-free cosmological models

Science.gov (United States)

Thorsrud, Mikjel

2018-05-01

We present a complete list of general relativistic shear-free solutions in a class of anisotropic, spatially homogeneous and orthogonal cosmological models containing a collection of n independent p-form gauge fields, where p\\in\\{0, 1, 2, 3\\} , in addition to standard ΛCDM matter fields modelled as perfect fluids. Here a (collection of) gauge field(s) balances anisotropic spatial curvature on the right-hand side of the shear propagation equation. The result is a class of solutions dynamically equivalent to standard FLRW cosmologies, with an effective curvature constant Keff that depends both on spatial curvature and the energy density of the gauge field(s). In the case of a single gauge field (n  =  1) we show that the only spacetimes that admit such solutions are the LRS Bianchi type III, Bianchi type VI0 and Kantowski–Sachs metric, which are dynamically equivalent to open (Keff0 ) FLRW models, respectively. With a collection of gauge fields (n  >  1) also Bianchi type II admits a shear-free solution (Keff>0 ). We identify the LRS Bianchi type III solution to be the unique shear-free solution with a gauge field Hamiltonian bounded from below in the entire class of models.

Curvature constraints from the causal entropic principle

International Nuclear Information System (INIS)

Bozek, Brandon; Albrecht, Andreas; Phillips, Daniel

2009-01-01

Current cosmological observations indicate a preference for a cosmological constant that is drastically smaller than what can be explained by conventional particle physics. The causal entropic principle (Bousso et al.) provides an alternative approach to anthropic attempts to predict our observed value of the cosmological constant by calculating the entropy created within a causal diamond. We have extended this work to use the causal entropic principle to predict the preferred curvature within the 'multiverse'. We have found that values larger than ρ k =40ρ m are disfavored by more than 99.99% peak value at ρ Λ =7.9x10 -123 and ρ k =4.3ρ m for open universes. For universes that allow only positive curvature or both positive and negative curvature, we find a correlation between curvature and dark energy that leads to an extended region of preferred values. Our universe is found to be disfavored to an extent depending on the priors on curvature. We also provide a comparison to previous anthropic constraints on open universes and discuss future directions for this work.

Introducing quantum Ricci curvature

Science.gov (United States)

Klitgaard, N.; Loll, R.

2018-02-01

Motivated by the search for geometric observables in nonperturbative quantum gravity, we define a notion of coarse-grained Ricci curvature. It is based on a particular way of extracting the local Ricci curvature of a smooth Riemannian manifold by comparing the distance between pairs of spheres with that of their centers. The quantum Ricci curvature is designed for use on non-smooth and discrete metric spaces, and to satisfy the key criteria of scalability and computability. We test the prescription on a variety of regular and random piecewise flat spaces, mostly in two dimensions. This enables us to quantify its behavior for short lattices distances and compare its large-scale behavior with that of constantly curved model spaces. On the triangulated spaces considered, the quantum Ricci curvature has good averaging properties and reproduces classical characteristics on scales large compared to the discretization scale.

The shear-free condition and constant-mean-curvature hyperboloidal initial data

International Nuclear Information System (INIS)

Allen, Paul T; Allen, Iva Stavrov; Isenberg, James; Lee, John M

2016-01-01

We consider the Einstein–Maxwell-fluid constraint equations, and make use of the conformal method to construct and parametrize constant-mean-curvature hyperboloidal initial data sets that satisfy the shear-free condition. This condition is known to be necessary in order that a spacetime development admit a regular conformal boundary at future null infinity; see (Andersson and Chruściel 1994 Commun. Math. Phys. 161 533–68). We work with initial data sets in a variety of regularity classes, primarily considering those data sets whose geometries are weakly asymptotically hyperbolic , as defined in (Allen et al 2015 arXiv:1506.03399). These metrics are C 1,1 conformally compact, but not necessarily C 2 conformally compact. In order to ensure that the data sets we construct are indeed shear-free, we make use of the conformally covariant traceless Hessian introduced in (Allen et al 2015 arXiv:1506.03399). We furthermore construct a class of initial data sets with weakly asymptotically hyerbolic metrics that may be only C 0,1 conformally compact; these data sets are insufficiently regular to make sense of the shear-free condition. (paper)

Curvature collineations for the field of gravitational waves

International Nuclear Information System (INIS)

Singh, K.P.; Singh, Gulab

1981-01-01

It has been shown that the space-times formed from a plane-fronted gravity wave and from a plane sandwich wave with constant polarisation admit proper curvature collineation in general. The curvature collineation vectors have been determined explicitly. (author)

Computation of the optical properties of turbid media from slope and curvature of spatially resolved reflectance curves

International Nuclear Information System (INIS)

Jäger, Marion; Foschum, Florian; Kienle, Alwin

2013-01-01

The optical properties of turbid media were calculated from the curvature at the radial distance ρ O and the slope at the radial distance ρ* of simulated spatially resolved reflectance curves (ρ O (ρ*) denotes a decrease of the spatially resolved reflectance curve of 0.75 (2.4) orders of magnitude relative to the reflectance value at 1.2 mm). We found correlations between the curvature at ρ O and the reduced scattering coefficient as well as the slope at ρ* and the absorption coefficient. For the determination of the optical properties we used these two correlations. The calculation of the reduced scattering coefficient from the curvature at ρ O is practically independent from the absorption coefficient. Knowing the reduced scattering coefficient within a certain accuracy allows the determination of the absorption coefficient from the slope at ρ*. Additionally, we investigated the performance of an artificial neural network for the determination of the optical properties using the above explained correlations. This means we used the derivatives as input data. Our artificial neural network was capable to learn the mapping between the optical properties and the derivatives. In effect, the results for the determined optical properties improved in comparison to the above explained method. Finally, the procedure was compared to an artificial neural network that was trained without using the derivatives. (note)

Superintegrability on Three-Dimensional Riemannian and Relativistic Spaces of Constant Curvature

Directory of Open Access Journals (Sweden)

Francisco José Herranz

2006-01-01

Full Text Available A family of classical superintegrable Hamiltonians, depending on an arbitrary radial function, which are defined on the 3D spherical, Euclidean and hyperbolic spaces as well as on the (2+1D anti-de Sitter, Minkowskian and de Sitter spacetimes is constructed. Such systems admit three integrals of the motion (besides the Hamiltonian which are explicitly given in terms of ambient and geodesic polar coordinates. The resulting expressions cover the six spaces in a unified way as these are parametrized by two contraction parameters that govern the curvature and the signature of the metric on each space. Next two maximally superintegrable Hamiltonians are identified within the initial superintegrable family by finding the remaining constant of the motion. The former potential is the superposition of a (curved central harmonic oscillator with other three oscillators or centrifugal barriers (depending on each specific space, so that this generalizes the Smorodinsky-Winternitz system. The latter one is a superposition of the Kepler-Coulomb potential with another two oscillators or centrifugal barriers. As a byproduct, the Laplace-Runge-Lenz vector for these spaces is deduced. Furthermore both potentials are analysed in detail for each particular space. Some comments on their generalization to arbitrary dimension are also presented.

Model-independent Constraints on Cosmic Curvature and Opacity

Energy Technology Data Exchange (ETDEWEB)

Wang, Guo-Jian; Li, Zheng-Xiang; Xia, Jun-Qing; Zhu, Zong-Hong [Department of Astronomy, Beijing Normal University, Beijing 100875 (China); Wei, Jun-Jie, E-mail: gjwang@mail.bnu.edu.cn, E-mail: zxli918@bnu.edu.cn, E-mail: xiajq@bnu.edu.cn, E-mail: zhuzh@bnu.edu.cn, E-mail: jjwei@pmo.ac.cn [Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008 (China)

2017-09-20

In this paper, we propose to estimate the spatial curvature of the universe and the cosmic opacity in a model-independent way with expansion rate measurements, H ( z ), and type Ia supernova (SNe Ia). On the one hand, using a nonparametric smoothing method Gaussian process, we reconstruct a function H ( z ) from opacity-free expansion rate measurements. Then, we integrate the H ( z ) to obtain distance modulus μ {sub H}, which is dependent on the cosmic curvature. On the other hand, distances of SNe Ia can be determined by their photometric observations and thus are opacity-dependent. In our analysis, by confronting distance moduli μ {sub H} with those obtained from SNe Ia, we achieve estimations for both the spatial curvature and the cosmic opacity without any assumptions for the cosmological model. Here, it should be noted that light curve fitting parameters, accounting for the distance estimation of SNe Ia, are determined in a global fit together with the cosmic opacity and spatial curvature to get rid of the dependence of these parameters on cosmology. In addition, we also investigate whether the inclusion of different priors for the present expansion rate ( H {sub 0}: global estimation, 67.74 ± 0.46 km s{sup −1} Mpc{sup −1}, and local measurement, 73.24 ± 1.74 km s{sup −1} Mpc{sup −1}) exert influence on the reconstructed H ( z ) and the following estimations of the spatial curvature and cosmic opacity. Results show that, in general, a spatially flat and transparent universe is preferred by the observations. Moreover, it is suggested that priors for H {sub 0} matter a lot. Finally, we find that there is a strong degeneracy between the curvature and the opacity.

Statistical mechanics of paths with curvature dependent action

International Nuclear Information System (INIS)

Ambjoern, J.; Durhuus, B.; Jonsson, T.

1987-01-01

We analyze the scaling limit of discretized random paths with curvature dependent action. For finite values of the curvature coupling constant the theory belongs to the universality class of simple random walk. It is possible to define a non-trivial scaling limit if the curvature coupling tends to infinity. We compute exactly the two point function in this limit and discuss the relevance of our results for random surfaces and string theories. (orig.)

Statistical mechanics of surfaces with curvature dependent action

International Nuclear Information System (INIS)

Jonsson, T.

1987-01-01

We review recent results about discretized random surfaces whose action (energy) depends on the extrinsic curvature. The surface tension scales to zero at an appropriate critical point if the coupling constant of the curvature term is taken to infinity. At this critical point one expects to be able to construct a continuum theory of smooth surfaces. (orig.)

On the asymptotically Poincaré-Einstein 4-manifolds with harmonic curvature

Science.gov (United States)

Hu, Xue

2018-06-01

In this paper, we discuss the mass aspect tensor and the rigidity of an asymptotically Poincaré-Einstein (APE) 4-manifold with harmonic curvature. We prove that the trace-free part of the mass aspect tensor of an APE 4-manifold with harmonic curvature and normalized Einstein conformal infinity is zero. As to the rigidity, we first show that a complete noncompact Riemannian 4-manifold with harmonic curvature and positive Yamabe constant as well as a L2-pinching condition is Einstein. As an application, we then obtain that an APE 4-manifold with harmonic curvature and positive Yamabe constant is isometric to the hyperbolic space provided that the L2-norm of the traceless Ricci tensor or the Weyl tensor is small enough and the conformal infinity is a standard round 3-sphere.

Tensor perturbations during inflation in a spatially closed Universe

Energy Technology Data Exchange (ETDEWEB)

Bonga, Béatrice; Gupt, Brajesh; Yokomizo, Nelson, E-mail: bpb165@psu.edu, E-mail: bgupt@gravity.psu.edu, E-mail: yokomizo@gravity.psu.edu [Institute for Gravitation and the Cosmos and Physics Department, The Pennsylvania State University, 104 Lavey Lab, University Park, PA 16802 (United States)

2017-05-01

In a recent paper [1], we studied the evolution of the background geometry and scalar perturbations in an inflationary, spatially closed Friedmann-Lemaȋtre-Robertson-Walker (FLRW) model having constant positive spatial curvature and spatial topology S{sup 3}. Due to the spatial curvature, the early phase of slow-roll inflation is modified, leading to suppression of power in the scalar power spectrum at large angular scales. In this paper, we extend the analysis to include tensor perturbations. We find that, similarly to the scalar perturbations, the tensor power spectrum also shows suppression for long wavelength modes. The correction to the tensor spectrum is limited to the very long wavelength modes, therefore the resulting observable CMB B-mode polarization spectrum remains practically the same as in the standard scenario with flat spatial sections. However, since both the tensor and scalar power spectra are modified, there are scale dependent corrections to the tensor-to-scalar ratio that leads to violation of the standard slow-roll consistency relation.

Non-minimally coupled varying constants quantum cosmologies

International Nuclear Information System (INIS)

Balcerzak, Adam

2015-01-01

We consider gravity theory with varying speed of light and varying gravitational constant. Both constants are represented by non-minimally coupled scalar fields. We examine the cosmological evolution in the near curvature singularity regime. We find that at the curvature singularity the speed of light goes to infinity while the gravitational constant vanishes. This corresponds to the Newton's Mechanics limit represented by one of the vertex of the Bronshtein-Zelmanov-Okun cube [1,2]. The cosmological evolution includes both the pre-big-bang and post-big-bang phases separated by the curvature singularity. We also investigate the quantum counterpart of the considered theory and find the probability of transition of the universe from the collapsing pre-big-bang phase to the expanding post-big-bang phase

Current observations with a decaying cosmological constant allow for chaotic cyclic cosmology

International Nuclear Information System (INIS)

Ellis, George F.R.; Platts, Emma; Weltman, Amanda; Sloan, David

2016-01-01

We use the phase plane analysis technique of Madsen and Ellis [1] to consider a universe with a true cosmological constant as well as a cosmological 'constant' that is decaying. Time symmetric dynamics for the inflationary era allows eternally bouncing models to occur. Allowing for scalar field dynamic evolution, we find that if dark energy decays in the future, chaotic cyclic universes exist provided the spatial curvature is positive. This is particularly interesting in light of current observations which do not yet rule out either closed universes or possible evolution of the cosmological constant. We present only a proof of principle, with no definite claim on the physical mechanism required for the present dark energy to decay

Path integration and separation of variables in spaces of constant curvature in two and three dimensions

International Nuclear Information System (INIS)

Grosche, C.

1993-10-01

In this paper path integration in two- and three-dimensional spaces of constant curvature is discussed: i.e. the flat spaces R 2 and R 3 , the two- and three-dimensional sphere and the two- and three dimensional pseudosphere. The Laplace operator in these spaces admits separation of variables in various coordinate systems. In all these coordinate systems the path integral formulation will be stated, however in most of them an explicit solution in terms of the spectral expansion can be given only on a formal level. What can be stated in all cases, are the propagator and the corresponding Green function, respectively, depending on the invariant distance which is a coordinate independent quantity. This property gives rise to numerous identities connecting the corresponding path integral representations and propagators in various coordinate systems with each other. (orig.)

Dissecting the Gravitational Lens B1608 656. II. Precision Measurements of the Hubble Constant, Spatial Curvature, and the Dark Energy Equation of State

Energy Technology Data Exchange (ETDEWEB)

Suyu, S.H.; /Argelander Inst. Astron.; Marshall, P.J.; /KIPAC, Menlo Park /UC, Santa Barbara; Auger, M.W.; /UC, Santa Barbara /UC, Davis; Hilbert, S.; /Argelander Inst. Astron. /Garching, Max Planck Inst.; Blandford, R.D.; /KIPAC, Menlo Park; Koopmans, L.V.E.; /Kapteyn Astron. Inst., Groningen; Fassnacht, C.D.; /UC, Davis; Treu, T.; /UC, Santa Barbara

2009-12-11

between {Omega}{sub m} and {Omega}{sub {Lambda}} at w = -1 and constrains the curvature parameter to be -0.031 < {Omega}{sub k} < 0.009 (95% CL), a level of precision comparable to that afforded by the current Type Ia SNe sample. Asserting a flat spatial geometry, we find that, in combination with WMAP, H{sub 0} = 69.7{sub 5.0}{sup +4.9} km s{sup -1} Mpc{sup -1} and w = -0.94{sub -0.19}{sup +0.17} (68% CL), suggesting that the observations of B1608+656 constrain w as tightly as do the current Baryon Acoustic Oscillation data.

Cosmic curvature from de Sitter equilibrium cosmology.

Science.gov (United States)

Albrecht, Andreas

2011-10-07

I show that the de Sitter equilibrium cosmology generically predicts observable levels of curvature in the Universe today. The predicted value of the curvature, Ω(k), depends only on the ratio of the density of nonrelativistic matter to cosmological constant density ρ(m)(0)/ρ(Λ) and the value of the curvature from the initial bubble that starts the inflation, Ω(k)(B). The result is independent of the scale of inflation, the shape of the potential during inflation, and many other details of the cosmology. Future cosmological measurements of ρ(m)(0)/ρ(Λ) and Ω(k) will open up a window on the very beginning of our Universe and offer an opportunity to support or falsify the de Sitter equilibrium cosmology.

Connections and curvatures on complex Riemannian manifolds

International Nuclear Information System (INIS)

Ganchev, G.; Ivanov, S.

1991-05-01

Characteristic connection and characteristic holomorphic sectional curvatures are introduced on a complex Riemannian manifold (not necessarily with holomorphic metric). For the class of complex Riemannian manifolds with holomorphic characteristic connection a classification of the manifolds with (pointwise) constant holomorphic characteristic curvature is given. It is shown that the conformal geometry of complex analytic Riemannian manifolds can be naturally developed on the class of locally conformal holomorphic Riemannian manifolds. Complex Riemannian manifolds locally conformal to the complex Euclidean space are characterized with zero conformal fundamental tensor and zero conformal characteristic tensor. (author). 12 refs

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.

Public and private space curvature in Robertson-Walker universes.

Science.gov (United States)

Rindler, W.

1981-05-01

The question is asked: what space curvature would a fundamental observer in an ideal Robertson-Walker universe obtain by direct local spatial measurements, i.e., without reference to the motion pattern of the other galaxies? The answer is that he obtains the curvatureK of his “private” space generated by all the geodesics orthogonal to his world line at the moment in question, and that ˜K is related to the usual curvatureK=k/R 2 of the “public” space of galaxies byK=K+H 2/c2, whereH is Hubble's parameter.

On the Calculation of Quantum Mechanical Ground States from Classical Geodesic Motion on Certain Spaces of Constant Negative Curvature

CERN Document Server

Tomaschitz, R

1989-01-01

We consider geodesic motion on three-dimensional Riemannian manifolds of constant negative curvature, topologically equivalent to S x ]0,1[, S a compact surface of genus two. To those trajectories which are bounded and recurrent in both directions of the time evolution a fractal limit set is associated whose Hausdorff dimension is intimately connected with the quantum mechanical energy ground state, determined by the Schrodinger operator on the manifold. We give a rather detailed and pictorial description of the hyperbolic spaces we have in mind, discuss various aspects of classical and quantum mechanical motion on them as far as they are needed to establish the connection between energy ground state and Hausdorff dimension and give finally some examples of ground state calculations in terms of Hausdorff dimensions of limit sets of classical trajectories.

Mineralogy of the clay fraction of Alfisols in two slope curvatures: III - spatial variability

Directory of Open Access Journals (Sweden)

Livia Arantes Camargo

2013-04-01

Full Text Available A good knowledge of the spatial distribution of clay minerals in the landscape facilitates the understanding of the influence of relief on the content and crystallographic attributes of soil minerals such as goethite, hematite, kaolinite and gibbsite. This study aimed at describing the relationships between the mineral properties of the clay fraction and landscape shapes by determining the mineral properties of goethite, hematite, kaolinite and gibbsite, and assessing their dependence and spatial variability, in two slope curvatures. To this end, two 100 × 100 m grids were used to establish a total of 121 regularly spaced georeferenced sampling nodes 10 m apart. Samples were collected from the layer 0.0-0.2 m and analysed for iron oxides, and kaolinite and gibbsite in the clay fraction. Minerals in the clay fraction were characterized from their X-ray diffraction (XRD patterns, which were interpreted and used to calculate the width at half height (WHH and mean crystallite dimension (MCD of iron oxides, kaolinite, and gibbsite, as well as aluminium substitution and specific surface area (SSA in hematite and goethite. Additional calculations included the goethite and hematite contents, and the goethite/(goethite+hematite [Gt/(Gt+Hm] and kaolinite/(kaolinite+gibbsite [Kt/(Kt+Gb] ratios. Mineral properties were established by statistical analysis of the XRD data, and spatial dependence was assessed geostatistically. Mineralogical properties differed significantly between the convex area and concave area. The geostatistical analysis showed a greater number of mineralogical properties with spatial dependence and a higher range in the convex than in the concave area.

Curvature contributions to the static electrical properties of push-pull molecules

International Nuclear Information System (INIS)

Squitieri, Emilio

2005-01-01

Calculations of the curvature contribution to the diagonals components of the static dipole moment (μ), polarizability (α), first (β) and second (γ) hyperpolarizability of push-pull molecules are presented. This contribution was obtained from the analytical evaluation of electrical properties method using the harmonic zero-point energy. The valence-bond charge-transfer model was employed to obtain the field-dependent force constant and their derivates with respect to electric field. Our results show a relationship between the curvature and electronic contributions. We have also found that the curvature contribution is important in a numerical estimation of β and γ

On the calculation of quantum mechanical ground states from classical geodesic motion on certain spaces of constant negative curvature

International Nuclear Information System (INIS)

Tomaschitz, R.

1989-01-01

We consider geodesic motion on three-dimensional Riemannian manifolds of constant negative curvature, topologically equivalent to S x ]0,1[, S a compact surface of genus two. To those trajectories which are recurrent in both directions of the time evolution t → +∞, t → -∞ a fractal limit set is associated whose Hausdorff dimension is intimately connected with the quantum mechanical energy ground state, determined by the Schroedinger operator on the manifold. We give a rather detailed and pictorial description of the hyperbolic spaces we have in mind, discuss various aspects of classical and quantum mechanical motion on them as far as they are needed to establish the connection between energy ground state and Hausdorff dimension and give finally some examples of ground state calculations in terms of Hausdorff dimensions of limit sets of classical trajectories. (orig.)

Gravitational lensing limits on the cosmological constant in a flat universe

International Nuclear Information System (INIS)

Turner, E.L.

1990-01-01

Inflationary cosmological theories predict, and some more general aesthetic criteria suggest, that the large-scale spatial curvature of the universe k should be accurately zero (i.e., flat), a condition which is satisfied when the universe's present mean density and the value of the cosmological constant Lambda have certain pairs of values. Available data on the frequency of multiple image-lensing of high-redshift quasars by galaxies suggest that the cosmological constant cannot make a dominant contribution to producing a flat universe. In particular, if the mean density of the universe is as small as the baryon density inferred from standard cosmic nucleosynthesis calculations or as determined from typical dynamical studies of galaxies and galaxy clusters, then a value of Lambda large enough to produce a k = 0 universe would result in a substantially higher frequency of multiple-image lensing of quasars than has been observed so far. Shortcomings of the available lens data and uncertainties concerning galaxy properties allow some possibility of escaping this conclusion, but systematic searches for a gravitational lenses and continuing investigations of galaxy mass distributions should soon provide decisive information. It is also noted that nonzero-curvature cosmological models can account for the observed frequency of galaxy-quasar lens systems and for a variety of other constraints. 61 refs

Non Lyapunov stability of a constant spatially developing 2-D gas flow

Science.gov (United States)

Balint, Agneta M.; Balint, Stefan; Tanasie, Loredana

2017-01-01

Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 2-D gas flow are analyzed in a particular phase space of continuously differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the plane. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1].

Novel tilt-curvature coupling in lipid membranes

Science.gov (United States)

Terzi, M. Mert; Deserno, Markus

2017-08-01

On mesoscopic scales, lipid membranes are well described by continuum theories whose main ingredients are the curvature of a membrane's reference surface and the tilt of its lipid constituents. In particular, Hamm and Kozlov [Eur. Phys. J. E 3, 323 (2000)] have shown how to systematically derive such a tilt-curvature Hamiltonian based on the elementary assumption of a thin fluid elastic sheet experiencing internal lateral pre-stress. Performing a dimensional reduction, they not only derive the basic form of the effective surface Hamiltonian but also express its emergent elastic couplings as trans-membrane moments of lower-level material parameters. In the present paper, we argue, though, that their derivation unfortunately missed a coupling term between curvature and tilt. This term arises because, as one moves along the membrane, the curvature-induced change of transverse distances contributes to the area strain—an effect that was believed to be small but nevertheless ends up contributing at the same (quadratic) order as all other terms in their Hamiltonian. We illustrate the consequences of this amendment by deriving the monolayer and bilayer Euler-Lagrange equations for the tilt, as well as the power spectra of shape, tilt, and director fluctuations. A particularly curious aspect of our new term is that its associated coupling constant is the second moment of the lipid monolayer's lateral stress profile—which within this framework is equal to the monolayer Gaussian curvature modulus, κ¯ m. On the one hand, this implies that many theoretical predictions now contain a parameter that is poorly known (because the Gauss-Bonnet theorem limits access to the integrated Gaussian curvature); on the other hand, the appearance of κ¯ m outside of its Gaussian curvature provenance opens opportunities for measuring it by more conventional means, for instance by monitoring a membrane's undulation spectrum at short scales.

Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature

Directory of Open Access Journals (Sweden)

Orlando Ragnisco

2007-02-01

Full Text Available An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3 integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden non-standard quantum sl(2,R Poisson coalgebra symmetry. As a concrete application, one of this Hamiltonians is shown to generate the geodesic motion on certain manifolds with a non-constant curvature that turns out to be a function of the deformation parameter z. Moreover, another Hamiltonian in this family is shown to generate geodesic motions on Riemannian and relativistic spaces all of whose sectional curvatures are constant and equal to the deformation parameter z. This approach can be generalized to arbitrary dimension by making use of coalgebra symmetry.

Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multicomponent, curvature, and rotation

International Nuclear Information System (INIS)

Hwang, Jai-chan; Noh, Hyerim

2007-01-01

We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a spatially flat background coincide exactly with the ones known in Newton's theory without using the gravitational potential. We also have shown the effect of gravitational waves to the second order, and pure general relativistic correction terms appearing in the third-order perturbations. Here, we present results of second-order perturbations relaxing all the assumptions made in our previous works. We derive the general relativistic correction terms arising due to (i) pressure, (ii) multicomponent, (iii) background spatial curvature, and (iv) rotation. In the case of multicomponent zero-pressure, irrotational fluids under the flat background, we effectively do not have relativistic correction terms, thus the relativistic equations expressed in terms of density and velocity perturbations again coincide with the Newtonian ones. In the other three cases we generally have pure general relativistic correction terms. In the case of pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the presence of background spatial curvature, or rotation, pure relativistic correction terms directly appear in the Newtonian equations of motion of density and velocity perturbations to the second order; to the linear order, without using the gravitational potential (or metric perturbations), we have relativistic/Newtonian correspondences for density and velocity perturbations of a single-component fluid including the rotation even in the presence of background spatial curvature. In the small-scale limit (far inside the horizon), to the second-order, relativistic equations of density and

Eigenvalue estimates for submanifolds with bounded f-mean curvature

Indian Academy of Sciences (India)

GUANGYUE HUANG

1College of Mathematics and Information Science, Henan Normal University,. Xinxiang 453007 ... submanifolds in a hyperbolic space with the norm of their mean curvature vector bounded above by a constant. ..... [2] Batista M, Cavalcante M P and Pyo J, Some isoperimetric inequalities and eigenvalue estimates in ...

Cosmological models with positive scalar spatial curvature and Λ>0

Science.gov (United States)

Ponce de Leon, J.

1987-12-01

Some exact spherically symmetric solutions of the Einstein field equations with Λ>0 and positive three-curvature are given. They have reasonable physical properties and represent universes which do not undergo inflation but have a non-de Sitter behaviour for large times. This paper extends some previous results in the literature. Permanent address: Apartado 2816, Caracas 1010-A, Venezuela.

The dark side of curvature

International Nuclear Information System (INIS)

Barenboim, Gabriela; Martínez, Enrique Fernández; Mena, Olga; Verde, Licia

2010-01-01

Geometrical tests such as the combination of the Hubble parameter H(z) and the angular diameter distance d A (z) can, in principle, break the degeneracy between the dark energy equation of state parameter w(z), and the spatial curvature Ω k in a direct, model-independent way. In practice, constraints on these quantities achievable from realistic experiments, such as those to be provided by Baryon Acoustic Oscillation (BAO) galaxy surveys in combination with CMB data, can resolve the cosmic confusion between the dark energy equation of state parameter and curvature only statistically and within a parameterized model for w(z). Combining measurements of both H(z) and d A (z) up to sufficiently high redshifts z ∼ 2 and employing a parameterization of the redshift evolution of the dark energy equation of state are the keys to resolve the w(z)−Ω k degeneracy

Fractional charge and inter-Landau-level states at points of singular curvature.

Science.gov (United States)

Biswas, Rudro R; Son, Dam Thanh

2016-08-02

The quest for universal properties of topological phases is fundamentally important because these signatures are robust to variations in system-specific details. Aspects of the response of quantum Hall states to smooth spatial curvature are well-studied, but challenging to observe experimentally. Here we go beyond this prevailing paradigm and obtain general results for the response of quantum Hall states to points of singular curvature in real space; such points may be readily experimentally actualized. We find, using continuum analytical methods, that the point of curvature binds an excess fractional charge and sequences of quantum states split away, energetically, from the degenerate bulk Landau levels. Importantly, these inter-Landau-level states are bound to the topological singularity and have energies that are universal functions of bulk parameters and the curvature. Our exact diagonalization of lattice tight-binding models on closed manifolds demonstrates that these results continue to hold even when lattice effects are significant. An important technological implication of these results is that these inter-Landau-level states, being both energetically and spatially isolated quantum states, are promising candidates for constructing qubits for quantum computation.

Fast backprojection-based reconstruction of spectral-spatial EPR images from projections with the constant sweep of a magnetic field.

Science.gov (United States)

Komarov, Denis A; Hirata, Hiroshi

2017-08-01

In this paper, we introduce a procedure for the reconstruction of spectral-spatial EPR images using projections acquired with the constant sweep of a magnetic field. The application of a constant field-sweep and a predetermined data sampling rate simplifies the requirements for EPR imaging instrumentation and facilitates the backprojection-based reconstruction of spectral-spatial images. The proposed approach was applied to the reconstruction of a four-dimensional numerical phantom and to actual spectral-spatial EPR measurements. Image reconstruction using projections with a constant field-sweep was three times faster than the conventional approach with the application of a pseudo-angle and a scan range that depends on the applied field gradient. Spectral-spatial EPR imaging with a constant field-sweep for data acquisition only slightly reduces the signal-to-noise ratio or functional resolution of the resultant images and can be applied together with any common backprojection-based reconstruction algorithm. Copyright © 2017 Elsevier Inc. All rights reserved.

Inflation with a smooth constant-roll to constant-roll era transition

Science.gov (United States)

Odintsov, S. D.; Oikonomou, V. K.

2017-07-01

In this paper, we study canonical scalar field models, with a varying second slow-roll parameter, that allow transitions between constant-roll eras. In the models with two constant-roll eras, it is possible to avoid fine-tunings in the initial conditions of the scalar field. We mainly focus on the stability of the resulting solutions, and we also investigate if these solutions are attractors of the cosmological system. We shall calculate the resulting scalar potential and, by using a numerical approach, we examine the stability and attractor properties of the solutions. As we show, the first constant-roll era is dynamically unstable towards linear perturbations, and the cosmological system is driven by the attractor solution to the final constant-roll era. As we demonstrate, it is possible to have a nearly scale-invariant power spectrum of primordial curvature perturbations in some cases; however, this is strongly model dependent and depends on the rate of the final constant-roll era. Finally, we present, in brief, the essential features of a model that allows oscillations between constant-roll eras.

Isometric surfaces with a common mean curvature and the problem of Bonnet pairs

International Nuclear Information System (INIS)

Sabitov, Idzhad Kh

2012-01-01

Simple methods are used to give new proofs, and sometimes to make them more precise, of basic theorems on isometric surfaces with a common mean curvature, which are usually called Bonnet pairs. The considerations are conducted under the assumption of minimally admissible smoothness of the objects in question, and certain necessary or sufficient criteria are given for the non-existence of Bonnet pairs with a common non-constant mean curvature among compact surfaces. Bibliography: 26 titles.

Observational constraints on dark energy and cosmic curvature

International Nuclear Information System (INIS)

Wang Yun; Mukherjee, Pia

2007-01-01

Current observational bounds on dark energy depend on our assumptions about the curvature of the universe. We present a simple and efficient method for incorporating constraints from cosmic microwave background (CMB) anisotropy data and use it to derive constraints on cosmic curvature and dark energy density as a free function of cosmic time using current CMB, Type Ia supernova (SN Ia), and baryon acoustic oscillation data. We show that there are two CMB shift parameters, R≡√(Ω m H 0 2 )r(z CMB ) (the scaled distance to recombination) and l a ≡πr(z CMB )/r s (z CMB ) (the angular scale of the sound horizon at recombination), with measured values that are nearly uncorrelated with each other. Allowing nonzero cosmic curvature, the three-year WMAP (Wilkinson Microwave Anisotropy Probe) data give R=1.71±0.03, l a =302.5±1.2, and Ω b h 2 =0.02173±0.00082, independent of the dark energy model. The corresponding bounds for a flat universe are R=1.70±0.03, l a =302.2±1.2, and Ω b h 2 =0.022±0.00082. We give the covariance matrix of (R,l a ,Ω b h 2 ) from the three-year WMAP data. We find that (R,l a ,Ω b h 2 ) provide an efficient and intuitive summary of CMB data as far as dark energy constraints are concerned. Assuming the Hubble Space Telescope (HST) prior of H 0 =72±8 (km/s) Mpc -1 , using 182 SNe Ia (from the HST/GOODS program, the first year Supernova Legacy Survey, and nearby SN Ia surveys), (R,l a ,Ω b h 2 ) from WMAP three-year data, and SDSS (Sloan Digital Sky Survey) measurement of the baryon acoustic oscillation scale, we find that dark energy density is consistent with a constant in cosmic time, with marginal deviations from a cosmological constant that may reflect current systematic uncertainties or true evolution in dark energy. A flat universe is allowed by current data: Ω k =-0.006 -0.012-0.025 +0.013+0.025 for assuming that the dark energy equation of state w X (z) is constant, and Ω k =-0.002 -0.018-0.032 +0.018+0.041 for w X (z

Path integral approach for superintegrable potentials on spaces of non-constant curvature. Pt. 2. Darboux spaces D{sub III} and D{sub IV}

Energy Technology Data Exchange (ETDEWEB)

Grosche, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Pogosyan, G.S. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics]|[Guadalajara Univ., Jalisco (Mexico). Dept. de Matematicas CUCEI; Sissakian, A.N. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics

2006-08-15

This is the second paper on the path integral approach of superintegrable systems on Darboux spaces, spaces of non-constant curvature. We analyze in the spaces D{sub III} and D{sub IV} five respectively four superintegrable potentials, which were first given by Kalnins et al. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is determined by a higher order polynomial equation. We show that also the free motion in Darboux space of type III can contain bound states, provided the boundary conditions are appropriate. We state the energy spectrum and the wave-functions, respectively. (orig.)

Anatomical study of the radius and center of curvature of the distal femoral condyle

KAUST Repository

Kosel, Jü rgen; Giouroudi, Ioanna; Scheffer, Cornie; Dillon, Edwin Mark; Erasmus, Pieter J.

2010-01-01

In this anatomical study, the anteroposterior curvature of the surface of 16 cadaveric distal femurs was examined in terms of radii and center point. Those two parameters attract high interest due to their significance for total knee arthroplasty. Basically, two different conclusions have been drawn in foregoing studies: (1) The curvature shows a constant radius and (2) the curvature shows a variable radius. The investigations were based on a new method combining three-dimensional laser-scanning and planar geometrical analyses. This method is aimed at providing high accuracy and high local resolution. The high-precision laser scanning enables the exact reproduction of the distal femurs - including their cartilage tissue - as a three-dimensional computer model. The surface curvature was investigated on intersection planes that were oriented perpendicularly to the surgical epicondylar line. Three planes were placed at the central part of each condyle. The intersection of either plane with the femur model was approximated with the help of a b-spline, yielding three b-splines on each condyle. The radii and center points of the circles, approximating the local curvature of the b-splines, were then evaluated. The results from all three b-splines were averaged in order to increase the reliability of the method. The results show the variation in the surface curvatures of the investigated samples of condyles. These variations are expressed in the pattern of the center points and the radii of the curvatures. The standard deviations of the radii for a 90 deg arc on the posterior condyle range from 0.6 mm up to 5.1 mm, with an average of 2.4 mm laterally and 2.2 mm medially. No correlation was found between the curvature of the lateral and medial condyles. Within the range of the investigated 16 samples, the conclusion can be drawn that the condyle surface curvature is not constant and different for all specimens when viewed along the surgical epicondylar axis. For the portion

Numerical study on the incompressible Euler equations as a Hamiltonian system: Sectional curvature and Jacobi field

Science.gov (United States)

Ohkitani, K.

2010-05-01

We study some of the key quantities arising in the theory of [Arnold "Sur la geometrie differentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluides parfaits," Annales de l'institut Fourier 16, 319 (1966)] of the incompressible Euler equations both in two and three dimensions. The sectional curvatures for the Taylor-Green vortex and the ABC flow initial conditions are calculated exactly in three dimensions. We trace the time evolution of the Jacobi fields by direct numerical simulations and, in particular, see how the sectional curvatures get more and more negative in time. The spatial structure of the Jacobi fields is compared to the vorticity fields by visualizations. The Jacobi fields are found to grow exponentially in time for the flows with negative sectional curvatures. In two dimensions, a family of initial data proposed by Arnold (1966) is considered. The sectional curvature is observed to change its sign quickly even if it starts from a positive value. The Jacobi field is shown to be correlated with the passive scalar gradient in spatial structure. On the basis of Rouchon's physical-space based expression for the sectional curvature (1984), the origin of negative curvature is investigated. It is found that a "potential" αξ appearing in the definition of covariant time derivative plays an important role, in that a rapid growth in its gradient makes a major contribution to the negative curvature.

Curvature, zero modes and quantum statistics

Energy Technology Data Exchange (ETDEWEB)

Calixto, M [Departamento de Matematica Aplicada y EstadIstica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain); Aldaya, V [Instituto de AstrofIsica de AndalucIa, Apartado Postal 3004, 18080 Granada (Spain)

2006-08-18

We explore an intriguing connection between the Fermi-Dirac and Bose-Einstein statistics and the thermal baths obtained from a vacuum radiation of coherent states of zero modes in a second quantized (many-particle) theory on the compact O(3) and noncompact O(2, 1) isometry subgroups of the de Sitter and anti-de Sitter spaces, respectively. The high frequency limit is retrieved as a (zero-curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the vacuum energy density and the cosmological constant problem. (letter to the editor)

Memory for curvature of objects: haptic touch vs. vision.

Science.gov (United States)

Ittyerah, Miriam; Marks, Lawrence E

2007-11-01

The present study examined the role of vision and haptics in memory for stimulus objects that vary along the dimension of curvature. Experiment 1 measured haptic-haptic (T-T) and haptic-visual (T-V) discrimination of curvature in a short-term memory paradigm, using 30-second retention intervals containing five different interpolated tasks. Results showed poorest performance when the interpolated tasks required spatial processing or movement, thereby suggesting that haptic information about shape is encoded in a spatial-motor representation. Experiment 2 compared visual-visual (V-V) and visual-haptic (V-T) short-term memory, again using 30-second delay intervals. The results of the ANOVA failed to show a significant effect of intervening activity. Intra-modal visual performance and cross-modal performance were similar. Comparing the four modality conditions (inter-modal V-T, T-V; intra-modal V-V, T-T, by combining the data of Experiments 1 and 2), in a global analysis, showed a reliable interaction between intervening activity and experiment (modality). Although there appears to be a general tendency for spatial and movement activities to exert the most deleterious effects overall, the patterns are not identical when the initial stimulus is encoded haptically (Experiment 1) and visually (Experiment 2).

Curvature-Controlled Topological Defects

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Luka Mesarec

2017-05-01

Full Text Available Effectively, two-dimensional (2D closed films exhibiting in-plane orientational ordering (ordered shells might be instrumental for the realization of scaled crystals. In them, ordered shells are expected to play the role of atoms. Furthermore, topological defects (TDs within them would determine their valence. Namely, bonding among shells within an isotropic liquid matrix could be established via appropriate nano-binders (i.e., linkers which tend to be attached to the cores of TDs exploiting the defect core replacement mechanism. Consequently, by varying configurations of TDs one could nucleate growth of scaled crystals displaying different symmetries. For this purpose, it is of interest to develop a simple and robust mechanism via which one could control the position and number of TDs in such atoms. In this paper, we use a minimal mesoscopic model, where variational parameters are the 2D curvature tensor and the 2D orientational tensor order parameter. We demonstrate numerically the efficiency of the effective topological defect cancellation mechanism to predict positional assembling of TDs in ordered films characterized by spatially nonhomogeneous Gaussian curvature. Furthermore, we show how one could efficiently switch among qualitatively different structures by using a relative volume v of ordered shells, which represents a relatively simple naturally accessible control parameter.

Updated constraints on spatial variations of the fine-structure constant

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A.M.M. Pinho

2016-05-01

Full Text Available Recent work by Webb et al. has provided indications of spatial variations of the fine-structure constant, α, at a level of a few parts per million. Using a dataset of 293 archival measurements, they further show that a dipole provides a statistically good fit to the data, a result subsequently confirmed by other authors. Here we show that a more recent dataset of dedicated measurements further constrains these variations: although there are only 10 such measurements, their uncertainties are considerably smaller. We find that a dipolar variation is still a good fit to the combined dataset, but the amplitude of such a dipole must be somewhat smaller: 8.1±1.7 ppm for the full dataset, versus 9.4±2.2 ppm for the Webb et al. data alone, both at the 68.3% confidence level. Constraints on the direction on the sky of such a dipole are also significantly improved. On the other hand the data can't yet discriminate between a pure spatial dipole and one with an additional redshift dependence.

Dark Energy, scalar-curvature couplings and a critical acceleration scale

CERN Document Server

Navarro, Ignacio

2008-01-01

We study the effects of coupling a cosmologically rolling scalar field to higher order curvature terms. We show that when the strong coupling scale of the theory is on the 10^{-3}-10^{-1}eV range, the model passes all experimental bounds on the existence of fifth forces even if the field has a mass of the order of the Hubble scale in vacuum and non-suppressed couplings to SM fields. The reason is that the coupling to certain curvature invariant acts as an effective mass that grows in regions of large curvature. This prevents the field from rolling down its potential near sources and makes its effects on fifth-force search experiments performed in the laboratory to be observable only at the sub-mm scale. We obtain the static spherically symmetric solutions of the theory and show that a long-range force appears but it is turned on only below a fixed Newtonian acceleration scale of the order of the Hubble constant. We comment on the possibility of using this feature of the model to alleviate the CDM small scale ...

General relativity with small cosmological constant from spontaneous compactification of Lovelock theory in vacuum

International Nuclear Information System (INIS)

Canfora, Fabrizio; Willison, Steven; Giacomini, Alex; Troncoso, Ricardo

2009-01-01

It is shown that Einstein gravity in four dimensions with small cosmological constant and small extra dimensions can be obtained by spontaneous compactification of Lovelock gravity in vacuum. Assuming that the extra dimensions are compact spaces of constant curvature, general relativity is recovered within a certain class of Lovelock theories possessing necessarily cubic or higher order terms in curvature. This bounds the higher dimension to at least 7. Remarkably, the effective gauge coupling and Newton constant in four dimensions are not proportional to the gravitational constant in higher dimensions, but are shifted with respect to their standard values. This effect opens up new scenarios where a maximally symmetric solution in higher dimensions could decay into the compactified spacetime either by tunneling or through a gravitational analog of ghost condensation. Indeed, this is what occurs requiring both the extra dimensions and the four-dimensional cosmological constant to be small.

The curvature coordinate system

DEFF Research Database (Denmark)

Almegaard, Henrik

2007-01-01

The paper describes a concept for a curvature coordinate system on regular curved surfaces from which faceted surfaces with plane quadrangular facets can be designed. The lines of curvature are used as parametric lines for the curvature coordinate system on the surface. A new conjugate set of lin...

On Gauss-Bonnet Curvatures

Directory of Open Access Journals (Sweden)

Mohammed Larbi Labbi

2007-12-01

Full Text Available The $(2k$-th Gauss-Bonnet curvature is a generalization to higher dimensions of the $(2k$-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for $k = 1$. The Gauss-Bonnet curvatures are used in theoretical physics to describe gravity in higher dimensional space times where they are known as the Lagrangian of Lovelock gravity, Gauss-Bonnet Gravity and Lanczos gravity. In this paper we present various aspects of these curvature invariants and review their variational properties. In particular, we discuss natural generalizations of the Yamabe problem, Einstein metrics and minimal submanifolds.

Implementing quantum Ricci curvature

Science.gov (United States)

Klitgaard, N.; Loll, R.

2018-05-01

Quantum Ricci curvature has been introduced recently as a new, geometric observable characterizing the curvature properties of metric spaces, without the need for a smooth structure. Besides coordinate invariance, its key features are scalability, computability, and robustness. We demonstrate that these properties continue to hold in the context of nonperturbative quantum gravity, by evaluating the quantum Ricci curvature numerically in two-dimensional Euclidean quantum gravity, defined in terms of dynamical triangulations. Despite the well-known, highly nonclassical properties of the underlying quantum geometry, its Ricci curvature can be matched well to that of a five-dimensional round sphere.

The Nature of the Cosmological Constant Problem

Science.gov (United States)

Maia, M. D.; Capistrano, A. J. S.; Monte, E. M.

General relativity postulates the Minkowski space-time as the standard (flat) geometry against which we compare all curved space-times and also as the gravitational ground state where particles, quantum fields and their vacua are defined. On the other hand, experimental evidences tell that there exists a non-zero cosmological constant, which implies in a deSitter ground state, which not compatible with the assumed Minkowski structure. Such inconsistency is an evidence of the missing standard of curvature in Riemann's geometry, which in general relativity manifests itself in the form of the cosmological constant problem. We show how the lack of a curvature standard in Riemann's geometry can be fixed by Nash's theorem on metric perturbations. The resulting higher dimensional gravitational theory is more general than general relativity, similar to brane-world gravity, but where the propagation of the gravitational field along the extra dimensions is a mathematical necessity, rather than a postulate. After a brief introduction to Nash's theorem, we show that the vacuum energy density must remain confined to four-dimensional space-times, but the cosmological constant resulting from the contracted Bianchi identity represents a gravitational term which is not confined. In this case, the comparison between the vacuum energy and the cosmological constant in general relativity does not make sense. Instead, the geometrical fix provided by Nash's theorem suggests that the vacuum energy density contributes to the perturbations of the gravitational field.

Lectures on mean curvature flows

CERN Document Server

Zhu, Xi-Ping

2002-01-01

"Mean curvature flow" is a term that is used to describe the evolution of a hypersurface whose normal velocity is given by the mean curvature. In the simplest case of a convex closed curve on the plane, the properties of the mean curvature flow are described by Gage-Hamilton's theorem. This theorem states that under the mean curvature flow, the curve collapses to a point, and if the flow is diluted so that the enclosed area equals \\pi, the curve tends to the unit circle. In this book, the author gives a comprehensive account of fundamental results on singularities and the asymptotic behavior of mean curvature flows in higher dimensions. Among other topics, he considers in detail Huisken's theorem (a generalization of Gage-Hamilton's theorem to higher dimension), evolution of non-convex curves and hypersurfaces, and the classification of singularities of the mean curvature flow. Because of the importance of the mean curvature flow and its numerous applications in differential geometry and partial differential ...

Temporal and spatial foliations of spacetimes.

Science.gov (United States)

Herold, H.

For the solution of initial-value problems in numerical relativity usually the (3+1) splitting of Einstein's equations is employed. An important part of this splitting is the choice of the temporal gauge condition. In order to estimate the quality of time-evolution schemes, different time slicings of given well-known spherically symmetric spacetimes have been studied. Besides the maximal slicing condition the harmonic slicing prescription has been used to calculate temporal foliations of the Schwarzschild and the Oppenheimer-Snyder spacetime. Additionally, the author has studied a recently proposed, geometrically motivated spatial gauge condition, which is defined by considering the foliations of the three-dimensional space-like hypersurfaces by 2-surfaces of constant mean extrinsic curvature. Apart from the equations for the shift vector, which can be derived for this gauge condition, he has investigated such spatial foliations for well-known stationary axially symmetric spacetimes, namely for the Kerr metric and for numerically determined solutions for rapidly rotating neutron stars.

Integrating 3D seismic curvature and curvature gradient attributes for fracture characterization: Methodologies and interpretational implications

Energy Technology Data Exchange (ETDEWEB)

Gao, Dengliang

2013-03-01

In 3D seismic interpretation, curvature is a popular attribute that depicts the geometry of seismic reflectors and has been widely used to detect faults in the subsurface; however, it provides only part of the solutions to subsurface structure analysis. This study extends the curvature algorithm to a new curvature gradient algorithm, and integrates both algorithms for fracture detection using a 3D seismic test data set over Teapot Dome (Wyoming). In fractured reservoirs at Teapot Dome known to be formed by tectonic folding and faulting, curvature helps define the crestal portion of the reservoirs that is associated with strong seismic amplitude and high oil productivity. In contrast, curvature gradient helps better define the regional northwest-trending and the cross-regional northeast-trending lineaments that are associated with weak seismic amplitude and low oil productivity. In concert with previous reports from image logs, cores, and outcrops, the current study based on an integrated seismic curvature and curvature gradient analysis suggests that curvature might help define areas of enhanced potential to form tensile fractures, whereas curvature gradient might help define zones of enhanced potential to develop shear fractures. In certain fractured reservoirs such as at Teapot Dome where faulting and fault-related folding contribute dominantly to the formation and evolution of fractures, curvature and curvature gradient attributes can be potentially applied to differentiate fracture mode, to predict fracture intensity and orientation, to detect fracture volume and connectivity, and to model fracture networks.

Some Inequalities for the -Curvature Image

Directory of Open Access Journals (Sweden)

Daijun Wei

2009-01-01

Full Text Available Lutwak introduced the notion of -curvature image and proved an inequality for the volumes of convex body and its -curvature image. In this paper, we first give an monotonic property of -curvature image. Further, we establish two inequalities for the -curvature image and its polar, respectively. Finally, an inequality for the volumes of -projection body and -curvature image is obtained.

Model-independent curvature determination with 21cm intensity mapping experiments

Science.gov (United States)

Witzemann, Amadeus; Bull, Philip; Clarkson, Chris; Santos, Mario G.; Spinelli, Marta; Weltman, Amanda

2018-04-01

Measurements of the spatial curvature of the Universe have improved significantly in recent years, but still tend to require strong assumptions to be made about the equation of state of dark energy (DE) in order to reach sub-percent precision. When these assumptions are relaxed, strong degeneracies arise that make it hard to disentangle DE and curvature, degrading the constraints. We show that forthcoming 21cm intensity mapping experiments such as HIRAX are ideally designed to carry out model-independent curvature measurements, as they can measure the clustering signal at high redshift with sufficient precision to break many of the degeneracies. We consider two different model-independent methods, based on `avoiding' the DE-dominated regime and non-parametric modelling of the DE equation of state respectively. Our forecasts show that HIRAX will be able to improve upon current model-independent constraints by around an order of magnitude, reaching percent-level accuracy even when an arbitrary DE equation of state is assumed. In the same model-independent analysis, the sample variance limit for a similar survey is another order of magnitude better.

