Symmetry rules for the indirect nuclear spin-spin coupling tensor revisited

NASA Astrophysics Data System (ADS)

Buckingham, A. D.; Pyykkö, P.; Robert, J. B.; Wiesenfeld, L.

The symmetry rules of Buckingham and Love (1970), relating the number of independent components of the indirect spin-spin coupling tensor J to the symmetry of the nuclear sites, are shown to require modification if the two nuclei are exchanged by a symmetry operation. In that case, the anti-symmetric part of J does not transform as a second-rank polar tensor under symmetry operations that interchange the coupled nuclei and may be called an anti-tensor. New rules are derived and illustrated by simple molecular models.

Notes on Translational and Rotational Properties of Tensor Fields in Relativistic Quantum Mechanics

NASA Astrophysics Data System (ADS)

Dvoeglazov, V. V.

Recently, several discussions on the possible observability of 4-vector fields have been published in literature. Furthermore, several authors recently claimed existence of the helicity=0 fundamental field. We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We study the massless limits. In fact, a theoretical motivation for this venture is the old papers of Ogievetskiĭ and Polubarinov, Hayashi, and Kalb and Ramond. Ogievetskiĭ and Polubarinov proposed the concept of the notoph, whose helicity properties are complementary to those of the photon. We analyze the quantum field theory with taking into account mass dimensions of the notoph and the photon. It appears to be possible to describe both photon and notoph degrees of freedom on the basis of the modified Bargmann-Wigner formalism for the symmetric second-rank spinor. Next, we proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. Due to serious problems with the interpretation of the results obtained on using the standard procedure we generalize it and obtain the spin-2 relativistic equations, which are consistent with the general relativity. Thus, in fact we deduced the gravitational field equations from relativistic quantum mechanics. The relations of this theory with the scalar-tensor theories of gravitation and f(R) are discussed. Particular attention has been paid to the correct definitions of the energy-momentum tensor and other Nöther currents in the electromagnetic theory, the relativistic theory of gravitation, the general relativity, and their generalizations. We estimate possible interactions, fermion-notoph, graviton-notoph, photon-notoph, and we conclude that they can probably be seen in experiments in the next few years.

A new unified theory of electromagnetic and gravitational interactions

NASA Astrophysics Data System (ADS)

Li, Li-Xin

2016-12-01

In this paper we present a new unified theory of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of field equations in the four-dimensional spacetime from the fivedimensional Einstein field equation. Besides the Einstein field equation in the four-dimensional spacetime, an electromagnetic field equation is obtained: ∇a F ab - ξ R b a A a = -4π J b with ξ = -2, where F ab is the antisymmetric electromagnetic field tensor defined by the potential vector A a , R ab is the Ricci curvature tensor of the hypersurface, and J a is the electric current density vector. The electromagnetic field equation differs from the Einstein-Maxwell equation by a curvature-coupled term ξ R b a A a , whose presence addresses the problem of incompatibility of the Einstein-Maxwell equation with a universe containing a uniformly distributed net charge, as discussed in a previous paper by the author [L.-X. Li, Gen. Relativ. Gravit. 48, 28 (2016)]. Hence, the new unified theory is physically different from Kaluza-Klein theory and its variants in which the Einstein-Maxwell equation is derived. In the four-dimensional Einstein field equation derived in the new theory, the source term includes the stress-energy tensor of electromagnetic fields as well as the stress-energy tensor of other unidentified matter. Under certain conditions the unidentified matter can be interpreted as a cosmological constant in the four-dimensional spacetime. We argue that, the electromagnetic field equation and hence the unified theory presented in this paper can be tested in an environment with a high mass density, e.g., inside a neutron star or a white dwarf, and in the early epoch of the universe.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahuatzin, G.; Bautista, I.; Hernandez-Lopez, J. A.

A constant antisymmetric 2-tensor can arise in general relativity with spontaneous symmetry breaking or in field theories formulated in a noncommutative space-time. In this work, the one-loop contribution of a nonstandard WW{gamma} vertex on the flavor violating quark transition q{sub i}{yields}q{sub j}{gamma} is studied in the context of the electroweak Yang-Mills sector extended with a Lorentz-violating constant 2-tensor. An exact analytical expression for the on-shell case is presented. It is found that the loop amplitude is gauge independent, electromagnetic gauge invariant, and free of ultraviolet divergences. The dipolar contribution to the b{yields}s{gamma} transition together with the experimental data on themore » B{yields}X{sub s{gamma}} decay is used to derive the constraint {Lambda}{sub LV}>1.96 TeV on the Lorentz-violating scale.« less

An efficient matrix-matrix multiplication based antisymmetric tensor contraction engine for general order coupled cluster.

PubMed

Hanrath, Michael; Engels-Putzka, Anna

2010-08-14

In this paper, we present an efficient implementation of general tensor contractions, which is part of a new coupled-cluster program. The tensor contractions, used to evaluate the residuals in each coupled-cluster iteration are particularly important for the performance of the program. We developed a generic procedure, which carries out contractions of two tensors irrespective of their explicit structure. It can handle coupled-cluster-type expressions of arbitrary excitation level. To make the contraction efficient without loosing flexibility, we use a three-step procedure. First, the data contained in the tensors are rearranged into matrices, then a matrix-matrix multiplication is performed, and finally the result is backtransformed to a tensor. The current implementation is significantly more efficient than previous ones capable of treating arbitrary high excitations.

Chiral discrimination in NMR spectroscopy: computation of the relevant molecular pseudoscalars

NASA Astrophysics Data System (ADS)

Buckingham, A. David; Lazzeretti, Paolo; Pelloni, Stefano

2015-07-01

Nuclear magnetic resonance (NMR) is normally blind to chirality but it has been predicted that precessing nuclear spins in a strong magnetic field induce a rotating electric polarisation that is of opposite sign for enantiomers. The polarisation is determined by two pseudoscalars, ? and ?. The former arises from the distortion of the electronic structure by the nuclear magnetic moment in the presence of the strong magnetic field and is equivalent to the linear effect of an electric field on the nuclear shielding tensor. ? determines the temperature-dependent partial orientation of the permanent electric dipole moment of the molecule by the antisymmetric part of the nuclear shielding tensor. Computations of these two contributions are reported for the nuclei in the chiral molecules N-methyloxaziridine, 2-methyloxirane, 1,3-dimethylallene, 1-fluoroethanol, 2-fluoroazirine, 1,2-M-dioxin, 1,2-M-dithiin, 1,2-M-diselenin and 1,2-M-ditellurin. For strongly dipolar molecules, ? is typically two to three orders of magnitude greater than ?, raising hopes for the detection of chirality in NMR spectroscopy. This paper is dedicated to the memory of Prof. Nicholas Handy, F.R.S.

Hydrodynamical model of anisotropic, polarized turbulent superfluids. I: constraints for the fluxes

NASA Astrophysics Data System (ADS)

Mongiovì, Maria Stella; Restuccia, Liliana

2018-02-01

This work is the first of a series of papers devoted to the study of the influence of the anisotropy and polarization of the tangle of quantized vortex lines in superfluid turbulence. A thermodynamical model of inhomogeneous superfluid turbulence previously formulated is here extended, to take into consideration also these effects. The model chooses as thermodynamic state vector the density, the velocity, the energy density, the heat flux, and a complete vorticity tensor field, including its symmetric traceless part and its antisymmetric part. The relations which constrain the constitutive quantities are deduced from the second principle of thermodynamics using the Liu procedure. The results show that the presence of anisotropy and polarization in the vortex tangle affects in a substantial way the dynamics of the heat flux, and allow us to give a physical interpretation of the vorticity tensor here introduced, and to better describe the internal structure of a turbulent superfluid.

Classical theory of radiating strings

NASA Technical Reports Server (NTRS)

Copeland, Edmund J.; Haws, D.; Hindmarsh, M.

1990-01-01

The divergent part of the self force of a radiating string coupled to gravity, an antisymmetric tensor and a dilaton in four dimensions are calculated to first order in classical perturbation theory. While this divergence can be absorbed into a renormalization of the string tension, demanding that both it and the divergence in the energy momentum tensor vanish forces the string to have the couplings of compactified N = 1 D = 10 supergravity. In effect, supersymmetry cures the classical infinities.

Coleman-Weinberg symmetry breaking in SU(8) induced by a third rank antisymmetric tensor scalar field II: the fermion spectrum

NASA Astrophysics Data System (ADS)

Adler, Stephen L.

2017-07-01

We continue our study of Coleman-Weinberg symmetry breaking induced by a third rank antisymmetric tensor scalar, in the context of the SU(8) model (Adler 2014 Int. J. Mod. Phys. A 29 1450130) we proposed earlier. We focus in this paper on qualitative features that will determine whether the model can make contact with the observed particle spectrum. We discuss the mechanism for giving the spin \\frac{3}{2} field a mass by the BEH mechanism, and analyze the remaining massless spin \\frac{1}{2} fermions, the global chiral symmetries, and the running couplings after symmetry breaking. We note that the smallest gluon mass matrix eigenvalue has an eigenvector suggestive of U(1) B-L , and conjecture that the theory runs to an infrared fixed point at which there is a massless gluon with 3 to  -1 ratios in generator components. Assuming this, we discuss a mechanism for making contact with the standard model, based on a conjectured asymmetric breaking of Sp(4) to SU(2) subgroups, one of which is the electroweak SU(2), and the other of which is a ‘technicolor’ group that binds the original SU(8) model fermions, which play the role of ‘preons’, into composites. Quarks can emerge as 5 preon composites and leptons as 3 preon composites, with consequent stability of the proton against decay to a single lepton plus a meson. A composite Higgs boson can emerge as a two preon composite. Since anomaly matching for the relevant conserved global symmetry current is not obeyed by three fermion families, emergence of three composite families requires formation of a Goldstone boson with quantum numbers matching this current, which can be a light dark matter candidate.

Separability of massive field equations for spin-0 and spin-1/2 charged particles in the general nonextremal rotating charged black hole spacetimes in minimal five-dimensional gauged supergravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu Shuangqing

We continue to investigate the separability of massive field equations for spin-0 and spin-1/2 charged particles in the general, nonextremal, rotating, charged, Chong-Cvetic-Lue-Pope black holes with two independent angular momenta and a nonzero cosmological constant in minimal D=5 gauged supergravity theory. We show that the complex Klein-Gordon equation and the modified Dirac equation with the inclusion of an extra counterterm can be separated by variables into purely radial and purely angular parts in this general Einstein-Maxwell-Chern-Simons background spacetime. A second-order symmetry operator that commutes with the complex Laplacian operator is constructed from the separated solutions and expressed compactly in termsmore » of a rank-2 Staeckel-Killing tensor which admits a simple diagonal form in the chosen pentad one-forms so that it can be understood as the square of a rank-3 totally antisymmetric tensor. A first-order symmetry operator that commutes with the modified Dirac operator is expressed in terms of a rank-3 generalized Killing-Yano tensor and its covariant derivative. The Hodge dual of this generalized Killing-Yano tensor is a generalized principal conformal Killing-Yano tensor of rank-2, which can generate a 'tower' of generalized (conformal) Killing-Yano and Staeckel-Killing tensors that are responsible for the whole hidden symmetries of this general, rotating, charged, Kerr-anti-de Sitter black hole geometry. In addition, the first laws of black hole thermodynamics have been generalized to the case that the cosmological constant can be viewed as a thermodynamical variable.« less

Computations of the chirality-sensitive effect induced by an antisymmetric indirect spin–spin coupling

NASA Astrophysics Data System (ADS)

Garbacz, Piotr

2018-05-01

Results of quantum mechanical computations of the antisymmetric part of the indirect spin-spin coupling tensor, ?, performed using the coupled-cluster method, the second-order polarisation propagator approximation, and the density functional theory for 25 molecules and nearly 100 spin-spin couplings are reported. These results are used for an estimation of the magnitude of the recently proposed liquid-state nuclear magnetic resonance chirality-sensitive effect, which allows to determine the molecular chirality directly, i.e. without the need for the application of any chiral agent. The following were found: (i) the antisymmetry J⋆ is usually larger for the coupling between spins separated by two chemical bonds in comparison with the coupling through one bond, (ii) promising samples are those which contain fluorine, and (iii) the antisymmetry of the spin-spin coupling tensor is of the order of a few hertz for commercially available chemical compounds. Therefore, the relevant property of the experiment, the pseudoscalar Jc, for them is of the order of 1 nHz m/V.

Lie-Santilli isoapproach to the unification of gravity and electromagnetism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Animalu, A.O.E.

1996-06-01

The author reviews the problem of Einstein`s original proposal for the unification of gravity and electromagnetism in space-time differential geometry along the lines of the recent contributions by A.A. Logunov, R.M. Santilli, D.F. Lopez and others. The author presents a new method of unification based on the Lie-Santilli isotopic theory whereby the unified field tensor g = (g{sub {mu}{nu}}) is constructed from the symmetric Riemannian gravitational tensor, g = (g{mu}{nu}), and the antisymmetric electromagnetic field tensor F = (F{sub {mu}{nu}}) via an isotopic lifting g {yields} {cflx g} = Fg of the type of Lax pairing, where det F {ne}more » 0, the unified field {cflx g} satisfies Logunov-Santilli equations while g and F are treated as Lax pair. Because of Santilli`s isotopic equivalence between Minkowskian and Riemannian geometries, the author infers that in the Minkowskian limit F = f, g = {eta}, the metric {eta} satisfies Lax`s equation of motion {partial_derivative}{eta}/{partial_derivative}t = f{eta} {minus} {eta}f which insures the conservation of the eigenvalues of g. The invariance of the electromagnetic group of transformations (F) in Minkowski space is determined by the eigenvalue equations, det (F{sub {mu}{nu}}){minus}{lambda}{eta}{sub {mu}{nu}} = 0, from which the author deduces a Lie-isotopic {open_quotes}extended{close_quotes} relativity principle. A wave equation for a spin-2 particle in the unified field is derived, and the experimental consequences of the theory are discussed.« less

Short-range correlation in high-momentum antisymmetrized molecular dynamics

NASA Astrophysics Data System (ADS)

Myo, Takayuki

2018-03-01

We propose a new variational method for treating short-range repulsion of bare nuclear force for nuclei in antisymmetrized molecular dynamics (AMD). In AMD, the short-range correlation is described in terms of large imaginary centroids of Gaussian wave packets of nucleon pairs in opposite signs, causing high-momentum components in the nucleon pairs. We superpose these AMD basis states and call this method "high-momentum AMD" (HM-AMD), which is capable of describing the strong tensor correlation [T. Myo et al., Prog. Theor. Exp. Phys., 2017, 111D01 (2017)]. In this letter, we extend HM-AMD by including up to two kinds of nucleon pairs in each AMD basis state utilizing the cluster expansion, which produces many-body correlations involving high-momentum components. We investigate how well HM-AMD describes the short-range correlation by showing the results for ^3H using the Argonne V4^' central potential. It is found that HM-AMD reproduces the results of few-body calculations and also the tensor-optimized AMD. This means that HM-AMD is a powerful approach to describe the short-range correlation in nuclei. In HM-AMD, the momentum directions of nucleon pairs isotropically contribute to the short-range correlation, which is different from the tensor correlation.

Irreversibility and higher-spin conformal field theory

NASA Astrophysics Data System (ADS)

Anselmi, Damiano

2000-08-01

I discuss the properties of the central charges c and a for higher-derivative and higher-spin theories (spin 2 included). Ordinary gravity does not admit a straightforward identification of c and a in the trace anomaly, because it is not conformal. On the other hand, higher-derivative theories can be conformal, but have negative c and a. A third possibility is to consider higher-spin conformal field theories. They are not unitary, but have a variety of interesting properties. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. There exists a conserved spin-2 current (not the canonical stress tensor) defining positive central charges c and a. I calculate the values of c and a and study the operator-product structure. Higher-spin conformal spinors have no gauge invariance, admit a standard definition of c and a and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a conformal window and non-trivial interacting fixed points. There are composite operators of high spin and low dimension, which violate the Ferrara-Gatto-Grillo theorem. Finally, other theories, such as conformal antisymmetric tensors, exhibit more severe internal problems. This research is motivated by the idea that fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points, and quantum irreversibility should be a general principle of nature.

Light-cone distribution amplitudes of light JPC = 2- tensor mesons in QCD

NASA Astrophysics Data System (ADS)

Aliev, T. M.; Bilmis, S.; Yang, Kwei-Chou

2018-06-01

We present a study for two-quark light-cone distribution amplitudes for the 13D2 light tensor meson states with quantum number JPC =2-. Because of the G-parity, the chiral-even two-quark light-cone distribution amplitudes of this tensor meson are antisymmetric under the interchange of momentum fractions of the quark and antiquark in the SU(3) limit, while the chiral-odd ones are symmetric. The asymptotic leading-twist LCDAs with the strange quark mass correction are shown. We estimate the relevant parameters, the decay constants fT and fT⊥, and first Gegenbauer moment a1⊥ , by using the QCD sum rule method. These parameters play a central role in the investigation of B meson decaying into the 2- tensor mesons.

Bosonization of free Weyl fermions

NASA Astrophysics Data System (ADS)

Marino, E. C.

2017-03-01

We generalize the method of bosonization, in its complete form, to a spacetime with 3  +  1 dimensions, and apply it to free Weyl fermion fields, which thereby, can be expressed in terms of a boson field, namely the Kalb-Ramond anti-symmetric tensor gauge field. The result may have interesting consequences both in condensed matter and in particle physics. In the former, the bosonized form of the Weyl chiral currents provides a simple explanation for the angle-dependent magneto-conductance recently observed in materials known as Weyl semimetals. In the latter, conversely, since electrons can be thought of as a combination of left and right Weyl fermions, our result suggests the possibility of a unified description of the elementary particles, which undergo the fundamental interactions, with the mediators of such interactions, namely, the gauge fields. This would fulfill the pioneering attempt of Skyrme, to unify the particles with their interaction mediators (Skyrme 1962 Nucl. Phys. 31 556).

Hamiltonian vs Lagrangian Embedding of a Massive Spin-One Theory Involving Two-Form Field

NASA Astrophysics Data System (ADS)

Harikumar, E.; Sivakumar, M.

We consider the Hamiltonian and Lagrangian embedding of a first-order, massive spin-one, gauge noninvariant theory involving antisymmetric tensor field. We apply the BFV-BRST generalized canonical approach to convert the model to a first class system and construct nilpotent BFV-BRST charge and a unitarizing Hamiltonian. The canonical analysis of the Stückelberg formulation of this model is presented. We bring out the contrasting feature in the constraint structure, specifically with respect to the reducibility aspect, of the Hamiltonian and the Lagrangian embedded model. We show that to obtain manifestly covariant Stückelberg Lagrangian from the BFV embedded Hamiltonian, phase space has to be further enlarged and show how the reducible gauge structure emerges in the embedded model.

Hall viscosity of a chiral two-orbital superconductor at finite temperatures

NASA Astrophysics Data System (ADS)

Yazdani-Hamid, Meghdad; Shahzamanian, Mohammad Ali

2018-06-01

The Hall viscosity known as the anti-symmetric part of the viscosity fourth-rank tensor. Such dissipationless response which appears for systems with broken time reversal symmetry. We calculate this non-dissipative quantity for a chiral two-orbital superconductor placed in a viscoelastic magnetic field using the linear response theory and apply our calculations to the putative multiband chiral superconductor Sr2RuO4. The chirality origin of a multiband superconductor arises from the interorbital coupling of the superconducting state. This feature leads to the robustness of the Hall viscosity against temperature and impurity effects. We study the temperature effect on the Hall viscosity at the one-loop approximation.

Compactification and inflation in the superstring theory from the condensation of gravitino pairs

NASA Astrophysics Data System (ADS)

Pollock, M. D.

1987-12-01

We discuss the possibility that inflation can occur in the E8×E8' heterotic superstring theory, if there is a pair condensation of the gravitino field ψA and also of the Majorana-Weyl spinor λ, as suggested by the Helayël-Neto and Smith. In the absence of a condensation of the anti-symmetric tensor field HMNP, then the associated potential V(θ,φ) is bounded from below and independent of the dilaton field φ. It can be made to vanish at the minimum, where the compactification scale θ is fixed. Alternatively, a small cosmological constant may remain (ultimately to be cancelled by radiative corrections at the lower energy scale of the gaugino condensation), which could in principle lead to inflation. Present address: Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Bombay 400 005, India.

The Kummer tensor density in electrodynamics and in gravity

NASA Astrophysics Data System (ADS)

Baekler, Peter; Favaro, Alberto; Itin, Yakov; Hehl, Friedrich W.

2014-10-01

Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, K. This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four T, which is antisymmetric in its first two and its last two indices: T=-T=-T. Thus, K∼T3, see Eq. (46). (i) If T is identified with the electromagnetic response tensor of local and linear media, the Kummer tensor density encompasses the generalized Fresnel wave surfaces for propagating light. In the reversible case, the wave surfaces turn out to be Kummer surfaces as defined in algebraic geometry (Bateman 1910). (ii) If T is identified with the curvature tensor R of a Riemann-Cartan spacetime, then K∼R3 and, in the special case of general relativity, K reduces to the Kummer tensor of Zund (1969). This K is related to the principal null directions of the curvature. We discuss the properties of the general Kummer tensor density. In particular, we decompose K irreducibly under the 4-dimensional linear group GL(4,R) and, subsequently, under the Lorentz group SO(1,3).

Nonsingular, big-bounce cosmology from spinor-torsion coupling

NASA Astrophysics Data System (ADS)

Popławski, Nikodem

2012-05-01

The Einstein-Cartan-Sciama-Kibble theory of gravity removes the constraint of general relativity that the affine connection be symmetric by regarding its antisymmetric part, the torsion tensor, as a dynamical variable. The minimal coupling between the torsion tensor and Dirac spinors generates a spin-spin interaction which is significant in fermionic matter at extremely high densities. We show that such an interaction averts the unphysical big-bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the Universe was contracting. This scenario also explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic.

Green-Kubo relations for the viscosity of biaxial nematic liquid crystals

NASA Astrophysics Data System (ADS)

Sarman, Sten

1996-09-01

We derive Green-Kubo relations for the viscosities of a biaxial nematic liquid crystal. In this system there are seven shear viscosities, three twist viscosities, and three cross coupling coefficients between the antisymmetric strain rate and the symmetric traceless pressure tensor. According to the Onsager reciprocity relations these couplings are equal to the cross couplings between the symmetric traceless strain rate and the antisymmetric pressure. Our method is based on a comparison of the microscopic linear response generated by the SLLOD equations of motion for planar Couette flow (so named because of their close connection to the Doll's tensor Hamiltonian) and the macroscopic linear phenomenological relations between the pressure tensor and the strain rate. In order to obtain simple Green-Kubo relations we employ an equilibrium ensemble where the angular velocities of the directors are identically zero. This is achieved by adding constraint torques to the equations for the molecular angular accelerations. One finds that all the viscosity coefficients can be expressed as linear combinations of time correlation function integrals (TCFIs). This is much simpler compared to the expressions in the conventional canonical ensemble, where the viscosities are complicated rational functions of the TCFIs. The reason for this is, that in the constrained angular velocity ensemble, the thermodynamic forces are given external parameters whereas the thermodynamic fluxes are ensemble averages of phase functions. This is not the case in the canonical ensemble. The simplest way of obtaining numerical estimates of viscosity coefficients of a particular molecular model system is to evaluate these fluctuation relations by equilibrium molecular dynamics simulations.

Chiral asymmetry of anti-symmetric coordinates studied by the Raman differential bond polarizability of S-phenylethylamine

NASA Astrophysics Data System (ADS)

Shen, Hong-Xia; Wu, Guo-Zhen; Wang, Pei-Jie

2012-12-01

The Raman optical activity (ROA) study on S-phenylethylamine is presented by the intensity analyses via bond polarizability and differential bond polarizability. Ample information concerning the physical picture of this chiral system is obtained, and its ROA mechanism is constructed. Especially, we propose that the asymmetric modes and/or the off-diagonal elements of the electronic polarizability tensor are the potential keys to the exploration of ROA.

On the geometry of mixed states and the Fisher information tensor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Contreras, I., E-mail: icontrer@illinois.edu; Ercolessi, E., E-mail: ercolessi@bo.infn.it; Schiavina, M., E-mail: michele.schiavina@math.uzh.ch

2016-06-15

In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant–Kirillov–Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to understand the symmetric logarithmic derivative as a proper 1-form, settling the issues about its very definition and explicit computation. Moreover, the fibration of co-adjointmore » orbits, seen as spaces of mixed states, is also discussed.« less

Renormalization and additional degrees of freedom within the chiral effective theory for spin-1 resonances

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kampf, Karol; Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University in Prague, V Holesovickach 2, 18000 Prague; Novotny, Jiri

2010-06-01

We study in detail various aspects of the renormalization of the spin-1 resonance propagator in the effective field theory framework. First, we briefly review the formalisms for the description of spin-1 resonances in the path integral formulation with the stress on the issue of propagating degrees of freedom. Then we calculate the one-loop 1{sup --} meson self-energy within the resonance chiral theory in the chiral limit using different methods for the description of spin-1 particles, namely, the Proca field, antisymmetric tensor field, and the first-order formalisms. We discuss in detail technical aspects of the renormalization procedure which are inherent tomore » the power-counting nonrenormalizable theory and give a formal prescription for the organization of both the counterterms and one-particle irreducible graphs. We also construct the corresponding propagators and investigate their properties. We show that the additional poles corresponding to the additional one-particle states are generated by loop corrections, some of which are negative norm ghosts or tachyons. We count the number of such additional poles and briefly discuss their physical meaning.« less

Rortex—A new vortex vector definition and vorticity tensor and vector decompositions

NASA Astrophysics Data System (ADS)

Liu, Chaoqun; Gao, Yisheng; Tian, Shuling; Dong, Xiangrui

2018-03-01

A vortex is intuitively recognized as the rotational/swirling motion of the fluids. However, an unambiguous and universally accepted definition for vortex is yet to be achieved in the field of fluid mechanics, which is probably one of the major obstacles causing considerable confusions and misunderstandings in turbulence research. In our previous work, a new vector quantity that is called vortex vector was proposed to accurately describe the local fluid rotation and clearly display vortical structures. In this paper, the definition of the vortex vector, named Rortex here, is revisited from the mathematical perspective. The existence of the possible rotational axis is proved through real Schur decomposition. Based on real Schur decomposition, a fast algorithm for calculating Rortex is also presented. In addition, new vorticity tensor and vector decompositions are introduced: the vorticity tensor is decomposed to a rigidly rotational part and a non-rotationally anti-symmetric part, and the vorticity vector is decomposed to a rigidly rotational vector which is called the Rortex vector and a non-rotational vector which is called the shear vector. Several cases, including the 2D Couette flow, 2D rigid rotational flow, and 3D boundary layer transition on a flat plate, are studied to demonstrate the justification of the definition of Rortex. It can be observed that Rortex identifies both the precise swirling strength and the rotational axis, and thus it can reasonably represent the local fluid rotation and provide a new powerful tool for vortex dynamics and turbulence research.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kulagin, D. V.; Levchenko, G. G.; Savchenko, A. S.

The features of refraction (including the Goos-Hanchen effect) of a TM or TE bulk electromagnetic wave incident from outside on the surface of a chiral magnetoelectric with the homogeneous antisymmetric magnetoelectric interaction has been analytically studied on an example of the two-sublattice model of a multiferroic. In particular, it has been shown that the requirement that the diagonal components of the permeability and permittivity tensors are simultaneously negative is not necessary for the implementation of the properties of a left-handed medium. The results have been generalized to the case of an easy-axis antiferromagnet with an antisymmetry center with the 4{submore » z}{sup {+-}}2{sub x}{sup +}I{sup -} structure in the static external magnetic field perpendicular to the easy axis of magnetization. Some results of this work were preliminarily reported in D.V. Kulagin, G.G. Levchenko, A.S. Savchenko, A.S. Tarasenko, and S.V. Tarasenko, JETP Lett. 92, 511 (2010).« less

The anomalous U(1)_{anom} symmetry and flavors from an SU(5) × SU(5)' GUT in Z_{12-I} orbifold compactification

NASA Astrophysics Data System (ADS)

Kim, Jihn E.; Kyae, Bumseok; Nam, Soonkeon

2017-12-01

In string compactifications, frequently the anomalous U(1) gauge symmetry appears which belongs to E_8 × E_8' of the heterotic string. This anomalous U(1) gauge boson obtains mass at the compactification scale (≈ 10^{18 } {GeV}) by absorbing one pseudoscalar (corresponding to the model-independent axion) from the second rank antisymmetric tensor field B_{MN}. Below the compactification scale a global symmetry U(1)_{anom} results whose charge Q_anom is the original gauge U(1) charge. This is the most natural global symmetry, realizing the "invisible" axion. This global symmetry U(1)_{anom} is suitable for a flavor symmetry. In the simplest compactification model with the flipped SU(5) grand unification, all the low energy parameters are calculated in terms of the vacuum expectation values of the standard model singlets.

Tribute to Emil Wolf: Science and Engineering Legacy of Physical Optics

DTIC Science & Technology

2004-09-23

K̂jm(x1, x2)σ̂= 0̂, where jkl is a Levi - Civita -unit antisymmetric tensor and x denotes spatial and temporal variables. From these equations of...6.2 Microscopic Origin of Source Correlations / 143 6.3 Source Correlation-Induced Two -Photon Resonance / 145 6.4 Spatial Coherence and Emission in...University, and the organizer of the two previous SPIE Conferences—also tributes to pioneers in optics (AdolphW. Lohmann; Yuri N. Denisyuk and Emmett N

Entanglement of heavy quark impurities and generalized gravitational entropy

NASA Astrophysics Data System (ADS)

Kumar, S. Prem; Silvani, Dorian

2018-01-01

We calculate the contribution from non-conformal heavy quark sources to the entanglement entropy (EE) of a spherical region in N=4 SUSY Yang-Mills theory. We apply the generalized gravitational entropy method to non-conformal probe D-brane embeddings in AdS5×S5, dual to pointlike impurities exhibiting flows between quarks in large-rank tensor representations and the fundamental representation. For the D5-brane embedding which describes the screening of fundamental quarks in the UV to the antisymmetric tensor representation in the IR, the EE excess decreases non-monotonically towards its IR asymptotic value, tracking the qualitative behaviour of the one-point function of static fields sourced by the impurity. We also examine two classes of D3-brane embeddings, one which connects a symmetric representation source in the UV to fundamental quarks in the IR, and a second category which yields the symmetric representation source on the Coulomb branch. The EE excess for the former increases from the UV to the IR, whilst decreasing and becoming negative for the latter. In all cases, the probe free energy on hyperbolic space with β = 2 π increases monotonically towards the IR, supporting its interpretation as a relative entropy. We identify universal corrections, depending logarithmically on the VEV, for the symmetric representation on the Coulomb branch.

Dispersive transport and symmetry of the dispersion tensor in porous media

NASA Astrophysics Data System (ADS)

Pride, Steven R.; Vasco, Donald W.; Flekkoy, Eirik G.; Holtzman, Ran

2017-04-01

The macroscopic laws controlling the advection and diffusion of solute at the scale of the porous continuum are derived in a general manner that does not place limitations on the geometry and time evolution of the pore space. Special focus is given to the definition and symmetry of the dispersion tensor that is controlling how a solute plume spreads out. We show that the dispersion tensor is not symmetric and that the asymmetry derives from the advective derivative in the pore-scale advection-diffusion equation. When flow is spatially variable across a voxel, such as in the presence of a permeability gradient, the amount of asymmetry can be large. As first shown by Auriault [J.-L. Auriault et al. Transp. Porous Med. 85, 771 (2010), 10.1007/s11242-010-9591-y] in the limit of low Péclet number, we show that at any Péclet number, the dispersion tensor Di j satisfies the flow-reversal symmetry Di j(+q ) =Dj i(-q ) where q is the mean flow in the voxel under analysis; however, Reynold's number must be sufficiently small that the flow is reversible when the force driving the flow changes sign. We also demonstrate these symmetries using lattice-Boltzmann simulations and discuss some subtle aspects of how to measure the dispersion tensor numerically. In particular, the numerical experiments demonstrate that the off-diagonal components of the dispersion tensor are antisymmetric which is consistent with the analytical dependence on the average flow gradients that we propose for these off-diagonal components.

Investigating the thermally induced acoustoelastic effect in isotropic media with Lamb waves

PubMed Central

Dodson, Jacob C.; Inman, Daniel J.

2014-01-01

Elastic wave velocities in metallic structures are affected by variations in environmental conditions such as changing temperature. This paper extends the theory of acoustoelasticity by allowing thermally induced strains in unconstrained isotropic media, and it experimentally examines the velocity variation of Lamb waves in aluminum plates (AL-6061) due to isothermal temperature deviations. This paper presents both thermally induced acoustoelastic constants and thermally varying effective Young's modulus and Poisson's ratio which include the third order elastic material constants. The experimental thermal sensitivity of the phase velocity (∂vP/∂θ) for both the symmetric and antisymmetric modes are bounded by two theories, the acoustoelastic Lamb wave theory with thermo-acoustoelastic tensors and the thermoelastic Lamb wave theory using an effective thermo-acoustoelastic moduli. This paper shows the theoretical thermally induced acoustoelastic Lamb wave thermal sensitivity (∂vP/∂θ) is an upper bound approximation of the experimental thermal changes, but the acoustoelastic Lamb wave theory is not valid for predicting the antisymmetric (A0) phase velocity at low frequency-thickness values, <1.55 MHz mm for various temperatures. PMID:25373955

InGaAs/InAlAs Double Quantum Wells as Starting Structures for Quantum Logic Gates

NASA Astrophysics Data System (ADS)

Marchewka, M.; Sheregii, E. M.

2011-12-01

The detection of both symmetric and anti-symmetric electron states in DQWs by an optical method is described in this paper. Values of the symmetric and anti-symmetric splitting (SAS-gap) determined in this way are used for interpretation of the beating effect in the SdH oscillations observed at low temperatures in the external magnetic field. SAS-splitting of electron states in DQWs clearly exists at room temperature and electrons in symmetric and anti-symmetric states have different statistics so these states can be identified in electron transport.

Symmetry properties of second harmonics generated by antisymmetric Lamb waves

NASA Astrophysics Data System (ADS)

Zhu, Wujun; Xiang, Yanxun; Liu, Chang-Jun; Deng, Mingxi; Xuan, Fu-Zhen

2018-03-01

Symmetry properties of second harmonics generated by antisymmetric primary Lamb waves are systematically studied in this work. In theory, the acoustic field of second harmonic Lamb waves is obtained by using the perturbation approximation and normal modal method, and the energy flux transfer from the primary Lamb waves to second harmonics is mainly explored. Symmetry analyses indicate that either the symmetric or antisymmetric Lamb waves can merely generate the symmetric second harmonics. Finite element simulations are performed on the nonlinear Lamb wave propagation of the antisymmetric A0 mode in the low frequency region. The signals of the second harmonics and the symmetric second harmonic s0 mode are found to be exactly equivalent in the time domain. The relative acoustic nonlinearity parameter A2/A12 oscillates with the propagation distance, and the oscillation amplitude and spatial period are well consistent with the theoretical prediction of the A0-s0 mode pair, which means that only the second harmonic s0 mode is generated by the antisymmetric primary A0 mode. Experiments are further conducted to examine the cumulative generation of symmetric second harmonics for the antisymmetric-symmetric mode pair A3-s6. Results show that A2/A12 increases linearly with the propagation distance, which means that the symmetric second harmonic s6 mode is generated cumulatively by the antisymmetric primary A3 mode. The present investigation systematically corroborates the proposed theory that only symmetric second harmonics can be generated accompanying the propagation of antisymmetric primary Lamb waves in a plate.

Antisymmetric Spin-Orbit Coupling in a d-p Model on a Zigzag Chain

DOE PAGES

Sugita, Yusuke; Hayami, Satoru; Motome, Yukitoshi

2015-12-29

In this paper, we theoretically investigate how an antisymmetric spin-orbit coupling emerges in electrons moving on lattice structures which are centrosymmetric but break the spatial inversion symme- try at atomic positions. We construct an effective d-p model on the simplest lattice structure, a zigzag chain of edge-sharing octahedra, with taking into account the crystalline electric field, the spin-orbit coupling, and on-site and inter-site d-p hybridizations. We show that an effective antisymmetric spin-orbit coupling arises in the sublattice-dependent form, which results in a hidden spin polarization in the band structure. Finally, we explicitly derive the effective antisymmetric spin-orbit coupling for dmore » electrons, which not only explains the hidden spin polarization but also indicates how to enhance it.« less

Antisymmetric Spin-Orbit Coupling in a d-p Model on a Zigzag Chain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sugita, Yusuke; Hayami, Satoru; Motome, Yukitoshi

In this paper, we theoretically investigate how an antisymmetric spin-orbit coupling emerges in electrons moving on lattice structures which are centrosymmetric but break the spatial inversion symme- try at atomic positions. We construct an effective d-p model on the simplest lattice structure, a zigzag chain of edge-sharing octahedra, with taking into account the crystalline electric field, the spin-orbit coupling, and on-site and inter-site d-p hybridizations. We show that an effective antisymmetric spin-orbit coupling arises in the sublattice-dependent form, which results in a hidden spin polarization in the band structure. Finally, we explicitly derive the effective antisymmetric spin-orbit coupling for dmore » electrons, which not only explains the hidden spin polarization but also indicates how to enhance it.« less

Covariant Hamiltonian tetrad approach to numerical relativity

NASA Astrophysics Data System (ADS)

Hamilton, Andrew J. S.

2017-12-01

A Hamiltonian approach to the equations of general relativity is proposed using the powerful mathematical language of multivector-valued differential forms. In the approach, the gravitational coordinates are the 12 spatial components of the line interval (the vierbein) including their antisymmetric parts, and their 12 conjugate momenta. A feature of the proposed formalism is that it allows Lorentz gauge freedoms to be imposed on the Lorentz connections rather than on the vierbein, which may facilitate numerical integration in some challenging problems. The 40 Hamilton's equations comprise 12 +12 =24 equations of motion, ten constraint equations (first class constraints, which must be arranged on the initial hypersurface of constant time, but which are guaranteed thereafter by conservation laws), and six identities (second class constraints). The six identities define a trace-free spatial tensor that is the gravitational analog of the magnetic field of electromagnetism. If the gravitational magnetic field is promoted to an independent field satisfying its own equation of motion, then the system becomes the Wahlquist-Estabrook-Buchman-Bardeen (WEBB) system, which is known to be strongly hyperbolic. Some other approaches, including Arnowitt-Deser-Misner, Baumgarte-Shapiro-Shibata-Nakamura, WEBB, and loop quantum gravity, are translated into the language of multivector-valued forms, bringing out their underlying mathematical structure.

Non-collinear interaction of guided elastic waves in an isotropic plate

NASA Astrophysics Data System (ADS)

Ishii, Yosuke; Biwa, Shiro; Adachi, Tadaharu

2018-04-01

The nonlinear wave propagation in a homogeneous and isotropic elastic plate is analyzed theoretically to investigate the non-collinear interaction of plate wave modes. In the presence of two primary plate waves (Rayleigh-Lamb or shear horizontal modes) propagating in arbitrary directions, an explicit expression for the modal amplitude of nonlinearly generated wave fields with the sum or difference frequency of the primary modes is derived by using the perturbation analysis. The modal amplitude is shown to grow in proportion with the propagation distance when the resonance condition is satisfied, i.e., when the wavevector of secondary wave coincides with the sum or difference of those of primary modes. Furthermore, the non-collinear interaction of two symmetric or two antisymmetric modes is shown to produce the secondary wave fields consisting only of the symmetric modes, while a pair of symmetric and antisymmetric primary modes is shown to produce only the antisymmetric modes. The influence of the intersection angle, the primary frequencies, and the mode combinations on the modal amplitude of secondary wave is examined for a low-frequency range where the lowest-order symmetric and antisymmetric Rayleigh-Lamb waves and the lowest-order symmetric shear horizontal wave are the only propagating modes.

Prediction of absolute infrared intensities for the fundamental vibrations of H2O2

NASA Technical Reports Server (NTRS)

Rogers, J. D.; Hillman, J. J.

1981-01-01

Absolute infrared intensities are predicted for the vibrational bands of gas-phase H2O2 by the use of a hydrogen atomic polar tensor transferred from the hydroxyl hydrogen atom of CH3OH. These predicted intensities are compared with intensities predicted by the use of a hydrogen atomic polar tensor transferred from H2O. The predicted relative intensities agree well with published spectra of gas-phase H2O2, and the predicted absolute intensities are expected to be accurate to within at least a factor of two. Among the vibrational degrees of freedom, the antisymmetric O-H bending mode nu(6) is found to be the strongest with a calculated intensity of 60.5 km/mole. The torsional band, a consequence of hindered rotation, is found to be the most intense fundamental with a predicted intensity of 120 km/mole. These results are compared with the recent absolute intensity determinations for the nu(6) band.

Quark ACM with topologically generated gluon mass

NASA Astrophysics Data System (ADS)

Choudhury, Ishita Dutta; Lahiri, Amitabha

2016-03-01

We investigate the effect of a small, gauge-invariant mass of the gluon on the anomalous chromomagnetic moment (ACM) of quarks by perturbative calculations at one-loop level. The mass of the gluon is taken to have been generated via a topological mass generation mechanism, in which the gluon acquires a mass through its interaction with an antisymmetric tensor field Bμν. For a small gluon mass ( < 10 MeV), we calculate the ACM at momentum transfer q2 = -M Z2. We compare those with the ACM calculated for the gluon mass arising from a Proca mass term. We find that the ACM of up, down, strange and charm quarks vary significantly with the gluon mass, while the ACM of top and bottom quarks show negligible gluon mass dependence. The mechanism of gluon mass generation is most important for the strange quarks ACM, but not so much for the other quarks. We also show the results at q2 = -m t2. We find that the dependence on gluon mass at q2 = -m t2 is much less than at q2 = -M Z2 for all quarks.

Twisted Hubbard model for Sr2IrO4: magnetism and possible high temperature superconductivity.

PubMed

Wang, Fa; Senthil, T

2011-04-01

Sr(2)IrO(4) has been suggested as a Mott insulator from a single J(eff)=1/2 band, similar to the cuprates. However, this picture is complicated by the measured large magnetic anisotropy and ferromagnetism. Based on a careful mapping to the J(eff)=1/2 (pseudospin-1/2) space, we propose that the low energy electronic structure of Sr(2)IrO(4) can indeed be described by a SU(2) invariant pseudospin-1/2 Hubbard model very similar to that of the cuprates, but with a twisted coupling to an external magnetic field (a g tensor with a staggered antisymmetric component). This perspective naturally explains the magnetic properties of Sr(2)IrO(4). We also derive several simple facts based on this mapping and the known results about the Hubbard model and the cuprates, which may be tested in future experiments on Sr(2)IrO(4). In particular, we propose that (electron-)doping Sr(2)IrO(4) can potentially realize high-temperature superconductivity. © 2011 American Physical Society

On equatorially symmetric and antisymmetric geomagnetic secular variation timescales

NASA Astrophysics Data System (ADS)

Amit, Hagay; Coutelier, Maélie; Christensen, Ulrich R.

2018-03-01

It has been suggested that the secular variation (SV) timescales of the geomagnetic field vary as 1 / ℓ (where ℓ is the spherical harmonic degree), except for the dipole. Here we propose that the same scaling law applies for SV timescales defined for different symmetry classes of the geomagnetic field and SV. We decompose the field and its SV into symmetric and antisymmetric parts and show in geomagnetic field models and numerical dynamo simulations that the corresponding SV timescales also vary as 1 / ℓ , again except for the dipole. The time-average antisymmetric/symmetric SV timescales are larger/smaller than the total, respectively. The difference in SV timescales between these two symmetry classes is probably due to different degrees of alignment of the core flow with different magnetic field structures at the core-mantle boundary. The symmetric dipole SV timescale in the recent geomagnetic field and in long-term time-averages from numerical dynamos is below the extrapolated 1 / ℓ curve, whereas before ∼ 1965 the geomagnetic dipole tilt was rather steady and the symmetric dipole SV timescale exceeded the extrapolated 1 / ℓ curve. We hypothesize that the period of nearly steady geomagnetic dipole tilt between 1810-1965 was anomalous for the geodynamo. Overall, the deviation of the dipole SV timescales from the 1 / ℓ curves may indicate that magnetic diffusion contributes to the dipole SV more than it does for higher degrees.

Selective coherent perfect absorption of subradiant mode in ultrathin bi-layer metamaterials via antisymmetric excitation

NASA Astrophysics Data System (ADS)

Tan, Wei; Zhang, Caihong; Li, Chun; Zhou, Xiaoying; Jia, Xiaoqing; Feng, Zheng; Su, Juan; Jin, Biaobing

2017-05-01

We demonstrate that the subradiant mode in ultrathin bi-layer metamaterials can be exclusively excited under two-antisymmetric-beam illumination (or equivalently, at a node of the standing wave field), while the superradiant mode is fully suppressed due to their different mode symmetry. Coherent perfect absorption (CPA) with the Lorentzian lineshape can be achieved corresponding to the subradiant mode. A theoretical model is established to distinguish the different behaviors of these two modes and to elucidate the CPA condition. Terahertz ultrathin bi-layer metamaterials on flexible polyimide substrates are fabricated and tested, exhibiting excellent agreement with theoretical predictions. This work provides physical insight into how to selectively excite the antisymmetric subradiant mode via coherence incidence.

Analysis of Functionally Graded Shells Subjected to Blast Loads

DTIC Science & Technology

2008-07-21

and antisymmetric about the midsurface , continuous distributions of the two constituent phases, ceramic and metal, are considered, in the sense that...through the wall-thickness temperature field is investigated. Two scenarios, symmetric and antisymmetric about the midsurface , continuous...and for 3 / 2x h= − , ( / 2) cP h P− ⇒ . At the midsurface , 3 0x = , and for 1k = , ( )(0) / 2c mP P P= + . 3 Kinematics and Constitutive

Saturn’s gravitational field induced by its equatorially antisymmetric zonal winds

NASA Astrophysics Data System (ADS)

Kong, Dali; Zhang, Keke; Schubert, Gerald; Anderson, John D.