Sensitive zone parameters and curvature radius evaluation for polymer optical fiber curvature sensors

Science.gov (United States)

Leal-Junior, Arnaldo G.; Frizera, Anselmo; José Pontes, Maria

2018-03-01

Polymer optical fibers (POFs) are suitable for applications such as curvature sensors, strain, temperature, liquid level, among others. However, for enhancing sensitivity, many polymer optical fiber curvature sensors based on intensity variation require a lateral section. Lateral section length, depth, and surface roughness have great influence on the sensor sensitivity, hysteresis, and linearity. Moreover, the sensor curvature radius increase the stress on the fiber, which leads on variation of the sensor behavior. This paper presents the analysis relating the curvature radius and lateral section length, depth and surface roughness with the sensor sensitivity, hysteresis and linearity for a POF curvature sensor. Results show a strong correlation between the decision parameters behavior and the performance for sensor applications based on intensity variation. Furthermore, there is a trade-off among the sensitive zone length, depth, surface roughness, and curvature radius with the sensor desired performance parameters, which are minimum hysteresis, maximum sensitivity, and maximum linearity. The optimization of these parameters is applied to obtain a sensor with sensitivity of 20.9 mV/°, linearity of 0.9992 and hysteresis below 1%, which represent a better performance of the sensor when compared with the sensor without the optimization.

Brane cosmology with curvature corrections

International Nuclear Information System (INIS)

Kofinas, Georgios; Maartens, Roy; Papantonopoulos, Eleftherios

2003-01-01

We study the cosmology of the Randall-Sundrum brane-world where the Einstein-Hilbert action is modified by curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. The combined effect of these curvature corrections to the action removes the infinite-density big bang singularity, although the curvature can still diverge for some parameter values. A radiation brane undergoes accelerated expansion near the minimal scale factor, for a range of parameters. This acceleration is driven by the geometric effects, without an inflation field or negative pressures. At late times, conventional cosmology is recovered. (author)

New Constraints on Spatial Variations of the Fine Structure Constant from Clusters of Galaxies

Directory of Open Access Journals (Sweden)

Ivan De Martino

2016-12-01

Full Text Available We have constrained the spatial variation of the fine structure constant using multi-frequency measurements of the thermal Sunyaev-Zeldovich effect of 618 X-ray selected clusters. Although our results are not competitive with the ones from quasar absorption lines, we improved by a factor 10 and ∼2.5 previous results from Cosmic Microwave Background power spectrum and from galaxy clusters, respectively.

Regularized strings with extrinsic curvature

International Nuclear Information System (INIS)

Ambjoern, J.; Durhuus, B.

1987-07-01

We analyze models of discretized string theories, where the path integral over world sheet variables is regularized by summing over triangulated surfaces. The inclusion of curvature in the action is a necessity for the scaling of the string tension. We discuss the physical properties of models with extrinsic curvature terms in the action and show that the string tension vanishes at the critical point where the bare extrinsic curvature coupling tends to infinity. Similar results are derived for models with intrinsic curvature. (orig.)

4-dimensional General Relativity from the instrinsic spatial geometry of SO(3) Yang-Mills theory

International Nuclear Information System (INIS)

Ita, Eyo Eyo

2011-01-01

In this paper we derive 4-dimensional General Relativity from three dimensions, using the intrinsic spatial geometry inherent in Yang-Mills theory which has been exposed by previous authors as well as some properties of the Ashtekar variables. We provide various interesting relations, including the fact that General Relativity can be written as a Yang-Mills theory where the antiself-dual Weyl curvature replaces the Yang-Mills coupling constant. We have generalized the results of some previous authors, covering Einstein's spaces, to include more general spacetime geometries.

Mineralogy of the clay fraction of alfisols in two slope curvatures: IV - spatial correlation with physical properties

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Livia Arantes Camargo

2013-04-01

Full Text Available Although the influence of clay mineralogy on soil physical properties has been widely studied, spatial relationships between these features in Alfisols have rarely been examined. The purpose of this work was to relate the clay minerals and physical properties of an Alfisol of sandstone origin in two slope curvatures. The crystallographic properties such as mean crystallite size (MCS and width at half height (WHH of hematite, goethite, kaolinite and gibbsite; contents of hematite and goethite; aluminium substitution (AS and specific surface area (SSA of hematite and goethite; the goethite/(goethite+hematite and kaolinite/(kaolinite+gibbsite ratios; and the citrate/bicarbonate/dithionite extractable Fe (Fe d were correlated with the soil physical properties through Pearson correlation coefficients and cross-semivariograms. The correlations found between aluminium substitution in goethite and the soil physical properties suggest that the degree of crystallinity of this mineral influences soil properties used as soil quality indicators. Thus, goethite with a high aluminium substitution resulted in large aggregate sizes and a high porosity, and also in a low bulk density and soil penetration resistance. The presence of highly crystalline gibbsite resulted in a high density and micropore content, as well as in smaller aggregates. Interpretation of the cross-semivariogram and classification of landscape compartments in terms of the spatial dependence pattern for the relief-dependent physical and mineralogical properties of the soil proved an effective supplementary method for assessing Pearson correlations between the soil physical and mineralogical properties.

Constraining spatial variations of the fine-structure constant in symmetron models

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A.M.M. Pinho

2017-06-01

Full Text Available We introduce a methodology to test models with spatial variations of the fine-structure constant α, based on the calculation of the angular power spectrum of these measurements. This methodology enables comparisons of observations and theoretical models through their predictions on the statistics of the α variation. Here we apply it to the case of symmetron models. We find no indications of deviations from the standard behavior, with current data providing an upper limit to the strength of the symmetron coupling to gravity (log⁡β2<−0.9 when this is the only free parameter, and not able to constrain the model when also the symmetry breaking scale factor aSSB is free to vary.

Total curvature and total torsion of knotted random polygons in confinement

Science.gov (United States)

Diao, Yuanan; Ernst, Claus; Rawdon, Eric J.; Ziegler, Uta

2018-04-01

Knots in nature are typically confined spatially. The confinement affects the possible configurations, which in turn affects the spectrum of possible knot types as well as the geometry of the configurations within each knot type. The goal of this paper is to determine how confinement, length, and knotting affect the total curvature and total torsion of random polygons. Previously published papers have investigated these effects in the unconstrained case. In particular, we analyze how the total curvature and total torsion are affected by (1) varying the length of polygons within a fixed confinement radius and (2) varying the confinement radius of polygons with a fixed length. We also compare the total curvature and total torsion of groups of knots with similar complexity (measured as crossing number). While some of our results fall in line with what has been observed in the studies of the unconfined random polygons, a few surprising results emerge from our study, showing some properties that are unique due to the effect of knotting in confinement.

The limit passage of space curvature in problems of celestial mechanics with the generalized Kepler and Hooke potentials

Science.gov (United States)

Vozmishcheva, Tatiana

2016-09-01

The connection between the problems of celestial mechanics: the Kepler problem, the two-center problem and the two body problem in spaces of constant curvature with the generalized Kepler and Hooke potentials is investigated. The limit passage in the two-center and two body problems in the Lobachevsky space and on a sphere is carried out as λto0 (λ is the curvature of the corresponding space) for the two potentials. The potentials and metrics in spaces under study are written in the gnomonic coordinates. It is shown that as the curvature radius tends to infinity, the generalized gravitational and elastic potentials transform to the Kepler and Hooke forms in the Euclidean space.

Constraining cosmic curvature by using age of galaxies and gravitational lenses

International Nuclear Information System (INIS)

Rana, Akshay; Mahajan, Shobhit; Mukherjee, Amitabha; Jain, Deepak

2017-01-01

We use two model-independent methods to constrain the curvature of the universe. In the first method, we study the evolution of the curvature parameter (Ω k 0 ) with redshift by using the observations of the Hubble parameter and transverse comoving distances obtained from the age of galaxies. Secondly, we also use an indirect method based on the mean image separation statistics of gravitationally lensed quasars. The basis of this methodology is that the average image separation of lensed images will show a positive, negative or zero correlation with the source redshift in a closed, open or flat universe respectively. In order to smoothen the datasets used in both the methods, we use a non-parametric method namely, Gaussian Process (GP). Finally from first method we obtain Ω k 0 = 0.025±0.57 for a presumed flat universe while the cosmic curvature remains constant throughout the redshift region 0 < z < 1.37 which indicates that the universe may be homogeneous. Moreover, the combined result from both the methods suggests that the universe is marginally closed. However, a flat universe can be incorporated at 3σ level.

Constraining cosmic curvature by using age of galaxies and gravitational lenses

Energy Technology Data Exchange (ETDEWEB)

Rana, Akshay; Mahajan, Shobhit; Mukherjee, Amitabha [Department of Physics and Astrophysics, University of Delhi, Delhi 110007 (India); Jain, Deepak, E-mail: arana@physics.du.ac.in, E-mail: djain@ddu.du.ac.in, E-mail: shobhit.mahajan@gmail.com, E-mail: amimukh@gmail.com [Deen Dayal Upadhyaya College, University of Delhi, Sector-3, Dwarka, Delhi 110078 (India)

2017-03-01

We use two model-independent methods to constrain the curvature of the universe. In the first method, we study the evolution of the curvature parameter (Ω {sub k} {sup 0}) with redshift by using the observations of the Hubble parameter and transverse comoving distances obtained from the age of galaxies. Secondly, we also use an indirect method based on the mean image separation statistics of gravitationally lensed quasars. The basis of this methodology is that the average image separation of lensed images will show a positive, negative or zero correlation with the source redshift in a closed, open or flat universe respectively. In order to smoothen the datasets used in both the methods, we use a non-parametric method namely, Gaussian Process (GP). Finally from first method we obtain Ω {sub k} {sup 0} = 0.025±0.57 for a presumed flat universe while the cosmic curvature remains constant throughout the redshift region 0 < z < 1.37 which indicates that the universe may be homogeneous. Moreover, the combined result from both the methods suggests that the universe is marginally closed. However, a flat universe can be incorporated at 3σ level.

Wormholes in higher dimensions with non-linear curvature terms from quantum gravity corrections

Energy Technology Data Exchange (ETDEWEB)

El-Nabulsi, Ahmad Rami [Neijiang Normal University, Neijiang, Sichuan (China)

2011-11-15

In this work, we discuss a 7-dimensional universe in the presence of a static traversable wormhole and a decaying cosmological constant and dominated by higher-order curvature effects expected from quantum gravity corrections. We confirmed the existence of wormhole solutions in the form of the Lovelock gravity. Many interesting and attractive features are discussed in some detail.

Curvature Entropy for Curved Profile Generation

Directory of Open Access Journals (Sweden)

Koichiro Sato

2012-03-01

Full Text Available In a curved surface design, the overall shape features that emerge from combinations of shape elements are important. However, controlling the features of the overall shape in curved profiles is difficult using conventional microscopic shape information such as dimension. Herein two types of macroscopic shape information, curvature entropy and quadrature curvature entropy, quantitatively represent the features of the overall shape. The curvature entropy is calculated by the curvature distribution, and represents the complexity of a shape (one of the overall shape features. The quadrature curvature entropy is an improvement of the curvature entropy by introducing a Markov process to evaluate the continuity of a curvature and to approximate human cognition of the shape. Additionally, a shape generation method using a genetic algorithm as a calculator and the entropy as a shape generation index is presented. Finally, the applicability of the proposed method is demonstrated using the side view of an automobile as a design example.

Model-independent curvature determination with 21 cm intensity mapping experiments

Science.gov (United States)

Witzemann, Amadeus; Bull, Philip; Clarkson, Chris; Santos, Mario G.; Spinelli, Marta; Weltman, Amanda

2018-06-01

Measurements of the spatial curvature of the Universe have improved significantly in recent years, but still tend to require strong assumptions to be made about the equation of state of dark energy (DE) in order to reach sub-percent precision. When these assumptions are relaxed, strong degeneracies arise that make it hard to disentangle DE and curvature, degrading the constraints. We show that forthcoming 21 cm intensity mapping experiments such as Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX) are ideally designed to carry out model-independent curvature measurements, as they can measure the clustering signal at high redshift with sufficient precision to break many of the degeneracies. We consider two different model-independent methods, based on `avoiding' the DE-dominated regime and non-parametric modelling of the DE equation of state, respectively. Our forecasts show that HIRAX will be able to improve upon current model-independent constraints by around an order of magnitude, reaching percent-level accuracy even when an arbitrary DE equation of state is assumed. In the same model-independent analysis, the sample variance limit for a similar survey is another order of magnitude better.

The Influence of Shoreline Curvature on Rates of Shoreline Change on Sandy Coasts

Science.gov (United States)

Murray, A. B.; Lauzon, R.; Cheng, S.; Liu, J.; Lazarus, E.

2017-12-01

The sandy, low-lying barrier islands which characterize much of the US East and Gulf coasts are popular spots to live and vacation, and are often heavily developed. However, sandy shorelines and barriers are also naturally mobile landforms, which are vulnerable to sea level rise and storms and can experience high rates of shoreline change. Many previous studies have attempted to understand and quantify the factors that contribute to those rates of shoreline change, such as grain size, underlying geology, sea level rise, and anthropogenic modification. Shoreline curvature has not been considered in such analyses, but previous research has demonstrated that subtle coastline curvature (and therefore alongshore variation in relative offshore wave angle) can result in gradients in net alongshore transport that cause significant shoreline erosion or accretion. Here we present the results of a spatially extensive analysis of the correlation between shoreline curvature and shoreline change rates for the sandy shorelines of the US East and Gulf coasts. We find that, for wave-dominated sandy coasts where nourishment and shoreline stabilization do not dominate the shoreline change signal (such as parts of Texas, North Carolina, and Florida), there is a significant negative correlation between shoreline curvature and shoreline change rates over 1 - 5 km and decadal to centurial space and time scales. This correlation indicates that a portion of the coastal erosion (and accretion) observed in these areas can be explained by the smoothing of subtle coastline curvature by gradients in alongshore transport, and suggests that shoreline curvature should be included in future attempts to understand historical and future rates of shoreline change. Shoreline stabilization, especially through beach nourishment, complicates the relationship between curvature and shoreline change. Beach construction during nourishment creates a seaward convex curvature in the part of the shoreline moves

Curvature Entropy for Curved Profile Generation

OpenAIRE

Ujiie, Yoshiki; Kato, Takeo; Sato, Koichiro; Matsuoka, Yoshiyuki

2012-01-01

In a curved surface design, the overall shape features that emerge from combinations of shape elements are important. However, controlling the features of the overall shape in curved profiles is difficult using conventional microscopic shape information such as dimension. Herein two types of macroscopic shape information, curvature entropy and quadrature curvature entropy, quantitatively represent the features of the overall shape. The curvature entropy is calculated by the curvature distribu...

Curvature-Induced Instabilities of Shells

Science.gov (United States)

Pezzulla, Matteo; Stoop, Norbert; Steranka, Mark P.; Bade, Abdikhalaq J.; Holmes, Douglas P.

2018-01-01

Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of spontaneous curvature and geometric frustration in curved shells remains poorly understood. Via a combination of precision experiments on elastomeric spherical shells, simulations, and theory, we show how a spontaneous curvature induces a rotational symmetry-breaking buckling as well as a snapping instability reminiscent of the Venus fly trap closure mechanism. The instabilities, and their dependence on geometry, are rationalized by reducing the spontaneous curvature to an effective mechanical load. This formulation reveals a combined pressurelike term in the bulk and a torquelike term in the boundary, allowing scaling predictions for the instabilities that are in excellent agreement with experiments and simulations. Moreover, the effective pressure analogy suggests a curvature-induced subcritical buckling in closed shells. We determine the critical buckling curvature via a linear stability analysis that accounts for the combination of residual membrane and bending stresses. The prominent role of geometry in our findings suggests the applicability of the results over a wide range of scales.

Inflation with a constant rate of roll

International Nuclear Information System (INIS)

Motohashi, Hayato; Starobinsky, Alexei A.; Yokoyama, Jun'ichi

2015-01-01

We consider an inflationary scenario where the rate of inflaton roll defined by ·· φ/H φ-dot remains constant. The rate of roll is small for slow-roll inflation, while a generic rate of roll leads to the interesting case of 'constant-roll' inflation. We find a general exact solution for the inflaton potential required for such inflaton behaviour. In this model, due to non-slow evolution of background, the would-be decaying mode of linear scalar (curvature) perturbations may not be neglected. It can even grow for some values of the model parameter, while the other mode always remains constant. However, this always occurs for unstable solutions which are not attractors for the given potential. The most interesting particular cases of constant-roll inflation remaining viable with the most recent observational data are quadratic hilltop inflation (with cutoff) and natural inflation (with an additional negative cosmological constant). In these cases even-order slow-roll parameters approach non-negligible constants while the odd ones are asymptotically vanishing in the quasi-de Sitter regime

Some Inequalities for the Lp-Curvature Image

Directory of Open Access Journals (Sweden)

Xiang Yu

2009-01-01

Full Text Available Lutwak introduced the notion of Lp-curvature image and proved an inequality for the volumes of convex body and its Lp-curvature image. In this paper, we first give an monotonic property of Lp-curvature image. Further, we establish two inequalities for the Lp-curvature image and its polar, respectively. Finally, an inequality for the volumes of Lp-projection body and Lp-curvature image is obtained.

Autonomous spatially adaptive sampling in experiments based on curvature, statistical error and sample spacing with applications in LDA measurements

Science.gov (United States)

Theunissen, Raf; Kadosh, Jesse S.; Allen, Christian B.

2015-06-01

Spatially varying signals are typically sampled by collecting uniformly spaced samples irrespective of the signal content. For signals with inhomogeneous information content, this leads to unnecessarily dense sampling in regions of low interest or insufficient sample density at important features, or both. A new adaptive sampling technique is presented directing sample collection in proportion to local information content, capturing adequately the short-period features while sparsely sampling less dynamic regions. The proposed method incorporates a data-adapted sampling strategy on the basis of signal curvature, sample space-filling, variable experimental uncertainty and iterative improvement. Numerical assessment has indicated a reduction in the number of samples required to achieve a predefined uncertainty level overall while improving local accuracy for important features. The potential of the proposed method has been further demonstrated on the basis of Laser Doppler Anemometry experiments examining the wake behind a NACA0012 airfoil and the boundary layer characterisation of a flat plate.

The continuous determination of spacetime geometry by the Riemann curvature tensor

International Nuclear Information System (INIS)

Rendall, A.D.

1988-01-01

It is shown that generically the Riemann tensor of a Lorentz metric on an n-dimensional manifold (n ≥ 4) determines the metric up to a constant factor and hence determines the associated torsion-free connection uniquely. The resulting map from Riemann tensors to connections is continuous in the Whitney Csup(∞) topology but, at least for some manifolds, constant factors cannot be chosen so as to make the map from Riemann tensors to metrics continuous in that topology. The latter map is, however, continuous in the compact open Csup(∞) topology so that estimates of the metric and its derivatives on a compact set can be obtained from similar estimates on the curvature and its derivatives. (author)

Curvature bound from gravitational catalysis

Science.gov (United States)

Gies, Holger; Martini, Riccardo

2018-04-01

We determine bounds on the curvature of local patches of spacetime from the requirement of intact long-range chiral symmetry. The bounds arise from a scale-dependent analysis of gravitational catalysis and its influence on the effective potential for the chiral order parameter, as induced by fermionic fluctuations on a curved spacetime with local hyperbolic properties. The bound is expressed in terms of the local curvature scalar measured in units of a gauge-invariant coarse-graining scale. We argue that any effective field theory of quantum gravity obeying this curvature bound is safe from chiral symmetry breaking through gravitational catalysis and thus compatible with the simultaneous existence of chiral fermions in the low-energy spectrum. With increasing number of dimensions, the curvature bound in terms of the hyperbolic scale parameter becomes stronger. Applying the curvature bound to the asymptotic safety scenario for quantum gravity in four spacetime dimensions translates into bounds on the matter content of particle physics models.

Coupling constant corrections in a holographic model of heavy ion collisions

NARCIS (Netherlands)

Grozdanov, Sašo; Schee, Wilke van der

2017-01-01

We initiate a holographic study of coupling-dependent heavy ion collisions by analysing for the first time the effects of leading-order, inverse coupling constant corrections. In the dual description, this amounts to colliding gravitational shock waves in a theory with curvature-squared terms. We

Hamiltonian analysis of curvature-squared gravity with or without conformal invariance

Science.gov (United States)

KlusoÅ, Josef; Oksanen, Markku; Tureanu, Anca

2014-03-01

We analyze gravitational theories with quadratic curvature terms, including the case of conformally invariant Weyl gravity, motivated by the intention to find a renormalizable theory of gravity in the ultraviolet region, yet yielding general relativity at long distances. In the Hamiltonian formulation of Weyl gravity, the number of local constraints is equal to the number of unstable directions in phase space, which in principle could be sufficient for eliminating the unstable degrees of freedom in the full nonlinear theory. All the other theories of quadratic type are unstable—a problem appearing as ghost modes in the linearized theory. We find that the full projection of the Weyl tensor onto a three-dimensional hypersurface contains an additional fully traceless component, given by a quadratic extrinsic curvature tensor. A certain inconsistency in the literature is found and resolved: when the conformal invariance of Weyl gravity is broken by a cosmological constant term, the theory becomes pathological, since a constraint required by the Hamiltonian analysis imposes the determinant of the metric of spacetime to be zero. In order to resolve this problem by restoring the conformal invariance, we introduce a new scalar field that couples to the curvature of spacetime, reminiscent of the introduction of vector fields for ensuring the gauge invariance.

The Locus of the apices of projectile trajectories under constant drag

OpenAIRE

Hernández-Saldaña, H.

2017-01-01

We present an analytical solution for the projectile coplanar motion under constant drag parametrised by the velocity angle. We found the locus formed by the apices of the projectile trajectories. The range and time of flight are obtained numerically and we find that the optimal launching angle is smaller than in the free drag case. This is a good example of problems with constant dissipation of energy that includes curvature, and it is proper for intermediate courses of mechanics.

A remark about the mean curvature

International Nuclear Information System (INIS)

Zhang Weitao.

1992-11-01

In this paper, we give an integral identity about the mean curvature in Sobolev space H 0 1 (Ω) intersection H 2 (Ω). Suppose the mean curvature on Γ=δΩ is positive, we prove some inequalities of the positive mean curvature and propose some open problems. (author). 4 refs

Dissecting the Gravitational lens B1608+656 : II. Precision Measurements of the Hubble Constant, Spatial Curvature, and the Dark Energy Equation of State

NARCIS (Netherlands)

Suyu, S. H.; Marshall, P. J.; Auger, M. W.; Hilbert, S.; Blandford, R. D.; Koopmans, L. V. E.; Fassnacht, C. D.; Treu, T.

2010-01-01

Strong gravitational lens systems with measured time delays between the multiple images provide a method for measuring the "time-delay distance" to the lens, and thus the Hubble constant. We present a Bayesian analysis of the strong gravitational lens system B1608+656, incorporating (1) new, deep

Discrete Curvature Theories and Applications

KAUST Repository

Sun, Xiang

2016-08-25

Discrete Di erential Geometry (DDG) concerns discrete counterparts of notions and methods in di erential geometry. This thesis deals with a core subject in DDG, discrete curvature theories on various types of polyhedral surfaces that are practically important for free-form architecture, sunlight-redirecting shading systems, and face recognition. Modeled as polyhedral surfaces, the shapes of free-form structures may have to satisfy di erent geometric or physical constraints. We study a combination of geometry and physics { the discrete surfaces that can stand on their own, as well as having proper shapes for the manufacture. These proper shapes, known as circular and conical meshes, are closely related to discrete principal curvatures. We study curvature theories that make such surfaces possible. Shading systems of freeform building skins are new types of energy-saving structures that can re-direct the sunlight. From these systems, discrete line congruences across polyhedral surfaces can be abstracted. We develop a new curvature theory for polyhedral surfaces equipped with normal congruences { a particular type of congruences de ned by linear interpolation of vertex normals. The main results are a discussion of various de nitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula. In addition to architecture, we consider the role of discrete curvatures in face recognition. We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold, which is an extension of the classical notion of asymptotic directions. We get a simple expression of these cones for polyhedral surfaces, as well as convergence and approximation theorems. We use the asymptotic cones as facial descriptors and demonstrate the

Environmental influences on DNA curvature

DEFF Research Database (Denmark)

Ussery, David; Higgins, C.F.; Bolshoy, A.

1999-01-01

DNA curvature plays an important role in many biological processes. To study environmentalinfluences on DNA curvature we compared the anomalous migration on polyacrylamide gels ofligation ladders of 11 specifically-designed oligonucleotides. At low temperatures (25 degreesC and below) most......, whilst spermine enhanced theanomalous migration of a different set of sequences. Sequences with a GGC motif exhibitedgreater curvature than predicted by the presently-used angles for the nearest-neighbour wedgemodel and are especially sensitive to Mg2+. The data have implications for models...... for DNAcurvature and for environmentally-sensitive DNA conformations in the regulation of geneexpression....

Effect of Tension and Curvature of Skin on Insertion Characteristics of Microneedle Array

Science.gov (United States)

Tachikawa, Hiroto; Takano, Naoki; Nishiyabu, Kazuaki; Miki, Norihisa; Ami, Yoshimichi

Recent MEMS (micro electro mechanical system) fabrication techniques have made it possible to produce painless microneedles precisely enough to be inserted into epidermis layer penetrating the stratum corneum of human skin. This paper presents a testing procedure to evaluate the insertion characteristics of microneedle array using cultured human skin considering the tension and the curvature. First, the biaxial strain applied to the cultured human skin was measured by optical technique with image processing. It was found that almost constant strain could be successfully given within a certain area and that error factors in the experiment except the thickness variation of the cultured skin were negligible. Next, using a microneedle square array for brain machine interface (BMI) application, the effects of biaxial tension and the curvature on insertion characteristics were discussed. Within the above mentioned area with high strain, the needles were successfully inserted.

A Numerical Study on the Impeller Meridional Curvature of High Pressure Multistage Pump

Energy Technology Data Exchange (ETDEWEB)

Kim, Deok Su; Jean, Sang Gyu; Mamatov, Sanjar [Hyosung Goodsprings, Inc., Busan (Korea, Republic of); Park, Warn Gyu [Pusan Nat’l Univ., Busan (Korea, Republic of)

2017-07-15

This paper presents the hydraulic design an impeller and radial diffuser of a high-pressure multistage pump for reverse osmosis. The flow distribution and hydraulic performance for the meridional design of the impeller were analyzed numerically. Optimization was conducted based on the response surface method by varying the hub and shroud meridional curvatures, while maintaining the impeller outlet diameter, outlet width, and eye diameter constant. The analysis results of the head and efficiency with the variation in the impeller meridional profile showed that angle of the front shroud near the impeller outlet (εDs) had the highest effect on head increase, while the hub inlet length (d1i) and shroud curvature (Rds) had the highest effect on efficiency. From the meridional profile variation, an approximately 0.5% increase in efficiency was observed compared with the base model (case 25).

The Relationship Between Surface Curvature and Abdominal Aortic Aneurysm Wall Stress.

Science.gov (United States)

de Galarreta, Sergio Ruiz; Cazón, Aitor; Antón, Raúl; Finol, Ender A

2017-08-01

The maximum diameter (MD) criterion is the most important factor when predicting risk of rupture of abdominal aortic aneurysms (AAAs). An elevated wall stress has also been linked to a high risk of aneurysm rupture, yet is an uncommon clinical practice to compute AAA wall stress. The purpose of this study is to assess whether other characteristics of the AAA geometry are statistically correlated with wall stress. Using in-house segmentation and meshing algorithms, 30 patient-specific AAA models were generated for finite element analysis (FEA). These models were subsequently used to estimate wall stress and maximum diameter and to evaluate the spatial distributions of wall thickness, cross-sectional diameter, mean curvature, and Gaussian curvature. Data analysis consisted of statistical correlations of the aforementioned geometry metrics with wall stress for the 30 AAA inner and outer wall surfaces. In addition, a linear regression analysis was performed with all the AAA wall surfaces to quantify the relationship of the geometric indices with wall stress. These analyses indicated that while all the geometry metrics have statistically significant correlations with wall stress, the local mean curvature (LMC) exhibits the highest average Pearson's correlation coefficient for both inner and outer wall surfaces. The linear regression analysis revealed coefficients of determination for the outer and inner wall surfaces of 0.712 and 0.516, respectively, with LMC having the largest effect on the linear regression equation with wall stress. This work underscores the importance of evaluating AAA mean wall curvature as a potential surrogate for wall stress.

Optics design for J-TEXT ECE imaging with field curvature adjustment lens

Energy Technology Data Exchange (ETDEWEB)

Zhu, Y.; Zhao, Z.; Liu, W. D.; Xie, J., E-mail: jlxie@ustc.edu.cn [School of Physics, University of Science and Technology of China, Anhui 230026 (China); Hu, X.; Muscatello, C. M.; Domier, C. W.; Luhmann, N. C.; Chen, M.; Ren, X. [University of California at Davis, Davis, California 95616 (United States); Tobias, B. J. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Zhuang, G.; Yang, Z. [College of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074 (China)

2014-11-15

Significant progress has been made in the imaging and visualization of magnetohydrodynamic and microturbulence phenomena in magnetic fusion plasmas. Of particular importance has been microwave electron cyclotron emission imaging (ECEI) for imaging T{sub e} fluctuations. Key to the success of ECEI is a large Gaussian optics system constituting a major portion of the focusing of the microwave radiation from the plasma to the detector array. Both the spatial resolution and observation range are dependent upon the imaging optics system performance. In particular, it is critical that the field curvature on the image plane is reduced to decrease crosstalk between vertical channels. The receiver optics systems for two ECEI on the J-TEXT device have been designed to ameliorate these problems and provide good performance with additional field curvature adjustment lenses with a meniscus shape to correct the aberrations from several spherical surfaces.

Fluctuation-dissipation theorem in general relativity and the cosmological constant

International Nuclear Information System (INIS)

Mottola, E.

1992-01-01

Vacuum fluctuations are an essential feature of quantum field theory. Yet, the smallness of the scalar curvature of our universe suggests that the zero-point energy associated with these fluctuations does not curve spacetime. A possible way out of this paradox is suggested by the fact that microscopic fluctuations are generally accompanied by dissipative behavior in macroscopic systems. The intimate relation between the two is expressed by a fluctuation-dissipation theorem which extends to general relativity. The connection between quantum fluctuations and dissipation suggests a mechanism for the conversion of coherent stresses in the curvature of space into ordinary matter or radiation, thereby relaxing the effective cosmological ''constant'' to zero over time. The expansion of the universe may be the effect of this time-asymmetric relaxation process

An Improved Method to Measure the Cosmic Curvature

Energy Technology Data Exchange (ETDEWEB)

Wei, Jun-Jie; Wu, Xue-Feng, E-mail: jjwei@pmo.ac.cn [Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008 (China)

2017-04-01

In this paper, we propose an improved model-independent method to constrain the cosmic curvature by combining the most recent Hubble parameter H ( z ) and supernovae Ia (SNe Ia) data. Based on the H ( z ) data, we first use the model-independent smoothing technique, Gaussian processes, to construct a distance modulus μ {sub H} ( z ), which is susceptible to the cosmic curvature parameter Ω{sub k}. In contrary to previous studies, the light-curve-fitting parameters, which account for the distance estimation of SN (μ {sub SN}( z )), are set free to investigate whether Ω {sub k} has a dependence on them. By comparing μ {sub H} ( z ) to μ {sub SN}(z), we put limits on Ω {sub k}. Our results confirm that Ω {sub k} is independent of the SN light-curve parameters. Moreover, we show that the measured Ω {sub k} is in good agreement with zero cosmic curvature, implying that there is no significant deviation from a flat universe at the current observational data level. We also test the influence of different H(z) samples and different Hubble constant H {sub 0} values, finding that different H(z) samples do not have a significant impact on the constraints. However, different H {sub 0} priors can affect the constraints of Ω {sub k} to some degree. The prior of H {sub 0} = 73.24 ± 1.74 km s{sup −1} Mpc{sup −1} gives a value of Ω {sub k}, a little bit above the 1 σ confidence level away from 0, but H{sub 0} = 69.6 ± 0.7 km s{sup −1} Mpc{sup −1} gives it below 1 σ .

Manifolds of positive scalar curvature

Energy Technology Data Exchange (ETDEWEB)

Stolz, S [Department of Mathematics, University of Notre Dame, Notre Dame (United States)

2002-08-15

This lecture gives an survey on the problem of finding a positive scalar curvature metric on a closed manifold. The Gromov-Lawson-Rosenberg conjecture and its relation to the Baum-Connes conjecture are discussed and the problem of finding a positive Ricci curvature metric on a closed manifold is explained.

Locus of the apices of projectile trajectories under constant drag

Science.gov (United States)

Hernández-Saldaña, H.

2017-11-01

Using the hodograph method, we present an analytical solution for projectile coplanar motion under constant drag, parametrised by the velocity angle. We find the locus formed by the apices of the projectile trajectories, and discuss its implementation for the motion of a particle on an inclined plane in presence of Coulomb friction. The range and time of flight are obtained numerically, and we find that the optimal launching angle is smaller than in the drag-free case. This is a good example of a problem with constant dissipation of energy that includes curvature; it is appropriate for intermediate courses of mechanics.

An analytical model to predict curvature effects of the carbon nanotube on the overall behavior of nanocomposites

International Nuclear Information System (INIS)

Yang, B. J.; Souri, H.; Lee, H. K.; Kim, Sunghwan; Ryu, Seunghwa

2014-01-01

In this study, analytical expressions are introduced to provide a better understanding of carbon nanotubes (CNTs) curvature on the overall behavior of nanocomposites. The curviness of CNT is modeled as the wave geometries, and the transformed physical characteristics are applied to micromechanical framework. Since five independent elastic constants of CNTs are essential to derive the waviness effect, atomistic molecular statics simulations with varying nanotube radii are conducted. Influences of CNT curviness on the effective stiffness of the nanocomposites are analyzed, noting that the curvature effect is significantly influential on the effective stiffness of the nanocomposites, and it may improve or reduce the reinforcing effect depending on the orientation of CNTs. In addition, the predictions are compared with experimental data of the CNT-reinforced nanocomposites to assess the reliability of the proposed method. The developed constitutive model is expected to be used to determine the volume concentration of the reinforcing CNTs and mechanical responses of CNT-reinforced composites under various CNT curvature, radius, and orientation conditions.

Integration of length and curvature in haptic perception.

Science.gov (United States)

Panday, Virjanand; Tiest, Wouter M Bergmann; Kappers, Astrid M L

2014-01-24

We investigated if and how length and curvature information are integrated when an object is explored in one hand. Subjects were asked to explore four types of objects between thumb and index finger. Objects differed in either length, curvature, both length and curvature correlated as in a circle, or anti-correlated. We found that when both length and curvature are present, performance is significantly better than when only one of the two cues is available. Therefore, we conclude that there is integration of length and curvature. Moreover, if the two cues are correlated in a circular cross-section instead of in an anti-correlated way, performance is better than predicted by a combination of two independent cues. We conclude that integration of curvature and length is highly efficient when the cues in the object are combined as in a circle, which is the most common combination of curvature and length in daily life.

Right thoracic curvature in the normal spine

Directory of Open Access Journals (Sweden)

Masuda Keigo

2011-01-01

Full Text Available Abstract Background Trunk asymmetry and vertebral rotation, at times observed in the normal spine, resemble the characteristics of adolescent idiopathic scoliosis (AIS. Right thoracic curvature has also been reported in the normal spine. If it is determined that the features of right thoracic side curvature in the normal spine are the same as those observed in AIS, these findings might provide a basis for elucidating the etiology of this condition. For this reason, we investigated right thoracic curvature in the normal spine. Methods For normal spinal measurements, 1,200 patients who underwent a posteroanterior chest radiographs were evaluated. These consisted of 400 children (ages 4-9, 400 adolescents (ages 10-19 and 400 adults (ages 20-29, with each group comprised of both genders. The exclusion criteria were obvious chest and spinal diseases. As side curvature is minimal in normal spines and the range at which curvature is measured is difficult to ascertain, first the typical curvature range in scoliosis patients was determined and then the Cobb angle in normal spines was measured using the same range as the scoliosis curve, from T5 to T12. Right thoracic curvature was given a positive value. The curve pattern was organized in each collective three groups: neutral (from -1 degree to 1 degree, right (> +1 degree, and left ( Results In child group, Cobb angle in left was 120, in neutral was 125 and in right was 155. In adolescent group, Cobb angle in left was 70, in neutral was 114 and in right was 216. In adult group, Cobb angle in left was 46, in neutral was 102 and in right was 252. The curvature pattern shifts to the right side in the adolescent group (p Conclusions Based on standing chest radiographic measurements, a right thoracic curvature was observed in normal spines after adolescence.

Four-Spacecraft Magnetic Curvature and Vorticity Analyses on Kelvin-Helmholtz Waves in MHD Simulations

Science.gov (United States)

Kieokaew, Rungployphan; Foullon, Claire; Lavraud, Benoit

2018-01-01

Four-spacecraft missions are probing the Earth's magnetospheric environment with high potential for revealing spatial and temporal scales of a variety of in situ phenomena. The techniques allowed by these four spacecraft include the calculation of vorticity and the magnetic curvature analysis (MCA), both of which have been used in the study of various plasma structures. Motivated by curved magnetic field and vortical structures induced by Kelvin- Helmholtz (KH) waves, we investigate the robustness of the MCA and vorticity techniques when increasing (regular) tetrahedron sizes, to interpret real data. Here for the first time, we test both techniques on a 2.5-D MHD simulation of KH waves at the magnetopause. We investigate, in particular, the curvature and flow vorticity across KH vortices and produce time series for static spacecraft in the boundary layers. The combined results of magnetic curvature and vorticity further help us to understand the development of KH waves. In particular, first, in the trailing edge, the magnetic curvature across the magnetopause points in opposite directions, in the wave propagation direction on the magnetosheath side and against it on the magnetospheric side. Second, the existence of a "turnover layer" in the magnetospheric side, defined by negative vorticity for the duskside magnetopause, which persists in the saturation phase, is reminiscent of roll-up history. We found significant variations in the MCA measures depending on the size of the tetrahedron. This study lends support for cross-scale observations to better understand the nature of curvature and its role in plasma phenomena.

SLED phenomenology: curvature vs. volume

International Nuclear Information System (INIS)

Niedermann, Florian; Schneider, Robert

2016-01-01

We assess the question whether the SLED (Supersymmetric Large Extra Dimensions) model admits phenomenologically viable solutions with 4D maximal symmetry. We take into account a finite brane width and a scale invariance (SI) breaking dilaton-brane coupling, both of which should be included in a realistic setup. Provided that the brane tension and the microscopic size of the brane take generic values set by the fundamental bulk Planck scale, we find that either the 4D curvature or the size of the extra dimensions is unacceptably large. Since this result is independent of the dilaton-brane couplings, it provides the biggest challenge to the SLED program. In addition, to quantify its potential with respect to the cosmological constant problem, we infer the amount of tuning on model parameters required to obtain a sufficiently small 4D curvature. A first answer was recently given in http://dx.doi.org/10.1007/JHEP02(2016)025, showing that 4D flat solutions are only ensured in the SI case by imposing a tuning relation, even if a brane-localized flux is included. In this companion paper, we find that the tuning can in fact be avoided for certain SI breaking brane-dilaton couplings, but only at the price of worsening the phenomenological problem. Our results are obtained by solving the full coupled Einstein-dilaton system in a completely consistent way. The brane width is implemented using a well-known ring regularization. In passing, we note that for the couplings considered here the results of http://dx.doi.org/10.1007/JHEP02(2016)025 (which only treated infinitely thin branes) are all consistently recovered in the thin brane limit, and how this can be reconciled with the concerns about their correctness, recently brought up in http://dx.doi.org/10.1007/JHEP01(2016)017.

(Anti-) selfdual Riemann curvature tensor in four spacelike compactified dimensions, O5 isometry group and chiral fermion zero modes

International Nuclear Information System (INIS)

Minkowski, P.

1986-01-01

The metric and contorsion tensors are constructed which yield a combined Riemann curvature tensor of the form Rsup(+-)sub(μνsigmatau)=(1/2a 2 )(gsub(μsigma)gsub(νtau) - gsub(μtau)gsub(νsigma)+-√g epsilonsub(μνsigmatau)). The metric with euclidean signature (++++) describes a sphere S 4 with radius a, i.e. admits the isometry group O5. For selfdual (antiselfdual) curvature tensor the contorsion tensor is given by the antiselfdual (selfdual) instanton configuration with respect to the spin gauge group SU2sub(R) (SU2sub(L)). The selfdual (antiselfdual) Riemann tensor admits two covariantly constant right-handed (left-handed) spin 1/2 fermion zero modes, one J=1/2 and one J=3/2 right-handed (left-handed) multiplet corresponding to L=1, transforming as a pseudoreal representation of O4 (SU2sub(R(L))). The hermitean Dirac equation retains only the two constant chiral modes. (orig.)

Curvature and torsion in growing actin networks

International Nuclear Information System (INIS)

Shaevitz, Joshua W; Fletcher, Daniel A

2008-01-01

Intracellular pathogens such as Listeria monocytogenes and Rickettsia rickettsii move within a host cell by polymerizing a comet-tail of actin fibers that ultimately pushes the cell forward. This dense network of cross-linked actin polymers typically exhibits a striking curvature that causes bacteria to move in gently looping paths. Theoretically, tail curvature has been linked to details of motility by considering force and torque balances from a finite number of polymerizing filaments. Here we track beads coated with a prokaryotic activator of actin polymerization in three dimensions to directly quantify the curvature and torsion of bead motility paths. We find that bead paths are more likely to have low rather than high curvature at any given time. Furthermore, path curvature changes very slowly in time, with an autocorrelation decay time of 200 s. Paths with a small radius of curvature, therefore, remain so for an extended period resulting in loops when confined to two dimensions. When allowed to explore a three-dimensional (3D) space, path loops are less evident. Finally, we quantify the torsion in the bead paths and show that beads do not exhibit a significant left- or right-handed bias to their motion in 3D. These results suggest that paths of actin-propelled objects may be attributed to slow changes in curvature, possibly associated with filament debranching, rather than a fixed torque

Thermodynamic laws for generalized f(R) gravity with curvature-matter coupling

International Nuclear Information System (INIS)

Wu Yabo; Zhao Yueyue; Cai Ronggen; Lu Jianbo; Lu Junwang; Gao Xiaojing

2012-01-01

The first law and the generalized second law (GSL) of thermodynamics for the generalized f(R) gravity with curvature-matter coupling are studied in the spatially homogeneous, isotropic FRW universe. The research results show that the field equations of the generalized f(R) gravity with curvature-matter coupling can be cast to the form of the first law of thermodynamics with the so-called the entropy production terms dS ¯ and the GSL can be given by considering the FRW universe filled only with ordinary matter enclosed by the dynamical apparent horizon with the Hawking temperature. Furthermore, as a concrete example, by utilizing the GSL the constraints on the gravitational model with f 1 (R)=R+αR l and f 2 (R)=R m are also discussed. It is worth noting these results given by us are quite general and can degenerate to the ones in Einstein's general relativity and pure f(R) gravity with non-coupling and non-minimal coupling as special cases. Comparing with the case of Einstein's general relativity, the appearance of the entropy production term dS ¯ in the first law of thermodynamics demonstrates that the horizon thermodynamics is non-equilibrium one for generalized f(R) gravity with curvature-matter coupling, which is consistent with the arguments given in Akbar and Cai (2007) [13] and Eling et al. (2006) [18].

Collineations of the curvature tensor in general relativity

Indian Academy of Sciences (India)

Curvature collineations for the curvature tensor, constructed from a fundamental Bianchi Type-V metric, are studied. We are concerned with a symmetry property of space-time which is called curvature collineation, and we briefly discuss the physical and kinematical properties of the models.

Haptic perception of object curvature in Parkinson's disease.

Directory of Open Access Journals (Sweden)

Jürgen Konczak

2008-07-01

Full Text Available The haptic perception of the curvature of an object is essential for adequate object manipulation and critical for our guidance of actions. This study investigated how the ability to perceive the curvature of an object is altered by Parkinson's disease (PD.Eight healthy subjects and 11 patients with mild to moderate PD had to judge, without vision, the curvature of a virtual "box" created by a robotic manipulandum. Their hands were either moved passively along a defined curved path or they actively explored the curved curvature of a virtual wall. The curvature was either concave or convex (bulging to the left or right and was judged in two locations of the hand workspace--a left workspace location, where the curved hand path was associated with curved shoulder and elbow joint paths, and a right workspace location in which these joint paths were nearly linear. After exploring the curvature of the virtual object, subjects had to judge whether the curvature was concave or convex. Based on these data, thresholds for curvature sensitivity were established. The main findings of the study are: First, 9 out 11 PD patients (82% showed elevated thresholds for detecting convex curvatures in at least one test condition. The respective median threshold for the PD group was increased by 343% when compared to the control group. Second, when distal hand paths became less associated with proximal joint paths (right workspace, haptic acuity was reduced substantially in both groups. Third, sensitivity to hand trajectory curvature was not improved during active exploration in either group.Our data demonstrate that PD is associated with a decreased acuity of the haptic sense, which may occur already at an early stage of the disease.

Bounds on the slope and curvature of Isgur-Wise function in a QCD-inspired quark model

Energy Technology Data Exchange (ETDEWEB)

Hazarika, Bhaskar Jyoti [Department of Physics, Pandu College, Guwahati (India); Choudhury, D.K. [Department of Physics, Gauhati University, Guwahati (India)

2011-09-15

The quantum chromodynamics-inspired potential model pursued by us earlier has been recently modified to incorporate an additional factor 'c' in the linear cum Coulomb potential. While it felicitates the inclusion of standard confinement parameter b = 0.183 GeV{sup 2} unlike in previous work, it still falls short of explaining the Isgur-Wise function for the B mesons without ad hoc adjustment of the strong coupling constant. In this work, we determine the factor 'c' from the experimental values of decay constants and masses and show that the reality constraint on 'c' yields bounds on the strong coupling constant as well as on slope and curvature of Isgur-Wise function allowing more flexibility to the model. (author)

Topological photonic crystals with zero Berry curvature

Science.gov (United States)

Liu, Feng; Deng, Hai-Yao; Wakabayashi, Katsunori

2018-02-01

Topological photonic crystals are designed based on the concept of Zak's phase rather than the topological invariants such as the Chern number and spin Chern number, which rely on the existence of a nonvanishing Berry curvature. Our photonic crystals (PCs) are made of pure dielectrics and sit on a square lattice obeying the C4 v point-group symmetry. Two varieties of PCs are considered: one closely resembles the electronic two-dimensional Su-Schrieffer-Heeger model, and the other continues as an extension of this analogy. In both cases, the topological transitions are induced by adjusting the lattice constants. Topological edge modes (TEMs) are shown to exist within the nontrivial photonic band gaps on the termination of those PCs. The high efficiency of these TEMs transferring electromagnetic energy against several types of disorders has been demonstrated using the finite-element method.

Induced cosmological constant in braneworlds with warped internal spaces

International Nuclear Information System (INIS)

Saharian, Aram A.

2006-01-01

We investigate the vacuum energy density induced by quantum fluctuations of a bulk scalar field with general curvature coupling parameter on two codimension one parallel branes in a (D + 1)-dimensional background spacetime AdS D1+1 x Σ with a warped internal space Σ. It is assumed that on the branes the field obeys Robin boundary conditions. Using the generalized zeta function technique in combination with contour integral representations, the surface energies on the branes are presented in the form of the sums of single brane and second brane induced parts. For the geometry of a single brane both regions, on the left (L-region) and on the right (R-region), of the brane are considered. The surface densities for separate L- and R-regions contain pole and finite contributions. For an infinitely thin brane taking these regions together, in odd spatial dimensions the pole parts cancel and the total surface energy is finite. The parts in the surface densities generated by the presence of the second brane are finite for all nonzero values of the interbrane separation. The contribution of the Kaluza-Klein modes along Σ is investigated in various limiting cases. It is shown that for large distances between the branes the induced surface densities give rise to an exponentially suppressed cosmological constant on the brane. In the higher dimensional generalization of the Randall-Sundrum braneworld model, for the interbrane distances solving the hierarchy problem, the cosmological constant generated on the visible brane is of the right order of magnitude with the value suggested by the cosmological observations. (author)

Longitudinal surface curvature effect in magnetohydrodynamics

International Nuclear Information System (INIS)

Bodas, N.G.

1975-01-01

The two-dimensional motion of an incompressible and electrically conducting fluid past an electrically insulated body surface (having curvature) is studied for a given O(1) basic flow and magnetic field, when (i) the applied magnetic field is aligned with the velocity in the basic flow, and (ii) the applied magnetic field is within the body surface. 01 and 0(Re sup(1/2)) mean the first and second order approximations respectively in an exansion scheme in powers of Resup(-1/2), Re being the Reynolds number). The technique of matched asymptotic expansions is used to solve the problem. The governing partial differential equations to 0(Resup(-1/2)) boundary layer approximation are found to give similarity solutions for a family of surface curvature and pressure gradient distributions in case (i), and for uniform basic flow with analytic surface curvature distributions in case (ii). The equations are solved numerically. In case (i) it is seen that the effect of the magnetic field on the skin-friction- correction due to the curvature is very small. Also the magnetic field at the wall is reduced by the curvature on the convex side. In case (ii) the magnetic field significantly increases the skin-friction-correction due to the curvature. The effect of the magnetic field on the O(1) and O(Resup(-1/2)) skin friction coefficients increases with the increase of the electrical conductivity of the fluid. Also, at higher values of the magnetic pressure, moderate changes in the electrical conductivity do not influence the correction to the skin-friction significantly. (Auth.)

Straight-line string with curvature

International Nuclear Information System (INIS)

Solov'ev, L.D.

1995-01-01

Classical and quantum solutions for the relativistic straight-line string with arbitrary dependence on the world surface curvature are obtained. They differ from the case of the usual Nambu-Goto interaction by the behaviour of the Regge trajectory which in general can be non-linear. A regularization of the action is considered and a comparison with relativistic point with curvature is made. 5 refs

Large curvature and background scale independence in single-metric approximations to asymptotic safety

Energy Technology Data Exchange (ETDEWEB)

Morris, Tim R. [STAG Research Centre & Department of Physics and Astronomy, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom)

2016-11-25

In single-metric approximations to the exact renormalization group (RG) for quantum gravity, it has been not been clear how to treat the large curvature domain beyond the point where the effective cutoff scale k is less than the lowest eigenvalue of the appropriate modified Laplacian. We explain why this puzzle arises from background dependence, resulting in Wilsonian RG concepts being inapplicable. We show that when properly formulated over an ensemble of backgrounds, the Wilsonian RG can be restored. This in turn implies that solutions should be smooth and well defined no matter how large the curvature is taken. Even for the standard single-metric type approximation schemes, this construction can be rigorously derived by imposing a modified Ward identity (mWI) corresponding to rescaling the background metric by a constant factor. However compatibility in this approximation requires the space-time dimension to be six. Solving the mWI and flow equation simultaneously, new variables are then derived that are independent of overall background scale.

Curvature of random walks and random polygons in confinement

International Nuclear Information System (INIS)

Diao, Y; Ernst, C; Montemayor, A; Ziegler, U

2013-01-01

The purpose of this paper is to study the curvature of equilateral random walks and polygons that are confined in a sphere. Curvature is one of several basic geometric properties that can be used to describe random walks and polygons. We show that confinement affects curvature quite strongly, and in the limit case where the confinement diameter equals the edge length the unconfined expected curvature value doubles from π/2 to π. To study curvature a simple model of an equilateral random walk in spherical confinement in dimensions 2 and 3 is introduced. For this simple model we derive explicit integral expressions for the expected value of the total curvature in both dimensions. These expressions are functions that depend only on the radius R of the confinement sphere. We then show that the values obtained by numeric integration of these expressions agrees with numerical average curvature estimates obtained from simulations of random walks. Finally, we compare the confinement effect on curvature of random walks with random polygons. (paper)

The curvature calculation mechanism based on simple cell model.