2018-05-01

The cloud-level zonal winds of Saturn are marked by a substantial equatorially antisymmetric component with a speed of about 50ms‑1 which, if they are sufficiently deep, can produce measurable odd zonal gravitational coefficients ΔJ 2k+1, k = 1, 2, 3, 4. This study, based on solutions of the thermal-gravitational wind equation, provides a theoretical basis for interpreting the odd gravitational coefficients of Saturn in terms of its equatorially antisymmetric zonal flow. We adopt a Saturnian model comprising an ice-rock core, a metallic dynamo region and an outer molecular envelope. We use an equatorially antisymmetric zonal flow that is parameterized, confined in the molecular envelope and satisfies the solvability condition required for the thermal-gravitational wind equation. The structure and amplitude of the zonal flow at the cloud level are chosen to be consistent with observations of Saturn. We calculate the odd zonal gravitational coefficients ΔJ 2k+1, k = 1, 2, 3, 4 by regarding the depth of the equatorially antisymmetric winds as a parameter. It is found that ΔJ 3 is ‑4.197 × 10‑8 if the zonal winds extend about 13 000 km downward from the cloud tops while it is ‑0.765 × 10‑8 if the depth is about 4000 km. The depth/profile of the equatorially antisymmetric zonal winds can eventually be estimated when the high-precision measurements of the Cassini Grand Finale become available.

Analysis of electrical-field-dependent Dzyaloshinskii-Moriya interaction and magnetocrystalline anisotropy in a two-dimensional ferromagnetic monolayer

NASA Astrophysics Data System (ADS)

Liu, Jie; Shi, Mengchao; Lu, Jiwu; Anantram, M. P.

2018-02-01

We analyze the impacts of the electric field on the Dzyaloshinskii-Moriya interaction, magnetocrystalline anisotropy, and intrinsic ferromagnetism of the recently discovered two-dimensional ferromagnetic chromium tri-iodide (Cr I3 ) monolayer, by combining density functional theory and Monte Carlo simulations. By taking advantage of the counterbalancing effects of anisotropic symmetric exchange energy and antisymmetric exchange energy, it is shown that the intrinsic ferromagnetism can be manipulated by externally applied off-plane electric fields. The results quantitatively reveal the impacts of off-plane electric field on the lattice structure, magnetic anisotropy energy, symmetric and antisymmetric exchange energies, Curie temperature, magnetic hysteresis, and coercive field. The physical mechanism of all-electrical control of magnetism proposed here is useful for creating next-generation magnetic device technologies based on the recently discovered two-dimensional ferromagnetic crystals.

Linear instabilities of a planar liquid sheet in a static electric field for intermediate relaxation and convection of surface charges

NASA Astrophysics Data System (ADS)

Yoshinaga, Takao

2018-04-01

Linear temporal instabilities of a two-dimensional planar liquid sheet in a static electric field are investigated when the relaxation and convection of surface electric charges are considered. Both viscous sheet liquid and inviscid surrounding liquid are placed between two parallel sheath walls, on which an external electric field is imposed. In particular, effects of the electric Peclet number {Pe} (charge relaxation time/convection time) and the electric Euler number Λ (electric pressure/liquid inertial) on the instabilities are emphasized for the symmetric and antisymmetric deformations of the sheet. It is found that the unstable mode is composed of the aerodynamic and electric modes, which are merged with each other for the symmetric deformation and separated for the antisymmetric deformation. For the symmetric deformation, the combined mode is more destabilized with the decrease of {Pe} and the increase of Λ. On the other hand, for the antisymmetric deformation, the electric mode is more destabilized and the aerodynamic mode is left unchanged with the decrease of {Pe}, while the electric mode is more destabilized but the aerodynamic mode is more stabilized with the increase of Λ. It is also found for both symmetric and antisymmetric deformations that the instabilities are most suppressed when {σ }R≃ 1/{ε }P ({σ }R: conductivity ratio of the surrounding to the sheet liquid, {ε }P: permittivity ratio of the sheet to the surrounding liquid), whose trend of the instabilities is more enhanced with the decrease of {Pe} except for vanishingly small {Pe}.

Visualizing second order tensor fields with hyperstreamlines

NASA Technical Reports Server (NTRS)

Delmarcelle, Thierry; Hesselink, Lambertus

1993-01-01

Hyperstreamlines are a generalization to second order tensor fields of the conventional streamlines used in vector field visualization. As opposed to point icons commonly used in visualizing tensor fields, hyperstreamlines form a continuous representation of the complete tensor information along a three-dimensional path. This technique is useful in visulaizing both symmetric and unsymmetric three-dimensional tensor data. Several examples of tensor field visualization in solid materials and fluid flows are provided.

Tensor gauge condition and tensor field decomposition

NASA Astrophysics Data System (ADS)

Zhu, Ben-Chao; Chen, Xiang-Song

2015-10-01

We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.

Field-aligned structure of the storm time Pc 5 wave of November 14-15, 1979

NASA Astrophysics Data System (ADS)

Takahashi, K.; Higbie, P. R.; Fennell, J. F.; Amata, E.

1988-02-01

Magnetic field data from the four satellites--SCATHA (P78-2), GOES 2, GOES 3, and GEOS 2--have been analyzed to examine the magnetic-field-aligned structure of a storm time Pc 5 wave which occurred on November 14-15, 1979. The wave had both transverse and compressional components. At a given instance, the compressional and the radial components oscillated in phase or 180 deg out of phase, and the compressional and the azimuthal components oscillated +90 deg or -90 deg out of phase. In addition, each component changed its amplitude with magnetic latitude: the compressional component had a minimum at the magnetic equator, whereas the transverse components had a maximum at the equator and minima several degrees off the equator. At 180 deg relative phase switching among the components occurred across the latitudes of amplitude minima. From these observations, the field-line displacement of the wave is confirmed to have an antisymmetric standing structure about the magnetic equator with a parallel wave length of a few earth radii. We aslo observed other intriguing properties of the wave, such as different parallel wavelengths of different field components and small-amplitude second harmonics near the nodes. A dielectric tensor appropriate for the ring current plasma is found to give an explanation for the relation between the polarization and the propagation of the wave. However, plasma data available from SCATHA do not support either the drift-mirror instability of Hasegawa or tht coupling between a drift mirror wave and a shear Alfven wave, as discussed by Walker et al.

The Topology of Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval

1997-01-01

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

Using Perturbation Theory to Reduce Noise in Diffusion Tensor Fields

PubMed Central

Bansal, Ravi; Staib, Lawrence H.; Xu, Dongrong; Laine, Andrew F.; Liu, Jun; Peterson, Bradley S.

2009-01-01

We propose the use of Perturbation theory to reduce noise in Diffusion Tensor (DT) fields. Diffusion Tensor Imaging (DTI) encodes the diffusion of water molecules along different spatial directions in a positive-definite, 3 × 3 symmetric tensor. Eigenvectors and eigenvalues of DTs allow the in vivo visualization and quantitative analysis of white matter fiber bundles across the brain. The validity and reliability of these analyses are limited, however, by the low spatial resolution and low Signal-to-Noise Ratio (SNR) in DTI datasets. Our procedures can be applied to improve the validity and reliability of these quantitative analyses by reducing noise in the tensor fields. We model a tensor field as a three-dimensional Markov Random Field and then compute the likelihood and the prior terms of this model using Perturbation theory. The prior term constrains the tensor field to be smooth, whereas the likelihood term constrains the smoothed tensor field to be similar to the original field. Thus, the proposed method generates a smoothed field that is close in structure to the original tensor field. We evaluate the performance of our method both visually and quantitatively using synthetic and real-world datasets. We quantitatively assess the performance of our method by computing the SNR for eigenvalues and the coherence measures for eigenvectors of DTs across tensor fields. In addition, we quantitatively compare the performance of our procedures with the performance of one method that uses a Riemannian distance to compute the similarity between two tensors, and with another method that reduces noise in tensor fields by anisotropically filtering the diffusion weighted images that are used to estimate diffusion tensors. These experiments demonstrate that our method significantly increases the coherence of the eigenvectors and the SNR of the eigenvalues, while simultaneously preserving the fine structure and boundaries between homogeneous regions, in the smoothed tensor field. PMID:19540791

The energy-momentum tensor(s) in classical gauge theories

DOE PAGES

Blaschke, Daniel N.; Gieres, François; Reboud, Méril; ...

2016-07-12

We give an introduction to, and review of, the energy-momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space-time. For the canonical energy-momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy-momentum tensor. In conclusion, the relationship with the Einstein-Hilbert tensor following from the coupling to a gravitational field is also discussed.

Non-classical continuum theory for fluids incorporating internal and Cosserat rotation rates

NASA Astrophysics Data System (ADS)

Surana, K. S.; Joy, A. D.; Reddy, J. N.

2017-11-01

This paper presents a non-classical continuum theory for fluent continua in which the conservation and balance laws are derived by incorporating both internal rotation rates arising from the velocity gradient tensor and the rotation rates of the Cosserats. Specifically, in this non-classical continuum theory we have (1) the usual velocities (\\bar{ ±b {\\varvec{v }}}), (2) the three internal rotation rates ({}_i^t\\bar{ ±b {\\varvec{Θ }}}) about the axes of a fixed triad whose axes are parallel to the x-frame arising from the velocity gradient tensor (\\bar{ ±b {\\varvec{L }}}) that are completely defined by the antisymmetric part of the velocity gradient tensor, and (3) three additional rotation rates ({}_e^t\\bar{ ±b {\\varvec{Θ }}}) about the axes of the same triad located at each material point as additional three unknown degrees of freedom, referred to as Cosserat rotation rates. This gives rise to \\bar{ ±b {\\varvec{v }}} and {}_e^t\\bar{ ±b {\\varvec{Θ }}} as six degrees of freedom at a material point. The internal rotation rates {}_i^t\\bar{ ±b {\\varvec{Θ }}}, often neglected in classical fluid mechanics, exist in all deforming fluent continua as these are due to velocity gradient tensor. When the internal rotation rates {}_i^t\\bar{ ±b {\\varvec{Θ }}} are resisted by deforming fluent continua, conjugate moment tensor arises that together with {}_i^t\\bar{ ±b {\\varvec{Θ }}} may result in energy storage and/or dissipation, which must be considered in the conservation and balance laws. The Cosserat rotation rations {}_e^t\\bar{ ±b {\\varvec{Θ }}} also result in conjugate moment tensor that together with {}_e^t\\bar{ ±b {\\varvec{Θ }}} may also result in energy storage and/or dissipation. The main focus of this paper is a consistent derivation of conservation and balance laws for fluent continua that incorporate the aforementioned physics and associated constitutive theories for thermofluids using the conditions resulting from the entropy inequality. The material coefficients derived in the constitutive theories are clearly defined and discussed.

Visualization of 3-D tensor fields

NASA Technical Reports Server (NTRS)

Hesselink, L.

1996-01-01

Second-order tensor fields have applications in many different areas of physics, such as general relativity and fluid mechanics. The wealth of multivariate information in tensor fields makes them more complex and abstract than scalar and vector fields. Visualization is a good technique for scientists to gain new insights from them. Visualizing a 3-D continuous tensor field is equivalent to simultaneously visualizing its three eigenvector fields. In the past, research has been conducted in the area of two-dimensional tensor fields. It was shown that degenerate points, defined as points where eigenvalues are equal to each other, are the basic singularities underlying the topology of tensor fields. Moreover, it was shown that eigenvectors never cross each other except at degenerate points. Since we live in a three-dimensional world, it is important for us to understand the underlying physics of this world. In this report, we describe a new method for locating degenerate points along with the conditions for classifying them in three-dimensional space. Finally, we discuss some topological features of three-dimensional tensor fields, and interpret topological patterns in terms of physical properties.

Geometric decomposition of the conformation tensor in viscoelastic turbulence

NASA Astrophysics Data System (ADS)

Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.

2018-05-01

This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.

Snake states and their symmetries in graphene

NASA Astrophysics Data System (ADS)

Liu, Yang; Tiwari, Rakesh P.; Brada, Matej; Bruder, C.; Kusmartsev, F. V.; Mele, E. J.

2015-12-01

Snake states are open trajectories for charged particles propagating in two dimensions under the influence of a spatially varying perpendicular magnetic field. In the quantum limit they are protected edge modes that separate topologically inequivalent ground states and can also occur when the particle density rather than the field is made nonuniform. We examine the correspondence of snake trajectories in single-layer graphene in the quantum limit for two families of domain walls: (a) a uniform doped carrier density in an antisymmetric field profile and (b) antisymmetric carrier distribution in a uniform field. These families support different internal symmetries but the same pattern of boundary and interface currents. We demonstrate that these physically different situations are gauge equivalent when rewritten in a Nambu doubled formulation of the two limiting problems. Using gauge transformations in particle-hole space to connect these problems, we map the protected interfacial modes to the Bogoliubov quasiparticles of an interfacial one-dimensional p -wave paired state. A variational model is introduced to interpret the interfacial solutions of both domain wall problems.

Snake states and their symmetries in graphene

NASA Astrophysics Data System (ADS)

Tiwari, Rakesh; Liu, Yang; Brada, Matej; Bruder, C.; Kusmartsev, F. V.; Mele, E. J.

Snake states are open trajectories for charged particles moving in two dimensions under the influence of a spatially varying perpendicular magnetic field. They can also occur in a constant perpendicular magnetic field when the particle density is made nonuniform as realized at a pn junction in a semiconductor, or in graphene. We examine the correspondence of such trajectories in monolayer graphene in the quantum limit for two families of domain walls: (a) a uniform doped carrier density in an antisymmetric perpendicular magnetic field and (b) antisymmetric carrier density distribution in a uniform perpendicular magnetic field. Although, these families support different internal symmetries, the pattern of the boundary and interface currents is the same in both cases. We demonstrate that these two physically different situations are gauge equivalent when rewritten in a Nambu doubled formulation of the two limiting problems. Using gauge transformations in particle-hole space to connect these two problems, we map the protected interfacial modes to the Bogoliubov quasiparticles of an interfacial one-dimensional p-wave paired state.

The Topology of Three-Dimensional Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus

1994-01-01

We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.

A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue.

PubMed

Pajevic, Sinisa; Aldroubi, Akram; Basser, Peter J

2002-01-01

The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical framework is proposed that uses measured DT-MRI data to produce a continuous approximation to D(x). One essential finding is that the continuous tensor field representation can be constructed by repeatedly performing one-dimensional B-spline transforms of the DT-MRI data. The fidelity and noise-immunity of this approximation are tested using a set of synthetically generated tensor fields to which background noise is added via Monte Carlo methods. Generally, these tensor field templates are reproduced faithfully except at boundaries where diffusion properties change discontinuously or where the tensor field is not microscopically homogeneous. Away from such regions, the tensor field approximation does not introduce bias in useful DT-MRI parameters, such as Trace(D(x)). It also facilitates the calculation of several new parameters, particularly differential quantities obtained from the tensor of spatial gradients of D(x). As an example, we show that they can identify tissue boundaries across which diffusion properties change rapidly using in vivo human brain data. One important application of this methodology is to improve the reliability and robustness of DT-MRI fiber tractography.

Resonance coupling in plasmonic nanomatryoshka homo- and heterodimers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahmadivand, Arash, E-mail: aahma011@fiu.edu; Sinha, Raju; Pala, Nezih

Here, we examine the electromagnetic (EM) energy coupling and hybridization of plasmon resonances between closely spaced concentric nanoshells known as “nanomatryoshka” (NM) units in symmetric and antisymmetric compositions using the Finite Difference Time Domain (FDTD) analysis. Utilizing plasmon hybridization model, we calculated the energy level diagrams and verified that, in the symmetric dimer (in-phase mode in a homodimer), plasmonic bonding modes are dominant and tunable within the considered bandwidth. In contrast, in the antisymmetric dimer (out-of-phase mode in a heterodimer), due to the lack of the geometrical symmetry, new antibonding modes appear in the extinction profile, and this condition givesmore » rise to repeal of dipolar field coupling. We also studied the extinction spectra and positions of the antibonding and bonding modes excited due to the energy coupling between silver and gold NM units in a heterodimer structure. Our analysis suggest abnormal shifts in the higher energy modes. We propose a method to analyze the behavior of multilayer concentric nanoshell particles in an antisymmetric orientation employing full dielectric function calculations and the Drude model based on interband transitions in metallic components. This study provides a method to predict the behavior of the higher energy plasmon resonant modes in entirely antisymmetric structures such as compositional heterodimers.« less

Resonance interatomic energy in a Schwarzschild spacetime

NASA Astrophysics Data System (ADS)

Zhou, Wenting; Yu, Hongwei

2017-08-01

We study, in the Schwarzschild spacetime, the resonance interatomic energy (RIE) of two static identical atoms with an interatomic separation L along the radial direction and correlated by a symmetric/antisymmetric entangled state. The atoms are assumed to be coupled to massless scalar fields in the Boulware, Unruh, and Hartle-Hawking vacua, and approximate analytical results are obtained both at infinity and near the horizon. Our results show that at infinity, the RIE approaches that in a flat spacetime, while, near the horizon, they can deviate dramatically from each other. Besides, different from other atomic radiative properties such as the Lamb shift of a single atom or the interatomic energy between two uncorrelated atoms, which can be obviously affected by the thermal character of quantum fields, the RIE of two atoms in a symmetric/antisymmetric entangled state in the Boulware, Unruh, and Hartle-Hawking vacua are exactly the same as a result of the fact that the RIE of two such atoms depends only on the atomic self-reaction, i.e., it does not feel the vacuum fluctuations. This suggests that the RIE of two static atoms in a symmetric/antisymmetric entangled state outside a black hole is oblivious to the Hawking radiation, in contrast to those uncorrelated atoms.

Similar Tensor Arrays - A Framework for Storage of Tensor Array Data

NASA Astrophysics Data System (ADS)

Brun, Anders; Martin-Fernandez, Marcos; Acar, Burak; Munoz-Moreno, Emma; Cammoun, Leila; Sigfridsson, Andreas; Sosa-Cabrera, Dario; Svensson, Björn; Herberthson, Magnus; Knutsson, Hans

This chapter describes a framework for storage of tensor array data, useful to describe regularly sampled tensor fields. The main component of the framework, called Similar Tensor Array Core (STAC), is the result of a collaboration between research groups within the SIMILAR network of excellence. It aims to capture the essence of regularly sampled tensor fields using a minimal set of attributes and can therefore be used as a “greatest common divisor” and interface between tensor array processing algorithms. This is potentially useful in applied fields like medical image analysis, in particular in Diffusion Tensor MRI, where misinterpretation of tensor array data is a common source of errors. By promoting a strictly geometric perspective on tensor arrays, with a close resemblance to the terminology used in differential geometry, (STAC) removes ambiguities and guides the user to define all necessary information. In contrast to existing tensor array file formats, it is minimalistic and based on an intrinsic and geometric interpretation of the array itself, without references to other coordinate systems.

UNIVERSE IN A BLACK HOLE IN EINSTEIN–CARTAN GRAVITY

DOE Office of Scientific and Technical Information (OSTI.GOV)

Popławski, Nikodem, E-mail: NPoplawski@newhaven.edu

The conservation law for the angular momentum in curved spacetime, consistent with relativistic quantum mechanics, requires that the antisymmetric part of the affine connection (torsion tensor) is a variable in the principle of least action. The coupling between the spin of elementary particles and torsion in the Einstein–Cartan theory of gravity generates gravitational repulsion at extremely high densities in fermionic matter, approximated as a spin fluid, and thus avoids the formation of singularities in black holes. The collapsing matter in a black hole should therefore bounce at a finite density and then expand into a new region of space onmore » the other side of the event horizon, which may be regarded as a nonsingular, closed universe. We show that quantum particle production caused by an extremely high curvature near a bounce can create enormous amounts of matter, produce entropy, and generate a finite period of exponential expansion (inflation) of this universe. This scenario can thus explain inflation without a scalar field and reheating. We show that, depending on the particle production rate, such a universe may undergo several nonsingular bounces until it has enough matter to reach a size at which the cosmological constant starts cosmic acceleration. The last bounce can be regarded as the big bang of this universe.« less

Universe in a Black Hole in Einstein-Cartan Gravity

NASA Astrophysics Data System (ADS)

Popławski, Nikodem

2016-12-01

The conservation law for the angular momentum in curved spacetime, consistent with relativistic quantum mechanics, requires that the antisymmetric part of the affine connection (torsion tensor) is a variable in the principle of least action. The coupling between the spin of elementary particles and torsion in the Einstein-Cartan theory of gravity generates gravitational repulsion at extremely high densities in fermionic matter, approximated as a spin fluid, and thus avoids the formation of singularities in black holes. The collapsing matter in a black hole should therefore bounce at a finite density and then expand into a new region of space on the other side of the event horizon, which may be regarded as a nonsingular, closed universe. We show that quantum particle production caused by an extremely high curvature near a bounce can create enormous amounts of matter, produce entropy, and generate a finite period of exponential expansion (inflation) of this universe. This scenario can thus explain inflation without a scalar field and reheating. We show that, depending on the particle production rate, such a universe may undergo several nonsingular bounces until it has enough matter to reach a size at which the cosmological constant starts cosmic acceleration. The last bounce can be regarded as the big bang of this universe.

Spin and charge controlled by antisymmetric spin-orbit coupling in a triangular-triple-quantum-dot Kondo system

NASA Astrophysics Data System (ADS)

Koga, M.; Matsumoto, M.; Kusunose, H.

2018-05-01

We study a local antisymmetric spin-orbit (ASO) coupling effect on a triangular-triple-quantum-dot (TTQD) system as a theoretical proposal for a new application of the Kondo physics to nanoscale devices. The electric polarization induced by the Kondo effect is strongly correlated with the spin configurations and molecular orbital degrees of freedom in the TTQD. In particular, an abrupt sign reversal of the emergent electric polarization is associated with a quantum critical point in a magnetic field, which can also be controlled by the ASO coupling that changes the mixing weight of different orbital components in the TTQD ground state.

Time evolution, Lamb shift, and emission spectra of spontaneous emission of two identical atoms

NASA Astrophysics Data System (ADS)

Wang, Da-Wei; Li, Zheng-Hong; Zheng, Hang; Zhu, Shi-Yao

2010-04-01

A unitary transformation method is used to investigate the dynamic evolution of two multilevel atoms, in the basis of symmetric and antisymmetric states, with one atom being initially prepared in the first excited state and the other in the ground state. The unitary transformation guarantees that our calculations are based on the ground state of the atom-field system and the self-energy is subtracted at the beginning. The total Lamb shifts of the symmetric and antisymmetric states are divided into transformed shift and dynamic shift. The transformed shift is due to emitting and reabsorbing of virtual photons, by a single atom (nondynamic single atomic shift) and between the two atoms (quasi-static shift). The dynamic shift is due to the emitting and reabsorbing of real photons, by a single atom (dynamic single atomic shift) and between the two atoms (dynamic interatomic shift). The emitting and reabsorbing of virtual and real photons between the two atoms result in the interatomic shift, which does not exist for the one-atom case. The spectra at the long-time limit are calculated. If the distance between the two atoms is shorter than or comparable to the wavelength, the strong coupling between the two atoms splits the spectrum into two peaks, one from the symmetric state and the other from the antisymmetric state. The origin of the red or blue shifts for the symmetric and antisymmetric states mainly lies in the negative or positive interaction energy between the two atoms. In the investigation of the short time evolution, we find the modification of the effective density of states by the interaction between two atoms can modulate the quantum Zeno and quantum anti-Zeno effects in the decays of the symmetric and antisymmetric states.

Surface‐wave Green’s tensors in the near field

USGS Publications Warehouse

Haney, Matt; Nakahara, Hisashi

2014-01-01

We demonstrate the connection between theoretical expressions for the correlation of ambient noise Rayleigh and Love waves and the exact surface‐wave Green’s tensors for a point force. The surface‐wave Green’s tensors are well known in the far‐field limit. On the other hand, the imaginary part of the exact Green’s tensors, including near‐field effects, arises in correlation techniques such as the spatial autocorrelation (SPAC) method. Using the imaginary part of the exact Green’s tensors from the SPAC method, we find the associated real part using the Kramers–Kronig relations. The application of the Kramers–Kronig relations is not straightforward, however, because the causality properties of the different tensor components vary. In addition to the Green’s tensors for a point force, we also derive expressions for a general point moment tensor source.

Perturbative quantum gravity as a double copy of gauge theory.

PubMed

Bern, Zvi; Carrasco, John Joseph M; Johansson, Henrik

2010-08-06

In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.

Dielectric tensor elements for the description of waves in rotating inhomogeneous magnetized plasma spheroids

NASA Astrophysics Data System (ADS)

Abdoli-Arani, A.; Ramezani-Arani, R.

2012-11-01

The dielectric permittivity tensor elements of a rotating cold collisionless plasma spheroid in an external magnetic field with toroidal and axial components are obtained. The effects of inhomogeneity in the densities of charged particles and the initial toroidal velocity on the dielectric permittivity tensor and field equations are investigated. The field components in terms of their toroidal components are calculated and it is shown that the toroidal components of the electric and magnetic fields are coupled by two differential equations. The influence of thermal and collisional effects on the dielectric tensor and field equations in the rotating plasma spheroid are also investigated. In the limiting spherical case, the dielectric tensor of a stationary magnetized collisionless cold plasma sphere is presented.

Symmetric and antisymmetric forms of the Pauli master equation.

PubMed

Klimenko, A Y

2016-07-21

When applied to matter and antimatter states, the Pauli master equation (PME) may have two forms: time-symmetric, which is conventional, and time-antisymmetric, which is suggested in the present work. The symmetric and antisymmetric forms correspond to symmetric and antisymmetric extensions of thermodynamics from matter to antimatter - this is demonstrated by proving the corresponding H-theorem. The two forms are based on the thermodynamic similarity of matter and antimatter and differ only in the directions of thermodynamic time for matter and antimatter (the same in the time-symmetric case and the opposite in the time-antisymmetric case). We demonstrate that, while the symmetric form of PME predicts an equibalance between matter and antimatter, the antisymmetric form of PME favours full conversion of antimatter into matter. At this stage, it is impossible to make an experimentally justified choice in favour of the symmetric or antisymmetric versions of thermodynamics since we have no experience of thermodynamic properties of macroscopic objects made of antimatter, but experiments of this kind may become possible in the future.

Spherical Tensor Calculus for Local Adaptive Filtering

NASA Astrophysics Data System (ADS)

Reisert, Marco; Burkhardt, Hans

In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.

Particle localization, spinor two-valuedness, and Fermi quantization of tensor systems

NASA Technical Reports Server (NTRS)

Reifler, Frank; Morris, Randall

1994-01-01

Recent studies of particle localization shows that square-integrable positive energy bispinor fields in a Minkowski space-time cannot be physically distinguished from constrained tensor fields. In this paper we generalize this result by characterizing all classical tensor systems, which admit Fermi quantization, as those having unitary Lie-Poisson brackets. Examples include Euler's tensor equation for a rigid body and Dirac's equation in tensor form.

Spin polarized phases in strongly interacting matter: Interplay between axial-vector and tensor mean fields

NASA Astrophysics Data System (ADS)

Maruyama, Tomoyuki; Nakano, Eiji; Yanase, Kota; Yoshinaga, Naotaka

2018-06-01

The spontaneous spin polarization of strongly interacting matter due to axial-vector- and tensor-type interactions is studied at zero temperature and high baryon-number densities. We start with the mean-field Lagrangian for the axial-vector and tensor interaction channels and find in the chiral limit that the spin polarization due to the tensor mean field (U ) takes place first as the density increases for sufficiently strong coupling constants, and then the spin polarization due to the axial-vector mean field (A ) emerges in the region of the finite tensor mean field. This can be understood as making the axial-vector mean-field finite requires a broken chiral symmetry somehow, which is achieved by the finite tensor mean field in the present case. It is also found from the symmetry argument that there appear the type I (II) Nambu-Goldstone modes with a linear (quadratic) dispersion in the spin polarized phase with U ≠0 and A =0 (U ≠0 and A ≠0 ), although these two phases exhibit the same symmetry breaking pattern.

Extremely low-frequency Lamb wave band gaps in a sandwich phononic crystal thin plate

NASA Astrophysics Data System (ADS)

Shen, Li; Wu, Jiu Hui; Liu, Zhangyi; Fu, Gang

2015-11-01

In this paper, a kind of sandwich phononic crystal (PC) plate with silicon rubber scatterers embedded in polymethyl methacrylate (PMMA) matrix is proposed to demonstrate its low-frequency Lamb wave band gap (BG) characteristics. The dispersion relationship and the displacement vector fields of the basic slab modes and the locally resonant modes are investigated to show the BG formation mechanism. The anti-symmetric Lamb wave BG is further studied due to its important function in reducing vibration. The analysis on the BG characteristics of the PC through changing their geometrical parameters is performed. By optimizing the structure, a sandwich PC plate with a thickness of only 3 mm and a lower boundary (as low as 23.9 Hz) of the first anti-symmetric BG is designed. Finally, sound insulation experiment on a sandwich PC plate with the thickness of only 2.5 mm is conducted, showing satisfactory noise reduction effect in the frequency range of the anti-symmetric Lamb BG. Therefore, this kind of sandwich PC plate has potential applications in controlling vibration and noise in low-frequency ranges.

Local White Matter Geometry from Diffusion Tensor Gradients

PubMed Central

Savadjiev, Peter; Kindlmann, Gordon L.; Bouix, Sylvain; Shenton, Martha E.; Westin, Carl-Fredrik

2009-01-01

We introduce a mathematical framework for computing geometrical properties of white matter fibres directly from diffusion tensor fields. The key idea is to isolate the portion of the gradient of the tensor field corresponding to local variation in tensor orientation, and to project it onto a coordinate frame of tensor eigenvectors. The resulting eigenframe-centered representation then makes it possible to define scalar indices (or measures) that describe the local white matter geometry directly from the diffusion tensor field and its gradient, without requiring prior tractography. We derive new scalar indices of (1) fibre dispersion and (2) fibre curving, and we demonstrate them on synthetic and in vivo data. Finally, we illustrate their applicability to a group study on schizophrenia. PMID:19896542

Local White Matter Geometry from Diffusion Tensor Gradients

PubMed Central

Savadjiev, Peter; Kindlmann, Gordon L.; Bouix, Sylvain; Shenton, Martha E.; Westin, Carl-Fredrik

2010-01-01

We introduce a mathematical framework for computing geometrical properties of white matter fibres directly from diffusion tensor fields. The key idea is to isolate the portion of the gradient of the tensor field corresponding to local variation in tensor orientation, and to project it onto a coordinate frame of tensor eigenvectors. The resulting eigenframe-centered representation then makes it possible to define scalar indices (or measures) that describe the local white matter geometry directly from the diffusion tensor field and its gradient, without requiring prior tractography. We derive new scalar indices of (1) fibre dispersion and (2) fibre curving, and we demonstrate them on synthetic and in vivo data. Finally, we illustrate their applicability to a group study on schizophrenia. PMID:20426006

Automatic deformable diffusion tensor registration for fiber population analysis.

PubMed

Irfanoglu, M O; Machiraju, R; Sammet, S; Pierpaoli, C; Knopp, M V

2008-01-01

In this work, we propose a novel method for deformable tensor-to-tensor registration of Diffusion Tensor Images. Our registration method models the distances in between the tensors with Geode-sic-Loxodromes and employs a version of Multi-Dimensional Scaling (MDS) algorithm to unfold the manifold described with this metric. Defining the same shape properties as tensors, the vector images obtained through MDS are fed into a multi-step vector-image registration scheme and the resulting deformation fields are used to reorient the tensor fields. Results on brain DTI indicate that the proposed method is very suitable for deformable fiber-to-fiber correspondence and DTI-atlas construction.

Symmetric and antisymmetric forms of the Pauli master equation

PubMed Central

Klimenko, A. Y.

2016-01-01

When applied to matter and antimatter states, the Pauli master equation (PME) may have two forms: time-symmetric, which is conventional, and time-antisymmetric, which is suggested in the present work. The symmetric and antisymmetric forms correspond to symmetric and antisymmetric extensions of thermodynamics from matter to antimatter — this is demonstrated by proving the corresponding H-theorem. The two forms are based on the thermodynamic similarity of matter and antimatter and differ only in the directions of thermodynamic time for matter and antimatter (the same in the time-symmetric case and the opposite in the time-antisymmetric case). We demonstrate that, while the symmetric form of PME predicts an equibalance between matter and antimatter, the antisymmetric form of PME favours full conversion of antimatter into matter. At this stage, it is impossible to make an experimentally justified choice in favour of the symmetric or antisymmetric versions of thermodynamics since we have no experience of thermodynamic properties of macroscopic objects made of antimatter, but experiments of this kind may become possible in the future. PMID:27440454

Curvature tensors unified field equations on SEXn

NASA Astrophysics Data System (ADS)

Chung, Kyung Tae; Lee, Il Young

1988-09-01

We study the curvature tensors and field equations in the n-dimensional SE manifold SEXn. We obtain several basic properties of the vectors S λ and U 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 SEXn and one of its particular solutions is constructed and displayed.

MRI diffusion tensor reconstruction with PROPELLER data acquisition.

PubMed

Cheryauka, Arvidas B; Lee, James N; Samsonov, Alexei A; Defrise, Michel; Gullberg, Grant T

2004-02-01

MRI diffusion imaging is effective in measuring the diffusion tensor in brain, cardiac, liver, and spinal tissue. Diffusion tensor tomography MRI (DTT MRI) method is based on reconstructing the diffusion tensor field from measurements of projections of the tensor field. Projections are obtained by appropriate application of rotated diffusion gradients. In the present paper, the potential of a novel data acquisition scheme, PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction), is examined in combination with DTT MRI for its capability and sufficiency for diffusion imaging. An iterative reconstruction algorithm is used to reconstruct the diffusion tensor field from rotated diffusion weighted blades by appropriate rotated diffusion gradients. DTT MRI with PROPELLER data acquisition shows significant potential to reduce the number of weighted measurements, avoid ambiguity in reconstructing diffusion tensor parameters, increase signal-to-noise ratio, and decrease the influence of signal distortion.

Optical implementation of neural learning algorithms based on cross-gain modulation in a semiconductor optical amplifier

NASA Astrophysics Data System (ADS)

Li, Qiang; Wang, Zhi; Le, Yansi; Sun, Chonghui; Song, Xiaojia; Wu, Chongqing

2016-10-01

Neuromorphic engineering has a wide range of applications in the fields of machine learning, pattern recognition, adaptive control, etc. Photonics, characterized by its high speed, wide bandwidth, low power consumption and massive parallelism, is an ideal way to realize ultrafast spiking neural networks (SNNs). Synaptic plasticity is believed to be critical for learning, memory and development in neural circuits. Experimental results have shown that changes of synapse are highly dependent on the relative timing of pre- and postsynaptic spikes. Synaptic plasticity in which presynaptic spikes preceding postsynaptic spikes results in strengthening, while the opposite timing results in weakening is called antisymmetric spike-timing-dependent plasticity (STDP) learning rule. And synaptic plasticity has the opposite effect under the same conditions is called antisymmetric anti-STDP learning rule. We proposed and experimentally demonstrated an optical implementation of neural learning algorithms, which can achieve both of antisymmetric STDP and anti-STDP learning rule, based on the cross-gain modulation (XGM) within a single semiconductor optical amplifier (SOA). The weight and height of the potentitation and depression window can be controlled by adjusting the injection current of the SOA, to mimic the biological antisymmetric STDP and anti-STDP learning rule more realistically. As the injection current increases, the width of depression and potentitation window decreases and height increases, due to the decreasing of recovery time and increasing of gain under a stronger injection current. Based on the demonstrated optical STDP circuit, ultrafast learning in optical SNNs can be realized.

Erratum to Surface‐wave green’s tensors in the near field

USGS Publications Warehouse

Haney, Matthew M.; Hisashi Nakahara,

2016-01-01

Haney and Nakahara (2014) derived expressions for surface‐wave Green’s tensors that included near‐field behavior. Building on the result for a force source, Haney and Nakahara (2014) further derived expressions for a general point moment tensor source using the exact Green’s tensors. However, it has come to our attention that, although the Green’s tensors were correct, the resulting expressions for a general point moment tensor source were missing some terms. In this erratum, we provide updated expressions with these missing terms. The inclusion of the missing terms changes the example given in Haney and Nakahara (2014).

A theoretical study of potentially observable chirality-sensitive NMR effects in molecules.

PubMed

Garbacz, Piotr; Cukras, Janusz; Jaszuński, Michał

2015-09-21

Two recently predicted nuclear magnetic resonance effects, the chirality-induced rotating electric polarization and the oscillating magnetization, are examined for several experimentally available chiral molecules. We discuss in detail the requirements for experimental detection of chirality-sensitive NMR effects of the studied molecules. These requirements are related to two parameters: the shielding polarizability and the antisymmetric part of the nuclear magnetic shielding tensor. The dominant second contribution has been computed for small molecules at the coupled cluster and density functional theory levels. It was found that DFT calculations using the KT2 functional and the aug-cc-pCVTZ basis set adequately reproduce the CCSD(T) values obtained with the same basis set. The largest values of parameters, thus most promising from the experimental point of view, were obtained for the fluorine nuclei in 1,3-difluorocyclopropene and 1,3-diphenyl-2-fluoro-3-trifluoromethylcyclopropene.

Optical Near-Field Plates

DTIC Science & Technology

2015-04-08

AFRL-OSR-VA-TR-2015-0085 OPTICAL NEAR-FILED PLATES Roberto Merlin UNIVERSITY OF MICHIGAN Final Report 04/08/2015 DISTRIBUTION A: Distribution...03-2015 Final 09/01/2009-12/31/2014 Optical Near-Field Plates FA9550-09-1-0636 erlin, Roberto, D. The University of Michigan Ann Arbor, MI 48109...distribution unlimited Optical near-field plates were designed using antisymmetric plasmon modes to generate abrupt phase changes within a fraction of a

Characteristics of the surface plasma wave in a self-gravitating magnetized dusty plasma slab

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Myoung-Jae; Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr; Department of Applied Physics and Department of Bionanotechnology, Hanyang University, Ansan, Kyunggi-Do 15588

2015-11-15

The dispersion properties of surface dust ion-acoustic waves in a self-gravitating magnetized dusty plasma slab are investigated. The dispersion relation is derived by using the low-frequency magnetized dusty dielectric function and the surface wave dispersion integral for the slab geometry. We find that the self-gravitating effect suppresses the frequency of surface dust ion-acoustic wave for the symmetric mode in the long wavelength regime, whereas it hardly changes the frequency for the anti-symmetric mode. As the slab thickness and the wave number increase, the surface wave frequency slowly decreases for the symmetric mode but increases significantly for the anti-symmetric mode. Themore » influence of external magnetic field is also investigated in the case of symmetric mode. We find that the strength of the magnetic field enhances the frequency of the symmetric-mode of the surface plasma wave. The increase of magnetic field reduces the self-gravitational effect and thus the self-gravitating collapse may be suppressed and the stability of dusty objects in space is enhanced.« less

Diffusion approximation with polarization and resonance effects for the modelling of seismic waves in strongly scattering small-scale media

NASA Astrophysics Data System (ADS)

Margerin, Ludovic

2013-01-01

This paper presents an analytical study of the multiple scattering of seismic waves by a collection of randomly distributed point scatterers. The theory assumes that the energy envelopes are smooth, but does not require perturbations to be small, thereby allowing the modelling of strong, resonant scattering. The correlation tensor of seismic coda waves recorded at a three-component sensor is decomposed into a sum of eigenmodes of the elastodynamic multiple scattering (Bethe-Salpeter) equation. For a general moment tensor excitation, a total number of four modes is necessary to describe the transport of seismic waves polarization. Their spatio-temporal dependence is given in closed analytical form. Two additional modes transporting exclusively shear polarizations may be excited by antisymmetric moment tensor sources only. The general solution converges towards an equipartition mixture of diffusing P and S waves which allows the retrieval of the local Green's function from coda waves. The equipartition time is obtained analytically and the impact of absorption on Green's function reconstruction is discussed. The process of depolarization of multiply scattered waves and the resulting loss of information is illustrated for various seismic sources. It is shown that coda waves may be used to characterize the source mechanism up to lapse times of the order of a few mean free times only. In the case of resonant scatterers, a formula for the diffusivity of seismic waves incorporating the effect of energy entrapment inside the scatterers is obtained. Application of the theory to high-contrast media demonstrates that coda waves are more sensitive to slow rather than fast velocity anomalies by several orders of magnitude. Resonant scattering appears as an attractive physical phenomenon to explain the small values of the diffusion constant of seismic waves reported in volcanic areas.

Retrodictive determinism. [covariant and transformational behavior of tensor fields in hydrodynamics and thermodynamics

NASA Technical Reports Server (NTRS)

Kiehn, R. M.

1976-01-01

With respect to irreversible, non-homeomorphic maps, contravariant and covariant tensor fields have distinctly natural covariance and transformational behavior. For thermodynamic processes which are non-adiabatic, the fact that the process cannot be represented by a homeomorphic map emphasizes the logical arrow of time, an idea which encompasses a principle of retrodictive determinism for covariant tensor fields.

More on the scalar-tensor BF theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, Harvendra

2009-09-15

This work is based on an earlier proposal [H. Singh, Phys. Lett. B 673, 68 (2009)] that the membrane BF theory consists of matter fields along with Chern-Simons fields as well as the auxiliary pairs of scalar and tensor fields. In particular, we discuss the supersymmetry aspects of such a membrane theory. It is concluded that the theory possesses maximal supersymmetry, and it is related to the L-BLG theory via a field map. We obtain fuzzy-sphere solution, and corresponding tensor field configuration is given.

Matter in transition

DOE PAGES

Anderson, Lara B.; Gray, James; Raghuram, Nikhil; ...

2016-04-13

In this study, we explore a novel type of transition in certain 6D and 4D quantum field theories, in which the matter content of the theory changes while the gauge group and other parts of the spectrum remain invariant. Such transitions can occur, for example, for SU(6) and SU(7) gauge groups, where matter fields in a three-index antisymmetric representation and the fundamental representation are exchanged in the transition for matter in the two-index antisymmetric representation. These matter transitions are realized by passing through superconformal theories at the transition point. We explore these transitions in dual F-theory and heterotic descriptions, wheremore » a number of novel features arise. For example, in the heterotic description the relevant 6D SU(7) theories are described by bundles on K3 surfaces where the geometry of the K3 is constrained in addition to the bundle structure. On the F-theory side, non-standard representations such as the three-index antisymmetric representation of SU(N) require Weierstrass models that cannot be realized from the standard SU(N) Tate form. We also briefly describe some other situations, with groups such as Sp(3), SO(12), and SU(3), where analogous matter transitions can occur between different representations. For SU(3), in particular, we find a matter transition between adjoint matter and matter in the symmetric representation, giving an explicit Weierstrass model for the F-theory description of the symmetric representation that complements another recent analogous construction.« less

Conservation laws and stress-energy-momentum tensors for systems with background fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gratus, Jonathan, E-mail: j.gratus@lancaster.ac.uk; The Cockcroft Institute, Daresbury Laboratory, Warrington WA4 4AD; Obukhov, Yuri N., E-mail: yo@thp.uni-koeln.de

2012-10-15

This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious arguments that have historically lead to the main contenders, viz the Belinfante-Rosenfeld stress-energy-momentum tensor derived from a Noether current and the Einstein-Hilbert stress-energy-momentum tensor derived in the context of Einstein's theory of general relativity. Emphasis is placed on the role played by non-dynamical background (phenomenological) structures that discriminate between properties of these tensors particularly in the context of electrodynamics inmore » media. These tensors are used to construct conservation laws in the presence of Killing Lie-symmetric background fields. - Highlights: Black-Right-Pointing-Pointer The role of background fields in diffeomorphism invariant actions is demonstrated. Black-Right-Pointing-Pointer Interrelations between different stress-energy-momentum tensors are emphasised. Black-Right-Pointing-Pointer The Abraham and Minkowski electromagnetic tensors are discussed in this context. Black-Right-Pointing-Pointer Conservation laws in the presence of nondynamic background fields are formulated. Black-Right-Pointing-Pointer The discussion is facilitated by the development of a new variational calculus.« less

Groupwise Registration and Atlas Construction of 4th-Order Tensor Fields Using the ℝ+ Riemannian Metric*

PubMed Central

Barmpoutis, Angelos

2010-01-01

Registration of Diffusion-Weighted MR Images (DW-MRI) can be achieved by registering the corresponding 2nd-order Diffusion Tensor Images (DTI). However, it has been shown that higher-order diffusion tensors (e.g. order-4) outperform the traditional DTI in approximating complex fiber structures such as fiber crossings. In this paper we present a novel method for unbiased group-wise non-rigid registration and atlas construction of 4th-order diffusion tensor fields. To the best of our knowledge there is no other existing method to achieve this task. First we define a metric on the space of positive-valued functions based on the Riemannian metric of real positive numbers (denoted by ℝ+). Then, we use this metric in a novel functional minimization method for non-rigid 4th-order tensor field registration. We define a cost function that accounts for the 4th-order tensor re-orientation during the registration process and has analytic derivatives with respect to the transformation parameters. Finally, the tensor field atlas is computed as the minimizer of the variance defined using the Riemannian metric. We quantitatively compare the proposed method with other techniques that register scalar-valued or diffusion tensor (rank-2) representations of the DWMRI. PMID:20436782

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakatsuji, Hiroshi, E-mail: h.nakatsuji@qcri.or.jp; Nakashima, Hiroyuki

The Schrödinger equation (SE) and the antisymmetry principle constitute the governing principle of chemistry. A general method of solving the SE was presented before as the free complement (FC) theory, which gave highly accurate solutions for small atoms and molecules. We assume here to use the FC theory starting from the local valence bond wave function. When this theory is applied to larger molecules, antisymmetrizations of electronic wave functions become time-consuming and therefore, an additional breakthrough is necessary concerning the antisymmetry principle. Usually, in molecular calculations, we first construct the wave function to satisfy the antisymmetry rule, “electronic wave functionsmore » must be prescribed to be antisymmetric for all exchanges of electrons, otherwise bosonic interference may disturb the basis of the science.” Starting from determinantal wave functions is typical. Here, we give an antisymmetrization theory, called inter-exchange (iExg) theory, by dividing molecular antisymmetrizations to those within atoms and between atoms. For the electrons belonging to distant atoms in a molecule, only partial antisymmetrizations or even no antisymmetrizations are necessary, depending on the distance between the atoms. So, the above antisymmetry rule is not necessarily followed strictly to get the results of a desired accuracy. For this and other reasons, the necessary parts of the antisymmetrization operations become very small as molecules become larger, leading finally to the operation counts of lower orders of N, the number of electrons. This theory creates a natural antisymmetrization method that is useful for large molecules.« less

Solving the Schrödinger equation of molecules by relaxing the antisymmetry rule: Inter-exchange theory.

PubMed

Nakatsuji, Hiroshi; Nakashima, Hiroyuki

2015-05-21

The Schrödinger equation (SE) and the antisymmetry principle constitute the governing principle of chemistry. A general method of solving the SE was presented before as the free complement (FC) theory, which gave highly accurate solutions for small atoms and molecules. We assume here to use the FC theory starting from the local valence bond wave function. When this theory is applied to larger molecules, antisymmetrizations of electronic wave functions become time-consuming and therefore, an additional breakthrough is necessary concerning the antisymmetry principle. Usually, in molecular calculations, we first construct the wave function to satisfy the antisymmetry rule, "electronic wave functions must be prescribed to be antisymmetric for all exchanges of electrons, otherwise bosonic interference may disturb the basis of the science." Starting from determinantal wave functions is typical. Here, we give an antisymmetrization theory, called inter-exchange (iExg) theory, by dividing molecular antisymmetrizations to those within atoms and between atoms. For the electrons belonging to distant atoms in a molecule, only partial antisymmetrizations or even no antisymmetrizations are necessary, depending on the distance between the atoms. So, the above antisymmetry rule is not necessarily followed strictly to get the results of a desired accuracy. For this and other reasons, the necessary parts of the antisymmetrization operations become very small as molecules become larger, leading finally to the operation counts of lower orders of N, the number of electrons. This theory creates a natural antisymmetrization method that is useful for large molecules.

Aspects Topologiques de la Theorie des Champs et leurs Applications

NASA Astrophysics Data System (ADS)

Caenepeel, Didier

This thesis is dedicated to the study of various topological aspects of field theory, and is divided in three parts. In two space dimensions the possibility of fractional statistics can be implemented by adding an appropriate "fictitious" electric charge and magnetic flux to each particle (after which they are known as anyons). Since the statistical interaction is rather difficult to handle, a mean-field approximation is used in order to describe a gas of anyons. We derive a criterion for the validity of this approximation using the inherent feature of parity violation in the scattering of anyons. We use this new method in various examples of anyons and show both analytically and numerically that the approximation is justified if the statistical interaction is weak, and that it must be more weak for boson-based than for fermion-based anyons. Chern-Simons theories give an elegant implementation of anyonic properties in field theories, which permits the emergence of new mechanisms for anyon superconductivity. Since it is reasonable to think that superconductivity is a low energy phenomenon, we have been interested in non-relativistic C-S systems. We present the scalar field effective potential for non-relativistic matter coupled to both Abelian and non-Abelian C-S gauge fields. We perform the calculations using functional methods in background fields. Finally, we compute the scalar effective potential in various gauges and treat divergences with various regularization schemes. In three space dimensions, a generalization of Chern-Simons theory may be achieved by introducing an antisymmetric tensor gauge field. We use these theories, called B wedge F theories, to present an alternative to the Higgs mechanism to generate masses for non-Abelian gauge fields. The initial Lagrangian is composed of a fermion with current-current and dipole-dipole type self -interactions minimally coupled to non-Abelian gauge fields. The mass generation occurs upon the fermionic functional integration. We show that by suitably adjusting the coupling constants the effective theory contains massive non-Abelian gauge fields without any residual scalars or other degrees of freedom.

Tensor non-Gaussianity from axion-gauge-fields dynamics: parameter search

NASA Astrophysics Data System (ADS)

Agrawal, Aniket; Fujita, Tomohiro; Komatsu, Eiichiro

2018-06-01

We calculate the bispectrum of scale-invariant tensor modes sourced by spectator SU(2) gauge fields during inflation in a model containing a scalar inflaton, a pseudoscalar axion and SU(2) gauge fields. A large bispectrum is generated in this model at tree-level as the gauge fields contain a tensor degree of freedom, and its production is dominated by self-coupling of the gauge fields. This is a unique feature of non-Abelian gauge theory. The shape of the tensor bispectrum is approximately an equilateral shape for 3lesssim mQlesssim 4, where mQ is an effective dimensionless mass of the SU(2) field normalised by the Hubble expansion rate during inflation. The amplitude of non-Gaussianity of the tensor modes, characterised by the ratio Bh/P2h, is inversely proportional to the energy density fraction of the gauge field. This ratio can be much greater than unity, whereas the ratio from the vacuum fluctuation of the metric is of order unity. The bispectrum is effective at constraining large mQ regions of the parameter space, whereas the power spectrum constrains small mQ regions.

Reflection and transmission characteristics of a layer obeying the two-pressure field poroelastic phenomenological model of Berryman and Wang.

PubMed

Kachkouch, F; Franklin, H; Tinel, A

2018-07-01

The characteristics of the reflection and transmission by a fluid-loaded double porosity layer are studied. The medium obeys the two-pressure field poroelastic phenomenological model of Berryman and Wang. The open pore hydraulic conditions applied at the interfaces yield factorized expressions for the coefficients exhibiting on the one hand a separation allowing to distinguish between symmetrical and antisymmetrical motions and on the other hand the way each of the three dilatational waves associate with the shear wave. The numerical study done for a layer of Berea sandstone saturated by water shows clearly the role of each of the dilatational waves. There are peculiarities such as the absence of the fundamental antisymmetrical mode (zero order) and a singular behaviour of the symmetrical fundamental mode. The low frequency approximation for this latter is derived from the proposed formulas and compared with the numerical results. Copyright © 2018 Elsevier B.V. All rights reserved.

Density matrix embedding in an antisymmetrized geminal power bath

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsuchimochi, Takashi; Welborn, Matthew; Van Voorhis, Troy, E-mail: tvan@mit.edu

2015-07-14

Density matrix embedding theory (DMET) has emerged as a powerful tool for performing wave function-in-wave function embedding for strongly correlated systems. In traditional DMET, an accurate calculation is performed on a small impurity embedded in a mean field bath. Here, we extend the original DMET equations to account for correlation in the bath via an antisymmetrized geminal power (AGP) wave function. The resulting formalism has a number of advantages. First, it allows one to properly treat the weak correlation limit of independent pairs, which DMET is unable to do with a mean-field bath. Second, it associates a size extensive correlationmore » energy with a given density matrix (for the models tested), which AGP by itself is incapable of providing. Third, it provides a reasonable description of charge redistribution in strongly correlated but non-periodic systems. Thus, AGP-DMET appears to be a good starting point for describing electron correlation in molecules, which are aperiodic and possess both strong and weak electron correlation.« less

On the energy-momentum tensor in Moyal space

DOE PAGES

Balasin, Herbert; Blaschke, Daniel N.; Gieres, François; ...

2015-06-26

We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another starproduct. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the latter two procedures are incompatible with each other if couplings of gaugemore » fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice-versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line.« less

Scalar field coupling to Einstein tensor in regular black hole spacetime

NASA Astrophysics Data System (ADS)

Zhang, Chi; Wu, Chen

2018-02-01

In this paper, we study the perturbation property of a scalar field coupling to Einstein's tensor in the background of the regular black hole spacetimes. Our calculations show that the the coupling constant η imprints in the wave equation of a scalar perturbation. We calculated the quasinormal modes of scalar field coupling to Einstein's tensor in the regular black hole spacetimes by the 3rd order WKB method.

Linear and angular coherence momenta in the classical second-order coherence theory of vector electromagnetic fields.

PubMed

Wang, Wei; Takeda, Mitsuo

2006-09-01

A new concept of vector and tensor densities is introduced into the general coherence theory of vector electromagnetic fields that is based on energy and energy-flow coherence tensors. Related coherence conservation laws are presented in the form of continuity equations that provide new insights into the propagation of second-order correlation tensors associated with stationary random classical electromagnetic fields.

Full magnetic gradient tensor from triaxial aeromagnetic gradient measurements: Calculation and application

NASA Astrophysics Data System (ADS)

Luo, Yao; Wu, Mei-Ping; Wang, Ping; Duan, Shu-Ling; Liu, Hao-Jun; Wang, Jin-Long; An, Zhan-Feng

2015-09-01

The full magnetic gradient tensor (MGT) refers to the spatial change rate of the three field components of the geomagnetic field vector along three mutually orthogonal axes. The tensor is of use to geological mapping, resources exploration, magnetic navigation, and others. However, it is very difficult to measure the full magnetic tensor gradient using existing engineering technology. We present a method to use triaxial aeromagnetic gradient measurements for deriving the full MGT. The method uses the triaxial gradient data and makes full use of the variation of the magnetic anomaly modulus in three dimensions to obtain a self-consistent magnetic tensor gradient. Numerical simulations show that the full MGT data obtained with the proposed method are of high precision and satisfy the requirements of data processing. We selected triaxial aeromagnetic gradient data from the Hebei Province for calculating the full MGT. Data processing shows that using triaxial tensor gradient data allows to take advantage of the spatial rate of change of the total field in three dimensions and suppresses part of the independent noise in the aeromagnetic gradient. The calculated tensor components have improved resolution, and the transformed full tensor gradient satisfies the requirement of geological mapping and interpretation.

Affine theory of gravitation

NASA Astrophysics Data System (ADS)

Popławski, Nikodem

2014-01-01

We propose a theory of gravitation, in which the affine connection is the only dynamical variable describing the gravitational field. We construct a simple dynamical Lagrangian density that is entirely composed from the connection, via its curvature and torsion, and is a polynomial function of its derivatives. It is given by the contraction of the Ricci tensor with a tensor which is inverse to the symmetric, contracted square of the torsion tensor, . We vary the total action for the gravitational field and matter with respect to the affine connection, assuming that the matter fields couple to the connection only through . We derive the resulting field equations and show that they are identical with the Einstein equations of general relativity with a nonzero cosmological constant if the tensor is regarded as proportional to the metric tensor. The cosmological constant is simply a constant of proportionality between the two tensors, which together with and provides a natural system of units in gravitational physics. This theory therefore provides a physical construction of the metric as a polynomial function of the connection, and explains dark energy as an intrinsic property of spacetime.

On the Tensorial Nature of Fluxes in Continuous Media.

ERIC Educational Resources Information Center

Stokes, Vijay Kumar; Ramkrishna, Doraiswami

1982-01-01

Argues that mass and energy fluxes in a fluid are vectors. Topics include the stress tensor, theorem for tensor fields, mass flux as a vector, stress as a second order tensor, and energy flux as a tensor. (SK)

Diffusion Tensor Image Registration Using Hybrid Connectivity and Tensor Features

PubMed Central

Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang

2014-01-01

Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. PMID:24293159

Killing vector fields in three dimensions: a method to solve massive gravity field equations

NASA Astrophysics Data System (ADS)

Gürses, Metin

2010-10-01

Killing vector fields in three dimensions play an important role in the construction of the related spacetime geometry. In this work we show that when a three-dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the Ricci tensor. Using this property we give ways to solve the field equations of topologically massive gravity (TMG) and new massive gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three-dimensional symmetric tensors of the geometry, the Ricci and Einstein tensors, their covariant derivatives at all orders, and their products of all orders are completely determined by the Killing vector field and the metric. Hence, the corresponding three-dimensional metrics are strong candidates for solving all higher derivative gravitational field equations in three dimensions.

Missing magnetism in Sr 4Ru 3O 10: Indication for Antisymmetric Exchange Interaction

DOE PAGES

Weickert, Franziska; Civale, Leonardo; Maiorov, Boris; ...

2017-06-20

Metamagnetism occuring inside a ferromagnetic phase is peculiar. Therefore, Sr 4Ru 3O 10, a T C = 105 K ferromagnet, has attracted much attention in recent years, because it develops a pronounced metamagnetic anomaly below T C for magnetic fields applied in the crystallographic ab-plane. The metamagnetic transition moves to higher fields for lower temperatures and splits into a double anomaly at critical fields H c1 = 2.3 T and H c2 = 2.8 T, respectively. Here, we report a detailed study of the different components of the magnetization vector as a function of temperature, applied magnetic field, and varyingmore » angle in Sr 4Ru 3O 10. We discover for the first time a reduction of the magnetic moment in the plane of rotation at the metamagnetic transition. The anomaly shifts to higher fields by rotating the field from H ⊥ c to H || c. We compare our experimental findings with numerical simulations based on spin reorientation models taking into account magnetocrystalline anisotropy, Zeeman effect and antisymmetric exchange interactions. While Magnetocrystalline anisotropy combined with a Zeeman term are sufficient to explain a metamagnetic transition in Sr 4Ru 3O 10, a Dzyaloshinskii-Moriya term is crucial to account for the reduction of the magnetic moment as observed in the experiments.« less

Missing magnetism in Sr 4Ru 3O 10: Indication for Antisymmetric Exchange Interaction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weickert, Franziska; Civale, Leonardo; Maiorov, Boris

Metamagnetism occuring inside a ferromagnetic phase is peculiar. Therefore, Sr 4Ru 3O 10, a T C = 105 K ferromagnet, has attracted much attention in recent years, because it develops a pronounced metamagnetic anomaly below T C for magnetic fields applied in the crystallographic ab-plane. The metamagnetic transition moves to higher fields for lower temperatures and splits into a double anomaly at critical fields H c1 = 2.3 T and H c2 = 2.8 T, respectively. Here, we report a detailed study of the different components of the magnetization vector as a function of temperature, applied magnetic field, and varyingmore » angle in Sr 4Ru 3O 10. We discover for the first time a reduction of the magnetic moment in the plane of rotation at the metamagnetic transition. The anomaly shifts to higher fields by rotating the field from H ⊥ c to H || c. We compare our experimental findings with numerical simulations based on spin reorientation models taking into account magnetocrystalline anisotropy, Zeeman effect and antisymmetric exchange interactions. While Magnetocrystalline anisotropy combined with a Zeeman term are sufficient to explain a metamagnetic transition in Sr 4Ru 3O 10, a Dzyaloshinskii-Moriya term is crucial to account for the reduction of the magnetic moment as observed in the experiments.« less

Simplified derivation of the gravitational wave stress tensor from the linearized Einstein field equations.

PubMed

Balbus, Steven A

2016-10-18

A conserved stress energy tensor for weak field gravitational waves propagating in vacuum is derived directly from the linearized general relativistic wave equation alone, for an arbitrary gauge. In any harmonic gauge, the form of the tensor leads directly to the classical expression for the outgoing wave energy. The method described here, however, is a much simpler, shorter, and more physically motivated approach than is the customary procedure, which involves a lengthy and cumbersome second-order (in wave-amplitude) calculation starting with the Einstein tensor. Our method has the added advantage of exhibiting the direct coupling between the outgoing wave energy flux and the work done by the gravitational field on the sources. For nonharmonic gauges, the directly derived wave stress tensor has an apparent index asymmetry. This coordinate artifact may be straightforwardly removed, and the symmetrized (still gauge-invariant) tensor then takes on its widely used form. Angular momentum conservation follows immediately. For any harmonic gauge, however, the stress tensor found is manifestly symmetric from the start, and its derivation depends, in its entirety, on the structure of the linearized wave equation.

Theory of electron g-tensor in bulk and quantum-well semiconductors

NASA Astrophysics Data System (ADS)

Lau, Wayne H.; Flatte', Michael E.

2004-03-01

We present quantitative calculations for the electron g-tensors in bulk and quantum-well semiconductors based on a generalized P.p envelope function theory solved in a fourteen-band restricted basis set. The dependences of g-tensor on structure, magnetic field, carrier density, temperature, and spin polarization have been explored and will be described. It is found that at temperatures of a few Kelvin and fields of a few Tesla, the g-tensors for bulk semiconductors develop quasi-steplike dependences on carrier density or magnetic field due to magnetic quantization, and this effect is even more pronounced in quantum-well semiconductors due to the additional electric quantization along the growth direction. The influence of quantum confinement on the electron g-tensors in QWs is studied by examining the dependence of electron g-tensors on well width. Excellent agreement between these calculated electron g-tensors and measurements [1-2] is found for GaAs/AlGaAs QWs. This work was supported by DARPA/ARO. [1] A. Malinowski and R. T. Harley, Phys. Rev. B 62, 2051 (2000);[2] Le Jeune et al., Semicond. Sci. Technol. 12, 380 (1997).

Tensor Galileons and gravity

NASA Astrophysics Data System (ADS)

Chatzistavrakidis, Athanasios; Khoo, Fech Scen; Roest, Diederik; Schupp, Peter

2017-03-01

The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian p-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixed-symmetry tensor fields and coupled systems thereof. We argue that these tensors are the natural generalization of scalars with Galileon symmetry, similar to p-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.

Electro-gravity via geometric chrononfield

NASA Astrophysics Data System (ADS)

Suchard, Eytan H.

2017-05-01

In De Sitter / Anti De Sitter space-time and in other geometries, reference sub-manifolds from which proper time is measured along integral curves, are described as events. We introduce here a foliation with the help of a scalar field. The scalar field need not be unique but from the gradient of the scalar field, an intrinsic Reeb vector of the foliations perpendicular to the gradient vector is calculated. The Reeb vector describes the acceleration of a physical particle that moves along the integral curves that are formed by the gradient of the scalar field. The Reeb vector appears as a component of an anti-symmetric matrix which is a part of a rank-2, 2-Form. The 2-form is extended into a non-degenerate 4-form and into rank-4 matrix of a 2-form, which when multiplied by a velocity of a particle, becomes the acceleration of the particle. The matrix has one U(1) degree of freedom and an additional SU(2) degrees of freedom in two vectors that span the plane perpendicular to the gradient of the scalar field and to the Reeb vector. In total, there are U(1) x SU(2) degrees of freedom. SU(3) degrees of freedom arise from three dimensional foliations but require an additional symmetry to exist in order to have a valid covariant meaning. Matter in the Einstein Grossmann equation is replaced by the action of the acceleration field, i.e. by a geometric action which is not anticipated by the metric alone. This idea leads to a new formalism that replaces the conventional stress-energy-momentum-tensor. The formalism will be mainly developed for classical physics but will also be discussed for quantized physics based on events instead of particles. The result is that a positive charge manifests small attracting gravity and a stronger but small repelling acceleration field that repels even uncharged particles that have a rest mass. Negative charge manifests a repelling anti-gravity but also a stronger acceleration field that attracts even uncharged particles that have rest mass. Preliminary version: http://sciencedomain.org/abstract/9858

A Review of Tensors and Tensor Signal Processing

NASA Astrophysics Data System (ADS)

Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.

Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.

High-power, surface-emitting quantum cascade laser operating in a symmetric grating mode

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boyle, C.; Sigler, C.; Kirch, J. D.

2016-03-21

Grating-coupled surface-emitting (GCSE) lasers generally operate with a double-lobed far-field beam pattern along the cavity-length direction, which is a result of lasing being favored in the antisymmetric grating mode. We experimentally demonstrate a GCSE quantum-cascade laser design allowing high-power, nearly single-lobed surface emission parallel to the longitudinal cavity. A 2nd-order Au-semiconductor distributed-feedback (DFB)/distributed-Bragg-reflector (DBR) grating is used for feedback and out-coupling. The DFB and DBR grating regions are 2.55 mm- and 1.28 mm-long, respectively, for a total grating length of 5.1 mm. The lasers are designed to operate in a symmetric (longitudinal) grating mode by causing resonant coupling of the guided optical modemore » to the antisymmetric surface-plasmon modes of the 2nd-order metal/semiconductor grating. Then, the antisymmetric modes are strongly absorbed by the metal in the grating, causing the symmetric mode to be favored to lase, which, in turn, produces a single-lobed beam over a range of grating duty-cycle values of 36%–41%. Simulations indicate that the symmetric mode is always favored to lase, independent of the random phase of reflections from the device's cleaved ends. Peak pulsed output powers of ∼0.4 W were measured with nearly single-lobe beam-pattern (in the longitudinal direction), single-spatial-mode operation near 4.75 μm wavelength. Far-field measurements confirm a diffraction-limited beam pattern, in agreement with simulations, for a source-to-detector separation of 2 m.« less

Calculation and Analysis of magnetic gradient tensor components of global magnetic models

NASA Astrophysics Data System (ADS)

Schiffler, Markus; Queitsch, Matthias; Schneider, Michael; Stolz, Ronny; Krech, Wolfram; Meyer, Hans-Georg; Kukowski, Nina

2014-05-01

Magnetic mapping missions like SWARM and its predecessors, e.g. the CHAMP and MAGSAT programs, offer high resolution Earth's magnetic field data. These datasets are usually combined with magnetic observatory and survey data, and subject to harmonic analysis. The derived spherical harmonic coefficients enable magnetic field modelling using a potential series expansion. Recently, new instruments like the JeSSY STAR Full Tensor Magnetic Gradiometry system equipped with very high sensitive sensors can directly measure the magnetic field gradient tensor components. The full understanding of the quality of the measured data requires the extension of magnetic field models to gradient tensor components. In this study, we focus on the extension of the derivation of the magnetic field out of the potential series magnetic field gradient tensor components and apply the new theoretical framework to the International Geomagnetic Reference Field (IGRF) and the High Definition Magnetic Model (HDGM). The gradient tensor component maps for entire Earth's surface produced for the IGRF show low values and smooth variations reflecting the core and mantle contributions whereas those for the HDGM gives a novel tool to unravel crustal structure and deep-situated ore bodies. For example, the Thor Suture and the Sorgenfrei-Thornquist Zone in Europe are delineated by a strong northward gradient. Derived from Eigenvalue decomposition of the magnetic gradient tensor, the scaled magnetic moment, normalized source strength (NSS) and the bearing of the lithospheric sources are presented. The NSS serves as a tool for estimating the lithosphere-asthenosphere boundary as well as the depth of plutons and ore bodies. Furthermore changes in magnetization direction parallel to the mid-ocean ridges can be obtained from the scaled magnetic moment and the normalized source strength discriminates the boundaries between the anomalies of major continental provinces like southern Africa or the Eastern European Craton.

Variational optical flow estimation based on stick tensor voting.

PubMed

Rashwan, Hatem A; Garcia, Miguel A; Puig, Domenec

2013-07-01

Variational optical flow techniques allow the estimation of flow fields from spatio-temporal derivatives. They are based on minimizing a functional that contains a data term and a regularization term. Recently, numerous approaches have been presented for improving the accuracy of the estimated flow fields. Among them, tensor voting has been shown to be particularly effective in the preservation of flow discontinuities. This paper presents an adaptation of the data term by using anisotropic stick tensor voting in order to gain robustness against noise and outliers with significantly lower computational cost than (full) tensor voting. In addition, an anisotropic complementary smoothness term depending on directional information estimated through stick tensor voting is utilized in order to preserve discontinuity capabilities of the estimated flow fields. Finally, a weighted non-local term that depends on both the estimated directional information and the occlusion state of pixels is integrated during the optimization process in order to denoise the final flow field. The proposed approach yields state-of-the-art results on the Middlebury benchmark.

Strain Analysis in Horizontal Geodetic Network of Dams for Control of Stability and Monitoring Deformation

NASA Astrophysics Data System (ADS)

Roohi, S.; Ardalan, A. A.; Khodakarami, M.

2009-04-01

Dams as one of the engineering structures play very important role in human life. Because, from primary human needs such as providing drinking water to professional needs such as water powerhouse creation in order to provide power for industrial centers, hospitals, manufactures and agriculture, have considerable dependent on dams. In addition destruction of a dam can be as dangerous as earthquake. Therefore maintenance, stability control and monitoring deformation of them is indispensable. In order to control stability of dams and their around lands and monitoring deformation a network is created by surveyor, geologist and dam experts on crest and body of dam or on land near the dam. Geodetic observations are done in this network by precise surveying instrument in deferent time then by using linear least square parametric adjustment method, adjusted coordinates with their variance- covariance matrix and error ellipses, redundancy numbers for observation, blunders and … are estimated in each epoch. Then displacement vectors are computed in each point of network, After that by use of Lagrangeian deformation idea and constitution of deformation equations movement, displacement model is determined and strain tensor is computed. we can induce deformation information from strain tensor in different ways such as strain ellipse then interpret deformation that happen in each point of network. Also we can compute rigid rotation from anti-symmetric part of displacement gradient tensor. After processing tow consequence epochs observations of horzontal geodetic network of Hnna dam in southwest of Esfahan, the most semi-major axis of error ellipse is estimated about 0.9mm for point D10, largest displacement is 1.4mm for point C3 that it's semimajor axis of displacement error ellipse is 1.3mm and there is different shear in all of network points exceptional points D2,C3 and C2. There is different dilatation in most of points. These amount of maximum shear and dilatation are justified because of horizontal displacement and subsidence of dam due to pressure of water that conserve behind it. Key word: strain tensor, monitoring deformation, Geodetic network, deformation equation movement, error ellipse, strain ellipse, shear, dilatation

Ostrogradsky in theories with multiple fields

NASA Astrophysics Data System (ADS)

de Rham, Claudia; Matas, Andrew

2016-06-01

We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.

A geometric description of Maxwell field in a Kerr spacetime

NASA Astrophysics Data System (ADS)

Jezierski, Jacek; Smołka, Tomasz

2016-06-01

We consider the Maxwell field in the exterior of a Kerr black hole. For this system, we propose a geometric construction of generalized Klein-Gordon equation called Fackerell-Ipser equation. Our model is based on conformal Yano-Killing tensor (CYK tensor). We present non-standard properties of CYK tensors in the Kerr spacetime which are useful in electrodynamics.

Group field theory and tensor networks: towards a Ryu–Takayanagi formula in full quantum gravity

NASA Astrophysics Data System (ADS)

Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi

2018-06-01

We establish a dictionary between group field theory (thus, spin networks and random tensors) states and generalized random tensor networks. Then, we use this dictionary to compute the Rényi entropy of such states and recover the Ryu–Takayanagi formula, in two different cases corresponding to two different truncations/approximations, suggested by the established correspondence.

Design for high-power, single-lobe, grating-surface-emitting quantum cascade lasers enabled by plasmon-enhanced absorption of antisymmetric modes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sigler, C.; Kirch, J. D.; Mawst, L. J.

2014-03-31

Resonant coupling of the transverse-magnetic polarized (guided) optical mode of a quantum-cascade laser (QCL) to the antisymmetric surface-plasmon modes of 2nd-order distributed-feedback (DFB) metal/semiconductor gratings results in strong antisymmetric-mode absorption. In turn, lasing in the symmetric mode, that is, surface emission in a single-lobe far-field beam pattern, is strongly favored over controllable ranges in grating duty cycle and tooth height. By using core-region characteristics of a published 4.6 μm-emitting QCL, grating-coupled surface-emitting (SE) QCLs are analyzed and optimized for highly efficient single-lobe operation. For infinite-length devices, it is found that when the antisymmetric mode is resonantly absorbed, the symmetric mode hasmore » negligible absorption loss (∼0.1 cm{sup −1}) while still being efficiently outcoupled, through the substrate, by the DFB grating. For finite-length devices, 2nd-order distributed Bragg reflector (DBR) gratings are used on both sides of the DFB grating to prevent uncontrolled reflections from cleaved facets. Equations for the threshold-current density and the differential quantum efficiency of SE DFB/DBR QCLs are derived. For 7 mm-long, 8.0 μm-wide, 4.6 μm-emitting devices, with an Ag/InP grating of ∼39% duty cycle, and ∼0.22 μm tooth height, threshold currents as low as 0.45 A are projected. Based on experimentally obtained internal efficiency values from high-performance QCLs, slope efficiencies as high as 3.4 W/A are projected; thus, offering a solution for watt-range, single-lobe CW operation from SE, mid-infrared QCLs.« less

IIB supergravity and the E 6(6) covariant vector-tensor hierarchy

DOE PAGES

Ciceri, Franz; de Wit, Bernard; Varela, Oscar

2015-04-20

IIB supergravity is reformulated with a manifest local USp(8) invariance that makes the embedding of five-dimensional maximal supergravities transparent. In this formulation the ten-dimensional theory exhibits all the 27 one-form fields and 22 of the 27 two-form fields that are required by the vector-tensor hierarchy of the five-dimensional theory. The missing 5 two-form fields must transform in the same representation as a descendant of the ten-dimensional ‘dual graviton’. The invariant E 6(6) symmetric tensor that appears in the vector-tensor hierarchy is reproduced. Generalized vielbeine are derived from the supersymmetry transformations of the vector fields, as well as consistent expressions formore » the USp(8) covariant fermion fields. Implications are further discussed for the consistency of the truncation of IIB supergravity compactified on the five-sphere to maximal gauged supergravity in five space-time dimensions with an SO(6) gauge group.« less

Seamless Warping of Diffusion Tensor Fields

PubMed Central

Hao, Xuejun; Bansal, Ravi; Plessen, Kerstin J.; Peterson, Bradley S.

2008-01-01

To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping deformations in an attempt to ensure that the local deformations in the warped image remains true to the orientation of the underlying fibers; forward mapping, however, can also create “seams” or gaps and consequently artifacts in the warped image by failing to define accurately the voxels in the template space where the magnitude of the deformation is large (e.g., |Jacobian| > 1). Backward mapping, in contrast, defines voxels in the template space by mapping them back to locations in the original imaging space. Backward mapping allows every voxel in the template space to be defined without the creation of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT datasets seamlessly from one imaging space to another. Once the bijection has been achieved and tensors have been correctly relocated to the template space, we can appropriately reorient tensors in the template space using a warping method based on Procrustean estimation. PMID:18334425

A gravitational energy–momentum and the thermodynamic description of gravity

NASA Astrophysics Data System (ADS)

Acquaviva, G.; Kofroň, D.; Scholtz, M.

2018-05-01

A proposal for the gravitational energy–momentum tensor, known in the literature as the square root of Bel–Robinson tensor (SQBR), is analyzed in detail. Being constructed exclusively from the Weyl part of the Riemann tensor, such tensor encapsulates the geometric properties of free gravitational fields in terms of optical scalars of null congruences: making use of the general decomposition of any energy–momentum tensor, we explore the thermodynamic interpretation of such geometric quantities. While the matter energy–momentum is identically conserved due to Einstein’s field equations, the SQBR is not necessarily conserved and dissipative terms could arise in its vacuum continuity equation. We discuss the possible physical interpretations of such mathematical properties.

Spin caloritronics, origin and outlook

NASA Astrophysics Data System (ADS)

Yu, Haiming; Brechet, Sylvain D.; Ansermet, Jean-Philippe

2017-03-01

Spin caloritronics refers to research efforts in spintronics when a heat current plays a role. In this review, we start out by reviewing the predictions that can be drawn from the thermodynamics of irreversible processes. This serves as a conceptual framework in which to analyze the interplay of charge, spin and heat transport. This formalism predicts tensorial relations between vectorial quantities such as currents and gradients of chemical potentials or of temperature. Transverse effects such as the Nernst or Hall effects are predicted on the basis that these tensors can include an anti-symmetric contribution, which can be written with a vectorial cross-product. The local symmetry of the system may determine the direction of the vector defining such transverse effects, such as the surface of an isotropic medium. By including magnetization as state field in the thermodynamic description, spin currents appear naturally from the continuity equation for the magnetization, and dissipative spin torques are derived, which are charge-driven or heat-driven. Thermodynamics does not give the strength of these effects, but may provide relationships between them. Based on this framework, the review proceeds by showing how these effects have been observed in various systems. Spintronics has become a vast field of research, and the experiments highlighted in this review pertain only to heat effects on transport and magnetization dynamics, such as magneto-thermoelectric power, or the spin-dependence of the Seebeck effect, the spin-dependence of the Peltier effect, the spin Seebeck effect, the magnetic Seebeck effect, or the Nernst effect. The review concludes by pointing out predicted effects that are yet to be verified experimentally, and in what novel materials the standard thermal spin effects could be investigated.

Generalization of Einstein's gravitational field equations

NASA Astrophysics Data System (ADS)

Moulin, Frédéric

2017-12-01

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory.

Four-body correlation embedded in antisymmetrized geminal power wave function.

PubMed

Kawasaki, Airi; Sugino, Osamu

2016-12-28

We extend the Coleman's antisymmetrized geminal power (AGP) to develop a wave function theory that can incorporate up to four-body correlation in a region of strong correlation. To facilitate the variational determination of the wave function, the total energy is rewritten in terms of the traces of geminals. This novel trace formula is applied to a simple model system consisting of one dimensional Hubbard ring with a site of strong correlation. Our scheme significantly improves the result obtained by the AGP-configuration interaction scheme of Uemura et al. and also achieves more efficient compression of the degrees of freedom of the wave function. We regard the result as a step toward a first-principles wave function theory for a strongly correlated point defect or adsorbate embedded in an AGP-based mean-field medium.

Mean-field study of correlation-induced antisymmetric spin-orbit coupling in a two-orbital honeycomb model

NASA Astrophysics Data System (ADS)

Hayami, Satoru; Kusunose, Hiroaki; Motome, Yukitoshi

2018-05-01

We investigate a two-orbital Hubbard model on a honeycomb structure, with a special focus on the antisymmetric spin-orbit coupling (ASOC) induced by symmetry breaking in the electronic degrees of freedom. By investigating the ground-state phase diagram by the mean-field approximation in addition to the analysis in the strong correlation limit, we obtain a variety of symmetry-broken phases that induce different types of effective ASOCs by breaking of spatial inversion symmetry. We find several unusual properties emergent from the ASOCs, such as a linear magnetoelectric effect in a spin-orbital ordered phase at 1/4 filling and a spin splitting in the band structure in charge ordered phases at 1/4 and 1/2 fillings. We also show that a staggered potential on the honeycomb structure leads to another type of ASOC, which gives rise to a valley splitting in the band structure at 1/2 filling. We discuss the experimental relevance of our results to candidate materials including transition metal dichalcogenides and trichalcogenides.

The Riemannian geometry is not sufficient for the geometrization of the Maxwell's equations

NASA Astrophysics Data System (ADS)

Kulyabov, Dmitry S.; Korolkova, Anna V.; Velieva, Tatyana R.

2018-04-01

The transformation optics uses geometrized Maxwell's constitutive equations to solve the inverse problem of optics, namely to solve the problem of finding the parameters of the medium along the paths of propagation of the electromagnetic field. For the geometrization of Maxwell's constitutive equations, the quadratic Riemannian geometry is usually used. This is due to the use of the approaches of the general relativity. However, there arises the question of the insufficiency of the Riemannian structure for describing the constitutive tensor of the Maxwell's equations. The authors analyze the structure of the constitutive tensor and correlate it with the structure of the metric tensor of Riemannian geometry. It is concluded that the use of the quadratic metric for the geometrization of Maxwell's equations is insufficient, since the number of components of the metric tensor is less than the number of components of the constitutive tensor. A possible solution to this problem may be a transition to Finslerian geometry, in particular, the use of the Berwald-Moor metric to establish the structural correspondence between the field tensors of the electromagnetic field.

An antisymmetric cell structure for high-performance zinc bromine flow battery

NASA Astrophysics Data System (ADS)

Kim, Yongbeom; Jeon, Joonhyeon

2017-12-01

Zinc-bromine flow batteries (ZBBs) remain a problem of designing a cell with high coulombic efficiency and stability. This problem is caused intrinsically by different phase transition in each side of the half-cells during charge-discharge process. This paper describes a ZBB with an antisymmetric cell structure, which uses anode and cathode with different surface morphologies, for high-discharge capacity and reliability. The structure of the antisymmetric ZBB cell contains a carbon-surface electrode and a carbon-volume electrode in zinc and bromine half cells, respectively. To demonstrate the effectiveness of this proposed ZBB cell structure, Cyclic Voltammetry measurement is performed on a graphite foil and a carbon felt which are used as the surface and electrodes. Charge and discharge cyclic operations are also carried out with symmetric and antisymmetric ZBB cells combined with the two electrode types. Experimental results show that the arrangement of antisymmetric cell structure in ZBB provides a solution to the high performance and durability.

Book Review:

NASA Astrophysics Data System (ADS)

Louko, Jorma

2007-04-01

Bastianelli and van Nieuwenhuizen's monograph `Path Integrals and Anomalies in Curved Space' collects in one volume the results of the authors' 15-year research programme on anomalies that arise in Feynman diagrams of quantum field theories on curved manifolds. The programme was spurred by the path-integral techniques introduced in Alvarez-Gaumé and Witten's renowned 1983 paper on gravitational anomalies which, together with the anomaly cancellation paper by Green and Schwarz, led to the string theory explosion of the 1980s. The authors have produced a tour de force, giving a comprehensive and pedagogical exposition of material that is central to current research. The first part of the book develops from scratch a formalism for defining and evaluating quantum mechanical path integrals in nonlinear sigma models, using time slicing regularization, mode regularization and dimensional regularization. The second part applies this formalism to quantum fields of spin 0, 1/2, 1 and 3/2 and to self-dual antisymmetric tensor fields. The book concludes with a discussion of gravitational anomalies in 10-dimensional supergravities, for both classical and exceptional gauge groups. The target audience is researchers and graduate students in curved spacetime quantum field theory and string theory, and the aims, style and pedagogical level have been chosen with this audience in mind. Path integrals are treated as calculational tools, and the notation and terminology are throughout tailored to calculational convenience, rather than to mathematical rigour. The style is closer to that of an exceedingly thorough and self-contained review article than to that of a textbook. As the authors mention, the first part of the book can be used as an introduction to path integrals in quantum mechanics, although in a classroom setting perhaps more likely as supplementary reading than a primary class text. Readers outside the core audience, including this reviewer, will gain from the book a heightened appreciation of the central role of regularization as a defining ingredient of a quantum field theory and will be impressed by the agreement of results arising from different regularization schemes. The readers may in particular enjoy the authors' `brief history of anomalies' in quantum field theory, as well as a similar historical discussion of path integrals in quantum mechanics.

Simultaneous inversion of seismic velocity and moment tensor using elastic-waveform inversion of microseismic data: Application to the Aneth CO2-EOR field

NASA Astrophysics Data System (ADS)

Chen, Y.; Huang, L.

2017-12-01

Moment tensors are key parameters for characterizing CO2-injection-induced microseismic events. Elastic-waveform inversion has the potential to providing accurate results of moment tensors. Microseismic waveforms contains information of source moment tensors and the wave propagation velocity along the wavepaths. We develop an elastic-waveform inversion method to jointly invert the seismic velocity model and moment tensor. We first use our adaptive moment-tensor joint inversion method to estimate moment tensors of microseismic events. Our adaptive moment-tensor inversion method jointly inverts multiple microseismic events with similar waveforms within a cluster to reduce inversion uncertainty for microseismic data recorded using a single borehole geophone array. We use this inversion result as the initial model for our elastic-waveform inversion to minimize the cross-correlated-based data misfit between observed data and synthetic data. We verify our method using synthetic microseismic data and obtain improved results of both moment tensors and seismic velocity model. We apply our new inversion method to microseismic data acquired at a CO2-enhanced oil recovery field in Aneth, Utah, using a single borehole geophone array. The results demonstrate that our new inversion method significantly reduces the data misfit compared to the conventional ray-theory-based moment-tensor inversion.

Spin and pseudospin symmetric Dirac particles in the field of Tietz—Hua potential including Coulomb tensor interaction

NASA Astrophysics Data System (ADS)

Sameer, M. Ikhdair; Majid, Hamzavi

2013-09-01

Approximate analytical solutions of the Dirac equation for Tietz—Hua (TH) potential including Coulomb-like tensor (CLT) potential with arbitrary spin—orbit quantum number κ are obtained within the Pekeris approximation scheme to deal with the spin—orbit coupling terms κ(κ ± 1)r-2. Under the exact spin and pseudospin symmetric limitation, bound state energy eigenvalues and associated unnormalized two-component wave functions of the Dirac particle in the field of both attractive and repulsive TH potential with tensor potential are found using the parametric Nikiforov—Uvarov (NU) method. The cases of the Morse oscillator with tensor potential, the generalized Morse oscillator with tensor potential, and the non-relativistic limits have been investigated.

Ostrogradsky in theories with multiple fields

DOE PAGES

de Rham, Claudia; Matas, Andrew

2016-06-23

We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamicalmore » or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.« less

Ostrogradsky in theories with multiple fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

de Rham, Claudia; Matas, Andrew

We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamicalmore » or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.« less

Vacuum polarization of the quantized massive fields in Friedman-Robertson-Walker spacetime

NASA Astrophysics Data System (ADS)

Matyjasek, Jerzy; Sadurski, Paweł; Telecka, Małgorzata

2014-04-01

The stress-energy tensor of the quantized massive fields in a spatially open, flat, and closed Friedman-Robertson-Walker universe is constructed using the adiabatic regularization (for the scalar field) and the Schwinger-DeWitt approach (for the scalar, spinor, and vector fields). It is shown that the stress-energy tensor calculated in the sixth adiabatic order coincides with the result obtained from the regularized effective action, constructed from the heat kernel coefficient a3. The behavior of the tensor is examined in the power-law cosmological models, and the semiclassical Einstein field equations are solved exactly in a few physically interesting cases, such as the generalized Starobinsky models.

Radiation Forces and Torques without Stress (Tensors)

ERIC Educational Resources Information Center

Bohren, Craig F.

2011-01-01

To understand radiation forces and torques or to calculate them does not require invoking photon or electromagnetic field momentum transfer or stress tensors. According to continuum electromagnetic theory, forces and torques exerted by radiation are a consequence of electric and magnetic fields acting on charges and currents that the fields induce…

Gravitational waves and large field inflation

NASA Astrophysics Data System (ADS)

Linde, Andrei

2017-02-01

According to the famous Lyth bound, one can confirm large field inflation by finding tensor modes with sufficiently large tensor-to-scalar ratio r. Here we will try to answer two related questions: is it possible to rule out all large field inflationary models by not finding tensor modes with r above some critical value, and what can we say about the scale of inflation by measuring r? However, in order to answer these questions one should distinguish between two different definitions of the large field inflation and three different definitions of the scale of inflation. We will examine these issues using the theory of cosmological α-attractors as a convenient testing ground.

Maxwell–Dirac stress–energy tensor in terms of Fierz bilinear currents

DOE Office of Scientific and Technical Information (OSTI.GOV)

Inglis, Shaun, E-mail: sminglis@utas.edu.au; Jarvis, Peter, E-mail: Peter.Jarvis@utas.edu.au

We analyse the stress–energy tensor for the self-coupled Maxwell–Dirac system in the bilinear current formalism, using two independent approaches. The first method used is that attributed to Belinfante: starting from the spinor form of the action, the well-known canonical stress–energy tensor is augmented, by extending the Noether symmetry current to include contributions from the Lorentz group, to a manifestly symmetric form. This form admits a transcription to bilinear current form. The second method used is the variational derivation based on the covariant coupling to general relativity. The starting point here at the outset is the transcription of the action using,more » as independent field variables, both the bilinear currents, together with a gauge invariant vector field (a proxy for the electromagnetic vector potential). A central feature of the two constructions is that they both involve the mapping of the Dirac contribution to the stress–energy from the spinor fields to the equivalent set of bilinear tensor currents, through the use of appropriate Fierz identities. Although this mapping is done at quite different stages, nonetheless we find that the two forms of the bilinear stress–energy tensor agree. Finally, as an application, we consider the reduction of the obtained stress–energy tensor in bilinear form, under the assumption of spherical symmetry. -- Highlights: •Maxwell–Dirac stress–energy tensor derived in manifestly gauge invariant bilinear form. •Dirac spinor Belinfante tensor transcribed to bilinear fields via Fierz mapping. •Variational stress–energy obtained via bilinearized action, in contrast to Belinfante case. •Independent derivations via the Belinfante and variational methods agree, as required. •Spherical symmetry reduction given as a working example for wider applications.« less

Mixed-pairing superconductivity in 5 d Mott insulators with antisymmetric exchange: Application to Sr2IrO4

NASA Astrophysics Data System (ADS)

Zare, Mohammad-Hossein; Biderang, Mehdi; Akbari, Alireza

2017-11-01

We study the symmetry of the potential superconducting order parameter in 5 d Mott insulators with an eye toward hole-doped Sr2IrO4 . Using a mean-field method, a mixed singlet-triplet superconductivity, d +p , is observed due to the antisymmetric exchange originating from a quasi-spin-orbit coupling. Our calculation on ribbon geometry shows the possible existence of the topologically protected edge states, because of the nodal structure of the superconducting gap. These edge modes are spin polarized and emerge as zero-energy flat bands, supporting a symmetry-protected Majorana state, verified by evaluation of the winding number and Z2 topological invariant. At the end, a possible experimental approach for observation of these edge states and determination of the superconducting gap symmetry is discussed based on the quasiparticle interference technique.

Partitioning strategy for efficient nonlinear finite element dynamic analysis on multiprocessor computers

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Peters, Jeanne M.

1989-01-01

A computational procedure is presented for the nonlinear dynamic analysis of unsymmetric structures on vector multiprocessor systems. The procedure is based on a novel hierarchical partitioning strategy in which the response of the unsymmetric and antisymmetric response vectors (modes), each obtained by using only a fraction of the degrees of freedom of the original finite element model. The three key elements of the procedure which result in high degree of concurrency throughout the solution process are: (1) mixed (or primitive variable) formulation with independent shape functions for the different fields; (2) operator splitting or restructuring of the discrete equations at each time step to delineate the symmetric and antisymmetric vectors constituting the response; and (3) two level iterative process for generating the response of the structure. An assessment is made of the effectiveness of the procedure on the CRAY X-MP/4 computers.