Science.gov (United States)

Yu, Haiyang; Fan, Xingyu; Song, Aiqi

2017-07-20

A conclusion has not yet been reached on how exactly the human visual system detects curvature. This paper demonstrates how orientation-selective simple cells can be used to construct curvature-detecting neural units. Through fixed arrangements, multiple plurality cells were constructed to simulate curvature cells with a proportional output to their curvature. In addition, this paper offers a solution to the problem of narrow detection range under fixed resolution by selecting an output value under multiple resolution. Curvature cells can be treated as concrete models of an end-stopped mechanism, and they can be used to further understand "curvature-selective" characteristics and to explain basic psychophysical findings and perceptual phenomena in current studies.

Coding chaotic billiards: I-Non-Compact billiards on a negative curvature manifold

International Nuclear Information System (INIS)

Giannoni, M.J.; Ullmo, D.

1989-03-01

This paper presents a method for coding billiards. The main device is to use a proper surface of section, the bounce mapping, and foliate the reduced phase space into regions associated with a given code. The alphabet is merely the ensemble of the labels of the sides of the billiard. The procedure is applied here to non-compact polygonal billiard defined on a manifold of constant negative curvature, with all vertices at infinity. A simple grammar rule is necessary and sufficient to insure existence and uniqueness of the coding

Integration of length and curvature in haptic perception

NARCIS (Netherlands)

Panday, V.; Bergmann Tiest, W.M.; Kappers, A.M.L.

2014-01-01

We investigated if and how length and curvature information are integrated when an object is explored in one hand. Subjects were asked to explore four types of objects between thumb and index finger. Objects differed in either length, curvature, both length and curvature correlated as in a circle,

Coupling constant metamorphosis and Nth-order symmetries in classical and quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Kalnins, E G [Department of Mathematics and Statistics, University of Waikato, Hamilton (New Zealand); Miller, W Jr; Post, S [School of Mathematics, University of Minnesota, Minneapolis, MN 55455 (United States)], E-mail: miller@ima.umn.edu

2010-01-22

We review the fundamentals of coupling constant metamorphosis (CCM) and the Staeckel transform, and apply them to map integrable and superintegrable systems of all orders into other such systems on different manifolds. In general, CCM does not preserve the order of constants of the motion or even take polynomials in the momenta to polynomials in the momenta. We study specializations of these actions which preserve polynomials and also the structure of the symmetry algebras in both the classical and quantum cases. We give several examples of non-constant curvature third- and fourth-order superintegrable systems in two space dimensions obtained via CCM, with some details on the structure of the symmetry algebras preserved by the transform action.

Coupling constant metamorphosis and Nth-order symmetries in classical and quantum mechanics

International Nuclear Information System (INIS)

Kalnins, E G; Miller, W Jr; Post, S

2010-01-01

We review the fundamentals of coupling constant metamorphosis (CCM) and the Staeckel transform, and apply them to map integrable and superintegrable systems of all orders into other such systems on different manifolds. In general, CCM does not preserve the order of constants of the motion or even take polynomials in the momenta to polynomials in the momenta. We study specializations of these actions which preserve polynomials and also the structure of the symmetry algebras in both the classical and quantum cases. We give several examples of non-constant curvature third- and fourth-order superintegrable systems in two space dimensions obtained via CCM, with some details on the structure of the symmetry algebras preserved by the transform action.

Evolution of the curvature perturbations during warm inflation

International Nuclear Information System (INIS)

Matsuda, Tomohiro

2009-01-01

This paper considers warm inflation as an interesting application of multi-field inflation. Delta-N formalism is used for the calculation of the evolution of the curvature perturbations during warm inflation. Although the perturbations considered in this paper are decaying after the horizon exit, the corrections to the curvature perturbations sourced by these perturbations can remain and dominate the curvature perturbations at large scales. In addition to the typical evolution of the curvature perturbations, inhomogeneous diffusion rate is considered for warm inflation, which may lead to significant non-Gaussianity of the spectrum

Weyl tensors for asymmetric complex curvatures

International Nuclear Information System (INIS)

Oliveira, C.G.

Considering a second rank Hermitian field tensor and a general Hermitian connection the associated complex curvature tensor is constructed. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory. (Author) [pt

Spherical Process Models for Global Spatial Statistics

KAUST Repository

Jeong, Jaehong; Jun, Mikyoung; Genton, Marc G.

2017-01-01

Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture

Cyclic fatigue of nickel-titanium rotary instruments in a double (S-shaped) simulated curvature.

Science.gov (United States)

Al-Sudani, Dina; Grande, Nicola M; Plotino, Gianluca; Pompa, Giorgio; Di Carlo, Stefano; Testarelli, Luca; Gambarini, Gianluca

2012-07-01

The goal of the present study was to test the fatigue resistance of nickel-titanium rotary files in a double curvature (S-shaped) artificial root canal and to compare those results with single curvature artificial root canals. Two nickel-titanium endodontic instruments consisting of identical instrument sizes (constant .06 taper and 0.25 tip diameter) were tested, ProFile instruments and Vortex instruments. Both instruments were tested for fatigue inside an artificial canal with a double curvature and inside a curved artificial canal with a single curvature. Ten instruments for each group were tested to fracture in continuous rotary motion at 300 rpm. Number of cycles to failure (NCF) was calculated to the nearest whole number, and the length of the fractured fragment was measured in millimeters. Data were statistically analyzed with a level of significance set at 95% confidence level. The NCF value was always statistically lower in the double curved artificial canal when compared with the single curve (P instruments of the same size of different brand only in the single curve; ProFile registered a mean of 633.5 ± 75.1 NCF, whereas Vortex registered a mean of 548 ± 48.9 NCF. Regardless of the differences between the instruments used in the present study, the results suggest that the more complex is the root canal, the more adverse are the effects on the cyclic fatigue resistance of the instruments. Copyright © 2012 American Association of Endodontists. Published by Elsevier Inc. All rights reserved.

Surface meshing with curvature convergence

KAUST Repository

Li, Huibin; Zeng, Wei; Morvan, Jean-Marie; Chen, Liming; Gu, Xianfengdavid

2014-01-01

Surface meshing plays a fundamental role in graphics and visualization. Many geometric processing tasks involve solving geometric PDEs on meshes. The numerical stability, convergence rates and approximation errors are largely determined by the mesh qualities. In practice, Delaunay refinement algorithms offer satisfactory solutions to high quality mesh generations. The theoretical proofs for volume based and surface based Delaunay refinement algorithms have been established, but those for conformal parameterization based ones remain wide open. This work focuses on the curvature measure convergence for the conformal parameterization based Delaunay refinement algorithms. Given a metric surface, the proposed approach triangulates its conformal uniformization domain by the planar Delaunay refinement algorithms, and produces a high quality mesh. We give explicit estimates for the Hausdorff distance, the normal deviation, and the differences in curvature measures between the surface and the mesh. In contrast to the conventional results based on volumetric Delaunay refinement, our stronger estimates are independent of the mesh structure and directly guarantee the convergence of curvature measures. Meanwhile, our result on Gaussian curvature measure is intrinsic to the Riemannian metric and independent of the embedding. In practice, our meshing algorithm is much easier to implement and much more efficient. The experimental results verified our theoretical results and demonstrated the efficiency of the meshing algorithm. © 2014 IEEE.

Surface meshing with curvature convergence

KAUST Repository

Li, Huibin

2014-06-01

Surface meshing plays a fundamental role in graphics and visualization. Many geometric processing tasks involve solving geometric PDEs on meshes. The numerical stability, convergence rates and approximation errors are largely determined by the mesh qualities. In practice, Delaunay refinement algorithms offer satisfactory solutions to high quality mesh generations. The theoretical proofs for volume based and surface based Delaunay refinement algorithms have been established, but those for conformal parameterization based ones remain wide open. This work focuses on the curvature measure convergence for the conformal parameterization based Delaunay refinement algorithms. Given a metric surface, the proposed approach triangulates its conformal uniformization domain by the planar Delaunay refinement algorithms, and produces a high quality mesh. We give explicit estimates for the Hausdorff distance, the normal deviation, and the differences in curvature measures between the surface and the mesh. In contrast to the conventional results based on volumetric Delaunay refinement, our stronger estimates are independent of the mesh structure and directly guarantee the convergence of curvature measures. Meanwhile, our result on Gaussian curvature measure is intrinsic to the Riemannian metric and independent of the embedding. In practice, our meshing algorithm is much easier to implement and much more efficient. The experimental results verified our theoretical results and demonstrated the efficiency of the meshing algorithm. © 2014 IEEE.

The influence of spatial congruency and movement preparation time on saccade curvature in simultaneous and sequential dual-tasks.

Science.gov (United States)

Moehler, Tobias; Fiehler, Katja

2015-11-01

Saccade curvature represents a sensitive measure of oculomotor inhibition with saccades curving away from covertly attended locations. Here we investigated whether and how saccade curvature depends on movement preparation time when a perceptual task is performed during or before saccade preparation. Participants performed a dual-task including a visual discrimination task at a cued location and a saccade task to the same location (congruent) or to a different location (incongruent). Additionally, we varied saccade preparation time (time between saccade cue and Go-signal) and the occurrence of the discrimination task (during saccade preparation=simultaneous vs. before saccade preparation=sequential). We found deteriorated perceptual performance in incongruent trials during simultaneous task performance while perceptual performance was unaffected during sequential task performance. Saccade accuracy and precision were deteriorated in incongruent trials during simultaneous and, to a lesser extent, also during sequential task performance. Saccades consistently curved away from covertly attended non-saccade locations. Saccade curvature was unaffected by movement preparation time during simultaneous task performance but decreased and finally vanished with increasing movement preparation time during sequential task performance. Our results indicate that the competing saccade plan to the covertly attended non-saccade location is maintained during simultaneous task performance until the perceptual task is solved while in the sequential condition, in which the discrimination task is solved prior to the saccade task, oculomotor inhibition decays gradually with movement preparation time. Copyright © 2015 Elsevier Ltd. All rights reserved.

3D face recognition with asymptotic cones based principal curvatures

KAUST Repository

Tang, Yinhang

2015-05-01

The classical curvatures of smooth surfaces (Gaussian, mean and principal curvatures) have been widely used in 3D face recognition (FR). However, facial surfaces resulting from 3D sensors are discrete meshes. In this paper, we present a general framework and define three principal curvatures on discrete surfaces for the purpose of 3D FR. These principal curvatures are derived from the construction of asymptotic cones associated to any Borel subset of the discrete surface. They describe the local geometry of the underlying mesh. First two of them correspond to the classical principal curvatures in the smooth case. We isolate the third principal curvature that carries out meaningful geometric shape information. The three principal curvatures in different Borel subsets scales give multi-scale local facial surface descriptors. We combine the proposed principal curvatures with the LNP-based facial descriptor and SRC for recognition. The identification and verification experiments demonstrate the practicability and accuracy of the third principal curvature and the fusion of multi-scale Borel subset descriptors on 3D face from FRGC v2.0.

3D face recognition with asymptotic cones based principal curvatures

KAUST Repository

Tang, Yinhang; Sun, Xiang; Huang, Di; Morvan, Jean-Marie; Wang, Yunhong; Chen, Liming

2015-01-01

The classical curvatures of smooth surfaces (Gaussian, mean and principal curvatures) have been widely used in 3D face recognition (FR). However, facial surfaces resulting from 3D sensors are discrete meshes. In this paper, we present a general framework and define three principal curvatures on discrete surfaces for the purpose of 3D FR. These principal curvatures are derived from the construction of asymptotic cones associated to any Borel subset of the discrete surface. They describe the local geometry of the underlying mesh. First two of them correspond to the classical principal curvatures in the smooth case. We isolate the third principal curvature that carries out meaningful geometric shape information. The three principal curvatures in different Borel subsets scales give multi-scale local facial surface descriptors. We combine the proposed principal curvatures with the LNP-based facial descriptor and SRC for recognition. The identification and verification experiments demonstrate the practicability and accuracy of the third principal curvature and the fusion of multi-scale Borel subset descriptors on 3D face from FRGC v2.0.

Robust estimation of adaptive tensors of curvature by tensor voting.

Science.gov (United States)

Tong, Wai-Shun; Tang, Chi-Keung

2005-03-01

Although curvature estimation from a given mesh or regularly sampled point set is a well-studied problem, it is still challenging when the input consists of a cloud of unstructured points corrupted by misalignment error and outlier noise. Such input is ubiquitous in computer vision. In this paper, we propose a three-pass tensor voting algorithm to robustly estimate curvature tensors, from which accurate principal curvatures and directions can be calculated. Our quantitative estimation is an improvement over the previous two-pass algorithm, where only qualitative curvature estimation (sign of Gaussian curvature) is performed. To overcome misalignment errors, our improved method automatically corrects input point locations at subvoxel precision, which also rejects outliers that are uncorrectable. To adapt to different scales locally, we define the RadiusHit of a curvature tensor to quantify estimation accuracy and applicability. Our curvature estimation algorithm has been proven with detailed quantitative experiments, performing better in a variety of standard error metrics (percentage error in curvature magnitudes, absolute angle difference in curvature direction) in the presence of a large amount of misalignment noise.

Higher-order curvature terms and extended inflation

International Nuclear Information System (INIS)

Wang Yun

1990-01-01

We consider higher-order curvature terms in context of the Brans-Dicke theory of gravity, and investigate the effects of these terms on extended inflationary theories. We find that the higher-order curvature terms tend to speed up inflation, although the original extended-inflation solutions are stable when these terms are small. Analytical solutions are found for two extreme cases: when the higher-order curvature terms are small, and when they dominate. A conformal transformation is employed in solving the latter case, and some of the subtleties in this technique are discussed. We note that percolation is less likely to occur when the higher-order curvature terms are present. An upper bound on α is expected if we are to avoid excessive and inadequate percolation of true-vacuum bubbles

Non Lyapunov stability of the constant spatially developing 1-D gas flow in presence of solutions having strictly positive exponential growth rate

Science.gov (United States)

Balint, Stefan; Balint, Agneta M.

2017-01-01

Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 1-D gas flow are analyzed in the phase space of continuously differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the real axis. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1].

Constraining inverse curvature gravity with supernovae

Energy Technology Data Exchange (ETDEWEB)

Mena, Olga; Santiago, Jose; /Fermilab; Weller, Jochen; /University Coll., London /Fermilab

2005-10-01

We show that the current accelerated expansion of the Universe can be explained without resorting to dark energy. Models of generalized modified gravity, with inverse powers of the curvature can have late time accelerating attractors without conflicting with solar system experiments. We have solved the Friedman equations for the full dynamical range of the evolution of the Universe. This allows us to perform a detailed analysis of Supernovae data in the context of such models that results in an excellent fit. Hence, inverse curvature gravity models represent an example of phenomenologically viable models in which the current acceleration of the Universe is driven by curvature instead of dark energy. If we further include constraints on the current expansion rate of the Universe from the Hubble Space Telescope and on the age of the Universe from globular clusters, we obtain that the matter content of the Universe is 0.07 {le} {omega}{sub m} {le} 0.21 (95% Confidence). Hence the inverse curvature gravity models considered can not explain the dynamics of the Universe just with a baryonic matter component.

The behaviour of effective coupling constants in 'finite' grand unification theories in curved spacetime

International Nuclear Information System (INIS)

Buchbinder, I.L.; Odintsov, S.D.; Lichtzier, I.M.

1989-01-01

The question of the behaviour of effective coupling constants in one-loop 'finite' grand unification theories in curved spacetime is investigated. It is shown that in strong gravitational fields the effective coupling constant, corresponding to the parameter of non-minimal interaction of scalar and gravitational fields, tends to the conformal value or increases in an exponential fashion. The one-loop effective potential is obtained with accuracy to linear curvature terms. It is shown that, in external supergravity, supersymmetric finite theories admit asymptotic conformal invariance. (Author)

Quantifying the quality of hand movement in stroke patients through three-dimensional curvature

Directory of Open Access Journals (Sweden)

Osu Rieko

2011-10-01

from paretic movements. Conclusions Measurement based on curvature was able to quantify movement irregularities and matched well with the examiner's observations. The results suggest that the quality of paretic movements is well characterized using spatial smoothness represented by curvature. The smaller computational costs associated with this measurement suggest that this method has potential clinical utility.

The curvature function in general relativity

International Nuclear Information System (INIS)

Hall, G S; MacNay, Lucy

2006-01-01

A function, here called the curvature function, is defined and which is constructed explicitly from the type (0, 4) curvature tensor. Although such a function may be defined for any manifold admitting a metric, attention is here concentrated on this function on a spacetime. Some properties of this function are explored and compared with a previous discussion of it given by Petrov

Curvature of Indoor Sensor Network: Clustering Coefficient

Directory of Open Access Journals (Sweden)

2009-03-01

Full Text Available We investigate the geometric properties of the communication graph in realistic low-power wireless networks. In particular, we explore the concept of the curvature of a wireless network via the clustering coefficient. Clustering coefficient analysis is a computationally simplified, semilocal approach, which nevertheless captures such a large-scale feature as congestion in the underlying network. The clustering coefficient concept is applied to three cases of indoor sensor networks, under varying thresholds on the link packet reception rate (PRR. A transition from positive curvature (“meshed” network to negative curvature (“core concentric” network is observed by increasing the threshold. Even though this paper deals with network curvature per se, we nevertheless expand on the underlying congestion motivation, propose several new concepts (network inertia and centroid, and finally we argue that greedy routing on a virtual positively curved network achieves load balancing on the physical network.

Inverse curvature flows in asymptotically Robertson Walker spaces

Science.gov (United States)

Kröner, Heiko

2018-04-01

In this paper we consider inverse curvature flows in a Lorentzian manifold N which is the topological product of the real numbers with a closed Riemannian manifold and equipped with a Lorentzian metric having a future singularity so that N is asymptotically Robertson Walker. The flow speeds are future directed and given by 1 / F where F is a homogeneous degree one curvature function of class (K*) of the principal curvatures, i.e. the n-th root of the Gauss curvature. We prove longtime existence of these flows and that the flow hypersurfaces converge to smooth functions when they are rescaled with a proper factor which results from the asymptotics of the metric.

Curvature driven instabilities in toroidal plasmas

International Nuclear Information System (INIS)

Andersson, P.

1986-11-01

The electromagnetic ballooning mode, the curvature driven trapped electron mode and the toroidally induced ion temperature gradient mode have been studies. Eigenvalue equations have been derived and solved both numerically and analytically. For electromagnetic ballooning modes the effects of convective damping, finite Larmor radius, higher order curvature terms, and temperature gradients have been investigated. A fully toroidal fluid ion model has been developed. It is shown that a necessary and sufficient condition for an instability below the MHD limit is the presence of an ion temperature gradient. Analytical dispersion relations giving results in good agreement with numerical solutions are also presented. The curvature driven trapped electron modes are found to be unstable for virtually all parameters with growth rates of the order of the diamagnetic drift frequency. Studies have been made, using both a gyrokinetic ion description and the fully toroidal ion model. Both analytical and numerical results are presented and are found to be in good agreement. The toroidally induced ion temperature gradients modes are found to have a behavior similar to that of the curvature driven trapped electron modes and can in the electrostatic limit be described by a simple quadratic dispersion equation. (author)

GDP growth and the yield curvature

DEFF Research Database (Denmark)

Møller, Stig Vinther

2014-01-01

This paper examines the forecastability of GDP growth using information from the term structure of yields. In contrast to previous studies, the paper shows that the curvature of the yield curve contributes with much more forecasting power than the slope of yield curve. The yield curvature also...... predicts bond returns, implying a common element to time-variation in expected bond returns and expected GDP growth....

Face recognition based on depth maps and surface curvature

Science.gov (United States)

Gordon, Gaile G.

1991-09-01

This paper explores the representation of the human face by features based on the curvature of the face surface. Curature captures many features necessary to accurately describe the face, such as the shape of the forehead, jawline, and cheeks, which are not easily detected from standard intensity images. Moreover, the value of curvature at a point on the surface is also viewpoint invariant. Until recently range data of high enough resolution and accuracy to perform useful curvature calculations on the scale of the human face had been unavailable. Although several researchers have worked on the problem of interpreting range data from curved (although usually highly geometrically structured) surfaces, the main approaches have centered on segmentation by signs of mean and Gaussian curvature which have not proved sufficient in themselves for the case of the human face. This paper details the calculation of principal curvature for a particular data set, the calculation of general surface descriptors based on curvature, and the calculation of face specific descriptors based both on curvature features and a priori knowledge about the structure of the face. These face specific descriptors can be incorporated into many different recognition strategies. A system that implements one such strategy, depth template comparison, giving recognition rates between 80% and 90% is described.

INVESTIGATION OF CURVES SET BY CUBIC DISTRIBUTION OF CURVATURE

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S. A. Ustenko

2014-03-01

Full Text Available Purpose. Further development of the geometric modeling of curvelinear contours of different objects based on the specified cubic curvature distribution and setpoints of curvature in the boundary points. Methodology. We investigate the flat section of the curvilinear contour generating under condition that cubic curvature distribution is set. Curve begins and ends at the given points, where angles of tangent slope and curvature are also determined. It was obtained the curvature equation of this curve, depending on the section length and coefficient c of cubic curvature distribution. The analysis of obtained equation was carried out. As well as, it was investigated the conditions, in which the inflection points of the curve are appearing. One should find such an interval of parameter change (depending on the input data and the section length, in order to place the inflection point of the curvature graph outside the curve section borders. It was determined the dependence of tangent slope of angle to the curve at its arbitrary point, as well as it was given the recommendations to solve a system of integral equations that allow finding the length of the curve section and the coefficient c of curvature cubic distribution. Findings. As the result of curves research, it is found that the criterion for their selection one can consider the absence of inflection points of the curvature on the observed section. Influence analysis of the parameter c on the graph of tangent slope angle to the curve showed that regardless of its value, it is provided the same rate of angle increase of tangent slope to the curve. Originality. It is improved the approach to geometric modeling of curves based on cubic curvature distribution with its given values at the boundary points by eliminating the inflection points from the observed section of curvilinear contours. Practical value. Curves obtained using the proposed method can be used for geometric modeling of curvilinear

Generalized Curvature-Matter Couplings in Modified Gravity

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Tiberiu Harko

2014-07-01

Full Text Available In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit nonminimal couplings, for instance, between an arbitrary function of the scalar curvature R and the Lagrangian density of matter, induces a non-vanishing covariant derivative of the energy-momentum tensor, implying non-geodesic motion and, consequently, leads to the appearance of an extra force. Applied to the cosmological context, these curvature-matter couplings lead to interesting phenomenology, where one can obtain a unified description of the cosmological epochs. We also consider the possibility that the behavior of the galactic flat rotation curves can be explained in the framework of the curvature-matter coupling models, where the extra terms in the gravitational field equations modify the equations of motion of test particles and induce a supplementary gravitational interaction. In addition to this, these models are extremely useful for describing dark energy-dark matter interactions and for explaining the late-time cosmic acceleration.

Translating solitons to symplectic and Lagrangian mean curvature flows

International Nuclear Information System (INIS)

Han Xiaoli; Li Jiayu

2007-05-01

In this paper, we construct finite blow-up examples for symplectic mean curvature flows and we study symplectic translating solitons. We prove that there is no translating solitons with vertical bar α vertical bar ≤ α 0 to the symplectic mean curvature flow or to the almost calibrated Lagrangian mean curvature flow for some α 0 . (author)

Curvature reduces bending strains in the quokka femur

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Kyle McCabe

2017-03-01

Full Text Available This study explores how curvature in the quokka femur may help to reduce bending strain during locomotion. The quokka is a small wallaby, but the curvature of the femur and the muscles active during stance phase are similar to most quadrupedal mammals. Our hypothesis is that the action of hip extensor and ankle plantarflexor muscles during stance phase place cranial bending strains that act to reduce the caudal curvature of the femur. Knee extensors and biarticular muscles that span the femur longitudinally create caudal bending strains in the caudally curved (concave caudal side bone. These opposing strains can balance each other and result in less strain on the bone. We test this idea by comparing the performance of a normally curved finite element model of the quokka femur to a digitally straightened version of the same bone. The normally curved model is indeed less strained than the straightened version. To further examine the relationship between curvature and the strains in the femoral models, we also tested an extra-curved and a reverse-curved version with the same loads. There appears to be a linear relationship between the curvature and the strains experienced by the models. These results demonstrate that longitudinal curvature in bones may be a manipulable mechanism whereby bone can induce a strain gradient to oppose strains induced by habitual loading.

"Big Bang" as a result result of the curvature-driven first-order phase transition in the early cold Universe

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Pashitskii, E. A.; Pentegov, V. I.

We suggest that the "Big Bang" may be a result of the first-order phase transition driven by changing scalar curvature of the 4D space-time in the expanding cold Universe, filled with nonlinear scalar field φ and neutral matter with equation of state p = vɛ (where p and ɛ are pressure and energy density of matter). We consider a Lagrangian for scalar field in curved space-time with nonlinearity φ, which along with the quadratic term -ΣR|φ|2 (where Σ is interaction constant and R is scalar curvature) contains a term ΣR(φ +φ+) linear in φ. Due to this term the condition for the extrema of the potential energy of the scalar field is given by a cubic equation. Provided v > 1/3 the scalar curvature R = [κ(3v-1)ɛ - 4Γ (where κ and Γ are Einstein's gravitational and cosmological constants) decreases along with decreasing " in the process of the Universe's expansion, and at some critical value Rc < 0 a first-order phase transition occurs, driven by an "external field" parameter proportional to R. Given certain conditions the critical radius of the early Universe at the point of the first-order phase transition may reach arbitrary large values, so this scenario of unrestricted "inflation" of the Universe may be called "hyperinflation". Beyond the point of phase transition the system is rolling down into the potential minimum releasing the potential energy of scalar field with subsequent powerful heating of the Universe playing the role of "Big Bang".

Sequence periodicity in nucleosomal DNA and intrinsic curvature.

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Nair, T Murlidharan

2010-05-17

Most eukaryotic DNA contained in the nucleus is packaged by wrapping DNA around histone octamers. Histones are ubiquitous and bind most regions of chromosomal DNA. In order to achieve smooth wrapping of the DNA around the histone octamer, the DNA duplex should be able to deform and should possess intrinsic curvature. The deformability of DNA is a result of the non-parallelness of base pair stacks. The stacking interaction between base pairs is sequence dependent. The higher the stacking energy the more rigid the DNA helix, thus it is natural to expect that sequences that are involved in wrapping around the histone octamer should be unstacked and possess intrinsic curvature. Intrinsic curvature has been shown to be dictated by the periodic recurrence of certain dinucleotides. Several genome-wide studies directed towards mapping of nucleosome positions have revealed periodicity associated with certain stretches of sequences. In the current study, these sequences have been analyzed with a view to understand their sequence-dependent structures. Higher order DNA structures and the distribution of molecular bend loci associated with 146 base nucleosome core DNA sequence from C. elegans and chicken have been analyzed using the theoretical model for DNA curvature. The curvature dispersion calculated by cyclically permuting the sequences revealed that the molecular bend loci were delocalized throughout the nucleosome core region and had varying degrees of intrinsic curvature. The higher order structures associated with nucleosomes of C.elegans and chicken calculated from the sequences revealed heterogeneity with respect to the deviation of the DNA axis. The results points to the possibility of context dependent curvature of varying degrees to be associated with nucleosomal DNA.

Coherent Spatial and Colour Blended Exemplar Inpainting

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ANAM AKBAR

2017-04-01

Full Text Available In an image processing field the digital image recovery is termed as inpainting. Efficient retrieval of an image, especially having large objects with high curvature and complex texture is an immensely challenging problem for image inpainting researchers and practitioner. This enthused researchers and emerge various inpainting algorithms and many are in progress. Generally inpainting techniques approaches the available area source of given image(s to restore the unavailable area target by the information available at the target edge. This paper represents a novel approach BSDD (Blended Spatial and Dimensional Distances by sampling patches at each pixel of the source region. From the given sample, selection of local edge patch is gradient based without priority computation overhead as previous techniques. These local patches are searched globally by linear distance in which both spatial and dimensional distances are considered with regularization factor. The main motive of this method consists in achieving the efficiency, curvature and textural challenges of inpainting without compromising the quality of inpainted image. We have tested the proposed method in real as well as synthetic images with high curvature and complex textures in all cases results are comparable with other well-known techniques. In view of quality and optical the proposed algorithm exhibits better results.

Lecture notes on mean curvature flow, barriers and singular perturbations

CERN Document Server

Bellettini, Giovanni

2013-01-01

The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems.

Dynamic curvature sensing employing ionic-polymer–metal composite sensors

International Nuclear Information System (INIS)

Bahramzadeh, Yousef; Shahinpoor, Mohsen

2011-01-01

A dynamic curvature sensor is presented based on ionic-polymer–metal composite (IPMC) for curvature monitoring of deployable/inflatable dynamic space structures. Monitoring the curvature variation is of high importance in various engineering structures including shape monitoring of deployable/inflatable space structures in which the structural boundaries undergo a dynamic deployment process. The high sensitivity of IPMCs to the applied deformations as well as its flexibility make IPMCs a promising candidate for sensing of dynamic curvature changes. Herein, we explore the dynamic response of an IPMC sensor strip with respect to controlled curvature deformations subjected to different forms of input functions. Using a specially designed experimental setup, the voltage recovery effect, phase delay, and rate dependency of the output voltage signal of an IPMC curvature sensor are analyzed. Experimental results show that the IPMC sensor maintains the linearity, sensitivity, and repeatability required for curvature sensing. Besides, in order to describe the dynamic phenomena such as the rate dependency of the IPMC sensor, a chemo-electro-mechanical model based on the Poisson–Nernst–Planck (PNP) equation for the kinetics of ion diffusion is presented. By solving the governing partial differential equations the frequency response of the IPMC sensor is derived. The physical model is able to describe the dynamic properties of the IPMC sensor and the dependency of the signal on rate of excitations

Diffusional falsification of kinetic constants on Lineweaver-Burk plots.

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Ghim, Y S; Chang, H N

1983-11-07

The effect of mass transfer resistances on the Lineweaver-Burk plots in immobilized enzyme systems has been investigated numerically and with analytical approximate solutions. While Hamilton, Gardner & Colton (1974) studied the effect of internal diffusion resistances in planar geometry, our study was extended to the combined effect of internal and external diffusion in cylindrical and spherical geometries as well. The variation of Lineweaver-Burk plots with respect to the geometries was minimized by modifying the Thiele modulus and the Biot number with the shape factor. Especially for a small Biot number all the three Lineweaver-Burk plots fell on a single line. As was discussed by Hamilton et al. (1974), the curvature of the line for large external diffusion resistances was small enough to be assumed linear, which was confirmed from the two approximate solutions for large and small substrate concentrations. Two methods for obtaining intrinsic kinetic constants were proposed: First, we obtained both maximum reaction rate and Michaelis constant by fitting experimental data to a straight line where external diffusion resistance was relatively large, and second, we obtained Michaelis constant from apparent Michaelis constant from the figure in case we knew maximum reaction rate a priori.

Continuous-Curvature Path Generation Using Fermat's Spiral

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Anastasios M. Lekkas

2013-10-01

Full Text Available This paper proposes a novel methodology, based on Fermat's spiral (FS, for constructing curvature-continuous parametric paths in a plane. FS has a zero curvature at its origin, a property that allows it to be connected with a straight line smoothly, that is, without the curvature discontinuity which occurs at the transition point between a line and a circular arc when constructing Dubins paths. Furthermore, contrary to the computationally expensive clothoids, FS is described by very simple parametric equations that are trivial to compute. On the downside, computing the length of an FS arc involves a Gaussian hypergeometric function. However, this function is absolutely convergent and it is also shown that it poses no restrictions to the domain within which the length can be calculated. In addition, we present an alternative parametrization of FS which eliminates the parametric speed singularity at the origin, hence making the spiral suitable for path-tracking applications. A detailed description of how to construct curvature-continuous paths with FS is given.

Influence of Coanda surface curvature on performance of bladeless fan

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Li, Guoqi; Hu, Yongjun; Jin, Yingzi; Setoguchi, Toshiaki; Kim, Heuy Dong

2014-10-01

The unique Coanda surface has a great influence on the performance of bladeless fan. However, there is few studies to explain the relationship between the performance and Coanda surface curvature at present. In order to gain a qualitative understanding of effect of the curvature on the performance of bladeless fan, numerical studies are performed in this paper. Firstly, three-dimensional numerical simulation is done by Fluent software. For the purpose to obtain detailed information of the flow field around the Coanda surface, two-dimensional numerical simulation is also conducted. Five types of Coanda surfaces with different curvature are designed, and the flow behaviour and the performance of them are analyzed and compared with those of the prototype. The analysis indicates that the curvature of Coanda surface is strongly related to blowing performance, It is found that there is an optimal curvature of Coanda surfaces among the studied models. Simulation result shows that there is a special low pressure region. With increasing curvature in Y direction, several low pressure regions gradually enlarged, then begin to merge slowly, and finally form a large area of low pressure. From the analyses of streamlines and velocity angle, it is found that the magnitude of the curvature affects the flow direction and reasonable curvature can induce fluid flow close to the wall. Thus, it leads to that the curvature of the streamlines is consistent with that of Coanda surface. Meanwhile, it also causes the fluid movement towards the most suitable direction. This study will provide useful information to performance improvements of bladeless fans.

Distributed mean curvature on a discrete manifold for Regge calculus

International Nuclear Information System (INIS)

Conboye, Rory; Miller, Warner A; Ray, Shannon

2015-01-01

The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector. (paper)

Distributed mean curvature on a discrete manifold for Regge calculus

Science.gov (United States)

Conboye, Rory; Miller, Warner A.; Ray, Shannon

2015-09-01

The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector.

Substrate curvature gradient drives rapid droplet motion.

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Lv, Cunjing; Chen, Chao; Chuang, Yin-Chuan; Tseng, Fan-Gang; Yin, Yajun; Grey, Francois; Zheng, Quanshui

2014-07-11

Making small liquid droplets move spontaneously on solid surfaces is a key challenge in lab-on-chip and heat exchanger technologies. Here, we report that a substrate curvature gradient can accelerate micro- and nanodroplets to high speeds on both hydrophilic and hydrophobic substrates. Experiments for microscale water droplets on tapered surfaces show a maximum speed of 0.42  m/s, 2 orders of magnitude higher than with a wettability gradient. We show that the total free energy and driving force exerted on a droplet are determined by the substrate curvature and substrate curvature gradient, respectively. Using molecular dynamics simulations, we predict nanoscale droplets moving spontaneously at over 100  m/s on tapered surfaces.

Effect of nano-scale curvature on the intrinsic blood coagulation system

Science.gov (United States)

Kushida, Takashi; Saha, Krishnendu; Subramani, Chandramouleeswaran; Nandwana, Vikas; Rotello, Vincent M.

2014-11-01

The intrinsic coagulation activity of silica nanoparticles strongly depends on their surface curvature. Nanoparticles with higher surface curvature do not denature blood coagulation factor XII on its surface, providing a coagulation `silent' surface, while nanoparticles with lower surface curvature show denaturation and concomitant coagulation.The intrinsic coagulation activity of silica nanoparticles strongly depends on their surface curvature. Nanoparticles with higher surface curvature do not denature blood coagulation factor XII on its surface, providing a coagulation `silent' surface, while nanoparticles with lower surface curvature show denaturation and concomitant coagulation. Electronic supplementary information (ESI) available: Physical properties and scanning electron micrographs (SEM) of silica NPs, intrinsic coagulation activity after 3 h. See DOI: 10.1039/c4nr04128c

Effect of Plate Curvature on Blast Response of Structural Steel Plates

Science.gov (United States)

Veeredhi, Lakshmi Shireen Banu; Ramana Rao, N. V.; Veeredhi, Vasudeva Rao

2018-04-01

In the present work an attempt is made, through simulation studies, to determine the effect of plate curvature on the blast response of a door structure made of ASTM A515 grade 50 steel plates. A door structure with dimensions of 5.142 m × 2.56 m × 10 mm having six different radii of curvatures is analyzed which is subjected to blast load. The radii of curvature investigated are infinity (flat plate), 16.63, 10.81, 8.26, 6.61 and 5.56 m. In the present study, a stand-off distance of 11 m is considered for all the cases. Results showed that the door structure with smallest radius of curvature experienced least plastic deformation and yielding when compared to a door with larger radius of curvature with same projected area. From the present Investigation, it is observed that, as the radius of curvature of the plate increases, the deformation mode gradually shifts from indentation mode to flexural mode. The plates with infinity and 16.63 m radius of curvature have undergone flexural mode of deformation and plates with 6.61 and 5.56 m radius of curvature undergo indentation mode of deformation. Whereas, mixed mode of deformation that consists of both flexural and indentation mode of deformations are seen in the plates with radius of curvature 10.81 and 8.26 m. As the radius of curvature of the plate decreases the ability of the plate to mitigate the effect the blast loads increased. It is observed that the plate with smaller radius of curvature deflects most of the blast energy and results in least indentation mode of deformation. The most significant observation made in the present investigation is that the strain energy absorbed by the steel plate gets reduced to 1/3 rd when the radius of curvature is approximately equal to the stand-off distance which could be the critical radius of curvature.

Cholera toxin B subunit induces local curvature on lipid bilayers

DEFF Research Database (Denmark)

Pezeshkian, Weria; Nåbo, Lina J.; Ipsen, John H.

2017-01-01

B induces a local membrane curvature that is essential for its clathrin-independent uptake. Using all-atom molecular dynamics, we show that CTxB induces local curvature, with the radius of curvature around 36 nm. The main feature of the CTxB molecular structure that causes membrane bending is the protruding...... alpha helices in the middle of the protein. Our study points to a generic protein design principle for generating local membrane curvature through specific binding to their lipid anchors....

Holonomy Attractor Connecting Spaces of Different Curvature Responsible for ``Anomalies''

Science.gov (United States)

Binder, Bernd

2009-03-01

SO(3). MAP can be extended to a neural network, where the synaptic connection of the holonomy attractor is just the mathematical condition adjusting and bridging spaces with positive (spherical) and negative (hyperbolic) curvature allowing for lossless/supra spin currents. Another strategy is to look for existing spin/precession anomalies and corresponding nonlinear holonomy conditions at the most fundamental level from the quark level to the cosmic scale. In these sceneries the geodesic attractor could control holonomy and curvature near the fixed points. It was proposed in 2002 that this should happen with electrons in atomic orbits showing a Berry phase part of the Rydberg or Sommerfeld fine structure constant and in 2003 that this effect could be responsible for (in)stabilities in the nuclear range and in superconductors. In 2008 it was shown that the attractor is part of the chaotic mechanical dynamics successfully at work in the Gyro-twister fitness device, and in 2007-2009 that there could be some deep relevance to "anomalies" in many scenarios even on the cosmic scales. Thus, we will point to and discuss some possible future applications that could be utilized for metric engineering: generating artificial holonomy and curvature (DC effect) for propulsion, or forcing holonomy waves (AC effect) in hyperbolic space-time, which are just gravitational waves interesting for communication.

Radion stabilization in higher curvature warped spacetime

Energy Technology Data Exchange (ETDEWEB)

Das, Ashmita [Indian Institute of Technology, Department of Physics, Guwahati, Assam (India); Mukherjee, Hiya; Paul, Tanmoy; SenGupta, Soumitra [Indian Association for the Cultivation of Science, Department of Theoretical Physics, Kolkata (India)

2018-02-15

We consider a five dimensional AdS spacetime in presence of higher curvature term like F(R) = R + αR{sup 2} in the bulk. In this model, we examine the possibility of modulus stabilization from the scalar degrees of freedom of higher curvature gravity free of ghosts. Our result reveals that the model stabilizes itself and the mechanism of modulus stabilization can be argued from a geometric point of view. We determine the region of the parametric space for which the modulus (or radion) can to be stabilized. We also show how the mass and coupling parameters of radion field are modified due to higher curvature term leading to modifications of its phenomenological implications on the visible 3-brane. (orig.)

Precision of anterior and posterior corneal curvature measurements taken with the Oculus Pentacam

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Elizabeth Chetty

2016-06-01

Full Text Available In the era of rapid advances in technology, new ophthalmic instruments are constantly influencing health sciences and necessitating investigations of the accuracy and precision of the new technology. The Oculus Pentacam (70700 has been available for some time now and numerous studies have investigated the precision of some of the parameters that the Pentacam is capable of measuring. Unfortunately some of these studies fall short in confusing the meaning of accuracy and precision and in not being able to analyse the data correctly or completely. The aim of this study was to investigate the precision of the anterior and posterior corneal curvature measurements taken with the Oculus Pentacam (70700 holistically with sound multivariate statistical methods. Twenty successive Pentacam measurements were taken over three different measuring sessions on one subject. Keratometric data for both the anterior and posterior corneal surfaces were analysed using multivariate statistics to determine the precision of the Oculus Pentacam. This instrument was found to have good precision both clinically and statistically for anterior corneal measurements but only good clinical precision for the posterior corneal surface. Key words: Oculus Pentacam; keratometric variation; corneal curvature; multivariate statistics

Observational constraints on the primordial curvature power spectrum

Science.gov (United States)

Emami, Razieh; Smoot, George F.

2018-01-01

CMB temperature fluctuation observations provide a precise measurement of the primordial power spectrum on large scales, corresponding to wavenumbers 10‑3 Mpc‑1 lesssim k lesssim 0.1 Mpc‑1, [1-7, 11]. Luminous red galaxies and galaxy clusters probe the matter power spectrum on overlapping scales (0.02 Mpc‑1 lesssim k lesssim 0.7 Mpc‑1 [10, 12-20]), while the Lyman-alpha forest reaches slightly smaller scales (0.3 Mpc‑1 lesssim k lesssim 3 Mpc‑1 [22]). These observations indicate that the primordial power spectrum is nearly scale-invariant with an amplitude close to 2 × 10‑9, [5, 23-28]. These observations strongly support Inflation and motivate us to obtain observations and constraints reaching to smaller scales on the primordial curvature power spectrum and by implication on Inflation. We are able to obtain limits to much higher values of k lesssim 105 Mpc‑1 and with less sensitivity even higher k lesssim 1019‑ 1023 Mpc‑1 using limits from CMB spectral distortions and other limits on ultracompact minihalo objects (UCMHs) and Primordial Black Holes (PBHs). PBHs are one of the known candidates for the Dark Matter (DM). Due to their very early formation, they could give us valuable information about the primordial curvature perturbations. These are complementary to other cosmological bounds on the amplitude of the primordial fluctuations. In this paper, we revisit and collect all the published constraints on both PBHs and UCMHs. We show that unless one uses the CMB spectral distortion, PBHs give us a very relaxed bounds on the primordial curvature perturbations. UCMHs, on the other hand, are very informative over a reasonable k range (3 lesssim k lesssim 106 Mpc‑1) and lead to significant upper-bounds on the curvature spectrum. We review the conditions under which the tighter constraints on the UCMHs could imply extremely strong bounds on the fraction of DM that could be PBHs in reasonable models. Failure to satisfy these conditions would

Heterotic M-theory, warped geometry and the cosmological constant problem

International Nuclear Information System (INIS)

Krause, A.

2001-01-01

The first part of this thesis analyzes whether a locally flat background represents a stable vacuum for the proposed heterotic M-theory. A calculation of the leading order supergravity exchange diagrams leads to the conclusion that the locally flat vacuum cannot be stable. Afterwards a comparison with the corresponding weakly coupled heterotic string amplitudes is made. Next, we consider compactifications of heterotic M-theory on a Calabi-Yau threefold, including a non-vanishing G-flux. The ensuing warped-geometry is determined completely and used to show that the variation of the Calabi-Yau volume along the orbifold direction varies quadratically with distance instead linearly as suggested by an earlier first order approximation. In the second part of this thesis we propose a mechanism for obtaining a small cosmological constant. This mechanism consists of the separation of two domain-walls, which together constitute our world, up to a distance 2l ≅1/M GUT . The resulting warped-geometry leads to an exponential suppression of the cosmological constant, which thereby can obtain its observed value without introducing a large hierarchy. An embedding of this set-up into IIB string-theory entails an SU(6) grand unified theory with a natural explanation of the Higgs doublet-triplet splitting. Finally, we examine to what extent the string-theory T-duality can influence curvature. To this aim we derive the full transformation of the curvature-tensor under T-duality. (orig.)

Robust modal curvature features for identifying multiple damage in beams

Science.gov (United States)

Ostachowicz, Wiesław; Xu, Wei; Bai, Runbo; Radzieński, Maciej; Cao, Maosen

2014-03-01

Curvature mode shape is an effective feature for damage detection in beams. However, it is susceptible to measurement noise, easily impairing its advantage of sensitivity to damage. To deal with this deficiency, this study formulates an improved curvature mode shape for multiple damage detection in beams based on integrating a wavelet transform (WT) and a Teager energy operator (TEO). The improved curvature mode shape, termed the WT - TEO curvature mode shape, has inherent capabilities of immunity to noise and sensitivity to damage. The proposed method is experimentally validated by identifying multiple cracks in cantilever steel beams with the mode shapes acquired using a scanning laser vibrometer. The results demonstrate that the improved curvature mode shape can identify multiple damage accurately and reliably, and it is fairly robust to measurement noise.

Surface Casimir densities and induced cosmological constant on parallel branes in AdS spacetime

International Nuclear Information System (INIS)

Saharian, Aram A.

2004-01-01

Vacuum expectation value of the surface energy-momentum tensor is evaluated for a massive scalar field with general curvature coupling parameter subject to Robin boundary conditions on two parallel branes located on (D+1)-dimensional anti-de Sitter bulk. The general case of different Robin coefficients on separate branes is considered. As a regularization procedure the generalized zeta function technique is used, in combination with contour integral representations. The surface energies on the branes are presented in the form of the sums of single brane and second brane-induced parts. For the geometry of a single brane both regions, on the left (L-region) and on the right (R-region), of the brane are considered. The surface densities for separate L- and R-regions contain pole and finite contributions. For an infinitely thin brane taking these regions together, in odd spatial dimensions the pole parts cancel and the total surface energy is finite. The parts in the surface densities generated by the presence of the second brane are finite for all nonzero values of the interbrane separation. It is shown that for large distances between the branes the induced surface densities give rise to an exponentially suppressed cosmological constant on the brane. In the Randall-Sundrum braneworld model, for the interbrane distances solving the hierarchy problem between the gravitational and electroweak mass scales, the cosmological constant generated on the visible brane is of the right order of magnitude with the value suggested by the cosmological observations

The cosmological constant filter without big bang singularity

International Nuclear Information System (INIS)

Bauer, Florian

2011-01-01

In the recently proposed cosmological constant (CC) filter mechanism based on modified gravity in the Palatini formalism, gravity in the radiation, matter and late-time de Sitter eras is insensitive to energy sources with the equation of state -1. This implies that finite vacuum energy shifts from phase transitions are filtered out too. In this work, we investigate the CC filter model at very early times. We find that the initial big bang singularity is replaced by a cosmic bounce, where the matter energy density and the curvature are finite. In a certain case, this finiteness can be already observed on the algebraic level. (paper)

Method of construction spatial transition curve

Directory of Open Access Journals (Sweden)

S.V. Didanov

2013-04-01

Full Text Available Purpose. The movement of rail transport (speed rolling stock, traffic safety, etc. is largely dependent on the quality of the track. In this case, a special role is the transition curve, which ensures smooth insertion of the transition from linear to circular section of road. The article deals with modeling of spatial transition curve based on the parabolic distribution of the curvature and torsion. This is a continuation of research conducted by the authors regarding the spatial modeling of curved contours. Methodology. Construction of the spatial transition curve is numerical methods for solving nonlinear integral equations, where the initial data are taken coordinate the starting and ending points of the curve of the future, and the inclination of the tangent and the deviation of the curve from the tangent plane at these points. System solutions for the numerical method are the partial derivatives of the equations of the unknown parameters of the law of change of torsion and length of the transition curve. Findings. The parametric equations of the spatial transition curve are calculated by finding the unknown coefficients of the parabolic distribution of the curvature and torsion, as well as the spatial length of the transition curve. Originality. A method for constructing the spatial transition curve is devised, and based on this software geometric modeling spatial transition curves of railway track with specified deviations of the curve from the tangent plane. Practical value. The resulting curve can be applied in any sector of the economy, where it is necessary to ensure a smooth transition from linear to circular section of the curved space bypass. An example is the transition curve in the construction of the railway line, road, pipe, profile, flat section of the working blades of the turbine and compressor, the ship, plane, car, etc.

The speed-curvature power law of movements: a reappraisal.

Science.gov (United States)

Zago, Myrka; Matic, Adam; Flash, Tamar; Gomez-Marin, Alex; Lacquaniti, Francesco

2018-01-01

Several types of curvilinear movements obey approximately the so called 2/3 power law, according to which the angular speed varies proportionally to the 2/3 power of the curvature. The origin of the law is debated but it is generally thought to depend on physiological mechanisms. However, a recent paper (Marken and Shaffer, Exp Brain Res 88:685-690, 2017) claims that this power law is simply a statistical artifact, being a mathematical consequence of the way speed and curvature are calculated. Here we reject this hypothesis by showing that the speed-curvature power law of biological movements is non-trivial. First, we confirm that the power exponent varies with the shape of human drawing movements and with environmental factors. Second, we report experimental data from Drosophila larvae demonstrating that the power law does not depend on how curvature is calculated. Third, we prove that the law can be violated by means of several mathematical and physical examples. Finally, we discuss biological constraints that may underlie speed-curvature power laws discovered in empirical studies.

Surface Casimir densities and induced cosmological constant in higher dimensional braneworlds

International Nuclear Information System (INIS)

Saharian, Aram A.

2006-01-01

We investigate the vacuum expectation value of the surface energy-momentum tensor for a massive scalar field with general curvature coupling parameter obeying the Robin boundary conditions on two codimension one parallel branes in a (D+1)-dimensional background spacetime AdS D 1 +1 xΣ with a warped internal space Σ. These vacuum densities correspond to a gravitational source of the cosmological constant type for both subspaces of the branes. Using the generalized zeta function technique in combination with contour integral representations, the surface energies on the branes are presented in the form of the sum of single-brane and second-brane-induced parts. For the geometry of a single brane both regions, on the left and on the right of the brane, are considered. At the physical point the corresponding zeta functions contain pole and finite contributions. For an infinitely thin brane taking these regions together, in odd spatial dimensions the pole parts cancel and the total zeta function is finite. The renormalization procedure for the surface energies and the structure of the corresponding counterterms are discussed. The parts in the surface densities generated by the presence of the second brane are finite for all nonzero values of the interbrane separation and are investigated in various asymptotic regions of the parameters. In particular, it is shown that for large distances between the branes the induced surface densities give rise to an exponentially suppressed cosmological constant on the brane. The total energy of the vacuum including the bulk and boundary contributions is evaluated by the zeta function technique and the energy balance between separate parts is discussed

Curvature perturbation and waterfall dynamics in hybrid inflation

International Nuclear Information System (INIS)

Abolhasani, Ali Akbar; Firouzjahi, Hassan; Sasaki, Misao

2011-01-01

We investigate the parameter spaces of hybrid inflation model with special attention paid to the dynamics of waterfall field and curvature perturbations induced from its quantum fluctuations. Depending on the inflaton field value at the time of phase transition and the sharpness of the phase transition inflation can have multiple extended stages. We find that for models with mild phase transition the induced curvature perturbation from the waterfall field is too large to satisfy the COBE normalization. We investigate the model parameter space where the curvature perturbations from the waterfall quantum fluctuations vary between the results of standard hybrid inflation and the results obtained here

Curvature perturbation and waterfall dynamics in hybrid inflation

Energy Technology Data Exchange (ETDEWEB)

Abolhasani, Ali Akbar [Department of Physics, Sharif University of Technology, Tehran (Iran, Islamic Republic of); Firouzjahi, Hassan [School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Sasaki, Misao, E-mail: abolhasani@mail.ipm.ir, E-mail: firouz@mail.ipm.ir, E-mail: misao@yukawa.kyoto-u.ac.jp [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)

2011-10-01

We investigate the parameter spaces of hybrid inflation model with special attention paid to the dynamics of waterfall field and curvature perturbations induced from its quantum fluctuations. Depending on the inflaton field value at the time of phase transition and the sharpness of the phase transition inflation can have multiple extended stages. We find that for models with mild phase transition the induced curvature perturbation from the waterfall field is too large to satisfy the COBE normalization. We investigate the model parameter space where the curvature perturbations from the waterfall quantum fluctuations vary between the results of standard hybrid inflation and the results obtained here.