Magnetospectroscopy of symmetric and anti-symmetric states in double quantum wells

NASA Astrophysics Data System (ADS)

Marchewka, M.; Sheregii, E. M.; Tralle, I.; Ploch, D.; Tomaka, G.; Furdak, M.; Kolek, A.; Stadler, A.; Mleczko, K.; Zak, D.; Strupinski, W.; Jasik, A.; Jakiela, R.

2008-02-01

The experimental results obtained for magnetotransport in the InGaAs/InAlAs double quantum well (DQW) structures of two different shapes of wells are reported. A beating effect occurring in the Shubnikov-de Haas (SdH) oscillations was observed for both types of structures at low temperatures in the parallel transport when the magnetic field was perpendicular to the layers. An approach for the calculation of the Landau level energies for DQW structures was developed and then applied to the analysis and interpretation of the experimental data related to the beating effect. We also argue that in order to account for the observed magnetotransport phenomena (SdH and integer quantum Hall effect), one should introduce two different quasi-Fermi levels characterizing two electron subsystems regarding the symmetry properties of their states, symmetric and anti-symmetric ones, which are not mixed by electron-electron interaction.

Tensorial analysis of Eshelby stresses in 3D supercooled liquids

NASA Astrophysics Data System (ADS)

Lemaître, Anaël

2015-10-01

It was recently proposed that the local rearrangements governing relaxation in supercooled liquids impress on the liquid medium long-ranged (Eshelby) stress fluctuations that accumulate over time. From this viewpoint, events must be characterized by elastic dipoles, which are second order tensors, and Eshelby fields are expected to show up in stress and stress increment correlations, which are fourth order tensor fields. We construct here an analytical framework that permits analyzing such tensorial correlations in isotropic media in view of accessing Eshelby fields. Two spherical bases are introduced, which correspond to Cartesian and spherical coordinates for tensors. We show how they can be used to decompose stress correlations and thus test such properties as isotropy and power-law scalings. Eshelby fields and the predicted stress correlations in an infinite medium are shown to belong to an algebra that can conveniently be described using the spherical tensor bases. Using this formalism, we demonstrate that the inherent stress field of 3D supercooled liquids is power law correlated and carries the signature of Eshelby fields, thus supporting the idea that relaxation events give rise to Eshelby stresses that accumulate over time.

Quantum description of a field in macroscopic electrodynamics and photon properties in transparent media

NASA Astrophysics Data System (ADS)

Toptygin, I. N.

2017-12-01

Applying a quantum mechanical treatment to a high-frequency macroscopic electromagnetic field and radiative phenomena in a medium, we construct quantum operators for energy-momentum tensor components in dispersive media and find their eigenvalues, which are different in the Minkowski and Abraham representations. It is shown that the photon momentum in a medium resulting from the quantization of the vector potential differs from that defined from Abraham’s symmetric energy-momentum-tensor but is equal to the momentum defined from the Minkowski tensor. A similar result is obtained by calculating the intrinsic angular momentum (spin) of an electro-magnetic field in the medium. Only the Minkowski tensor leads to the experimentally confirmed spin values that are multiples of ħ, providing the grounds for choosing the Minkowski representation as the proper form for the momentum density of a transverse electromagnetic field in a transparent medium, in both classical and quantum descriptions of the field. The Abraham representation is unsuitable for this purpose and leads to contradictions. The conclusion drawn does not apply to quasistatic and static fields.

Energy-momentum tensors in linearized Einstein's theory and massive gravity: The question of uniqueness

NASA Astrophysics Data System (ADS)

Bičák, Jiří; Schmidt, Josef

2016-01-01

The question of the uniqueness of energy-momentum tensors in the linearized general relativity and in the linear massive gravity is analyzed without using variational techniques. We start from a natural ansatz for the form of the tensor (for example, that it is a linear combination of the terms quadratic in the first derivatives), and require it to be conserved as a consequence of field equations. In the case of the linear gravity in a general gauge we find a four-parametric system of conserved second-rank tensors which contains a unique symmetric tensor. This turns out to be the linearized Landau-Lifshitz pseudotensor employed often in full general relativity. We elucidate the relation of the four-parametric system to the expression proposed recently by Butcher et al. "on physical grounds" in harmonic gauge, and we show that the results coincide in the case of high-frequency waves in vacuum after a suitable averaging. In the massive gravity we show how one can arrive at the expression which coincides with the "generalized linear symmetric Landau-Lifshitz" tensor. However, there exists another uniquely given simpler symmetric tensor which can be obtained by adding the divergence of a suitable superpotential to the canonical energy-momentum tensor following from the Fierz-Pauli action. In contrast to the symmetric tensor derived by the Belinfante procedure which involves the second derivatives of the field variables, this expression contains only the field and its first derivatives. It is simpler than the generalized Landau-Lifshitz tensor but both yield the same total quantities since they differ by the divergence of a superpotential. We also discuss the role of the gauge conditions in the proofs of the uniqueness. In the Appendix, the symbolic tensor manipulation software cadabra is briefly described. It is very effective in obtaining various results which would otherwise require lengthy calculations.

Local recovery of lithospheric stress tensor from GOCE gravitational tensor

NASA Astrophysics Data System (ADS)

Eshagh, Mehdi

2017-04-01

The sublithospheric stress due to mantle convection can be computed from gravity data and propagated through the lithosphere by solving the boundary-value problem of elasticity for the Earth's lithosphere. In this case, a full tensor of stress can be computed at any point inside this elastic layer. Here, we present mathematical foundations for recovering such a tensor from gravitational tensor measured at satellite altitudes. The mathematical relations will be much simpler in this way than the case of using gravity data as no derivative of spherical harmonics (SHs) or Legendre polynomials is involved in the expressions. Here, new relations between the SH coefficients of the stress and gravitational tensor elements are presented. Thereafter, integral equations are established from them to recover the elements of stress tensor from those of the gravitational tensor. The integrals have no closed-form kernels, but they are easy to invert and their spatial truncation errors are reducible. The integral equations are used to invert the real data of the gravity field and steady-state ocean circulation explorer mission (GOCE), in 2009 November, over the South American plate and its surroundings to recover the stress tensor at a depth of 35 km. The recovered stress fields are in good agreement with the tectonic and geological features of the area.

Effective field theory of statistical anisotropies for primordial bispectrum and gravitational waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rostami, Tahereh; Karami, Asieh; Firouzjahi, Hassan, E-mail: t.rostami@ipm.ir, E-mail: karami@ipm.ir, E-mail: firouz@ipm.ir

2017-06-01

We present the effective field theory studies of primordial statistical anisotropies in models of anisotropic inflation. The general action in unitary gauge is presented to calculate the leading interactions between the gauge field fluctuations, the curvature perturbations and the tensor perturbations. The anisotropies in scalar power spectrum and bispectrum are calculated and the dependence of these anisotropies to EFT couplings are presented. In addition, we calculate the statistical anisotropy in tensor power spectrum and the scalar-tensor cross correlation. Our EFT approach incorporates anisotropies generated in models with non-trivial speed for the gauge field fluctuations and sound speed for scalar perturbationsmore » such as in DBI inflation.« less

Tensor modes on the string theory landscape

NASA Astrophysics Data System (ADS)

Westphal, Alexander

2013-04-01

We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.

Spin dynamics of paramagnetic centers with anisotropic g tensor and spin of ½

PubMed Central

Maryasov, Alexander G.

2012-01-01

The influence of g tensor anisotropy on spin dynamics of paramagnetic centers having real or effective spin of 1/2 is studied. The g anisotropy affects both the excitation and the detection of EPR signals, producing noticeable differences between conventional continuous-wave (cw) EPR and pulsed EPR spectra. The magnitudes and directions of the spin and magnetic moment vectors are generally not proportional to each other, but are related to each other through the g tensor. The equilibrium magnetic moment direction is generally parallel to neither the magnetic field nor the spin quantization axis due to the g anisotropy. After excitation with short microwave pulses, the spin vector precesses around its quantization axis, in a plane that is generally not perpendicular to the applied magnetic field. Paradoxically, the magnetic moment vector precesses around its equilibrium direction in a plane exactly perpendicular to the external magnetic field. In the general case, the oscillating part of the magnetic moment is elliptically polarized and the direction of precession is determined by the sign of the g tensor determinant (g tensor signature). Conventional pulsed and cw EPR spectrometers do not allow determination of the g tensor signature or the ellipticity of the magnetic moment trajectory. It is generally impossible to set a uniform spin turning angle for simple pulses in an unoriented or ‘powder’ sample when g tensor anisotropy is significant. PMID:22743542

Spin dynamics of paramagnetic centers with anisotropic g tensor and spin of 1/2

NASA Astrophysics Data System (ADS)

Maryasov, Alexander G.; Bowman, Michael K.

2012-08-01

The influence of g tensor anisotropy on spin dynamics of paramagnetic centers having real or effective spin of 1/2 is studied. The g anisotropy affects both the excitation and the detection of EPR signals, producing noticeable differences between conventional continuous-wave (cw) EPR and pulsed EPR spectra. The magnitudes and directions of the spin and magnetic moment vectors are generally not proportional to each other, but are related to each other through the g tensor. The equilibrium magnetic moment direction is generally parallel to neither the magnetic field nor the spin quantization axis due to the g anisotropy. After excitation with short microwave pulses, the spin vector precesses around its quantization axis, in a plane that is generally not perpendicular to the applied magnetic field. Paradoxically, the magnetic moment vector precesses around its equilibrium direction in a plane exactly perpendicular to the external magnetic field. In the general case, the oscillating part of the magnetic moment is elliptically polarized and the direction of precession is determined by the sign of the g tensor determinant (g tensor signature). Conventional pulsed and cw EPR spectrometers do not allow determination of the g tensor signature or the ellipticity of the magnetic moment trajectory. It is generally impossible to set a uniform spin turning angle for simple pulses in an unoriented or 'powder' sample when g tensor anisotropy is significant.

Quantitative analysis of hypertrophic myocardium using diffusion tensor magnetic resonance imaging

PubMed Central

Tran, Nicholas; Giannakidis, Archontis; Gullberg, Grant T.; Seo, Youngho

2016-01-01

Abstract. Systemic hypertension is a causative factor in left ventricular hypertrophy (LVH). This study is motivated by the potential to reverse or manage the dysfunction associated with structural remodeling of the myocardium in this pathology. Using diffusion tensor magnetic resonance imaging, we present an analysis of myocardial fiber and laminar sheet orientation in ex vivo hypertrophic (6 SHR) and normal (5 WKY) rat hearts using the covariance of the diffusion tensor. First, an atlas of normal cardiac microstructure was formed using the WKY b0 images. Then, the SHR and WKY b0 hearts were registered to the atlas. The acquired deformation fields were applied to the SHR and WKY heart tensor fields followed by the preservation of principal direction (PPD) reorientation strategy. A mean tensor field was then formed from the registered WKY tensor images. Calculating the covariance of the registered tensor images about this mean for each heart, the hypertrophic myocardium exhibited significantly increased myocardial fiber derangement (p=0.017) with a mean dispersion of 38.7 deg, and an increased dispersion of the laminar sheet normal (p=0.030) of 54.8 deg compared with 34.8 deg and 51.8 deg, respectively, in the normal hearts. Results demonstrate significantly altered myocardial fiber and laminar sheet structure in rats with hypertensive LVH. PMID:27872872

Nonthermal and geometric effects on the symmetric and anti-symmetric surface waves in a Lorentzian dusty plasma slab

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Myoung-Jae; Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr; Department of Applied Physics and Department of Bionanotechnology, Hanyang University, Ansan, Kyunggi-Do 426-791

2015-02-15

The nonthermal and geometric effects on the propagation of the surface dust acoustic waves are investigated in a Lorentzian dusty plasma slab. The symmetric and anti-symmetric dispersion modes of the dust acoustic waves are obtained by the plasma dielectric function with the spectral reflection conditions the slab geometry. The variation of the nonthermal and geometric effects on the symmetric and the anti-symmetric modes of the surface plasma waves is also discussed.

Nonlinear conductance in weakly disordered mesoscopic wires: Interaction and magnetic field asymmetry

NASA Astrophysics Data System (ADS)

Texier, Christophe; Mitscherling, Johannes

2018-02-01

We study the nonlinear conductance G ˜∂2I /∂ V2|V =0 in coherent quasi-one-dimensional weakly disordered metallic wires. Our analysis is based on the scattering approach and includes the effect of Coulomb interaction. The nonlinear conductance correlations can be related to integrals of two fundamental correlation functions: the correlator of functional derivatives of the conductance and the correlator of injectivities (the injectivity is the contribution to the local density of states of eigenstates incoming from one contact). These correlators are obtained explicitly by using diagrammatic techniques for weakly disordered metals. In a coherent wire of length L , we obtain rms (G )≃0.006 ETh-1 (and =0 ), where ETh=ℏ D /L2 is the Thouless energy of the wire and D the diffusion constant; the small dimensionless factor results from screening, i.e., cannot be obtained within a simple theory for noninteracting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal; the antisymmetric part of the nonlinear conductance (at high magnetic field) being much smaller than the symmetric one, rms (Ga)≃0.001 (gETh) -1 , where g ≫1 is the dimensionless (linear) conductance of the wire. In a weakly coherent wire (i.e., Lφ≪L , where Lφ is the phase coherence length), the nonlinear conductance is of the same order as the result G0 of a free electron calculation (although screening again strongly reduces the dimensionless prefactor); we get G ˜G0˜(Lφ/L ) 7 /2ETh-1 , while the antisymmetric part (at high magnetic field) now behaves as Ga˜(Lφ/L ) 11 /2(gETh) -1≪G . The effect of thermal fluctuations is studied: when the thermal length LT=√{ℏ D /kBT } is the smallest length scale, LT≪Lφ≪L , the free electron result G0˜(LT/L ) 3(Lφ/L ) 1 /2ETh-1 is negligible and the dominant contribution is provided by screening, G ˜(LT/L ) (Lφ/L ) 7 /2ETh-1 ; in this regime, the antisymmetric part is Ga˜(LT/L ) 2(Lφ/L ) 7 /2(gETh) -1 . All the precise dimensionless prefactors are obtained. Crossovers from zero to strong magnetic field regimes are also analyzed.

Using tensor-based morphometry to detect structural brain abnormalities in rats with adolescent intermittent alcohol exposure

NASA Astrophysics Data System (ADS)

Paniagua, Beatriz; Ehlers, Cindy; Crews, Fulton; Budin, Francois; Larson, Garrett; Styner, Martin; Oguz, Ipek

2011-03-01

Understanding the effects of adolescent binge drinking that persist into adulthood is a crucial public health issue. Adolescent intermittent ethanol exposure (AIE) is an animal model that can be used to investigate these effects in rodents. In this work, we investigate the application of a particular image analysis technique, tensor-based morphometry, for detecting anatomical differences between AIE and control rats using Diffusion Tensor Imaging (DTI). Deformation field analysis is a popular method for detecting volumetric changes analyzing Jacobian determinants calculated on deformation fields. Recent studies showed that computing deformation field metrics on the full deformation tensor, often referred to as tensor-based morphometry (TBM), increases the sensitivity to anatomical differences. In this paper we conduct a comprehensive TBM study for precisely locating differences between control and AIE rats. Using a DTI RARE sequence designed for minimal geometric distortion, 12-directional images were acquired postmortem for control and AIE rats (n=9). After preprocessing, average images for the two groups were constructed using an unbiased atlas building approach. We non-rigidly register the two atlases using Large Deformation Diffeomorphic Metric Mapping, and analyze the resulting deformation field using TBM. In particular, we evaluate the tensor determinant, geodesic anisotropy, and deformation direction vector (DDV) on the deformation field to detect structural differences. This yields data on the local amount of growth, shrinkage and the directionality of deformation between the groups. We show that TBM can thus be used to measure group morphological differences between rat populations, demonstrating the potential of the proposed framework.

Thermal convection currents in NMR: flow profiles and implications for coherence pathway selection

PubMed

Jerschow

2000-07-01

Rayleigh-Benard convection currents are visualized in a vertical cylindrical tube by means of magnetic resonance imaging. Axially antisymmetric flow, multiple vertical rolls, and twisted node planes are observed. The flow can also be induced by strong RF irradiation. Its effects on the coherence pathways in NMR experiments employing field gradients are discussed. Copyright 2000 Academic Press.

Induced vacuum energy-momentum tensor in the background of a cosmic string

NASA Astrophysics Data System (ADS)

Sitenko, Yu A.; Vlasii, N. D.

2012-05-01

A massive scalar field is quantized in the background of a cosmic string which is generalized to a static flux-carrying codimension-2 brane in the locally flat multidimensional spacetime. We find that the finite energy-momentum tensor is induced in the vacuum. The dependence of the tensor components on the brane flux and tension, as well as on the coupling to the spacetime curvature scalar, is comprehensively analyzed. The tensor components are holomorphic functions of space dimension, decreasing exponentially with the distance from the brane. The case of the massless quantized scalar field is also considered, and the relevance of Bernoulli’s polynomials of even order for this case is discussed.

Information geometry and its application to theoretical statistics and diffusion tensor magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Wisniewski, Nicholas Andrew

This dissertation is divided into two parts. First we present an exact solution to a generalization of the Behrens-Fisher problem by embedding the problem in the Riemannian manifold of Normal distributions. From this we construct a geometric hypothesis testing scheme. Secondly we investigate the most commonly used geometric methods employed in tensor field interpolation for DT-MRI analysis and cardiac computer modeling. We computationally investigate a class of physiologically motivated orthogonal tensor invariants, both at the full tensor field scale and at the scale of a single interpolation by doing a decimation/interpolation experiment. We show that Riemannian-based methods give the best results in preserving desirable physiological features.

Direct coordinate-free derivation of the compatibility equation for finite strains

NASA Astrophysics Data System (ADS)

Ryzhak, E. I.

2014-07-01

The compatibility equation for the Cauchy-Green tensor field (squared tensor of pure extensionwith respect to the reference configuration) is directly derived from the well-known relation expressing this tensor via the vector field determining the mapping (transformation) of the reference configuration into the actual one. The derivation is based on the use of the apparatus of coordinatefree tensor calculus and does not apply any notions and relations of Riemannian geometry at all. The method is illustrated by deriving the well-known compatibility equation for small strains. It is shown that when the obtained compatibility equation for finite strains is linearized, it becomes the compatibility equation for small strains which indirectly confirms its correctness.

Diffusion with finite-helicity field tensor: A mechanism of generating heterogeneity

NASA Astrophysics Data System (ADS)

Sato, N.; Yoshida, Z.

2018-02-01

Topological constraints on a dynamical system often manifest themselves as breaking of the Hamiltonian structure; well-known examples are nonholonomic constraints on Lagrangian mechanics. The statistical mechanics under such topological constraints is the subject of this study. Conventional arguments based on phase spaces, Jacobi identity, invariant measure, or the H theorem are no longer applicable since all these notions stem from the symplectic geometry underlying canonical Hamiltonian systems. Remembering that Hamiltonian systems are endowed with field tensors (canonical 2-forms) that have zero helicity, our mission is to extend the scope toward the class of systems governed by finite-helicity field tensors. Here, we introduce a class of field tensors that are characterized by Beltrami vectors. We prove an H theorem for this Beltrami class. The most general class of energy-conserving systems are non-Beltrami, for which we identify the "field charge" that prevents the entropy to maximize, resulting in creation of heterogeneous distributions. The essence of the theory can be delineated by classifying three-dimensional dynamics. We then generalize to arbitrary (finite) dimensions.

Development of a vector-tensor system to measure the absolute magnetic flux density and its gradient in magnetically shielded rooms.

PubMed

Voigt, J; Knappe-Grüneberg, S; Gutkelch, D; Haueisen, J; Neuber, S; Schnabel, A; Burghoff, M

2015-05-01

Several experiments in fundamental physics demand an environment of very low, homogeneous, and stable magnetic fields. For the magnetic characterization of such environments, we present a portable SQUID system that measures the absolute magnetic flux density vector and the gradient tensor. This vector-tensor system contains 13 integrated low-critical temperature (LTc) superconducting quantum interference devices (SQUIDs) inside a small cylindrical liquid helium Dewar with a height of 31 cm and 37 cm in diameter. The achievable resolution depends on the flux density of the field under investigation and its temporal drift. Inside a seven-layer mu-metal shield, an accuracy better than ±23 pT for the components of the static magnetic field vector and ±2 pT/cm for each of the nine components of the gradient tensor is reached by using the shifting method.

Development of a vector-tensor system to measure the absolute magnetic flux density and its gradient in magnetically shielded rooms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Voigt, J.; Knappe-Grüneberg, S.; Gutkelch, D.

2015-05-15

Several experiments in fundamental physics demand an environment of very low, homogeneous, and stable magnetic fields. For the magnetic characterization of such environments, we present a portable SQUID system that measures the absolute magnetic flux density vector and the gradient tensor. This vector-tensor system contains 13 integrated low-critical temperature (LTc) superconducting quantum interference devices (SQUIDs) inside a small cylindrical liquid helium Dewar with a height of 31 cm and 37 cm in diameter. The achievable resolution depends on the flux density of the field under investigation and its temporal drift. Inside a seven-layer mu-metal shield, an accuracy better than ±23more » pT for the components of the static magnetic field vector and ±2 pT/cm for each of the nine components of the gradient tensor is reached by using the shifting method.« less

General Second-Order Scalar-Tensor Theory and Self-Tuning

NASA Astrophysics Data System (ADS)

Charmousis, Christos; Copeland, Edmund J.; Padilla, Antonio; Saffin, Paul M.

2012-02-01

Starting from the most general scalar-tensor theory with second-order field equations in four dimensions, we establish the unique action that will allow for the existence of a consistent self-tuning mechanism on Friedmann-Lemaître-Robertson-Walker backgrounds, and show how it can be understood as a combination of just four base Lagrangians with an intriguing geometric structure dependent on the Ricci scalar, the Einstein tensor, the double dual of the Riemann tensor, and the Gauss-Bonnet combination. Spacetime curvature can be screened from the net cosmological constant at any given moment because we allow the scalar field to break Poincaré invariance on the self-tuning vacua, thereby evading the Weinberg no-go theorem. We show how the four arbitrary functions of the scalar field combine in an elegant way opening up the possibility of obtaining nontrivial cosmological solutions.

Primordial perturbations from dilaton-induced gauge fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, Kiwoon; Choi, Ki-Young; Kim, Hyungjin

2015-10-01

We study the primordial scalar and tensor perturbations in inflation scenario involving a spectator dilaton field. In our setup, the rolling spectator dilaton causes a tachyonic instability of gauge fields, leading to a copious production of gauge fields in the superhorizon regime, which generates additional scalar and tensor perturbations through gravitational interactions. Our prime concern is the possibility to enhance the tensor-to-scalar ratio r relative to the standard result, while satisfying the observational constraints. To this end, we allow the dilaton field to be stabilized before the end of inflation, but after the CMB scales exit the horizon. We showmore » that for the inflaton slow roll parameter ε ∼> 10{sup −3}, the tensor-to-scalar ratio in our setup can be enhanced only by a factor of O(1) compared to the standard result. On the other hand, for smaller ε corresponding to a lower inflation energy scale, a much bigger enhancement can be achieved, so that our setup can give rise to an observably large r∼> 10{sup −2} even when ε|| 10{sup −3}. The tensor perturbation sourced by the spectator dilaton can have a strong scale dependence, and is generically red-tilted. We also discuss a specific model to realize our scenario, and identify the parameter region giving an observably large r for relatively low inflation energy scales.« less

Symmetric and anti-symmetric LS hyperon potentials from lattice QCD

NASA Astrophysics Data System (ADS)

Ishii, Noriyoshi; Murano, Keiko; Nemura, Hidekatsu; Sasaki, Kenji; Inoue, Takashi; HAL QCD Collaboration

2014-09-01

We present recent results of odd-parity hyperon-hyperon potentials from lattice QCD. By using HAL QCD method, we generate hyperon-hyperon potentials from Nambu-Bethe-Salpeter (NBS) wave functions generated by lattice QCD simulation in the flavor SU(3) limit. Potentials in the irreducible flavor SU(3) representations are combined to make a Lambda-N potential which has a strong symmetric LS potential and a weak anti-symmetric LS potential. We discuss a possible cancellation between symmetric and anti-symmetric LS (Lambda-N) potentials after the coupled Sigma-N sector is integrated out. We present recent results of odd-parity hyperon-hyperon potentials from lattice QCD. By using HAL QCD method, we generate hyperon-hyperon potentials from Nambu-Bethe-Salpeter (NBS) wave functions generated by lattice QCD simulation in the flavor SU(3) limit. Potentials in the irreducible flavor SU(3) representations are combined to make a Lambda-N potential which has a strong symmetric LS potential and a weak anti-symmetric LS potential. We discuss a possible cancellation between symmetric and anti-symmetric LS (Lambda-N) potentials after the coupled Sigma-N sector is integrated out. This work is supported by JSPS KAKENHI Grant Number 25400244.

A tensorial description of particle perception in black-hole physics

NASA Astrophysics Data System (ADS)

Barbado, Luis C.; Barceló, Carlos; Garay, Luis J.; Jannes, G.

2016-09-01

In quantum field theory in curved backgrounds, one typically distinguishes between objective, tensorial quantities such as the renormalized stress-energy tensor (RSET) and subjective, nontensorial quantities such as Bogoliubov coefficients which encode perception effects associated with the specific trajectory of a detector. In this work, we propose a way to treat both objective and subjective notions on an equal tensorial footing. For that purpose, we define a new tensor which we will call the perception renormalized stress-energy tensor (PeRSET). The PeRSET is defined as the subtraction of the RSET corresponding to two different vacuum states. Based on this tensor, we can define perceived energy densities and fluxes. The PeRSET helps us to have a more organized and systematic understanding of various results in the literature regarding quantum field theory in black hole spacetimes. We illustrate the physics encoded in this tensor by working out various examples of special relevance.

Antisymmetrization effects and the form factor of the real part of the. cap alpha. -nucleus potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Majka, Z.; Budzanowski, A.; Grotowski, K.

1978-07-01

Antisymmetrization effects in the ..cap alpha..-nucleus interaction are investigated on the basis of a microscopic model in an one nucleon exchange approximation. It influences the form factor, increasing the halfway radius and decreasing the diffuseness as compared with the direct term of the potential only. Antisymmetrization preserves the shape of the potential which can be parametrized by a Woods-Saxon squared form. The phenomenological potential with the energy independent form factor of the above shape fits experimental data in a wide energy region.

Introduction to Vector Field Visualization

NASA Technical Reports Server (NTRS)

Kao, David; Shen, Han-Wei

2010-01-01

Vector field visualization techniques are essential to help us understand the complex dynamics of flow fields. These can be found in a wide range of applications such as study of flows around an aircraft, the blood flow in our heart chambers, ocean circulation models, and severe weather predictions. The vector fields from these various applications can be visually depicted using a number of techniques such as particle traces and advecting textures. In this tutorial, we present several fundamental algorithms in flow visualization including particle integration, particle tracking in time-dependent flows, and seeding strategies. For flows near surfaces, a wide variety of synthetic texture-based algorithms have been developed to depict near-body flow features. The most common approach is based on the Line Integral Convolution (LIC) algorithm. There also exist extensions of LIC to support more flexible texture generations for 3D flow data. This tutorial reviews these algorithms. Tensor fields are found in several real-world applications and also require the aid of visualization to help users understand their data sets. Examples where one can find tensor fields include mechanics to see how material respond to external forces, civil engineering and geomechanics of roads and bridges, and the study of neural pathway via diffusion tensor imaging. This tutorial will provide an overview of the different tensor field visualization techniques, discuss basic tensor decompositions, and go into detail on glyph based methods, deformation based methods, and streamline based methods. Practical examples will be used when presenting the methods; and applications from some case studies will be used as part of the motivation.

Tensor Minkowski Functionals for random fields on the sphere

NASA Astrophysics Data System (ADS)

Chingangbam, Pravabati; Yogendran, K. P.; Joby, P. K.; Ganesan, Vidhya; Appleby, Stephen; Park, Changbom

2017-12-01

We generalize the translation invariant tensor-valued Minkowski Functionals which are defined on two-dimensional flat space to the unit sphere. We apply them to level sets of random fields. The contours enclosing boundaries of level sets of random fields give a spatial distribution of random smooth closed curves. We outline a method to compute the tensor-valued Minkowski Functionals numerically for any random field on the sphere. Then we obtain analytic expressions for the ensemble expectation values of the matrix elements for isotropic Gaussian and Rayleigh fields. The results hold on flat as well as any curved space with affine connection. We elucidate the way in which the matrix elements encode information about the Gaussian nature and statistical isotropy (or departure from isotropy) of the field. Finally, we apply the method to maps of the Galactic foreground emissions from the 2015 PLANCK data and demonstrate their high level of statistical anisotropy and departure from Gaussianity.

Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame

NASA Astrophysics Data System (ADS)

Du, J.; Chen, C.; Lesur, V.; Wang, L.

2014-12-01

General expressions of magnetic vector (MV) and magnetic gradient tensor (MGT) in terms of the first- and second-order derivatives of spherical harmonics at different degrees and orders, are relatively complicated and singular at the poles. In this paper, we derived alternative non-singular expressions for the MV, the MGT and also the higher-order partial derivatives of the magnetic field in local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (version 0.0) and the main magnetic field model of IGRF11. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the potential field.

A Communication-Optimal Framework for Contracting Distributed Tensors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rajbhandari, Samyam; NIkam, Akshay; Lai, Pai-Wei

Tensor contractions are extremely compute intensive generalized matrix multiplication operations encountered in many computational science fields, such as quantum chemistry and nuclear physics. Unlike distributed matrix multiplication, which has been extensively studied, limited work has been done in understanding distributed tensor contractions. In this paper, we characterize distributed tensor contraction algorithms on torus networks. We develop a framework with three fundamental communication operators to generate communication-efficient contraction algorithms for arbitrary tensor contractions. We show that for a given amount of memory per processor, our framework is communication optimal for all tensor contractions. We demonstrate performance and scalability of our frameworkmore » on up to 262,144 cores of BG/Q supercomputer using five tensor contraction examples.« less

Compactly supported linearised observables in single-field inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fröob, Markus B.; Higuchi, Atsushi; Hack, Thomas-Paul, E-mail: mbf503@york.ac.uk, E-mail: thomas-paul.hack@itp.uni-leipzig.de, E-mail: atsushi.higuchi@york.ac.uk

We investigate the gauge-invariant observables constructed by smearing the graviton and inflaton fields by compactly supported tensors at linear order in general single-field inflation. These observables correspond to gauge-invariant quantities that can be measured locally. In particular, we show that these observables are equivalent to (smeared) local gauge-invariant observables such as the linearised Weyl tensor, which have better infrared properties than the graviton and inflaton fields. Special cases include the equivalence between the compactly supported gauge-invariant graviton observable and the smeared linearised Weyl tensor in Minkowski and de Sitter spaces. Our results indicate that the infrared divergences in the tensormore » and scalar perturbations in single-field inflation have the same status as in de Sitter space and are both a gauge artefact, in a certain technical sense, at tree level.« less

Flexible Force Field Parameterization through Fitting on the Ab Initio-Derived Elastic Tensor

PubMed Central

2017-01-01

Constructing functional forms and their corresponding force field parameters for the metal–linker interface of metal–organic frameworks is challenging. We propose fitting these parameters on the elastic tensor, computed from ab initio density functional theory calculations. The advantage of this top-down approach is that it becomes evident if functional forms are missing when components of the elastic tensor are off. As a proof-of-concept, a new flexible force field for MIL-47(V) is derived. Negative thermal expansion is observed and framework flexibility has a negligible effect on adsorption and transport properties for small guest molecules. We believe that this force field parametrization approach can serve as a useful tool for developing accurate flexible force field models that capture the correct mechanical behavior of the full periodic structure. PMID:28661672

Forward modeling and inversion of tensor CSAMT in 3D anisotropic media

NASA Astrophysics Data System (ADS)

Wang, Tao; Wang, Kun-Peng; Tan, Han-Dong

2017-12-01

Tensor controlled-source audio-frequency magnetotellurics (CSAMT) can yield information about electric and magnetic fields owing to its multi-transmitter configuration compared with the common scalar CSAMT. The most current theories, numerical simulations, and inversion of tensor CSAMT are based on far-field measurements and the assumption that underground media have isotropic resistivity. We adopt a three-dimensional (3D) staggered-grid finite difference numerical simulation method to analyze the resistivity in axial anisotropic and isotropic media. We further adopt the limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) method to perform 3D tensor CSAMT axial anisotropic inversion. The inversion results suggest that when the underground structure is anisotropic, the isotropic inversion will introduce errors to the interpretation.

Anisotropy of electromagnetically induced left-handedness in atomic three-level media based upon bianisotropic polarizabilities and tensor character

NASA Astrophysics Data System (ADS)

Krowne, Clifford M.

2008-05-01

A three-level atomic system, configured as either a gaseous medium or a solid state material, with a driving field establishing a Rabi frequency of control, is tested by a probe field. The medium has bianisotropic microscopic polarizability and magnetizability, from which the permittivity and permeability tensors are derived. Non-isotropy and polarization dependence for left-handedness (negative index of refraction) is demonstrated through examination of tensor components in the detuning frequency spectrum. These results have important implications for use in optical or electronic devices.

Tensor tomography on Cartan–Hadamard manifolds

NASA Astrophysics Data System (ADS)

Lehtonen, Jere; Railo, Jesse; Salo, Mikko

2018-04-01

We study the geodesic x-ray transform on Cartan–Hadamard manifolds, generalizing the x-ray transforms on Euclidean and hyperbolic spaces that arise in medical and seismic imaging. We prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the sectional curvature is bounded, and polynomially decaying if the sectional curvature decays at infinity. This work extends the results of Lehtonen (2016 arXiv:1612.04800) to dimensions n ≥slant 3 and to the case of tensor fields of any order.

The gravitational wave stress–energy (pseudo)-tensor in modified gravity

NASA Astrophysics Data System (ADS)

Saffer, Alexander; Yunes, Nicolás; Yagi, Kent

2018-03-01

The recent detections of gravitational waves by the advanced LIGO and Virgo detectors open up new tests of modified gravity theories in the strong-field and dynamical, extreme gravity regime. Such tests rely sensitively on the phase evolution of the gravitational waves, which is controlled by the energy–momentum carried by such waves out of the system. We here study four different methods for finding the gravitational wave stress–energy pseudo-tensor in gravity theories with any combination of scalar, vector, or tensor degrees of freedom. These methods rely on the second variation of the action under short-wavelength averaging, the second perturbation of the field equations in the short-wavelength approximation, the construction of an energy complex leading to a Landau–Lifshitz tensor, and the use of Noether’s theorem in field theories about a flat background. We apply these methods in general relativity, Jordan–Fierz–Brans–Dicky theoy, and Einstein-Æther theory to find the gravitational wave stress–energy pseudo-tensor and calculate the rate at which energy and linear momentum is carried away from the system. The stress–energy tensor and the rate of linear momentum loss in Einstein-Æther theory are presented here for the first time. We find that all methods yield the same rate of energy loss, although the stress–energy pseudo-tensor can be functionally different. We also find that the Noether method yields a stress–energy tensor that is not symmetric or gauge-invariant, and symmetrization via the Belinfante procedure does not fix these problems because this procedure relies on Lorentz invariance, which is spontaneously broken in Einstein-Æther theory. The methods and results found here will be useful for the calculation of predictions in modified gravity theories that can then be contrasted with observations.

On the energy-momentum tensor of light in strong fields: an all optical view of the Abraham-Minkowski controversy

NASA Astrophysics Data System (ADS)

Macleod, Alexander J.; Noble, Adam; Jaroszynski, Dino A.

2017-05-01

The Abraham-Minkowski controversy is the debate surrounding the "correct" form of the energy-momentum tensor of light in a medium. Over a century of theoretical and experimental studies have consistently produced conflicting results, with no consensus being found on how best to describe the influence of a material on the propagation of light. It has been argued that the total energy-momentum tensor for each of the theories, which includes both wave and material components, are equal. The difficulty in separating the full energy-momentum tensor is generally attributed to the fact that one cannot obtain the energy-momentum tensor of the medium for real materials. Non-linear electrodynamics provides an opportunity to approach the debate from an all optical set up, where the role of the medium is replaced by the vacuum under the influence of a strong background field. We derive, from first principles, the general form of the energy-momentum tensor in such theories, and use our results to shed some light on this long standing issue.

One-loop pseudo-Goldstone masses in the minimal S O (10 ) Higgs model

NASA Astrophysics Data System (ADS)

Gráf, Lukáš; Malinský, Michal; Mede, Timon; Susič, Vasja

2017-04-01

We calculate the prominent perturbative contributions shaping the one-loop scalar spectrum of the minimal renormalizable nonsupersymmetric S O (10 ) Higgs model whose unified gauge symmetry is spontaneously broken by an adjoint scalar. Focusing on its potentially realistic 45 ⊕126 variant in which the rank is reduced by a vacuum expectation value of the 5-index antisymmetric self-dual tensor, we provide a thorough analysis of the corresponding Coleman-Weinberg one-loop effective potential, paying particular attention to the masses of the potentially tachyonic pseudo-Goldstone bosons transforming as (1, 3, 0) and (8, 1, 0) under the standard model (SM) gauge group. The results confirm the assumed existence of extended regions in the parameter space supporting a locally stable SM-like quantum vacuum inaccessible at the tree level. The effective potential tedium is compared to that encountered in the previously studied 45 ⊕16 S O (10 ) Higgs model where the polynomial corrections to the relevant pseudo-Goldstone masses turn out to be easily calculable within a very simplified purely diagrammatic approach.

The spectral expansion of the elasticity random field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Malyarenko, Anatoliy; Ostoja-Starzewski, Martin

2014-12-10

We consider a deformable body that occupies a region D in the plane. In our model, the body’s elasticity tensor H(x) is the restriction to D of a second-order mean-square continuous random field. Under translation, the expected value and the correlation tensor of the field H(x) do not change. Under action of an arbitrary element k of the orthogonal group O(2), they transform according to the reducible orthogonal representation k ⟼ S{sup 2}(S{sup 2}(k)) of the above group. We find the spectral expansion of the correlation tensor R(x) of the elasticity field as well as the expansion of the fieldmore » itself in terms of stochastic integrals with respect to a family of orthogonal scattered random measures.« less

Complete Moment Tensor Determination of Induced Seismicity in Unconventional and Conventional Oil/Gas Fields

NASA Astrophysics Data System (ADS)

Gu, C.; Li, J.; Toksoz, M. N.

2013-12-01

Induced seismicity occurs both in conventional oil/gas fields due to production and water injection and in unconventional oil/gas fields due to hydraulic fracturing. Source mechanisms of these induced earthquakes are of great importance for understanding their causes and the physics of the seismic processes in reservoirs. Previous research on the analysis of induced seismic events in conventional oil/gas fields assumed a double couple (DC) source mechanism. However, recent studies have shown a non-negligible percentage of a non-double-couple (non-DC) component of source moment tensor in hydraulic fracturing events (Šílený et al., 2009; Warpinski and Du, 2010; Song and Toksöz, 2011). In this study, we determine the full moment tensor of the induced seismicity data in a conventional oil/gas field and for hydrofrac events in an unconventional oil/gas field. Song and Toksöz (2011) developed a full waveform based complete moment tensor inversion method to investigate a non-DC source mechanism. We apply this approach to the induced seismicity data from a conventional gas field in Oman. In addition, this approach is also applied to hydrofrac microseismicity data monitored by downhole geophones in four wells in US. We compare the source mechanisms of induced seismicity in the two different types of gas fields and explain the differences in terms of physical processes.

Volume illustration of muscle from diffusion tensor images.

PubMed

Chen, Wei; Yan, Zhicheng; Zhang, Song; Crow, John Allen; Ebert, David S; McLaughlin, Ronald M; Mullins, Katie B; Cooper, Robert; Ding, Zi'ang; Liao, Jun

2009-01-01

Medical illustration has demonstrated its effectiveness to depict salient anatomical features while hiding the irrelevant details. Current solutions are ineffective for visualizing fibrous structures such as muscle, because typical datasets (CT or MRI) do not contain directional details. In this paper, we introduce a new muscle illustration approach that leverages diffusion tensor imaging (DTI) data and example-based texture synthesis techniques. Beginning with a volumetric diffusion tensor image, we reformulate it into a scalar field and an auxiliary guidance vector field to represent the structure and orientation of a muscle bundle. A muscle mask derived from the input diffusion tensor image is used to classify the muscle structure. The guidance vector field is further refined to remove noise and clarify structure. To simulate the internal appearance of the muscle, we propose a new two-dimensional example based solid texture synthesis algorithm that builds a solid texture constrained by the guidance vector field. Illustrating the constructed scalar field and solid texture efficiently highlights the global appearance of the muscle as well as the local shape and structure of the muscle fibers in an illustrative fashion. We have applied the proposed approach to five example datasets (four pig hearts and a pig leg), demonstrating plausible illustration and expressiveness.

Mysteries of R ik = 0: A novel paradigm in Einstein's theory of gravitation

NASA Astrophysics Data System (ADS)

Vishwakarma, Ram Gopal

2014-02-01

Despite a century-long effort, a proper energy-stress tensor of the gravitational field, could not have been discovered. Furthermore, it has been discovered recently that the standard formulation of the energy-stress tensor of matter, suffers from various inconsistencies and paradoxes, concluding that the tensor is not consistent with the geometric formulation of gravitation [Astrophys. Space Sci., 2009, 321: 151; Astrophys. Space Sci., 2012, 340: 373]. This perhaps hints that a consistent theory of gravitation should not have any bearing on the energy-stress tensor. It is shown here that the so-called "vacuum" field equations R ik = 0 do not represent an empty spacetime, and the energy, momenta and angular momenta of the gravitational and the matter fields are revealed through the geometry, without including any formulation thereof in the field equations. Though, this novel discovery appears baffling and orthogonal to the usual understanding, is consistent with the observations at all scales, without requiring the hypothetical dark matter, dark energy or inflation. Moreover, the resulting theory circumvents the long-standing problems of the standard cosmology, besides explaining some unexplained puzzles.

The role of electron heat flux in guide-field magnetic reconnection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hesse, Michael; Kuznetsova, Masha; Birn, Joachim

2004-12-01

A combination of analytical theory and particle-in-cell simulations are employed in order to investigate the electron dynamics near and at the site of guide field magnetic reconnection. A detailed analysis of the contributions to the reconnection electric field shows that both bulk inertia and pressure-based quasiviscous processes are important for the electrons. Analytic scaling demonstrates that conventional approximations for the electron pressure tensor behavior in the dissipation region fail, and that heat flux contributions need to be accounted for. Based on the evolution equation of the heat flux three tensor, which is derived in this paper, an approximate form ofmore » the relevant heat flux contributions to the pressure tensor is developed, which reproduces the numerical modeling result reasonably well. Based on this approximation, it is possible to develop a scaling of the electron current layer in the central dissipation region. It is shown that the pressure tensor contributions become important at the scale length defined by the electron Larmor radius in the guide magnetic field.« less

Fine-scale features in the far-field of a turbulent jet

NASA Astrophysics Data System (ADS)

Buxton, Oliver; Ganapathisubramani, Bharathram

2008-11-01

The structure of a fully turbulent axisymmetric jet, at Reynolds number based on jet exit conditions of 5000, is investigated with cinematographic (1 kHz) stereoscopic PIV in a plane normal to the jet axis. Taylor's hypothesis is employed to calculate all three velocity gradients in the axial direction. The technique's resolution allows all terms of the velocity gradient tensor, hence strain rate tensor and kinetic energy dissipation, to be computed at each point within the plane. The data reveals that the vorticity field is dominated by high enstrophy tube-like structures. Conversely, the dissipation field appears to consist of sheet-like structures. Several criteria for isolating these strongly swirling vortical structures from the background turbulence were employed. One such technique involves isolating points in which the velocity gradient tensor has a real and a pair of complex conjugate eigenvectors. Once identified, the alignment of the various structures with relation to the vorticity vector and the real velocity gradient tensor eigenvector is investigated. The effect of the strain field on the geometry of the structures is also examined.

Spacetimes with Killing tensors. [for Einstein-Maxwell fields with certain spinor indices

NASA Technical Reports Server (NTRS)

Hughston, L. P.; Sommers, P.

1973-01-01

The characteristics of the Killing equation and the Killing tensor are discussed. A conformal Killing tensor is of interest inasmuch as it gives rise to a quadratic first integral for null geodesic orbits. The Einstein-Maxwell equations are considered together with the Bianchi identity and the conformal Killing tensor. Two examples for the application of the considered relations are presented, giving attention to the charged Kerr solution and the charged C-metric.

Experimental determination of the carboxylate oxygen electric-field-gradient and chemical shielding tensors in L-alanine and L-phenylalanine

NASA Astrophysics Data System (ADS)

Yamada, Kazuhiko; Asanuma, Miwako; Honda, Hisashi; Nemoto, Takahiro; Yamazaki, Toshio; Hirota, Hiroshi

2007-10-01

We report a solid-state 17O NMR study of the 17O electric-field-gradient (EFG) and chemical shielding (CS) tensors for each carboxylate group in polycrystalline L-alanine and L-phenylalanine. The magic angle spinning (MAS) and stationary 17O NMR spectra of these compounds were obtained at 9.4, 14.1, and 16.4 T. Analyzes of these 17O NMR spectra yielded reliable experimental NMR parameters including 17O CS tensor components, 17O quadrupole coupling parameters, and the relative orientations between the 17O CS and EFG tensors. The extensive quantum chemical calculations at both the restricted Hartree-Fock and density-functional theories were carried out with various basis sets to evaluate the quality of quantum chemical calculations for the 17O NMR tensors in L-alanine. For 17O CS tensors, the calculations at the B3LYP/D95 ∗∗ level could reasonably reproduce 17O CS tensors, but they still showed some discrepancies in the δ11 components by approximately 36 ppm. For 17O EFG calculations, it was advantageous to use calibrated Q value to give acceptable CQ values. The calculated results also demonstrated that not only complete intermolecular hydrogen-bonding networks to target oxygen in L-alanine, but also intermolecular interactions around the NH3+ group were significant to reproduce the 17O NMR tensors.

Electromagnetic momentum and the energy–momentum tensor in a linear medium with magnetic and dielectric properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crenshaw, Michael E., E-mail: michael.e.crenshaw4.civ@mail.mil

2014-04-15

In a continuum setting, the energy–momentum tensor embodies the relations between conservation of energy, conservation of linear momentum, and conservation of angular momentum. The well-defined total energy and the well-defined total momentum in a thermodynamically closed system with complete equations of motion are used to construct the total energy–momentum tensor for a stationary simple linear material with both magnetic and dielectric properties illuminated by a quasimonochromatic pulse of light through a gradient-index antireflection coating. The perplexing issues surrounding the Abraham and Minkowski momentums are bypassed by working entirely with conservation principles, the total energy, and the total momentum. We derivemore » electromagnetic continuity equations and equations of motion for the macroscopic fields based on the material four-divergence of the traceless, symmetric total energy–momentum tensor. We identify contradictions between the macroscopic Maxwell equations and the continuum form of the conservation principles. We resolve the contradictions, which are the actual fundamental issues underlying the Abraham–Minkowski controversy, by constructing a unified version of continuum electrodynamics that is based on establishing consistency between the three-dimensional Maxwell equations for macroscopic fields, the electromagnetic continuity equations, the four-divergence of the total energy–momentum tensor, and a four-dimensional tensor formulation of electrodynamics for macroscopic fields in a simple linear medium.« less

Magnetic-Field Control Of Tunnel-Coupling In Strongly Confined One-Dimensional Electron Systems

NASA Astrophysics Data System (ADS)

Fischer, S. F.; Apetrii, G.; Kunze, U.; Schuh, D.; Abstreiter, G.

2007-04-01

One-dimensional (1D) ballistic electron transport is studied through stacked 1D quantum conductors separated by a thin tunneling barrier. The 1D electron systems of large 1D subband spacings (more than 10 meV) allow single mode operation. Degeneracies of 1D subbands of equal lateral mode index are lifted by the formation of symmetric and antisymmetric states and are depicted by anti-crossings of transconductance maxima. We observe a mode-dependent turnover from level anti-crossings to crossings in longitudinal magnetic fields.

Magnification effect of Kerr metric by configurations of collisionless particles in non-isotropic kinetic equilibria

NASA Astrophysics Data System (ADS)

Cremaschini, Claudio; Stuchlík, Zdeněk

2018-05-01

A test fluid composed of relativistic collisionless neutral particles in the background of Kerr metric is expected to generate non-isotropic equilibrium configurations in which the corresponding stress-energy tensor exhibits pressure and temperature anisotropies. This arises as a consequence of the constraints placed on single-particle dynamics by Killing tensor symmetries, leading to a peculiar non-Maxwellian functional form of the kinetic distribution function describing the continuum system. Based on this outcome, in this paper the generation of Kerr-like metric by collisionless N -body systems of neutral matter orbiting in the field of a rotating black hole is reported. The result is obtained in the framework of covariant kinetic theory by solving the Einstein equations in terms of an analytical perturbative treatment whereby the gravitational field is decomposed as a prescribed background metric tensor described by the Kerr solution plus a self-field correction. The latter one is generated by the uncharged fluid at equilibrium and satisfies the linearized Einstein equations having the non-isotropic stress-energy tensor as source term. It is shown that the resulting self-metric is again of Kerr type, providing a mechanism of magnification of the background metric tensor and its qualitative features.

Quasinormal modes, bifurcations, and nonuniqueness of charged scalar-tensor black holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Doneva, Daniela D.; Theoretical Astrophysics, Eberhard-Karls University of Tuebingen, Tuebingen 72076; Yazadjiev, Stoytcho S.

In the present paper, we study the scalar sector of the quasinormal modes of charged general relativistic, static, and spherically symmetric black holes coupled to nonlinear electrodynamics and embedded in a class of scalar-tensor theories. We find that for a certain domain of the parametric space, there exists unstable quasinormal modes. The presence of instabilities implies the existence of scalar-tensor black holes with primary hair that bifurcate from the embedded general relativistic black-hole solutions at critical values of the parameters corresponding to the static zero modes. We prove that such scalar-tensor black holes really exist by solving the full systemmore » of scalar-tensor field equations for the static, spherically symmetric case. The obtained solutions for the hairy black holes are nonunique, and they are in one-to-one correspondence with the bounded states of the potential governing the linear perturbations of the scalar field. The stability of the nonunique hairy black holes is also examined, and we find that the solutions for which the scalar field has zeros are unstable against radial perturbations. The paper ends with a discussion of possible formulations of a new classification conjecture.« less

Projector Augmented-Wave formulation of response to strain and electric field perturbation within the density-functional perturbation theory

NASA Astrophysics Data System (ADS)

Martin, Alexandre; Torrent, Marc; Caracas, Razvan

2015-03-01

A formulation of the response of a system to strain and electric field perturbations in the pseudopotential-based density functional perturbation theory (DFPT) has been proposed by D.R Hamman and co-workers. It uses an elegant formalism based on the expression of DFT total energy in reduced coordinates, the key quantity being the metric tensor and its first and second derivatives. We propose to extend this formulation to the Projector Augmented-Wave approach (PAW). In this context, we express the full elastic tensor including the clamped-atom tensor, the atomic-relaxation contributions (internal stresses) and the response to electric field change (piezoelectric tensor and effective charges). With this we are able to compute the elastic tensor for all materials (metals and insulators) within a fully analytical formulation. The comparison with finite differences calculations on simple systems shows an excellent agreement. This formalism has been implemented in the plane-wave based DFT ABINIT code. We apply it to the computation of elastic properties and seismic-wave velocities of iron with impurity elements. By analogy with the materials contained in meteorites, tested impurities are light elements (H, O, C, S, Si).

Waveform-based Bayesian full moment tensor inversion and uncertainty determination for the induced seismicity in an oil/gas field

NASA Astrophysics Data System (ADS)

Gu, Chen; Marzouk, Youssef M.; Toksöz, M. Nafi

2018-03-01

Small earthquakes occur due to natural tectonic motions and are induced by oil and gas production processes. In many oil/gas fields and hydrofracking processes, induced earthquakes result from fluid extraction or injection. The locations and source mechanisms of these earthquakes provide valuable information about the reservoirs. Analysis of induced seismic events has mostly assumed a double-couple source mechanism. However, recent studies have shown a non-negligible percentage of non-double-couple components of source moment tensors in hydraulic fracturing events, assuming a full moment tensor source mechanism. Without uncertainty quantification of the moment tensor solution, it is difficult to determine the reliability of these source models. This study develops a Bayesian method to perform waveform-based full moment tensor inversion and uncertainty quantification for induced seismic events, accounting for both location and velocity model uncertainties. We conduct tests with synthetic events to validate the method, and then apply our newly developed Bayesian inversion approach to real induced seismicity in an oil/gas field in the sultanate of Oman—determining the uncertainties in the source mechanism and in the location of that event.

Theoretical antisymmetric span loading for wings of arbitrary plan form at subsonic speeds

NASA Technical Reports Server (NTRS)

Deyoung, John

1951-01-01

A simplified lifting-surface theory that includes effects of compressibility and spanwise variation of section lift-curve slope is used to provide charts with which antisymmetric loading due to arbitrary antisymmetric angle of attack can be found for wings having symmetric plan forms with a constant spanwise sweep angle of the quarter-chord line. Consideration is given to the flexible wing in roll. Aerodynamic characteristics due to rolling, deflected ailerons, and sideslip of wings with dihedral are considered. Solutions are presented for straight-tapered wings for a range of swept plan forms.

Interaction of non-Abelian tensor gauge fields

NASA Astrophysics Data System (ADS)

Savvidy, George

2018-01-01

The non-Abelian tensor gauge fields take value in extended Poincaré algebra. In order to define the invariant Lagrangian we introduce a vector variable in two alternative ways: through the transversal representation of the extended Poincaré algebra and through the path integral over the auxiliary vector field with the U(1) Abelian action. We demonstrate that this allows to fix the unitary gauge and derive scattering amplitudes in spinor representation.

On scalar and vector fields coupled to the energy-momentum tensor

NASA Astrophysics Data System (ADS)

Jiménez, Jose Beltrán; Cembranos, Jose A. R.; Sánchez Velázquez, Jose M.

2018-05-01

We consider theories for scalar and vector fields coupled to the energy-momentum tensor. Since these fields also carry a non-trivial energy-momentum tensor, the coupling prescription generates self-interactions. In analogy with gravity theories, we build the action by means of an iterative process that leads to an infinite series, which can be resumed as the solution of a set of differential equations. We show that, in some particular cases, the equations become algebraic and that is also possible to find solutions in the form of polynomials. We briefly review the case of the scalar field that has already been studied in the literature and extend the analysis to the case of derivative (disformal) couplings. We then explore theories with vector fields, distinguishing between gauge-and non-gauge-invariant couplings. Interactions with matter are also considered, taking a scalar field as a proxy for the matter sector. We also discuss the ambiguity introduced by superpotential (boundary) terms in the definition of the energy-momentum tensor and use them to show that it is also possible to generate Galileon-like interactions with this procedure. We finally use collider and astrophysical observations to set constraints on the dimensionful coupling which characterises the phenomenology of these models.

Solar System constraints on massless scalar-tensor gravity with positive coupling constant upon cosmological evolution of the scalar field

NASA Astrophysics Data System (ADS)

Anderson, David; Yunes, Nicolás

2017-09-01

Scalar-tensor theories of gravity modify general relativity by introducing a scalar field that couples nonminimally to the metric tensor, while satisfying the weak-equivalence principle. These theories are interesting because they have the potential to simultaneously suppress modifications to Einstein's theory on Solar System scales, while introducing large deviations in the strong field of neutron stars. Scalar-tensor theories can be classified through the choice of conformal factor, a scalar that regulates the coupling between matter and the metric in the Einstein frame. The class defined by a Gaussian conformal factor with a negative exponent has been studied the most because it leads to spontaneous scalarization (i.e. the sudden activation of the scalar field in neutron stars), which consequently leads to large deviations from general relativity in the strong field. This class, however, has recently been shown to be in conflict with Solar System observations when accounting for the cosmological evolution of the scalar field. We here study whether this remains the case when the exponent of the conformal factor is positive, as well as in another class of theories defined by a hyperbolic conformal factor. We find that in both of these scalar-tensor theories, Solar System tests are passed only in a very small subset of coupling parameter space, for a large set of initial conditions compatible with big bang nucleosynthesis. However, while we find that it is possible for neutron stars to scalarize, one must carefully select the coupling parameter to do so, and even then, the scalar charge is typically 2 orders of magnitude smaller than in the negative-exponent case. Our study suggests that future work on scalar-tensor gravity, for example in the context of tests of general relativity with gravitational waves from neutron star binaries, should be carried out within the positive coupling parameter class.

Killing(-Yano) tensors in string theory

NASA Astrophysics Data System (ADS)

Chervonyi, Yuri; Lunin, Oleg

2015-09-01

We construct the Killing(-Yano) tensors for a large class of charged black holes in higher dimensions and study general properties of such tensors, in particular, their behavior under string dualities. Killing(-Yano) tensors encode the symmetries beyond isometries, which lead to insights into dynamics of particles and fields on a given geometry by providing a set of conserved quantities. By analyzing the eigenvalues of the Killing tensor, we provide a prescription for constructing several conserved quantities starting from a single object, and we demonstrate that Killing tensors in higher dimensions are always associated with ellipsoidal coordinates. We also determine the transformations of the Killing(-Yano) tensors under string dualities, and find the unique modification of the Killing-Yano equation consistent with these symmetries. These results are used to construct the explicit form of the Killing(-Yano) tensors for the Myers-Perry black hole in arbitrary number of dimensions and for its charged version.

Development of the Tensoral Computer Language

NASA Technical Reports Server (NTRS)

Ferziger, Joel; Dresselhaus, Eliot

1996-01-01

The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.

Higher derivative extensions of 3 d Chern-Simons models: conservation laws and stability

NASA Astrophysics Data System (ADS)

Kaparulin, D. S.; Karataeva, I. Yu.; Lyakhovich, S. L.

2015-11-01

We consider the class of higher derivative 3 d vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For the nth-order theory of this type, we provide a general recipe for constructing n-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability.

2PI effective action for the SYK model and tensor field theories

NASA Astrophysics Data System (ADS)

Benedetti, Dario; Gurau, Razvan

2018-05-01

We discuss the two-particle irreducible (2PI) effective action for the SYK model and for tensor field theories. For the SYK model the 2PI effective action reproduces the bilocal reformulation of the model without using replicas. In general tensor field theories the 2PI formalism is the only way to obtain a bilocal reformulation of the theory, and as such is a precious instrument for the identification of soft modes and for possible holographic interpretations. We compute the 2PI action for several models, and push it up to fourth order in the 1 /N expansion for the model proposed by Witten in [1], uncovering a one-loop structure in terms of an auxiliary bilocal action.

Current-sheet formation in two-dimensional coronal fields

NASA Astrophysics Data System (ADS)

Billinghurst, M. N.; Craig, I. J. D.; Sneyd, A. D.

1993-11-01

The formation of current sheets by shearing motions in line-tied twin-lobed fields is examined. A general analytic argument shows that current sheets form along the fieldline bounding the two lobes in the case of both symmetric and asymmetric footpoint motions. In the case of strictly antisymmetric motions however no current sheets can form. These findings are reinforced by magnetic relaxation experiments involving sheared two-lobed fields represented by Clebsh variables. It is pointed out that, although current singularites cannot be expected to form when the line-tying assumption is relaxed, the two-lobed geometry is still consistent with the formation of highly localised currents - and strong resistive dissipation - along field lines close to the bounding fieldline.

Numerical simulation of magnetic interactions in polycrystalline YFeO 3

NASA Astrophysics Data System (ADS)

Lima, E.; Martins, T. B.; Rechenberg, H. R.; Goya, G. F.; Cavelius, C.; Rapalaviciute, R.; Hao, S.; Mathur, S.

The magnetic behavior of polycrystalline yttrium orthoferrite was studied from the experimental and theoretical points of view. Magnetization measurements up to 170 kOe were carried out on a single-phase YFeO 3 sample synthesized from heterobimetallic alkoxides. The complex interplay between weak-ferromagnetic and antiferromagnetic interactions, observed in the experimental M( H) curves, was successfully simulated by locally minimizing the magnetic energy of two interacting Fe sublattices. The resulting values of exchange field ( HE=5590 kOe), anisotropy field ( HA=0.5 kOe) and Dzyaloshinsky-Moriya antisymmetric field ( HD=149 kOe) are in good agreement with previous reports on this system.

Poiseuille flow of a Quincke suspension

NASA Astrophysics Data System (ADS)

CÄ`bers, A.

2014-09-01

The controversy of models of dielectric particle suspensions with antisymmetric stress, which predict a nonphysical cusp of the velocity profile in plane Poiseuille flow under the action of the electrical field, is resolved. In the mean-field approximation, the nonlinear kinetic equation is derived for coupled due to the flow translational and rotational motion of the particles. By its numerical solution, it is shown that the velocity profile is smeared due to the translational diffusion of the particles with opposite directions of rotation. The obtained results for the velocity profiles and flow rates as a function of the electric field strength are in qualitative agreement with the existing experimental results.

Poiseuille flow of a Quincke suspension.

PubMed

Cēbers, A

2014-09-01

The controversy of models of dielectric particle suspensions with antisymmetric stress, which predict a nonphysical cusp of the velocity profile in plane Poiseuille flow under the action of the electrical field, is resolved. In the mean-field approximation, the nonlinear kinetic equation is derived for coupled due to the flow translational and rotational motion of the particles. By its numerical solution, it is shown that the velocity profile is smeared due to the translational diffusion of the particles with opposite directions of rotation. The obtained results for the velocity profiles and flow rates as a function of the electric field strength are in qualitative agreement with the existing experimental results.

Propagation of symmetric and anti-symmetric surface waves in aself-gravitating magnetized dusty plasma layer with generalized (r, q) distribution

NASA Astrophysics Data System (ADS)

Lee, Myoung-Jae; Jung, Young-Dae

2018-05-01

The dispersion properties of surface dust ion-acoustic waves in a self-gravitating magnetized dusty plasma layer with the (r, q) distribution are investigated. The result shows that the wave frequency of the symmetric mode in the plasma layer decreases with an increase in the wave number. It is also shown that the wave frequency of the symmetric mode decreases with an increase in the spectral index r. However, the wave frequency of the anti-symmetric mode increases with an increase in the wave number. It is also found that the anti-symmetric mode wave frequency increases with an increase in the spectral index r. In addition, it is found that the influence of the self-gravitation on the symmetric mode wave frequency decreases with increasing scaled Jeans frequency. Moreover, it is found that the wave frequency of the symmetric mode increases with an increase in the dust charge; however, the anti-symmetric mode shows opposite behavior.

Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Alal Hosen, Md.; Chowdhury, M. S. H.; Yeakub Ali, Mohammad; Faris Ismail, Ahmad

2017-12-01

A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpose of the present paper is to propose an analytical approximation technique based on the HBM for obtaining approximate angular frequencies and the corresponding periodic solutions of the oscillators with anti-symmetric quadratic nonlinearity. After applying HBM, a set of complicated nonlinear algebraic equations is found. Analytical approach is not always fruitful for solving such kinds of nonlinear algebraic equations. In this article, two small parameters are found, for which the power series solution produces desired results. Moreover, the amplitude-frequency relationship has also been determined in a novel analytical way. The presented technique gives excellent results as compared with the corresponding numerical results and is better than the existing ones.

Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame

NASA Astrophysics Data System (ADS)

Du, J.; Chen, C.; Lesur, V.; Wang, L.

2015-07-01

General expressions of magnetic vector (MV) and magnetic gradient tensor (MGT) in terms of the first- and second-order derivatives of spherical harmonics at different degrees/orders are relatively complicated and singular at the poles. In this paper, we derived alternative non-singular expressions for the MV, the MGT and also the third-order partial derivatives of the magnetic potential field in the local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields and also the third-order partial derivatives of the magnetic potential field at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (GFZ Reference Internal Magnetic Model, version 0.0) with spherical harmonic degrees 16-90. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the magnetic potential field.

Conformal and Nearly Conformal Theories at Large N

NASA Astrophysics Data System (ADS)

Tarnoplskiy, Grigory M.

In this thesis we present new results in conformal and nearly conformal field theories in various dimensions. In chapter two, we study different properties of the conformal Quantum Electrodynamics (QED) in continuous dimension d. At first we study conformal QED using large Nf methods, where Nf is the number of massless fermions. We compute its sphere free energy as a function of d, ignoring the terms of order 1/Nf and higher. For finite Nf we use the epsilon-expansion. Next we use a large Nf diagrammatic approach to calculate the leading corrections to CT, the coefficient of the two-point function of the stress-energy tensor, and CJ, the coefficient of the two-point function of the global symmetry current. We present explicit formulae as a function of d and check them versus the expectations in 2 and 4 - epsilon dimensions. In chapter three, we discuss vacuum stability in 1 + 1 dimensional conformal field theories with external background fields. We show that the vacuum decay rate is given by a non-local two-form. This two-form is a boundary term that must be added to the effective in/out Lagrangian. The two-form is expressed in terms of a Riemann-Hilbert decomposition for background gauge fields, and is given by its novel "functional'' version in the gravitational case. In chapter four, we explore Tensor models. Such models possess the large N limit dominated by the melon diagrams. The quantum mechanics of a real anti-commuting rank-3 tensor has a large N limit similar to the Sachdev-Ye-Kitaev (SYK) model. We also discuss the quantum mechanics of a complex 3-index anti-commuting tensor and argue that it is equivalent in the large N limit to a version of SYK model with complex fermions. Finally, we discuss models of a commuting tensor in dimension d. We study the spectrum of the large N quantum field theory of bosonic rank-3 tensors using the Schwinger-Dyson equations. We compare some of these results with the 4 - epsilon expansion, finding perfect agreement. We also study the spectra of bosonic theories of rank q - 1 tensors with φq interactions.

Ryu-Takayanagi formula for symmetric random tensor networks

NASA Astrophysics Data System (ADS)

Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi

2018-06-01

We consider the special case of random tensor networks (RTNs) endowed with gauge symmetry constraints on each tensor. We compute the Rényi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large-bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background-independent quantum gravity, and for importing quantum gravity tools into tensor network research.

Spatial mode filters realized with multimode interference couplers

NASA Astrophysics Data System (ADS)

Leuthold, J.; Hess, R.; Eckner, J.; Besse, P. A.; Melchior, H.

1996-06-01

Spatial mode filters based on multimode interference couplers (MMI's) that offer the possibility of splitting off antisymmetric from symmetric modes are presented, and realizations of these filters in InGaAsP / InP are demonstrated. Measured suppression of the antisymmetric first-order modes at the output for the symmetric mode is better than 18 dB. Such MMI's are useful for monolithically integrating mode filters with all-optical devices, which are controlled through an antisymmetric first-order mode. The filtering out of optical control signals is necessary for cascading all-optical devices. Another application is the improvement of on-off ratios in optical switches.

Chiral fluctuations in MnSi above the Curie temperature.

PubMed

Roessli, B; Böni, P; Fischer, W E; Endoh, Y

2002-06-10

Polarized neutrons are used to determine the antisymmetric part of the magnetic susceptibility in noncentrosymmetric MnSi. The paramagnetic fluctuations are found to be incommensurate with the chemical lattice and to have a chiral character. We argue that antisymmetric interactions must be taken into account to properly describe the critical dynamics in MnSi above T(C). The possibility of directly measuring the polarization dependent part of the dynamical susceptibility in a large class of compounds by polarized inelastic neutron scattering is outlined as it can yield evidence for antisymmetric interactions such as spin-orbit coupling in metals as well as in insulators.

Buckling and weight optimization for non-coupled antisymmetric laminates

NASA Astrophysics Data System (ADS)

Bhatnagar, Aditi

This research work describes the application of genetic algorithms to weight minimization and buckling load maximization of the non-coupled antisymmetric composite laminated plates. Previous studies of composite tailoring were limited to symmetric and balanced laminates. With the availability of many methodologies for composite tailoring, genetic algorithm is preferably used because of its ability to handle discrete design variable and attain multiple near optimum design solutions. A comparative study is made between optimum symmetric-balanced laminate designs and optimum non-coupled antisymmetric laminate designs, both of which are subjected to biaxial in-plane compressive loads. With the implementation of various genetic algorithm operators such as selection, crossover and mutation, critical buckling load factors are obtained for the optimum stacking sequence for both types of laminates. The mechanical properties for non-coupled antisymmetric laminates is independent of all types of coupling effects such as bending-twisting coupling, bending-extension coupling, and shear-extension coupling, thus giving the laminate a non-coupling behavior. This is in contrast to that of symmetric-balanced laminates where finite bending-twisting coupling terms are present. Optimized laminate layups satisfying the constraints of balance, buckling and adjoining were obtained for two types of graphite epoxy rectangular composite laminated plates. The current research augments the laminate thickness minimization designs with both odd and even number of layers, and the optimum buckling load maximization designs by the introduction of non-coupled antisymmetric laminates.

On the possibility of using X-ray Compton scattering to study magnetoelectrical properties of crystals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Collins, S. P., E-mail: steve.collins@diamond.ac.uk; Laundy, D.; Connolley, T.

2016-02-16

The possibility of using X-ray Compton scattering to reveal antisymmetric components of the electron momentum density, as a fingerprint of magnetoelectric sample properties, is investigated experimentally and theoretically by studying the polar ferromagnet GaFeO{sub 3}. This paper discusses the possibility of using Compton scattering – an inelastic X-ray scattering process that yields a projection of the electron momentum density – to probe magnetoelectrical properties. It is shown that an antisymmetric component of the momentum density is a unique fingerprint of such time- and parity-odd physics. It is argued that polar ferromagnets are ideal candidates to demonstrate this phenomenon and themore » first experimental results are shown, on a single-domain crystal of GaFeO{sub 3}. The measured antisymmetric Compton profile is very small (≃ 10{sup −5} of the symmetric part) and of the same order of magnitude as the statistical errors. Relativistic first-principles simulations of the antisymmetric Compton profile are presented and it is shown that, while the effect is indeed predicted by theory, and scales with the size of the valence spin–orbit interaction, its magnitude is significantly overestimated. The paper outlines some important constraints on the properties of the antisymmetric Compton profile arising from the underlying crystallographic symmetry of the sample.« less

View-Dependent Streamline Deformation and Exploration

PubMed Central

Tong, Xin; Edwards, John; Chen, Chun-Ming; Shen, Han-Wei; Johnson, Chris R.; Wong, Pak Chung

2016-01-01

Occlusion presents a major challenge in visualizing 3D flow and tensor fields using streamlines. Displaying too many streamlines creates a dense visualization filled with occluded structures, but displaying too few streams risks losing important features. We propose a new streamline exploration approach by visually manipulating the cluttered streamlines by pulling visible layers apart and revealing the hidden structures underneath. This paper presents a customized view-dependent deformation algorithm and an interactive visualization tool to minimize visual clutter in 3D vector and tensor fields. The algorithm is able to maintain the overall integrity of the fields and expose previously hidden structures. Our system supports both mouse and direct-touch interactions to manipulate the viewing perspectives and visualize the streamlines in depth. By using a lens metaphor of different shapes to select the transition zone of the targeted area interactively, the users can move their focus and examine the vector or tensor field freely. PMID:26600061

View-Dependent Streamline Deformation and Exploration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tong, Xin; Edwards, John; Chen, Chun-Ming

Occlusion presents a major challenge in visualizing 3D flow and tensor fields using streamlines. Displaying too many streamlines creates a dense visualization filled with occluded structures, but displaying too few streams risks losing important features. We propose a new streamline exploration approach by visually manipulating the cluttered streamlines by pulling visible layers apart and revealing the hidden structures underneath. This paper presents a customized view-dependent deformation algorithm and an interactive visualization tool to minimize visual cluttering for visualizing 3D vector and tensor fields. The algorithm is able to maintain the overall integrity of the fields and expose previously hidden structures.more » Our system supports both mouse and direct-touch interactions to manipulate the viewing perspectives and visualize the streamlines in depth. By using a lens metaphor of different shapes to select the transition zone of the targeted area interactively, the users can move their focus and examine the vector or tensor field freely.« less

View-Dependent Streamline Deformation and Exploration.

PubMed

Tong, Xin; Edwards, John; Chen, Chun-Ming; Shen, Han-Wei; Johnson, Chris R; Wong, Pak Chung

2016-07-01

Occlusion presents a major challenge in visualizing 3D flow and tensor fields using streamlines. Displaying too many streamlines creates a dense visualization filled with occluded structures, but displaying too few streams risks losing important features. We propose a new streamline exploration approach by visually manipulating the cluttered streamlines by pulling visible layers apart and revealing the hidden structures underneath. This paper presents a customized view-dependent deformation algorithm and an interactive visualization tool to minimize visual clutter in 3D vector and tensor fields. The algorithm is able to maintain the overall integrity of the fields and expose previously hidden structures. Our system supports both mouse and direct-touch interactions to manipulate the viewing perspectives and visualize the streamlines in depth. By using a lens metaphor of different shapes to select the transition zone of the targeted area interactively, the users can move their focus and examine the vector or tensor field freely.

Compensation of Gradient-Induced Magnetic Field Perturbations

PubMed Central

Nixon, Terence W.; McIntyre, Scott; Rothman, Douglas L.; de Graaf, Robin A.

2008-01-01

Pulsed magnetic field gradients are essential for MR imaging and localized spectroscopy applications. However, besides the desired linear field gradients, pulsed currents in a strong external magnetic field also generate unwanted effects like eddy currents, gradient coil vibrations and acoustic noise. While the temporal magnetic field perturbations associated with eddy currents lead to spectral line shape distortions and signal loss, the vibration-related modulations lead to anti-symmetrical sidebands of any large signal (i.e. water), thereby obliterating the signals from smaller signals (i.e. metabolites). Here the measurement, characterization and compensation of vibrations-related magnetic field perturbations is presented. Following a quantitative evaluation of the various temporal components of the main magnetic field, a digital B0 magnetic field waveform is generated which reduces all temporal variations of the main magnetic field to within the spectral noise level. PMID:18329304

On symmetry inheritance of nonminimally coupled scalar fields

NASA Astrophysics Data System (ADS)

Barjašić, Irena; Smolić, Ivica

2018-04-01

We present the first symmetry inheritance analysis of fields non-minimally coupled to gravity. In this work we are focused on the real scalar field ϕ with nonminimal coupling of the form ξφ2 R . Possible cases of symmetry noninheriting fields are constrained by the properties of the Ricci tensor and the scalar potential. Examples of such spacetimes can be found among those which are ‘dressed’ with the stealth scalar field, a nontrivial scalar field configuration with the vanishing energy–momentum tensor. We classify the scalar field potentials which allow symmetry noninheriting stealth field configurations on top of the exact solutions of the Einstein’s gravitational field equation with the cosmological constant.

Tensor hierarchy and generalized Cartan calculus in SL(3) × SL(2) exceptional field theory

NASA Astrophysics Data System (ADS)

Hohm, Olaf; Wang, Yi-Nan

2015-04-01

We construct exceptional field theory for the duality group SL(3) × SL(2). The theory is defined on a space with 8 `external' coordinates and 6 `internal' coordinates in the (3, 2) fundamental representation, leading to a 14-dimensional generalized spacetime. The bosonic theory is uniquely determined by gauge invariance under generalized external and internal diffeomorphisms. The latter invariance can be made manifest by introducing higher form gauge fields and a so-called tensor hierarchy, which we systematically develop to much higher degree than in previous studies. To this end we introduce a novel Cartan-like tensor calculus based on a covariant nil-potent differential, generalizing the exterior derivative of conventional differential geometry. The theory encodes the full D = 11 or type IIB supergravity, respectively.

Covariant Approach of the Dynamics of Particles in External Gauge Fields, Killing Tensors and Quantum Gravitational Anomalies

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2011-04-01

We give an overview of the first integrals of motion of particles in the presence of external gauge fields in a covariant Hamiltonian approach. The special role of Stäckel-Killing and Killing-Yano tensors is pointed out. Some nontrivial examples involving Runge-Lenz type conserved quantities are explicitly worked out. A condition of the electromagnetic field to maintain the hidden symmetry of the system is stated. A concrete realization of this condition is given by the Killing-Maxwell system and exemplified with the Kerr metric. Quantum symmetry operators for the Klein-Gordon and Dirac equations are constructed from Killing tensors. The transfer of the classical conserved quantities to the quantum mechanical level is analyzed in connection with quantum anomalies.

Anisotropic tensor power spectrum at interferometer scales induced by tensor squeezed non-Gaussianity

NASA Astrophysics Data System (ADS)

Ricciardone, Angelo; Tasinato, Gianmassimo

2018-02-01

We develop a scenario of inflation with spontaneously broken time and space diffeomorphisms, with distinctive features for the primordial tensor modes. Inflationary tensor fluctuations are not conserved outside the horizon, and can acquire a mass during the inflationary epoch. They can evade the Higuchi bound around de Sitter space, thanks to interactions with the fields driving expansion. Correspondingly, the primordial stochastic gravitational wave background (SGWB) is characterised by a tuneable scale dependence, and can be detectable at interferometer scales. In this set-up, tensor non-Gaussianity can be parametrically enhanced in the squeezed limit. This induces a coupling between long and short tensor modes, leading to a specific quadrupolar anisotropy in the primordial SGWB spectrum, which can be used to build estimators for tensor non-Gaussianity. We analyse how our inflationary system can be tested with interferometers, also discussing how an interferometer can be sensitive to a primordial anisotropic SGWB.

Extended effective field theory of inflation

NASA Astrophysics Data System (ADS)

Ashoorioon, Amjad; Casadio, Roberto; Cicoli, Michele; Geshnizjani, Ghazal; Kim, Hyung J.

2018-02-01

We present a general framework where the effective field theory of single field inflation is extended by the inclusion of operators with mass dimension 3 and 4 in the unitary gauge. These higher dimensional operators introduce quartic and sextic corrections to the dispersion relation. We study the regime of validity of this extended effective field theory of inflation and the effect of these higher dimensional operators on CMB observables associated with scalar perturbations, such as the speed of sound, the amplitude of the power spectrum and the tensor-to-scalar ratio. Tensor perturbations remain instead, unaltered.

Measurement tensors in diffusion MRI: generalizing the concept of diffusion encoding.

PubMed

Westin, Carl-Fredrik; Szczepankiewicz, Filip; Pasternak, Ofer; Ozarslan, Evren; Topgaard, Daniel; Knutsson, Hans; Nilsson, Markus

2014-01-01

In traditional diffusion MRI, short pulsed field gradients (PFG) are used for the diffusion encoding. The standard Stejskal-Tanner sequence uses one single pair of such gradients, known as single-PFG (sPFG). In this work we describe how trajectories in q-space can be used for diffusion encoding. We discuss how such encoding enables the extension of the well-known scalar b-value to a tensor-valued entity we call the diffusion measurement tensor. The new measurements contain information about higher order diffusion propagator covariances not present in sPFG. As an example analysis, we use this new information to estimate a Gaussian distribution over diffusion tensors in each voxel, described by its mean (a diffusion tensor) and its covariance (a 4th order tensor).

Chemical shift and electric field gradient tensors for the amide and carboxyl hydrogens in the model peptide N-acetyl-D,L-valine. Single-crystal deuterium NMR study.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gerald, R. E., II; Bernhard, T.; Haeberlen, U.

1993-01-01

Solid-state NMR spectroscopy is well established as a method for describing molecular structure with resolution on the atomic scale. Many of the NMR observables result from anisotropic interactions between the nuclear spin and its environment. These observables can be described by second-rank tensors. For example, the eigenvalues of the traceless symmetric part of the hydrogen chemical shift (CS) tensor provide information about the strength of inter- or intramolecular hydrogen bonding. On the other hand, the eigenvectors of the deuterium electric field gradient (EFG) tensor give deuteron/proton bond directions with an accuracy rivalled only by neutron diffraction. In this paper themore » authors report structural information of this type for the amide and carboxyl hydrogen sites in a single crystal of the model peptide N-acetyl-D,L-valine (NAV). They use deuterium NMR to infer both the EFG and CS tensors at the amide and carboxyl hydrogen sites in NAV. Advantages of this technique over multiple-pulse proton NMR are that it works in the presence of {sup 14}N spins which are very hard to decouple from protons and that additional information in form of the EFG tensors can be derived. The change in the CS and EFG tensors upon exchange of a deuteron for a proton (the isotope effect) is anticipated to be very small; the effect on the CS tensors is certainly smaller than the experimental errors. NAV has served as a model peptide before in a variety of NMR studies, including those concerned with developing solid-state NMR spectroscopy as a method for determining the structure of proteins. NMR experiments on peptide or protein samples which are oriented in at least one dimension can provide important information about the three-dimensional structure of the peptide or the protein. In order to interpret the NMR data in terms of the structure of the polypeptide, the relationship of the CS and EFG tensors to the local symmetry elements of an amino acide, e.g., the peptide plane, is essential. The main purpose of this work is to investigate this relationship for the amide hydrogen CS tensor. The amide hydrogen CS tensor will also provide orientational information for peptide bonds in proteins complementary to that from the nitrogen CS and EFG tensors and the nitrogen-hydrogen heteronuclear dipole-dipole coupling which have been used previously to determine protein structures by solid-state NMR spectroscopy. This information will be particularly valuable because the amide hydrogen CS tensor is not axially symmetric. In addition, the use of the amide hydrogen CS interaction in high-field solid-state NMR experiments will increase the available resolution among peptide sites.« less

Faraday Wave Turbulence on a Spherical Liquid Shell

NASA Technical Reports Server (NTRS)

Holt, R. Glynn; Trinh, Eugene H.

1996-01-01

Millimeter-radius liquid shells are acoustically levitated in an ultrasonic field. Capillary waves are observed on the shells. At low energies (minimal acoustic amplitude, thick shell) a resonance is observed between the symmetric and antisymmetric thin film oscillation modes. At high energies (high acoustic pressure, thin shell) the shell becomes fully covered with high-amplitude waves. Temporal spectra of scattered light from the shell in this regime exhibit a power-law decay indicative of turbulence.

Metric-affine f (R ,T ) theories of gravity and their applications

NASA Astrophysics Data System (ADS)

Barrientos, E.; Lobo, Francisco S. N.; Mendoza, S.; Olmo, Gonzalo J.; Rubiera-Garcia, D.

2018-05-01

We study f (R ,T ) theories of gravity, where T is the trace of the energy-momentum tensor Tμ ν, with independent metric and affine connection (metric-affine theories). We find that the resulting field equations share a close resemblance with their metric-affine f (R ) relatives once an effective energy-momentum tensor is introduced. As a result, the metric field equations are second-order and no new propagating degrees of freedom arise as compared to GR, which contrasts with the metric formulation of these theories, where a dynamical scalar degree of freedom is present. Analogously to its metric counterpart, the field equations impose the nonconservation of the energy-momentum tensor, which implies nongeodesic motion and consequently leads to the appearance of an extra force. The weak field limit leads to a modified Poisson equation formally identical to that found in Eddington-inspired Born-Infeld gravity. Furthermore, the coupling of these gravity theories to perfect fluids, electromagnetic, and scalar fields, and their potential applications are discussed.

Casimir forces on a bi-anisotropic absorbing magneto-dielectric slab between two parallel conducting plates

NASA Astrophysics Data System (ADS)

Amooshahi, Majid; Shoughi, Ali

2018-05-01

A fully canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric slab is demonstrated. The electric and the magnetic polarization densities of the magneto-dielectric slab are defined in terms of the dynamical variables modeling the slab and the coupling tensors that couple the electromagnetic field to the slab. The four susceptibility tensors of the bi-anisotropic magneto-dielectric slab are expressed in terms of the coupling tensors that couple an electromagnetic field to the slab. It is shown that the four susceptibility tensors of the bi-anisotropic magneto-dielectric slab satisfy Kramers-Kronig relations. The Maxwell’s equations are exactly solved in the presence of the bi-anisotropic magneto-dielectric slab. The tangential and the normal components of the Casimir forces exerted on the bi-anisotropic magnet-dielectric slab exactly are calculated in the vacuum state and thermal state of the total system. It is shown that the tangential components of the Casimir forces vanish when the bi-anisotropic slab is converted to an isotropic slab.

Gaussian mixtures on tensor fields for segmentation: applications to medical imaging.

PubMed

de Luis-García, Rodrigo; Westin, Carl-Fredrik; Alberola-López, Carlos

2011-01-01

In this paper, we introduce a new approach for tensor field segmentation based on the definition of mixtures of Gaussians on tensors as a statistical model. Working over the well-known Geodesic Active Regions segmentation framework, this scheme presents several interesting advantages. First, it yields a more flexible model than the use of a single Gaussian distribution, which enables the method to better adapt to the complexity of the data. Second, it can work directly on tensor-valued images or, through a parallel scheme that processes independently the intensity and the local structure tensor, on scalar textured images. Two different applications have been considered to show the suitability of the proposed method for medical imaging segmentation. First, we address DT-MRI segmentation on a dataset of 32 volumes, showing a successful segmentation of the corpus callosum and favourable comparisons with related approaches in the literature. Second, the segmentation of bones from hand radiographs is studied, and a complete automatic-semiautomatic approach has been developed that makes use of anatomical prior knowledge to produce accurate segmentation results. Copyright © 2010 Elsevier Ltd. All rights reserved.

Estimation of integral curves from high angular resolution diffusion imaging (HARDI) data.

PubMed

Carmichael, Owen; Sakhanenko, Lyudmila

2015-05-15

We develop statistical methodology for a popular brain imaging technique HARDI based on the high order tensor model by Özarslan and Mareci [10]. We investigate how uncertainty in the imaging procedure propagates through all levels of the model: signals, tensor fields, vector fields, and fibers. We construct asymptotically normal estimators of the integral curves or fibers which allow us to trace the fibers together with confidence ellipsoids. The procedure is computationally intense as it blends linear algebra concepts from high order tensors with asymptotical statistical analysis. The theoretical results are illustrated on simulated and real datasets. This work generalizes the statistical methodology proposed for low angular resolution diffusion tensor imaging by Carmichael and Sakhanenko [3], to several fibers per voxel. It is also a pioneering statistical work on tractography from HARDI data. It avoids all the typical limitations of the deterministic tractography methods and it delivers the same information as probabilistic tractography methods. Our method is computationally cheap and it provides well-founded mathematical and statistical framework where diverse functionals on fibers, directions and tensors can be studied in a systematic and rigorous way.

Estimation of integral curves from high angular resolution diffusion imaging (HARDI) data

PubMed Central

Carmichael, Owen; Sakhanenko, Lyudmila

2015-01-01

We develop statistical methodology for a popular brain imaging technique HARDI based on the high order tensor model by Özarslan and Mareci [10]. We investigate how uncertainty in the imaging procedure propagates through all levels of the model: signals, tensor fields, vector fields, and fibers. We construct asymptotically normal estimators of the integral curves or fibers which allow us to trace the fibers together with confidence ellipsoids. The procedure is computationally intense as it blends linear algebra concepts from high order tensors with asymptotical statistical analysis. The theoretical results are illustrated on simulated and real datasets. This work generalizes the statistical methodology proposed for low angular resolution diffusion tensor imaging by Carmichael and Sakhanenko [3], to several fibers per voxel. It is also a pioneering statistical work on tractography from HARDI data. It avoids all the typical limitations of the deterministic tractography methods and it delivers the same information as probabilistic tractography methods. Our method is computationally cheap and it provides well-founded mathematical and statistical framework where diverse functionals on fibers, directions and tensors can be studied in a systematic and rigorous way. PMID:25937674

The Spacetime Between Einstein and Kaluza-Klein: Further Explorations

NASA Astrophysics Data System (ADS)

Vuille, Chris

2017-01-01

Tensor multinomials can be used to create a generalization of Einstein's general relativity that in a mathematical sense falls between Einstein's original theory in four dimensions and the Kaluza-Klein theory in five dimensions. In the extended theory there are only four physical dimensions, but the tensor multinomials are expanded operators that can accommodate other forces of nature. The equivalent Ricci tensor of this geometry yields vacuum general relativity and electromagnetism, as well as a Klein-Gordon-like quantum scalar field. With a generalization of the stress-energy tensor, an exact solution for a plane-symmetric dust can be found where the scalar portion of the field drives early universe inflation, levels off for a period, then causes a later continued universal acceleration, a possible geometric mechanism for the inflaton or dark energy. Some new explorations of the equations, the problems, and possibilities will be presented and discussed.

Discrete gravity on random tensor network and holographic Rényi entropy

NASA Astrophysics Data System (ADS)

Han, Muxin; Huang, Shilin

2017-11-01

In this paper we apply the discrete gravity and Regge calculus to tensor networks and Anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We construct the boundary many-body quantum state |Ψ〉 using random tensor networks as the holographic mapping, applied to the Wheeler-deWitt wave function of bulk Euclidean discrete gravity in 3 dimensions. The entanglement Rényi entropy of |Ψ〉 is shown to holographically relate to the on-shell action of Einstein gravity on a branch cover bulk manifold. The resulting Rényi entropy S n of |Ψ〉 approximates with high precision the Rényi entropy of ground state in 2-dimensional conformal field theory (CFT). In particular it reproduces the correct n dependence. Our results develop the framework of realizing the AdS3/CFT2 correspondence on random tensor networks, and provide a new proposal to approximate the CFT ground state.

Charmless hadronic B decays into a tensor meson

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheng, Hai-Yang; C. N. Yang Institute for Theoretical Physics, State University of New York Stony Brook, Stony Brook, New York 11794; Yang, Kwei-Chou

2011-02-01

Two-body charmless hadronic B decays involving a tensor meson in the final state are studied within the framework of QCD factorization (QCDF). Because of the G-parity of the tensor meson, both the chiral-even and chiral-odd two-parton light-cone distribution amplitudes of the tensor meson are antisymmetric under the interchange of momentum fractions of the quark and antiquark in the SU(3) limit. Our main results are: (i) In the naieve factorization approach, the decays such as B{sup -}{yields}K{sub 2}*{sup 0}{pi}{sup -} and B{sup 0}{yields}K{sub 2}*{sup -}{pi}{sup +} with a tensor meson emitted are prohibited because a tensor meson cannot be created frommore » the local V-A or tensor current. Nevertheless, the decays receive nonfactorizable contributions in QCDF from vertex, penguin and hard spectator corrections. The experimental observation of B{sup -}{yields}K{sub 2}*{sup 0}{pi}{sup -} indicates the importance of nonfactorizable effects. (ii) For penguin-dominated B{yields}TP and TV decays, the predicted rates in naieve factorization are usually too small by 1 to 2 orders of magnitude. In QCDF, they are enhanced by power corrections from penguin annihilation and nonfactorizable contributions. (iii) The dominant penguin contributions to B{yields}K{sub 2}*{eta}{sup (')} arise from the processes: (a) b{yields}sss{yields}s{eta}{sub s} and (b) b{yields}sqq{yields}qK{sub 2}* with {eta}{sub q}=(uu+dd)/{radical}(2) and {eta}{sub s}=ss. The interference, constructive for K{sub 2}*{eta}{sup '} and destructive for K{sub 2}*{eta}, explains why {Gamma}(B{yields}K{sub 2}*{eta}{sup '})>>{Gamma}(B{yields}K{sub 2}*{eta}). (iv) We use the measured rates of B{yields}K{sub 2}*({omega},{phi}) to extract the penguin-annihilation parameters {rho}{sub A}{sup TV} and {rho}{sub A}{sup VT} and the observed longitudinal polarization fractions f{sub L}(K{sub 2}*{omega}) and f{sub L}(K{sub 2}*{phi}) to fix the phases {phi}{sub A}{sup VT} and {phi}{sub A}{sup TV}. (v) The experimental observation that f{sub T}/f{sub L}<<1 for B{yields}K{sub 2}*(1430){phi}, whereas f{sub T}/f{sub L}{approx}1 for B{yields}K{sub 2}*(1430){omega} with f{sub T} being the transverse polarization fraction, can be accommodated in QCDF, but it cannot be dynamically explained at first place. For penguin-dominated B{yields}TV decays, we find f{sub L}(K{sub 2}*{rho}){approx}f{sub L}(K{sub 2}*{omega}){approx}0.65, whereas f{sub L}(K*f{sub 2}){approx}0.93. It will be of great interest to measure f{sub L} for these modes to test QCDF. Theoretically, transverse polarization is expected to be small in tree-dominated B{yields}TV decays except for the a{sub 2}{sup -}{rho}{sup 0}, a{sub 2}{sup -}{rho}{sup +}, K{sub 2}*{sup 0}K*{sup -} and K{sub 2}*{sup 0}K*{sup 0} modes. (vi) For tree-dominated decays, their rates are usually very small except for the a{sub 2}{sup 0}({pi}{sup -},{rho}{sup -}), a{sub 2}{sup +}({pi}{sup -},{rho}{sup -}) and f{sub 2}({pi}{sup -},{rho}{sup -}) modes with branching fractions of order 10{sup -6} or even larger.« less

The Theory of Quantized Fields. II

DOE R&D Accomplishments Database

Schwinger, J.