Influence of implant rod curvature on sagittal correction of scoliosis deformity.

Science.gov (United States)

Salmingo, Remel Alingalan; Tadano, Shigeru; Abe, Yuichiro; Ito, Manabu

2014-08-01

Deformation of in vivo-implanted rods could alter the scoliosis sagittal correction. To our knowledge, no previous authors have investigated the influence of implanted-rod deformation on the sagittal deformity correction during scoliosis surgery. To analyze the changes of the implant rod's angle of curvature during surgery and establish its influence on sagittal correction of scoliosis deformity. A retrospective analysis of the preoperative and postoperative implant rod geometry and angle of curvature was conducted. Twenty adolescent idiopathic scoliosis patients underwent surgery. Average age at the time of operation was 14 years. The preoperative and postoperative implant rod angle of curvature expressed in degrees was obtained for each patient. Two implant rods were attached to the concave and convex side of the spinal deformity. The preoperative implant rod geometry was measured before surgical implantation. The postoperative implant rod geometry after surgery was measured by computed tomography. The implant rod angle of curvature at the sagittal plane was obtained from the implant rod geometry. The angle of curvature between the implant rod extreme ends was measured before implantation and after surgery. The sagittal curvature between the corresponding spinal levels of healthy adolescents obtained by previous studies was compared with the implant rod angle of curvature to evaluate the sagittal curve correction. The difference between the postoperative implant rod angle of curvature and normal spine sagittal curvature of the corresponding instrumented level was used to evaluate over or under correction of the sagittal deformity. The implant rods at the concave side of deformity of all patients were significantly deformed after surgery. The average degree of rod deformation Δθ at the concave and convex sides was 15.8° and 1.6°, respectively. The average preoperative and postoperative implant rod angle of curvature at the concave side was 33.6° and 17.8�

Bacterial cell curvature through mechanical control of cell growth

DEFF Research Database (Denmark)

Cabeen, M.; Charbon, Godefroid; Vollmer, W.

2009-01-01

The cytoskeleton is a key regulator of cell morphogenesis. Crescentin, a bacterial intermediate filament-like protein, is required for the curved shape of Caulobacter crescentus and localizes to the inner cell curvature. Here, we show that crescentin forms a single filamentous structure...... that collapses into a helix when detached from the cell membrane, suggesting that it is normally maintained in a stretched configuration. Crescentin causes an elongation rate gradient around the circumference of the sidewall, creating a longitudinal cell length differential and hence curvature. Such curvature...... can be produced by physical force alone when cells are grown in circular microchambers. Production of crescentin in Escherichia coli is sufficient to generate cell curvature. Our data argue for a model in which physical strain borne by the crescentin structure anisotropically alters the kinetics...

Discrimination of curvature from motion during smooth pursuit eye movements and fixation.

Science.gov (United States)

Ross, Nicholas M; Goettker, Alexander; Schütz, Alexander C; Braun, Doris I; Gegenfurtner, Karl R

2017-09-01

Smooth pursuit and motion perception have mainly been investigated with stimuli moving along linear trajectories. Here we studied the quality of pursuit movements to curved motion trajectories in human observers and examined whether the pursuit responses would be sensitive enough to discriminate various degrees of curvature. In a two-interval forced-choice task subjects pursued a Gaussian blob moving along a curved trajectory and then indicated in which interval the curve was flatter. We also measured discrimination thresholds for the same curvatures during fixation. Motion curvature had some specific effects on smooth pursuit properties: trajectories with larger amounts of curvature elicited lower open-loop acceleration, lower pursuit gain, and larger catch-up saccades compared with less curved trajectories. Initially, target motion curvatures were underestimated; however, ∼300 ms after pursuit onset pursuit responses closely matched the actual curved trajectory. We calculated perceptual thresholds for curvature discrimination, which were on the order of 1.5 degrees of visual angle (°) for a 7.9° curvature standard. Oculometric sensitivity to curvature discrimination based on the whole pursuit trajectory was quite similar to perceptual performance. Oculometric thresholds based on smaller time windows were higher. Thus smooth pursuit can quite accurately follow moving targets with curved trajectories, but temporal integration over longer periods is necessary to reach perceptual thresholds for curvature discrimination. NEW & NOTEWORTHY Even though motion trajectories in the real world are frequently curved, most studies of smooth pursuit and motion perception have investigated linear motion. We show that pursuit initially underestimates the curvature of target motion and is able to reproduce the target curvature ∼300 ms after pursuit onset. Temporal integration of target motion over longer periods is necessary for pursuit to reach the level of precision found

The role of curvature in silica mesoporous crystals

KAUST Repository

Miyasaka, Keiichi

2012-02-08

Silica mesoporous crystals (SMCs) offer a unique opportunity to study micellar mesophases. Replication of non-equilibrium mesophases into porous silica structures allows the characterization of surfactant phases under a variety of chemical and physical perturbations, through methods not typically accessible to liquid crystal chemists. A poignant example is the use of electron microscopy and crystallography, as discussed herein, for the purpose of determining the fundamental role of amphiphile curvature, namely mean curvature and Gaussian curvature, which have been extensively studied in various fields such as polymer, liquid crystal, biological membrane, etc. The present work aims to highlight some current studies devoted to the interface curvature on SMCs, in which electron microscopy and electron crystallography (EC) are used to understand the geometry of silica wall surface in bicontinuous and cage-type mesostructures through the investigation of electrostatic potential maps. Additionally, we show that by altering the synthesis conditions during the preparation of SMCs, it is possible to isolate particles during micellar mesophase transformations in the cubic bicontinuous system, allowing us to view and study epitaxial relations under the specific synthesis conditions. By studying the relationship between mesoporous structure, interface curvature and micellar mesophases using electron microscopy and EC, we hope to bring new insights into the formation mechanism of these unique materials but also contribute a new way of understanding periodic liquid crystal systems. © 2012 The Royal Society.

The role of curvature in silica mesoporous crystals

KAUST Repository

Miyasaka, Keiichi; Bennett, Alfonso Garcia; Han, Lu; Han, Yu; Xiao, Changhong; Fujita, Nobuhisa; Castle, Toen; Sakamoto, Yasuhiro; Che, Shunai; Terasaki, Osamu

2012-01-01

Silica mesoporous crystals (SMCs) offer a unique opportunity to study micellar mesophases. Replication of non-equilibrium mesophases into porous silica structures allows the characterization of surfactant phases under a variety of chemical and physical perturbations, through methods not typically accessible to liquid crystal chemists. A poignant example is the use of electron microscopy and crystallography, as discussed herein, for the purpose of determining the fundamental role of amphiphile curvature, namely mean curvature and Gaussian curvature, which have been extensively studied in various fields such as polymer, liquid crystal, biological membrane, etc. The present work aims to highlight some current studies devoted to the interface curvature on SMCs, in which electron microscopy and electron crystallography (EC) are used to understand the geometry of silica wall surface in bicontinuous and cage-type mesostructures through the investigation of electrostatic potential maps. Additionally, we show that by altering the synthesis conditions during the preparation of SMCs, it is possible to isolate particles during micellar mesophase transformations in the cubic bicontinuous system, allowing us to view and study epitaxial relations under the specific synthesis conditions. By studying the relationship between mesoporous structure, interface curvature and micellar mesophases using electron microscopy and EC, we hope to bring new insights into the formation mechanism of these unique materials but also contribute a new way of understanding periodic liquid crystal systems. © 2012 The Royal Society.

Single Lipid Molecule Dynamics on Supported Lipid Bilayers with Membrane Curvature

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Philip P. Cheney

2017-03-01

Full Text Available The plasma membrane is a highly compartmentalized, dynamic material and this organization is essential for a wide variety of cellular processes. Nanoscale domains allow proteins to organize for cell signaling, endo- and exocytosis, and other essential processes. Even in the absence of proteins, lipids have the ability to organize into domains as a result of a variety of chemical and physical interactions. One feature of membranes that affects lipid domain formation is membrane curvature. To directly test the role of curvature in lipid sorting, we measured the accumulation of two similar lipids, 1,2-Dihexadecanoyl-sn-glycero-3-phosphoethanolamine (DHPE and hexadecanoic acid (HDA, using a supported lipid bilayer that was assembled over a nanopatterned surface to obtain regions of membrane curvature. Both lipids studied contain 16 carbon, saturated tails and a head group tag for fluorescence microscopy measurements. The accumulation of lipids at curvatures ranging from 28 nm to 55 nm radii was measured and fluorescein labeled DHPE accumulated more than fluorescein labeled HDA at regions of membrane curvature. We then tested whether single biotinylated DHPE molecules sense curvature using single particle tracking methods. Similar to groups of fluorescein labeled DHPE accumulating at curvature, the dynamics of single molecules of biotinylated DHPE was also affected by membrane curvature and highly confined motion was observed.

New curvature-torsion relations through decomposition of the Bianchi identities

International Nuclear Information System (INIS)

Davies, J.B.

1988-01-01

The Bianchi Identities relating asymmetric curvature to torsion are obtained as a new set of equations governing second-order curvature tensors. The usual contribution of symmetric curvature to the gravitational field is found to be a subset of these identities though with an added contribution due to torsion gradients. The antisymmetric curvature two-tensor is shown to be related to the divergence of the torsion. Using a model of particle-antiparticle pair production, identification of certain torsion components with electroweak fields is proposed. These components obey equations, similar to Maxwell's that are subsets of these linear Bianchi identities. These results are shown to be consistent with gauge and other previous analyses

Effects on Buildings of Surface Curvature Caused by Underground Coal Mining

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Haifeng Hu

2016-08-01

Full Text Available Ground curvature caused by underground mining is one of the most obvious deformation quantities in buildings. To study the influence of surface curvature on buildings and predict the movement and deformation of buildings caused by ground curvature, a prediction model of the influence function on mining subsidence was used to establish the relationship between surface curvature and wall deformation. The prediction model of wall deformation was then established and the surface curvature was obtained from mining subsidence prediction software. Five prediction lines were set up in the wall from bottom to top and the predicted deformation of each line was used to calculate the crack positions in the wall. Thus, the crack prediction model was obtained. The model was verified by a case study from a coalmine in Shanxi, China. The results show that when the ground curvature is positive, the crack in the wall is shaped like a “V”; when the ground curvature is negative, the crack is shaped like a “∧”. The conclusion provides the basis for a damage evaluation method for buildings in coalmine areas.

Advanced Curvature Deformable Mirrors

Science.gov (United States)

2010-09-01

ORGANIZATION NAME(S) AND ADDRESS(ES) University of Hawaii ,Institute for Astronomy,640 North A‘ohoku Place, #209 , Hilo ,HI,96720-2700 8. PERFORMING...Advanced Curvature Deformable Mirrors Christ Ftaclas1,2, Aglae Kellerer2 and Mark Chun2 Institute for Astronomy, University of Hawaii

Effect of nano-scale curvature on the intrinsic blood coagulation system

Science.gov (United States)

Kushida, Takashi; Saha, Krishnendu; Subramani, Chandramouleeswaran; Nandwana, Vikas; Rotello, Vincent M.

2014-01-01

The intrinsic coagulation activity of silica nanoparticles strongly depends on their surface curvature. Nanoparticles with higher surface curvature do not denature blood coagulation factor XII on its surface, providing a coagulation ‘silent’ surface, while nanoparticles with lower surface curvature shows denaturation and concomitant coagulation. PMID:25341004

A geometric construction of the Riemann scalar curvature in Regge calculus

International Nuclear Information System (INIS)

McDonald, Jonathan R; Miller, Warner A

2008-01-01

The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe is it ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a new fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a vertex-based weighted average of deficits per weighted average of dual areas

A geometric construction of the Riemann scalar curvature in Regge calculus

Science.gov (United States)

McDonald, Jonathan R.; Miller, Warner A.

2008-10-01

The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe is it ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a new fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a vertex-based weighted average of deficits per weighted average of dual areas.

Long-term Results of Ventral Penile Curvature Repair in Childhood.

Science.gov (United States)

Golomb, Dor; Sivan, Bezalel; Livne, Pinhas M; Nevo, Amihay; Ben-Meir, David

2018-02-01

To assess the postpubertal outcome of ventral penile curvature repaired in infancy in terms of recurrence and aesthetics. Postpubertal patients treated for hypospadias and ventral penile curvature in infancy at a tertiary medical center were invited to undergo assessment of the quality of the repair. Findings were compared between patients with a straight penis after skin release and patients who required dorsal plication. The cohort included 27 patients of mean age 16.5 years who were reported with straight penis after surgery. Postpubertal curvature was found in 6 of 14 patients (43%) successfully treated by skin release and 10 of 13 patients (77%) who underwent dorsal plication (P = .087). Significant curvature (≥30 degrees) was found in 1 of 14 patients in the skin-release group and 4 of 13 in the dorsal plication group (P = .16). Rates of redo urethroplasty were 2 of 14 (14%) and 5 of 10 (50%), respectively. Patient satisfaction with the appearance of the penis did not differ significantly. Ventral penile curvature repaired in infancy often recurs after puberty. The need for dorsal plication has a trend-level association with recurrence of penile curvature in puberty. It might also be related to the degree of postpubertal penile curvature and the need for redo urethroplasty. Procedure type does not affect patient satisfaction with the postpubertal appearance of the penis. Copyright © 2017 Elsevier Inc. All rights reserved.

On the scalar curvature of self-dual manifolds

International Nuclear Information System (INIS)

Kim, J.

1992-08-01

We generalize LeBrun's explicit ''hyperbolic ansatz'' construction of self-dual metrics on connected sums of conformally flat manifolds and CP 2 's through a systematic use of the theory of hyperbolic geometry and Kleinian groups. (This construction produces, for example, all self-dual manifolds with semi-free S 1 -action and with either nonnegative scalar curvature or positive-definite intersection form.) We then point out a simple criterion for determining the sign of the scalar curvature of these conformal metrics. Exploiting this, we then show that the sign of the scalar curvature can change on connected components of the moduli space of self-dual metrics, thereby answering a question raised by King and Kotschick. (author). Refs

Intensity-Curvature Measurement Approaches for the Diagnosis of Magnetic Resonance Imaging Brain Tumors

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Carlo Ciulla

2015-11-01

Full Text Available This research presents signal-image post-processing techniques called Intensity-Curvature Measurement Approaches with application to the diagnosis of human brain tumors detected through Magnetic Resonance Imaging (MRI. Post-processing of the MRI of the human brain encompasses the following model functions: (i bivariate cubic polynomial, (ii bivariate cubic Lagrange polynomial, (iii monovariate sinc, and (iv bivariate linear. The following Intensity-Curvature Measurement Approaches were used: (i classic-curvature, (ii signal resilient to interpolation, (iii intensity-curvature measure and (iv intensity-curvature functional. The results revealed that the classic-curvature, the signal resilient to interpolation and the intensity-curvature functional are able to add additional information useful to the diagnosis carried out with MRI. The contribution to the MRI diagnosis of our study are: (i the enhanced gray level scale of the tumor mass and the well-behaved representation of the tumor provided through the signal resilient to interpolation, and (ii the visually perceptible third dimension perpendicular to the image plane provided through the classic-curvature and the intensity-curvature functional.

A 1 + 5-dimensional gravitational-wave solution. Curvature singularity and spacetime singularity

Energy Technology Data Exchange (ETDEWEB)

Chen, Yu-Zhu [Tianjin University, Department of Physics, Tianjin (China); Li, Wen-Du [Tianjin University, Department of Physics, Tianjin (China); Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Dai, Wu-Sheng [Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Nankai University and Tianjin University, LiuHui Center for Applied Mathematics, Tianjin (China)

2017-12-15

We solve a 1 + 5-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities. (orig.)

Numerical and Theoretical Investigations Concerning the Continuous-Surface-Curvature Effect in Compressor Blades

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Yin Song

2014-12-01

Full Text Available Though the importance of curvature continuity on compressor blade performances has been realized, there are two major questions that need to be solved, i.e., the respective effects of curvature continuity at the leading-edge blend point and the main surface, and the contradiction between the traditional theory and experimental observations in the effect of those novel leading-edge shapes with smaller curvature discontinuity and sharper nose. In this paper, an optimization method to design continuous-curvature blade profiles which deviate little from datum blades is proposed, and numerical and theoretical analysis is carried out to investigate the continuous-curvature effect on blade performances. The results show that the curvature continuity at the leading-edge blend point helps to eliminate the separation bubble, thus improving the blade performance. The main-surface curvature continuity is also beneficial, although its effects are much smaller than those of the blend-point curvature continuity. Furthermore, it is observed that there exist two factors controlling the leading-edge spike, i.e., the curvature discontinuity at the blend point which dominates at small incidences, and the nose curvature which dominates at large incidences. To the authors’ knowledge, such mechanisms have not been reported before, and they can help to solve the sharp-leading-edge paradox.

Higher Curvature Gravity from Entanglement in Conformal Field Theories

Science.gov (United States)

Haehl, Felix M.; Hijano, Eliot; Parrikar, Onkar; Rabideau, Charles

2018-05-01

By generalizing different recent works to the context of higher curvature gravity, we provide a unifying framework for three related results: (i) If an asymptotically anti-de Sitter (AdS) spacetime computes the entanglement entropies of ball-shaped regions in a conformal field theory using a generalized Ryu-Takayanagi formula up to second order in state deformations around the vacuum, then the spacetime satisfies the correct gravitational equations of motion up to second order around the AdS background. (ii) The holographic dual of entanglement entropy in higher curvature theories of gravity is given by the Wald entropy plus a particular correction term involving extrinsic curvatures. (iii) Conformal field theory relative entropy is dual to gravitational canonical energy (also in higher curvature theories of gravity). Especially for the second point, our novel derivation of this previously known statement does not involve the Euclidean replica trick.

On Semi-classical Degravitation and the Cosmological Constant Problems

CERN Document Server

Patil, Subodh P

2010-01-01

In this report, we discuss a candidate mechanism through which one might address the various cosmological constant problems. We first observe that the renormalization of gravitational couplings (induced by integrating out various matter fields) manifests non-local modifications to Einstein's equations as quantum corrected equations of motion. That is, at the loop level, matter sources curvature through a gravitational coupling that is a non-local function of the covariant d'Alembertian. If the functional form of the resulting Newton's `constant' is such that it annihilates very long wavelength sources, but reduces to $1/M^2_{pl}$ ($M_{pl}$ being the 4d Planck mass) for all sources with cosmologically observable wavelengths, we would have a complimentary realization of the degravitation paradigm-- a realization through which its non-linear completion and the corresponding modified Bianchi identities are readily understood. We proceed to consider various theories whose coupling to gravity may a priori induce no...

Amphipathic motifs in BAR domains are essential for membrane curvature sensing

DEFF Research Database (Denmark)

Bhatia, Vikram K; Madsen, Kenneth L; Bolinger, Pierre-Yves

2009-01-01

BAR (Bin/Amphiphysin/Rvs) domains and amphipathic alpha-helices (AHs) are believed to be sensors of membrane curvature thus facilitating the assembly of protein complexes on curved membranes. Here, we used quantitative fluorescence microscopy to compare the binding of both motifs on single...... nanosized liposomes of different diameters and therefore membrane curvature. Characterization of members of the three BAR domain families showed surprisingly that the crescent-shaped BAR dimer with its positively charged concave face is not able to sense membrane curvature. Mutagenesis on BAR domains showed...... that membrane curvature sensing critically depends on the N-terminal AH and furthermore that BAR domains sense membrane curvature through hydrophobic insertion in lipid packing defects and not through electrostatics. Consequently, amphipathic motifs, such as AHs, that are often associated with BAR domains...

Improved curvature-based inpainting applied to fine art: recovering van Gogh's partially hidden brush strokes

Science.gov (United States)

Kuang, Yubin; Stork, David G.; Kahl, Fredrik

2011-03-01

Underdrawings and pentimenti-typically revealed through x-ray imaging and infrared reflectography-comprise important evidence about the intermediate states of an artwork and thus the working methods of its creator.1 To this end, Shahram, Stork and Donoho introduced the De-pict algorithm, which recovers layers of brush strokes in paintings with open brush work where several layers are partially visible, such as in van Gogh's Self portrait with a grey felt hat.2 While that preliminary work served as a proof of concept that computer image analytic methods could recover some occluded brush strokes, the work needed further refinement before it could be a tool for art scholars. Our current work makes several steps to improve that algorithm. Specifically, we refine the inpainting step through the inclusion of curvature-based constraints, in which a mathematical curvature penalty biases the reconstruction toward matching the artist's smooth hand motion. We refine and test our methods using "ground truth" image data: passages of four layers of brush strokes in which the intermediate layers were recorded photographically. At each successive top layer (currently identified by the user), we used k-means clustering combined with graph cuts to obtain chromatically and spatially coherent segmentation of brush strokes. We then reconstructed strokes at the deeper layer with our new curvature-based inpainting algorithm based on chromatic level lines. Our methods are clearly superior to previous versions of the De-pict algorithm on van Gogh's works giving smoother, natural strokes that more closely match the shapes of unoccluded strokes. Our improved method might be applied to the classic drip paintings of Jackson Pollock, where the drip work is more open and the physics of splashing paint ensures that the curvature more uniform than in the brush strokes of van Gogh.

On the curvature of transmitted intensity plots in broad beam studies

International Nuclear Information System (INIS)

El-Kateb, A.H.

2000-01-01

Transmission of a broad beam of gamma rays of 81- and 356-keV energies from 133 Ba is studied singly and dually. This study is the first to deal with the curvatures of the intensity plots. The targets are dextrose solutions of percentage concentrations up to 0.125 and soil containing water with concentrations up to 0.319. The logarithmic intensity plots are expressed in terms of a polynomial in the concentration. The curvatures of the plots are measured and calculated on the basis of the theoretical mass attenuation coefficients. The results are discussed in conjunction with buildup factors and the probability of photoelectric and Compton interactions. The curvatures show maxima when incoherent interaction prevails. This is evidently proved in case of the single 356-keV and of the dual 81- and 356-keV applied energies. Comparison is performed between the measured and calculated curvatures. The concept of curvature is applied and discussed for published results of narrow beam geometry. Correspondingly, this is the first search to introduce curvature instead of buildup as a measure for transmitted collided photons

Evolution of curvature perturbation in generalized gravity theories

International Nuclear Information System (INIS)

Matsuda, Tomohiro

2009-01-01

Using the cosmological perturbation theory in terms of the δN formalism, we find the simple formulation of the evolution of the curvature perturbation in generalized gravity theories. Compared with the standard gravity theory, a crucial difference appears in the end-boundary of the inflationary stage, which is due to the non-ideal form of the energy-momentum tensor that depends explicitly on the curvature scalar. Recent study shows that ultraviolet-complete quantum theory of gravity (Horava-Lifshitz gravity) can be approximated by using a generalized gravity action. Our paper may give an important step in understanding the evolution of the curvature perturbation during inflation, where the energy-momentum tensor may not be given by the ideal form due to the corrections from the fundamental theory.

Vibration Analysis of Circular Arch Element Using Curvature

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H. Saffari

2008-01-01

Full Text Available In this paper, a finite element technique was used to determine the natural frequencies, and the mode shapes of a circular arch element was based on the curvature, which can fully represent the bending energy and by the equilibrium equations, the shear and axial strain energy were incorporated into the formulation. The treatment of general boundary conditions dose need a consideration when the element is incorporated by the curvature-based formula. This can be obtained by the introduction of a transformation matrix between nodal curvatures and nodal displacements. The equation of the motion for the element was obtained by the Lagrangian equation. Four examples are presented in order to verify the element formulation and its analytical capability.

A major QTL controls susceptibility to spinal curvature in the curveback guppy

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Dreyer Christine

2011-01-01

Full Text Available Abstract Background Understanding the genetic basis of heritable spinal curvature would benefit medicine and aquaculture. Heritable spinal curvature among otherwise healthy children (i.e. Idiopathic Scoliosis and Scheuermann kyphosis accounts for more than 80% of all spinal curvatures and imposes a substantial healthcare cost through bracing, hospitalizations, surgery, and chronic back pain. In aquaculture, the prevalence of heritable spinal curvature can reach as high as 80% of a stock, and thus imposes a substantial cost through production losses. The genetic basis of heritable spinal curvature is unknown and so the objective of this work is to identify quantitative trait loci (QTL affecting heritable spinal curvature in the curveback guppy. Prior work with curveback has demonstrated phenotypic parallels to human idiopathic-type scoliosis, suggesting shared biological pathways for the deformity. Results A major effect QTL that acts in a recessive manner and accounts for curve susceptibility was detected in an initial mapping cross on LG 14. In a second cross, we confirmed this susceptibility locus and fine mapped it to a 5 cM region that explains 82.6% of the total phenotypic variance. Conclusions We identify a major QTL that controls susceptibility to curvature. This locus contains over 100 genes, including MTNR1B, a candidate gene for human idiopathic scoliosis. The identification of genes associated with heritable spinal curvature in the curveback guppy has the potential to elucidate the biological basis of spinal curvature among humans and economically important teleosts.

Geometry-specific scaling of detonation parameters from front curvature

International Nuclear Information System (INIS)

Jackson, Scott I.; Short, Mark

2011-01-01

It has previously been asserted that classical detonation curvature theory predicts that the critical diameter and the diameter-effect curve of a cylindrical high-explosive charge should scale with twice the thickness of an analogous two-dimensional explosive slab. The varied agreement of experimental results with this expectation have led some to question the ability of curvature-based concepts to predict detonation propagation in non-ideal explosives. This study addresses such claims by showing that the expected scaling relationship (hereafter referred to d = 2w) is not consistent with curvature-based Detonation Shock Dynamics (DSD) theory.

Studying biomolecule localization by engineering bacterial cell wall curvature.

Directory of Open Access Journals (Sweden)

Lars D Renner

Full Text Available In this article we describe two techniques for exploring the relationship between bacterial cell shape and the intracellular organization of proteins. First, we created microchannels in a layer of agarose to reshape live bacterial cells and predictably control their mean cell wall curvature, and quantified the influence of curvature on the localization and distribution of proteins in vivo. Second, we used agarose microchambers to reshape bacteria whose cell wall had been chemically and enzymatically removed. By combining microstructures with different geometries and fluorescence microscopy, we determined the relationship between bacterial shape and the localization for two different membrane-associated proteins: i the cell-shape related protein MreB of Escherichia coli, which is positioned along the long axis of the rod-shaped cell; and ii the negative curvature-sensing cell division protein DivIVA of Bacillus subtilis, which is positioned primarily at cell division sites. Our studies of intracellular organization in live cells of E. coli and B. subtilis demonstrate that MreB is largely excluded from areas of high negative curvature, whereas DivIVA localizes preferentially to regions of high negative curvature. These studies highlight a unique approach for studying the relationship between cell shape and intracellular organization in intact, live bacteria.

Codimension two branes and distributional curvature

International Nuclear Information System (INIS)

Traschen, Jennie

2009-01-01

In general relativity, there is a well-developed formalism for working with the approximation that a gravitational source is concentrated on a shell, or codimension one surface. In contrast, there are obstacles to concentrating sources on surfaces that have a higher codimension, for example, a string in a spacetime with a dimension greater than or equal to four. Here it is shown that, by giving up some of the generality of the codimension one case, curvature can be concentrated on submanifolds that have codimension two. A class of metrics is identified such that (1) the scalar curvature and Ricci densities exist as distributions with support on a codimension two submanifold, and (2) using the Einstein equation, the distributional curvature corresponds to a concentrated stress-energy with equation of state p = -ρ, where p is the isotropic pressure tangent to the submanifold, and ρ is the energy density. This is the appropriate stress-energy to describe a self-gravitating brane that is governed by an area action, or a braneworld deSitter cosmology. The possibility of having a different equation of state arise from a wider class of metrics is discussed.

Directable weathering of concave rock using curvature estimation.

Science.gov (United States)

Jones, Michael D; Farley, McKay; Butler, Joseph; Beardall, Matthew

2010-01-01

We address the problem of directable weathering of exposed concave rock for use in computer-generated animation or games. Previous weathering models that admit concave surfaces are computationally inefficient and difficult to control. In nature, the spheroidal and cavernous weathering rates depend on the surface curvature. Spheroidal weathering is fastest in areas with large positive mean curvature and cavernous weathering is fastest in areas with large negative mean curvature. We simulate both processes using an approximation of mean curvature on a voxel grid. Both weathering rates are also influenced by rock durability. The user controls rock durability by editing a durability graph before and during weathering simulation. Simulations of rockfall and colluvium deposition further improve realism. The profile of the final weathered rock matches the shape of the durability graph up to the effects of weathering and colluvium deposition. We demonstrate the top-down directability and visual plausibility of the resulting model through a series of screenshots and rendered images. The results include the weathering of a cube into a sphere and of a sheltered inside corner into a cavern as predicted by the underlying geomorphological models.

Virialisation-induced curvature as a physical explanation for dark energy

International Nuclear Information System (INIS)

Roukema, Boudewijn F.; Ostrowski, Jan J.; Buchert, Thomas

2013-01-01

The geometry of the dark energy and cold dark matter dominated cosmological model (ΛCDM) is commonly assumed to be given by a Friedmann-Lemaître-Robertson-Walker (FLRW) metric, i.e. it assumes homogeneity in the comoving spatial section. The homogeneity assumption fails most strongly at (i) small distance scales and (ii) recent epochs, implying that the FLRW approximation is most likely to fail at these scales. We use the virialisation fraction to quantify (i) and (ii), which approximately coincide with each other on the observational past light cone. For increasing time, the virialisation fraction increases above 10% at about the same redshift ( ∼ 1–3) at which Ω Λ grows above 10% ( ≈ 1.8). Thus, instead of non-zero Ω Λ , we propose an approximate, general-relativistic correction to the matter-dominated (Ω m ; = 1,Ω Λ = 0), homogeneous metric (Einstein-de Sitter, EdS). A low-redshift effective matter-density parameter of Ω m eff (0) = 0.26±0.05 is inferred. Over redshifts 0 < z < 3, the distance modulus of the virialisation-corrected EdS model approximately matches the ΛCDM distance modulus. This rough approximation assumes ''old physics'' (general relativity), not ''new physics''. Thus, pending more detailed calculations, we strengthen the claim that ''dark energy'' should be considered as an artefact of emerging average curvature in the void-dominated Universe, via a novel approach that quantifies the relation between virialisation and average curvature evolution

CURVATURE-DRIVEN MOLECULAR FLOW ON MEMBRANE SURFACE.

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Mikucki, Michael; Zhou, Y C

2017-01-01

This work presents a mathematical model for the localization of multiple species of diffusion molecules on membrane surfaces. Morphological change of bilayer membrane in vivo is generally modulated by proteins. Most of these modulations are associated with the localization of related proteins in the crowded lipid environments. We start with the energetic description of the distributions of molecules on curved membrane surface, and define the spontaneous curvature of bilayer membrane as a function of the molecule concentrations on membrane surfaces. A drift-diffusion equation governs the gradient flow of the surface molecule concentrations. We recast the energetic formulation and the related governing equations by using an Eulerian phase field description to define membrane morphology. Computational simulations with the proposed mathematical model and related numerical techniques predict (i) the molecular localization on static membrane surfaces at locations with preferred mean curvatures, and (ii) the generation of preferred mean curvature which in turn drives the molecular localization.

Scalar curvature in conformal geometry of Connes-Landi noncommutative manifolds

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Liu, Yang

2017-11-01

We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on noncommutative two tori, the quantum part of the curvature consists of actions of the modular derivation through two local curvature functions. Explicit expressions for those functions are obtained for all even dimensions (greater than two). In dimension four, the one variable function shows striking similarity to the analytic functions of the characteristic classes appeared in the Atiyah-Singer local index formula, namely, it is roughly a product of the j-function (which defines the A ˆ -class of a manifold) and an exponential function (which defines the Chern character of a bundle). By performing two different computations for the variation of the Einstein-Hilbert action, we obtain deep internal relations between two local curvature functions. Straightforward verification for those relations gives a strong conceptual confirmation for the whole computational machinery we have developed so far, especially the Mathematica code hidden behind the paper.

Quantitative analysis and prediction of curvature in leucine-rich repeat proteins.

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Hindle, K Lauren; Bella, Jordi; Lovell, Simon C

2009-11-01

Leucine-rich repeat (LRR) proteins form a large and diverse family. They have a wide range of functions most of which involve the formation of protein-protein interactions. All known LRR structures form curved solenoids, although there is large variation in their curvature. It is this curvature that determines the shape and dimensions of the inner space available for ligand binding. Unfortunately, large-scale parameters such as the overall curvature of a protein domain are extremely difficult to predict. Here, we present a quantitative analysis of determinants of curvature of this family. Individual repeats typically range in length between 20 and 30 residues and have a variety of secondary structures on their convex side. The observed curvature of the LRR domains correlates poorly with the lengths of their individual repeats. We have, therefore, developed a scoring function based on the secondary structure of the convex side of the protein that allows prediction of the overall curvature with a high degree of accuracy. We also demonstrate the effectiveness of this method in selecting a suitable template for comparative modeling. We have developed an automated, quantitative protocol that can be used to predict accurately the curvature of leucine-rich repeat proteins of unknown structure from sequence alone. This protocol is available as an online resource at http://www.bioinf.manchester.ac.uk/curlrr/.

Spinal curvature and characteristics of postural change in pregnant women.

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Okanishi, Natsuko; Kito, Nobuhiro; Akiyama, Mitoshi; Yamamoto, Masako

2012-07-01

Pregnant women often report complaints due to physiological and postural changes. Postural changes during pregnancy may cause low back pain and pelvic girdle pain. This study aimed to compare the characteristics of postural changes in pregnant compared with non-pregnant women. Prospective case-control study. Pregnancy care center. Fifteen women at 17-34 weeks pregnancy comprised the study group, while 10 non-pregnant female volunteers comprised the control group. Standing posture was evaluated in the sagittal plane with static digital pictures. Two angles were measured by image analysis software: (1) between the trunk and pelvis; and (2) between the trunk and lower extremity. Spinal curvature was measured with Spinal Mouse® to calculate the means of sacral inclination, thoracic and lumbar curvature and inclination. The principal components were calculated until eigenvalues surpassed 1. Three distinct factors with eigenvalues of 1.00-2.49 were identified, consistent with lumbosacral spinal curvature and inclination, thoracic spine curvature, and inclination of the body. These factors accounted for 77.2% of the total variance in posture variables. Eleven pregnant women showed postural characteristics of lumbar kyphosis and sacral posterior inclination. Body inclination showed a variety of patterns compared with those in healthy women. Spinal curvature demonstrated a tendency for lumbar kyphosis in pregnant women. Pregnancy may cause changes in spinal curvature and posture, which may in turn lead to relevant symptoms. Our data provide a basis for investigating the effects of spinal curvature and postural changes on symptoms during pregnancy. © 2012 The Authors Acta Obstetricia et Gynecologica Scandinavica© 2012 Nordic Federation of Societies of Obstetrics and Gynecology.

Waterfall field in hybrid inflation and curvature perturbation

International Nuclear Information System (INIS)

Gong, Jinn-Ouk; Sasaki, Misao

2011-01-01

We study carefully the contribution of the waterfall field to the curvature perturbation at the end of hybrid inflation. In particular we clarify the parameter dependence analytically under reasonable assumptions on the model parameters. After calculating the mode function of the waterfall field, we use the δN formalism and confirm the previously obtained result that the power spectrum is very blue with the index 4 and is absolutely negligible on large scales. However, we also find that the resulting curvature perturbation is highly non-Gaussian and hence we calculate the bispectrum. We find that the bispectrum is at leading order independent of momentum and exhibits its peak at the equilateral limit, though it is unobservably small on large scales. We also present the one-point probability distribution function of the curvature perturbation

Waterfall field in hybrid inflation and curvature perturbation

Energy Technology Data Exchange (ETDEWEB)

Gong, Jinn-Ouk [Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, 2333 CA Leiden (Netherlands); Sasaki, Misao, E-mail: jgong@lorentz.leidenuniv.nl, E-mail: misao@yukawa.kyoto-u.ac.jp [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)

2011-03-01

We study carefully the contribution of the waterfall field to the curvature perturbation at the end of hybrid inflation. In particular we clarify the parameter dependence analytically under reasonable assumptions on the model parameters. After calculating the mode function of the waterfall field, we use the δN formalism and confirm the previously obtained result that the power spectrum is very blue with the index 4 and is absolutely negligible on large scales. However, we also find that the resulting curvature perturbation is highly non-Gaussian and hence we calculate the bispectrum. We find that the bispectrum is at leading order independent of momentum and exhibits its peak at the equilateral limit, though it is unobservably small on large scales. We also present the one-point probability distribution function of the curvature perturbation.

What is the role of curvature on the properties of nanomaterials for biomedical applications?

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Gonzalez Solveyra, Estefania; Szleifer, Igal

2016-05-01

The use of nanomaterials for drug delivery and theranostics applications is a promising paradigm in nanomedicine, as it brings together the best features of nanotechnolgy, molecular biology, and medicine. To fully exploit the synergistic potential of such interdisciplinary strategy, a comprehensive description of the interactions at the interface between nanomaterials and biological systems is not only crucial, but also mandatory. Routine strategies to engineer nanomaterial-based drugs comprise modifying their surface with biocompatible and targeting ligands, in many cases resorting to modular approaches that assume additive behavior. However, emergent behavior can be observed when combining confinement and curvature. The final properties of functionalized nanomaterials become dependent not only on the properties of their constituents but also on the geometry of the nano-bio interface, and on the local molecular environment. Modularity no longer holds, and the coupling between interactions, chemical equilibrium, and molecular organization has to be directly addressed in order to design smart nanomaterials with controlled spatial functionalization envisioning optimized biomedical applications. Nanoparticle's curvature becomes an integral part of the design strategy, enabling to control and engineer the chemical and surface properties with molecular precision. Understanding how nanoparticle size, morphology, and surface chemistry are interrelated will put us one step closer to engineering nanobiomaterials capable of mimicking biological structures and their behaviors, paving the way into applications and the possibility to elucidate the use of curvature by biological systems. WIREs Nanomed Nanobiotechnol 2016, 8:334-354. doi: 10.1002/wnan.1365 For further resources related to this article, please visit the WIREs website. © 2015 Wiley Periodicals, Inc.

Differential geometric structures of stream functions: incompressible two-dimensional flow and curvatures

International Nuclear Information System (INIS)

Yamasaki, K; Iwayama, T; Yajima, T

2011-01-01

The Okubo-Weiss field, frequently used for partitioning incompressible two-dimensional (2D) fluids into coherent and incoherent regions, corresponds to the Gaussian curvature of the stream function. Therefore, we consider the differential geometric structures of stream functions and calculate the Gaussian curvatures of some basic flows. We find the following. (I) The vorticity corresponds to the mean curvature of the stream function. Thus, the stream-function surface for an irrotational flow and that for a parallel shear flow correspond to the minimal surface and a developable surface, respectively. (II) The relationship between the coherency and the magnitude of the vorticity is interpreted by the curvatures. (III) Using the Gaussian curvature, stability of single and double point vortex streets is analyzed. The results of this analysis are compared with the well-known linear stability analysis. (IV) Conformal mapping in fluid mechanics is the physical expression of the geometric fact that the sign of the Gaussian curvature does not change in conformal mapping. These findings suggest that the curvatures of stream functions are useful for understanding the geometric structure of an incompressible 2D flow.

Modern approaches to discrete curvature

CERN Document Server

Romon, Pascal

2017-01-01

 This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.

The Riemann-Lovelock curvature tensor

International Nuclear Information System (INIS)

Kastor, David

2012-01-01

In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k ≤ D < 4k. In D = 2k + 1 this identity implies that all solutions of pure kth-order Lovelock gravity are 'Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle spacetimes, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D = 3, which corresponds to the k = 1 case. We speculate about some possible further consequences of Riemann-Lovelock curvature. (paper)

Curvature-driven acceleration: a utopia or a reality?

International Nuclear Information System (INIS)

Das, Sudipta; Banerjee, Narayan; Dadhich, Naresh

2006-01-01

The present work shows that a combination of nonlinear contributions from the Ricci curvature in Einstein field equations can drive a late time acceleration of expansion of the universe. The transit from the decelerated to the accelerated phase of expansion takes place smoothly without having to resort to a study of asymptotic behaviour. This result emphasizes the need for thorough and critical examination of models with nonlinear contribution from the curvature

Curvature-driven acceleration: a utopia or a reality?

Energy Technology Data Exchange (ETDEWEB)

Das, Sudipta [Relativity and Cosmology Research Centre, Department of Physics, Jadavpur University, Calcutta-700 032 (India); Banerjee, Narayan [Relativity and Cosmology Research Centre, Department of Physics, Jadavpur University, Calcutta-700 032 (India); Dadhich, Naresh [Inter University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune 411 007 (India)

2006-06-21

The present work shows that a combination of nonlinear contributions from the Ricci curvature in Einstein field equations can drive a late time acceleration of expansion of the universe. The transit from the decelerated to the accelerated phase of expansion takes place smoothly without having to resort to a study of asymptotic behaviour. This result emphasizes the need for thorough and critical examination of models with nonlinear contribution from the curvature.

Berry Curvature in Magnon-Phonon Hybrid Systems.

Science.gov (United States)

Takahashi, Ryuji; Nagaosa, Naoto

2016-11-18

We study theoretically the Berry curvature of the magnon induced by the hybridization with the acoustic phonons via the spin-orbit and dipolar interactions. We first discuss the magnon-phonon hybridization via the dipolar interaction, and show that the dispersions have gapless points in momentum space, some of which form a loop. Next, when both spin-orbit and dipolar interactions are considered, we show anisotropic texture of the Berry curvature and its divergence with and without gap closing. Realistic evaluation of the consequent anomalous velocity is given for yttrium iron garnet.

Curvature dependence of single-walled carbon nanotubes for SO2 adsorption and oxidation

Science.gov (United States)

Chen, Yanqiu; Yin, Shi; Li, Yueli; Cen, Wanglai; Li, Jianjun; Yin, Huaqiang

2017-05-01

Porous carbon-based catalysts showing high catalytic activity for SO2 oxidation to SO3 is often used in flue gas desulfurization. Their catalytic activity has been ascribed in many publications to the microporous structure and the effect of its spatial confinement. First principles method was used to investigate the adsorption and oxidation of SO2 on the inner and outer surface of single-walled carbon nanotubes (SWCNTs) with different diameters. It is interesting to found that there is a direct correlation: the barrier for the oxidation O_SWCNT + SO2 → SO3 + SWCNT monotonically decreases with the increase of SWCNTs' curvature. The oxygen functional located at the inner wall of SWCNTs with small radius is of higher activity for SO2 oxidation, which is extra enhanced by the spatial confinement effects of SWCNTs. These findings can be useful for the development of carbon-based catalysts and provide clues for the optimization and design of porous carbon catalysts.

The influence of road curvature on fatal crashes in New Zealand

DEFF Research Database (Denmark)

Haynes, Robin; Lake, Iain R.; Kingham, Simon

2008-01-01

Bends in roads can cause crashes but a recent study in the UK found that areas with mostly curved roads had lower crash rates than areas with straighter roads. This present study aimed to replicate the previous research in a different country. Variations in the number of fatal road crashes...... occurring between 1996 and 2005 in 73 territorial local authorities across New Zealand were modelled against possible predictors. The predictors were traffic flow, population counts and characteristics, car use, socio-economic deprivation, climate, altitude and road characteristics including four measures...... of average road curvature. The best predictors of the number of fatal crashes on urban roads, rural state highways and other rural roads were traffic flow, speed limitation and socio-economic deprivation. Holding significant factors constant, there was no evidence that TLAs with the most curved roads had...

Quadratic curvature terms and deformed Schwarzschild–de Sitter black hole analogues in the laboratory

Directory of Open Access Journals (Sweden)

R. da Rocha

2017-12-01

Full Text Available Sound waves on a fluid stream, in a de Laval nozzle, are shown to correspond to quasinormal modes emitted by black holes that are physical solutions in a quadratic curvature gravity with cosmological constant. Sound waves patterns in transsonic regimes at a laboratory are employed here to provide experimental data regarding generalized theories of gravity, comprised by the exact de Sitter-like solution and a perturbative solution around the Schwarzschild–de Sitter standard solution as well. Using the classical tests of General Relativity to bound free parameters in these solutions, acoustic perturbations on fluid flows in nozzles are then regarded, to study quasinormal modes of these black holes solutions, providing deviations of the de Laval nozzle cross-sectional area, when compared to the Schwarzschild solution. The fluid sonic point in the nozzle, for sound waves in the fluid, is shown to implement the acoustic event horizon corresponding to quasinormal modes. Keywords: Black holes, Fluid branes, Fluid dynamics, Quadratic curvature gravity, de Laval nozzle

A curvature theory for discrete surfaces based on mesh parallelity

KAUST Repository

Bobenko, Alexander Ivanovich; Pottmann, Helmut; Wallner, Johannes

2009-01-01

We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces' areas and mixed areas. Remarkably these notions are capable

First contact: understanding the relationship between hominoid incisor curvature and diet.

Science.gov (United States)

Deane, Andrew

2009-03-01

Accurately interpreting fossil primate dietary behaviour is necessary to fully understand a species' ecology and connection to its environment. Traditional methods developed to infer diet from hominoid teeth successfully group taxa into broad dietary categories (i.e., folivore, frugivore) but often fail to represent the range of dietary variability characteristic of living apes. This oversimplification is not only a consequence of poor resolution, but may also reflect the use of similar fallback resources by closely related taxa with dissimilar diets. This study demonstrates that additional dietary specificity can be achieved using a morphometric approach to hominoid incisor curvature. High-resolution polynomial curve fitting (HR-PCF) was used to quantify the incisor curvatures of closely related hominoid taxa that have dissimilar diets but similar morphological adaptations to specific keystone resources (e.g., Gorilla gorilla beringei vs. G. g. gorilla). Given the key role of incisors in food processing, it is reasonable to assume that these teeth will be at least partially influenced by the unique selective pressures imposed by the mechanical loading specific to individual diets. Results from this study identify a strong correlation between hominoid dietary proportions and incisor linear dimensions and curvature, indicating that more pronounced incisor curvature is positively correlated with higher levels of frugivory. Hard-object frugivores have the greatest mesiodistal and cervico-incisal curvature and dedicated folivores have the least curved incisors. Mixed folivore/frugivores are morphological intermediates between dedicated folivores and hard- and soft-object frugivores. Mesiodistal curvature varied only in the degree of curvature; however, cervico-incisal curvature was shown to differ qualitatively between more frugivorous and more folivorous taxa. In addition to identifying a greater range of dietary variability among hominoids, this study also

Curvature-Continuous 3D Path-Planning Using QPMI Method

Directory of Open Access Journals (Sweden)

Seong-Ryong Chang

2015-06-01

Full Text Available It is impossible to achieve vertex movement and rapid velocity control in aerial robots and aerial vehicles because of momentum from the air. A continuous-curvature path ensures such robots and vehicles can fly with stable and continuous movements. General continuous path-planning methods use spline interpolation, for example B-spline and Bézier curves. However, these methods cannot be directly applied to continuous path planning in a 3D space. These methods use a subset of the waypoints to decide curvature and some waypoints are not included in the planned path. This paper proposes a method for constructing a curvature-continuous path in 3D space that includes every waypoint. The movements in each axis, x, y and z, are separated by the parameter u. Waypoint groups are formed, each with its own continuous path derived using quadratic polynomial interpolation. The membership function then combines each continuous path into one continuous path. The continuity of the path is verified and the curvature-continuous path is produced using the proposed method.

Inflation in a shear-or curvature-dominated universe

International Nuclear Information System (INIS)

Steigman, G.; Turner, M.S.

1983-01-01

We show that new inflation occurs even if the universe is shear-or (negative) curvature-dominated when the phase transition begins. In such situations the size of a causally coherent region, after inflation, is only slightly smaller (by powers, but not by exponential factors) than the usual result. The creation and evolution of density perturbations is unaffected. This result is marked contrast to 'old' inflation, where shear- or curvature-domination could quench inflation. (orig.)

Inflationary scenario from higher curvature warped spacetime

International Nuclear Information System (INIS)

Banerjee, Narayan; Paul, Tanmoy

2017-01-01

We consider a five dimensional warped spacetime, in presence of the higher curvature term like F(R) = R + αR 2 in the bulk, in the context of the two-brane model. Our universe is identified with the TeV scale brane and emerges as a four dimensional effective theory. From the perspective of this effective theory, we examine the possibility of ''inflationary scenario'' by considering the on-brane metric ansatz as an FRW one. Our results reveal that the higher curvature term in the five dimensional bulk spacetime generates a potential term for the radion field. Due to the presence of radion potential, the very early universe undergoes a stage of accelerated expansion and, moreover, the accelerating period of the universe terminates in a finite time. We also find the spectral index of curvature perturbation (n s ) and the tensor to scalar ratio (r) in the present context, which match with the observational results based on the observations of Planck (Astron. Astrophys. 594, A20, 2016). (orig.)

Inflationary scenario from higher curvature warped spacetime

Energy Technology Data Exchange (ETDEWEB)

Banerjee, Narayan [Indian Institute of Science Education and Research Kolkata, Department of Physical Sciences, Nadia, West Bengal (India); Paul, Tanmoy [Indian Association for the Cultivation of Science, Department of Theoretical Physics, Kolkata (India)

2017-10-15

We consider a five dimensional warped spacetime, in presence of the higher curvature term like F(R) = R + αR{sup 2} in the bulk, in the context of the two-brane model. Our universe is identified with the TeV scale brane and emerges as a four dimensional effective theory. From the perspective of this effective theory, we examine the possibility of ''inflationary scenario'' by considering the on-brane metric ansatz as an FRW one. Our results reveal that the higher curvature term in the five dimensional bulk spacetime generates a potential term for the radion field. Due to the presence of radion potential, the very early universe undergoes a stage of accelerated expansion and, moreover, the accelerating period of the universe terminates in a finite time. We also find the spectral index of curvature perturbation (n{sub s}) and the tensor to scalar ratio (r) in the present context, which match with the observational results based on the observations of Planck (Astron. Astrophys. 594, A20, 2016). (orig.)

Computational methods for investigation of surface curvature effects on airfoil boundary layer behavior

Directory of Open Access Journals (Sweden)

Xiang Shen

2017-03-01

Full Text Available This article presents computational algorithms for the design, analysis, and optimization of airfoil aerodynamic performance. The prescribed surface curvature distribution blade design (CIRCLE method is applied to a symmetrical airfoil NACA0012 and a non-symmetrical airfoil E387 to remove their surface curvature and slope-of-curvature discontinuities. Computational fluid dynamics analysis is used to investigate the effects of curvature distribution on aerodynamic performance of the original and modified airfoils. An inviscid–viscid interaction scheme is introduced to predict the positions of laminar separation bubbles. The results are compared with experimental data obtained from tests on the original airfoil geometry. The computed aerodynamic advantages of the modified airfoils are analyzed in different operating conditions. The leading edge singularity of NACA0012 is removed and it is shown that the surface curvature discontinuity affects aerodynamic performance near the stalling angle of attack. The discontinuous slope-of-curvature distribution of E387 results in a larger laminar separation bubble at lower angles of attack and lower Reynolds numbers. It also affects the inherent performance of the airfoil at higher Reynolds numbers. It is shown that at relatively high angles of attack, a continuous slope-of-curvature distribution reduces the skin friction by suppressing both laminar and turbulent separation, and by delaying laminar-turbulent transition. It is concluded that the surface curvature distribution has significant effects on the boundary layer behavior and consequently an improved curvature distribution will lead to higher aerodynamic efficiency.

Phase-space curvature in spin-orbit-coupled ultracold atomic systems

Science.gov (United States)

Armaitis, J.; Ruseckas, J.; Anisimovas, E.

2017-04-01

We consider a system with spin-orbit coupling and derive equations of motion which include the effects of Berry curvatures. We apply these equations to investigate the dynamics of particles with equal Rashba-Dresselhaus spin-orbit coupling in one dimension. In our derivation, the adiabatic transformation is performed first and leads to quantum Heisenberg equations of motion for momentum and position operators. These equations explicitly contain position-space, momentum-space, and phase-space Berry curvature terms. Subsequently, we perform the semiclassical approximation and obtain the semiclassical equations of motion. Taking the low-Berry-curvature limit results in equations that can be directly compared to previous results for the motion of wave packets. Finally, we show that in the semiclassical regime, the effective mass of the equal Rashba-Dresselhaus spin-orbit-coupled system can be viewed as a direct effect of the phase-space Berry curvature.

Forelimb bone curvature in terrestrial and arboreal mammals

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Keith Henderson

2017-04-01

Full Text Available It has recently been proposed that the caudal curvature (concave caudal side observed in the radioulna of terrestrial quadrupeds is an adaptation to the habitual action of the triceps muscle which causes cranial bending strains (compression on cranial side. The caudal curvature is proposed to be adaptive because longitudinal loading induces caudal bending strains (increased compression on the caudal side, and these opposing bending strains counteract each other leaving the radioulna less strained. If this is true for terrestrial quadrupeds, where triceps is required for habitual elbow extension, then we might expect that in arboreal species, where brachialis is habitually required to maintain elbow flexion, the radioulna should instead be cranially curved. This study measures sagittal curvature of the ulna in a range of terrestrial and arboreal primates and marsupials, and finds that their ulnae are curved in opposite directions in these two locomotor categories. This study also examines sagittal curvature in the humerus in the same species, and finds differences that can be attributed to similar adaptations: the bone is curved to counter the habitual muscle action required by the animal’s lifestyle, the difference being mainly in the distal part of the humerus, where arboreal animals tend have a cranial concavity, thought to be in response the carpal and digital muscles that pull cranially on the distal humerus.

Curvature-induced microswarming and clustering of self-propelled particles

Science.gov (United States)

Bruss, Isaac; Glotzer, Sharon

Non-equilibrium active matter systems exhibit many unique phenomena, such as motility-induced phase separation and swarming. However, little is known about how these behaviors depend on the geometry of the environment. To answer this question, we use Brownian dynamics simulations to study the effects of Gaussian curvature on self-propelled particles by confining them to the surface of a sphere. We find that a modest amount of curvature promotes phase separation by altering the shape of a cluster's boundary. Alternatively, particles on surfaces of high curvature experience reduced phase separation and instead form microswarms, where particles share a common orbit. We show that this novel flocking behavior is distinct from other previously studied examples, in that it is not explicitly incorporated into our model through Vicsek-like alignment rules nor torques. Rather, we find that microswarms emerge solely due to the geometric link between orientation and velocity, a property exclusive to surfaces with non-zero Gaussian curvature. These findings reveal the important role of local environment on the global emergent behavior of non-equilibrium systems. Center for Bio-Inspired Engineering (DOE Award # DE-SC0000989).

Unsteady laminar flow with convective heat transfer through a rotating curved square duct with small curvature

Energy Technology Data Exchange (ETDEWEB)

Mondal, Rabindra Nath, E-mail: rnmondal71@yahoo.com; Shaha, Poly Rani [Department of Mathematics, Jagannath University, Dhaka-1100 (Bangladesh); Roy, Titob [Department of Mathematics, Vikarunnesa Nun School and College, Boshundhara, Dhaka (Bangladesh); Yanase, Shinichiro, E-mail: yanase@okayama-u.ac.jp [Department of Mechanical and Systems Engineering, Okayama University, Okayama 700-8530 (Japan)

2016-07-12

Unsteady laminar flow with convective heat transfer through a curved square duct rotating at a constant angular velocity about the center of curvature is investigated numerically by using a spectral method, and covering a wide range of the Taylor number −300≤Tr≤1000 for the Dean number Dn = 1000. A temperature difference is applied across the vertical sidewalls for the Grashof number Gr = 100, where the outer wall is heated and the inner wall cooled, the top and bottom walls being adiabatic. Flow characteristics are investigated with the effects of rotational parameter, Tr, and the pressure-driven parameter, Dn, for the constant curvature 0.001. Time evolution calculations as well as their phase spaces show that the unsteady flow undergoes through various flow instabilities in the scenario ‘multi-periodic → chaotic → steady-state → periodic → multi-periodic → chaotic’, if Tr is increased in the positive direction. For negative rotation, however, time evolution calculations show that the flow undergoes in the scenario ‘multi-periodic → periodic → steady-state’, if Tr is increased in the negative direction. Typical contours of secondary flow patterns and temperature profiles are obtained at several values of Tr, and it is found that the unsteady flow consists of two- to six-vortex solutions if the duct rotation is involved. External heating is shown to generate a significant temperature gradient at the outer wall of the duct. This study also shows that there is a strong interaction between the heating-induced buoyancy force and the centrifugal-Coriolis instability in the curved channel that stimulates fluid mixing and consequently enhances heat transfer in the fluid.

Curvature effects in two-dimensional optical devices inspired by transformation optics

KAUST Repository

Yuan, Shuhao

2016-11-14

Light transport in curved quasi two-dimensional waveguides is considered theoretically. Within transformation optics and tensor theory, a concise description of curvature effects on transverse electric and magnetic waves is derived. We show that the curvature can induce light focusing and photonic crystal properties, which are confirmed by finite element simulations. Our results indicate that the curvature is an effective parameter for designing quasi two-dimensional optical devices in the fields of micro and nano photonics. © 2016 Author(s).

Quantifying the Relationship Between Curvature and Electric Potential in Lipid Bilayers

DEFF Research Database (Denmark)

Bruhn, Dennis Skjøth; Lomholt, Michael Andersen; Khandelia, Himanshu

2016-01-01

Cellular membranes mediate vital cellular processes by being subject to curvature and transmembrane electrical potentials. Here we build upon the existing theory for flexoelectricity in liquid crystals to quantify the coupling between lipid bilayer curvature and membrane potentials. Using molecular...... dynamics simulations, we show that head group dipole moments, the lateral pressure profile across the bilayer and spontaneous curvature all systematically change with increasing membrane potentials. In particu- lar, there is a linear dependence between the bending moment (the product of bending rigidity...

Distal root curvatures in mandibular molars: analysis using digital panoramic X-rays.

Science.gov (United States)

Fuentes, R; Farfán, C; Astete, N; Navarro, P; Arias, A

2018-01-01

The aim of this study was to describe the degree of curvature in distal roots in the first and second permanent mandibular molars in a Chilean patient sample. A cross-sectional descriptive study was conducted in which digital panoramic X-rays were analysed. Examinations of patients under 18 years, with signs of distortion or alteration in the contrast or the presence of pathologies that affected visualisation of the roots and pulp-chamber floor of the teeth to be analysed were excluded. Using the AutoCad software, an angle was drawn to represent the curve of the root in its different thirds, drawing lines inside the root canal from the pulp-chamber floor to the dental apex. Using the classic definition of dilaceration (root curvature > 90°), its prevalence was established. 412 teeth and roots were analysed, finding a dilaceration prevalence of 0.73% (n = 3). 84.72% of the roots presented some type of curvature. The middle third had the highest percentage of curvatures and the greatest average of angular curvature, whereas the cervical third was the straightest. No significant differences were found between the degree of curvature and the gender of the subjects, except for the apical third of tooth 3.6. The analysis of curvature by root third offers to the clinician a better perspective of the directional change of the roots and does not limit it to just the presence of curves in the apical third. The report of the angular degree of the curvatures, in addition to the prevalence of dilacerations, informs to the clinicians about the likelihood of finding difficulties when treating root canals. (Folia Morphol 2018; 77, 1: 131-137).

The spinning particle with extrinsic curvature

International Nuclear Information System (INIS)

Dhar, A.

1988-01-01

We construct and analyse an action for the spinning particle which contains an extrinsic curvature term. A possible generalization of this construction to the case of the spinning string is also discussed. (orig.)

Curvature effects on the electronic and transport properties of semiconductor films

Science.gov (United States)

Batista, F. F.; Chaves, Andrey; da Costa, D. R.; Farias, G. A.

2018-05-01

Within the effective mass approximation, we study the curvature effects on the electronic and transport properties of semiconductor films. We investigate how the geometry-induced potential resulting exclusively from periodic ripples in the film induces electronic confinement and a superlattice band structure. For fixed curvature parameters, such a confinement can be easily tuned by an external electric field, hence features of the superlattice band structure such as its energy gaps and band curvature can be controlled by an external parameter. We also show that, for some values of curvature and electric field, it is possible to obtain massless Dirac bands for a smooth curved structure. Moreover, we use a wave packet propagation method to demonstrate that the ripples are responsible for a significant inter-sub-band transition, specially for moderate values of the ripple height.

Measurement of curvature and twist of a deformed object using digital holography

International Nuclear Information System (INIS)

Chen Wen; Quan Chenggen; Cho Jui Tay

2008-01-01

Measurement of curvature and twist is an important aspect in the study of object deformation. In recent years, several methods have been proposed to determine curvature and twist of a deformed object using digital shearography. Here we propose a novel method to determine the curvature and twist of a deformed object using digital holography and a complex phasor. A sine/cosine transformation method and two-dimensional short time Fourier transform are proposed subsequently to process the wrapped phase maps. It is shown that high-quality phase maps corresponding to curvature and twist can be obtained. An experiment is conducted to demonstrate the validity of the proposed method

Numerical studies of transverse curvature effects on transonic flow stability

Science.gov (United States)

Macaraeg, M. G.; Daudpota, Q. I.

1992-01-01

A numerical study of transverse curvature effects on compressible flow temporal stability for transonic to low supersonic Mach numbers is presented for axisymmetric modes. The mean flows studied include a similar boundary-layer profile and a nonsimilar axisymmetric boundary-layer solution. The effect of neglecting curvature in the mean flow produces only small quantitative changes in the disturbance growth rate. For transonic Mach numbers (1-1.4) and aerodynamically relevant Reynolds numbers (5000-10,000 based on displacement thickness), the maximum growth rate is found to increase with curvature - the maximum occurring at a nondimensional radius (based on displacement thickness) between 30 and 100.

Influence of firing time and framework thickness on veneered Y-TZP discs curvature.

Science.gov (United States)

Jakubowicz-Kohen, Boris D; Sadoun, Michaël J; Douillard, Thierry; Mainjot, Amélie K

2014-02-01

The objective of the present work was to study the curvature of very thinly, veneered Y-TZP discs of different framework thicknesses submitted to different firing times. Fifteen 20-mm-wide Y-TZP discs were produced in three different thicknesses: 0.75, 1, 1.5mm. One disc from each group was left unveneered while the others were layered with a 0.1mm veneering ceramic layer. All discs underwent five firing cycles for a total cumulative firing time of 30 min, 1, 2, 5 and 10h at 900°C. The curvature profile was measured using a profilometer after the veneering process and after each firing cycle respectively. A fitted curve was then used to estimate the, curvature radius. The coefficient of thermal expansion (CTE) measurements were taken on veneering, ceramic and Y-TZP beam samples that underwent the same firing schedule. Those data were used to calculate the curvature generated by CTE variations over firing time. All bilayered samples exhibited a curvature that increased over firing time inversely to framework thickness. However non-veneered samples did not exhibit any curvature modification. The results of the present study reveal that even a very thin veneer layer (0.1mm) can induce a significant curvature of Y-TZP discs. The dilatometric results showed that Tg and CTE, variations are not sufficient to explain this curvature. A chemical-induced zirconia volume, augmentation located at the framework sub-surface near the interface could explain the sample, curvature and its increase with firing time. Copyright © 2013 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Shape discrimination by total curvature, with a view to cancer diagnostics

DEFF Research Database (Denmark)

Gardner, R.J.; Hobolth, Asger; Jensen, Eva Bjørn Vedel

2005-01-01

This paper investigates the use of total curvature for shape discrimination of objects via profiles of their planar sections (not assumed to be star shaped). Methods of estimating total curvature from observation of a finite number of points on the boundary of the object are investigated, includi...... a simple discrete approximation method and various interpolation methods. Total curvature is capable of revealing shape differences on a local scale, as demonstrated by the analysis of two data sets of malignant and normal or benign tumour cell nuclear profiles....

Discrete Curvatures and Discrete Minimal Surfaces

KAUST Repository

Sun, Xiang

2012-01-01

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads

Dynamics of the cosmological and Newton’s constant

International Nuclear Information System (INIS)

Smolin, Lee

2016-01-01

A modification of general relativity is presented in which Newton’s constant, G, and the cosmological constant, Λ, become a conjugate pair of dynamical variables. These are functions of a global time, hence the theory is presented in the framework of shape dynamics, which trades many-fingered time for a local scale invariance and an overall reparametrization of the global time. As a result, due to the fact that these global dynamical variables are canonically conjugate, the field equations are consistent. The theory predicts a relationship with no free parameters between the rates of change of Newton’s constant and the cosmological constant, in terms of the spatial average of the matter Lagrangian density. (paper)

Awareness Becomes Necessary Between Adaptive Pattern Coding of Open and Closed Curvatures

Science.gov (United States)

Sweeny, Timothy D.; Grabowecky, Marcia; Suzuki, Satoru

2012-01-01

Visual pattern processing becomes increasingly complex along the ventral pathway, from the low-level coding of local orientation in the primary visual cortex to the high-level coding of face identity in temporal visual areas. Previous research using pattern aftereffects as a psychophysical tool to measure activation of adaptive feature coding has suggested that awareness is relatively unimportant for the coding of orientation, but awareness is crucial for the coding of face identity. We investigated where along the ventral visual pathway awareness becomes crucial for pattern coding. Monoptic masking, which interferes with neural spiking activity in low-level processing while preserving awareness of the adaptor, eliminated open-curvature aftereffects but preserved closed-curvature aftereffects. In contrast, dichoptic masking, which spares spiking activity in low-level processing while wiping out awareness, preserved open-curvature aftereffects but eliminated closed-curvature aftereffects. This double dissociation suggests that adaptive coding of open and closed curvatures straddles the divide between weakly and strongly awareness-dependent pattern coding. PMID:21690314

Modeling curvature-dependent subcellular localization of a small sporulation protein in Bacillus subtilis

Science.gov (United States)

Wasnik, Vaibhav; Wingreen, Ned; Mukhopadhyay, Ranjan

2012-02-01

Recent experiments suggest that in the bacterium, B. subtilis, the cue for the localization of small sporulation protein, SpoVM, that plays a central role in spore coat formation, is curvature of the bacterial plasma membrane. This curvature-dependent localization is puzzling given the orders of magnitude difference in lengthscale of an individual protein and radius of curvature of the membrane. Here we develop a minimal model to study the relationship between curvature-dependent membrane absorption of SpoVM and clustering of membrane-associated SpoVM and compare our results with experiments.

Curvature effects in carbon nanomaterials: Exohedral versus endohedral supercapacitors

OpenAIRE

Huang, Jingsong; Bobby,; Sumpter, Bobby G.; Meunier, Vincent; Yushin, Gleb; Portet, Cristelle; Gogotsi, Yury

2010-01-01

Capacitive energy storage mechanisms in nanoporous carbon supercapacitors hinge on endohedral interactions in carbon materials with macro-, meso-, and micropores that have negative surface curvature. In this article, we show that because of the positive curvature found in zero-dimensional carbon onions or one-dimensional carbon nanotube arrays, exohedral interactions cause the normalized capacitance to increase with decreasing particle size or tube diameter, in sharp contrast to the behavior ...

A non-differential elastomer curvature sensor for softer-than-skin electronics

International Nuclear Information System (INIS)

Majidi, C; Kramer, R; Wood, R J

2011-01-01

We extend soft lithography microfabrication and design methods to introduce curvature sensors that are elastically soft (modulus 0.1–1 MPa) and stretchable (100–1000% strain). In contrast to existing curvature sensors that measure differential strain, sensors in this new class measure curvature directly and allow for arbitrary gauge factor and film thickness. Moreover, each sensor is composed entirely of a soft elastomer (PDMS (polydimethylsiloxane) or Ecoflex ® ) and conductive liquid (eutectic gallium indium, eGaIn) and thus remains functional even when stretched to several times its natural length. The electrical resistance in the embedded eGaIn microchannel is measured as a function of the bending curvature for a variety of sensor designs. In all cases, the experimental measurements are in reasonable agreement with closed-form algebraic approximations derived from elastic plate theory and Ohm's law

A non-differential elastomer curvature sensor for softer-than-skin electronics

Science.gov (United States)

Majidi, C.; Kramer, R.; Wood, R. J.

2011-10-01

We extend soft lithography microfabrication and design methods to introduce curvature sensors that are elastically soft (modulus 0.1-1 MPa) and stretchable (100-1000% strain). In contrast to existing curvature sensors that measure differential strain, sensors in this new class measure curvature directly and allow for arbitrary gauge factor and film thickness. Moreover, each sensor is composed entirely of a soft elastomer (PDMS (polydimethylsiloxane) or Ecoflex®) and conductive liquid (eutectic gallium indium, eGaIn) and thus remains functional even when stretched to several times its natural length. The electrical resistance in the embedded eGaIn microchannel is measured as a function of the bending curvature for a variety of sensor designs. In all cases, the experimental measurements are in reasonable agreement with closed-form algebraic approximations derived from elastic plate theory and Ohm's law.

Some curvature properties of quarter symmetric metric connections

International Nuclear Information System (INIS)

Rastogi, S.C.

1986-08-01

A linear connection Γ ji h with torsion tensor T j h P i -T i h P j , where T j h is an arbitrary (1,1) tensor field and P i is a 1-form, has been called a quarter-symmetric connection by Golab. Some properties of such connections have been studied by Rastogi, Mishra and Pandey, and Yano and Imai. In this paper based on the curvature tensor of quarter-symmetric metric connection we define a tensor analogous to conformal curvature tensor and study some properties of such a tensor. (author)

No large scale curvature perturbations during the waterfall phase transition of hybrid inflation

International Nuclear Information System (INIS)

Abolhasani, Ali Akbar; Firouzjahi, Hassan

2011-01-01

In this paper the possibility of generating large scale curvature perturbations induced from the entropic perturbations during the waterfall phase transition of the standard hybrid inflation model is studied. We show that whether or not appreciable amounts of large scale curvature perturbations are produced during the waterfall phase transition depends crucially on the competition between the classical and the quantum mechanical backreactions to terminate inflation. If one considers only the classical evolution of the system, we show that the highly blue-tilted entropy perturbations induce highly blue-tilted large scale curvature perturbations during the waterfall phase transition which dominate over the original adiabatic curvature perturbations. However, we show that the quantum backreactions of the waterfall field inhomogeneities produced during the phase transition dominate completely over the classical backreactions. The cumulative quantum backreactions of very small scale tachyonic modes terminate inflation very efficiently and shut off the curvature perturbation evolution during the waterfall phase transition. This indicates that the standard hybrid inflation model is safe under large scale curvature perturbations during the waterfall phase transition.

Intracellular magnetophoresis of amyloplasts and induction of root curvature

Science.gov (United States)

Kuznetsov, O. A.; Hasenstein, K. H.

1996-01-01

High-gradient magnetic fields (HGMFs) were used to induce intracellular magnetophoresis of amyloplasts. The HGMFs were generated by placing a small ferromagnetic wedge into a uniform magnetic field or at the gap edge between two permanent magnets. In the vicinity of the tip of the wedge the dynamic factor of the magnetic field, delta(H2/2), was about 10(9) Oe2.cm-1, which subjected the amyloplasts to a force comparable to that of gravity. When roots of 2-d-old seedlings of flax (Linum usitatissimum L.) were positioned vertically and exposed to an HGMF, curvature away from the wedge was transient and lasted approximately 1 h. Average curvature obtained after placing magnets, wedge and seedlings on a 1-rpm clinostat for 2 h was 33 +/- 5 degrees. Roots of horizontally placed control seedlings without rotation curved about 47 +/- 4 degrees. The time course of curvature and changes in growth rate were similar for gravicurvature and for root curvature induced by HGMFs. Microscopy showed displacement of amyloplasts in vitro and in vivo. Studies with Arabidopsis thaliana (L.) Heynh. showed that the wild type responded to HGMFs but the starchless mutant TC7 did not. The data indicate that a magnetic force can be used to study the gravisensing and response system of roots.

Local divergence and curvature divergence in first order optics

Science.gov (United States)

Mafusire, Cosmas; Krüger, Tjaart P. J.

2018-06-01

The far-field divergence of a light beam propagating through a first order optical system is presented as a square root of the sum of the squares of the local divergence and the curvature divergence. The local divergence is defined as the ratio of the beam parameter product to the beam width whilst the curvature divergence is a ratio of the space-angular moment also to the beam width. It is established that the beam’s focusing parameter can be defined as a ratio of the local divergence to the curvature divergence. The relationships between the two divergences and other second moment-based beam parameters are presented. Their various mathematical properties are presented such as their evolution through first order systems. The efficacy of the model in the analysis of high power continuous wave laser-based welding systems is briefly discussed.

On $L_p$ Affine Surface Area and Curvature Measures

OpenAIRE

Zhao, Yiming

2015-01-01

The relationship between $L_p$ affine surface area and curvature measures is investigated. As a result, a new representation of the existing notion of $L_p$ affine surface area depending only on curvature measures is derived. Direct proofs of the equivalence between this new representation and those previously known are provided. The proofs show that the new representation is, in a sense, "polar" to that of Lutwak's and "dual" to that of Sch\\"utt & Werner's.

On harmonic curvatures of a Frenet curve in Lorentzian space

International Nuclear Information System (INIS)

Kuelahci, Mihriban; Bektas, Mehmet; Erguet, Mahmut

2009-01-01

In this paper, we consider curves of AW(k)-type, 1 ≤ k ≤ 3, in Lorentzian space. We give curvature conditions of these kind of curves. Furthermore, we study harmonic curvatures of curves of AW(k)-type. We investigate that under what conditions AW(k)-type curves are helix. Some related theorems and corollaries are also proved.

Non-linear realizations and higher curvature supergravity

Energy Technology Data Exchange (ETDEWEB)

Farakos, F. [Dipartimento di Fisica e Astronomia ' ' Galileo Galilei' ' , Universita di Padova (Italy); INFN, Sezione di Padova (Italy); Ferrara, S. [Department of Theoretical Physics, Geneva (Switzerland); INFN - Laboratori Nazionali di Frascati, Frascati (Italy); Department of Physics and Astronomy, Mani L. Bhaumik Institute for Theoretical Physics, U.C.L.A., Los Angeles, CA (United States); Kehagias, A. [Physics Division, National Technical University of Athens (Greece); Luest, D. [Arnold Sommerfeld Center for Theoretical Physics, Muenchen (Germany); Max-Planck-Institut fuer Physik, Muenchen (Germany)

2017-12-15

We focus on non-linear realizations of local supersymmetry as obtained by using constrained superfields in supergravity. New constraints, beyond those of rigid supersymmetry, are obtained whenever curvature multiplets are affected as well as higher derivative interactions are introduced. In particular, a new constraint, which removes a very massive gravitino is introduced, and in the rigid limit it merely reduces to an explicit supersymmetry breaking. Higher curvature supergravities free of ghosts and instabilities are also obtained in this way. Finally, we consider direct coupling of the goldstino multiplet to the super Gauss-Bonnet multiplet and discuss the emergence of a new scalar degree of freedom. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Curvature perturbation spectra from waterfall transition, black hole constraints and non-Gaussianity

Energy Technology Data Exchange (ETDEWEB)

Bugaev, Edgar; Klimai, Peter, E-mail: bugaev@pcbai10.inr.ruhep.ru, E-mail: pklimai@gmail.com [Institute for Nuclear Research, Russian Academy of Sciences, 60th October Anniversary Prospect 7a, 117312 Moscow (Russian Federation)

2011-11-01

We carried out numerical calculations of a contribution of the waterfall field to the primordial curvature perturbation (on uniform density hypersurfaces) ζ, which is produced during waterfall transition in hybrid inflation scenario. The calculation is performed for a broad interval of values of the model parameters. We show that there is a strong growth of amplitudes of the curvature perturbation spectrum in the limit when the bare mass-squared of the waterfall field becomes comparable with the square of Hubble parameter. We show that in this limit the primordial black hole constraints on the curvature perturbations must be taken into account. It is shown that, in the same limit, peak values of the curvature perturbation spectra are far beyond horizon, and the spectra are strongly non-Gaussian.

Curvature perturbation spectra from waterfall transition, black hole constraints and non-Gaussianity

International Nuclear Information System (INIS)

Bugaev, Edgar; Klimai, Peter

2011-01-01

We carried out numerical calculations of a contribution of the waterfall field to the primordial curvature perturbation (on uniform density hypersurfaces) ζ, which is produced during waterfall transition in hybrid inflation scenario. The calculation is performed for a broad interval of values of the model parameters. We show that there is a strong growth of amplitudes of the curvature perturbation spectrum in the limit when the bare mass-squared of the waterfall field becomes comparable with the square of Hubble parameter. We show that in this limit the primordial black hole constraints on the curvature perturbations must be taken into account. It is shown that, in the same limit, peak values of the curvature perturbation spectra are far beyond horizon, and the spectra are strongly non-Gaussian

Measurements of the Curvature of Protrusions/Retrusions on Migrating Recrystallization Boundaries

DEFF Research Database (Denmark)

Zhang, Yubin; Godfrey, A.; Juul Jensen, Dorte

2009-01-01

Two methods to quantify protrusions/retrusions and to estimate local boundary curvature from sample plane sections are proposed. The methods are used to evaluate the driving force due to curvature of the protrusions/retrusions for partially recrystallized pure nickel cold rolled to 96% reduction...

A high resolution electron microscopy investigation of curvature in carbon nanotubes

Science.gov (United States)

Weldon, D. N.; Blau, W. J.; Zandbergen, H. W.

1995-07-01

Evidence for heptagon inclusion in multi-walled carbon nanotubes was sought in arc-produced carbon deposits. Transmission electron microscopy revealed many curved nanotubes although their relative abundance was low. Close examination of the micrographs in the regions of expected heptagon inclusion shows that the curvature is accomplished by folding or fracture of the lattice planes. This observed phenomenon contradicts the theoretical modelling studies which predict stable structures with negative curvature accomplished by heptagon/pentagon pairs. A possible explanation for curvature in single-walled tubes is presented based on a molecular mechanics geometry optimisation study of spa inclusion in a graphite sheet.

Refraction in the lower troposphere: Higher order image distortion effects due to refractive profile curvature

Science.gov (United States)

Short, Daniel J.

the arrival angles shows the target viewed by an observer will appear stretched, or magnified (towering). Conversely, with a negative lensing action the target viewed will appear shortened or compressed (stooping). The lensing can be modeled with a parabolic refractive index profile and the curvature of the profile is characterized by the curvature parameter alpha (units: m-1). The objective of chapter 4 is to estimate the curvature parameter from an analysis of the images collected by the camera system. In effect, the camera acts as a device that measures ray angle of arrival so image changes that appear as a stretch can be related to changes in the curvature of the index profile. Time-lapse images of the F & A Dairy products building in Las Cruces, NM (15.3 km range from the camera at the NMSU campus) were analyzed using a manual cursor-marking MATLAB script developed for this project. For several different dates, we found the largest stretches occur in the morning. For example, a comparison of two morning images separated by an hour shows the apparent height of the building in a second image gained about 34 pixels compared to the first image. The refractive index curvature change for this case is calculated and found to be alpha = 6.0 x 10-5 m-1 . As the day progressed the image slowly compressed back to the early morning size. Optical measurements of the local index of refraction profile of the atmosphere have been made in the past but usually only for isolated events or time periods. There is little data to describe occurrence probabilities, spatial or temporal properties, or relative strength of effects for different seasons, or even durations of weeks. In this dissertation, time-lapse image data from two separate weeks were analyzed for daily stretching/compressing events and presented graphically. The results show a systematic trend of dramatic size changes in the morning and a slow progression to normal building size as the day continues. Using the optical

Curvature-induced stiffness and the spatial variation of wavelength in wrinkled sheets.

Science.gov (United States)

Paulsen, Joseph D; Hohlfeld, Evan; King, Hunter; Huang, Jiangshui; Qiu, Zhanlong; Russell, Thomas P; Menon, Narayanan; Vella, Dominic; Davidovitch, Benny

2016-02-02

Wrinkle patterns in compressed thin sheets are ubiquitous in nature and technology, from the furrows on our foreheads to crinkly plant leaves, from ripples on plastic-wrapped objects to the protein film on milk. The current understanding of an elementary descriptor of wrinkles--their wavelength--is restricted to deformations that are parallel, spatially uniform, and nearly planar. However, most naturally occurring wrinkles do not satisfy these stipulations. Here we present a scheme that quantitatively explains the wrinkle wavelength beyond such idealized situations. We propose a local law that incorporates both mechanical and geometrical effects on the spatial variation of wrinkle wavelength. Our experiments on thin polymer films provide strong evidence for its validity. Understanding how wavelength depends on the properties of the sheet and the underlying liquid or elastic subphase is crucial for applications where wrinkles are used to sculpt surface topography, to measure properties of the sheet, or to infer forces applied to a film.

Frame-Covariant Formulation of Inflation in Scalar-Curvature Theories

CERN Document Server

Burns, Daniel; Pilaftsis, Apostolos

2016-01-01

We develop a frame-covariant formulation of inflation in the slow-roll approximation by generalizing the inflationary attractor solution for scalar-curvature theories. Our formulation gives rise to new generalized forms for the potential slow-roll parameters, which enable us to examine the effect of conformal transformations and inflaton reparameterizations in scalar-curvature theories. We find that cosmological observables, such as the power spectrum, the spectral indices and their runnings, can be expressed in a concise manner in terms of the generalized potential slow-roll parameters which depend on the scalar-curvature coupling function, the inflaton wavefunction, and the inflaton potential. We show how the cosmological observables of inflation are frame-invariant in this generalized potential slow-roll formalism, as long as the end-of-inflation condition is appropriately extended to become frame-invariant as well. We then apply our formalism to specific scenarios, such as the induced gravity inflation, H...

The scalar curvature problem on the four dimensional half sphere

CERN Document Server

Ben-Ayed, M; El-Mehdi, K

2003-01-01

In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the standard four dimensional half sphere. We provide an Euler-Hopf type criterion for a given function to be a scalar curvature for some metric conformal to the standard one. Our proof involves the study of critical points at infinity of the associated variational problem.

Phase separation in artificial vesicles driven by light and curvature

Science.gov (United States)

Rinaldin, Melissa; Pomp, Wim; Schmidt, Thomas; Giomi, Luca; Kraft, Daniela; Physics of Life Processes Team; Soft; Bio Mechanics Collaboration; Self-Assembly in Soft Matter Systems Collaboration

The role of phase-demixing in living cells, leading to the lipid-raft hypothesis, has been extensively studied. Lipid domains of higher lipid chain order are proposed to regulate protein spatial organization. Giant Unilamellar Vesicles provide an artificial model to study phase separation. So far temperature was used to initiate the process. Here we introduce a new methodology based on the induction of phase separation by light. To this aim, the composition of the lipid membrane is varied by photo-oxidation of lipids. The control of the process gained by using light allowed us to observe vesicle shape fluctuations during phase-demixing. The presence of fluctuations near the critical mixing point resembles features of a critical process. We quantitatively analyze these fluctuations using a 2d elastic model, from which we can estimate the material parameters such as bending rigidity and surface tension, demonstrating the non-equilibrium critical behaviour. Finally, I will describe recent attempts toward tuning the membrane composition by controlling the vesicle curvature.

Directional effects in transitional resonance spectra and group constants

International Nuclear Information System (INIS)

Hill, R.N.; Oh, K.O.; Rhodes, J.D.

1989-01-01

Analytical exploratory investigations indicate that transition effects such as streaming cause a considerable spatial variation in the neutron spectra across resonances; streaming leads to opposite effects in the forward and backward directions. The neglect of this coupled spatial/angular variations of the transitory resonance spectra is an approximation that is common to all current group constant generation methodologies. This paper presents a description of the spatial/angular coupling of the neutron flux across isolated resonances. It appears to be necessary to differentiate between forward-and backward-directed neutron flux components or even to consider components in narrower angular cones. The effects are illustrated for an isolated actinide resonance in a simplified fast reactor blanket problem. The resonance spectra of the directional flux components φ + and φ - , and even more so the 90-deg cone components, are shown to deviate significantly from the infinite medium approximation, and the differences increase with penetration. The charges in φ + lead to a decreasing scattering group constant that enhances neutron transmission; the changes in φ - lead to an increasing group constant inhibiting backward scattering. Therefore, the changes in the forward-and backward-directed spectra both lead to increased neutron transmission. Conversely, the flux (φ = φ + +φ - ) is shown to agree closely with the infinite medium approximation both in the analytical formulas and in the numerical solution. The directional effect cancel in the summation. The forward-and backward-directed flux components are used as weighting spectra to illustrate the group constant changes for a single resonance

Prescribed curvature tensor in locally conformally flat manifolds

Science.gov (United States)

Pina, Romildo; Pieterzack, Mauricio

2018-01-01

A global existence theorem for the prescribed curvature tensor problem in locally conformally flat manifolds is proved for a special class of tensors R. Necessary and sufficient conditions for the existence of a metric g ¯ , conformal to Euclidean g, are determined such that R ¯ = R, where R ¯ is the Riemannian curvature tensor of the metric g ¯ . The solution to this problem is given explicitly for special cases of the tensor R, including the case where the metric g ¯ is complete on Rn. Similar problems are considered for locally conformally flat manifolds.

Principal Curvature Measures Estimation and Application to 3D Face Recognition

KAUST Repository

Tang, Yinhang

2017-04-06

This paper presents an effective 3D face keypoint detection, description and matching framework based on three principle curvature measures. These measures give a unified definition of principle curvatures for both smooth and discrete surfaces. They can be reasonably computed based on the normal cycle theory and the geometric measure theory. The strong theoretical basis of these measures provides us a solid discrete estimation method on real 3D face scans represented as triangle meshes. Based on these estimated measures, the proposed method can automatically detect a set of sparse and discriminating 3D facial feature points. The local facial shape around each 3D feature point is comprehensively described by histograms of these principal curvature measures. To guarantee the pose invariance of these descriptors, three principle curvature vectors of these principle curvature measures are employed to assign the canonical directions. Similarity comparison between faces is accomplished by matching all these curvature-based local shape descriptors using the sparse representation-based reconstruction method. The proposed method was evaluated on three public databases, i.e. FRGC v2.0, Bosphorus, and Gavab. Experimental results demonstrated that the three principle curvature measures contain strong complementarity for 3D facial shape description, and their fusion can largely improve the recognition performance. Our approach achieves rank-one recognition rates of 99.6, 95.7, and 97.9% on the neutral subset, expression subset, and the whole FRGC v2.0 databases, respectively. This indicates that our method is robust to moderate facial expression variations. Moreover, it also achieves very competitive performance on the pose subset (over 98.6% except Yaw 90°) and the occlusion subset (98.4%) of the Bosphorus database. Even in the case of extreme pose variations like profiles, it also significantly outperforms the state-of-the-art approaches with a recognition rate of 57.1%. The

Discrete Curvatures and Discrete Minimal Surfaces

KAUST Repository

Sun, Xiang

2012-06-01

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.

Measuring the composition-curvature coupling in binary lipid membranes by computer simulations

International Nuclear Information System (INIS)

Barragán Vidal, I. A.; Müller, M.; Rosetti, C. M.; Pastorino, C.

2014-01-01

The coupling between local composition fluctuations in binary lipid membranes and curvature affects the lateral membrane structure. We propose an efficient method to compute the composition-curvature coupling in molecular simulations and apply it to two coarse-grained membrane models—a minimal, implicit-solvent model and the MARTINI model. Both the weak-curvature behavior that is typical for thermal fluctuations of planar bilayer membranes as well as the strong-curvature regime corresponding to narrow cylindrical membrane tubes are studied by molecular dynamics simulation. The simulation results are analyzed by using a phenomenological model of the thermodynamics of curved, mixed bilayer membranes that accounts for the change of the monolayer area upon bending. Additionally the role of thermodynamic characteristics such as the incompatibility between the two lipid species and asymmetry of composition are investigated

Measuring the composition-curvature coupling in binary lipid membranes by computer simulations

Energy Technology Data Exchange (ETDEWEB)

Barragán Vidal, I. A., E-mail: vidal@theorie.physik.uni-goettingen.de; Müller, M., E-mail: mmueller@theorie.physik.uni-goettingen.de [Institut für Theoretische Physik, Georg-August-Universität, Friedrich-Hund-Platz 1, 37077 Göttingen (Germany); Rosetti, C. M., E-mail: carla@dqb.fcq.unc.edu.ar [Centro de Investigaciones en Química Biológica de Córdoba, Departamento de Química Biológica, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba (Argentina); Pastorino, C., E-mail: pastor@cnea.gov.ar [Departamento de Física de la Materia Condensada, Centro Atómico Constituyentes, CNEA/CONICET, Av. Gral. Paz 1499, 1650 Pcia. de Buenos Aires (Argentina)

2014-11-21

The coupling between local composition fluctuations in binary lipid membranes and curvature affects the lateral membrane structure. We propose an efficient method to compute the composition-curvature coupling in molecular simulations and apply it to two coarse-grained membrane models—a minimal, implicit-solvent model and the MARTINI model. Both the weak-curvature behavior that is typical for thermal fluctuations of planar bilayer membranes as well as the strong-curvature regime corresponding to narrow cylindrical membrane tubes are studied by molecular dynamics simulation. The simulation results are analyzed by using a phenomenological model of the thermodynamics of curved, mixed bilayer membranes that accounts for the change of the monolayer area upon bending. Additionally the role of thermodynamic characteristics such as the incompatibility between the two lipid species and asymmetry of composition are investigated.

Plan curvature and landslide probability in regions dominated by earth flows and earth slides

Science.gov (United States)

Ohlmacher, G.C.

2007-01-01

Damaging landslides in the Appalachian Plateau and scattered regions within the Midcontinent of North America highlight the need for landslide-hazard mapping and a better understanding of the geomorphic development of landslide terrains. The Plateau and Midcontinent have the necessary ingredients for landslides including sufficient relief, steep slope gradients, Pennsylvanian and Permian cyclothems that weather into fine-grained soils containing considerable clay, and adequate precipitation. One commonly used parameter in landslide-hazard analysis that is in need of further investigation is plan curvature. Plan curvature is the curvature of the hillside in a horizontal plane or the curvature of the contours on a topographic map. Hillsides can be subdivided into regions of concave outward plan curvature called hollows, convex outward plan curvature called noses, and straight contours called planar regions. Statistical analysis of plan-curvature and landslide datasets indicate that hillsides with planar plan curvature have the highest probability for landslides in regions dominated by earth flows and earth slides in clayey soils (CH and CL). The probability of landslides decreases as the hillsides become more concave or convex. Hollows have a slightly higher probability for landslides than noses. In hollows landslide material converges into the narrow region at the base of the slope. The convergence combined with the cohesive nature of fine-grained soils creates a buttressing effect that slows soil movement and increases the stability of the hillside within the hollow. Statistical approaches that attempt to determine landslide hazard need to account for the complex relationship between plan curvature, type of landslide, and landslide susceptibility. ?? 2007 Elsevier B.V. All rights reserved.

Soliton surfaces via a zero-curvature representation of differential equations

International Nuclear Information System (INIS)

Grundland, A M; Post, S

2012-01-01

The main aim of this paper is to introduce a new version of the Fokas–Gel’fand formula for immersion of soliton surfaces in Lie algebras. The paper contains a detailed exposition of the technique for obtaining exact forms of 2D surfaces associated with any solution of a given nonlinear ordinary differential equation which can be written in the zero-curvature form. That is, for any generalized symmetry of the zero-curvature condition of the associated integrable model, it is possible to construct soliton surfaces whose Gauss–Mainardi–Codazzi equations are equivalent to infinitesimal deformations of the zero-curvature representation of the considered model. Conversely, it is shown (proposition 1) that for a given immersion function of a 2D soliton surface in a Lie algebra, it is possible to derive the associated generalized vector field in the evolutionary form which characterizes all symmetries of the zero-curvature condition. The theoretical considerations are illustrated via surfaces associated with the Painlevé equations P1, P2 and P3, including transcendental functions, the special cases of the rational and Airy solutions of P2 and the classical solutions of P3. (paper)

Harmonic curvatures and generalized helices in En

International Nuclear Information System (INIS)

Camci, Cetin; Ilarslan, Kazim; Kula, Levent; Hacisalihoglu, H. Hilmi

2009-01-01

In n-dimensional Euclidean space E n , harmonic curvatures of a non-degenerate curve defined by Ozdamar and Hacisalihoglu [Ozdamar E, Hacisalihoglu HH. A characterization of Inclined curves in Euclidean n-space. Comm Fac Sci Univ Ankara, Ser A1 1975;24:15-23]. In this paper, we give some characterizations for a non-degenerate curve α to be a generalized helix by using its harmonic curvatures. Also we define the generalized Darboux vector D of a non-degenerate curve α in n-dimensional Euclidean space E n and we show that the generalized Darboux vector D lies in the kernel of Frenet matrix M(s) if and only if the curve α is a generalized helix in the sense of Hayden.

Mean cortical curvature reflects cytoarchitecture restructuring in mild traumatic brain injury

Directory of Open Access Journals (Sweden)

Jace B. King

2016-01-01

Full Text Available In the United States alone, the number of persons living with the enduring consequences of traumatic brain injuries is estimated to be between 3.2 and 5 million. This number does not include individuals serving in the United States military or seeking care at Veterans Affairs hospitals. The importance of understanding the neurobiological consequences of mild traumatic brain injury (mTBI has increased with the return of veterans from conflicts overseas, many of who have suffered this type of brain injury. However, identifying the neuroanatomical regions most affected by mTBI continues to prove challenging. The aim of this study was to assess the use of mean cortical curvature as a potential indicator of progressive tissue loss in a cross-sectional sample of 54 veterans with mTBI compared to 31 controls evaluated with MRI. It was hypothesized that mean cortical curvature would be increased in veterans with mTBI, relative to controls, due in part to cortical restructuring related to tissue volume loss. Mean cortical curvature was assessed in 60 bilateral regions (31 sulcal, 29 gyral. Of the 120 regions investigated, nearly 50% demonstrated significantly increased mean cortical curvature in mTBI relative to controls with 25% remaining significant following multiple comparison correction (all, pFDR < .05. These differences were most prominent in deep gray matter regions of the cortex. Additionally, significant relationships were found between mean cortical curvature and gray and white matter volumes (all, p < .05. These findings suggest potentially unique patterns of atrophy by region and indicate that changes in brain microstructure due to mTBI are sensitive to measures of mean curvature.

Testable solution of the cosmological constant and coincidence problems

International Nuclear Information System (INIS)

Shaw, Douglas J.; Barrow, John D.

2011-01-01

We present a new solution to the cosmological constant (CC) and coincidence problems in which the observed value of the CC, Λ, is linked to other observable properties of the Universe. This is achieved by promoting the CC from a parameter that must be specified, to a field that can take many possible values. The observed value of Λ≅(9.3 Gyrs) -2 [≅10 -120 in Planck units] is determined by a new constraint equation which follows from the application of a causally restricted variation principle. When applied to our visible Universe, the model makes a testable prediction for the dimensionless spatial curvature of Ω k0 =-0.0056(ζ b /0.5), where ζ b ∼1/2 is a QCD parameter. Requiring that a classical history exist, our model determines the probability of observing a given Λ. The observed CC value, which we successfully predict, is typical within our model even before the effects of anthropic selection are included. When anthropic selection effects are accounted for, we find that the observed coincidence between t Λ =Λ -1/2 and the age of the Universe, t U , is a typical occurrence in our model. In contrast to multiverse explanations of the CC problems, our solution is independent of the choice of a prior weighting of different Λ values and does not rely on anthropic selection effects. Our model includes no unnatural small parameters and does not require the introduction of new dynamical scalar fields or modifications to general relativity, and it can be tested by astronomical observations in the near future.

Curvature Derivative Surface used to characterize the complexity of the seafloor around St. John, USVI

Data.gov (United States)

National Oceanic and Atmospheric Administration, Department of Commerce — Curvature was calculated from the bathymetry surface for each raster cell using the ArcGIS 3D Analyst "Curvature" Tool. Curvature describes the rate of change of...

Effects of ethylene on the kinetics of curvature and auxin redistribution in gravistimulated roots of Zea mays

Science.gov (United States)

Lee, J. S.; Evans, M. L.

1990-01-01

We tested the involvement of ethylene in maize (Zea mays L.) root gravitropism by measuring the kinetics of curvature and lateral auxin movement in roots treated with ethylene, inhibitors of ethylene synthesis, or inhibitors of ethylene action. In the presence of ethylene the latent period of gravitropic curvature appeared to be increased somewhat. However, ethylene-treated roots continued to curve after control roots had reached their final angle of curvature. Consequently, maximum curvature in the presence of ethylene was much greater in ethylene-treated roots than in controls. Inhibitors of ethylene biosynthesis or action had effects on the kinetics of curvature opposite to that of ethylene, i.e. the latent period appeared to be shortened somewhat while total curvature was reduced relative to that of controls. Label from applied 3H-indole-3-acetic acid was preferentially transported toward the lower side of stimulated roots. In parallel with effects on curvature, ethylene treatment delayed the development of gravity-induced asymmetric auxin movement across the root but extended its duration once initiated. The auxin transport inhibitor, 1-N-naphthylphthalamic acid reduced both gravitropic curvature and the effect of ethylene on curvature. Since neither ethylene nor inhibitors of ethylene biosynthesis or action prevented curvature, we conclude that ethylene does not mediate the primary differential growth response causing curvature. Because ethylene affects curvature and auxin transport in parallel, we suggest that ethylene modifies curvature by affecting gravity-induced lateral transport of auxin, perhaps by interfering with adaptation of the auxin transport system to the gravistimulus.

Constant Flux of Spatial Niche Partitioning through High-Resolution Sampling of Magnetotactic Bacteria.

Science.gov (United States)

He, Kuang; Gilder, Stuart A; Orsi, William D; Zhao, Xiangyu; Petersen, Nikolai

2017-10-15

Magnetotactic bacteria (MTB) swim along magnetic field lines in water. They are found in aquatic habitats throughout the world, yet knowledge of their spatial and temporal distribution remains limited. To help remedy this, we took MTB-bearing sediment from a natural pond, mixed the thoroughly homogenized sediment into two replicate aquaria, and then counted three dominant MTB morphotypes (coccus, spirillum, and rod-shaped MTB cells) at a high spatiotemporal sampling resolution: 36 discrete points in replicate aquaria were sampled every ∼30 days over 198 days. Population centers of the MTB coccus and MTB spirillum morphotypes moved in continual flux, yet they consistently inhabited separate locations, displaying significant anticorrelation. Rod-shaped MTB were initially concentrated toward the northern end of the aquaria, but at the end of the experiment, they were most densely populated toward the south. The finding that the total number of MTB cells increased over time during the experiment argues that population reorganization arose from relative changes in cell division and death and not from migration. The maximum net growth rates were 10, 3, and 1 doublings day -1 and average net growth rates were 0.24, 0.11, and 0.02 doublings day -1 for MTB cocci, MTB spirilla, and rod-shaped MTB, respectively; minimum growth rates for all three morphotypes were -0.03 doublings day -1 Our results suggest that MTB cocci and MTB spirilla occupy distinctly different niches: their horizontal positioning in sediment is anticorrelated and under constant flux. IMPORTANCE Little is known about the horizontal distribution of magnetotactic bacteria in sediment or how the distribution changes over time. We therefore measured three dominant magnetotactic bacterium morphotypes at 36 places in two replicate aquaria each month for 7 months. We found that the spatial positioning of population centers changed over time and that the two most abundant morphotypes (MTB cocci and MTB spirilla

Existence of conformal metrics on spheres with prescribed Paneitz curvature

International Nuclear Information System (INIS)

Ben Ayed, Mohamed; El Mehdi, Khalil

2003-07-01

In this paper we study the problem of prescribing a fourth order conformal invariant (the Paneitz curvature) on the n-spheres, with n ≥ 5. Using tools from the theory of critical points at infinity, we provide some topological conditions on the level sets of a given function defined on the sphere, under which we prove the existence of conformal metric with prescribed Paneitz curvature. (author)

Existence of conformal metrics on spheres with prescribed Paneitz curvature

CERN Document Server

Ben-Ayed, M

2003-01-01

In this paper we study the problem of prescribing a fourth order conformal invariant (the Paneitz curvature) on the n-spheres, with n >= 5. Using tools from the theory of critical points at infinity, we provide some topological conditions on the level sets of a given function defined on the sphere, under which we prove the existence of conformal metric with prescribed Paneitz curvature.

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

Resolving curvature singularities in holomorphic gravity

NARCIS (Netherlands)

Mantz, C.L.M.; Prokopec, T.

2011-01-01

We formulate a holomorphic theory of gravity and study how the holomorphy symmetry alters the two most important singular solutions of general relativity: black holes and cosmology. We show that typical observers (freely) falling into a holomorphic black hole do not encounter a curvature

Biharmonic Submanifolds with Parallel Mean Curvature Vector in Pseudo-Euclidean Spaces

Energy Technology Data Exchange (ETDEWEB)

Fu, Yu, E-mail: yufudufe@gmail.com [Dongbei University of Finance and Economics, School of Mathematics and Quantitative Economics (China)

2013-12-15

In this paper, we investigate biharmonic submanifolds in pseudo-Euclidean spaces with arbitrary index and dimension. We give a complete classification of biharmonic spacelike submanifolds with parallel mean curvature vector in pseudo-Euclidean spaces. We also determine all biharmonic Lorentzian surfaces with parallel mean curvature vector field in pseudo-Euclidean spaces.

Biharmonic Submanifolds with Parallel Mean Curvature Vector in Pseudo-Euclidean Spaces

International Nuclear Information System (INIS)

Fu, Yu

2013-01-01

In this paper, we investigate biharmonic submanifolds in pseudo-Euclidean spaces with arbitrary index and dimension. We give a complete classification of biharmonic spacelike submanifolds with parallel mean curvature vector in pseudo-Euclidean spaces. We also determine all biharmonic Lorentzian surfaces with parallel mean curvature vector field in pseudo-Euclidean spaces

A prescribing geodesic curvature problem

International Nuclear Information System (INIS)

Chang, K.C.; Liu, J.Q.

1993-09-01

Let D be the unit disk and k be a function on S 1 = δD. Find a flat metric which is pointwise conformal to the standard metric and has k as the geodesic curvature of S 1 . A sufficient condition for the existence of such a metric is that the harmonic extension of k in D has saddle points. (author). 11 refs

Linearized curvatures for auxiliary fields in the de Sitter space

Energy Technology Data Exchange (ETDEWEB)

Vasiliev, M A

1988-09-19

New consistent linearized curvatures in the de Sitter space are constructed. The sequence of actions, describing bosonic and fermionic gauge auxiliary fields, is found based on these curvatures. The proposed actions are parametrized by two integer parameters, n greater than or equal to 0 and m greater than or equal to 0. The simplest case n=m=0 corresponds in the flat limit to the auxiliary fields of 'new minimal' supergravity. The hamiltonian formulation is developed for the auxiliary fields suggested; hamiltonians and first- and second-class constraints are constructed. Using these results, it is shown that the systems of fields proposed possess no dynamical degrees of freedom in de Sitter and flat spaces. In addition the hamiltonian formalism is analysed for some free dynamical systems based on linearized higher-spin curvatures introduced previously.