1951-01-01

The arguments leading to the formulation of the Action Principle for a general field are presented. In association with the complete reduction of all numerical matrices into symmetrical and anti-symmetrical parts, the general field is decomposed into two sets, which are identified with Bose-Einstein and Fermi-Dirac fields. The spin restriction on the two kinds of fields is inferred from the time reflection invariance requirement. The consistency of the theory is verified in terms of a criterion involving the various generators of infinitesimal transformations. Following a discussion of charged fields, the electromagnetic field is introduced to satisfy the postulate of general gauge invariance. As an aspect of the latter, it is recognized that the electromagnetic field and charged fields are not kinematically independent. After a discussion of the field-strength commutation relations, the independent dynamical variable of the electromagnetic field are exhibited in terms of a special gauge.

Minkowski Tensors in Two Dimensions: Probing the Morphology and Isotropy of the Matter and Galaxy Density Fields

NASA Astrophysics Data System (ADS)

Appleby, Stephen; Chingangbam, Pravabati; Park, Changbom; Hong, Sungwook E.; Kim, Juhan; Ganesan, Vidhya

2018-05-01

We apply the Minkowski tensor statistics to two-dimensional slices of the three-dimensional matter density field. The Minkowski tensors are a set of functions that are sensitive to directionally dependent signals in the data and, furthermore, can be used to quantify the mean shape of density fields. We begin by reviewing the definition of Minkowski tensors and introducing a method of calculating them from a discretely sampled field. Focusing on the statistic {W}21,1—a 2 × 2 matrix—we calculate its value for both the entire excursion set and individual connected regions and holes within the set. To study the morphology of structures within the excursion set, we calculate the eigenvalues λ 1, λ 2 for the matrix {W}21,1 of each distinct connected region and hole and measure their mean shape using the ratio β \\equiv < {λ }2/{λ }1> . We compare both {W}21,1 and β for a Gaussian field and a smoothed density field generated from the latest Horizon Run 4 cosmological simulation to study the effect of gravitational collapse on these functions. The global statistic {W}21,1 is essentially independent of gravitational collapse, as the process maintains statistical isotropy. However, β is modified significantly, with overdensities becoming relatively more circular compared to underdensities at low redshifts. When applying the statistics to a redshift-space distorted density field, the matrix {W}21,1 is no longer proportional to the identity matrix, and measurements of its diagonal elements can be used to probe the large-scale velocity field.

Large-scale magnetic fields, non-Gaussianity, and gravitational waves from inflation

NASA Astrophysics Data System (ADS)

Bamba, Kazuharu

2017-12-01

We explore the generation of large-scale magnetic fields in the so-called moduli inflation. The hypercharge electromagnetic fields couple to not only a scalar field but also a pseudoscalar one, so that the conformal invariance of the hypercharge electromagnetic fields can be broken. We explicitly analyze the strength of the magnetic fields on the Hubble horizon scale at the present time, the local non-Gaussianity of the curvature perturbations originating from the massive gauge fields, and the tensor-to-scalar ratio of the density perturbations. As a consequence, we find that the local non-Gaussianity and the tensor-to-scalar ratio are compatible with the recent Planck results.

Optical detection of symmetric and antisymmetric states in double quantum wells at room temperature

NASA Astrophysics Data System (ADS)

Marchewka, M.; Sheregii, E. M.; Tralle, I.; Marcelli, A.; Piccinini, M.; Cebulski, J.

2009-09-01

We studied the optical reflectivity of a specially grown double quantum well (DQW) structure characterized by a rectangular shape and a high electron density at room temperature. Assuming that the QWs depth is known, reflectivity spectra in the mid-IR range allow to carry out the precise measurements of the SAS-gap values (the energy gap between the symmetric and anti-symmetric states) and the absolute energies of both symmetric and antisymmetric electron states. The results of our experiments are in favor of the existence of the SAS splitting in the DQWs at room temperature. Here we have shown that the SAS gap increases proportionally to the subband quantum number and the optical electron transitions between symmetric and antisymmetric states belonging to different subbands are allowed. These results were used for interpretation of the beating effect in the Shubnikov-de Haas (SdH) oscillations at low temperatures (0.6 and 4.2 K). The approach to the calculation of the Landau-levels energies for DQW structures developed earlier [D. Ploch , Phys. Rev. B 79, 195434 (2009)] is used for the analysis and interpretation of the experimental data related to the beating effect. We also argue that in order to explain the beating effect in the SdH oscillations, one should introduce two different quasi-Fermi levels characterizing the two electron subsystems regarding symmetry properties of their wave functions, symmetric and antisymmetric ones. These states are not mixed neither by electron-electron interaction nor probably by electron-phonon interaction.

Renormalization of the diffusion tensor for high-frequency, electromagnetic modes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Litwin, C.; Sudan, R.N.

The resonance broadening theory is used to derive the diffusion tensor for resonant particles in a spectrum of electromagnetic modes propagating parallel to the magnetic field. The magnetic trapping limit for saturation of wave amplitudes is discussed.

Higher order first integrals, Killing tensors and Killing-Maxwell system

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2012-02-01

Higher order first integrals of motion of particles in the presence of external gauge fields in a covariant Hamiltonian approach are investigated. The special role of Stackel-Killing and Killing-Yano tensors is pointed out. A condition of the electromagnetic field to maintain the hidden symmetry of the system is stated. A concrete realization of this condition is given by the Killing-Maxwell system and exemplified with the Kerr metric. Another application of the gauge covariant approach is provided by a non relativistic point charge in the field of a Dirac monopole. The corresponding dynamical system possessing a Kepler type symmetry is associated with the Taub-NUT metric using a reduction procedure of symplectic manifolds with symmetries. The reverse of the reduction procedure can be used to investigate higher-dimensional spacetimes admitting Killing tensors.

Axial point groups: rank 1, 2, 3 and 4 property tensor tables.

PubMed

Litvin, Daniel B

2015-05-01

The form of a physical property tensor of a quasi-one-dimensional material such as a nanotube or a polymer is determined from the material's axial point group. Tables of the form of rank 1, 2, 3 and 4 property tensors are presented for a wide variety of magnetic and non-magnetic tensor types invariant under each point group in all 31 infinite series of axial point groups. An application of these tables is given in the prediction of the net polarization and magnetic-field-induced polarization in a one-dimensional longitudinal conical magnetic structure in multiferroic hexaferrites.

Highly efficient all-dielectric optical tensor impedance metasurfaces for chiral polarization control.

PubMed

Kim, Minseok; Eleftheriades, George V

2016-10-15

We propose a highly efficient (nearly lossless and impedance-matched) all-dielectric optical tensor impedance metasurface that mimics chiral effects at optical wavelengths. By cascading an array of rotated crossed silicon nanoblocks, we realize chiral optical tensor impedance metasurfaces that operate as circular polarization selective surfaces. Their efficiencies are maximized through a nonlinear numerical optimization process in which the tensor impedance metasurfaces are modeled via multi-conductor transmission line theory. From rigorous full-wave simulations that include all material losses, we show field transmission efficiencies of 94% for right- and left-handed circular polarization selective surfaces at 800 nm.

Two formalisms, one renormalized stress-energy tensor

NASA Astrophysics Data System (ADS)

Barceló, C.; Carballo, R.; Garay, L. J.

2012-04-01

We explicitly compare the structure of the renormalized stress-energy tensor of a massless scalar field in a (1+1) curved spacetime as obtained by two different strategies: normal-mode construction of the field operator and one-loop effective action. We pay special attention to where and how the information related to the choice of vacuum state in both formalisms is encoded. By establishing a clear translation map between both procedures, we show that these two potentially different renormalized stress-energy tensors are actually equal, when using vacuum-state choices related by this map. One specific aim of the analysis is to facilitate the comparison of results regarding semiclassical effects in gravitational collapse as obtained within these different formalisms.

Theory of the Maxwell pressure tensor and the tension in a water bridge.

PubMed

Widom, A; Swain, J; Silverberg, J; Sivasubramanian, S; Srivastava, Y N

2009-07-01

A water bridge refers to an experimental "flexible cable" made up of pure de-ionized water, which can hang across two supports maintained with a sufficiently large voltage difference. The resulting electric fields within the de-ionized water flexible cable maintain a tension that sustains the water against the downward force of gravity. A detailed calculation of the water bridge tension will be provided in terms of the Maxwell pressure tensor in a dielectric fluid medium. General properties of the dielectric liquid pressure tensor are discussed along with unusual features of dielectric fluid Bernoulli flows in an electric field. The "frictionless" Bernoulli flow is closely analogous to that of a superfluid.

Director Field Analysis (DFA): Exploring Local White Matter Geometric Structure in Diffusion MRI.

PubMed

Cheng, Jian; Basser, Peter J

2018-01-01

In Diffusion Tensor Imaging (DTI) or High Angular Resolution Diffusion Imaging (HARDI), a tensor field or a spherical function field (e.g., an orientation distribution function field), can be estimated from measured diffusion weighted images. In this paper, inspired by the microscopic theoretical treatment of phases in liquid crystals, we introduce a novel mathematical framework, called Director Field Analysis (DFA), to study local geometric structural information of white matter based on the reconstructed tensor field or spherical function field: (1) We propose a set of mathematical tools to process general director data, which consists of dyadic tensors that have orientations but no direction. (2) We propose Orientational Order (OO) and Orientational Dispersion (OD) indices to describe the degree of alignment and dispersion of a spherical function in a single voxel or in a region, respectively; (3) We also show how to construct a local orthogonal coordinate frame in each voxel exhibiting anisotropic diffusion; (4) Finally, we define three indices to describe three types of orientational distortion (splay, bend, and twist) in a local spatial neighborhood, and a total distortion index to describe distortions of all three types. To our knowledge, this is the first work to quantitatively describe orientational distortion (splay, bend, and twist) in general spherical function fields from DTI or HARDI data. The proposed DFA and its related mathematical tools can be used to process not only diffusion MRI data but also general director field data, and the proposed scalar indices are useful for detecting local geometric changes of white matter for voxel-based or tract-based analysis in both DTI and HARDI acquisitions. The related codes and a tutorial for DFA will be released in DMRITool. Copyright © 2017 Elsevier B.V. All rights reserved.

More on the tensor response of the QCD vacuum to an external magnetic field

NASA Astrophysics Data System (ADS)

Gorsky, A.; Kopnin, P. N.; Krikun, A.; Vainshtein, A.

2012-04-01

In this paper we discuss a few issues concerning the magnetic susceptibility of the quark condensate and the Son-Yamamoto anomaly matching equation. It is shown that the Son-Yamamoto relation in the IR implies a nontrivial interplay between the kinetic and Wess-Zumino-Witten terms in the chiral Lagrangian. It is also demonstrated that in a holographic framework an external magnetic field triggers mixing between scalar and tensor fields. Accounting for this, one may calculate the magnetic susceptibility of the quark condensate to all orders in the magnetic field.

The 3 + 1 decomposition of conformal Yano-Killing tensors and ‘momentary’ charges for the spin-2 field

NASA Astrophysics Data System (ADS)

Jezierski, Jacek; Migacz, Szymon

2015-02-01

The ‘fully charged’ spin-2 field solution is presented. This is an analog of the Coulomb solution in electrodynamics and represents the ‘non-waving’ part of the spin-2 field theory. Basic facts and definitions of the spin-2 field and conformal Yano-Killing tensors are introduced. Application of those two objects provides a precise definition of quasi-local gravitational charge. Next, the 3 + 1 decomposition leads to the construction of the momentary gravitational charges on the initial surface, which is applicable for Schwarzschild-like spacetimes.

Symmetries, supersymmetries and cohomologies in gauge theories

NASA Astrophysics Data System (ADS)

Bǎbǎlîc, Elena-Mirela

2009-12-01

The main subjects approached in the thesis are the following: a) the derivation of the interactions in two space-time dimensions in a particular class of topological BF models; b) the construction of the couplings in D ≥ 5 dimensions between one massless tensor field with the mixed symmetry (3, 1) and one with the mixed symmetry of the Riemann tensor; c) the evaluation of the existence of interactions in D ≥ 5 dimensions between two different collections of massless tensor fields with the mixed symmetries (3, 1) and (2, 2); d) the analysis of the relation between the BRST charges obtained in the pure-spinor formalism, respectively in the κ-symmetric one for the supermembrane in eleven dimensions. Our procedure for the first three subjects is based on solving the equations that describe the deformation of the solution to the master equation by means of specific cohomological techniques, while for the fourth one we will use techniques specific to the BRST Hamiltonian approach in order to write the BRST charge. The interactions are obtained under the following hypotheses: locality, Lorentz covariance, Poincare invariance, analyticity of the deformations, and preservation of the number of derivatives on each field. The first three assumptions imply that the interacting theory is local in space-time, Lorentz covariant and Poincare invariant. The analyticity of the deformations refers to the fact that the deformed solution to the master equation is analytical in the coupling constant and reduces to the original solution in the free limit. The conservation of the number of derivatives on each field with respect to the free theory means here that the following two requirements are simultaneously satisfied: (i) the derivative order of the equations of motion on each field is the same for the free and respectively for the interacting theory; (ii) the maximum number of derivatives in the interaction vertices is equal to two, i.e. the maximum number of derivatives from the free Lagrangian. The main results of the thesis are: interactions in two space-time dimensions for a particular class of BF models; interactions between one massless tensor field with the mixed symmetry (3, 1) and one with the mixed symmetry of the Riemann tensor; interactions between collections of massless tensor fields with the mixed symmetries (3, 1) and (2, 2); relating the kappa-symmetric and pure-spinor versions of the supermembrane in eleven dimensions.

Combined analysis of magnetic and gravity anomalies using normalized source strength (NSS)

NASA Astrophysics Data System (ADS)

Li, L.; Wu, Y.

2017-12-01

Gravity field and magnetic field belong to potential fields which lead inherent multi-solution. Combined analysis of magnetic and gravity anomalies based on Poisson's relation is used to determinate homology gravity and magnetic anomalies and decrease the ambiguity. The traditional combined analysis uses the linear regression of the reduction to pole (RTP) magnetic anomaly to the first order vertical derivative of the gravity anomaly, and provides the quantitative or semi-quantitative interpretation by calculating the correlation coefficient, slope and intercept. In the calculation process, due to the effect of remanent magnetization, the RTP anomaly still contains the effect of oblique magnetization. In this case the homology gravity and magnetic anomalies display irrelevant results in the linear regression calculation. The normalized source strength (NSS) can be transformed from the magnetic tensor matrix, which is insensitive to the remanence. Here we present a new combined analysis using NSS. Based on the Poisson's relation, the gravity tensor matrix can be transformed into the pseudomagnetic tensor matrix of the direction of geomagnetic field magnetization under the homologous condition. The NSS of pseudomagnetic tensor matrix and original magnetic tensor matrix are calculated and linear regression analysis is carried out. The calculated correlation coefficient, slope and intercept indicate the homology level, Poisson's ratio and the distribution of remanent respectively. We test the approach using synthetic model under complex magnetization, the results show that it can still distinguish the same source under the condition of strong remanence, and establish the Poisson's ratio. Finally, this approach is applied in China. The results demonstrated that our approach is feasible.

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE

PubMed Central

Wang, Miaoyan; Duc, Khanh Dao; Fischer, Jonathan; Song, Yun S.

2017-01-01

Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. Despite the popularity of such techniques, how the functional properties of a tensor changes upon unfolding is currently not well understood. In contrast to the body of existing work which has focused almost exclusively on matricizations, we here consider all possible unfoldings of an order-k tensor, which are in one-to-one correspondence with the set of partitions of {1, …, k}. We derive general inequalities between the lp-norms of arbitrary unfoldings defined on the partition lattice. In particular, we demonstrate how the spectral norm (p = 2) of a tensor is bounded by that of its unfoldings, and obtain an improved upper bound on the ratio of the Frobenius norm to the spectral norm of an arbitrary tensor. For specially-structured tensors satisfying a generalized definition of orthogonal decomposability, we prove that the spectral norm remains invariant under specific subsets of unfolding operations. PMID:28286347

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE.

PubMed

Wang, Miaoyan; Duc, Khanh Dao; Fischer, Jonathan; Song, Yun S

2017-05-01

Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. Despite the popularity of such techniques, how the functional properties of a tensor changes upon unfolding is currently not well understood. In contrast to the body of existing work which has focused almost exclusively on matricizations, we here consider all possible unfoldings of an order- k tensor, which are in one-to-one correspondence with the set of partitions of {1, …, k }. We derive general inequalities between the l p -norms of arbitrary unfoldings defined on the partition lattice. In particular, we demonstrate how the spectral norm ( p = 2) of a tensor is bounded by that of its unfoldings, and obtain an improved upper bound on the ratio of the Frobenius norm to the spectral norm of an arbitrary tensor. For specially-structured tensors satisfying a generalized definition of orthogonal decomposability, we prove that the spectral norm remains invariant under specific subsets of unfolding operations.

Measuring Nematic Susceptibilities from the Elastoresistivity Tensor

NASA Astrophysics Data System (ADS)

Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian

The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.

Classification of materials for conducting spheroids based on the first order polarization tensor

NASA Astrophysics Data System (ADS)

Khairuddin, TK Ahmad; Mohamad Yunos, N.; Aziz, ZA; Ahmad, T.; Lionheart, WRB

2017-09-01

Polarization tensor is an old terminology in mathematics and physics with many recent industrial applications including medical imaging, nondestructive testing and metal detection. In these applications, it is theoretically formulated based on the mathematical modelling either in electrics, electromagnetics or both. Generally, polarization tensor represents the perturbation in the electric or electromagnetic fields due to the presence of conducting objects and hence, it also desribes the objects. Understanding the properties of the polarization tensor is necessary and important in order to apply it. Therefore, in this study, when the conducting object is a spheroid, we show that the polarization tensor is positive-definite if and only if the conductivity of the object is greater than one. In contrast, we also prove that the polarization tensor is negative-definite if and only if the conductivity of the object is between zero and one. These features categorize the conductivity of the spheroid based on in its polarization tensor and can then help to classify the material of the spheroid.

A Local Fast Marching-Based Diffusion Tensor Image Registration Algorithm by Simultaneously Considering Spatial Deformation and Tensor Orientation

PubMed Central

Xue, Zhong; Li, Hai; Guo, Lei; Wong, Stephen T.C.

2010-01-01

It is a key step to spatially align diffusion tensor images (DTI) to quantitatively compare neural images obtained from different subjects or the same subject at different timepoints. Different from traditional scalar or multi-channel image registration methods, tensor orientation should be considered in DTI registration. Recently, several DTI registration methods have been proposed in the literature, but deformation fields are purely dependent on the tensor features not the whole tensor information. Other methods, such as the piece-wise affine transformation and the diffeomorphic non-linear registration algorithms, use analytical gradients of the registration objective functions by simultaneously considering the reorientation and deformation of tensors during the registration. However, only relatively local tensor information such as voxel-wise tensor-similarity, is utilized. This paper proposes a new DTI image registration algorithm, called local fast marching (FM)-based simultaneous registration. The algorithm not only considers the orientation of tensors during registration but also utilizes the neighborhood tensor information of each voxel to drive the deformation, and such neighborhood tensor information is extracted from a local fast marching algorithm around the voxels of interest. These local fast marching-based tensor features efficiently reflect the diffusion patterns around each voxel within a spherical neighborhood and can capture relatively distinctive features of the anatomical structures. Using simulated and real DTI human brain data the experimental results show that the proposed algorithm is more accurate compared with the FA-based registration and is more efficient than its counterpart, the neighborhood tensor similarity-based registration. PMID:20382233

Calculation and Analysis of Magnetic Gradient Tensor Components of Global Magnetic Models

NASA Astrophysics Data System (ADS)

Schiffler, M.; Queitsch, M.; Schneider, M.; Goepel, A.; Stolz, R.; Krech, W.; Meyer, H. G.; Kukowski, N.

2014-12-01

Global Earth's magnetic field models like the International Geomagnetic Reference Field (IGRF), the World Magnetic Model (WMM) or the High Definition Geomagnetic Model (HDGM) are harmonic analysis regressions to available magnetic observations stored as spherical harmonic coefficients. Input data combine recordings from magnetic observatories, airborne magnetic surveys and satellite data. The advance of recent magnetic satellite missions like SWARM and its predecessors like CHAMP offer high resolution measurements while providing a full global coverage. This deserves expansion of the theoretical framework of harmonic synthesis to magnetic gradient tensor components. Measurement setups for Full Tensor Magnetic Gradiometry equipped with high sensitive gradiometers like the JeSSY STAR system can directly measure the gradient tensor components, which requires precise knowledge about the background regional gradients which can be calculated with this extension. In this study we develop the theoretical framework for calculation of the magnetic gradient tensor components from the harmonic series expansion and apply our approach to the IGRF and HDGM. The gradient tensor component maps for entire Earth's surface produced for the IGRF show low gradients reflecting the variation from the dipolar character, whereas maps for the HDGM (up to degree N=729) reveal new information about crustal structure, especially across the oceans, and deeply situated ore bodies. From the gradient tensor components, the rotational invariants, the Eigenvalues, and the normalized source strength (NSS) are calculated. The NSS focuses on shallower and stronger anomalies. Euler deconvolution using either the tensor components or the NSS applied to the HDGM reveals an estimate of the average source depth for the entire magnetic crust as well as individual plutons and ore bodies. The NSS reveals the boundaries between the anomalies of major continental provinces like southern Africa or the Eastern European Craton.

The instantaneous apparent resistivity tensor: a visualization scheme for LOTEM electric field measurements

NASA Astrophysics Data System (ADS)

Caldwell, T. Grant; Bibby, Hugh M.

1998-12-01

Long-offset transient electromagnetic (LOTEM) data have traditionally been represented as early- and late-time apparent resistivities. Time-varying electric field data recorded in a LOTEM survey made with multiple sources can be represented by an `instantaneous apparent resistivity tensor'. Three independent, coordinate-invariant, time-varying apparent resistivities can be derived from this tensor. For dipolar sources, the invariants are also independent of source orientation. In a uniform-resistivity half-space, the invariant given by the square root of the tensor determinant remains almost constant with time, deviating from the half-space resistivity by a maximum of 6 per cent. For a layered half-space, a distance-time pseudo-section of the determinant apparent resistivity produces an image of the layering beneath the measurement profile. As time increases, the instantaneous apparent resistivity tensor approaches the direct current apparent resistivity tensor. An approximate time-to-depth conversion can be achieved by integrating the diffusion depth formula with time, using the determinant apparent resistivity at each instant to represent the resistivity of the conductive medium. Localized near-surface inhomogeneities produce shifts in the time-domain apparent resistivity sounding curves that preserve the gradient, analogous to static shifts seen in magnetotelluric soundings. Instantaneous apparent resistivity tensors calculated for 3-D resistivity models suggest that profiles of LOTEM measurements across a simple 3-D structure can be used to create an image that reproduces the main features of the subsurface resistivity. Where measurements are distributed over an area, maps of the tensor invariants can be made into a sequence of images, which provides a way of `time slicing' down through the target structure.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peng, Cheng

Here, we consider the relation between SYK-like models and vector models by studying a toy model where a tensor field is coupled with a vector field. By integrating out the tensor field, the toy model reduces to the Gross-Neveu model in 1 dimension. On the other hand, a certain perturbation can be turned on and the toy model flows to an SYK-like model at low energy. Furthermore, a chaotic-nonchaotic phase transition occurs as the sign of the perturbation is altered. We further study similar models that possess chaos and enhanced reparameterization symmetries.

Vector models and generalized SYK models

DOE PAGES

Peng, Cheng

2017-05-23

Here, we consider the relation between SYK-like models and vector models by studying a toy model where a tensor field is coupled with a vector field. By integrating out the tensor field, the toy model reduces to the Gross-Neveu model in 1 dimension. On the other hand, a certain perturbation can be turned on and the toy model flows to an SYK-like model at low energy. Furthermore, a chaotic-nonchaotic phase transition occurs as the sign of the perturbation is altered. We further study similar models that possess chaos and enhanced reparameterization symmetries.

Fermionic vacuum polarization by an Abelian magnetic tube in the cosmic string spacetime

NASA Astrophysics Data System (ADS)

Maior de Sousa, M. S.; Ribeiro, R. F.; Bezerra de Mello, E. R.

2017-02-01

In this paper, we consider a charged massive fermionic quantum field in the idealized cosmic string spacetime and in the presence of a magnetic field confined in a cylindrical tube of finite radius. Three distinct configurations for the magnetic fields are taken into account: (i) a cylindrical shell of radius a , (ii) a magnetic field proportional to 1 /r , and (iii) a constant magnetic field. In these three cases, the axis of the infinitely long tube of radius a coincides with the cosmic string. Our main objectives in this paper are to analyze the fermionic condensate (FC) and the vacuum expectation value (VEV) of the fermionic energy-momentum tensor. In order to do that, we explicitly construct the complete set of normalized wave functions for each configuration of the magnetic field. We show that in the region outside the tube, the FC and the VEV of the energy-momentum tensor are decomposed into two parts: The first ones correspond to the zero-thickness magnetic flux contributions, and the second ones are induced by the nontrivial structure of the magnetic field, named core-induced contributions. The latter present specific forms depending on the magnetic field configuration considered. We also show that the VEV of the energy-momentum tensor is diagonal and obeys the conservation condition, and its trace is expressed in terms of the fermionic condensate. The zero-thickness contributions to the FC and VEV of the energy-momentum tensor depend only on the fractional part of the ration of the magnetic flux inside the tube by the quantum one. As to the core-induced contributions, they depend on the total magnetic flux inside the tube and, consequently, in general, are not a periodic function of the magnetic flux.

Contribution of the polarization moments of different rank to the integral CPT signal

NASA Astrophysics Data System (ADS)

Taskova, E.; Alipieva, E.; Todorov, G.

2016-01-01

In the present work we investigate the relation of the polarization moments having different ranks with the tensor components which form the observable integral CPT signal, in the presence of a stray magnetic field. A numerical experiment with parameters close to the real ones is performed, using a program based on the irreducible tensor operator formalism1. The integral fluorescent signal is calculated for the non-polarized fluorescence at different laser power excitation. Detailed analysis of the numerical solutions for all tensor components which describe population and alignment allows visualizing the dynamics of their behavior in dependence on the experimental geometry and laboratory magnetic field B'. The dependence of population f00, longitudinal f02 and transverse f22 alignment in the presence of transverse magnetic field is investigated. The shape and sign of the resonance change with laser power.

Averaging problem in general relativity, macroscopic gravity and using Einstein's equations in cosmology.

NASA Astrophysics Data System (ADS)

Zalaletdinov, R. M.

1998-04-01

The averaging problem in general relativity is briefly discussed. A new setting of the problem as that of macroscopic description of gravitation is proposed. A covariant space-time averaging procedure is described. The structure of the geometry of macroscopic space-time, which follows from averaging Cartan's structure equations, is described and the correlation tensors present in the theory are discussed. The macroscopic field equations (averaged Einstein's equations) derived in the framework of the approach are presented and their structure is analysed. The correspondence principle for macroscopic gravity is formulated and a definition of the stress-energy tensor for the macroscopic gravitational field is proposed. It is shown that the physical meaning of using Einstein's equations with a hydrodynamic stress-energy tensor in looking for cosmological models means neglecting all gravitational field correlations. The system of macroscopic gravity equations to be solved when the correlations are taken into consideration is given and described.

Derivation of the Schwartzchild Metric From the ``Self Censorship'' of the ZPF (Zero Point Energy) in the GEM Theory

NASA Astrophysics Data System (ADS)

Brandenburg, John

2012-10-01

The GEM theory (1) links the EM stress tensor directly to the metric tensor by the principle of ``self censorship'' of the ZPF (2) where the definition of guv = FuwF^wv/ 4 for Planck scale fields makes the stress tensor vanish even when fields are present. The first order form of the metric is recovered as Lorentzian due to alternating regions of strong electric and magnetic fields similar to that seen in models of spacetime in ``Loop Gravity,'' where the model admits perturbations. The GEM ExB drift models of gravity is used The first order perturbations on the fields are considered to be of the order of the fine structure constant alpha. Radiation fields due to a single charged particle of mass M fall off as 1/r and give the values (G=c=1) gtt = 1-2M/r and grr = (1-2M/r). (1) Brandenburg, J.E. (2012)., (2) STAIF II Conference Albuquerque NM 2.Brandenburg, J.E. (2007). IEEE Transactions On Plasma Science, Vol. 35, No. 4., p845.

Differentiating G-inflation from string gas cosmology using the effective field theory approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Minxi; Liu, Junyu; Lu, Shiyun

A characteristic signature of String Gas Cosmology is primordial power spectra for scalar and tensor modes which are almost scale-invariant but with a red tilt for scalar modes but a blue tilt for tensor modes. This feature, however, can also be realized in the so-called G-inflation model, in which Horndeski operators are introduced which leads to a blue tensor tilt by softly breaking the Null Energy Condition. In this article we search for potential observational differences between these two cosmologies by performing detailed perturbation analyses based on the Effective Field Theory approach. Our results show that, although both two modelsmore » produce blue tilted tensor perturbations, they behave differently in three aspects. Firstly, String Gas Cosmology predicts a specific consistency relation between the index of the scalar modes n {sub s} and that of tensor ones n {sub t} , which is hard to be reproduced by G-inflation. Secondly, String Gas Cosmology typically predicts non-Gaussianities which are highly suppressed on observable scales, while G-inflation gives rise to observationally large non-Gaussianities because the kinetic terms in the action become important during inflation. However, after finely tuning the model parameters of G-inflation it is possible to obtain a blue tensor spectrum and negligible non-Gaussianities with a degeneracy between the two models. This degeneracy can be broken by a third observable, namely the scale dependence of the nonlinearity parameter, which vanishes for G-inflation but has a blue tilt in the case of String Gas Cosmology. Therefore, we conclude that String Gas Cosmology is in principle observationally distinguishable from the single field inflationary cosmology, even allowing for modifications such as G-inflation.« less

Einstein gravity 3-point functions from conformal field theory

NASA Astrophysics Data System (ADS)

Afkhami-Jeddi, Nima; Hartman, Thomas; Kundu, Sandipan; Tajdini, Amirhossein

2017-12-01

We study stress tensor correlation functions in four-dimensional conformal field theories with large N and a sparse spectrum. Theories in this class are expected to have local holographic duals, so effective field theory in anti-de Sitter suggests that the stress tensor sector should exhibit universal, gravity-like behavior. At the linearized level, the hallmark of locality in the emergent geometry is that stress tensor three-point functions 〈 T T T 〉, normally specified by three constants, should approach a universal structure controlled by a single parameter as the gap to higher spin operators is increased. We demonstrate this phenomenon by a direct CFT calculation. Stress tensor exchange, by itself, violates causality and unitarity unless the three-point functions are carefully tuned, and the unique consistent choice exactly matches the prediction of Einstein gravity. Under some assumptions about the other potential contributions, we conclude that this structure is universal, and in particular, that the anomaly coefficients satisfy a ≈ c as conjectured by Camanho et al. The argument is based on causality of a four-point function, with kinematics designed to probe bulk locality, and invokes the chaos bound of Maldacena, Shenker, and Stanford.

Computational tools for Breakthrough Propulsion Physics: State of the art and future prospects

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2000-01-01

To address problems in Breakthrough Propulsion Physics (BPP) one needs sheer computing capabilities. This is because General Relativity and Quantum Field Theory are so mathematically sophisticated that the amount of analytical calculations is prohibitive and one can hardly do all of them by hand. In this paper we make a comparative review of the main tensor calculus capabilities of the three most advanced and commercially available ``symbolic manipulator'' codes: Macsyma, Maple V and Mathematica. We also point out that currently one faces such a variety of different conventions in tensor calculus that it is difficult or impossible to compare results obtained by different scholars in General Relativity and Quantum Field Theory. Mathematical physicists, experimental physicists and engineers have each their own way of customizing tensors, especially by using the different metric signatures, different metric determinant signs, different definitions of the basic Riemann and Ricci tensors, and by adopting different systems of physical units. This chaos greatly hampers progress toward the chief NASA BPP goal: the design of the NASA Warp Drive. It is thus concluded that NASA should put order by establishing international standards in symbolic tensor calculus and enforcing anyone working in BPP to adopt these NASA BPP Standards. .

Vacuum quantum stress tensor fluctuations: A diagonalization approach

NASA Astrophysics Data System (ADS)

Schiappacasse, Enrico D.; Fewster, Christopher J.; Ford, L. H.

2018-01-01

Large vacuum fluctuations of a quantum stress tensor can be described by the asymptotic behavior of its probability distribution. Here we focus on stress tensor operators which have been averaged with a sampling function in time. The Minkowski vacuum state is not an eigenstate of the time-averaged operator, but can be expanded in terms of its eigenstates. We calculate the probability distribution and the cumulative probability distribution for obtaining a given value in a measurement of the time-averaged operator taken in the vacuum state. In these calculations, we study a specific operator that contributes to the stress-energy tensor of a massless scalar field in Minkowski spacetime, namely, the normal ordered square of the time derivative of the field. We analyze the rate of decrease of the tail of the probability distribution for different temporal sampling functions, such as compactly supported functions and the Lorentzian function. We find that the tails decrease relatively slowly, as exponentials of fractional powers, in agreement with previous work using the moments of the distribution. Our results lend additional support to the conclusion that large vacuum stress tensor fluctuations are more probable than large thermal fluctuations, and may have observable effects.

Full Moment Tensor Analysis Using First Motion Data at The Geysers Geothermal Field

NASA Astrophysics Data System (ADS)

Boyd, O.; Dreger, D. S.; Lai, V. H.; Gritto, R.

2012-12-01

Seismicity associated with geothermal energy production at The Geysers Geothermal Field in northern California has been increasing during the last forty years. We investigate source models of over fifty earthquakes with magnitudes ranging from Mw 3.5 up to Mw 4.5. We invert three-component, complete waveform data from broadband stations of the Berkeley Digital Seismic Network, the Northern California Seismic Network and the USA Array deployment (2005-2007) for the complete, six-element moment tensor. Some solutions are double-couple while others have substantial non-double-couple components. To assess the stability and significance of non-double-couple components, we use a suite of diagnostic tools including the F-test, Jackknife test, bootstrap and network sensitivity solution (NSS). The full moment tensor solutions of the studied events tend to plot in the upper half of the Hudson source type diagram where the fundamental source types include +CLVD, +LVD, tensile-crack, DC and explosion. Using the F-test to compare the goodness-of-fit values between the full and deviatoric moment tensor solutions, most of the full moment tensor solutions do not show a statistically significant improvement in fit over the deviatoric solutions. Because a small isotropic component may not significantly improve the fit, we include first motion polarity data to better constrain the full moment tensor solutions.

Calcium-43 chemical shift tensors as probes of calcium binding environments. Insight into the structure of the vaterite CaCO3 polymorph by 43Ca solid-state NMR spectroscopy.

PubMed

Bryce, David L; Bultz, Elijah B; Aebi, Dominic

2008-07-23

Natural-abundance (43)Ca solid-state NMR spectroscopy at 21.1 T and gauge-including projector-augmented-wave (GIPAW) DFT calculations are developed as tools to provide insight into calcium binding environments, with special emphasis on the calcium chemical shift (CS) tensor. The first complete analysis of a (43)Ca solid-state NMR spectrum, including the relative orientation of the CS and electric field gradient (EFG) tensors, is reported for calcite. GIPAW calculations of the (43)Ca CS and EFG tensors for a series of small molecules are shown to reproduce experimental trends; for example, the trend in available solid-state chemical shifts is reproduced with a correlation coefficient of 0.983. The results strongly suggest the utility of the calcium CS tensor as a novel probe of calcium binding environments in a range of calcium-containing materials. For example, for three polymorphs of CaCO3 the CS tensor span ranges from 8 to 70 ppm and the symmetry around calcium is manifested differently in the CS tensor as compared with the EFG tensor. The advantages of characterizing the CS tensor are particularly evident in very high magnetic fields where the effect of calcium CS anisotropy is augmented in hertz while the effect of second-order quadrupolar broadening is often obscured for (43)Ca because of its small quadrupole moment. Finally, as an application of the combined experimental-theoretical approach, the solid-state structure of the vaterite polymorph of calcium carbonate is probed and we conclude that the hexagonal P6(3)/mmc space group provides a better representation of the structure than does the orthorhombic Pbnm space group, thereby demonstrating the utility of (43)Ca solid-state NMR as a complementary tool to X-ray crystallographic methods.

Energy Flux Positivity and Unitarity in Conformal Field Theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kulaxizi, Manuela; Parnachev, Andrei

2011-01-07

We show that in most conformal field theories the condition of the energy flux positivity, proposed by Hofman and Maldacena, is equivalent to the absence of ghosts. At finite temperature and large energy and momenta, the two-point functions of the stress energy tensor develop light like poles. The residues of the poles can be computed, as long as the only spin-two conserved current, which appears in the stress energy tensor operator-product expansion and acquires a nonvanishing expectation value at finite temperature, is the stress energy tensor. The condition for the residues to stay positive and the theory to remain ghost-freemore » is equivalent to the condition of positivity of energy flux.« less

Extended scalar-tensor theories of gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crisostomi, Marco; Koyama, Kazuya; Tasinato, Gianmassimo

2016-04-21

We study new consistent scalar-tensor theories of gravity recently introduced by Langlois and Noui with potentially interesting cosmological applications. We derive the conditions for the existence of a primary constraint that prevents the propagation of an additional dangerous mode associated with higher order equations of motion. We then classify the most general, consistent scalar-tensor theories that are at most quadratic in the second derivatives of the scalar field. In addition, we investigate the possible connection between these theories and (beyond) Horndeski through conformal and disformal transformations. Finally, we point out that these theories can be associated with new operators inmore » the effective field theory of dark energy, which might open up new possibilities to test dark energy models in future surveys.« less

The Multi-Orientable Random Tensor Model, a Review

NASA Astrophysics Data System (ADS)

Tanasa, Adrian

2016-06-01

After its introduction (initially within a group field theory framework) in [Tanasa A., J. Phys. A: Math. Theor. 45 (2012), 165401, 19 pages, arXiv:1109.0694], the multi-orientable (MO) tensor model grew over the last years into a solid alternative of the celebrated colored (and colored-like) random tensor model. In this paper we review the most important results of the study of this MO model: the implementation of the 1/N expansion and of the large N limit (N being the size of the tensor), the combinatorial analysis of the various terms of this expansion and finally, the recent implementation of a double scaling limit.

A space-time tensor formulation for continuum mechanics in general curvilinear, moving, and deforming coordinate systems

NASA Technical Reports Server (NTRS)

Avis, L. M.

1976-01-01

Tensor methods are used to express the continuum equations of motion in general curvilinear, moving, and deforming coordinate systems. The space-time tensor formulation is applicable to situations in which, for example, the boundaries move and deform. Placing a coordinate surface on such a boundary simplifies the boundary condition treatment. The space-time tensor formulation is also applicable to coordinate systems with coordinate surfaces defined as surfaces of constant pressure, density, temperature, or any other scalar continuum field function. The vanishing of the function gradient components along the coordinate surfaces may simplify the set of governing equations. In numerical integration of the equations of motion, the freedom of motion of the coordinate surfaces provides a potential for enhanced resolution of the continuum field function. An example problem of an incompressible, inviscid fluid with a top free surface is considered, where the surfaces of constant pressure (including the top free surface) are coordinate surfaces.

An ab initio MO study of heavy atom effects on the zero-field splitting tensors of high-spin nitrenes: how the spin-orbit contributions are affected.

PubMed

Sugisaki, Kenji; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Kitagawa, Masahiro; Takui, Takeji

2014-05-21

The CASSCF and the hybrid CASSCF-MRMP2 methods are applied to the calculations of spin-spin and spin-orbit contributions to the zero-field splitting tensors (D tensors) of the halogen-substituted spin-septet 2,4,6-trinitrenopyridines, focusing on the heavy atom effects on the spin-orbit term of the D tensors (D(SO) tensors). The calculations reproduced experimentally determined |D| values within an error of 15%. Halogen substitutions at the 3,5-positions are less influential in the spin-spin dipolar (D(SS)) term of 2,4,6-trinitrenopyridines, although the D(SO) terms are strongly affected by the introduction of heavier halogens. The absolute sign of the D(SO) value (D = D(ZZ) - (D(XX) + D(YY))/2) of 3,5-dibromo derivative 3 is predicted to be negative, which contradicts the Pederson-Khanna (PK) DFT result previously reported. The large negative contributions to the D(SO) value of 3 arise from the excited spin-septet states ascribed mainly to the excitations of in-plane lone pair of bromine atoms → SOMO of π nature. The importance of the excited states involving electron transitions from the lone pair orbital of the halogen atom is also confirmed in the D(SO) tensors of halogen-substituted para-phenylnitrenes. A new scheme based on the orbital region partitioning is proposed for the analysis of the D(SO) tensors as calculated by means of the PK-DFT approach.

Further investigations of the aeroelastic behavior of the AFW wind-tunnel model using transonic small disturbance theory

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Bennett, Robert M.

1992-01-01

The Computational Aeroelasticity Program-Transonic Small Disturbance (CAP-TSD) code, developed at LaRC, is applied to the active flexible wing wind-tunnel model for prediction of transonic aeroelastic behavior. A semi-span computational model is used for evaluation of symmetric motions, and a full-span model is used for evaluation of antisymmetric motions, and a full-span model is used for evaluation of antisymmetric motions. Static aeroelastic solutions using CAP-TSD are computed. Dynamic deformations are presented as flutter boundaries in terms of Mach number and dynamic pressure. Flutter boundaries that take into account modal refinements, vorticity and entropy corrections, antisymmetric motion, and sensitivity to the modeling of the wing tip ballast stores are also presented with experimental flutter results.

Wigner functions for nonparaxial, arbitrarily polarized electromagnetic wave fields in free space.

PubMed

Alonso, Miguel A

2004-11-01

New representations are defined for describing electromagnetic wave fields in free space exactly in terms of rays for any wavelength, level of coherence or polarization, and numerical aperture, as long as there are no evanescent components. These representations correspond to tensors assigned to each ray such that the electric and magnetic energy densities, the Poynting vector, and the polarization properties of the field correspond to simple integrals involving these tensors for the rays that go through the specified point. For partially coherent fields, the ray-based approach provided by the new representations can reduce dramatically the computation times for the physical properties mentioned earlier.

Spinorial characterizations of surfaces into three-dimensional homogeneous manifolds

NASA Astrophysics Data System (ADS)

Roth, Julien

2010-06-01

We give spinorial characterizations of isometrically immersed surfaces into three-dimensional homogeneous manifolds with four-dimensional isometry group in terms of the existence of a particular spinor field. This generalizes works by Friedrich for R3 and Morel for S3 and H3. The main argument is the interpretation of the energy-momentum tensor of such a spinor field as the second fundamental form up to a tensor depending on the structure of the ambient space.

On the local field method with the account of spatial dispersion. Application to the optical activity theory

NASA Astrophysics Data System (ADS)

Tyu, N. S.; Ekhilevsky, S. G.

1992-07-01

For the perfect molecular crystals the equations of the local field method (LFM) with the account of spatial dispersion are formulated. They are used to derive the expression for the crystal polarizability tensor. For the first time within the framework of this method the formula for the gyrotropy tensor of an arbitrary optically active molecular crystal is obtained. This formula is analog of well known relationships of Lorentz-Lorenz.

On the initial conditions of scalar and tensor fluctuations in f(R,φ ) gravity

NASA Astrophysics Data System (ADS)

Cheraghchi, S.; Shojai, F.

2018-05-01

We have considered the perturbation equations governing the growth of fluctuations during inflation in generalized scalar tensor theory f(R,φ ). We have found that the scalar metric perturbations at very early times are negligible compared to the scalar field perturbation, just like general relativity. At sufficiently early times, when the physical momentum of perturbation mode, q / a is much larger than the Hubble parameter H, i.e. q/a≫ H, we have obtained the metric and scalar field perturbation in the form of WKB solutions up to an undetermined coefficient. Then we have quantized the scalar fluctuations and expanded the metric and the scalar field perturbations with the help of annihilation and creation operators of the scalar field perturbation. The standard commutation relations of annihilation and creation operators fix the unknown coefficient. Going over to the gauge invariant quantities which are conserved beyond the horizon, we have obtained the initial condition of the generalized Mukhanov-Sasaki equation. Then a similar procedure is performed for the case of tensor metric perturbation. As an example of the generalized Mukhanov-Sasaki equation and its initial condition, we have proposed a power-law functional form as f(R,φ )=f_0 R^m φ ^n and obtained an exact inflationary solution. In this background, then we have discussed how the scalar and tensor fluctuations grow.

Electron spin resonance modes in a strong-leg ladder in the Tomonaga-Luttinger liquid phase

NASA Astrophysics Data System (ADS)

Ozerov, M.; Maksymenko, M.; Wosnitza, J.; Honecker, A.; Landee, C. P.; Turnbull, M. M.; Furuya, S. C.; Giamarchi, T.; Zvyagin, S. A.

2015-12-01

Magnetic excitations in the strong-leg quantum spin ladder compound (C7H10N) 2CuBr4 (known as DIMPY) in the field-induced Tomonaga-Luttinger spin-liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual nonlinear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact-diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a fingerprint of the spin dynamics in a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder and owe their ESR observability to the uniform Dzyaloshinskii-Moriya interaction.

Ab initio and DFT studies of the spin-orbit and spin-spin contributions to the zero-field splitting tensors of triplet nitrenes with aryl scaffolds.

PubMed

Sugisaki, Kenji; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Kitagawa, Masahiro; Takui, Takeji

2011-04-21

Spin-orbit and spin-spin contributions to the zero-field splitting (ZFS) tensors (D tensors) of spin-triplet phenyl-, naphthyl-, and anthryl-nitrenes in their ground state are investigated by quantum chemical calculations, focusing on the effects of the ring size and substituted position of nitrene on the D tensor. A hybrid CASSCF/MRMP2 approach to the spin-orbit term of the D tensor (D(SO) tensor), which was recently proposed by us, has shown that the spin-orbit contribution to the entire D value, termed the ZFS parameter or fine-structure constant, is about 10% in all the arylnitrenes under study and less depends on the size and connectivity of the aryl groups. Order of the absolute values for D(SO) can be explained by the perturbation on the energy level and spatial distributions of π-SOMO through the orbital interaction between SOMO of the nitrene moiety and frontier orbitals of the aryl scaffolds. Spin-spin contribution to the D tensor (D(SS) tensor) has been calculated in terms of the McWeeny-Mizuno equation with the DFT/EPR-II spin densities. The D(SS) value calculated with the RO-B3LYP spin density agrees well with the D(Exptl) -D(SO) reference value in phenylnitrene, but agreement with the reference value gradually becomes worse as the D value decreases. Exchange-correlation functional dependence on the D(SS) tensor has been explored with standard 23 exchange-correlation functionals in both RO- and U-DFT methodologies, and the RO-HCTH/407 method gives the best agreement with the D(Exptl) -D(SO) reference value. Significant exchange-correlation functional dependence is observed in spin-delocalized systems such as 9-anthrylnitrene (6). By employing the hybrid CASSCF/MRMP2 approach and the McWeeny-Mizuno equation combined with the RO-HCTH/407/EPR-II//U-HCTH/407/6-31G* spin densities for D(SO) and D(SS), respectively, a quantitative agreement with the experiment is achieved with errors less than 10% in all the arylnitrenes under study. Guidelines to the putative approaches to D(SS) tensor calculations are given.

Evidence for Nuclear Tensor Polarization of Deuterium Molecules in Storage Cells

DOE Office of Scientific and Technical Information (OSTI.GOV)

van den Brand, J.; Bulten, H.; Zhou, Z.

1997-02-01

Deuterium molecules were obtained by recombination, on a copper surface, of deuterium atoms prepared in specific hyperfine states. The molecules were stored for about 5ms in an open-ended cylindrical cell, placed in a 23mT magnetic field, and their tensor polarization was measured by elastic scattering of 704MeV electrons. The results of the measurements are consistent with the deuterium molecules retaining the tensor polarization of the initial atoms. {copyright} {ital 1997} {ital The American Physical Society}

Tensor modes in pure natural inflation

NASA Astrophysics Data System (ADS)

Nomura, Yasunori; Yamazaki, Masahito

2018-05-01

We study tensor modes in pure natural inflation [1], a recently-proposed inflationary model in which an axionic inflaton couples to pure Yang-Mills gauge fields. We find that the tensor-to-scalar ratio r is naturally bounded from below. This bound originates from the finiteness of the number of metastable branches of vacua in pure Yang-Mills theories. Details of the model can be probed by future cosmic microwave background experiments and improved lattice gauge theory calculations of the θ-angle dependence of the vacuum energy.

Study the sensitivity of molecular functional groups to bioethanol processing in lipid biopolymer of co-products using DRIFT molecular spectroscopy

NASA Astrophysics Data System (ADS)

Yu, Peiqiang

2011-11-01

To date, there is no study on bioethanol processing-induced changes in molecular structural profiles mainly related to lipid biopolymer. The objectives of this study were to: (1) determine molecular structural changes of lipid related functional groups in the co-products that occurred during bioethanol processing; (2) relatively quantify the antisymmetric CH 3 and CH 2 (ca. 2959 and 2928 cm -1, respectively), symmetric CH 3 and CH 2 (ca. 2871 and 2954 cm -1, respectively) functional groups, carbonyl C dbnd O ester (ca. 1745 cm -1) and unsaturated groups (CH attached to C dbnd C) (ca. 3007 cm -1) spectral intensities as well as their ratios of antisymmetric CH 3 to antisymmetric CH 2, and (3) illustrate the molecular spectral analyses as a research tool to detect for the sensitivity of individual moleculars to the bioethanol processing in a complex plant-based feed and food system without spectral parameterization. The hypothesis of this study was that bioethanol processing changed the molecular structure profiles in the co-products as opposed to original cereal grains. These changes could be detected by infrared molecular spectroscopy and will be related to nutrient utilization. The results showed that bioethanol processing had effects on the functional groups spectral profiles in the co-products. It was found that the CH 3-antisymmetric to CH 2-antisymmetric stretching intensity ratio was changed. The spectral features of carbonyl C dbnd O ester group and unsaturated group were also different. Since the different types of cereal grains (wheat vs. corn) had different sensitivity to the bioethanol processing, the spectral patterns and band component profiles differed between their co-products (wheat DDGS vs. corn DDGS). The multivariate molecular spectral analyses, cluster analysis and principal component analysis of original spectra (without spectral parameterization), distinguished the structural differences between the wheat and wheat DDGS and between the corn and corn DDGS in the antisymmetric and symmetric CH 3 and CH 2 spectral region (ca. 2994-2800 cm -1) and unsaturated group band region (3025-2996 cm -1). Further study is needed to quantify molecular structural changes in relation to nutrient utilization of lipid biopolymer.

A closed-form solution to tensor voting: theory and applications.

PubMed

Wu, Tai-Pang; Yeung, Sai-Kit; Jia, Jiaya; Tang, Chi-Keung; Medioni, Gérard

2012-08-01

We prove a closed-form solution to tensor voting (CFTV): Given a point set in any dimensions, our closed-form solution provides an exact, continuous, and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence in structure propagation. We then embed structure-aware tensor into expectation maximization (EM) for optimizing a single linear structure to achieve efficient and robust parameter estimation. Specifically, our EMTV algorithm optimizes both the tensor and fitting parameters and does not require random sampling consensus typically used in existing robust statistical techniques. We performed quantitative evaluation on its accuracy and robustness, showing that EMTV performs better than the original TV and other state-of-the-art techniques in fundamental matrix estimation for multiview stereo matching. The extensions of CFTV and EMTV for extracting multiple and nonlinear structures are underway.

Dark energy simulacrum in nonlinear electrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Labun, Lance; Rafelski, Johann

2010-03-15

Quasiconstant external fields in nonlinear electromagnetism generate a global contribution proportional to g{sup {mu}{nu}}in the energy-momentum tensor, thus a simulacrum of dark energy. To provide a thorough understanding of the origin and strength of its effects, we undertake a complete theoretical and numerical study of the energy-momentum tensor T{sup {mu}{nu}}for nonlinear electromagnetism. The Euler-Heisenberg nonlinearity due to quantum fluctuations of spinor and scalar matter fields is considered and contrasted with the properties of classical nonlinear Born-Infeld electromagnetism. We address modifications of charged particle kinematics by strong background fields.

Eshelby's problem of non-elliptical inclusions

NASA Astrophysics Data System (ADS)

Zou, Wennan; He, Qichang; Huang, Mojia; Zheng, Quanshui

2010-03-01

The Eshelby problem consists in determining the strain field of an infinite linearly elastic homogeneous medium due to a uniform eigenstrain prescribed over a subdomain, called inclusion, of the medium. The salient feature of Eshelby's solution for an ellipsoidal inclusion is that the strain tensor field inside the latter is uniform. This uniformity has the important consequence that the solution to the fundamental problem of determination of the strain field in an infinite linearly elastic homogeneous medium containing an embedded ellipsoidal inhomogeneity and subjected to remote uniform loading can be readily deduced from Eshelby's solution for an ellipsoidal inclusion upon imposing appropriate uniform eigenstrains. Based on this result, most of the existing micromechanics schemes dedicated to estimating the effective properties of inhomogeneous materials have been nevertheless applied to a number of materials of practical interest where inhomogeneities are in reality non-ellipsoidal. Aiming to examine the validity of the ellipsoidal approximation of inhomogeneities underlying various micromechanics schemes, we first derive a new boundary integral expression for calculating Eshelby's tensor field (ETF) in the context of two-dimensional isotropic elasticity. The simple and compact structure of the new boundary integral expression leads us to obtain the explicit expressions of ETF and its average for a wide variety of non-elliptical inclusions including arbitrary polygonal ones and those characterized by the finite Laurent series. In light of these new analytical results, we show that: (i) the elliptical approximation to the average of ETF is valid for a convex non-elliptical inclusion but becomes inacceptable for a non-convex non-elliptical inclusion; (ii) in general, the Eshelby tensor field inside a non-elliptical inclusion is quite non-uniform and cannot be replaced by its average; (iii) the substitution of the generalized Eshelby tensor involved in various micromechanics schemes by the average Eshelby tensor for non-elliptical inhomogeneities is in general inadmissible.

Radiative corrections from heavy fast-roll fields during inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jain, Rajeev Kumar; Sandora, McCullen; Sloth, Martin S., E-mail: jain@cp3.dias.sdu.dk, E-mail: sandora@cp3.dias.sdu.dk, E-mail: sloth@cp3.dias.sdu.dk

2015-06-01

We investigate radiative corrections to the inflaton potential from heavy fields undergoing a fast-roll phase transition. We find that a logarithmic one-loop correction to the inflaton potential involving this field can induce a temporary running of the spectral index. The induced running can be a short burst of strong running, which may be related to the observed anomalies on large scales in the cosmic microwave spectrum, or extend over many e-folds, sustaining an effectively constant running to be searched for in the future. We implement this in a general class of models, where effects are mediated through a heavy messengermore » field sitting in its minimum. Interestingly, within the present framework it is a generic outcome that a large running implies a small field model with a vanishing tensor-to-scalar ratio, circumventing the normal expectation that small field models typically lead to an unobservably small running of the spectral index. An observable level of tensor modes can also be accommodated, but, surprisingly, this requires running to be induced by a curvaton. If upcoming observations are consistent with a small tensor-to-scalar ratio as predicted by small field models of inflation, then the present study serves as an explicit example contrary to the general expectation that the running will be unobservable.« less

Radiative corrections from heavy fast-roll fields during inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jain, Rajeev Kumar; Sandora, McCullen; Sloth, Martin S.

2015-06-09

We investigate radiative corrections to the inflaton potential from heavy fields undergoing a fast-roll phase transition. We find that a logarithmic one-loop correction to the inflaton potential involving this field can induce a temporary running of the spectral index. The induced running can be a short burst of strong running, which may be related to the observed anomalies on large scales in the cosmic microwave spectrum, or extend over many e-folds, sustaining an effectively constant running to be searched for in the future. We implement this in a general class of models, where effects are mediated through a heavy messengermore » field sitting in its minimum. Interestingly, within the present framework it is a generic outcome that a large running implies a small field model with a vanishing tensor-to-scalar ratio, circumventing the normal expectation that small field models typically lead to an unobservably small running of the spectral index. An observable level of tensor modes can also be accommodated, but, surprisingly, this requires running to be induced by a curvaton. If upcoming observations are consistent with a small tensor-to-scalar ratio as predicted by small field models of inflation, then the present study serves as an explicit example contrary to the general expectation that the running will be unobservable.« less

Flux-transport Dynamos Driven by a Tachocline α -effect; a Solution to Magnetic Parity Selection in the Sun

NASA Astrophysics Data System (ADS)

Dikpati, M.; Gilman, P. A.

2001-05-01

We propose here an α Ω flux-transport dynamo driven by a tachocline α -effect, produced by the global hydrodynamic instability of tachocline differential rotation as calculated using a shallow-water model (Dikpati & Gilman, 2001, ApJ, Mar.20 issue). Growing, unstable shallow-water modes propagating longitudinally in the tachocline create alternate vortices which correlate with upward/downward radial motion of top boundary, associated with convergence/divergence of the disturbance flow to produce a longitude-averaged net kinetic helicity, and hence an α -effect. We show that a flux-transport dynamo driven by a tachocline α -effect is equally successful as a Babcock-Leighton flux-transport dynamo (Dikpati & Charbonneau 1999, ApJ, 518, 508) in reproducing many large-scale solar cycle features, including the most difficult feature of phase relationship between the subsurface toroidal field and surface radial field. In view of the success of flux-transport dynamos, whether the α -effect is at the surface or in the tachocline, we argue that the solar dynamo should be considered to involve three basic processes, rather than two (α -effect and Ω -effect only). The third important process is the advective transport of flux by meridional circulation. In reality, both α -effects (Babcock-Leighton type and tachocline α -effect) are likely to exist, but it is hard to estimate their relative magnitudes. We show, by extending the simulation in a full spherical shell model that a flux-transport dynamo driven by a tachocline α -effect selects toroidal field that is antisymmetric about the equator, while a Babcock-Leighton flux-transport dynamo selects symmetric toroidal field. Since our present Sun selects antisymmetric toroidal fields, we argue that the flux-transport solar dynamo is primarily driven by a tachocline α -effect. Acknowledgements: This work is supported by NASA grants W-19752 and S-10145-X. National Center for Atmospheric Research is sponsored by National Science Foundation.

The "Fermi hole" and the correlation introduced by the symmetrization or the anti-symmetrization of the wave function.

PubMed

Giner, Emmanuel; Tenti, Lorenzo; Angeli, Celestino; Malrieu, Jean-Paul

2016-09-28

The impact of the antisymmetrization is often addressed as a local property of the many-electron wave function, namely that the wave function should vanish when two electrons with parallel spins are in the same position in space. In this paper, we emphasize that this presentation is unduly restrictive: we illustrate the strong non-local character of the antisymmetrization principle, together with the fact that it is a matter of spin symmetry rather than spin parallelism. To this aim, we focus our attention on the simplest representation of various states of two-electron systems, both in atomic (helium atom) and molecular (H 2 and the π system of the ethylene molecule) cases. We discuss the non-local property of the nodal structure of some two-electron wave functions, both using analytical derivations and graphical representations of cuttings of the nodal hypersurfaces. The attention is then focussed on the impact of the antisymmetrization on the maxima of the two-body density, and we show that it introduces strong correlation effects (radial and/or angular) with a non-local character. These correlation effects are analyzed in terms of inflation and depletion zones, which are easily identifiable, thanks to the nodes of the orbitals composing the wave function. Also, we show that the correlation effects induced by the antisymmetrization occur also for anti-parallel spins since all M s components of a given spin state have the same N-body densities. Finally, we illustrate that these correlation effects occur also for the singlet states, but they have strictly opposite impacts: the inflation zones in the triplet become depletion zones in the singlet and vice versa.

Multipole analysis in the radiation field for linearized f (R ) gravity with irreducible Cartesian tensors

NASA Astrophysics Data System (ADS)

Wu, Bofeng; Huang, Chao-Guang

2018-04-01

The 1 /r expansion in the distance to the source is applied to the linearized f (R ) gravity, and its multipole expansion in the radiation field with irreducible Cartesian tensors is presented. Then, the energy, momentum, and angular momentum in the gravitational waves are provided for linearized f (R ) gravity. All of these results have two parts, which are associated with the tensor part and the scalar part in the multipole expansion of linearized f (R ) gravity, respectively. The former is the same as that in General Relativity, and the latter, as the correction to the result in General Relativity, is caused by the massive scalar degree of freedom and plays an important role in distinguishing General Relativity and f (R ) gravity.

Active tensor magnetic gradiometer system final report for Project MM–1514

USGS Publications Warehouse

Smith, David V.; Phillips, Jeffrey D.; Hutton, S. Raymond

2014-01-01

An interactive computer simulation program, based on physical models of system sensors, platform geometry, Earth environment, and spheroidal magnetically-permeable targets, was developed to generate synthetic magnetic field data from a conceptual tensor magnetic gradiometer system equipped with an active primary field generator. The system sensors emulate the prototype tensor magnetic gradiometer system (TMGS) developed under a separate contract for unexploded ordnance (UXO) detection and classification. Time-series data from different simulation scenarios were analyzed to recover physical dimensions of the target source. Helbig-Euler simulations were run with rectangular and rod-like source bodies to determine whether such a system could separate the induced component of the magnetization from the remanent component for each target. This report concludes with an engineering assessment of a practical system design.

Chameleons with field-dependent couplings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brax, Philippe; Bruck, Carsten van de; Mota, David F.

2010-10-15

Certain scalar-tensor theories exhibit the so-called chameleon mechanism, whereby observational signatures of scalar fields are hidden by a combination of self-interactions and interactions with ambient matter. Not all scalar-tensor theories exhibit such a chameleon mechanism, which has been originally found in models with inverse power runaway potentials and field-independent couplings to matter. In this paper we investigate field theories with field-dependent couplings and a power-law potential for the scalar field. We show that the theory indeed is a chameleon field theory. We find the thin-shell solution for a spherical body and investigate the consequences for Eoet-Wash experiments, fifth-force searches andmore » Casimir-force experiments. Requiring that the scalar field evades gravitational tests, we find that the coupling is sensitive to a mass scale which is of order of the Hubble scale today.« less

Landau damping of the dust-acoustic surface waves in a Lorentzian dusty plasma slab

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Myoung-Jae; Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr; Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590

2016-01-15

Landau damping of a dust-acoustic surface wave propagating at the interfaces of generalized Lorentzian dusty plasma slab bounded by a vacuum is kinetically derived as the surface wave displays the symmetric and the anti-symmetric mode in a plasma slab. In the limiting case of small scaled wave number, we have found that Landau damping is enhanced as the slab thickness is increased. In particular, the damping of anti-symmetric mode is much stronger for a Lorentzian plasma than for a Maxwellian plasma. We have also found that the damping is more affected by superthermal particles in a Lorentzian plasma than bymore » a Maxwellian plasma for both of the symmetric and the anti-symmetric cases. The variations of Landau damping with various parameters are also discussed.« less

Weakly Interacting Symmetric and Anti-Symmetric States in the Bilayer Systems

NASA Astrophysics Data System (ADS)

Marchewka, M.; Sheregii, E. M.; Tralle, I.; Tomaka, G.; Ploch, D.

We have studied the parallel magneto-transport in DQW-structures of two different potential shapes: quasi-rectangular and quasi-triangular. The quantum beats effect was observed in Shubnikov-de Haas (SdH) oscillations for both types of the DQW structures in perpendicular magnetic filed arrangement. We developed a special scheme for the Landau levels energies calculation by means of which we carried out the necessary simulations of beating effect. In order to obtain the agreement between our experimental data and the results of simulations, we introduced two different quasi-Fermi levels which characterize symmetric and anti-symmetric states in DQWs. The existence of two different quasi Fermi-Levels simply means, that one can treat two sub-systems (charge carriers characterized by symmetric and anti-symmetric wave functions) as weakly interacting and having their own rate of establishing the equilibrium state.

On the `simple' form of the gravitational action and the self-interacting graviton

NASA Astrophysics Data System (ADS)

Tomboulis, E. T.

2017-09-01

The so-called ΓΓ-form of the gravitational Lagrangian, long known to provide its most compact expression as well as the most efficient generation of the graviton vertices, is taken as the starting point for discussing General Relativity as a theory of the self-interacting graviton. A straightforward but general method of converting to a covariant formulation by the introduction of a reference metric is given. It is used to recast the Einstein field equation as the equation of motion of a spin-2 particle interacting with the canonical energy-momentum tensor symmetrized by the standard Belinfante method applicable to any field carrying nonzero spin. This represents the graviton field equation in a form complying with the precepts of standard field theory. It is then shown how representations based on other, at face value completely unrelated definitions of energy-momentum (pseudo)tensors are all related by the addition of appropriate superpotential terms. Specifically, the superpotentials are explicitly constructed which connect to: i) the common definition consisting simply of the nonlinear part of the Einstein tensor; ii) the Landau-Lifshitz definition.

On synthetic gravitational waves from multi-field inflation

NASA Astrophysics Data System (ADS)

Ozsoy, Ogan

2018-04-01

We revisit the possibility of producing observable tensor modes through a continuous particle production process during inflation. Particularly, we focus on the multi-field realization of inflation where a spectator pseudoscalar σ induces a significant amplification of the U(1) gauge fields through the coupling propto σFμνtilde Fμν. In this model, both the scalar σ and the Abelian gauge fields are gravitationally coupled to the inflaton sector, therefore they can only affect the primordial scalar and tensor fluctuations through their mixing with gravitational fluctuations. Recent studies on this scenario show that the sourced contributions to the scalar correlators can be dangerously large to invalidate a large tensor power spectrum through the particle production mechanism. In this paper, we re-examine these recent claims by explicitly calculating the dominant contribution to the scalar power and bispectrum. Particularly, we show that once the current limits from CMB data are taken into account, it is still possible to generate a signal as large as r ≈ 10‑3 and the limitations on the model building are more relaxed than what was considered before.

Ising versus XY anisotropy in frustrated R(2)Ti(2)O(7) compounds as "Seen" by Polarized Neutrons.

PubMed

Cao, H; Gukasov, A; Mirebeau, I; Bonville, P; Decorse, C; Dhalenne, G

2009-07-31

We studied the field induced magnetic order in R(2)Ti(2)O(7) pyrochlore compounds with either uniaxial (R=Ho, Tb) or planar (R=Er, Yb) anisotropy, by polarized neutron diffraction. The determination of the local susceptibility tensor {chi(parallel to),chi(perpendicular)} provides a universal description of the field induced structures in the paramagnetic phase (2-270 K), whatever the field value (1-7 T) and direction. Comparison of the thermal variations of chi(parallel to) and chi(perpendicular) with calculations using the rare earth crystal field shows that exchange and dipolar interactions must be taken into account. We determine the molecular field tensor in each case and show that it can be strongly anisotropic.

Concepts and procedures required for successful reduction of tensor magnetic gradiometer data obtained from an unexploded ordnance detection demonstration at Yuma Proving Grounds, Arizona

USGS Publications Warehouse

Bracken, Robert E.; Brown, Philip J.

2006-01-01

On March 12, 2003, data were gathered at Yuma Proving Grounds, in Arizona, using a Tensor Magnetic Gradiometer System (TMGS). This report shows how these data were processed and explains concepts required for successful TMGS data reduction. Important concepts discussed include extreme attitudinal sensitivity of vector measurements, low attitudinal sensitivity of gradient measurements, leakage of the common-mode field into gradient measurements, consequences of thermal drift, and effects of field curvature. Spatial-data collection procedures and a spin-calibration method are addressed. Discussions of data-reduction procedures include tracking of axial data by mathematically matching transfer functions among the axes, derivation and application of calibration coefficients, calculation of sensor-pair gradients, thermal-drift corrections, and gradient collocation. For presentation, the magnetic tensor at each data station is converted to a scalar quantity, the I2 tensor invariant, which is easily found by calculating the determinant of the tensor. At important processing junctures, the determinants for all stations in the mapped area are shown in shaded relief map-view. Final processed results are compared to a mathematical model to show the validity of the assumptions made during processing and the reasonableness of the ultimate answer obtained.

Viable tensor-to-scalar ratio in a symmetric matter bounce

NASA Astrophysics Data System (ADS)

Nath Raveendran, Rathul; Chowdhury, Debika; Sriramkumar, L.

2018-01-01

Matter bounces refer to scenarios wherein the universe contracts at early times as in a matter dominated epoch until the scale factor reaches a minimum, after which it starts expanding. While such scenarios are known to lead to scale invariant spectra of primordial perturbations after the bounce, the challenge has been to construct completely symmetric bounces that lead to a tensor-to-scalar ratio which is small enough to be consistent with the recent cosmological data. In this work, we construct a model involving two scalar fields (a canonical field and a non-canonical ghost field) to drive the symmetric matter bounce and study the evolution of the scalar perturbations in the model. We find that the model can be completely described in terms of a single parameter, viz. the ratio of the scale associated with the bounce to the value of the scale factor at the bounce. We evolve the scalar perturbations numerically across the bounce and evaluate the scalar power spectra after the bounce. We show that, while the scalar and tensor perturbation spectra are scale invariant over scales of cosmological interest, the tensor-to-scalar ratio proves to be much smaller than the current upper bound from the observations of the cosmic microwave background anisotropies by the Planck mission. We also support our numerical analysis with analytical arguments.

Tensor-based tracking of the aorta in phase-contrast MR images

NASA Astrophysics Data System (ADS)

Azad, Yoo-Jin; Malsam, Anton; Ley, Sebastian; Rengier, Fabian; Dillmann, Rüdiger; Unterhinninghofen, Roland

2014-03-01

The velocity-encoded magnetic resonance imaging (PC-MRI) is a valuable technique to measure the blood flow velocity in terms of time-resolved 3D vector fields. For diagnosis, presurgical planning and therapy control monitoring the patient's hemodynamic situation is crucial. Hence, an accurate and robust segmentation of the diseased vessel is the basis for further methods like the computation of the blood pressure. In the literature, there exist some approaches to transfer the methods of processing DT-MR images to PC-MR data, but the potential of this approach is not fully exploited yet. In this paper, we present a method to extract the centerline of the aorta in PC-MR images by applying methods from the DT-MRI. On account of this, in the first step the velocity vector fields are converted into tensor fields. In the next step tensor-based features are derived and by applying a modified tensorline algorithm the tracking of the vessel course is accomplished. The method only uses features derived from the tensor imaging without the use of additional morphology information. For evaluation purposes we applied our method to 4 volunteer as well as 26 clinical patient datasets with good results. In 29 of 30 cases our algorithm accomplished to extract the vessel centerline.

Einstein-Cartan Gravity with Torsion Field Serving as an Origin for the Cosmological Constant or Dark Energy Density

NASA Astrophysics Data System (ADS)

Ivanov, A. N.; Wellenzohn, M.

2016-09-01

We analyse the Einstein-Cartan gravity in its standard form { R }=R+{{ K }}2, where { R } {and} R are the Ricci scalar curvatures in the Einstein-Cartan and Einstein gravity, respectively, and {{ K }}2 is the quadratic contribution of torsion in terms of the contorsion tensor { K }. We treat torsion as an external (or background) field and show that its contribution to the Einstein equations can be interpreted in terms of the torsion energy-momentum tensor, local conservation of which in a curved spacetime with an arbitrary metric or an arbitrary gravitational field demands a proportionality of the torsion energy-momentum tensor to a metric tensor, a covariant derivative of which vanishes owing to the metricity condition. This allows us to claim that torsion can serve as an origin for the vacuum energy density, given by the cosmological constant or dark energy density in the universe. This is a model-independent result that may explain the small value of the cosmological constant, which is a long-standing problem in cosmology. We show that the obtained result is valid also in the Poincaré gauge gravitational theory of Kibble, where the Einstein-Hilbert action can be represented in the same form: { R }=R+{{ K }}2.

Second rank direction cosine spherical tensor operators and the nuclear electric quadrupole hyperfine structure Hamiltonian of rotating molecules

NASA Astrophysics Data System (ADS)

di Lauro, C.

2018-03-01

Transformations of vector or tensor properties from a space-fixed to a molecule-fixed axis system are often required in the study of rotating molecules. Spherical components λμ,ν of a first rank irreducible tensor can be obtained from the direction cosines between the two axis systems, and a second rank tensor with spherical components λμ,ν(2) can be built from the direct product λ × λ. It is shown that the treatment of the interaction between molecular rotation and the electric quadrupole of a nucleus is greatly simplified, if the coefficients in the axis-system transformation of the gradient of the electric field of the outer charges at the coupled nucleus are arranged as spherical components λμ,ν(2). Then the reduced matrix elements of the field gradient operators in a symmetric top eigenfunction basis, including their dependence on the molecule-fixed z-angular momentum component k, can be determined from the knowledge of those of λ(2) . The hyperfine structure Hamiltonian Hq is expressed as the sum of terms characterized each by a value of the molecule-fixed index ν, whose matrix elements obey the rule Δk = ν. Some of these terms may vanish because of molecular symmetry, and the specific cases of linear and symmetric top molecules, orthorhombic molecules, and molecules with symmetry lower than orthorhombic are considered. Each ν-term consists of a contraction of the rotational tensor λ(2) and the nuclear quadrupole tensor in the space-fixed frame, and its matrix elements in the rotation-nuclear spin coupled representation can be determined by the standard spherical tensor methods.

One-way mode transmission in one-dimensional phononic crystal plates

NASA Astrophysics Data System (ADS)

Zhu, Xuefeng; Zou, Xinye; Liang, Bin; Cheng, Jianchun

2010-12-01

We investigate theoretically the band structures of one-dimensional phononic crystal (PC) plates with both antisymmetric and symmetric structures, and show how unidirectional transmission behavior can be obtained for either antisymmetric waves (A modes) or symmetric waves (S modes) by exploiting mode conversion and selection in the linear plate systems. The theoretical approach is illustrated for one PC plate example where unidirectional transmission behavior is obtained in certain frequency bands. Employing harmonic frequency analysis, we numerically demonstrate the one-way mode transmission for the PC plate with finite superlattice by calculating the steady-state displacement fields under A modes source (or S modes source) in forward and backward direction, respectively. The results show that the incident waves from A modes source (or S modes source) are transformed into S modes waves (or A modes waves) after passing through the superlattice in the forward direction and the Lamb wave rejections in the backward direction are striking with a power extinction ratio of more than 1000. The present structure can be easily extended to two-dimensional PC plate and efficiently encourage practical studies of experimental realization which is believed to have much significance for one-way Lamb wave mode transmission.

Higher-derivative operators and effective field theory for general scalar-tensor theories

NASA Astrophysics Data System (ADS)

Solomon, Adam R.; Trodden, Mark

2018-02-01

We discuss the extent to which it is necessary to include higher-derivative operators in the effective field theory of general scalar-tensor theories. We explore the circumstances under which it is correct to restrict to second-order operators only, and demonstrate this using several different techniques, such as reduction of order and explicit field redefinitions. These methods are applied, in particular, to the much-studied Horndeski theories. The goal is to clarify the application of effective field theory techniques in the context of popular cosmological models, and to explicitly demonstrate how and when higher-derivative operators can be cast into lower-derivative forms suitable for numerical solution techniques.

Virtual viewpoint generation for three-dimensional display based on the compressive light field

NASA Astrophysics Data System (ADS)

Meng, Qiao; Sang, Xinzhu; Chen, Duo; Guo, Nan; Yan, Binbin; Yu, Chongxiu; Dou, Wenhua; Xiao, Liquan

2016-10-01

Virtual view-point generation is one of the key technologies the three-dimensional (3D) display, which renders the new scene image perspective with the existing viewpoints. The three-dimensional scene information can be effectively recovered at different viewing angles to allow users to switch between different views. However, in the process of multiple viewpoints matching, when N free viewpoints are received, we need to match N viewpoints each other, namely matching C 2N = N(N-1)/2 times, and even in the process of matching different baselines errors can occur. To address the problem of great complexity of the traditional virtual view point generation process, a novel and rapid virtual view point generation algorithm is presented in this paper, and actual light field information is used rather than the geometric information. Moreover, for better making the data actual meaning, we mainly use nonnegative tensor factorization(NTF). A tensor representation is introduced for virtual multilayer displays. The light field emitted by an N-layer, M-frame display is represented by a sparse set of non-zero elements restricted to a plane within an Nth-order, rank-M tensor. The tensor representation allows for optimal decomposition of a light field into time-multiplexed, light-attenuating layers using NTF. Finally, the compressive light field of multilayer displays information synthesis is used to obtain virtual view-point by multiple multiplication. Experimental results show that the approach not only the original light field is restored with the high image quality, whose PSNR is 25.6dB, but also the deficiency of traditional matching is made up and any viewpoint can obtained from N free viewpoints.

Global diffusion of cosmic rays in random magnetic fields

NASA Astrophysics Data System (ADS)

Snodin, A. P.; Shukurov, A.; Sarson, G. R.; Bushby, P. J.; Rodrigues, L. F. S.

2016-04-01

The propagation of charged particles, including cosmic rays, in a partially ordered magnetic field is characterized by a diffusion tensor whose components depend on the particle's Larmor radius RL and the degree of order in the magnetic field. Most studies of the particle diffusion presuppose a scale separation between the mean and random magnetic fields (e.g. there being a pronounced minimum in the magnetic power spectrum at intermediate scales). Scale separation is often a good approximation in laboratory plasmas, but not in most astrophysical environments such as the interstellar medium (ISM). Modern simulations of the ISM have numerical resolution of the order of 1 pc, so the Larmor radius of the cosmic rays that dominate in energy density is at least 106 times smaller than the resolved scales. Large-scale simulations of cosmic ray propagation in the ISM thus rely on oversimplified forms of the diffusion tensor. We take the first steps towards a more realistic description of cosmic ray diffusion for such simulations, obtaining direct estimates of the diffusion tensor from test particle simulations in random magnetic fields (with the Larmor radius scale being fully resolved), for a range of particle energies corresponding to 10-2 ≲ RL/lc ≲ 103, where lc is the magnetic correlation length. We obtain explicit expressions for the cosmic ray diffusion tensor for RL/lc ≪ 1, that might be used in a sub-grid model of cosmic ray diffusion. The diffusion coefficients obtained are closely connected with existing transport theories that include the random walk of magnetic lines.

Kinematic assumptions and their consequences on the structure of field equations in continuum dislocation theory

NASA Astrophysics Data System (ADS)

Silbermann, C. B.; Ihlemann, J.

2016-03-01

Continuum Dislocation Theory (CDT) relates gradients of plastic deformation in crystals with the presence of geometrically necessary dislocations. Therefore, the dislocation tensor is introduced as an additional thermodynamic state variable which reflects tensorial properties of dislocation ensembles. Moreover, the CDT captures both the strain energy from the macroscopic deformation of the crystal and the elastic energy of the dislocation network, as well as the dissipation of energy due to dislocation motion. The present contribution deals with the geometrically linear CDT. More precise, the focus is on the role of dislocation kinematics for single and multi-slip and its consequences on the field equations. Thereby, the number of active slip systems plays a crucial role since it restricts the degrees of freedom of plastic deformation. Special attention is put on the definition of proper, well-defined invariants of the dislocation tensor in order to avoid any spurious dependence of the resulting field equations on the coordinate system. It is shown how a slip system based approach can be in accordance with the tensor nature of the involved quantities. At first, only dislocation glide in one active slip system of the crystal is allowed. Then, the special case of two orthogonal (interacting) slip systems is considered and the governing field equations are presented. In addition, the structure and symmetry of the backstress tensor is investigated from the viewpoint of thermodynamical consistency. The results will again be used in order to facilitate the set of field equations and to prepare for a robust numerical implementation.

Homogenized moment tensor and the effect of near-field heterogeneities on nonisotropic radiation in nuclear explosion

NASA Astrophysics Data System (ADS)

Burgos, Gaël.; Capdeville, Yann; Guillot, Laurent

2016-06-01

We investigate the effect of small-scale heterogeneities close to a seismic explosive source, at intermediate periods (20-50 s), with an emphasis on the resulting nonisotropic far-field radiation. First, using a direct numerical approach, we show that small-scale elastic heterogeneities located in the near-field of an explosive source, generate unexpected phases (i.e., long period S waves). We then demonstrate that the nonperiodic homogenization theory applied to 2-D and 3-D elastic models, with various pattern of small-scale heterogeneities near the source, leads to accurate waveforms at a reduced computational cost compared to direct modeling. Further, it gives an interpretation of how nearby small-scale features interact with the source at low frequencies, through an explicit correction to the seismic moment tensor. In 2-D simulations, we find a deviatoric contribution to the moment tensor, as high as 21% for near-source heterogeneities showing a 25% contrast of elastic values (relative to a homogeneous background medium). In 3-D this nonisotropic contribution reaches 27%. Second, we analyze intermediate-periods regional seismic waveforms associated with some underground nuclear explosions conducted at the Nevada National Security Site and invert for the full moment tensor, in order to quantify the relative contribution of the isotropic and deviatoric components of the tensor. The average value of the deviatoric part is about 35%. We conclude that the interactions between an explosive source and small-scale local heterogeneities of moderate amplitude may lead to a deviatoric contribution to the seismic moment, close to what is observed using regional data from nuclear test explosions.

Behaviour of DFT-based approaches to the spin-orbit term of zero-field splitting tensors: a case study of metallocomplexes, MIII(acac)3 (M = V, Cr, Mn, Fe and Mo).

PubMed

Sugisaki, Kenji; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Takui, Takeji

2017-11-15

Spin-orbit contributions to the zero-field splitting (ZFS) tensor (D SO tensor) of M III (acac) 3 complexes (M = V, Cr, Mn, Fe and Mo; acac = acetylacetonate anion) are evaluated by means of ab initio (a hybrid CASSCF/MRMP2) and DFT (Pederson-Khanna (PK) and natural orbital-based Pederson-Khanna (NOB-PK)) methods, focusing on the behaviour of DFT-based approaches to the D SO tensors against the valence d-electron configurations of the transition metal ions in octahedral coordination. Both the DFT-based approaches reproduce trends in the D tensors. Significantly, the differences between the theoretical and experimental D (D = D ZZ - (D XX + D YY )/2) values are smaller in NOB-PK than in PK, emphasising the usefulness of the natural orbital-based approach to the D tensor calculations of transition metal ion complexes. In the case of d 2 and d 4 electronic configurations, the D SO (NOB-PK) values are considerably underestimated in the absolute magnitude, compared with the experimental ones. The D SO tensor analysis based on the orbital region partitioning technique (ORPT) revealed that the D SO contributions attributed to excitations from the singly occupied region (SOR) to the unoccupied region (UOR) are significantly underestimated in the DFT-based approaches to all the complexes under study. In the case of d 3 and d 5 configurations, the (SOR → UOR) excitations contribute in a nearly isotropic manner, which causes fortuitous error cancellations in the DFT-based D SO values. These results indicate that more efforts to develop DFT frameworks should be directed towards the reproduction of quantitative D SO tensors of transition metal complexes with various electronic configurations and local symmetries around metal ions.

Tensor scale: An analytic approach with efficient computation and applications☆

PubMed Central

Xu, Ziyue; Saha, Punam K.; Dasgupta, Soura

2015-01-01

Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as “tensor scale” using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, the application of tensor scale in 3-D using the previous framework is not practical due to high computational complexity. In this paper, an analytic definition of tensor scale is formulated for n-dimensional (n-D) images that captures local structure size, orientation and anisotropy. Also, an efficient computational solution in 2- and 3-D using several novel differential geometric approaches is presented and the accuracy of results is experimentally examined. Also, a matrix representation of tensor scale is derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Finally, the applications of tensor scale in image filtering and n-linear interpolation are presented and the performance of their results is examined in comparison with respective state-of-art methods. Specifically, the performance of tensor scale based image filtering is compared with gradient and Weickert’s structure tensor based diffusive filtering algorithms. Also, the performance of tensor scale based n-linear interpolation is evaluated in comparison with standard n-linear and windowed-sinc interpolation methods. PMID:26236148

Partially massless fields during inflation

NASA Astrophysics Data System (ADS)

Baumann, Daniel; Goon, Garrett; Lee, Hayden; Pimentel, Guilherme L.

2018-04-01

The representation theory of de Sitter space allows for a category of partially massless particles which have no flat space analog, but could have existed during inflation. We study the couplings of these exotic particles to inflationary perturbations and determine the resulting signatures in cosmological correlators. When inflationary perturbations interact through the exchange of these fields, their correlation functions inherit scalings that cannot be mimicked by extra massive fields. We discuss in detail the squeezed limit of the tensor-scalar-scalar bispectrum, and show that certain partially massless fields can violate the tensor consistency relation of single-field inflation. We also consider the collapsed limit of the scalar trispectrum, and find that the exchange of partially massless fields enhances its magnitude, while giving no contribution to the scalar bispectrum. These characteristic signatures provide clean detection channels for partially massless fields during inflation.

Covariant formulation of scalar-torsion gravity

NASA Astrophysics Data System (ADS)

Hohmann, Manuel; Järv, Laur; Ualikhanova, Ulbossyn

2018-05-01

We consider a generalized teleparallel theory of gravitation, where the action contains an arbitrary function of the torsion scalar and a scalar field, f (T ,ϕ ) , thus encompassing the cases of f (T ) gravity and a nonminimally coupled scalar field as subclasses. The action is manifestly Lorentz invariant when besides the tetrad one allows for a flat but nontrivial spin connection. We derive the field equations and demonstrate how the antisymmetric part of the tetrad equations is automatically satisfied when the spin connection equation holds. The spin connection equation is a vital part of the covariant formulation, since it determines the spin connection associated with a given tetrad. We discuss how the spin connection equation can be solved in general and provide the cosmological and spherically symmetric examples. Finally, we generalize the theory to an arbitrary number of scalar fields.

Calculation of Thermal Conductivity Coefficients of Electrons in Magnetized Dense Matter

NASA Astrophysics Data System (ADS)

Bisnovatyi-Kogan, G. S.; Glushikhina, M. V.

2018-04-01

The solution of Boltzmann equation for plasma in magnetic field with arbitrarily degenerate electrons and nondegenerate nuclei is obtained by Chapman-Enskog method. Functions generalizing Sonine polynomials are used for obtaining an approximate solution. Fully ionized plasma is considered. The tensor of the heat conductivity coefficients in nonquantized magnetic field is calculated. For nondegenerate and strongly degenerate plasma the asymptotic analytic formulas are obtained and compared with results of previous authors. The Lorentz approximation with neglecting of electron-electron encounters is asymptotically exact for strongly degenerate plasma. For the first time, analytical expressions for the heat conductivity tensor for nondegenerate electrons in the presence of a magnetic field are obtained in the three-polynomial approximation with account of electron-electron collisions. Account of the third polynomial improved substantially the precision of results. In the two-polynomial approximation, the obtained solution coincides with the published results. For strongly degenerate electrons, an asymptotically exact analytical solution for the heat conductivity tensor in the presence of a magnetic field is obtained for the first time. This solution has a considerably more complicated dependence on the magnetic field than those in previous publications and gives a several times smaller relative value of the thermal conductivity across the magnetic field at ωτ * 0.8.

Cosmology of non-minimal derivative coupling to gravity in Palatini formalism and its chaotic inflation

NASA Astrophysics Data System (ADS)

Kaewkhao, Narakorn; Gumjudpai, Burin

2018-06-01

We consider, in Palatini formalism, a modified gravity of which the scalar field derivative couples to Einstein tensor. In this scenario, Ricci scalar, Ricci tensor and Einstein tensor are functions of connection field. As a result, the connection field gives rise to relation, hμν = fgμν between effective metric, hμν and the usual metric gμν where f = 1 - κϕ,αϕ,α / 2. In FLRW universe, NMDC coupling constant is limited in a range of - 2 /ϕ˙2 < κ ≤ ∞ preserving Lorentz signature of the effective metric. Slowly-rolling regime provides κ < 0 forbidding graviton from traveling at superluminal speed. Effective gravitational coupling and entropy of blackhole's apparent horizon are derived. In case of negative coupling, acceleration could happen even with weff > - 1 / 3. Power-law potentials of chaotic inflation are considered. For V ∝ϕ2 and V ∝ϕ4, it is possible to obtain tensor-to-scalar ratio lower than that of GR so that it satisfies r < 0 . 12 as constrained by Planck 2015 (Ade et al., 2016). The V ∝ϕ2 case yields acceptable range of spectrum index and r values. The quartic potential's spectrum index is disfavored by the Planck results. Viable range of κ for V ∝ϕ2 case lies in positive region, resulting in less blackhole's entropy, superluminal metric, more amount of inflation, avoidance of super-Planckian field initial value and stronger gravitational constant.

Projective mappings and dimensions of vector spaces of three types of Killing-Yano tensors on pseudo Riemannian manifolds of constant curvature

NASA Astrophysics Data System (ADS)

Mikeš, Josef; Stepanov, Sergey; Hinterleitner, Irena

2012-07-01

In our paper we have determined the dimension of the space of conformal Killing-Yano tensors and the dimensions of its two subspaces of closed conformal Killing-Yano and Killing-Yano tensors on pseudo Riemannian manifolds of constant curvature. This result is a generalization of well known results on sharp upper bounds of the dimensions of the vector spaces of conformal Killing-Yano, Killing-Yano and concircular vector fields on pseudo Riemannian manifolds of constant curvature.

Extended Applicability of the Spherical-Harmonic and Point-Mass Modeling of the Gravity Field,

DTIC Science & Technology

1980-02-01

the metric in spherical coordinates {X,F, rl reads ds2 = r2cos 2j dX2 + r 2d 2 + dr2 yielding the metric tensor and the associated metric tensor: {grs...leading to (3.52) would have required considerably more space if the tensor approach to this problem had been avoided, whether for pedagogical or other...useful, especially from the pedagogical point of view, since it addresses itself to large audiences and exposes the treated subject in great depth. On

Symmetric factorization of the conformation tensor in viscoelastic fluid models

NASA Astrophysics Data System (ADS)

Thomases, Becca; Balci, Nusret; Renardy, Michael; Doering, Charles

2010-11-01

The positive definite symmetric polymer conformation tensor possesses a unique symmetric square root that satisfies a closed evolution equation in the Oldroyd-B and FENE-P models of viscoelastic fluid flow. When expressed in terms of the velocity field and the symmetric square root of the conformation tensor, these models' equations of motion formally constitute an evolution in a Hilbert space with a total energy functional that defines a norm. Moreover, this formulation is easily implemented in direct numerical simulations resulting in significant practical advantages in terms of both accuracy and stability.