Higher curvature corrections to primordial fluctuations in slow-roll inflation

International Nuclear Information System (INIS)

Satoh, Masaki; Soda, Jiro

2008-01-01

We study higher curvature corrections to the scalar spectral index, the tensor spectral index, the tensor-to-scalar ratio, and the polarization of gravitational waves. We find that there are cases where the higher curvature corrections cannot be negligible in the dynamics of the scalar field, although they are always negligible energetically. Indeed, it turns out that the tensor-to-scalar ratio could be enhanced and the tensor spectral index could be blue due to the Gauss–Bonnet term. We estimate the degree of circular polarization of gravitational waves generated during the slow-roll inflation. We argue that the circular polarization could be observable with the help of both the Gauss–Bonnet and the parity violating terms. We also present several examples to reveal observational implications of higher curvature corrections for chaotic inflationary models

The geometric curvature of the lumbar spine during restricted and unrestricted squats.

Science.gov (United States)

Hebling Campos, Mário; Furtado Alaman, Laizi I; Seffrin-Neto, Aldo A; Vieira, Carlos A; Costa de Paula, Marcelo; Barbosa de Lira, Claudio A

2017-06-01

The main purpose of this study was to analyze the behavior of the geometric curvature of the lumbar spine during restricted and unrestricted squats, using a novel investigative method. The rationale for our hypothesis is that the lumbar curvature has different patterns at different spine levels depending on the squat technique used. Spine motion was collected via stereo-photogrammetric analysis in nineteen participants (11 males, 8 females). The reconstructed spine points at the upright neutral position and at the deepest position of the squat exercise were projected onto the sagittal plane of the trunk, a polynomial was fitted to the data, and were quantified the two-dimensional geometric curvature at lower, central and higher lumbar levels, besides the inclination of trunk and lumbosacral region, the overall geometric curvature and overall angle of the lumbar spine. The mean values for each variable were analysed with paired t-test (Psquat techniques and these effects are also reduced in unrestricted squats. The data collected in the study are evidence that during barbell squats the lumbar curvature has different patterns at different spinal levels depending on the exercise technique. The lower lumbar spine appears to be less overloaded during unrestricted squats.

Generalization of the swelling method to measure the intrinsic curvature of lipids

Science.gov (United States)

Barragán Vidal, I. A.; Müller, M.

2017-12-01

Via computer simulation of a coarse-grained model of two-component lipid bilayers, we compare two methods of measuring the intrinsic curvatures of the constituting monolayers. The first one is a generalization of the swelling method that, in addition to the assumption that the spontaneous curvature linearly depends on the composition of the lipid mixture, incorporates contributions from its elastic energy. The second method measures the effective curvature-composition coupling between the apposing leaflets of bilayer structures (planar bilayers or cylindrical tethers) to extract the spontaneous curvature. Our findings demonstrate that both methods yield consistent results. However, we highlight that the two-leaflet structure inherent to the latter method has the advantage of allowing measurements for mixed lipid systems up to their critical point of demixing as well as in the regime of high concentration (of either species).

Global and local curvature in density functional theory.

Science.gov (United States)

Zhao, Qing; Ioannidis, Efthymios I; Kulik, Heather J

2016-08-07

Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within density functional theory (DFT) fail to reproduce this behavior, giving rise to deviations from linearity with a convex global curvature that is evidence of many-electron, self-interaction error and electron delocalization. Popular functional tuning strategies focus on reproducing piecewise linearity, especially to improve predictions of optical properties. In a divergent approach, Hubbard U-augmented DFT (i.e., DFT+U) treats self-interaction errors by reducing the local curvature of the energy with respect to electron removal or addition from one localized subshell to the surrounding system. Although it has been suggested that DFT+U should simultaneously alleviate global and local curvature in the atomic limit, no detailed study on real systems has been carried out to probe the validity of this statement. In this work, we show when DFT+U should minimize deviations from linearity and demonstrate that a "+U" correction will never worsen the deviation from linearity of the underlying xc approximation. However, we explain varying degrees of efficiency of the approach over 27 octahedral transition metal complexes with respect to transition metal (Sc-Cu) and ligand strength (CO, NH3, and H2O) and investigate select pathological cases where the delocalization error is invisible to DFT+U within an atomic projection framework. Finally, we demonstrate that the global and local curvatures represent different quantities that show opposing behavior with increasing ligand field strength, and we identify where these two may still coincide.

Comparative effectiveness of metal ions in inducing curvature of primary roots of Zea mays

Science.gov (United States)

Hasenstein, K. H.; Evans, M. L.; Stinemetz, C. L.; Moore, R.; Fondren, W. M.; Koon, E. C.; Higby, M. A.; Smucker, A. J.

1988-01-01

We used five cultivars of Zea mays (Bear Hybrid WF9 * 38MS, B73 * Missouri 17, Yellow Dent, Merit, and Great Lakes Hybrid 422) to reinvestigate the specificity of metal ions for inducing root curvature. Of 17 cations tested, 6 (Al3+, Ba2+, Ca2+, Cd2+, Cu2+, Zn2+) induced curvature. Roots curved away from Al3+, Ba2+, and Cd2+. Roots curved away from low (0.1 millimolar) concentrations of Cu2+ but toward higher (1-5 millimolar) concentrations. Roots initially curved away from Zn2+ but the direction of the subsequent curvature was unpredictable. In most cases, roots of all cultivars curved towards calcium. However, in some tests there was no response to calcium or even (especially in the cultivars Merit and B73 * Missouri 17) substantial curvature away from calcium. The results indicate that the induction of root curvature is not specific for calcium. The results are discussed relative to the possible role of calmodulin as a mediator of ion-induced root curvature.

Nonlinear saturated states of the magnetic-curvature-driven Rayleigh-Taylor instability in three dimensions

International Nuclear Information System (INIS)

Das, Amita; Sen, Abhijit; Kaw, Predhiman; Benkadda, S.; Beyer, Peter

2005-01-01

Three-dimensional electromagnetic fluid simulations of the magnetic-curvature-driven Rayleigh-Taylor instability are presented. Issues related to the existence of nonlinear saturated states and the nature of the temporal evolution to such states from random initial conditions are addressed. It is found that nonlinear saturated states arising from generation of zonal shear flows continue to exist in certain parametric domains but their spectrum and spatial characteristics have important differences from earlier two-dimensional results reported in Phys. Plasmas 4, 1018 (1997) and Phys. Plasmas 8, 5104 (2001). In particular, the three-dimensional nonlinear states possess a significant power level in short scales and the spatial structures of the potential and density fluctuations appear not to develop any functional correlations. Electromagnetic effects are found to inhibit the formation of zonal flows and thereby to considerably restrict the parametric domain of nonlinear stabilization. The role of finite k parallel and the contribution of the unstable drift wave branch are also discussed and delineated through a number of simulation studies carried out in special simplified limits

No Large Scale Curvature Perturbations during Waterfall of Hybrid Inflation

OpenAIRE

Abolhasani, Ali Akbar; Firouzjahi, Hassan

2010-01-01

In this paper the possibility of generating large scale curvature perturbations induced from the entropic perturbations during the waterfall phase transition of standard hybrid inflation model is studied. We show that whether or not appreciable amounts of large scale curvature perturbations are produced during the waterfall phase transition depend crucially on the competition between the classical and the quantum mechanical back-reactions to terminate inflation. If one considers only the clas...

Protein shape and crowding drive domain formation and curvature in biological membranes

NARCIS (Netherlands)

Frese, R.N.; Pamies, Josep C.; Olsen, John D.; Bahatyrova, S.; van der Weij-de Wit, Chantal D.; Aartsma, Thijs J.; Otto, Cornelis; Hunter, C. Neil; Frenkel, Daan; van Grondelle, Rienk

2007-01-01

Folding, curvature, and domain formation are characteristics of many biological membranes. Yet the mechanisms that drive both curvature and the formation of specialized domains enriched in particular protein complexes are unknown. For this reason, studies in membranes whose shape and organization

Spatiotemporal analysis of endocytosis and membrane distribution of fluorescent sterols in living cells

DEFF Research Database (Denmark)

Wüstner, Daniel; Faergeman, Nils J

2008-01-01

proximity to the cell membrane. Spatial surface intensity patterns of DHE as well as that of the lipid marker DiIC12 being assessed by statistical image analysis persisted over several minutes in cells having a constant overall curvature. Sites of sterol endocytosis appeared indistinguishable from other...

Real-time 3D reconstruction of road curvature in far look-ahead distance from analysis of image sequences

Science.gov (United States)

Behringer, Reinhold

1995-12-01

A system for visual road recognition in far look-ahead distance, implemented in the autonomous road vehicle VaMP (a passenger car), is described. Visual cues of a road in a video image are the bright lane markings and the edges formed at the road borders. In a distance of more than 100 m, the most relevant road cue is the homogeneous road area, limited by the two border edges. These cues can be detected by the image processing module KRONOS applying edge detection techniques and areal 2D segmentation based on resolution triangles (analogous to a resolution pyramid). An estimation process performs an update of a state vector, which describes spatial road shape and vehicle orientation relative to the road. This state vector is estimated every 40 ms by exploiting knowledge about the vehicle movement (spatio-temporal model of vehicle dynamics) and the road design rules (clothoidal segments). Kalman filter techniques are applied to obtain an optimal estimate of the state vector by evaluating the measurements of the road border positions in the image sequence taken by a set of CCD cameras. The road consists of segments with piecewise constant curvature parameters. The borders between these segments can be detected by applying methods which have been developed for detection of discontinuities during time-discrete measurements. The road recognition system has been tested in autonomous rides with VaMP on public Autobahnen in real traffic at speeds up to 130 km/h.

Correlations between gravitropic curvature and auxin movement across gravistimulated roots of Zea mays

Science.gov (United States)

Young, L. M.; Evans, M. L.; Hertel, R.

1990-01-01

We compared the kinetics of auxin redistribution across the caps of primary roots of 2-day-old maize (Zea mays, cv Merit) seedlings with the time course of gravitropic curvature. [3H] indoleacetic acid was applied to one side of the cap in an agar donor and radioactivity moving across the cap was collected in an agar receiver applied to the opposite side. Upon gravistimulation the roots first curved upward slightly, then returned to the horizontal and began curving downward, reaching a final angle of about 67 degrees. Movement of label across the caps of gravistimulated roots was asymmetric with preferential downward movement (ratio downward/upward = ca. 1.6, radioactivity collected during the 90 min following beginning of gravistimulation). There was a close correlation between the development of asymmetric auxin movement across the root cap and the rate of curvature, with both values increasing to a maximum and then declining as the roots approached the final angle of curvature. In roots preadapted to gravity (alternate brief stimulation on opposite flanks over a period of 1 hour) the initial phase of upward curvature was eliminated and downward bending began earlier than for controls. The correlation between asymmetric auxin movement and the kinetics of curvature also held in comparisons between control and preadapted roots. Both downward auxin transport asymmetry and downward curvature occurred earlier in preadapted roots than in controls. These findings are consistent with suggestions that the root cap is not only the site of perception but also the location of the initial redistribution of effectors that ultimately leads to curvature.

Gauge and non-gauge curvature tensor copies

International Nuclear Information System (INIS)

Srivastava, P.P.

1982-10-01

A procedure for constructing curvature tensor copies is discussed using the anholonomic geometrical framework. The corresponding geometries are compared and the notion of gauge copy is elucidated. An explicit calculation is also made. (author)

Curvature effect on nuclear 'pasta': Is it helpful for gyroid appearance?

International Nuclear Information System (INIS)

Nakazato, Ken'ichiro; Iida, Kei; Oyamatsu, Kazuhiro

2011-01-01

In supernova cores and neutron star crusts, nuclei are thought to deform to rodlike and slablike shapes, which are often called nuclear pasta. We study the equilibrium properties of the nuclear pasta by using a liquid-drop model with curvature corrections. It is confirmed that the curvature effect acts to lower the transition densities between different shapes. We also examine the gyroid structure, which was recently suggested as a different type of nuclear pasta by analogy with the polymer systems. The gyroid structure investigated in this paper is approximately formulated as an extension of the periodic minimal surface whose mean curvature vanishes. In contrast to our expectations, we find, from the present approximate formulation, that the curvature corrections act to slightly disfavor the appearance of the gyroid structure. By comparing the energy corrections in the gyroid phase and the hypothetical phases composed of d-dimensional spheres, where d is a general dimensionality, we show that the gyroid is unlikely to belong to a family of the generalized dimensional spheres.

FY 2016 Status Report: CIRFT Testing Data Analyses and Updated Curvature Measurements

Energy Technology Data Exchange (ETDEWEB)

Wang, Jy-An John [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Wang, Hong [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

2016-08-01

This report provides a detailed description of FY15 test result corrections/analysis based on the FY16 Cyclic Integrated Reversible-Bending Fatigue Tester (CIRFT) test program methodology update used to evaluate the vibration integrity of spent nuclear fuel (SNF) under normal transportation conditions. The CIRFT consists of a U-frame testing setup and a real-time curvature measurement method. The three-component U-frame setup of the CIRFT has two rigid arms and linkages to a universal testing machine. The curvature of rod bending is obtained through a three-point deflection measurement method. Three linear variable differential transformers (LVDTs) are used and clamped to the side connecting plates of the U-frame to capture the deformation of the rod. The contact-based measurement, or three-LVDT-based curvature measurement system, on SNF rods has been proven to be quite reliable in CIRFT testing. However, how the LVDT head contacts the SNF rod may have a significant effect on the curvature measurement, depending on the magnitude and direction of rod curvature. It has been demonstrated that the contact/curvature issues can be corrected by using a correction on the sensor spacing. The sensor spacing defines the separation of the three LVDT probes and is a critical quantity in calculating the rod curvature once the deflections are obtained. The sensor spacing correction can be determined by using chisel-type probes. The method has been critically examined this year and has been shown to be difficult to implement in a hot cell environment, and thus cannot be implemented effectively. A correction based on the proposed equivalent gauge-length has the required flexibility and accuracy and can be appropriately used as a correction factor. The correction method based on the equivalent gauge length has been successfully demonstrated in CIRFT data analysis for the dynamic tests conducted on Limerick (LMK) (17 tests), North Anna (NA) (6 tests), and Catawba mixed oxide (MOX

On Mass, Spacetime Curvature, and Gravity

Science.gov (United States)

Janis, Allen I.

2018-01-01

The frequently used analogy of a massive ball distorting an elastic sheet, which is used to illustrate why mass causes spacetime curvature and gravitational attraction, is criticized in this article. A different analogy that draws on the students' previous knowledge of spacetime diagrams in special relativity is suggested.

Black hole production in particle collisions and higher curvature gravity

International Nuclear Information System (INIS)

Rychkov, Vyacheslav S.

2004-01-01

The problem of black hole production in trans-Planckian particle collisions is revisited, in the context of large extra dimensions scenarios of TeV-scale gravity. The validity of the standard description of this process (two colliding Aichelburg-Sexl shock waves in classical Einstein gravity) is questioned. It is observed that the classical spacetime has large curvature along the transverse collision plane, as signaled by the curvature invariant (R μνλσ ) 2 . Thus quantum gravity effects, and in particular higher curvature corrections to the Einstein gravity, cannot be ignored. To give a specific example of what may happen, the collision is reanalyzed in the Einstein-Lanczos-Lovelock gravity theory, which modifies the Einstein-Hilbert Lagrangian by adding a particular 'Gauss-Bonnet' combination of curvature squared terms. The analysis uses a series of approximations, which reduce the field equations to a tractable second order nonlinear PDE of the Monge-Ampere type. It is found that the resulting spacetime is significantly different from the pure Einstein case in the future of the transverse collision plane. These considerations cast serious doubts on the geometric cross section estimate, which is based on the classical Einstein gravity description of the black hole production process

Curvature correction of retinal OCTs using graph-based geometry detection

Science.gov (United States)

Kafieh, Raheleh; Rabbani, Hossein; Abramoff, Michael D.; Sonka, Milan

2013-05-01

In this paper, we present a new algorithm as an enhancement and preprocessing step for acquired optical coherence tomography (OCT) images of the retina. The proposed method is composed of two steps, first of which is a denoising algorithm with wavelet diffusion based on a circular symmetric Laplacian model, and the second part can be described in terms of graph-based geometry detection and curvature correction according to the hyper-reflective complex layer in the retina. The proposed denoising algorithm showed an improvement of contrast-to-noise ratio from 0.89 to 1.49 and an increase of signal-to-noise ratio (OCT image SNR) from 18.27 to 30.43 dB. By applying the proposed method for estimation of the interpolated curve using a full automatic method, the mean ± SD unsigned border positioning error was calculated for normal and abnormal cases. The error values of 2.19 ± 1.25 and 8.53 ± 3.76 µm were detected for 200 randomly selected slices without pathological curvature and 50 randomly selected slices with pathological curvature, respectively. The important aspect of this algorithm is its ability in detection of curvature in strongly pathological images that surpasses previously introduced methods; the method is also fast, compared to the relatively low speed of similar methods.

Imaging performance of an isotropic negative dielectric constant slab.

Science.gov (United States)

Shivanand; Liu, Huikan; Webb, Kevin J

2008-11-01

The influence of material and thickness on the subwavelength imaging performance of a negative dielectric constant slab is studied. Resonance in the plane-wave transfer function produces a high spatial frequency ripple that could be useful in fabricating periodic structures. A cost function based on the plane-wave transfer function provides a useful metric to evaluate the planar slab lens performance, and using this, the optimal slab dielectric constant can be determined.

Vertex Normals and Face Curvatures of Triangle Meshes

KAUST Repository

Sun, Xiang

2016-08-12

This study contributes to the discrete differential geometry of triangle meshes, in combination with discrete line congruences associated with such meshes. In particular we discuss when a congruence defined by linear interpolation of vertex normals deserves to be called a ʼnormal’ congruence. Our main results are a discussion of various definitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula.

Experimental and numerical investigation of laser forming of cylindrical surfaces with arbitrary radius of curvature

Directory of Open Access Journals (Sweden)

Mehdi Safari

2016-09-01

Full Text Available In this work, laser forming of cylindrical surfaces with arbitrary radius of curvature is investigated experimentally and numerically. For laser forming of cylindrical surfaces with arbitrary radius of curvature, a new and comprehensive method is proposed in this paper. This method contains simple linear irradiating lines and using an analytical method, required process parameters for laser forming of a cylindrical surface with a specific radius of curvature is proposed. In this method, laser output power, laser scanning speed and laser beam diameter are selected based on laser machine and process limitations. As in the laser forming of a cylindrical surface, parallel irradiating lines are needed; therefore key parameter for production of a cylindrical surface with a specific radius of curvature is the number of irradiating lines. Hence, in the proposed analytical method, the required number of irradiating lines for production of a cylindrical surface with a specific radius of curvature is suggested. Performance of the proposed method for production of cylindrical surface with a specific radius of curvature is verified with experimental tests. The results show that using proposed analytical method, cylindrical surfaces with any radius of curvature can be produced successfully.

The Role of Membrane Curvature in Nanoscale Topography-Induced Intracellular Signaling.

Science.gov (United States)

Lou, Hsin-Ya; Zhao, Wenting; Zeng, Yongpeng; Cui, Bianxiao

2018-05-15

Over the past decade, there has been growing interest in developing biosensors and devices with nanoscale and vertical topography. Vertical nanostructures induce spontaneous cell engulfment, which enhances the cell-probe coupling efficiency and the sensitivity of biosensors. Although local membranes in contact with the nanostructures are found to be fully fluidic for lipid and membrane protein diffusions, cells appear to actively sense and respond to the surface topography presented by vertical nanostructures. For future development of biodevices, it is important to understand how cells interact with these nanostructures and how their presence modulates cellular function and activities. How cells recognize nanoscale surface topography has been an area of active research for two decades before the recent biosensor works. Extensive studies show that surface topographies in the range of tens to hundreds of nanometers can significantly affect cell functions, behaviors, and ultimately the cell fate. For example, titanium implants having rough surfaces are better for osteoblast attachment and host-implant integration than those with smooth surfaces. At the cellular level, nanoscale surface topography has been shown by a large number of studies to modulate cell attachment, activity, and differentiation. However, a mechanistic understanding of how cells interact and respond to nanoscale topographic features is still lacking. In this Account, we focus on some recent studies that support a new mechanism that local membrane curvature induced by nanoscale topography directly acts as a biochemical signal to induce intracellular signaling, which we refer to as the curvature hypothesis. The curvature hypothesis proposes that some intracellular proteins can recognize membrane curvatures of a certain range at the cell-to-material interface. These proteins then recruit and activate downstream components to modulate cell signaling and behavior. We discuss current technologies

Quantitative three-dimensional analysis of root canal curvature in maxillary first molars using micro-computed tomography.

Science.gov (United States)

Lee, Jong-Ki; Ha, Byung-Hyun; Choi, Jeong-Ho; Heo, Seok-Mo; Perinpanayagam, Hiran

2006-10-01

In endodontic therapy, access and instrumentation are strongly affected by root canal curvature. However, the few studies that have actually measured curvature are mostly from two-dimensional radiographs. The purpose of this study was to measure the three-dimensional (3D) canal curvature in maxillary first molars using micro-computed tomography (microCT) and mathematical modeling. Extracted maxillary first molars (46) were scanned by microCT (502 image slices/tooth, 1024 X 1024 pixels, voxel size of 19.5 x 19.5 x 39.0 microm) and their canals reconstructed by 3D modeling software. The intersection of major and minor axes in the canal space of each image slice were connected to create an imaginary central axis for each canal. The radius of curvature of the tangential circle was measured and inverted as a measure of curvature using custom-made mathematical modeling software. Root canal curvature was greatest in the apical third and least in the middle third for all canals. The greatest curvatures were in the mesiobuccal (MB) canal (0.76 +/- 0.48 mm(-1)) with abrupt curves, and the least curvatures were in the palatal (P) canal (0.38 +/- 0.34 mm(-1)) with a gradual curve. This study has measured the 3D curvature of root canals in maxillary first molars and reinforced the value of microCT with mathematical modeling.

Higher Curvature Supergravity, Supersymmetry Breaking and Inflation

CERN Document Server

Ferrara, Sergio

2017-01-01

In these lectures, after a short introduction to cosmology, we discuss the supergravity embedding of higher curvature models of inflation. The supergravity description of such models is presented for the two different formulations of minimal supergravity.

Revisiting the decoupling effects in the running of the Cosmological Constant

International Nuclear Information System (INIS)

Antipin, Oleg; Melic, Blazenka

2017-01-01

We revisit the decoupling effects associated with heavy particles in the renormalization group running of the vacuum energy in a mass-dependent renormalization scheme. We find the running of the vacuum energy stemming from the Higgs condensate in the entire energy range and show that it behaves as expected from the simple dimensional arguments meaning that it exhibits the quadratic sensitivity to the mass of the heavy particles in the infrared regime. The consequence of such a running to the fine-tuning problem with the measured value of the Cosmological Constant is analyzed and the constraint on the mass spectrum of a given model is derived. We show that in the Standard Model (SM) this fine-tuning constraint is not satisfied while in the massless theories this constraint formally coincides with the well known Veltman condition. We also provide a remarkably simple extension of the SM where saturation of this constraint enables us to predict the radiative Higgs mass correctly. Generalization to constant curvature spaces is also given. (orig.)

Revisiting the decoupling effects in the running of the Cosmological Constant

Energy Technology Data Exchange (ETDEWEB)

Antipin, Oleg; Melic, Blazenka [Rudjer Boskovic Institute, Division of Theoretical Physics, Zagreb (Croatia)

2017-09-15

We revisit the decoupling effects associated with heavy particles in the renormalization group running of the vacuum energy in a mass-dependent renormalization scheme. We find the running of the vacuum energy stemming from the Higgs condensate in the entire energy range and show that it behaves as expected from the simple dimensional arguments meaning that it exhibits the quadratic sensitivity to the mass of the heavy particles in the infrared regime. The consequence of such a running to the fine-tuning problem with the measured value of the Cosmological Constant is analyzed and the constraint on the mass spectrum of a given model is derived. We show that in the Standard Model (SM) this fine-tuning constraint is not satisfied while in the massless theories this constraint formally coincides with the well known Veltman condition. We also provide a remarkably simple extension of the SM where saturation of this constraint enables us to predict the radiative Higgs mass correctly. Generalization to constant curvature spaces is also given. (orig.)

Regional surface geometry of the rat stomach based on three-dimensional curvature analysis

Energy Technology Data Exchange (ETDEWEB)

Liao Donghua [Center of Excellence in Visceral Biomechanics and Pain, Aalborg Hospital, DK-9100 Aalborg (Denmark); Zhao Jingbo [Center of Excellence in Visceral Biomechanics and Pain, Aalborg Hospital, DK-9100 Aalborg (Denmark); Gregersen, Hans [Center of Excellence in Visceral Biomechanics and Pain, Aalborg Hospital, DK-9100 Aalborg (Denmark)

2005-01-21

A better understanding of gastric accommodation and gastric perception requires knowledge of regional gastric geometry and local gastric tension throughout the stomach. An analytic method based on medical imaging data was developed in this study to describe the three-dimensional (3D) rat stomach geometry and tension distribution. The surface principal radii of curvatures were simulated and the surface tension was calculated in the glandular and non-glandular region of the stomach at pressures from 0 Pa to 800 Pa. The radii of curvature and tension distribution in the stomach were non-homogeneous. The radii of curvature in the glandular stomach were larger than those in the non-glandular region at pressures less than 100 Pa (P < 0.001). When the pressure increased to more than 200 Pa, the radii of curvature in the non-glandular stomach was larger than in the glandular stomach (P < 0.05). The curvature and tension distribution mapping using medical imaging technology and 3D models can be used to characterize and distinguish the physical behaviour in separate regions of the stomach.

Regional surface geometry of the rat stomach based on three-dimensional curvature analysis

International Nuclear Information System (INIS)

Liao Donghua; Zhao Jingbo; Gregersen, Hans

2005-01-01

A better understanding of gastric accommodation and gastric perception requires knowledge of regional gastric geometry and local gastric tension throughout the stomach. An analytic method based on medical imaging data was developed in this study to describe the three-dimensional (3D) rat stomach geometry and tension distribution. The surface principal radii of curvatures were simulated and the surface tension was calculated in the glandular and non-glandular region of the stomach at pressures from 0 Pa to 800 Pa. The radii of curvature and tension distribution in the stomach were non-homogeneous. The radii of curvature in the glandular stomach were larger than those in the non-glandular region at pressures less than 100 Pa (P < 0.001). When the pressure increased to more than 200 Pa, the radii of curvature in the non-glandular stomach was larger than in the glandular stomach (P < 0.05). The curvature and tension distribution mapping using medical imaging technology and 3D models can be used to characterize and distinguish the physical behaviour in separate regions of the stomach

Natural inflation in SUSY and gauge-mediated curvature of the flat directions

CERN Document Server

Dvali, Gia

1996-01-01

Supersymmetric theories often include the non-compact directions in the field space along which the tree level potential grows only up to a certain limited value (determined by the mass scale of the theory) and then stays constant for the arbitrarily large expectation value of the field parametrizing the direction. Above the critical value, the tree-level curvature is large and positive in the other directions. Such plateaux are natural candidates for the hybrid inflaton. The non-zero F-term density along the plateau spontaneously breaks SUSY and induces the one-loop logarithmic slope for the inflaton potential. The coupling of the inflaton to the Higgs fields in the complex representations of the gauge group, may result in a radiatively induced Fayet--Iliopoulos D-term during inflation, which destabilizes some of the squark and slepton flat directions. Corresponding soft masses can be larger than the Hubble parameter and thus, play a crucial role for the Affleck--Dine baryogenesis.

Local curvature entropy-based 3D terrain representation using a comprehensive Quadtree

Science.gov (United States)

Chen, Qiyu; Liu, Gang; Ma, Xiaogang; Mariethoz, Gregoire; He, Zhenwen; Tian, Yiping; Weng, Zhengping

2018-05-01

Large scale 3D digital terrain modeling is a crucial part of many real-time applications in geoinformatics. In recent years, the improved speed and precision in spatial data collection make the original terrain data more complex and bigger, which poses challenges for data management, visualization and analysis. In this work, we presented an effective and comprehensive 3D terrain representation based on local curvature entropy and a dynamic Quadtree. The Level-of-detail (LOD) models of significant terrain features were employed to generate hierarchical terrain surfaces. In order to reduce the radical changes of grid density between adjacent LODs, local entropy of terrain curvature was regarded as a measure of subdividing terrain grid cells. Then, an efficient approach was presented to eliminate the cracks among the different LODs by directly updating the Quadtree due to an edge-based structure proposed in this work. Furthermore, we utilized a threshold of local entropy stored in each parent node of this Quadtree to flexibly control the depth of the Quadtree and dynamically schedule large-scale LOD terrain. Several experiments were implemented to test the performance of the proposed method. The results demonstrate that our method can be applied to construct LOD 3D terrain models with good performance in terms of computational cost and the maintenance of terrain features. Our method has already been deployed in a geographic information system (GIS) for practical uses, and it is able to support the real-time dynamic scheduling of large scale terrain models more easily and efficiently.

Moment-Curvature Behaviors of Concrete Beams Singly Reinforced by Steel-FRP Composite Bars

Directory of Open Access Journals (Sweden)

Zeyang Sun

2017-01-01

Full Text Available A steel-fiber-reinforced polymer (FRP composite bar (SFCB is a kind of rebar with inner steel bar wrapped by FRP, which can achieve a better anticorrosion performance than that of ordinary steel bar. The high ultimate strength of FRP can also provide a significant increase in load bearing capacity. Based on the adequate simulation of the load-displacement behaviors of concrete beams reinforced by SFCBs, a parametric analysis of the moment-curvature behaviors of concrete beams that are singly reinforced by SFCB was conducted. The critical reinforcement ratio for differentiating the beam’s failure mode was presented, and the concept of the maximum possible peak curvature (MPPC was proposed. After the ultimate curvature reached MPPC, it decreased with an increase in the postyield stiffness ratio (rsf, and the theoretical calculation method about the curvatures before and after the MPPC was derived. The influence of the reinforcement ratio, effective depth, and FRP ultimate strain on the ultimate point was studied by the dimensionless moment and curvature. By calculating the envelope area under the moment-curvature curve, the energy ductility index can obtain a balance between the bearing capacity and the deformation ability. This paper can provide a reference for the design of concrete beams that are reinforced by SFCB or hybrid steel bar/FRP bar.

Incorporating contact angles in the surface tension force with the ACES interface curvature scheme

Science.gov (United States)

Owkes, Mark

2017-11-01

In simulations of gas-liquid flows interacting with solid boundaries, the contact line dynamics effect the interface motion and flow field through the surface tension force. The surface tension force is directly proportional to the interface curvature and the problem of accurately imposing a contact angle must be incorporated into the interface curvature calculation. Many commonly used algorithms to compute interface curvatures (e.g., height function method) require extrapolating the interface, with defined contact angle, into the solid to allow for the calculation of a curvature near a wall. Extrapolating can be an ill-posed problem, especially in three-dimensions or when multiple contact lines are near each other. We have developed an accurate methodology to compute interface curvatures that allows for contact angles to be easily incorporated while avoiding extrapolation and the associated challenges. The method, known as Adjustable Curvature Evaluation Scale (ACES), leverages a least squares fit of a polynomial to points computed on the volume-of-fluid (VOF) representation of the gas-liquid interface. The method is tested by simulating canonical test cases and then applied to simulate the injection and motion of water droplets in a channel (relevant to PEM fuel cells).

Effects of curvature and rotation on turbulence in the NASA low-speed centrifugal compressor impeller

Science.gov (United States)

Moore, Joan G.; Moore, John

1992-01-01

The flow in the NASA Low-Speed Impeller is affected by both curvature and rotation. The flow curves due to the following: (1) geometric curvature, e.g. the curvature of the hub and shroud profiles in the meridional plane and the curvature of the backswept impeller blades; and (2) secondary flow vortices, e.g. the tip leakage vortex. Changes in the turbulence and effective turbulent viscosity in the impeller are investigated. The effects of these changes on three-dimensional flow development are discussed. Two predictions of the flow in the impeller, one with, and one without modification to the turbulent viscosity due to rotation and curvature, are compared. Some experimental and theoretical background for the modified mixing length model of turbulent viscosity will also be presented.

Profile Curvature Derivative Surface used to characterize the complexity of the seafloor around St. John, USVI

Data.gov (United States)

National Oceanic and Atmospheric Administration, Department of Commerce — Profile curvature was calculated from the bathymetry surface for each raster cell using the ArcGIS 3D Analyst "Curvature" Tool. Profile curvature describes the rate...

Computing magnetic anisotropy constants of single molecule magnets

Indian Academy of Sciences (India)

We present here a theoretical approach to compute the molecular magnetic anisotropy parameters, and for single molecule magnets in any given spin eigenstate of exchange spin Hamiltonian. We first describe a hybrid constant -valence bond (VB) technique of solving spin Hamiltonians employing full spatial ...

ON THE CURVATURE OF DUST LANES IN GALACTIC BARS

International Nuclear Information System (INIS)

Comeron, Sebastien; MartInez-Valpuesta, Inma; Knapen, Johan H.; Beckman, John E.

2009-01-01

We test the theoretical prediction that the straightest dust lanes in bars are found in strongly barred galaxies, or more specifically, that the degree of curvature of the dust lanes is inversely proportional to the strength of the bar. The test uses archival images of barred galaxies for which a reliable nonaxisymmetric torque parameter (Q b ) and the radius at which Q b has been measured (r(Q b )) have been published in the literature. Our results confirm the theoretical prediction but show a large spread that cannot be accounted for by measurement errors. We simulate 238 galaxies with different bar and bulge parameters in order to investigate the origin of the spread in the dust lane curvature versus Q b relation. From these simulations, we conclude that the spread is greatly reduced when describing the bar strength as a linear combination of the bar parameters Q b and the quotient of the major and minor axes of the bar, a/b. Thus, we conclude that the dust lane curvature is predominantly determined by the parameters of the bar.

Generic Properties of Curvature Sensing through Vision and Touch

Directory of Open Access Journals (Sweden)

Birgitta Dresp-Langley

2013-01-01

Full Text Available Generic properties of curvature representations formed on the basis of vision and touch were examined as a function of mathematical properties of curved objects. Virtual representations of the curves were shown on a computer screen for visual scaling by sighted observers (experiment 1. Their physical counterparts were placed in the two hands of blindfolded and congenitally blind observers for tactile scaling. The psychophysical data show that curvature representations in congenitally blind individuals, who never had any visual experience, and in sighted observers, who rely on vision most of the time, are statistically linked to the same mathematical properties of the curves. The perceived magnitude of object curvature, sensed through either vision or touch, is related by a mathematical power law, with similar exponents for the two sensory modalities, to the aspect ratio of the curves, a scale invariant geometric property. This finding supports biologically motivated models of sensory integration suggesting a universal power law for the adaptive brain control and balance of motor responses to environmental stimuli from any sensory modality.

Gaussian curvature on hyperelliptic Riemann surfaces

Indian Academy of Sciences (India)

Indian Acad. Sci. (Math. Sci.) Vol. 124, No. 2, May 2014, pp. 155–167. c Indian Academy of Sciences. Gaussian curvature on hyperelliptic Riemann surfaces. ABEL CASTORENA. Centro de Ciencias Matemáticas (Universidad Nacional Autónoma de México,. Campus Morelia) Apdo. Postal 61-3 Xangari, C.P. 58089 Morelia,.

The Riemann-Lovelock Curvature Tensor

OpenAIRE

Kastor, David

2012-01-01

In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \\le D

Factors affecting root curvature of mandibular first molar

International Nuclear Information System (INIS)

Choi, Hang Moon; Yi, Won Jin; Heo, Min Suk; Kim, Jung Hwa; Choi, Soon Chul; Park, Tae Won

2006-01-01

To find the cause of root curvature by use of panoramic and lateral cephalometric radiograph. Twenty six 1st graders whose mandibular 1st molars just emerged into the mouth were selected. Panoramic and lateral cephalometric radiograph were taken at grade 1 and 6, longitudinally. In cephalometric radio graph, mandibular plane angle, ramus-occlusal place angle, gonial angle, and gonion-gnathion distance(Go-Gn distance) were measured. In panoramic radiograph, elongated root length and root angle were measured by means of digital subtraction radiography. Occlusal plane-tooth axis angle was measured, too. Pearson correlations were used to evaluate the relationships between root curvature and elongated length and longitudinal variations of all variables. Multiple regression equation using related variables was computed. The pearson correlation coefficient between curved angle and longitudinal variations of occlusal plane-tooth axis angle and ramus-occlusal plane angle was 0.350 and 0.401, respectively (p 1 +0.745X 2 (Y: root angle, X 1 : variation of occlusal plane-tooth axis angle, X 2 : variation of ramus-occlusal plane angle). It was suspected that the reasons of root curvature were change of tooth axis caused by contact with 2nd deciduous tooth and amount of mesial and superior movement related to change of occlusal plane

Predicting the cosmological constant with the scale-factor cutoff measure

International Nuclear Information System (INIS)

De Simone, Andrea; Guth, Alan H.; Salem, Michael P.; Vilenkin, Alexander

2008-01-01

It is well known that anthropic selection from a landscape with a flat prior distribution of cosmological constant Λ gives a reasonable fit to observation. However, a realistic model of the multiverse has a physical volume that diverges with time, and the predicted distribution of Λ depends on how the spacetime volume is regulated. A very promising method of regulation uses a scale-factor cutoff, which avoids a number of serious problems that arise in other approaches. In particular, the scale-factor cutoff avoids the 'youngness problem' (high probability of living in a much younger universe) and the 'Q and G catastrophes' (high probability for the primordial density contrast Q and gravitational constant G to have extremely large or small values). We apply the scale-factor cutoff measure to the probability distribution of Λ, considering both positive and negative values. The results are in good agreement with observation. In particular, the scale-factor cutoff strongly suppresses the probability for values of Λ that are more than about 10 times the observed value. We also discuss qualitatively the prediction for the density parameter Ω, indicating that with this measure there is a possibility of detectable negative curvature.

An optomechatronic curvature measurement array based on fiber Bragg gratings

International Nuclear Information System (INIS)

Chang, Hsing-Cheng; Lin, Shyan-Lung; Hung, San-Shan; Chang, I-Nan; Chen, Ya-Hui; Lin, Jung-Chih; Liu, Wen-Fung

2014-01-01

This study investigated an optomechatronic array-integrated signal processing module and a human–machine interface based on fiber Bragg grating sensing elements embedded in an elastic support matrix that involves using a self-located electromagnetic mechanism for curvature sensing and solid contour reconstruction. Using bilinear interpolation and average calculation methods, the smooth and accurate surface contours of convex and concave lenses are reconstructed in real-time. The elastic supporting optical sensing array is self-balanced to reduce operational errors. Compared with our previous single-head sensor, the sensitivity of the proposed array is improved by more than 15%. In the curvature range from −20.15 to +27.09 m −1 , the sensitivities are 3.53 pm m for the convex measurement and 2.15 pm m for the concave measurement with an error rate below 8.89%. The curvature resolutions are 0.283 and 0.465 m −1 for convex and concave lenses, respectively. This array could be applied in the curvature measurement of solar collectors to monitor energy conversion efficiency or could be used to monitor the wafer-level thin-film fabrication process. (paper)

Fermion localization in higher curvature and scalar-tensor theories of gravity

Energy Technology Data Exchange (ETDEWEB)

Mitra, Joydip [Scottish Church College, Department of Physics, Kolkata (India); Paul, Tanmoy; SenGupta, Soumitra [Indian Association for the Cultivation of Science, Department of Theoretical Physics, Kolkata (India)

2017-12-15

It is well known that, in a braneworld model, the localization of fermions on a lower dimensional submanifold (say a TeV 3-brane) is governed by the gravity in the bulk, which also determines the corresponding phenomenology on the brane. Here we consider a five dimensional warped spacetime where the bulk geometry is governed by higher curvature like F(R) gravity. In such a scenario, we explore the role of higher curvature terms on the localization of bulk fermions which in turn determines the effective radion-fermion coupling on the brane. Our result reveals that, for appropriate choices of the higher curvature parameter, the profiles of the massless chiral modes of the fermions may get localized near the TeV brane, while those for massive Kaluza-Klein (KK) fermions localize towards the Planck brane. We also explore these features in the dual scalar-tensor model by appropriate transformations. The localization property turns out to be identical in the two models. This rules out the possibility of any signature of massive KK fermions in TeV scale collider experiments due to higher curvature gravity effects. (orig.)

Curvature correction of retinal OCTs using graph-based geometry detection

International Nuclear Information System (INIS)

Kafieh, Raheleh; Rabbani, Hossein; Abramoff, Michael D; Sonka, Milan

2013-01-01

In this paper, we present a new algorithm as an enhancement and preprocessing step for acquired optical coherence tomography (OCT) images of the retina. The proposed method is composed of two steps, first of which is a denoising algorithm with wavelet diffusion based on a circular symmetric Laplacian model, and the second part can be described in terms of graph-based geometry detection and curvature correction according to the hyper-reflective complex layer in the retina. The proposed denoising algorithm showed an improvement of contrast-to-noise ratio from 0.89 to 1.49 and an increase of signal-to-noise ratio (OCT image SNR) from 18.27 to 30.43 dB. By applying the proposed method for estimation of the interpolated curve using a full automatic method, the mean ± SD unsigned border positioning error was calculated for normal and abnormal cases. The error values of 2.19 ± 1.25 and 8.53 ± 3.76 µm were detected for 200 randomly selected slices without pathological curvature and 50 randomly selected slices with pathological curvature, respectively. The important aspect of this algorithm is its ability in detection of curvature in strongly pathological images that surpasses previously introduced methods; the method is also fast, compared to the relatively low speed of similar methods. (paper)

Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature

OpenAIRE

Loveridge, Lee C.

2004-01-01

Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.

Intelligent estimation of spatially distributed soil physical properties

Science.gov (United States)

Iwashita, F.; Friedel, M.J.; Ribeiro, G.F.; Fraser, Stephen J.

2012-01-01

Spatial analysis of soil samples is often times not possible when measurements are limited in number or clustered. To obviate potential problems, we propose a new approach based on the self-organizing map (SOM) technique. This approach exploits underlying nonlinear relation of the steady-state geomorphic concave-convex nature of hillslopes (from hilltop to bottom of the valley) to spatially limited soil textural data. The topographic features are extracted from Shuttle Radar Topographic Mission elevation data; whereas soil textural (clay, silt, and sand) and hydraulic data were collected in 29 spatially random locations (50 to 75. cm depth). In contrast to traditional principal component analysis, the SOM identifies relations among relief features, such as, slope, horizontal curvature and vertical curvature. Stochastic cross-validation indicates that the SOM is unbiased and provides a way to measure the magnitude of prediction uncertainty for all variables. The SOM cross-component plots of the soil texture reveals higher clay proportions at concave areas with convergent hydrological flux and lower proportions for convex areas with divergent flux. The sand ratio has an opposite pattern with higher values near the ridge and lower values near the valley. Silt has a trend similar to sand, although less pronounced. The relation between soil texture and concave-convex hillslope features reveals that subsurface weathering and transport is an important process that changed from loss-to-gain at the rectilinear hillslope point. These results illustrate that the SOM can be used to capture and predict nonlinear hillslope relations among relief, soil texture, and hydraulic conductivity data. ?? 2011 Elsevier B.V.

Non-Euclidean geometry and curvature two-dimensional spaces, volume 3

CERN Document Server

Cannon, James W

2017-01-01

This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. Einstein showed how to interpret gravity as the dynamic response to the curvature of space-time. Bill Thurston showed us that non-Euclidean geometries and curvature are essential to the understanding of low-dimensional spaces. This third and final volume aims to give the reader a firm intuitive understanding of these concepts in dimension 2. The volume first demonstrates a number of the most important properties of non-Euclidean geometry by means of simple infinite graphs that approximate that geometry. This is followed by a long chapter taken from lectures the author gave at MSRI, wh...

Weyl curvature tensor in static spherical sources

International Nuclear Information System (INIS)

Ponce de Leon, J.

1988-01-01

The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ''purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed

Curvature tensors and unified field equations on SEX/sub n/

International Nuclear Information System (INIS)

Chung, K.T.; Lee, I.L.

1988-01-01

We study the curvature tensors and field equations in the n-dimensional SE manifold SEX/sub n/. We obtain several basic properties of the vectors S/subλ/ and U/sub λ/ and then of the SE curvature tensor and its contractions, such as a generalized Ricci identity, a generalized Bianchi identity, and two variations of the Bianchi identity satisfied by the SE Einstein tensor. Finally, a system of field equations is discussed in SEX/sub n/ an done of its particular solutions is constructed and displayed

Cosmic censorship, persistent curvature and asymptotic causal pathology

International Nuclear Information System (INIS)

Newman, R.P.A.C.

1984-01-01

The paper examines cosmic censorship in general relativity theory. Conformally flat space-times; persistent curvature; weakly asymptotically simple and empty asymptotes; censorship conditions; and the censorship theorem; are all discussed. (U.K.)

The effects of curvature on the flow field in rapidly rotating gas centrifuges

International Nuclear Information System (INIS)

Wood, H.G.; Jordan, J.A.

1984-01-01

The effects of curvature on the fluid dynamics of rapidly rotating gas centrifuges are studied. A governing system of a linear partial differential equation and boundary conditions is derived based on a linearization of the equations for viscous compressible flow. This system reduces to the Onsager pancake model if the effects of curvature are neglected. Approximations to the solutions of the governing equations with and without curvature terms are obtained via a finite-element method. Two examples are considered: first where the flow is driven by a thermal gradient at the wall of the centrifuge, and then for the flow being driven by the introduction and removal of mass through the ends of the centrifuge. Comparisons of the results obtained show that, especially for the second example, the inclusion of the terms due to curvature in the model can have an appreciable effect on the solution. (author)

Controllable soliton propagation based on phase-front curvature in asymmetrical nonlocal media

Science.gov (United States)

Zhang, Huafeng; Lü, Hua; Luo, Jianghua; Sun, Lihui

2016-08-01

The influence of phase-front curvature on the dynamical behavior of the fundamental mode soliton during its transmission in asymmetrical nonlocal media is studied in detail and the phase-front curvature can be imposed on the fundamental mode soliton by reshaping or phase imprinting technologies. By changing the phase-front curvature or its imposed position, controllable soliton propagation in asymmetrical nonlocal media can be achieved. Project supported by the National Natural Science Foundation of China (Grants Nos. 11547007 and 11304024), the Innovation Personnel Training Plan for Excellent Youth of Guangdong University Project (Grant No. 2013LYM_0023), and the Yangtze Fund for Youth Teams of Science and Technology Innovation (Grant No. 2015cqt03).

Finger vein extraction using gradient normalization and principal curvature

Science.gov (United States)

Choi, Joon Hwan; Song, Wonseok; Kim, Taejeong; Lee, Seung-Rae; Kim, Hee Chan

2009-02-01

Finger vein authentication is a personal identification technology using finger vein images acquired by infrared imaging. It is one of the newest technologies in biometrics. Its main advantage over other biometrics is the low risk of forgery or theft, due to the fact that finger veins are not normally visible to others. Extracting finger vein patterns from infrared images is the most difficult part in finger vein authentication. Uneven illumination, varying tissues and bones, and changes in the physical conditions and the blood flow make the thickness and brightness of the same vein different in each acquisition. Accordingly, extracting finger veins at their accurate positions regardless of their thickness and brightness is necessary for accurate personal identification. For this purpose, we propose a new finger vein extraction method which is composed of gradient normalization, principal curvature calculation, and binarization. As local brightness variation has little effect on the curvature and as gradient normalization makes the curvature fairly uniform at vein pixels, our method effectively extracts finger vein patterns regardless of the vein thickness or brightness. In our experiment, the proposed method showed notable improvement as compared with the existing methods.

Curvature-driven instabilities in the Elmo Bumpy Torus (EBT)

International Nuclear Information System (INIS)

Abe, H.; Spong, D.A.; Antonsen, T.M. Jr.; Tsang, K.T.; Nguyen, K.T.

1982-01-01

Curvature-driven instabilities are analyzed for an EBT configuration which consists of plasma interacting with a hot electron ring whose drift frequencies are larger than the growth rates predicted from conventional magnetohydrodynamic (MHD) theory. Stability criteria are obtained for five possible modes: the conventional hot electron interchange, a high-frequency hot electron interchange (at frequencies greater than the ion-cyclotron frequency), a compressional instability, a background plasma interchange, and an interacting pressure-driven interchange. A wide parameter regime for stable operation is found, which, however, severely deteriorates for a band of intermediate mode numbers. Finite Larmor radius effects can eliminate this deterioration; moreover, all short-wavelength curvature-driven modes are stabilized if the hot electron Larmor radius rho/sub h/ satisfies (kappa/sub perpendicular/rho/sub h/) 2 > 2Δ/[Rβ/sub h/(1 + P'/sub parallel//P'/sub perpendicular/)], where kappa/sub perpendicular/ is the transverse wavenumber, Δ is the ring half-width, R is the mid-plane radius of curvature, β/sub h/ is the hot electron beta value, and P' is the pressure gradient. Resonant wave-particle instabilities predicted by a new low frequency variational principle show that a variety of remnant instabilities may still persist

The zero curvature formulation of the KP and the sKP equations

International Nuclear Information System (INIS)

Barcelos Neto, J.; Das, A.; Panda, S.; Roy, S.

1992-01-01

The Kadomtsev-Petviashvili equation is derived from the zero curvature condition associated with the gauge group SL(2,R) in 2+1 dimensions. A fermionic extension of the KP equation is also obtained using the zero curvature condition of the super group OS p (2/1), which reduces upon appropriate restriction to the Kupershmidt equation. (author). 17 refs

Comprehensive Use of Curvature for Robust and Accurate Online Surface Reconstruction.

Science.gov (United States)

Lefloch, Damien; Kluge, Markus; Sarbolandi, Hamed; Weyrich, Tim; Kolb, Andreas

2017-12-01

Interactive real-time scene acquisition from hand-held depth cameras has recently developed much momentum, enabling applications in ad-hoc object acquisition, augmented reality and other fields. A key challenge to online reconstruction remains error accumulation in the reconstructed camera trajectory, due to drift-inducing instabilities in the range scan alignments of the underlying iterative-closest-point (ICP) algorithm. Various strategies have been proposed to mitigate that drift, including SIFT-based pre-alignment, color-based weighting of ICP pairs, stronger weighting of edge features, and so on. In our work, we focus on surface curvature as a feature that is detectable on range scans alone and hence does not depend on accurate multi-sensor alignment. In contrast to previous work that took curvature into consideration, however, we treat curvature as an independent quantity that we consistently incorporate into every stage of the real-time reconstruction pipeline, including densely curvature-weighted ICP, range image fusion, local surface reconstruction, and rendering. Using multiple benchmark sequences, and in direct comparison to other state-of-the-art online acquisition systems, we show that our approach significantly reduces drift, both when analyzing individual pipeline stages in isolation, as well as seen across the online reconstruction pipeline as a whole.

3D Facial Similarity Measure Based on Geodesic Network and Curvatures

Directory of Open Access Journals (Sweden)

Junli Zhao

2014-01-01

Full Text Available Automated 3D facial similarity measure is a challenging and valuable research topic in anthropology and computer graphics. It is widely used in various fields, such as criminal investigation, kinship confirmation, and face recognition. This paper proposes a 3D facial similarity measure method based on a combination of geodesic and curvature features. Firstly, a geodesic network is generated for each face with geodesics and iso-geodesics determined and these network points are adopted as the correspondence across face models. Then, four metrics associated with curvatures, that is, the mean curvature, Gaussian curvature, shape index, and curvedness, are computed for each network point by using a weighted average of its neighborhood points. Finally, correlation coefficients according to these metrics are computed, respectively, as the similarity measures between two 3D face models. Experiments of different persons’ 3D facial models and different 3D facial models of the same person are implemented and compared with a subjective face similarity study. The results show that the geodesic network plays an important role in 3D facial similarity measure. The similarity measure defined by shape index is consistent with human’s subjective evaluation basically, and it can measure the 3D face similarity more objectively than the other indices.

Accuracy evaluation of automatic quantification of the articular cartilage surface curvature from MRI

DEFF Research Database (Denmark)

Folkesson, Jenny; Dam, Erik B; Olsen, Ole F

2007-01-01

for intersubject comparisons. Digital phantoms were created to establish the accuracy of the curvature estimation methods. RESULTS: A comparison of the two curvature estimation methods to ground truth yielded absolute pairwise differences of 1.1%, and 4.8%, respectively. The interscan reproducibility for the two...

Fine-structure constant: Is it really a constant

International Nuclear Information System (INIS)

Bekenstein, J.D.

1982-01-01

It is often claimed that the fine-structure ''constant'' α is shown to be strictly constant in time by a variety of astronomical and geophysical results. These constrain its fractional rate of change alpha-dot/α to at least some orders of magnitude below the Hubble rate H 0 . We argue that the conclusion is not as straightforward as claimed since there are good physical reasons to expect alpha-dot/α 0 . We propose to decide the issue by constructing a framework for a variability based on very general assumptions: covariance, gauge invariance, causality, and time-reversal invariance of electromagnetism, as well as the idea that the Planck-Wheeler length (10 -33 cm) is the shortest scale allowable in any theory. The framework endows α with well-defined dynamics, and entails a modification of Maxwell electrodynamics. It proves very difficult to rule it out with purely electromagnetic experiments. In a cosmological setting, the framework predicts an alpha-dot/α which can be compatible with the astronomical constraints; hence, these are too insensitive to rule out α variability. There is marginal conflict with the geophysical constraints: however, no firm decision is possible because of uncertainty about various cosmological parameters. By contrast the framework's predictions for spatial gradients of α are in fatal conflict with the results of the Eoetvoes-Dicke-Braginsky experiments. Hence these tests of the equivalence principle rule out with confidence spacetime variability of α at any level

Experimental study of curvature effects on jet impingement heat transfer on concave surfaces

Directory of Open Access Journals (Sweden)

Ying Zhou

2017-04-01

Full Text Available Experimental study of the local and average heat transfer characteristics of a single round jet impinging on the concave surfaces was conducted in this work to gain in-depth knowledge of the curvature effects. The experiments were conducted by employing a piccolo tube with one single jet hole over a wide range of parameters: jet Reynolds number from 27000 to 130000, relative nozzle to surface distance from 3.3 to 30, and relative surface curvature from 0.005 to 0.030. Experimental results indicate that the surface curvature has opposite effects on heat transfer characteristics. On one hand, an increase of relative nozzle to surface distance (increasing jet diameter in fact enhances the average heat transfer around the surface for the same curved surface. On the other hand, the average Nusselt number decreases as relative nozzle to surface distance increases for a fixed jet diameter. Finally, experimental data-based correlations of the average Nusselt number over the curved surface were obtained with consideration of surface curvature effect. This work contributes to a better understanding of the curvature effects on heat transfer of a round jet impingement on concave surfaces, which is of high importance to the design of the aircraft anti-icing system.

Synthetic Strategies for High Dielectric Constant Silicone Elastomers

DEFF Research Database (Denmark)

Madsen, Frederikke Bahrt

synthetic strategies were developed in this Ph.D. thesis, in order to create silicone elastomers with high dielectric constants and thereby higher energy densities. The work focused on maintaining important properties such as dielectric loss, electrical breakdown strength and elastic modulus....... The methodology therefore involved chemically grafting high dielectric constant chemical groups onto the elastomer network, as this would potentially provide a stable elastomer system upon continued activation of the material. The first synthetic strategy involved the synthesis of a new type of cross...... extender’ that allowed for chemical modifications such as Cu- AAC. This route was promising for one-pot elastomer preparation and as a high dielectric constant additive to commercial silicone systems. The second approach used the borane-catalysed Piers-Rubinsztajn reaction to form spatially well...

Norm of the Riemannian Curvature Tensor

Indian Academy of Sciences (India)

We consider the Riemannian functional R p ( g ) = ∫ M | R ( g ) | p d v g defined on the space of Riemannian metrics with unit volume on a closed smooth manifold where R ( g ) and d v g denote the corresponding Riemannian curvature tensor and volume form and p ∈ ( 0 , ∞ ) . First we prove that the Riemannian metrics ...

Zero curvature conditions and conformal covariance

International Nuclear Information System (INIS)

Akemann, G.; Grimm, R.

1992-05-01

Two-dimensional zero curvature conditions were investigated in detail, with special emphasis on conformal properties, and the appearance of covariant higher order differential operators constructed in terms of a projective connection was elucidated. The analysis is based on the Kostant decomposition of simple Lie algebras in terms of representations with respect to their 'principal' SL(2) subalgebra. (author) 27 refs

Random paths with curvature dependent action

International Nuclear Information System (INIS)

Ambjoern, J.; Durhuus, B.

1986-11-01

We study discretized random paths with a curvature dependent action. The scaling limits of the corresponding statistical mechanical models can be constructed explicitly and are either usual Brownian motion or a theory where the correlations of tangents are nonzero and described by diffusion on the unit sphere. In the latter case the two point function has an anomalous dimension η = 1. (orig.)

Curvature properties of four-dimensional Walker metrics

International Nuclear Information System (INIS)

Chaichi, M; Garcia-Rio, E; Matsushita, Y

2005-01-01

A Walker n-manifold is a semi-Riemannian manifold, which admits a field of parallel null r-planes, r ≤ n/2. In the present paper we study curvature properties of a Walker 4-manifold (M, g) which admits a field of parallel null 2-planes. The metric g is necessarily of neutral signature (+ + - -). Such a Walker 4-manifold is the lowest dimensional example not of Lorentz type. There are three functions of coordinates which define a Walker metric. Some recent work shows that a Walker 4-manifold of restricted type whose metric is characterized by two functions exhibits a large variety of symplectic structures, Hermitian structures, Kaehler structures, etc. For such a restricted Walker 4-manifold, we shall study mainly curvature properties, e.g., conditions for a Walker metric to be Einstein, Osserman, or locally conformally flat, etc. One of our main results is the exact solutions to the Einstein equations for a restricted Walker 4-manifold

Curvature and Strength of Ni-YSZ Solid Oxide Half-Cells After Redox Treatments

DEFF Research Database (Denmark)

Faes, Antonin; Frandsen, Henrik Lund; Pihlatie, Mikko

2010-01-01

One of the main drawbacks of anode-supported solid oxide fuel cell technology is the limited capability to withstand reduction and oxidation (“RedOx”) of the Ni phase. This study compares the effect of RedOx cycles on curvature and strength of half-cells, composed of a nickel-yttria-stabilized-zi......One of the main drawbacks of anode-supported solid oxide fuel cell technology is the limited capability to withstand reduction and oxidation (“RedOx”) of the Ni phase. This study compares the effect of RedOx cycles on curvature and strength of half-cells, composed of a nickel...... it is calculated analytically from the force. In this calculation the thermal stresses are estimated from the curvature of the half-cell. For each treatment, more than 30 samples are tested. About 20 ball-on-ring samples are laser cut from one original 12×12 cm2 half-cell. Curvature and porosity are measured...

The effect of spontaneous curvature on a two-phase vesicle

International Nuclear Information System (INIS)

Cox, Geoffrey; Lowengrub, John

2015-01-01

Vesicles are membrane-bound structures commonly known for their roles in cellular transport and the shape of a vesicle is determined by its surrounding membrane (lipid bilayer). When the membrane is composed of different lipids, it is natural for the lipids of similar molecular structure to migrate towards one another (via spinodal decomposition), creating a multi-phase vesicle. In this article, we consider a two-phase vesicle model which is driven by nature's propensity to maintain a minimal state of elastic energy. The model assumes a continuum limit, thereby treating the membrane as a closed three-dimensional surface. The main purpose of this study is to reveal the complexity of the Helfrich two-phase vesicle model with non-zero spontaneous curvature and provide further evidence to support the relevance of spontaneous curvature as a modelling parameter. In this paper, we illustrate the complexity of the Helfrich two-phase model by providing multiple examples of undocumented solutions and energy hysteresis. We also investigate the influence of spontaneous curvature on morphological effects and membrane phenomena such as budding and fusion. (paper)

On the improvement of two-dimensional curvature computation and its application to turbulent premixed flame correlations

International Nuclear Information System (INIS)

Chrystie, R S M; Burns, I S; Hult, J; Kaminski, C F

2008-01-01

Measurement of curvature of the flamefront of premixed turbulent flames is important for the validation of numerical models for combustion. In this work, curvature is measured from contours that outline the flamefront, which are generated from laser-induced fluorescence images. The contours are inherently digitized, resulting in pixelation effects that lead to difficulties in computing curvature of the flamefront accurately. A common approach is to fit functions locally to short sections along the flame contour, and this approach is also followed in this work; the method helps smoothen the pixelation before curvature is measured. However, the length and degree of the polynomial, and hence the amount of smoothing, must be correctly set in order to maximize the precision and accuracy of the curvature measurements. Other researchers have applied polynomials of different orders and over different segment lengths to circles of known curvature as a test to determine the appropriate choice of polynomial; it is shown here that this method results in a sub-optimal choice of polynomial function. Here, we determine more suitable polynomial functions through use of a circle whose radius is sinusoidally modulated. We show that this leads to a more consistent and reliable choice for the local polynomial functions fitted to experimental data. A polynomial function thus determined is then applied to flame contour data to measure curvature of experimentally acquired flame contours. The results show that there is an enhancement in local flame speed at sections of the flamefront with a non-zero curvature, and this agrees with numerical models

Curvature and the visual perception of shape: theory on information along object boundaries and the minima rule revisited.

Science.gov (United States)

Lim, Ik Soo; Leek, E Charles

2012-07-01

Previous empirical studies have shown that information along visual contours is known to be concentrated in regions of high magnitude of curvature, and, for closed contours, segments of negative curvature (i.e., concave segments) carry greater perceptual relevance than corresponding regions of positive curvature (i.e., convex segments). Lately, Feldman and Singh (2005, Psychological Review, 112, 243-252) proposed a mathematical derivation to yield information content as a function of curvature along a contour. Here, we highlight several fundamental errors in their derivation and in its associated implementation, which are problematic in both mathematical and psychological senses. Instead, we propose an alternative mathematical formulation for information measure of contour curvature that addresses these issues. Additionally, unlike in previous work, we extend this approach to 3-dimensional (3D) shape by providing a formal measure of information content for surface curvature and outline a modified version of the minima rule relating to part segmentation using curvature in 3D shape. Copyright 2012 APA, all rights reserved.

Curvature effects on carbon nanomaterials: Exohedral versus endhohedral supercapacitors

Energy Technology Data Exchange (ETDEWEB)

Huang, J; Sumpter, B. G.; Meunier, V.; Yushin, G.; Portet, C.; Gogotsi, Y.

2011-01-31

Capacitive energy storage mechanisms in nanoporous carbon supercapacitors hinge on endohedral interactions in carbon materials with macro-, meso-, and micropores that have negative surface curvature. In this article, we show that because of the positive curvature found in zero-dimensional carbon onions or one-dimensional carbon nanotube arrays, exohedral interactions cause the normalized capacitance to increase with decreasing particle size or tube diameter, in sharp contrast to the behavior of nanoporous carbon materials. This finding is in good agreement with the trend of recent experimental data. Our analysis suggests that electrical energy storage can be improved by exploiting the highly curved surfaces of carbon nanotube arrays with diameters on the order of 1 nm.

Curvature effects in carbon nanomaterials: Exohedral versus endohedral supercapacitors

Energy Technology Data Exchange (ETDEWEB)

Huang, Jingsong [ORNL; Sumpter, Bobby G [ORNL; Meunier, Vincent [ORNL; Gogotsi, Yury G. [Drexel University; Yushin, Gleb [Georgia Institute of Technology; Portet, Cristelle [Drexel University

2010-01-01

Capacitive energy storage mechanisms in nanoporous carbon supercapacitors hinge on endohedral interactions in carbon materials with macro-, meso-, and micropores that have negative surface curvature. In this article, we show that because of the positive curvature found in zero-dimensional carbon onions or one-dimensional carbon nanotube arrays, exohedral interactions cause the normalized capacitance to increase with decreasing particle size or tube diameter, in sharp contrast to the behavior of nanoporous carbon materials. This finding is in good agreement with the trend of recent experimental data. Our analysis suggests that electrical energy storage can be improved by exploiting the highly curved surfaces of carbon nanotube arrays with diameters on the order of 1 nm.

Estimation of Curvature Changes for Steel-Concrete Composite Bridge Using Fiber Bragg Grating Sensors

Directory of Open Access Journals (Sweden)

Donghoon Kang

2013-01-01

Full Text Available This study is focused on the verification of the key idea of a newly developed steel-concrete composite bridge. The key idea of the proposed bridge is to reduce the design moment by applying vertical prestressing force to steel girders, so that a moment distribution of a continuous span bridge is formed in a simple span bridge. For the verification of the key technology, curvature changes of the bridge should be monitored sequentially at every construction stage. A pair of multiplexed FBG sensor arrays is proposed in order to measure curvature changes in this study. They are embedded in a full-scale test bridge and measured local strains, which are finally converted to curvatures. From the result of curvature changes, it is successfully ensured that the key idea of the proposed bridge, expected theoretically, is viable.

Berry Curvature and Nonlocal Transport Characteristics of Antidot Graphene

Directory of Open Access Journals (Sweden)

Jie Pan

2017-09-01

Full Text Available Antidot graphene denotes a monolayer of graphene structured by a periodic array of holes. Its energy dispersion is known to display a gap at the Dirac point. However, since the degeneracy between the A and B sites is preserved, antidot graphene cannot be described by the 2D massive Dirac equation, which is suitable for systems with an inherent A/B asymmetry. From inversion and time-reversal-symmetry considerations, antidot graphene should therefore have zero Berry curvature. In this work, we derive the effective Hamiltonian of antidot graphene from its tight-binding wave functions. The resulting Hamiltonian is a 4×4 matrix with a nonzero intervalley scattering term, which is responsible for the gap at the Dirac point. Furthermore, nonzero Berry curvature is obtained from the effective Hamiltonian, owing to the double degeneracy of the eigenfunctions. The topological manifestation is shown to be robust against randomness perturbations. Since the Berry curvature is expected to induce a transverse conductance, we have experimentally verified this feature through nonlocal transport measurements, by fabricating three antidot graphene samples with a triangular array of holes, a fixed periodicity of 150 nm, and hole diameters of 100, 80, and 60 nm. All three samples display topological nonlocal conductance, with excellent agreement with the theory predictions.

ORNL Interim Progress Report on Static CIRFT Testing Curvature Data Update

Energy Technology Data Exchange (ETDEWEB)

Wang, Jy-An John [ORNL; Wang, Hong [ORNL

2016-10-10

Since the CIRFT tests reported in NUREG-7198 were generated, a number of factors that influence the recorded curvature measurement data were identified. In 2016, a data reanalysis task was undertaken to implement the lessons learned. This letter report provides the revised results of previous CIRFT tests, after implementing the following data reanalysis procedures: (A) experimental data smoothing and LVDT reset, (B) LVDT probe contact and sensor spacing correction for curvature data, and (C) LVDT probe dynamic vibration adjustment procedure development.

Influence of implant rod curvature on sagittal correction of scoliosis deformity

DEFF Research Database (Denmark)

Salmingo, Remel A.; Tadano, Shigeru; Abe, Yuichiro

2014-01-01

of the implant rod’s angle of curvature during surgery and establish its influence on sagittal correction of scoliosis deformity. STUDY DESIGN: A retrospective analysis of the preoperative and postoperative implant rod geometry and angle of curvature was conducted. PATIENT SAMPLE: Twenty adolescent idiopathic......BACKGROUND CONTEXT: Deformation of in vivo–implanted rods could alter the scoliosis sagittal correction. To our knowledge, no previous authors have investigated the influence of implanted-rod deformation on the sagittal deformity correction during scoliosis surgery. PURPOSE: To analyze the changes...... scoliosis patients underwent surgery. Average age at the time of operation was 14 years. OUTCOME MEASURES: The preoperative and postoperative implant rod angle of curvature expressed in degrees was obtained for each patient. METHODS: Two implant rods were attached to the concave and convex side...

Simultaneous reflectometry and interferometry for measuring thin-film thickness and curvature

Science.gov (United States)

Arends, A. A.; Germain, T. M.; Owens, J. F.; Putnam, S. A.

2018-05-01

A coupled reflectometer-interferometer apparatus is described for thin-film thickness and curvature characterization in the three-phase contact line region of evaporating fluids. Validation reflectometry studies are provided for Au, Ge, and Si substrates and thin-film coatings of SiO2 and hydrogel/Ti/SiO2. For interferometry, liquid/air and solid/air interferences are studied, where the solid/air samples consisted of glass/air/glass wedges, cylindrical lenses, and molded polydimethylsiloxane lenses. The liquid/air studies are based on steady-state evaporation experiments of water and isooctane on Si and SiO2/Ti/SiO2 wafers. The liquid thin-films facilitate characterization of both (i) the nano-scale thickness of the absorbed fluid layer and (ii) the macro-scale liquid meniscus thickness, curvature, and curvature gradient profiles. For our validation studies with commercial lenses, the apparatus is shown to measure thickness profiles within 4.1%-10.8% error.

Numerical Investigation on Fluid Flow in a 90-Degree Curved Pipe with Large Curvature Ratio

Directory of Open Access Journals (Sweden)

Yan Wang

2015-01-01

Full Text Available In order to understand the mechanism of fluid flows in curved pipes, a large number of theoretical and experimental researches have been performed. As a critical parameter of curved pipe, the curvature ratio δ has received much attention, but most of the values of δ are very small (δ<0.1 or relatively small (δ≤0.5. As a preliminary study and simulation this research studied the fluid flow in a 90-degree curved pipe of large curvature ratio. The Detached Eddy Simulation (DES turbulence model was employed to investigate the fluid flows at the Reynolds number range from 5000 to 20000. After validation of the numerical strategy, the pressure and velocity distribution, pressure drop, fluid flow, and secondary flow along the curved pipe were illustrated. The results show that the fluid flow in a curved pipe with large curvature ratio seems to be unlike that in a curved pipe with small curvature ratio. Large curvature ratio makes the internal flow more complicated; thus, the flow patterns, the separation region, and the oscillatory flow are different.

Curvature controlled wetting in two dimensions

DEFF Research Database (Denmark)

Gil, Tamir; Mikheev, Lev V.

1995-01-01

. As the radius of the substrate r0→∞, the leading effect of the curvature is adding the Laplace pressure ΠL∝r0-1 to the pressure balance in the film. At temperatures and pressures under which the wetting is complete in planar geometry, Laplace pressure suppresses divergence of the mean thickness of the wetting...... term reduces the thickness by the amount proportional to r0-1/3...

Role of parallel flow curvature on the mitigation of Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Sarmah, D.; Sen, S.; Cairns, R.A.

2001-01-01

The effect of a radially varying parallel equilibrium flow on the stability of the Rayleigh-Taylor (RT) mode is studied analytically in the presence of a sheared magnetic field. It is shown that the parallel flow curvature can completely stabilize the RT mode. The flow curvature also has a robust effect on the radial structure of the mode. Possible implications of these theoretical findings to recent experiments are also discussed

The big bang as a result of the first-order phase transition driven by a change of the scalar curvature in an expanding early Universe: The “hyperinflation” scenario

Energy Technology Data Exchange (ETDEWEB)

Pashitskii, E. A., E-mail: pashitsk@iop.kiev.ua; Pentegov, V. I. [National Academy of Sciences of Ukraine, Institute of Physics (Ukraine)

2016-01-15

We suggest that the Big Bang could be a result of the first-order phase transition driven by a change in the scalar curvature of the 4D spacetime in an expanding cold Universe filled with a nonlinear scalar field φ and neutral matter with an equation of state p = νε (where p and ε are the pressure and energy density of the matter, respectively). We consider the Lagrangian of a scalar field with nonlinearity φ{sup 4} in a curved spacetime that, along with the term–ξR|φ|{sup 2} quadratic in φ (where ξ is the interaction constant between the scalar and gravitational fields and R is the scalar curvature), contains the term ξRφ{sub 0}(φ + φ{sup +}) linear in φ, where φ{sub 0} is the vacuum mean of the scalar field amplitude. As a consequence, the condition for the existence of extrema of the scalar-field potential energy is reduced to an equation cubic in φ. Provided that ν > 1/3, the scalar curvature R = [κ(3ν–1)ε–4Λ] (where κ and Λ are Einstein’s gravitational and cosmological constants, respectively) decreases with decreasing ε as the Universe expands, and a first-order phase transition in variable “external field” parameter proportional to R occurs at some critical value R{sub c} < 0. Under certain conditions, the critical radius of the early Universe at the point of the first-order phase transition can reach an arbitrary large value, so that this scenario of unrestricted “inflation” of the Universe may be called “hyperinflation.” After the passage through the phase-transition point, the scalar-field potential energy should be rapidly released, which must lead to strong heating of the Universe, playing the role of the Big Bang.

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

Science.gov (United States)

Ramakrishnan, N.; Sunil Kumar, P. B.; Radhakrishnan, Ravi

2014-01-01

Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across the various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham - Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

Energy Technology Data Exchange (ETDEWEB)

Ramakrishnan, N., E-mail: ramn@seas.upenn.edu [Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA-19104 (United States); Department of Bioengineering, University of Pennsylvania, Philadelphia, PA-19104 (United States); Department of Biochemistry and Biophysics, University of Pennsylvania, Philadelphia, PA-19104 (United States); Sunil Kumar, P.B., E-mail: sunil@physics.iitm.ac.in [Department of Physics, Indian Institute of Technology Madras, Chennai, 600036 (India); Radhakrishnan, Ravi, E-mail: rradhak@seas.upenn.edu [Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA-19104 (United States); Department of Bioengineering, University of Pennsylvania, Philadelphia, PA-19104 (United States); Department of Biochemistry and Biophysics, University of Pennsylvania, Philadelphia, PA-19104 (United States)

2014-10-01

Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein–lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham–Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this description

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

International Nuclear Information System (INIS)

Ramakrishnan, N.; Sunil Kumar, P.B.; Radhakrishnan, Ravi

2014-01-01

Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein–lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham–Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this description

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins.

Science.gov (United States)

Ramakrishnan, N; Sunil Kumar, P B; Radhakrishnan, Ravi

2014-10-01

Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across the various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham - Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this

Nonsmooth differential geometry-an approach tailored for spaces with Ricci curvature bounded from below

CERN Document Server

Gigli, Nicola

2018-01-01

The author discusses in which sense general metric measure spaces possess a first order differential structure. Building on this, spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting the author to define Hessian, covariant/exterior derivatives and Ricci curvature.

Curvature computation in volume-of-fluid method based on point-cloud sampling

Science.gov (United States)

Kassar, Bruno B. M.; Carneiro, João N. E.; Nieckele, Angela O.

2018-01-01

This work proposes a novel approach to compute interface curvature in multiphase flow simulation based on Volume of Fluid (VOF) method. It is well documented in the literature that curvature and normal vector computation in VOF may lack accuracy mainly due to abrupt changes in the volume fraction field across the interfaces. This may cause deterioration on the interface tension forces estimates, often resulting in inaccurate results for interface tension dominated flows. Many techniques have been presented over the last years in order to enhance accuracy in normal vectors and curvature estimates including height functions, parabolic fitting of the volume fraction, reconstructing distance functions, coupling Level Set method with VOF, convolving the volume fraction field with smoothing kernels among others. We propose a novel technique based on a representation of the interface by a cloud of points. The curvatures and the interface normal vectors are computed geometrically at each point of the cloud and projected onto the Eulerian grid in a Front-Tracking manner. Results are compared to benchmark data and significant reduction on spurious currents as well as improvement in the pressure jump are observed. The method was developed in the open source suite OpenFOAM® extending its standard VOF implementation, the interFoam solver.

A linearization time-domain CMOS smart temperature sensor using a curvature compensation oscillator.

Science.gov (United States)

Chen, Chun-Chi; Chen, Hao-Wen

2013-08-28

This paper presents an area-efficient time-domain CMOS smart temperature sensor using a curvature compensation oscillator for linearity enhancement with a -40 to 120 °C temperature range operability. The inverter-based smart temperature sensors can substantially reduce the cost and circuit complexity of integrated temperature sensors. However, a large curvature exists on the temperature-to-time transfer curve of the inverter-based delay line and results in poor linearity of the sensor output. For cost reduction and error improvement, a temperature-to-pulse generator composed of a ring oscillator and a time amplifier was used to generate a thermal sensing pulse with a sufficient width proportional to the absolute temperature (PTAT). Then, a simple but effective on-chip curvature compensation oscillator is proposed to simultaneously count and compensate the PTAT pulse with curvature for linearization. With such a simple structure, the proposed sensor possesses an extremely small area of 0.07 mm2 in a TSMC 0.35-mm CMOS 2P4M digital process. By using an oscillator-based scheme design, the proposed sensor achieves a fine resolution of 0.045 °C without significantly increasing the circuit area. With the curvature compensation, the inaccuracy of -1.2 to 0.2 °C is achieved in an operation range of -40 to 120 °C after two-point calibration for 14 packaged chips. The power consumption is measured as 23 mW at a sample rate of 10 samples/s.

Dynamic Double Curvature Mould System

DEFF Research Database (Denmark)

Jepsen, Christian Raun; Kristensen, Mathias Kræmmergaard; Kirkegaard, Poul Henning

2011-01-01

The present paper describes a concept for a reconfigurable mould surface which is designed to fit the needs of contemporary architecture. The core of the concept presented is a dynamic surface manipulated into a given shape using a digital signal created directly from the CAD drawing of the design....... This happens fast, automatic and without production of waste, and the manipulated surface is fair and robust, eliminating the need for additional, manual treatment. Limitations to the possibilities of the flexible form are limited curvature and limited level of detail, making it especially suited for larger...

Investigating undergraduate students’ ideas about the curvature of the Universe

Directory of Open Access Journals (Sweden)

Kim Coble

2018-06-01

Full Text Available [This paper is part of the Focused Collection on Astronomy Education Research.] As part of a larger project studying undergraduate students’ understanding of cosmology, we explored students’ ideas about the curvature of the Universe. We investigated preinstruction ideas held by introductory astronomy (ASTRO 101 students at three participating universities and postinstruction ideas at one. Through thematic analysis of responses to questions on three survey forms and preinstruction interviews, we found that prior to instruction a significant fraction of students said the Universe is round. Students’ reasoning for this included that the Universe contains round objects, therefore it must also be round, or an incorrect idea that the big bang theory describes an explosion from a central point. We also found that a majority of students think that astronomers use the term curvature to describe properties, such as dimensions, angles, or size, of the Universe or objects in the Universe, or that astronomers use the term curvature to describe the bending of space due to gravity. Students are skeptical that the curvature of the Universe can be measured, to a greater or lesser degree depending on question framing. Postinstruction responses to a multiple-choice exam question and interviews at one university indicate that students are more likely to correctly respond that the Universe as a whole is not curved postinstruction, though the idea that the Universe is round still persists for some students. While we see no evidence that priming with an elliptical or rectangular map of the cosmic microwave background on a postinstruction exam affects responses, students do cite visualizations such as diagrams among the reasons for their responses in preinstruction surveys.

Star formation in the multiverse

International Nuclear Information System (INIS)

Bousso, Raphael; Leichenauer, Stefan

2009-01-01

We develop a simple semianalytic model of the star formation rate as a function of time. We estimate the star formation rate for a wide range of values of the cosmological constant, spatial curvature, and primordial density contrast. Our model can predict such parameters in the multiverse, if the underlying theory landscape and the cosmological measure are known.

Generating ekpyrotic curvature perturbations before the big bang

International Nuclear Information System (INIS)

Lehners, Jean-Luc; Turok, Neil; McFadden, Paul; Steinhardt, Paul J.

2007-01-01

We analyze a general mechanism for producing a nearly scale-invariant spectrum of cosmological curvature perturbations during a contracting phase preceding a big bang, which can be entirely described using 4D effective field theory. The mechanism, based on first producing entropic perturbations and then converting them to curvature perturbations, can be naturally incorporated in cyclic and ekpyrotic models in which the big bang is modeled as a brane collision, as well as other types of cosmological models with a pre-big bang phase. We show that the correct perturbation amplitude can be obtained and that the spectral tilt n s tends to range from slightly blue to red, with 0.97 s <1.02 for the simplest models, a range compatible with current observations but shifted by a few percent towards the blue compared to the prediction of the simplest, large-field inflationary models

Curvature profiles as initial conditions for primordial black hole formation

International Nuclear Information System (INIS)

Polnarev, Alexander G; Musco, Ilia

2007-01-01

This work is part of an ongoing research programme to study possible primordial black hole (PBH) formation during the radiation-dominated era of the early universe. Working within spherical symmetry, we specify an initial configuration in terms of a curvature profile, which represents initial conditions for the large amplitude metric perturbations, away from the homogeneous Friedmann-Robertson-Walker model, which are required for PBH formation. Using an asymptotic quasi-homogeneous solution, we relate the curvature profile with the density and velocity fields, which at an early enough time, when the length scale of the configuration is much larger than the cosmological horizon, can be treated as small perturbations of the background values. We present general analytic solutions for the density and velocity profiles. These solutions enable us to consider in a self-consistent way the formation of PBHs in a wide variety of cosmological situations with the cosmological fluid being treated as an arbitrary mixture of different components with different equations of state. We obtain the analytical solutions for the density and velocity profiles as functions of the initial time. We then use two different parametrizations for the curvature profile and follow numerically the evolution of initial configurations

Distributional curvature of time-dependent cosmic strings

OpenAIRE

Wilson, J P

1997-01-01

Colombeau's theory of generalised functions is used to calculate the contributions, at the rotation axis, to the distributional curvature for a time-dependent radiating cosmic string, and hence the mass per unit length of the string source. This mass per unit length is compared with the mass at null infinity, giving evidence for a global energy conservation law.

An evaluation of canal curvature at the apical one third in type II mesial canals of mandibular molars

Directory of Open Access Journals (Sweden)

Hye-Rim Yun

2012-05-01

Full Text Available Objectives The purpose of this study was to evaluate the buccolingual curvature at the apical one third in type II mesial canals of mandibular molars using the radius and angle of curvature. Materials and Methods Total 100 mandibular molars were selected. Following an endodontic access in the teeth, their distal roots were removed. #15 H- or K-files (Dentsply Maillefer were inserted into the mesiobuccal and mesiolingual canals of the teeth. Radiographs of the teeth were taken for the proximal view. Among them, type II canals were selected and divided into two subgroups, IIa and IIb. In type IIa, two separate canals merged into one canal before reaching the apex and in type IIb, two separate canals merged into one canal within the apical foramen. The radius and angle of curvature of specimens were examined. Results In type II, mean radius of curvature in mesiolingual and mesiobuccal canals were 2.82 mm and 3.58 mm, respectively. The radius of the curvature of mesiolingual canals were significantly smaller than that of mesiobuccal canals in type II, and especially in type IIa. However, there were no statistically significant differences in radius of curvature between mesiobuccal and mesiolingual canals in type IIb and there were no significant differences in angle of curvature between type IIa and IIb. Conclusion In this study, type II mesial canals of mandibular molars showed severe curvature in the proximal view. Especially, mesiolingual canals of type IIa had more abrupt curvature than mesiobuccal canals at the apical one third.

Convective mass transfer in helical pipes: effect of curvature and torsion

Energy Technology Data Exchange (ETDEWEB)

Litster, S.; Djilali, N. [University of Victoria, Department of Mechanical Engineering, Victoria, BC (Canada); Pharoah, J.G. [University of Victoria, Department of Mechanical Engineering, Victoria, BC (Canada); Queen' s University at Kingston, Department of Mechanical Engineering, Kingston, ON (Canada)

2006-03-01

A 3D numerical analysis of the flow and mass transfer in helical pipes is presented. The interpretation of the flow patterns and their impact on mass transfer is shown to require a non-orthogonal pseudo-stream function based visualization. The strong coupling between torsion and curvature effects, and the resulting secondary flow regimes are well characterized by a parameter combining both the Dean (Dn) and Germano numbers (Gn). For membrane separation applications, helical modules combining high curvature with low torsion would alleviate concentration polarization and yield appreciable flux improvement. (orig.)

Curvature-induced symmetry breaking in nonlinear Schrodinger models

DEFF Research Database (Denmark)

Gaididei, Yuri Borisovich; Mingaleev, S. F.; Christiansen, Peter Leth

2000-01-01

We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a symmetry breaking when an asymmetric stationary state becomes energetically more favorable than a symmetric stationary state. We show that the energy of localized states...

Papapetrou's naked singularity is a strong curvature singularity

International Nuclear Information System (INIS)

Hollier, G.P.

1986-01-01

Following Papapetrou [1985, a random walk in General Relativity ed. J. Krishna-Rao (New Delhi: Wiley Eastern)], a spacetime with a naked singularity is analysed. This singularity is shown to be a strong curvature singularity and thus a counterexample to a censorship conjecture. (author)

On the projective curvature tensor of generalized Sasakian-space ...

African Journals Online (AJOL)

space-forms under some conditions regarding projective curvature tensor. All the results obtained in this paper are in the form of necessary and sufficient conditions. Keywords: Generalized Sasakian-space-forms; projectively flat; ...

Endoscopes and robots for tight surgical spaces: use of precurved elastic elements to enhance curvature

Science.gov (United States)

Remirez, Andria A.; Webster, Robert J.

2016-03-01

Many applications in medicine require flexible surgical manipulators and endoscopes capable of reaching tight curvatures. The maximum curvature these devices can achieve is often restricted either by a strain limit, or by a maximum actuation force that the device's components can tolerate without risking mechanical failure. In this paper we propose the use of precurvature to "bias" the workspace of the device in one direction. Combined with axial shaft rotation, biasing increases the size of the device's workspace, enabling it to reach tighter curvatures than a comparable device without biasing can achieve, while still being able to fully straighten. To illustrate this effect, we describe several example prototype devices which use flexible nitinol strips that can be pushed and pulled to generate bending. We provide a statics model that relates the manipulator curvature to actuation force, and validate it experimentally.

Comparing Spatial Predictions

KAUST Repository

Hering, Amanda S.

2011-11-01

Under a general loss function, we develop a hypothesis test to determine whether a significant difference in the spatial predictions produced by two competing models exists on average across the entire spatial domain of interest. The null hypothesis is that of no difference, and a spatial loss differential is created based on the observed data, the two sets of predictions, and the loss function chosen by the researcher. The test assumes only isotropy and short-range spatial dependence of the loss differential but does allow it to be non-Gaussian, non-zero-mean, and spatially correlated. Constant and nonconstant spatial trends in the loss differential are treated in two separate cases. Monte Carlo simulations illustrate the size and power properties of this test, and an example based on daily average wind speeds in Oklahoma is used for illustration. Supplemental results are available online. © 2011 American Statistical Association and the American Society for Qualitys.

Translating Solitons of Mean Curvature Flow of Noncompact Submanifolds

International Nuclear Information System (INIS)

Li Guanghan; Tian Daping; Wu Chuanxi

2011-01-01

We prove the existence and asymptotic behavior of rotationally symmetric solitons of mean curvature flow for noncompact submanifolds in Euclidean and Minkowski spaces, which generalizes part of the corresponding results for hypersurfaces of Jian.

Curvature and elasticity of substitution: what is the link?

Czech Academy of Sciences Publication Activity Database

Matveenko, Andrei; Matveenko, V.

2014-01-01

Roč. 10, č. 2 (2014), s. 7-20 ISSN 1800-5845 Grant - others:UK(CZ) GAUK 308214 Institutional support: PRVOUK-P23 Keywords : curvature * elasticity of substitution * production function Subject RIV: AH - Economics

On M-theory fourfold vacua with higher curvature terms

International Nuclear Information System (INIS)

Grimm, Thomas W.; Pugh, Tom G.; Weißenbacher, Matthias

2015-01-01

We study solutions to the eleven-dimensional supergravity action, including terms quartic and cubic in the Riemann curvature, that admit an eight-dimensional compact space. The internal background is found to be a conformally Kähler manifold with vanishing first Chern class. The metric solution, however, is non-Ricci-flat even when allowing for a conformal rescaling including the warp factor. This deviation is due to the possible non-harmonicity of the third Chern-form in the leading order Ricci-flat metric. We present a systematic derivation of the background solution by solving the Killing spinor conditions including higher curvature terms. These are translated into first-order differential equations for a globally defined real two-form and complex four-form on the fourfold. We comment on the supersymmetry properties of the described solutions

Substrate Curvature Regulates Cell Migration -A Computational Study

Science.gov (United States)

He, Xiuxiu; Jiang, Yi

Cell migration in host microenvironment is essential to cancer etiology, progression and metastasis. Cellular processes of adhesion, cytoskeletal polymerization, contraction, and matrix remodeling act in concert to regulate cell migration, while local extracellular matrix architecture modulate these processes. In this work we study how stromal microenvironment with native and cell-derived curvature at micron-meter scale regulate cell motility pattern. We developed a 3D model of single cell migration on a curved substrate. Mathematical analysis of cell morphological adaption to the cell-substrate interface shows that cell migration on convex surfaces deforms more than on concave surfaces. Both analytical and simulation results show that curved surfaces regulate the cell motile force for cell's protruding front through force balance with focal adhesion and cell contraction. We also found that cell migration on concave substrates is more persistent. These results offer a novel biomechanical explanation to substrate curvature regulation of cell migration. NIH 1U01CA143069.

Thermodynamic curvature of soft-sphere fluids and solids

Science.gov (United States)

Brańka, A. C.; Pieprzyk, S.; Heyes, D. M.

2018-02-01

The influence of the strength of repulsion between particles on the thermodynamic curvature scalar R for the fluid and solid states is investigated for particles interacting with the inverse power (r-n) potential, where r is the pair separation and 1 /n is the softness. Exact results are obtained for R in certain limiting cases, and the R behavior determined for the systems in the fluid and solid phases. It is found that in such systems the thermodynamic curvature can be positive for very soft particles, negative for steeply repulsive (or large n ) particles across almost the entire density range, and can change sign between negative and positive at a certain density. The relationship between R and the form of the interaction potential is more complex than previously suggested, and it may be that R is an indicator of the relative importance of energy and entropy contributions to the thermodynamic properties of the system.

Local curvature analysis for classifying breast tumors: Preliminary analysis in dedicated breast CT

International Nuclear Information System (INIS)

Lee, Juhun; Nishikawa, Robert M.; Reiser, Ingrid; Boone, John M.; Lindfors, Karen K.

2015-01-01

Purpose: The purpose of this study is to measure the effectiveness of local curvature measures as novel image features for classifying breast tumors. Methods: A total of 119 breast lesions from 104 noncontrast dedicated breast computed tomography images of women were used in this study. Volumetric segmentation was done using a seed-based segmentation algorithm and then a triangulated surface was extracted from the resulting segmentation. Total, mean, and Gaussian curvatures were then computed. Normalized curvatures were used as classification features. In addition, traditional image features were also extracted and a forward feature selection scheme was used to select the optimal feature set. Logistic regression was used as a classifier and leave-one-out cross-validation was utilized to evaluate the classification performances of the features. The area under the receiver operating characteristic curve (AUC, area under curve) was used as a figure of merit. Results: Among curvature measures, the normalized total curvature (C_T) showed the best classification performance (AUC of 0.74), while the others showed no classification power individually. Five traditional image features (two shape, two margin, and one texture descriptors) were selected via the feature selection scheme and its resulting classifier achieved an AUC of 0.83. Among those five features, the radial gradient index (RGI), which is a margin descriptor, showed the best classification performance (AUC of 0.73). A classifier combining RGI and C_T yielded an AUC of 0.81, which showed similar performance (i.e., no statistically significant difference) to the classifier with the above five traditional image features. Additional comparisons in AUC values between classifiers using different combinations of traditional image features and C_T were conducted. The results showed that C_T was able to replace the other four image features for the classification task. Conclusions: The normalized curvature measure

On a class of graphs with prescribed mean curvature

International Nuclear Information System (INIS)

Duong Minh Duc; Costa Salavessa, I.M. de

1989-11-01

We study a class of quasilinear elliptic equations on the unit ball of R n and apply these results to get the existence of graphs with prescribed mean curvature on n-hyperbolic spaces. (author). 18 refs

River banks and channel axis curvature: Effects on the longitudinal dispersion in alluvial rivers

Science.gov (United States)

Lanzoni, Stefano; Ferdousi, Amena; Tambroni, Nicoletta

2018-03-01

The fate and transport of soluble contaminants released in natural streams are strongly dependent on the spatial variations of the flow field and of the bed topography. These variations are essentially related to the presence of the channel banks and to the planform configuration of the channel. Large velocity gradients arise near to the channel banks, where the flow depth decreases to zero. Moreover, single thread alluvial rivers are seldom straight, and usually exhibit meandering planforms and a bed topography that deviates from the plane configuration. Channel axis curvature and movable bed deformations drive secondary helical currents which enhance both cross sectional velocity gradients and transverse mixing, thus crucially influencing longitudinal dispersion. The present contribution sets up a rational framework which, assuming mild sloping banks and taking advantage of the weakly meandering character often exhibited by natural streams, leads to an analytical estimate of the contribution to longitudinal dispersion associated with spatial non-uniformities of the flow field. The resulting relationship stems from a physics-based modeling of the flow in natural rivers, and expresses the bend averaged longitudinal dispersion coefficient as a function of the relevant hydraulic and morphologic parameters. The treatment of the problem is river specific, since it relies on an explicit spatial description, although linearized, of the flow field that establishes in the investigated river. Comparison with field data available from tracer tests supports the robustness of the proposed framework, given also the complexity of the processes that affect dispersion dynamics in real streams.

Effects of curvature on rarefied gas flows between rotating concentric cylinders

Science.gov (United States)

Dongari, Nishanth; White, Craig; Scanlon, Thomas J.; Zhang, Yonghao; Reese, Jason M.

2013-05-01

The gas flow between two concentric rotating cylinders is considered in order to investigate non-equilibrium effects associated with the Knudsen layers over curved surfaces. We investigate the nonlinear flow physics in the near-wall regions using a new power-law (PL) wall-scaling approach. This PL model incorporates Knudsen layer effects in near-wall regions by taking into account the boundary limiting effects on the molecular free paths. We also report new direct simulation Monte Carlo results covering a wide range of Knudsen numbers and accommodation coefficients, and for various outer-to-inner cylinder radius ratios. Our simulation data are compared with both the classical slip flow theory and the PL model, and we find that non-equilibrium effects are not only dependent on Knudsen number and accommodation coefficient but are also significantly affected by the surface curvature. The relative merits and limitations of both theoretical models are explored with respect to rarefaction and curvature effects. The PL model is able to capture some of the nonlinear trends associated with Knudsen layers up to the early transition flow regime. The present study also illuminates the limitations of classical slip flow theory even in the early slip flow regime for higher curvature test cases, although the model does exhibit good agreement throughout the slip flow regime for lower curvature cases. Torque and velocity profile comparisons also convey that a good prediction of integral flow properties does not necessarily guarantee the accuracy of the theoretical model used, and it is important to demonstrate that field variables are also predicted satisfactorily.

Asymmetric vibrations of shells of revolution having meridionally varying curvature and thickness

International Nuclear Information System (INIS)

Suzuki, Katsuyoshi; Kosawada, Tadashi; Miura, Kazuyuki.

1988-01-01

An exact method using power series expansions is presented for solving asymmetric free vibration problems for shells of revolution having meridionally varying curvature and thickness. The gaverning equations of motion and the boundary conditions are derived from the stationary conditions of the Lagrangian of the shells of revolution. The method is demonstrated for shells of revolution having elliptical, cycloidal, parabolical, catenary and hyperbolical meridional curvature. The natural frequencies are numerically calculated for these shells having second degree thickness variation. (author)

Influence of Global and Local Membrane Curvature on Mechanosensitive Ion Channels: A Finite Element Approach

Directory of Open Access Journals (Sweden)

Omid Bavi

2016-02-01

Full Text Available Mechanosensitive (MS channels are ubiquitous molecular force sensors that respond to a number of different mechanical stimuli including tensile, compressive and shear stress. MS channels are also proposed to be molecular curvature sensors gating in response to bending in their local environment. One of the main mechanisms to functionally study these channels is the patch clamp technique. However, the patch of membrane surveyed using this methodology is far from physiological. Here we use continuum mechanics to probe the question of how curvature, in a standard patch clamp experiment, at different length scales (global and local affects a model MS channel. Firstly, to increase the accuracy of the Laplace’s equation in tension estimation in a patch membrane and to be able to more precisely describe the transient phenomena happening during patch clamping, we propose a modified Laplace’s equation. Most importantly, we unambiguously show that the global curvature of a patch, which is visible under the microscope during patch clamp experiments, is of negligible energetic consequence for activation of an MS channel in a model membrane. However, the local curvature (RL < 50 and the direction of bending are able to cause considerable changes in the stress distribution through the thickness of the membrane. Not only does local bending, in the order of physiologically relevant curvatures, cause a substantial change in the pressure profile but it also significantly modifies the stress distribution in response to force application. Understanding these stress variations in regions of high local bending is essential for a complete understanding of the effects of curvature on MS channels.

Using geometric algebra to represent curvature in shell theory with applications to Starling resistors.

Science.gov (United States)

Gregory, A L; Agarwal, A; Lasenby, J

2017-11-01

We present a novel application of rotors in geometric algebra to represent the change of curvature tensor that is used in shell theory as part of the constitutive law. We introduce a new decomposition of the change of curvature tensor, which has explicit terms for changes of curvature due to initial curvature combined with strain, and changes in rotation over the surface. We use this decomposition to perform a scaling analysis of the relative importance of bending and stretching in flexible tubes undergoing self-excited oscillations. These oscillations have relevance to the lung, in which it is believed that they are responsible for wheezing. The new analysis is necessitated by the fact that the working fluid is air, compared to water in most previous work. We use stereographic imaging to empirically measure the relative importance of bending and stretching energy in observed self-excited oscillations. This enables us to validate our scaling analysis. We show that bending energy is dominated by stretching energy, and the scaling analysis makes clear that this will remain true for tubes in the airways of the lung.

Curvature vector smart sensing with a long-period fibre grating probed by artificial intelligence

International Nuclear Information System (INIS)

Costa, R Z V; Possetti, G R C; De Arruda, L V R; Muller, M; Fabris, J L

2010-01-01

This work shows a curvature vector sensing device based on a single long-period grating written in a commercial photosensitive optical fibre. The sensing approach uses an artificial neural network based on multilayer perceptrons for data analysis. Curvatures from 0.00 to 3.13 m −1 and angular orientations from 0 to 180° were measured with the device, with combined standard uncertainties of 0.05 m −1 and 1.5°, respectively. The root mean square errors for curvature and angular orientation were 0.0008 m −1 and 0.3° in the training stage and 0.002 m −1 and 0.9° in the test stage, respectively

Complete set of homogeneous isotropic analytic solutions in scalar-tensor cosmology with radiation and curvature

Science.gov (United States)

Bars, Itzhak; Chen, Shih-Hung; Steinhardt, Paul J.; Turok, Neil

2012-10-01

We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the Universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions analytically without any restrictions on the parameter space of the model or initial values of the fields. We find that for generic solutions the Universe goes through a singular (zero-size) bounce by entering a period of antigravity at each big crunch and exiting from it at the following big bang. This happens cyclically again and again without violating the null-energy condition. There is a special subset of geodesically complete nongeneric solutions which perform zero-size bounces without ever entering the antigravity regime in all cycles. For these, initial values of the fields are synchronized and quantized but the parameters of the model are not restricted. There is also a subset of spatial curvature-induced solutions that have finite-size bounces in the gravity regime and never enter the antigravity phase. These exist only within a small continuous domain of parameter space without fine-tuning the initial conditions. To obtain these results, we identified 25 regions of a 6-parameter space in which the complete set of analytic solutions are explicitly obtained.

On the geometry of null cones to infinity under curvature flux bounds

International Nuclear Information System (INIS)

Alexakis, Spyros; Shao, Arick

2014-01-01

The main objective of this paper is to control the geometry of a future outgoing truncated null cone extending smoothly toward infinity in an Einstein-vacuum spacetime. In particular, we wish to do this under minimal regularity assumptions, namely, at the (weighted) L 2 -curvature level. We show that if the curvature flux and the data on an initial sphere of the cone are sufficiently close to the corresponding values in a standard Minkowski or Schwarzschild null cone, then we can obtain quantitative bounds on the geometry of the entire infinite cone. The same bounds also imply the existence of limits at infinity, along the null cone, of naturally scaled geometric quantities. In Alexakis and Shao (2013 Bounds on the Bondi energy by a flux of curvature arXiv:1308.4170), we will apply these results in order to control various physical quantities—e.g., the Bondi energy and (linear and angular) momenta—associated with such infinite null cones in vacuum spacetimes. (paper)

Elongational flow of polymer melts at constant strain rate, constant stress and constant force

Science.gov (United States)

Wagner, Manfred H.; Rolón-Garrido, Víctor H.

2013-04-01

Characterization of polymer melts in elongational flow is typically performed at constant elongational rate or rarely at constant tensile stress conditions. One of the disadvantages of these deformation modes is that they are hampered by the onset of "necking" instabilities according to the Considère criterion. Experiments at constant tensile force have been performed even more rarely, in spite of the fact that this deformation mode is free from necking instabilities and is of considerable industrial relevance as it is the correct analogue of steady fiber spinning. It is the objective of the present contribution to present for the first time a full experimental characterization of a long-chain branched polyethylene melt in elongational flow. Experiments were performed at constant elongation rate, constant tensile stress and constant tensile force by use of a Sentmanat Extensional Rheometer (SER) in combination with an Anton Paar MCR301 rotational rheometer. The accessible experimental window and experimental limitations are discussed. The experimental data are modelled by using the Wagner I model. Predictions of the steady-start elongational viscosity in constant strain rate and creep experiments are found to be identical, albeit only by extrapolation of the experimental data to Hencky strains of the order of 6. For constant stress experiments, a minimum in the strain rate and a corresponding maximum in the elongational viscosity is found at a Hencky strain of the order of 3, which, although larger than the steady-state value, follows roughly the general trend of the steady-state elongational viscosity. The constitutive analysis also reveals that constant tensile force experiments indicate a larger strain hardening potential than seen in constant elongation rate or constant tensile stress experiments. This may be indicative of the effect of necking under constant elongation rate or constant tensile stress conditions according to the Considère criterion.

Value of the Cosmological Constant in Emergent Quantum Gravity

Energy Technology Data Exchange (ETDEWEB)

Hogan, Craig [Fermilab

2018-03-30

It is suggested that the exact value of the cosmological constant could be derived from first principles, based on entanglement of the Standard Model field vacuum with emergent holographic quantum geometry. For the observed value of the cosmological constant, geometrical information is shown to agree closely with the spatial information density of the QCD vacuum, estimated in a free-field approximation. The comparison is motivated by a model of exotic rotational fluctuations in the inertial frame that can be precisely tested in laboratory experiments. Cosmic acceleration in this model is always positive, but fluctuates with characteristic coherence length $\\approx 100$km and bandwidth $\\approx 3000$ Hz.

Adjuvant Maneuvers for Residual Curvature Correction During Penile Prosthesis Implantation in Men with Peyronie's Disease.

Science.gov (United States)

Berookhim, Boback M; Karpman, Edward; Carrion, Rafael

2015-11-01

The surgical treatment of comorbid erectile dysfunction and Peyronie's disease has long included the implantation of an inflatable penile prosthesis as well as a number of adjuvant maneuvers to address residual curvature after prosthesis placement. To review the various surgical options for addressing curvature after prosthesis placement, with specific attention paid to an original article by Wilson et al. reporting on modeling over a penile prosthesis for the management of Peyronie's disease. A literature review was performed analyzing articles reporting the management of penile curvature in patients undergoing implantation of an inflatable penile prosthesis. Reported improvement in Peyronie's deformity as well as the complication rate associated with the various surgical techniques described. Modeling is a well-established treatment modality among patients with Peyronie's disease undergoing penile prosthesis implantation. A variety of other adjuvant maneuvers to address residual curvature when modeling alone is insufficient has been presented in the literature. Over 20 years of experience with modeling over a penile prosthesis have proven the efficacy and safety of this treatment option, providing the surgeon a simple initial step for the management of residual curvature after penile implantation which allows for the use of additional adjuvant maneuvers in those with significant deformities. © 2015 International Society for Sexual Medicine.

Influence of piezoceramic to fused silica plate thickness on the radii of curvature of piezoelectric bimorph mirror

International Nuclear Information System (INIS)

Libu, M.; Susanth, S.; Vasanthakumari, K. G.; Dileep Kumar, C. J.; Raghu, N.

2012-01-01

Piezoelectric based bimorph mirrors (PBM) find extensive use in focusing of x-ray beams. Many optical instruments require use of PBM whose radii of curvature can be tuned precisely. The 100 mm and 300 mm PBMs were fabricated with varying piezoelectric to fused silica plate thicknesses. The radii of curvature of free standing mirrors were measured as a function of voltage and it was found to decrease with increasing voltage. For a given piezoelectric plate thickness, as the fused silica thickness increases, the radii of curvature was found to increase owing to increase in stiffness of the mirror. On the other hand, for a given fused silica plate thickness, when the piezoelectric plate thickness is increased, the radii of curvature are decreased for a given electric field, due to increase in generated force. This study brings out the influence of piezoceramic to fused silica plate thickness on the radii of curvature of PBM.

Glauber theory and the quantum coherence of curvature inhomogeneities

CERN Document Server

Giovannini, Massimo

2017-01-12

The curvature inhomogeneities are systematically scrutinized in the framework of the Glauber approach. The amplified quantum fluctuations of the scalar and tensor modes of the geometry are shown to be first-order coherent while the interference of the corresponding intensities is larger than in the case of Bose-Einstein correlations. After showing that the degree of second-order coherence does not suffice to characterize unambiguously the curvature inhomogeneities, we argue that direct analyses of the degrees of third and fourth-order coherence are necessary to discriminate between different correlated states and to infer more reliably the statistical properties of the large-scale fluctuations. We speculate that the moments of the multiplicity distributions of the relic phonons might be observationally accessible thanks to new generations of instruments able to count the single photons of the Cosmic Microwave Background in the THz region.

Flow Curvature Effects for VAWT: a Review of Virtual Airfoil Transformations and Implementation in XFOIL

DEFF Research Database (Denmark)

van der Horst, Sander; van de Wiel, Jelmer E.; Ferreira, Carlos Simao

2016-01-01

Blades on a Vertical Axis Wind Turbine (VAWT) experience curved streamlines, caused by the rotation of the turbine. This phenomenon is known as flow curvature and has effects on the aerodynamic loading of the blades. Several authors have proposed methods to account for flow curvature, resulting...

The Paneitz curvature problem on lower dimensional spheres

CERN Document Server

Ben-Ayed, M

2003-01-01

In this paper we prescribe a fourth order conformal invariant (the Paneitz curvature) on the n-spheres, with n is an element of left brace 5, 6 right brace. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem, we prove some existence results.

Test of the FLRW Metric and Curvature with Strong Lens Time Delays

International Nuclear Information System (INIS)

Liao, Kai; Li, Zhengxiang; Wang, Guo-Jian; Fan, Xi-Long

2017-01-01

We present a new model-independent strategy for testing the Friedmann–Lemaître–Robertson–Walker (FLRW) metric and constraining cosmic curvature, based on future time-delay measurements of strongly lensed quasar-elliptical galaxy systems from the Large Synoptic Survey Telescope and supernova observations from the Dark Energy Survey. The test only relies on geometric optics. It is independent of the energy contents of the universe and the validity of the Einstein equation on cosmological scales. The study comprises two levels: testing the FLRW metric through the distance sum rule (DSR) and determining/constraining cosmic curvature. We propose an effective and efficient (redshift) evolution model for performing the former test, which allows us to concretely specify the violation criterion for the FLRW DSR. If the FLRW metric is consistent with the observations, then on the second level the cosmic curvature parameter will be constrained to ∼0.057 or ∼0.041 (1 σ ), depending on the availability of high-redshift supernovae, which is much more stringent than current model-independent techniques. We also show that the bias in the time-delay method might be well controlled, leading to robust results. The proposed method is a new independent tool for both testing the fundamental assumptions of homogeneity and isotropy in cosmology and for determining cosmic curvature. It is complementary to cosmic microwave background plus baryon acoustic oscillation analyses, which normally assume a cosmological model with dark energy domination in the late-time universe.

Test of the FLRW Metric and Curvature with Strong Lens Time Delays

Energy Technology Data Exchange (ETDEWEB)

Liao, Kai [School of Science, Wuhan University of Technology, Wuhan 430070 (China); Li, Zhengxiang; Wang, Guo-Jian [Department of Astronomy, Beijing Normal University, Beijing 100875 (China); Fan, Xi-Long, E-mail: liaokai@whut.edu.cn, E-mail: xilong.fan@glasgow.ac.uk [Department of Physics and Mechanical and Electrical Engineering, Hubei University of Education, Wuhan 430205 (China)

2017-04-20

We present a new model-independent strategy for testing the Friedmann–Lemaître–Robertson–Walker (FLRW) metric and constraining cosmic curvature, based on future time-delay measurements of strongly lensed quasar-elliptical galaxy systems from the Large Synoptic Survey Telescope and supernova observations from the Dark Energy Survey. The test only relies on geometric optics. It is independent of the energy contents of the universe and the validity of the Einstein equation on cosmological scales. The study comprises two levels: testing the FLRW metric through the distance sum rule (DSR) and determining/constraining cosmic curvature. We propose an effective and efficient (redshift) evolution model for performing the former test, which allows us to concretely specify the violation criterion for the FLRW DSR. If the FLRW metric is consistent with the observations, then on the second level the cosmic curvature parameter will be constrained to ∼0.057 or ∼0.041 (1 σ ), depending on the availability of high-redshift supernovae, which is much more stringent than current model-independent techniques. We also show that the bias in the time-delay method might be well controlled, leading to robust results. The proposed method is a new independent tool for both testing the fundamental assumptions of homogeneity and isotropy in cosmology and for determining cosmic curvature. It is complementary to cosmic microwave background plus baryon acoustic oscillation analyses, which normally assume a cosmological model with dark energy domination in the late-time universe.

WHEN THE DISTURBANCES ARE SPATIALLY CORRELATED

African Journals Online (AJOL)

correlation, spatial error process. INTRODUCTION. Consider the linear regression model for spatial correlation y=XB +u, u=Ce, (1) where y is a Txl observable random vector, X is a Txk matrix of known constants with full column rank k, B is a k xl vector of unknown parameters,. :2 is a Txl random vector with expectation zero ...

Multi-Objective Optimization of Experiments Using Curvature and Fisher Information Matrix

Directory of Open Access Journals (Sweden)

Erica Manesso

2017-11-01

Full Text Available The bottleneck in creating dynamic models of biological networks and processes often lies in estimating unknown kinetic model parameters from experimental data. In this regard, experimental conditions have a strong influence on parameter identifiability and should therefore be optimized to give the maximum information for parameter estimation. Existing model-based design of experiment (MBDOE methods commonly rely on the Fisher information matrix (FIM for defining a metric of data informativeness. When the model behavior is highly nonlinear, FIM-based criteria may lead to suboptimal designs, as the FIM only accounts for the linear variation in the model outputs with respect to the parameters. In this work, we developed a multi-objective optimization (MOO MBDOE, for which the model nonlinearity was taken into consideration through the use of curvature. The proposed MOO MBDOE involved maximizing data informativeness using a FIM-based metric and at the same time minimizing the model curvature. We demonstrated the advantages of the MOO MBDOE over existing FIM-based and other curvature-based MBDOEs in an application to the kinetic modeling of fed-batch fermentation of baker’s yeast.

Stretchable Dual-Capacitor Multi-Sensor for Touch-Curvature-Pressure-Strain Sensing.

Science.gov (United States)

Jin, Hanbyul; Jung, Sungchul; Kim, Junhyung; Heo, Sanghyun; Lim, Jaeik; Park, Wonsang; Chu, Hye Yong; Bien, Franklin; Park, Kibog

2017-09-07

We introduce a new type of multi-functional capacitive sensor that can sense several different external stimuli. It is fabricated only with polydimethylsiloxane (PDMS) films and silver nanowire electrodes by using selective oxygen plasma treatment method without photolithography and etching processes. Differently from the conventional single-capacitor multi-functional sensors, our new multi-functional sensor is composed of two vertically-stacked capacitors (dual-capacitor). The unique dual-capacitor structure can detect the type and strength of external stimuli including curvature, pressure, strain, and touch with clear distinction, and it can also detect the surface-normal directionality of curvature, pressure, and touch. Meanwhile, the conventional single-capacitor sensor has ambiguity in distinguishing curvature and pressure and it can detect only the strength of external stimulus. The type, directionality, and strength of external stimulus can be determined based on the relative capacitance changes of the two stacked capacitors. Additionally, the logical flow reflected on a tree structure with its branches reaching the direction and strength of the corresponding external stimulus unambiguously is devised. This logical flow can be readily implemented in the sensor driving circuit if the dual-capacitor sensor is commercialized actually in the future.

Numerical calculation and analysis of single-curvature polyhedron hydro-bulging process for manufacturing spherical vessels

International Nuclear Information System (INIS)

Dong Jianling; Zhang Fengke; Yin Dejian

2005-01-01

Single-curvature polyhedron hydro-bulging technology is a new technology for manufacturing spherical vessels and it has a good application foreground. This technology has been used in practice. But the designing and manufacturing of polyhedron is based on experiences, and the final quality of spherical vessels cannot be forecast quantitatively. In the paper, the FEM code, MARC, is used to simulate the hydrobulging process of a single-curvature polyhedron, including loading and offloading. And the distributions of stress and strain are acquired as well as other important data. Comparing with the experimental results, it shows that single-curvature polyhedron hydro-bulging process can be simulated well by the FEM code. (authors)

Curved nanocarbon materials: probing the curvature and topology effects using phonon spectra

Energy Technology Data Exchange (ETDEWEB)

Saxena, Avadh Baheri [Los Alamos National Laboratory; Gupta, Sanju [UNIV OF MISSOURI

2008-01-01

In spite of detailed structural characterization of nanoscale carbons, they still possess some features that are not entirely understood particularly in terms of topological characteristics. By means of resonance Raman spectroscopy, we elucidated the notion of global topology and curvature by determining the prominent Raman bands variation for various carbon nanostructures including tubular (single-, double- and multiwalled nanotubes, peapod), spherical (hypo- and hyperfullerenes, onion-like carbon) and complex (nanocones, nanohorns, nanodisks and nanorings) geometries. This knowledge points to an unprecedented emergent paradigm of global topology/curvature {yields} property {yields} functionality relationship.

Asymmetric vibrations of thick shells of revolution having meridionally varying curvature

International Nuclear Information System (INIS)

Suzuki, Katsuyoshi; Kosawada, Tadashi; Yachita, Takumi.

1988-01-01

An exact method using power series expansions is presented for solving asymmetric free vibration problems for thick shells of revolution having meridionally varying curvature. Based on the improved thick shell theory, the Lagrangian of the shells of revolution are obtained, and the equations of motion and the boundary conditions are derived from the stationary condition of the Lagrangian. The method is demonstrated for thick shells of revolution having elliptical, cycloidal, parabolical, catenary and hyperbolical meridional curvature. The results by the present method are compared with those by the thin shell theory and the effects of the rotatory inertia and the shear deformation upon the natural frequencies are clarified. (author)

Supported lipid bilayers with controlled curvature via colloidal lithography

DEFF Research Database (Denmark)

Sundh, Maria; Manandhar, Michal; Svedhem, Sofia

2011-01-01

Supported lipid bilayers (SLBs) at surfaces provide a route to quantitatively study molecular interactions with and at lipid membranes via different surface-based analytical techniques. Here, a method to fabricate SLBs with controlled curvatures, in the nanometer regime over large areas, is prese...

Limited capacity for contour curvature in iconic memory.

Science.gov (United States)

Sakai, Koji

2006-06-01

We measured the difference threshold for contour curvature in iconic memory by using the cued discrimination method. The study stimulus consisting of 2 to 6 curved contours was briefly presented in the fovea, followed by two lines as cues. Subjects discriminated the curvature of two cued curves. The cue delays were 0 msec. and 300 msec. in Exps. 1 and 2, respectively, and 50 msec. before the study offset in Exp. 3. Analysis of data from Exps. 1 and 2 showed that the Weber fraction rose monotonically with the increase in set size. Clear set-size effects indicate that iconic memory has a limited capacity. Moreover, clear set-size effect in Exp. 3 indicates that perception itself has a limited capacity. Larger set-size effects in Exp. 1 than in Exp. 3 suggest that iconic memory after perceptual process has limited capacity. These properties of iconic memory at threshold level are contradictory to the traditional view that iconic memory has a high capacity both at suprathreshold and categorical levels.

Strain transfer through film-substrate interface and surface curvature evolution during a tensile test

Science.gov (United States)

He, Wei; Han, Meidong; Goudeau, Philippe; Bourhis, Eric Le; Renault, Pierre-Olivier; Wang, Shibin; Li, Lin-an

2018-03-01

Uniaxial tensile tests on polyimide-supported thin metal films are performed to respectively study the macroscopic strain transfer through an interface and the surface curvature evolution. With a dual digital image correlation (DIC) system, the strains of the film and the substrate can be simultaneously measured in situ during the tensile test. For the true strains below 2% (far beyond the films' elastic limit), a complete longitudinal strain transfer is present irrespective of the film thickness, residual stresses and microstructure. By means of an optical surface profiler, the three-dimensional (3D) topography of film surface can be obtained during straining. As expected, the profile of the specimen center remains almost flat in the tensile direction. Nevertheless, a relatively significant curvature evolution (of the same order with the initial curvature induced by residual stresses) is observed along the transverse direction as a result of a Poisson's ratio mismatch between the film and the substrate. Furthermore, finite element method (FEM) has been performed to simulate the curvature evolution considering the geometric nonlinearity and the perfect strain transfer at the interface, which agrees well with the experimental results.

Constant physics and characteristics of fundamental constant

International Nuclear Information System (INIS)

Tarrach, R.

1998-01-01

We present some evidence which supports a surprising physical interpretation of the fundamental constants. First, we relate two of them through the renormalization group. This leaves as many fundamental constants as base units. Second, we introduce and a dimensional system of units without fundamental constants. Third, and most important, we find, while interpreting the units of the a dimensional system, that is all cases accessible to experimentation the fundamental constants indicate either discretization at small values or boundedness at large values of the corresponding physical quantity. (Author) 12 refs

Preputial reconstruction and tubularized incised plate urethroplasty in proximal hypospadias with ventral penile curvature.

Science.gov (United States)

Bhat, Amilal; Gandhi, Ajay; Saxena, Gajendra; Choudhary, Gautam Ram

2010-10-01

Objective of this study was to assess the feasibility and results of preputial reconstruction and tubularized incised plate urethroplasty (TIP) in patients of proximal hypospadias with ventral penile curvature. Twenty-seven patients of proximal hypospadias who underwent preputioplasty with TIP were evaluated retrospectively. Ventral curvature was corrected by mobilization of the urethral plate with the corpus spongiosum and the proximal urethra; dorsal plication was added according to the severity of curvature. Feasibility of preputial reconstruction was assessed by applying 3 stay sutures-the first to fix the skin at the corona, the second at the junction of the inner and outer preputial skin for pulling up the skin over the glans, and the third stay on penile skin at the level of the corona for retracting the skin. Preputial reconstruction consisted of a standard 3 layered re-approximation of the margins of the dorsal hood. Age of the patients varied from 10 months to 21 years with an average of 6 years and 4 months. Ventral curvature (mild 10, moderate 13, and severe 4 cases) was corrected by the mobilization of the urethral plate and spongiosum in 14 patients, 11 cases had mobilization of the proximal urethra in addition and 2 patients required single stitch dorsal plication with the above-mentioned steps. Two patients developed urethral fistula and 1 had preputial dehiscence. Preputioplasty with TIP is feasible in proximal hypospadias with curvature without increasing the complication rate. Postoperative phimosis can be prevented by on-table testing of the adequacy of preputial skin by 3 stay sutures.

Preputial reconstruction and tubularized incised plate urethroplasty in proximal hypospadias with ventral penile curvature

OpenAIRE

Bhat, Amilal; Gandhi, Ajay; Saxena, Gajendra; Choudhary, Gautam Ram

2010-01-01

Aims : Objective of this study was to assess the feasibility and results of preputial reconstruction and tubularized incised plate urethroplasty (TIP) in patients of proximal hypospadias with ventral penile curvature. Materials and Methods : Twenty-seven patients of proximal hypospadias who underwent preputioplasty with TIP were evaluated retrospectively. Ventral curvature was corrected by mobilization of the urethral plate with the corpus spongiosum and the proximal urethra; dorsal plica...

Polarized curvature radiation in pulsar magnetosphere

Science.gov (United States)

Wang, P. F.; Wang, C.; Han, J. L.

2014-07-01

The propagation of polarized emission in pulsar magnetosphere is investigated in this paper. The polarized waves are generated through curvature radiation from the relativistic particles streaming along curved magnetic field lines and corotating with the pulsar magnetosphere. Within the 1/γ emission cone, the waves can be divided into two natural wave-mode components, the ordinary (O) mode and the extraordinary (X) mode, with comparable intensities. Both components propagate separately in magnetosphere, and are aligned within the cone by adiabatic walking. The refraction of O mode makes the two components separated and incoherent. The detectable emission at a given height and a given rotation phase consists of incoherent X-mode and O-mode components coming from discrete emission regions. For four particle-density models in the form of uniformity, cone, core and patches, we calculate the intensities for each mode numerically within the entire pulsar beam. If the corotation of relativistic particles with magnetosphere is not considered, the intensity distributions for the X-mode and O-mode components are quite similar within the pulsar beam, which causes serious depolarization. However, if the corotation of relativistic particles is considered, the intensity distributions of the two modes are very different, and the net polarization of outcoming emission should be significant. Our numerical results are compared with observations, and can naturally explain the orthogonal polarization modes of some pulsars. Strong linear polarizations of some parts of pulsar profile can be reproduced by curvature radiation and subsequent propagation effect.

A generic double-curvature piezoelectric shell energy harvester: Linear/nonlinear theory and applications

Science.gov (United States)

Zhang, X. F.; Hu, S. D.; Tzou, H. S.

2014-12-01

Converting vibration energy to useful electric energy has attracted much attention in recent years. Based on the electromechanical coupling of piezoelectricity, distributed piezoelectric zero-curvature type (e.g., beams and plates) energy harvesters have been proposed and evaluated. The objective of this study is to develop a generic linear and nonlinear piezoelectric shell energy harvesting theory based on a double-curvature shell. The generic piezoelectric shell energy harvester consists of an elastic double-curvature shell and piezoelectric patches laminated on its surface(s). With a current model in the closed-circuit condition, output voltages and energies across a resistive load are evaluated when the shell is subjected to harmonic excitations. Steady-state voltage and power outputs across the resistive load are calculated at resonance for each shell mode. The piezoelectric shell energy harvesting mechanism can be simplified to shell (e.g., cylindrical, conical, spherical, paraboloidal, etc.) and non-shell (beam, plate, ring, arch, etc.) distributed harvesters using two Lamé parameters and two curvature radii of the selected harvester geometry. To demonstrate the utility and simplification procedures, the generic linear/nonlinear shell energy harvester mechanism is simplified to three specific structures, i.e., a cantilever beam case, a circular ring case and a conical shell case. Results show the versatility of the generic linear/nonlinear shell energy harvesting mechanism and the validity of the simplification procedures.

Probability distribution for the Gaussian curvature of the zero level surface of a random function

Science.gov (United States)

Hannay, J. H.

2018-04-01

A rather natural construction for a smooth random surface in space is the level surface of value zero, or ‘nodal’ surface f(x,y,z)  =  0, of a (real) random function f; the interface between positive and negative regions of the function. A physically significant local attribute at a point of a curved surface is its Gaussian curvature (the product of its principal curvatures) because, when integrated over the surface it gives the Euler characteristic. Here the probability distribution for the Gaussian curvature at a random point on the nodal surface f  =  0 is calculated for a statistically homogeneous (‘stationary’) and isotropic zero mean Gaussian random function f. Capitalizing on the isotropy, a ‘fixer’ device for axes supplies the probability distribution directly as a multiple integral. Its evaluation yields an explicit algebraic function with a simple average. Indeed, this average Gaussian curvature has long been known. For a non-zero level surface instead of the nodal one, the probability distribution is not fully tractable, but is supplied as an integral expression.

Spatial variability of physical attributes of an alfisol under different hillslope curvatures Variabilidade espacial de atributos físicos de um argissolo sob diferentes curvaturas do relevo

Directory of Open Access Journals (Sweden)

Livia Arantes Camargo

2010-06-01

Full Text Available The influence of relief forms has been studied by several authors and explains the variability in the soil attributes of a landscape. Soil physical attributes depend on relief forms, and their assessment is important in mechanized agricultural systems, such as of sugarcane. This study aimed to characterize the spatial variability in the physical soil attributes and their relationship to the hillslope curvatures in an Alfisol developed from sandstone and growing sugarcane. Grids of 100 x 100 m were delimited in a convex and a concave area. The grids had a regular spacing of 10 x 10 m, and the crossing points of this spacing determined a total of 121 georeferenced sampling points. Samples were collected to determine the physical attributes related to soil aggregates, porosity, bulk density, resistance to penetration and moisture within the 0-0.2 and 0.2-0.4 m depth. Statistical analyses, geostatistics and Student's t-tests were performed with the means of the areas. All attributes, except aggregates > 2 mm in the 0-0.2 m depth and macroporosity at both depths, showed significant differences between the hillslope curvatures. The convex area showed the highest values of the mean weighted diameter, mean geometric diameter, aggregates > 2 mm, 1-2 mm aggregates, total porosity and moisture and lower values of bulk density and resistance to penetration in both depth compared to the concave area. The number of soil attributes with greater spatial variability was higher in the concave area.A influência das formas do relevo tem sido estudada por diversos autores e explica a variabilidade dos atributos do solo na paisagem. Os atributos físicos do solo são dependentes das formas do relevo, e a avaliação desses atributos é importante em sistemas mecanizados como o da cultura de cana-de-açúcar. O presente estudo teve como objetivo caracterizar a variabilidade espacial dos atributos físicos de Argissolos desenvolvidos de arenito e cultivados com cana

Space-Variant Post-Filtering for Wavefront Curvature Correction in Polar-Formatted Spotlight-Mode SAR Imagery

Energy Technology Data Exchange (ETDEWEB)

DOREN,NEALL E.

1999-10-01

Wavefront curvature defocus effects occur in spotlight-mode SAR imagery when reconstructed via the well-known polar-formatting algorithm (PFA) under certain imaging scenarios. These include imaging at close range, using a very low radar center frequency, utilizing high resolution, and/or imaging very large scenes. Wavefront curvature effects arise from the unrealistic assumption of strictly planar wavefronts illuminating the imaged scene. This dissertation presents a method for the correction of wavefront curvature defocus effects under these scenarios, concentrating on the generalized: squint-mode imaging scenario and its computational aspects. This correction is accomplished through an efficient one-dimensional, image domain filter applied as a post-processing step to PF.4. This post-filter, referred to as SVPF, is precalculated from a theoretical derivation of the wavefront curvature effect and varies as a function of scene location. Prior to SVPF, severe restrictions were placed on the imaged scene size in order to avoid defocus effects under these scenarios when using PFA. The SVPF algorithm eliminates the need for scene size restrictions when wavefront curvature effects are present, correcting for wavefront curvature in broadside as well as squinted collection modes while imposing little additional computational penalty for squinted images. This dissertation covers the theoretical development, implementation and analysis of the generalized, squint-mode SVPF algorithm (of which broadside-mode is a special case) and provides examples of its capabilities and limitations as well as offering guidelines for maximizing its computational efficiency. Tradeoffs between the PFA/SVPF combination and other spotlight-mode SAR image formation techniques are discussed with regard to computational burden, image quality, and imaging geometry constraints. It is demonstrated that other methods fail to exhibit a clear computational advantage over polar-formatting in conjunction

Quantitative analysis of spinal curvature in 3D: application to CT images of normal spine

Energy Technology Data Exchange (ETDEWEB)

Vrtovec, Tomaz; Likar, Bostjan; Pernus, Franjo [University of Ljubljana, Faculty of Electrical Engineering, Trzaska 25, SI-1000 Ljubljana (Slovenia)

2008-04-07

The purpose of this study is to present a framework for quantitative analysis of spinal curvature in 3D. In order to study the properties of such complex 3D structures, we propose two descriptors that capture the characteristics of spinal curvature in 3D. The descriptors are the geometric curvature (GC) and curvature angle (CA), which are independent of the orientation and size of spine anatomy. We demonstrate the two descriptors that characterize the spinal curvature in 3D on 30 computed tomography (CT) images of normal spine and on a scoliotic spine. The descriptors are determined from 3D vertebral body lines, which are obtained by two different methods. The first method is based on the least-squares technique that approximates the manually identified vertebra centroids, while the second method searches for vertebra centroids in an automated optimization scheme, based on computer-assisted image analysis. Polynomial functions of the fourth and fifth degree were used for the description of normal and scoliotic spinal curvature in 3D, respectively. The mean distance to vertebra centroids was 1.1 mm ({+-}0.6 mm) for the first and 2.1 mm ({+-}1.4 mm) for the second method. The distributions of GC and CA values were obtained along the 30 images of normal spine at each vertebral level and show that maximal thoracic kyphosis (TK), thoracolumbar junction (TJ) and maximal lumbar lordosis (LL) on average occur at T3/T4, T12/L1 and L4/L5, respectively. The main advantage of GC and CA is that the measurements are independent of the orientation and size of the spine, thus allowing objective intra- and inter-subject comparisons. The positions of maximal TK, TJ and maximal LL can be easily identified by observing the GC and CA distributions at different vertebral levels. The obtained courses of the GC and CA for the scoliotic spine were compared to the distributions of GC and CA for the normal spines. The significant difference in values indicates that the descriptors of GC and

Quantitative analysis of spinal curvature in 3D: application to CT images of normal spine

International Nuclear Information System (INIS)

Vrtovec, Tomaz; Likar, Bostjan; Pernus, Franjo

2008-01-01

The purpose of this study is to present a framework for quantitative analysis of spinal curvature in 3D. In order to study the properties of such complex 3D structures, we propose two descriptors that capture the characteristics of spinal curvature in 3D. The descriptors are the geometric curvature (GC) and curvature angle (CA), which are independent of the orientation and size of spine anatomy. We demonstrate the two descriptors that characterize the spinal curvature in 3D on 30 computed tomography (CT) images of normal spine and on a scoliotic spine. The descriptors are determined from 3D vertebral body lines, which are obtained by two different methods. The first method is based on the least-squares technique that approximates the manually identified vertebra centroids, while the second method searches for vertebra centroids in an automated optimization scheme, based on computer-assisted image analysis. Polynomial functions of the fourth and fifth degree were used for the description of normal and scoliotic spinal curvature in 3D, respectively. The mean distance to vertebra centroids was 1.1 mm (±0.6 mm) for the first and 2.1 mm (±1.4 mm) for the second method. The distributions of GC and CA values were obtained along the 30 images of normal spine at each vertebral level and show that maximal thoracic kyphosis (TK), thoracolumbar junction (TJ) and maximal lumbar lordosis (LL) on average occur at T3/T4, T12/L1 and L4/L5, respectively. The main advantage of GC and CA is that the measurements are independent of the orientation and size of the spine, thus allowing objective intra- and inter-subject comparisons. The positions of maximal TK, TJ and maximal LL can be easily identified by observing the GC and CA distributions at different vertebral levels. The obtained courses of the GC and CA for the scoliotic spine were compared to the distributions of GC and CA for the normal spines. The significant difference in values indicates that the descriptors of GC and CA

Geometric Thermodynamics: Black Holes and the Meaning of the Scalar Curvature

Directory of Open Access Journals (Sweden)

Miguel Ángel García-Ariza

2014-12-01

Full Text Available In this paper we show that the vanishing of the scalar curvature of Ruppeiner-like metrics does not characterize the ideal gas. Furthermore, we claim through an example that flatness is not a sufficient condition to establish the absence of interactions in the underlying microscopic model of a thermodynamic system, which poses a limitation on the usefulness of Ruppeiner’s metric and conjecture. Finally, we address the problem of the choice of coordinates in black hole thermodynamics. We propose an alternative energy representation for Kerr-Newman black holes that mimics fully Weinhold’s approach. The corresponding Ruppeiner’s metrics become degenerate only at absolute zero and have non-vanishing scalar curvatures.

Tubular bending and pull-out forces in high-curvature well bores

International Nuclear Information System (INIS)

Dareing, D.W.; Ahlers, C.A.

1991-01-01

This paper is concerned with drag forces developed on tubulars in high-curvature well bores typically found in drainhole and horizontal drilling. The dog-leg severity of these types of boreholes are considerably higher than those typically found in conventional directional drilling. The objective of the study was to determine the significance of bending stiffness on drag forces in the pull-out mode. The method of analysis treats the tubular as a multi-spanned curved beam under tension and solves for radial displacements, slope, shear and bending moment over each span. Calculations show that bending stiffness is a minor factor provided there are no locally severe dog legs superimposed in the high-curvature well bore

A high resolution electron microscopy investigation of curvature in multilayer graphite sheets

International Nuclear Information System (INIS)

Wang Zhenxia; Hu Jun; Wang Wenmin; Yu Guoqing

1998-01-01

Here the authors report a carbon sample generated by ultrasonic wave high oriented pyrolytic graphite (HOPG) in ethanol, water or ethanol-water mixed solution. High resolution transmission electron microscopy (HRTEM) revealed many multilayer graphite sheets with a total curved angle that is multiples of θ 0 (= 30 degree C). Close examination of the micrographs showed that the curvature is accomplished by bending the lattice planes. A possible explanation for the curvature in multilayer graphite sheets is discussed based on the conformation of graphite symmetry axes and the formation of sp 3 -like line defects in the sp 2 graphitic network

Spin-curvature interaction from curved Dirac equation: Application to single-wall carbon nanotubes

Science.gov (United States)

Zhang, Kai; Zhang, Erhu; Chen, Huawei; Zhang, Shengli

2017-06-01

The spin-curvature interaction (SCI) and its effects are investigated based on curved Dirac equation. Through the low-energy approximation of curved Dirac equation, the Hamiltonian of SCI is obtained and depends on the geometry and spinor structure of manifold. We find that the curvature can be considered as field strength and couples with spin through Zeeman-like term. Then, we use dimension reduction to derive the local Hamiltonian of SCI for cylinder surface, which implies that the effective Hamiltonian of single-wall carbon nanotubes results from the geometry and spinor structure of lattice and includes two types of interactions: one does not break any symmetries of the lattice and only shifts the Dirac points for all nanotubes, while the other one does and opens the gaps except for armchair nanotubes. At last, analytical expressions of the band gaps and the shifts of their positions induced by curvature are given for metallic nanotubes. These results agree well with experiments and can be verified experimentally.

A curvature-based weighted fuzzy c-means algorithm for point clouds de-noising

Science.gov (United States)

Cui, Xin; Li, Shipeng; Yan, Xiutian; He, Xinhua

2018-04-01

In order to remove the noise of three-dimensional scattered point cloud and smooth the data without damnify the sharp geometric feature simultaneity, a novel algorithm is proposed in this paper. The feature-preserving weight is added to fuzzy c-means algorithm which invented a curvature weighted fuzzy c-means clustering algorithm. Firstly, the large-scale outliers are removed by the statistics of r radius neighboring points. Then, the algorithm estimates the curvature of the point cloud data by using conicoid parabolic fitting method and calculates the curvature feature value. Finally, the proposed clustering algorithm is adapted to calculate the weighted cluster centers. The cluster centers are regarded as the new points. The experimental results show that this approach is efficient to different scale and intensities of noise in point cloud with a high precision, and perform a feature-preserving nature at the same time. Also it is robust enough to different noise model.

Prediction of residual stress distribution in multi-stacked thin film by curvature measurement and iterative FEA

International Nuclear Information System (INIS)

Choi, Hyeon Chang; Park, Jun Hyub

2005-01-01

In this study, residual stress distribution in multi-stacked film by MEMS (Micro-Electro Mechanical System) process is predicted using Finite Element Method (FEM). We develop a finite element program for REsidual Stress Analysis (RESA) in multi-stacked film. The RESA predicts the distribution of residual stress field in multi-stacked film. Curvatures of multi-stacked film and single layers which consist of the multi-stacked film are used as the input to the RESA. To measure those curvatures is easier than to measure a distribution of residual stress. To verify the RESA, mean stresses and stress gradients of single and multilayers are measured. The mean stresses are calculated from curvatures of deposited wafer by using Stoney's equation. The stress gradients are calculated from the vertical deflection at the end of cantilever beam. To measure the mean stress of each layer in multi-stacked film, we measure the curvature of wafer with the film after etching layer by layer in multi-stacked film

Penrose inequality in anti-de Sitter space

Science.gov (United States)

Husain, Viqar; Singh, Suprit

2017-11-01

For asymptotically flat spacetimes the Penrose inequality gives an initial data test for the weak cosmic censorship hypothesis. We give a formulation of this inequality for asymptotically anti-de Sitter (AAdS) spacetimes, and show that the inequality holds for time asymmetric data in spherical symmetry. Our analysis is motivated by the constant-negative-spatial-curvature form of the AdS black hole metric.

Error in the determination of the deformed shape of prismatic beams using the double integration of curvature

Science.gov (United States)

Sigurdardottir, Dorotea H.; Stearns, Jett; Glisic, Branko

2017-07-01

The deformed shape is a consequence of loading the structure and it is defined by the shape of the centroid line of the beam after deformation. The deformed shape is a universal parameter of beam-like structures. It is correlated with the curvature of the cross-section; therefore, any unusual behavior that affects the curvature is reflected through the deformed shape. Excessive deformations cause user discomfort, damage to adjacent structural members, and may ultimately lead to issues in structural safety. However, direct long-term monitoring of the deformed shape in real-life settings is challenging, and an alternative is indirect determination of the deformed shape based on curvature monitoring. The challenge of the latter is an accurate evaluation of error in the deformed shape determination, which is directly correlated with the number of sensors needed to achieve the desired accuracy. The aim of this paper is to study the deformed shape evaluated by numerical double integration of the monitored curvature distribution along the beam, and create a method to predict the associated errors and suggest the number of sensors needed to achieve the desired accuracy. The error due to the accuracy in the curvature measurement is evaluated within the scope of this work. Additionally, the error due to the numerical integration is evaluated. This error depends on the load case (i.e., the shape of the curvature diagram), the magnitude of curvature, and the density of the sensor network. The method is tested on a laboratory specimen and a real structure. In a laboratory setting, the double integration is in excellent agreement with the beam theory solution which was within the predicted error limits of the numerical integration. Consistent results are also achieved on a real structure—Streicker Bridge on Princeton University campus.

Critical dimension of strings with an extrinsic curvature

International Nuclear Information System (INIS)

Matsuki, T.; Viswanathan, K.S.

1988-01-01

The conformal anomaly is calculated by using the path-integral method to determine the critical dimension for a string theory with an extrinsic curvature by appropriately defining the first-order form of this Lagrangian. The critical dimension, defined by the vanishing of the Liouville kinetic term, is found to be D = 26, the same as for the ordinary bosonic string theory

Curvature of super Diff(S1)/S1

International Nuclear Information System (INIS)

Oh, P.; Ramond, P.

1987-01-01

Motivated by the work of Bowick and Rajeev, we calculate the curvature of the infinite-dimensional flag manifolds Diff(S 1 )/S 1 and Super Diff(S 1 )/S 1 using standard finite-dimensional coset space techniques. We regularize the infinite by ζ-function regularization and recover the conformal and superconformal anomalies respectively for a specific choice of the torsion. (orig.)

Dielectric constant and electrical conductivity of contaminated fine-grained soils and barrier materials

International Nuclear Information System (INIS)

Kaya, A.; Fang, H.Y.; Inyang, H.I.

1997-01-01

Characterization of contaminated fine-grained soils and tracking of contaminant migration within barriers have been challenging because current methods and/or procedures are labor and time-intensive, and destructive. To demonstrate the effective use of both dielectric constant and electrical conductivity in the characterization of contaminated fine-grained soils, pore fluids were prepared at different ionic strengths, and were used as permeates for kaolinite, bentonite and a local soil. Then, both dielectric constant and electrical conductivity of the soils were measured by means of a capacitor over a wide range of frequencies and moisture content. It was observed that although each soil has its unique dielectric constant and electrical conductivity at a given moisture content, increases in ionic strength cause a decrease in the dielectric constant of the system at very high frequencies (MHZ), whereas the dielectric constant increases at low frequencies (kHz). Electrical conductivity of a soil-water system is independent of frequency. However, it is a function of ionic strength of the pore fluid. It is clearly demonstrated that dielectric constant and electrical conductivity of soils are functions of both moisture content and ionic strength, and can be used to characterize the spatial and temporal levels of contamination. This method/procedure can be used in estimating the level of contamination as well as the direction of contaminant movement in the subsurface without the use of extensive laboratory testing. Based on obtained results, it was concluded that the proposed method/procedure is promising because it is non-destructive and provides a quick means of assessing the spatial distribution of contaminants in fine-grained soils and barriers

On the Curvature and Heat Flow on Hamiltonian Systems

Directory of Open Access Journals (Sweden)

Ohta Shin-ichi

2014-01-01

Full Text Available We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theorem, and study the heat flow.

Axial Length/Corneal Radius of Curvature Ratio and Refractive ...

African Journals Online (AJOL)

2017-12-05

Dec 5, 2017 ... variously described as determined by the ocular biometric variables. There have been many studies on the relationship between refractive error and ocular axial length (AL), anterior chamber depth, corneal radius of curvature (CR), keratometric readings as well as other ocular biometric variables such as ...

Rigidity of complete noncompact bach-flat n-manifolds

Science.gov (United States)

Chu, Yawei; Feng, Pinghua

2012-11-01

Let (Mn,g) be a complete noncompact Bach-flat n-manifold with the positive Yamabe constant and constant scalar curvature. Assume that the L2-norm of the trace-free Riemannian curvature tensor R∘m is finite. In this paper, we prove that (Mn,g) is a constant curvature space if the L-norm of R∘m is sufficiently small. Moreover, we get a gap theorem for (Mn,g) with positive scalar curvature. This can be viewed as a generalization of our earlier results of 4-dimensional Bach-flat manifolds with constant scalar curvature R≥0 [Y.W. Chu, A rigidity theorem for complete noncompact Bach-flat manifolds, J. Geom. Phys. 61 (2011) 516-521]. Furthermore, when n>9, we derive a rigidity result for R<0.

A Hybrid Interpolation Method for Geometric Nonlinear Spatial Beam Elements with Explicit Nodal Force

Directory of Open Access Journals (Sweden)

Huiqing Fang

2016-01-01

Full Text Available Based on geometrically exact beam theory, a hybrid interpolation is proposed for geometric nonlinear spatial Euler-Bernoulli beam elements. First, the Hermitian interpolation of the beam centerline was used for calculating nodal curvatures for two ends. Then, internal curvatures of the beam were interpolated with a second interpolation. At this point, C1 continuity was satisfied and nodal strain measures could be consistently derived from nodal displacement and rotation parameters. The explicit expression of nodal force without integration, as a function of global parameters, was founded by using the hybrid interpolation. Furthermore, the proposed beam element can be degenerated into linear beam element under the condition of small deformation. Objectivity of strain measures and patch tests are also discussed. Finally, four numerical examples are discussed to prove the validity and effectivity of the proposed beam element.

Surgical Outcomes of Plaque Excision and Grafting and Supplemental Tunica Albuginea Plication for Treatment of Peyronie's Disease With Severe Compound Curvature.

Science.gov (United States)

Chow, Alexander K; Sidelsky, Steven A; Levine, Laurence A

2018-05-22

There are limited data in the literature that describe the management of Peyronie's disease (PD) with severe compound curvature, which often requires additional straightening procedures after plaque excision and grafting (PEG) to achieve functional penile straightening (compound curvature treated with PEG and supplemental tunica albuginea plication (TAP). We performed a retrospective chart review of patients with PD and acute angulation who underwent PEG (group 1) and patients with compound curvature who underwent PEG with TAP (group 2) between 2007 and 2016. Primary post-operative outcomes of interest include change in penile curvature, change in measured stretched penile length, and subjective report on penile sensation and sexually induced penile rigidity. 240 Men with PD were included in the study, of which 79 (33%) patients in group 1 underwent PEG and 161 (67%) in group 2 underwent PEG and TAP. There was no difference in associated PD co-morbidities including age, hypertension, hyperlipidemia, hypogonadism, diabetes, or tobacco use. After artificial induction of erection with intracorporal trimix injection, the average primary curvature was 73 (range, 20-120) degrees for group 1 compared to 79 (range, 35-140) degrees for group 2 (P = .01). Group 2 had an average secondary curvature of 36 (20-80 degrees). After completion of PEG, men in group 2 had an average residual curvature of 30 (range, 20-50) degrees which required 1-6 TAPs to achieve functional straightness (compound curvature to date. Limitations of this study include the retrospective nature of the analysis as well as the lack of a validated objective measurement of erectile function after penile straightening. Our study found no baseline difference in underlying co-morbidities in men with severe compound curvature compared with men with acute severe angulated curvature. Men with severe compound curvature represent a severe and under-recognized population of men with PD who can be surgically

Gravitational curvature an introduction to Einstein's theory

CERN Document Server

Frankel, Theodore Thomas

1979-01-01

This classic text and reference monograph applies modern differential geometry to general relativity. A brief mathematical introduction to gravitational curvature, it emphasizes the subject's geometric essence, replacing the often-tedious analytical computations with geometric arguments. Clearly presented and physically motivated derivations express the deflection of light, Schwarzchild's exterior and interior solutions, and the Oppenheimer-Volkoff equations. A perfect choice for advanced students of mathematics, this volume will also appeal to mathematicians interested in physics. It stresses

Efficacy of prophylactic splenectomy for proximal advanced gastric cancer invading greater curvature.

Science.gov (United States)

Ohkura, Yu; Haruta, Shusuke; Shindoh, Junichi; Tanaka, Tsuyoshi; Ueno, Masaki; Udagawa, Harushi

2017-05-25

For proximal gastric cancer invading the greater curvature, concomitant splenectomy is frequently performed to secure the clearance of lymph node metastases. However, prognostic impact of prophylactic splenectomy remains unclear. The aim of this study was to clarify the oncological significance of prophylactic splenectomy for advanced proximal gastric cancer invading the greater curvature. Retrospective review of 108 patients who underwent total or subtotal gastrectomy for advanced proximal gastric cancer involving the greater curvature was performed. Short-term and long-term outcomes were compared between the patients who underwent splenectomy (n = 63) and those who did not (n = 45). Patients who underwent splenectomy showed higher amount of blood loss (538 vs. 450 mL, p = 0.016) and morbidity rate (30.2 vs. 13.3, p = 0.041) compared with those who did not undergo splenectomy. In particular, pancreas-related complications were frequently observed among patients who received splenectomy (17.4 vs. 0%, p = 0.003). However, no significant improvement of long-term outcomes were confirmed in the cases with splenectomy (5-year recurrence-free rate, 60.2 vs. 67.3%; p = 0.609 and 5-year overall survival rates, 63.7 vs. 73.6%; p = 0.769). On the other hand, splenectomy was correlated with marginally better survival in patients with Borrmann type 1 or 2 gastric cancer (p = 0.072). For advanced proximal gastric cancer involving the greater curvature, prophylactic splenectomy may have no significant prognostic impact despite the increased morbidity rate after surgery. Such surgical procedure should be avoided as long as lymph node involvement is not evident.

The transformation of spinal curvature into spinal deformity: pathological processes and implications for treatment

Directory of Open Access Journals (Sweden)

Hawes Martha C

2006-03-01

Full Text Available Abstract Background This review summarizes what is known about the pathological processes (e.g. structural and functional changes, by which spinal curvatures develop and evolve into spinal deformities. Methods Comprehensive review of articles (English language only published on 'scoliosis,' whose content yielded data on the pathological changes associated with spinal curvatures. Medline, Science Citation Index and other searches yielded > 10,000 titles each of which was surveyed for content related to 'pathology' and related terms such as 'etiology,' 'inheritance,' 'pathomechanism,' 'signs and symptoms.' Additional resources included all books published on 'scoliosis' and available through the Arizona Health Sciences Library, Interlibrary Loan, or through direct contact with the authors or publishers. Results A lateral curvature of the spine–'scoliosis'–can develop in association with postural imbalance due to genetic defects and injury as well as pain and scarring from trauma or surgery. Irrespective of the factor that triggers its appearance, a sustained postural imbalance can result, over time, in establishment of a state of continuous asymmetric loading relative to the spinal axis. Recent studies support the longstanding hypothesis that spinal deformity results directly from such postural imbalance, irrespective of the primary trigger, because the dynamics of growth within vertebrae are altered by continuous asymmetric mechanical loading. These data suggest that, as long as growth potential remains, evolution of a spinal curvature into a spinal deformity can be prevented by reversing the state of continuous asymmetric loading. Conclusion Spinal curvatures can routinely be diagnosed in early stages, before pathological deformity of the vertebral elements is induced in response to asymmetric loading. Current clinical approaches involve 'watching and waiting' while mild reversible spinal curvatures develop into spinal deformities with

On the calculation of principle curvatures of the left-ventricular surfaces.

Science.gov (United States)

Claus, Piet; Choi, Hon Fai; D'hooge, Jan; Rademakers, Frank E

2008-01-01

A local description of the shape of the left ventricle is relevant in assessing the process of adverse ventricular remodeling, associated with most cardiac pathologies, and in monitoring reverse remodeling by therapy. To quantify local shape of the left ventricle, one can calculate the curvature of its epicardial or endocardial surface. The 3D geometry of the heart and especially the ventricles, can typically be described using finite element meshes. From a mathematical point of view these meshes provide a local parametrization of the surface in the 3-dimensional space. We discuss the analytic derivation of the principle curvatures of the left-ventricular surfaces given their smooth finite-element meshes and apply this derivation to assess the regional shape of the normal porcine left ventricle.

Twistor theory and the energy-momentum and angular momentum of the gravitational field at spatial infinity

International Nuclear Information System (INIS)

Shaw, W.T.

1983-01-01

Penrose's 'quasi-local mass and angular momentum' is investigated for 2-surfaces near spatial infinity in both linearized theory on Minkowski space and full general relativity. It is shown that for space-times that are radially smooth of order one in the sense of Beig and Schmidt with asymptotically electric Weyl curvature, there exists a global concept of a twistor space at spatial infinity. Global conservation laws for the energy-momentum and angular momentum are obtained, and the ten conserved quantities are shown to be invariant under asymptotic coordinate transformations. The relation to other definitions is discussed briefly. (author)

Constraining inverse-curvature gravity with supernovae.

Science.gov (United States)

Mena, Olga; Santiago, José; Weller, Jochen

2006-02-03

We show that models of generalized modified gravity, with inverse powers of the curvature, can explain the current accelerated expansion of the Universe without resorting to dark energy and without conflicting with solar system experiments. We have solved the Friedmann equations for the full dynamical range of the evolution of the Universe and performed a detailed analysis of supernovae data in the context of such models that results in an excellent fit. If we further include constraints on the current expansion of the Universe and on its age, we obtain that the matter content of the Universe is 0.07baryonic matter component.

Zero curvature-surface driven small objects

Science.gov (United States)

Dou, Xiaoxiao; Li, Shanpeng; Liu, Jianlin

2017-08-01

In this study, we investigate the spontaneous migration of small objects driven by surface tension on a catenoid, formed by a layer of soap constrained by two rings. Although the average curvature of the catenoid is zero at each point, the small objects always migrate to the position near the ring. The force and energy analyses have been performed to uncover the mechanism, and it is found that the small objects distort the local shape of the liquid film, thus making the whole system energetically favorable. These findings provide some inspiration to design microfluidics, aquatic robotics, and miniature boats.

Torsion and curvature in higher dimensional supergravity theories

International Nuclear Information System (INIS)

Smith, A.W.; Pontificia Univ. Catolica do Rio de Janeiro

1983-01-01

This work is an extension of Dragon's theorems to higher dimensional space-time. It is shown that the first set of Bianchi identities allow us to express the curvature components in terms of torsion components and its covariant derivatives. It is also shown that the second set of Bianchi identities does not give any new information which is not already contained in the first one. (Author) [pt

Reflectionlessness, kurtosis and top curvature of potential barriers

International Nuclear Information System (INIS)

Ahmed, Zafar

2006-01-01

Apart from the rectangular barrier, other barriers having a single maximum generally display reflectivity, R(E), as a smoothly decreasing function of energy. We conjecture that symmetric potential barriers with a single maximum entail zeros or sharp minima in R(E) provided they have either their coefficient of kurtosis lying in the range (1.8, 3.0), or their top curvature as zero, or both

Induction of Plant Curvature by Magnetophoresis and Cytoskeletal Changes during Root Graviresponse

Science.gov (United States)

Hasenstein, Karl H.; Kuznetsov, Oleg A.; Blancaflor, Eilson B.

1996-01-01

High gradient magnetic fields (HGMF) induce curvature in roots and shoots. It is considered that this response is likely to be based on the intracellular displacement of bulk starch (amyloplasts) by the ponderomotive force generated by the HGMF. This process is called magnetophoresis. The differential elongation during the curvature along the concave and convex flanks of growing organs may be linked to the microtubular and/or microfilament cytoskeleton. The possible existence of an effect of the HGMF on the cytoskeleton was tested for, but none was found. The application of cytoskeletal stabilizers or depolymerizers showed that neither microtubules, nor microfilaments, are involved in the graviresponse.

Distance constant of the Risø cup anemometer

DEFF Research Database (Denmark)

Kristensen, L.; Frost Hansen, O.

2002-01-01

The theory for cup-anemometer dynamics is presented in some detail and two methods of obtaining the distance constant lo are discussed. The first method is based on wind tunnel measurements: with a constant wind speed the cup anemometer is released from alocked position of the rotor...... and the increasing rotation rate recorded. It is concluded that the rapid increase in rotation rate makes the method very inaccurate. The second method consists of an analysis of turbulent, atmospheric of wind speed asmeasured by the cup anemometer and a fast-responding sonic anemometer with a spatial eddy...... resolution which is significantly better than that which can be obtained by a cup anemometer. The ratio between the measured power spectra of the horizontal windspeed by the two instruments contains the necessary information for determining the response characteristics of the cup anemometer and thereby lo...