Pryce-Hoyle Tensor in a Combined Einstein-Cartan-Brans-Dicke Model

NASA Astrophysics Data System (ADS)

Berman, Marcelo Samuel

2009-03-01

In addition to introducing matter injection through a scalar field determined by Pryce-Hoyle tensor, we also combine it with a BCDE (Brans-Dicke-Einstein-Cartan) theory with lambda-term developed earlier by Berman (Astrophys. Space Sci. 314:79-82, 2008), for inflationary scenario. It involves a variable cosmological constant, which decreases with time, jointly with energy density, cosmic pressure, shear, vorticity, and Hubble’s parameter, while the scale factor, total spin and scalar field increase exponentially. The post-inflationary fluid resembles a perfect one, though total spin grows, but not the angular speed (Berman, in Astrophys. Space Sci. 312:275, 2007). The Pryce-Hoyle tensor, which can measured by the number of injected particles per unit proper volume and time, as well as shear and vorticity, can be neglected in the aftermath of inflation (“no-hair”).

Chiral primordial blue tensor spectra from the axion-gauge couplings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Obata, Ippei, E-mail: obata@tap.scphys.kyoto-u.ac.jp

We suggest the new feature of primordial gravitational waves sourced by the axion-gauge couplings, whose forms are motivated by the dimensional reduction of the form field in the string theory. In our inflationary model, as an inflaton we adopt two types of axion, dubbed the model-independent axion and the model-dependent axion, which couple with two gauge groups with different sign combination each other. Due to these forms both polarization modes of gauge fields are amplified and enhance both helicies of tensor modes during inflation. We point out the possibility that a primordial blue-tilted tensor power spectra with small chirality aremore » provided by the combination of these axion-gauge couplings, intriguingly both amplitudes and chirality are potentially testable by future space-based gravitational wave interferometers such as DECIGO and BBO project.« less

Covariant conserved currents for scalar-tensor Horndeski theory

NASA Astrophysics Data System (ADS)

Schmidt, J.; Bičák, J.

2018-04-01

The scalar-tensor theories have become popular recently in particular in connection with attempts to explain present accelerated expansion of the universe, but they have been considered as a natural extension of general relativity long time ago. The Horndeski scalar-tensor theory involving four invariantly defined Lagrangians is a natural choice since it implies field equations involving at most second derivatives. Following the formalisms of defining covariant global quantities and conservation laws for perturbations of spacetimes in standard general relativity, we extend these methods to the general Horndeski theory and find the covariant conserved currents for all four Lagrangians. The current is also constructed in the case of linear perturbations involving both metric and scalar fields. As a specific illustration, we derive a superpotential that leads to the covariantly conserved current in the Branse-Dicke theory.

δ M formalism and anisotropic chaotic inflation power spectrum

NASA Astrophysics Data System (ADS)

Talebian-Ashkezari, A.; Ahmadi, N.

2018-05-01

A new analytical approach to linear perturbations in anisotropic inflation has been introduced in [A. Talebian-Ashkezari, N. Ahmadi and A.A. Abolhasani, JCAP 03 (2018) 001] under the name of δ M formalism. In this paper we apply the mentioned approach to a model of anisotropic inflation driven by a scalar field, coupled to the kinetic term of a vector field with a U(1) symmetry. The δ M formalism provides an efficient way of computing tensor-tensor, tensor-scalar as well as scalar-scalar 2-point correlations that are needed for the analysis of the observational features of an anisotropic model on the CMB. A comparison between δ M results and the tedious calculations using in-in formalism shows the aptitude of the δ M formalism in calculating accurate two point correlation functions between physical modes of the system.

Communication: Equivalence between symmetric and antisymmetric stretching modes of NH 3 in promoting H + NH 3 → H 2 + NH 2 reaction

DOE PAGES

Song, Hongwei; Yang, Minghui; Guo, Hua

2016-10-07

Vibrational excitations of reactants sometimes promote reactions more effectively than the same amount of translational energy. Such mode specificity provides insights into the transition-state modulation of reactivity and might be used to control chemical reactions. We report here a state-ofthe- art full-dimensional quantum dynamical study of the hydrogen abstraction reaction H + NH 3 → H 2 + NH 2 on an accurate ab initio based global potential energy surface. This reaction serves as an ideal candidate to study the relative efficacies of symmetric and degenerate antisymmetric stretching modes. Strong mode specificity, particularly for the NH 3 stretching modes, ismore » demonstrated. In conclusion, it is further shown that nearly identical efficacies of the symmetric and antisymmetric stretching modes of NH 3 in promoting the reaction can be understood in terms of local-mode stretching vibrations of the reactant molecule.« less

Communication: Equivalence between symmetric and antisymmetric stretching modes of NH3 in promoting H + NH3 → H2 + NH2 reaction

NASA Astrophysics Data System (ADS)

Song, Hongwei; Yang, Minghui; Guo, Hua

2016-10-01

Vibrational excitations of reactants sometimes promote reactions more effectively than the same amount of translational energy. Such mode specificity provides insights into the transition-state modulation of reactivity and might be used to control chemical reactions. We report here a state-of-the-art full-dimensional quantum dynamical study of the hydrogen abstraction reaction H + NH3 → H2 + NH2 on an accurate ab initio based global potential energy surface. This reaction serves as an ideal candidate to study the relative efficacies of symmetric and degenerate antisymmetric stretching modes. Strong mode specificity, particularly for the NH3 stretching modes, is demonstrated. It is further shown that nearly identical efficacies of the symmetric and antisymmetric stretching modes of NH3 in promoting the reaction can be understood in terms of local-mode stretching vibrations of the reactant molecule.

Einstein-aether theory with a Maxwell field: General formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balakin, Alexander B., E-mail: Alexander.Balakin@kpfu.ru; Lemos, José P.S., E-mail: joselemos@ist.utl.pt

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shearmore » and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.« less

Microprocessor implementation of an FFT for ionospheric VLF observations

NASA Technical Reports Server (NTRS)

Elvidge, J.; Kintner, P.; Holzworth, R.

1984-01-01

A fast Fourier transform algorithm is implemented on a CMOS microprocessor for application to very low-frequency electric fields (less than 10 kHz) sensed on high-altitude scientific balloons. Two FFT's are calculated simultaneously by associating them with conjugate symmetric and conjugate antisymmetric results. One goal of the system was to detect spectral signatures associated with fast time variations present in natural signals such as whistlers and chorus. Although a full evaluation of the system was not possible for operational reasons, a measure of the system's success has been defined and evaluated.

An Analysis of the Tensor Dielectric Constant of Sea Ice at Microwave Frequencies.

DTIC Science & Technology

1985-10-01

36.8 > t a -43.2 0 C (5) is convenient. The above equations for p in the range t > -22.9 0 C were first published by Frankenstein and Garner [12). III...Em 0 (6) for the mean electric field propagating in the medium. Here ko is the free space propagation constant, K. the quasi-static dielectric tensor...C. Essen- " tially identical results were found for the real part of the dielectric con- stant whether the polarization of the electric field was

Berry phase of primordial scalar and tensor perturbations in single-field inflationary models

NASA Astrophysics Data System (ADS)

Balajany, Hamideh; Mehrafarin, Mohammad

2018-06-01

In the framework of the single-field slow-roll inflation, we derive the Hamiltonian of the linear primordial scalar and tensor perturbations in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes in terms of the Lewis-Riesenfeld phase. We conclude by discussing the discrepancy in the results of Pal et al. (2013) [21] for these Berry phases, which is resolved to yield agreement with our results.

Covariant Uniform Acceleration

NASA Astrophysics Data System (ADS)

Friedman, Yaakov; Scarr, Tzvi

2013-04-01

We derive a 4D covariant Relativistic Dynamics Equation. This equation canonically extends the 3D relativistic dynamics equation , where F is the 3D force and p = m0γv is the 3D relativistic momentum. The standard 4D equation is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. This solves a problem of Einstein and Planck. We compute explicit solutions for uniformly accelerated motion. The solutions are divided into four Lorentz-invariant types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion. We use Generalized Fermi-Walker transport to construct a uniformly accelerated family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame K' to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. We obtain velocity and acceleration transformations from a uniformly accelerated system K' to an inertial frame K. We introduce the 4D velocity, an adaptation of Horwitz and Piron s notion of "off-shell." We derive the general formula for the time dilation between accelerated clocks. We obtain a formula for the angular velocity of a uniformly accelerated object. Every rest point of K' is uniformly accelerated, and its acceleration is a function of the observer's acceleration and its position. We obtain an interpretation of the Lorentz-Abraham-Dirac equation as an acceleration transformation from K' to K.

The competition of particle-vibration coupling and tensor interaction in spherical nuclei

NASA Astrophysics Data System (ADS)

Afanasjev, Anatoli; Litvinova, Elena

2014-09-01

The search for missing terms in the energy density functionals (EDF) is one of the leading directions in the development of nuclear density functional theory (DFT). Tensor force is one of possible candidates. However, despite extensive studies the questions about its effective strength and unambiguous signals still remain open. One of the main experimental benchmarks for the studies of tensor interaction is provided by the data on the single-particle states in the N = 82 and Z = 50 isotopes. The energy splittings of the proton h11 / 2 and g7 / 2 states in the Z = 50 isotopes and neutron 1i13 / 2 and 1h9 / 2 states in the N = 82 isotones are used in the definition of tensor force in the Skyrme DFT. However, in experiment these states are not ``mean-field'' states because of coupling with vibrations. Employing relativistic particle-vibration coupling (PVC) model we show that many features of these splittings can be reproduced when PVC is taken into account. This suggests the competition of PVC and tensor interaction and that tensor interaction should be weaker as compared with previous estimates. The search for missing terms in the energy density functionals (EDF) is one of the leading directions in the development of nuclear density functional theory (DFT). Tensor force is one of possible candidates. However, despite extensive studies the questions about its effective strength and unambiguous signals still remain open. One of the main experimental benchmarks for the studies of tensor interaction is provided by the data on the single-particle states in the N = 82 and Z = 50 isotopes. The energy splittings of the proton h11 / 2 and g7 / 2 states in the Z = 50 isotopes and neutron 1i13 / 2 and 1h9 / 2 states in the N = 82 isotones are used in the definition of tensor force in the Skyrme DFT. However, in experiment these states are not ``mean-field'' states because of coupling with vibrations. Employing relativistic particle-vibration coupling (PVC) model we show that many features of these splittings can be reproduced when PVC is taken into account. This suggests the competition of PVC and tensor interaction and that tensor interaction should be weaker as compared with previous estimates. This work has been supported by the U.S. Department of Energy under the Grant DE-FG02-07ER41459 and National Science Foundation Award PHY-1204486.

Conformal Collineations of the Ricci and Energy-Momentum Tensors in Static Plane Symmetric Space-Times

NASA Astrophysics Data System (ADS)

Akhtar, S. S.; Hussain, T.; Bokhari, A. H.; Khan, F.

2018-04-01

We provide a complete classification of static plane symmetric space-times according to conformal Ricci collineations (CRCs) and conformal matter collineations (CMCs) in both the degenerate and nondegenerate cases. In the case of a nondegenerate Ricci tensor, we find a general form of the vector field generating CRCs in terms of unknown functions of t and x subject to some integrability conditions. We then solve the integrability conditions in different cases depending upon the nature of the Ricci tensor and conclude that the static plane symmetric space-times have a 7-, 10- or 15-dimensional Lie algebra of CRCs. Moreover, we find that these space-times admit an infinite number of CRCs if the Ricci tensor is degenerate. We use a similar procedure to study CMCs in the case of a degenerate or nondegenerate matter tensor. We obtain the exact form of some static plane symmetric space-time metrics that admit nontrivial CRCs and CMCs. Finally, we present some physical applications of our obtained results by considering a perfect fluid as a source of the energy-momentum tensor.

Generation of large-scale magnetic fields, non-Gaussianity, and primordial gravitational waves in inflationary cosmology

NASA Astrophysics Data System (ADS)

Bamba, Kazuharu

2015-02-01

The generation of large-scale magnetic fields in inflationary cosmology is explored, in particular, in a kind of moduli inflation motivated by racetrack inflation in the context of the type IIB string theory. In this model, the conformal invariance of the hypercharge electromagnetic fields is broken thanks to the coupling of both the scalar and pseudoscalar fields to the hypercharge electromagnetic fields. The following three cosmological observable quantities are first evaluated: the current magnetic field strength on the Hubble horizon scale, which is much smaller than the upper limit from the backreaction problem, local non-Gaussianity of the curvature perturbations due to the existence of the massive gauge fields, and the tensor-to-scalar ratio. It is explicitly demonstrated that the resultant values of local non-Gaussianity and the tensor-to-scalar ratio are consistent with the Planck data.

Hidden role of Maxwell superalgebras in the free differential algebras of D = 4 and D = 11 supergravity

NASA Astrophysics Data System (ADS)

Ravera, Lucrezia

2018-03-01

The purpose of this paper is to show that the so-called Maxwell superalgebra in four dimensions, which naturally involves the presence of a nilpotent fermionic generator, can be interpreted as a hidden superalgebra underlying N=1, {D}=4 supergravity extended to include a 2-form gauge potential associated to a 2-index antisymmetric tensor. In this scenario, the theory is appropriately discussed in the context of Free Differential Algebras (an extension of the Maurer-Cartan equations to involve higher-degree differential forms). The study is then extended to the Free Differential Algebra describing D = 11 supergravity, showing that, also in this case, there exists a super-Maxwell algebra underlying the theory. The same extra spinors dual to the nilpotent fermionic generators whose presence is crucial for writing a supersymmetric extension of the Maxwell algebras, both in the D = 4 and in the D = 11 case, turn out to be fundamental ingredients also to reproduce the D = 4 and D = 11 Free Differential Algebras on ordinary superspace, whose basis is given by the supervielbein. The analysis of the gauge structure of the supersymmetric Free Differential Algebras is carried on taking into account the gauge transformations from the hidden supergroup-manifold associated with the Maxwell superalgebras.

Stochastic Gravity: Theory and Applications.

PubMed

Hu, Bei Lok; Verdaguer, Enric

2004-01-01

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operatorvalued) stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole (enclosed in a box). We derive a fluctuation-dissipation relation between the fluctuations in the radiation and the dissipative dynamics of metric fluctuations.

Interpolation of orientation distribution functions in diffusion weighted imaging using multi-tensor model.

PubMed

Afzali, Maryam; Fatemizadeh, Emad; Soltanian-Zadeh, Hamid

2015-09-30

Diffusion weighted imaging (DWI) is a non-invasive method for investigating the brain white matter structure and can be used to evaluate fiber bundles. However, due to practical constraints, DWI data acquired in clinics are low resolution. This paper proposes a method for interpolation of orientation distribution functions (ODFs). To this end, fuzzy clustering is applied to segment ODFs based on the principal diffusion directions (PDDs). Next, a cluster is modeled by a tensor so that an ODF is represented by a mixture of tensors. For interpolation, each tensor is rotated separately. The method is applied on the synthetic and real DWI data of control and epileptic subjects. Both experiments illustrate capability of the method in increasing spatial resolution of the data in the ODF field properly. The real dataset show that the method is capable of reliable identification of differences between temporal lobe epilepsy (TLE) patients and normal subjects. The method is compared to existing methods. Comparison studies show that the proposed method generates smaller angular errors relative to the existing methods. Another advantage of the method is that it does not require an iterative algorithm to find the tensors. The proposed method is appropriate for increasing resolution in the ODF field and can be applied to clinical data to improve evaluation of white matter fibers in the brain. Copyright © 2015 Elsevier B.V. All rights reserved.

The TT, TB, EB and BB correlations in anisotropic inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Xingang; Emami, Razieh; Firouzjahi, Hassan

2014-08-01

The ongoing and future experiments will measure the B-mode from different sky coverage and frequency bands, with the potential to reveal non-trivial features in polarization map. In this work we study the TT, TB, EB and BB correlations associated with the B-mode polarization of CMB map in models of charged anisotropic inflation. The model contains a chaotic-type large field complex inflaton which is charged under the U(1) gauge field. We calculate the statistical anisotropies generated in the power spectra of the curvature perturbation, the tensor perturbation and their cross-correlation. It is shown that the asymmetry in tensor power spectrum ismore » a very sensitive probe of the gauge coupling. While the level of statistical anisotropy in temperature power spectrum can be small and satisfy the observational bounds, the interactions from the gauge coupling can induce large directional dependence in tensor modes. This will leave interesting anisotropic fingerprints in various correlations involving the B-mode polarization such as the TB cross-correlation which may be detected in upcoming Planck polarization data. In addition, the TT correlation receives an anisotropic contribution from the tensor sector which naturally decays after l ∼> 100. We expect that the mechanism of using tensor sector to induce asymmetry at low l to be generic which can also be applied to address other low l CMB anomalies.« less

Collision Dynamics of Rydberg Atoms and Molecules at Ultralow Energies

DTIC Science & Technology

2005-12-31

body recombination between electrons, ions and neural gas atoms. We wish to study the interaction and collisions between two Rydberg atoms in the...transitions, Exact solutions of Stark mixing in atomic hydro- where Ekjn is the Levi - Civita antisymmetric symbol gen induced by the time-dependent...L and U do not close under commutation to form a Lie algebra because [Ui, Uj] = (-2g)iCijkLk, where cijk is the Levi - Civita antisymmetric symbol for

Detailed fault structure of the 2000 Western Tottori, Japan, earthquake sequence

USGS Publications Warehouse

Fukuyama, E.; Ellsworth, W.L.; Waldhauser, F.; Kubo, A.

2003-01-01

We investigate the faulting process of the aftershock region of the 2000 western Tottori earthquake (Mw 6.6) by combining aftershock hypocenters and moment tensor solutions. Aftershock locations were precisely determined by the double difference method using P- and S-phase arrival data of the Japan Meteorological Agency unified catalog. By combining the relocated hypocenters and moment tensor solutions of aftershocks by broadband waveform inversion of FREESIA (F-net), we successfully resolved very detailed fault structures activated by the mainshock. The estimated fault model resolves 15 individual fault segments that are consistent with both aftershock distribution and focal mechanism solutions. Rupture in the mainshock was principally confined to the three fault elements in the southern half of the zone, which is also where the earliest aftershocks concentrate. With time, the northern part of the zone becomes activated, which is also reflected in the postseismic deformation field. From the stress tensor analysis of aftershock focal mechanisms, we found a rather uniform stress field in the aftershock region, although fault strikes were scattered. The maximum stress direction is N107??E, which is consistent with the tectonic stress field in this region. In the northern part of the fault, where no slip occurred during the mainshock but postseismic slip was observed, the maximum stress direction of N130??E was possible as an alternative solution of stress tensor inversion.

The Riemann-Lanczos equations in general relativity and their integrability

NASA Astrophysics Data System (ADS)

Dolan, P.; Gerber, A.

2008-06-01

The aim of this paper is to examine the Riemann-Lanczos equations and how they can be made integrable. They consist of a system of linear first-order partial differential equations that arise in general relativity, whereby the Riemann curvature tensor is generated by an unknown third-order tensor potential field called the Lanczos tensor. Our approach is based on the theory of jet bundles, where all field variables and all their partial derivatives of all relevant orders are treated as independent variables alongside the local manifold coordinates (xa) on the given space-time manifold M. This approach is adopted in (a) Cartan's method of exterior differential systems, (b) Vessiot's dual method using vector field systems, and (c) the Janet-Riquier theory of systems of partial differential equations. All three methods allow for the most general situations under which integrability conditions can be found. They give equivalent results, namely, that involutivity is always achieved at all generic points of the jet manifold M after a finite number of prolongations. Two alternative methods that appear in the general relativity literature to find integrability conditions for the Riemann-Lanczos equations generate new partial differential equations for the Lanczos potential that introduce a source term, which is nonlinear in the components of the Riemann tensor. We show that such sources do not occur when either of method (a), (b), or (c) are used.

Propagation of electromagnetic soliton in a spin polarized current driven weak ferromagnetic nanowire

NASA Astrophysics Data System (ADS)

Senthil Kumar, V.; Kavitha, L.; Gopi, D.

2017-11-01

We investigate the nonlinear spin dynamics of a spin polarized current driven anisotropic ferromagnetic nanowire with Dzyaloshinskii-Moriya interaction (DMI) under the influence of electromagnetic wave (EMW) propagating along the axis of the nanowire. The magnetization dynamics and electromagnetic wave propagation in the ferromagnetic nanowire with weak anti-symmetric interaction is governed by a coupled vector Landau-Lifshitz-Gilbert and Maxwell's equations. These coupled nonlinear vector equations are recasted into the extended derivative nonlinear Schrödinger (EDNLS) equation in the framework of reductive perturbation method. As it is well known, the modulational instability is a precursor for the emergence of localized envelope structures of various kinds, we compute the instability criteria for the weak ferromagnetic nanowire through linear stability analysis. Further, we invoke the homogeneous balance method to construct kink and anti-solitonic like electromagnetic (EM) soliton profiles for the EDNLS equation. We also explore the appreciable effect of the anti-symmetric weak interaction on the magnetization components of the propagating EM soliton. We find that the combination of spin-polarized current and the anti-symmetric DMI have a profound effect on the propagating EMW in a weak ferromagnetic nanowire. Thus, the anti-symmetric DMI in a spin polarized current driven ferromagnetic nanowire supports the lossless propagation of EM solitons, which may have potential applications in magnetic data storage devices.

Complex brittle deformation pattern along the Southern Patagonian Andes (Argentina)

NASA Astrophysics Data System (ADS)

Barberón, Vanesa; Sue, Christian; Ronda, Gonzalo; Ghiglione, Matías

2016-04-01

The Southern Patagonian Andes is located in the southern extreme of the Pacific subduction zone, where the Antartic oceanic plate sinks underneath South America. The history of the area begins with compression during Paleozoic, Jurassic extension associated to the rift and opening of the South Atlantic Ocean, then a sag stage in the Lower Cretaceous followed by a foreland phase as a result of plate tectonics (Ghiglione et al., 2016). The kinematic study is concentrated in the Argentinean foothills, between 46°40' and 48° SL. We measured around 800 fault planes and their striaes with the sense of movement in order to characterize the stress field. The software used to make the stress inversion were Tensor (Delvaux, 2011) and Multiple Inverse Method MIM (Yamaji et al., 2011). The stress field map was built with the results of the MIM. We present new data from 48 sites located in the northern sector of the Southern Patagonian Andes. The measurements were made in several rocks from Paleozoic to Lower Cretaceous, even though most were taken in pyroclastic jurassic rocks from El Quemado Complex. Paleostress tensors obtained are mostly strike-slip, although a 25% is normal and there are a few compresional. The pattern of faults found is complex. In some sites the tensor can be locally linked to satellite images and observations from the field or be related to a major thrust front. There is no clear correlation between the age and/or lithology with the tensor since the youngest rocks measured are Lower Cretaceous. Probably there are several generations of family faults connected to different and recent tectonic phases then the paleostress tensors might correspond to the latest tectonic events.

Solutions on a brane in a bulk spacetime with Kalb–Ramond field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chakraborty, Sumanta, E-mail: sumanta@iucaa.in; SenGupta, Soumitra, E-mail: tpssg@iacs.res.in

Effective gravitational field equations on a brane have been derived, when the bulk spacetime is endowed with the second rank antisymmetric Kalb–Ramond field. Since both the graviton and the Kalb–Ramond field are closed string excitations, they can propagate in the bulk. After deriving the effective gravitational field equations on the brane, we solve them for a static spherically symmetric solution. It turns out that the solution so obtained represents a black hole or naked singularity depending on the parameter space of the model. The stability of this model is also discussed. Cosmological solutions to the gravitational field equations have beenmore » obtained, where the Kalb–Ramond field is found to behave as normal pressure free matter. For certain specific choices of the parameters in the cosmological solution, the solution exhibits a transition in the behaviour of the scale factor and hence a transition in the expansion history of the universe. The possibility of accelerated expansion of the universe in this scenario is also discussed.« less

The total energy-momentum tensor for electromagnetic fields in a dielectric

NASA Astrophysics Data System (ADS)

Crenshaw, Michael E.

2017-08-01

Radiation pressure is an observable consequence of optically induced forces on materials. On cosmic scales, radiation pressure is responsible for the bending of the tails of comets as they pass near the sun. At a much smaller scale, optically induced forces are being investigated as part of a toolkit for micromanipulation and nanofabrication technology [1]. A number of practical applications of the mechanical effects of light-matter interaction are discussed by Qiu, et al. [2]. The promise of the nascent nanophotonic technology for manufacturing small, low-power, high-sensitivity sensors and other devices has likely motivated the substantial current interest in optical manipulation of materials at the nanoscale, see, for example, Ref. [2] and the references therein. While substantial progress toward optical micromanipulation has been achieved, e.g. optical tweezers [1], in this report we limit our consideration to the particular issue of optically induced forces on a transparent dielectric material. As a matter of electromagnetic theory, these forces remain indeterminate and controversial. Due to the potential applications in nanotechnology, the century-old debate regarding these forces, and the associated momentums, has ramped up considerably in the physics community. The energy-momentum tensor is the centerpiece of conservation laws for the unimpeded, inviscid, incompressible flow of non-interacting particles in the continuum limit in an otherwise empty volume. The foundations of the energy-momentum tensor and the associated tensor conservation theory come to electrodynamics from classical continuum dynamics by applying the divergence theorem to a Taylor series expansion of a property density field of a continuous flow in an otherwise empty volume. The dust tensor is a particularly simple example of an energy-momentum tensor that deals with particles of matter in the continuum limit in terms of the mass density ρm, energy density ρmc 2 , and momentum density ρmv. Newtonian fluids can behave very much like dust with the same energy-momentum tensor. The energy and momentum conservation properties of light propagating in the vacuum were long-ago cast in the energy-momentum tensor formalism in terms of the electromagnetic energy density and electromagnetic momentum density. However, extrapolating the tensor theory of energy-momentum conservation for propagation of light in the vacuum to propagation of light in a simple linear dielectric medium has proven to be problematic and controversial. A dielectric medium is not "otherwise empty" and it is typically assumed that optically induced forces accelerate and decelerate nanoscopic material constituents of the dielectric. The corresponding material energy-momentum tensor is added to the electromagnetic energy-momentum tensor to form the total energy-momentum tensor, thereby ensuring that the total energy and the total momentum of the thermodynamically closed system remain constant in time.

Detection, localization and classification of multiple dipole-like magnetic sources using magnetic gradient tensor data

NASA Astrophysics Data System (ADS)

Gang, Yin; Yingtang, Zhang; Hongbo, Fan; Zhining, Li; Guoquan, Ren

2016-05-01

We have developed a method for automatic detection, localization and classification (DLC) of multiple dipole sources using magnetic gradient tensor data. First, we define modified tilt angles to estimate the approximate horizontal locations of the multiple dipole-like magnetic sources simultaneously and detect the number of magnetic sources using a fixed threshold. Secondly, based on the isotropy of the normalized source strength (NSS) response of a dipole, we obtain accurate horizontal locations of the dipoles. Then the vertical locations are calculated using magnitude magnetic transforms of magnetic gradient tensor data. Finally, we invert for the magnetic moments of the sources using the measured magnetic gradient tensor data and forward model. Synthetic and field data sets demonstrate effectiveness and practicality of the proposed method.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berezhiani, Lasha; Khoury, Justin; Wang, Junpu, E-mail: lashaber@gmail.com, E-mail: jkhoury@sas.upenn.edu, E-mail: jwang217@jhu.edu

Single-field perturbations satisfy an infinite number of consistency relations constraining the squeezed limit of correlation functions at each order in the soft momentum. These can be understood as Ward identities for an infinite set of residual global symmetries, or equivalently as Slavnov-Taylor identities for spatial diffeomorphisms. In this paper, we perform a number of novel, non-trivial checks of the identities in the context of single field inflationary models with arbitrary sound speed. We focus for concreteness on identities involving 3-point functions with a soft external mode, and consider all possible scalar and tensor combinations for the hard-momentum modes. In allmore » these cases, we check the consistency relations up to and including cubic order in the soft momentum. For this purpose, we compute for the first time the 3-point functions involving 2 scalars and 1 tensor, as well as 2 tensors and 1 scalar, for arbitrary sound speed.« less

Electronic structures and magnetic/optical properties of metal phthalocyanine complexes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baba, Shintaro; Suzuki, Atsushi, E-mail: suzuki@mat.usp.ac.jp; Oku, Takeo

2016-02-01

Electronic structures and magnetic / optical properties of metal phthalocyanine complexes were studied by quantum calculations using density functional theory. Effects of central metal and expansion of π orbital on aromatic ring as conjugation system on the electronic structures, magnetic, optical properties and vibration modes of infrared and Raman spectra of metal phthalocyanines were investigated. Electron and charge density distribution and energy levels near frontier orbital and excited states were influenced by the deformed structures varied with central metal and charge. The magnetic parameters of chemical shifts in {sup 13}C-nuclear magnetic resonance ({sup 13}C-NMR), principle g-tensor, A-tensor, V-tensor of electricmore » field gradient and asymmetry parameters derived from the deformed structures with magnetic interaction of nuclear quadruple interaction based on electron and charge density distribution with a bias of charge near ligand under crystal field.« less

Observational constraints on monomial warm inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Visinelli, Luca, E-mail: Luca.Visinelli@studio.unibo.it

Warm inflation is, as of today, one of the best motivated mechanisms for explaining an early inflationary period. In this paper, we derive and analyze the current bounds on warm inflation with a monomial potential U ∝ φ {sup p} , using the constraints from the PLANCK mission. In particular, we discuss the parameter space of the tensor-to-scalar ratio r and the potential coupling λ of the monomial warm inflation in terms of the number of e-folds. We obtain that the theoretical tensor-to-scalar ratio r ∼ 10{sup −8} is much smaller than the current observational constrain r ∼< 0.12, despitemore » a relatively large value of the field excursion Δ φ ∼ 0.1 M {sub Pl}. Warm inflation thus eludes the Lyth bound set on the tensor-to-scalar ratio by the field excursion.« less

Extended vector-tensor theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: rampei@th.phys.titech.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: yoshida@th.phys.titech.ac.jp

Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Procamore » theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.« less

Topological Triply Degenerate Points Induced by Spin-Tensor-Momentum Couplings

NASA Astrophysics Data System (ADS)

Hu, Haiping; Hou, Junpeng; Zhang, Fan; Zhang, Chuanwei

2018-06-01

The recent discovery of triply degenerate points (TDPs) in topological materials has opened a new perspective toward the realization of novel quasiparticles without counterparts in quantum field theory. The emergence of such protected nodes is often attributed to spin-vector-momentum couplings. We show that the interplay between spin-tensor- and spin-vector-momentum couplings can induce three types of TDPs, classified by different monopole charges (C =±2 , ±1 , 0). A Zeeman field can lift them into Weyl points with distinct numbers and charges. Different TDPs of the same type are connected by intriguing Fermi arcs at surfaces, and transitions between different types are accompanied by level crossings along high-symmetry lines. We further propose an experimental scheme to realize such TDPs in cold-atom optical lattices. Our results provide a framework for studying spin-tensor-momentum coupling-induced TDPs and other exotic quasiparticles.

Theoretical frameworks for testing relativistic gravity. IV - A compendium of metric theories of gravity and their post-Newtonian limits.

NASA Technical Reports Server (NTRS)

Ni, W.-T.

1972-01-01

Metric theories of gravity are compiled and classified according to the types of gravitational fields they contain, and the modes of interaction among those fields. The gravitation theories considered are classified as (1) general relativity, (2) scalar-tensor theories, (3) conformally flat theories, and (4) stratified theories with conformally flat space slices. The post-Newtonian limit of each theory is constructed and its Parametrized Post-Newtonian (PPN) values are obtained by comparing it with Will's version of the formalism. Results obtained here, when combined with experimental data and with recent work by Nordtvedt and Will and by Ni, show that, of all theories thus far examined by our group, the only currently viable ones are general relativity, the Bergmann-Wagoner scalar-tensor theory and its special cases (Nordtvedt; Brans-Dicke-Jordan), and a recent, new vector-tensor theory by Nordtvedt, Hellings, and Will.

Statistical Decoupling of a Lagrangian Fluid Parcel in Newtonian Cosmology

NASA Astrophysics Data System (ADS)

Wang, Xin; Szalay, Alex

2016-03-01

The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.

STATISTICAL DECOUPLING OF A LAGRANGIAN FLUID PARCEL IN NEWTONIAN COSMOLOGY

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Xin; Szalay, Alex, E-mail: xwang@cita.utoronto.ca

The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differentialmore » equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.« less

Compact objects in relativistic theories of gravity

NASA Astrophysics Data System (ADS)

Okada da Silva, Hector

2017-05-01

In this dissertation we discuss several aspects of compact objects, i.e. neutron stars and black holes, in relativistic theories of gravity. We start by studying the role of nuclear physics (encoded in the so-called equation of state) in determining the properties of neutron stars in general relativity. We show that low-mass neutron stars are potentially useful astrophysical laboratories that can be used to constrain the properties of the equation of state. More specifically, we show that various bulk properties of these objects, such as their quadrupole moment and tidal deformability, are tightly correlated. Next, we develop a formalism that aims to capture how generic modifications from general relativity affect the structure of neutron stars, as predicted by a broad class of gravity theories, in the spirit of the parametrized post-Newtonian formalism (PPN). Our "post-Tolman-Oppenheimer-Volkoff" formalism provides a toolbox to study both stellar structure and the interior/exterior geometries of static, spherically symmetric relativistic stars. We also apply the formalism to parametrize deviations from general relativity in various astrophysical observables related with neutron stars, including surface redshift, apparent radius, Eddington luminosity. We then turn our attention to what is arguably the most well-motivated and well-investigated generalization of general relativity: scalar-tensor theory. We start by considering theories where gravity is mediated by a single extra scalar degree of freedom (in addition to the metric tensor). An interesting class of scalar-tensor theories passes all experimental tests in the weak-field regime of gravity, yet considerably deviates from general relativity in the strong-field regime in the presence of matter. A common assumption in modeling neutron stars is that the pressure within these object is spatially isotropic. We relax this assumption and examine how pressure anisotropy affects the mass, radius and moment of inertia of slowly rotating neutron stars, both in general relativity and in scalar-tensor gravity. We show that a sufficient amount of pressure anisotropy results in neutron star models whose properties in scalar-tensor theory deviate significantly from their general relativistic counterparts. Moreover, the presence of anisotropy allows these deviations to be considerable even for values of the theory's coupling parameter for which neutron stars in scalar-tensor theory would be otherwise indistinguishable from those in general relativity. Within scalar-tensor theory we also investigate the effects of the scalar field on the crustal torsional oscillations of neutron stars, which have been associated to quasi-periodic oscillations in the X-ray spectra in the aftermath of giant flares. We show that the presence of the scalar field has an influence on the thickness of the stellar crust, and investigate how it affects the oscillation frequencies. Deviations from the predictions of general relativity can be large for certain values of the theory's coupling parameter. However, the influence of the scalar field is degenerate with uncertainties in the equation of state of the star's crust and microphysics effects (electron screening) for values of the coupling allowed by binary pulsar observations. We also derive the stellar structure equations for slowly-rotating neutron stars in a broader class of scalar-tensor theories in which matter and scalar field are coupled through the so-called disformal coupling. We study in great detail how the disformal coupling affects the structure of neutron stars, and we investigate the existence of universal (equation of state-independent) relations connecting the stellar compactness and moment of inertia. In particular, we find that these universal relations can deviate considerably from the predictions of general relativity. (Abstract shortened by ProQuest.).

Compact Feeding Network for Array Radiations of Spoof Surface Plasmon Polaritons

NASA Astrophysics Data System (ADS)

Xu, Jun Jun; Yin, Jia Yuan; Zhang, Hao Chi; Cui, Tie Jun

2016-03-01

We propose a splitter feeding network for array radiations of spoof surface plasmon polaritons (SPPs), which are guided by ultrathin corrugated metallic strips. Based on the coupled mode theory, SPP fields along a single waveguide in a certain frequency range can be readily coupled into two adjacent branch waveguides with the same propagation constants. We propose to load U-shaped particles anti-symmetrically at the ends of such two branch waveguides, showing a high integration degree of the feeding network. By controlling linear phase modulations produced by the U-shaped particle chain, we demonstrate theoretically and experimentally that the SPP fields based on bound modes can be efficiently radiated to far fields in broadside direction. The proposed method shows that the symmetry of electromagnetic field modes can be exploited to the SPP transmission network, providing potential solutions to compact power dividers and combiners for microwave and optical devices and systems.

Photo-Nernst current in graphene

NASA Astrophysics Data System (ADS)

Cao, Helin; Aivazian, Grant; Fei, Zaiyao; Ross, Jason; Cobden, David H.; Xu, Xiaodong

2016-03-01

Photocurrent measurements provide a powerful means of studying the spatially resolved optoelectronic and electrical properties of a material or device. Generally speaking there are two classes of mechanism for photocurrent generation: those involving separation of electrons and holes, and thermoelectric effects driven by electron temperature gradients. Here we introduce a new member in the latter class: the photo-Nernst effect. In graphene devices in a perpendicular magnetic field we observe photocurrent generated uniformly along the free edges, with opposite sign at opposite edges. The signal is antisymmetric in field, shows a peak versus gate voltage at the neutrality point flanked by wings of opposite sign at low fields, and exhibits quantum oscillations at higher fields. These features are all explained by the Nernst effect associated with laser-induced electron heating. This `photo-Nernst’ current provides a simple and clear demonstration of the Shockley-Ramo nature of long-range photocurrent generation in a gapless material.

Quantum field theory in spaces with closed timelike curves

NASA Astrophysics Data System (ADS)

Boulware, David G.

1992-11-01

Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.

Physics of Gravitational Interaction: Geometry of Space or Quantum Field in Space

NASA Astrophysics Data System (ADS)

Baryshev, Yurij

2006-03-01

Thirring-Feynman's tensor field approach to gravitation opens new understanding on the physics of gravitational interaction and stimulates novel experiments on the nature of gravity. According to Field Gravity, the universal gravity force is caused by exchange of gravitons - the quanta of gravity field. Energy of this field is well-defined and excludes the singularity. All classical relativistic effects are the same as in General Relativity. The intrinsic scalar (spin 0) part of gravity field corresponds to ``antigravity'' and only together with the pure tensor (spin 2) part gives the usual Newtonian force. Laboratory and astrophysical experiments which may test the predictions of FG, will be performed in near future. In particular, observations at gravity observatories with bar and interferometric detectors, like Explorer, Nautilus, LIGO and VIRGO, will check the predicted scalar gravitational waves from supernova explosions. New types of cosmological models in Minkowski space are possible too.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Park, Jong-Kyu; Logan, Nikolas C.

Toroidal torque is one of the most important consequences of non-axisymmetric fields in tokamaks. The well-known neoclassical toroidal viscosity (NTV) is due to the second-order toroidal force from anisotropic pressure tensor in the presence of these asymmetries. This work shows that the first-order toroidal force originating from the same anisotropic pressure tensor, despite having no flux surface average, can significantly modify the local perturbed force balance and thus must be included in perturbed equilibrium self-consistent with NTV. The force operator with an anisotropic pressure tensor is not self-adjoint when the NTV torque is finite and thus is solved directly formore » each component. This approach yields a modified, non-self-adjoint Euler-Lagrange equation that can be solved using a variety of common drift-kinetic models in generalized tokamak geometry. The resulting energy and torque integral provides a unique way to construct a torque response matrix, which contains all the information of self-consistent NTV torque profiles obtainable by applying non-axisymmetric fields to the plasma. This torque response matrix can then be used to systematically optimize non-axisymmetric field distributions for desired NTV profiles. Published by AIP Publishing.« less

Computer Tensor Codes to Design the War Drive

NASA Astrophysics Data System (ADS)

Maccone, C.

To address problems in Breakthrough Propulsion Physics (BPP) and design the Warp Drive one needs sheer computing capabilities. This is because General Relativity (GR) and Quantum Field Theory (QFT) are so mathematically sophisticated that the amount of analytical calculations is prohibitive and one can hardly do all of them by hand. In this paper we make a comparative review of the main tensor calculus capabilities of the three most advanced and commercially available “symbolic manipulator” codes. We also point out that currently one faces such a variety of different conventions in tensor calculus that it is difficult or impossible to compare results obtained by different scholars in GR and QFT. Mathematical physicists, experimental physicists and engineers have each their own way of customizing tensors, especially by using different metric signatures, different metric determinant signs, different definitions of the basic Riemann and Ricci tensors, and by adopting different systems of physical units. This chaos greatly hampers progress toward the design of the Warp Drive. It is thus suggested that NASA would be a suitable organization to establish standards in symbolic tensor calculus and anyone working in BPP should adopt these standards. Alternatively other institutions, like CERN in Europe, might consider the challenge of starting the preliminary implementation of a Universal Tensor Code to design the Warp Drive.

Intrinsic Decomposition of The Stretch Tensor for Fibrous Media

NASA Astrophysics Data System (ADS)

Kellermann, David C.

2010-05-01

This paper presents a novel mechanism for the description of fibre reorientation based on the decomposition of the stretch tensor according to a given material's intrinsic constitutive properties. This approach avoids the necessity for fibre directors, structural tensors or specialised model such as the ideal fibre reinforced model, which are commonly applied to the analysis of fibre kinematics in the finite deformation of fibrous media for biomechanical problems. The proposed approach uses Intrinsic-Field Tensors (IFTs) that build upon the linear orthotropic theory presented in a previous paper entitled Strongly orthotropic continuum mechanics and finite element treatment. The intrinsic decomposition of the stretch tensor therein provides superior capacity to represent the intermediary kinematics driven by finite orthotropic ratios, where the benefits are predominantly expressed in cases of large deformation as is typical in the biomechanical studies. Satisfaction of requirements such as Material Frame-Indifference (MFI) and Euclidean objectivity are demonstrated here—these factors being necessary for the proposed IFTs to be valid tensorial quantities. The resultant tensors, initially for the simplest case of linear elasticity, are able to describe the same fibre reorientation as would the contemporary approaches such as with use of structural tensors and the like, while additionally being capable of showing results intermediary to classical isotropy and the infinitely orthotropic representations. This intermediary case is previously unreported.

Inflation in Einstein-Cartan theory with energy-momentum tensor with spin

NASA Technical Reports Server (NTRS)

Fennelly, A. J.; Bradas, James C.; Smalley, Larry L.

1988-01-01

Generalized, or power-law, inflation is shown to necessarily exist for a simple, anisotropic (Bianchi Type I) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley (RS) improved energy-momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density.

Quantum corrections to the stress-energy tensor in thermodynamic equilibrium with acceleration

NASA Astrophysics Data System (ADS)

Becattini, F.; Grossi, E.

2015-08-01

We show that the stress-energy tensor has additional terms with respect to the ideal form in states of global thermodynamic equilibrium in flat spacetime with nonvanishing acceleration and vorticity. These corrections are of quantum origin and their leading terms are second order in the gradients of the thermodynamic fields. Their relevant coefficients can be expressed in terms of correlators of the stress-energy tensor operator and the generators of the Lorentz group. With respect to previous assessments, we find that there are more second-order coefficients and that all thermodynamic functions including energy density receive acceleration and vorticity dependent corrections. Notably, also the relation between ρ and p , that is, the equation of state, is affected by acceleration and vorticity. We have calculated the corrections for a free real scalar field—both massive and massless—and we have found that they increase, particularly for a massive field, at very high acceleration and vorticity and very low temperature. Finally, these nonideal terms depend on the explicit form of the stress-energy operator, implying that different stress-energy tensors of the scalar field—canonical or improved—are thermodynamically inequivalent.

Generalized wave operators, weighted Killing fields, and perturbations of higher dimensional spacetimes

NASA Astrophysics Data System (ADS)

Araneda, Bernardo

2018-04-01

We present weighted covariant derivatives and wave operators for perturbations of certain algebraically special Einstein spacetimes in arbitrary dimensions, under which the Teukolsky and related equations become weighted wave equations. We show that the higher dimensional generalization of the principal null directions are weighted conformal Killing vectors with respect to the modified covariant derivative. We also introduce a modified Laplace–de Rham-like operator acting on tensor-valued differential forms, and show that the wave-like equations are, at the linear level, appropriate projections off shell of this operator acting on the curvature tensor; the projection tensors being made out of weighted conformal Killing–Yano tensors. We give off shell operator identities that map the Einstein and Maxwell equations into weighted scalar equations, and using adjoint operators we construct solutions of the original field equations in a compact form from solutions of the wave-like equations. We study the extreme and zero boost weight cases; extreme boost corresponding to perturbations of Kundt spacetimes (which includes near horizon geometries of extreme black holes), and zero boost to static black holes in arbitrary dimensions. In 4D our results apply to Einstein spacetimes of Petrov type D and make use of weighted Killing spinors.

Gauge-origin dependence in electronic g-tensor calculations

NASA Astrophysics Data System (ADS)

Glasbrenner, Michael; Vogler, Sigurd; Ochsenfeld, Christian

2018-06-01

We present a benchmark study on the gauge-origin dependence of the electronic g-tensor using data from unrestricted density functional theory calculations with the spin-orbit mean field ansatz. Our data suggest in accordance with previous studies that g-tensor calculations employing a common gauge-origin are sufficiently accurate for small molecules; however, for extended molecules, the introduced errors can become relevant and significantly exceed the basis set error. Using calculations with the spin-orbit mean field ansatz and gauge-including atomic orbitals as a reference, we furthermore show that the accuracy and reliability of common gauge-origin approaches in larger molecules depends strongly on the locality of the spin density distribution. We propose a new pragmatic ansatz for choosing the gauge-origin which takes the spin density distribution into account and gives reasonably accurate values for molecules with a single localized spin center. For more general cases like molecules with several spatially distant spin centers, common gauge-origin approaches are shown to be insufficient for consistently achieving high accuracy. Therefore the computation of g-tensors using distributed gauge-origin methods like gauge-including atomic orbitals is considered as the ideal approach and is recommended for larger molecular systems.

Azimuthally and radially excited charge transfer plasmon and Fano lineshapes in conductive sublayer-mediated nanoassemblies.

PubMed

Ahmadivand, Arash; Gerislioglu, Burak; Pala, Nezih

2017-11-01

Here, the plasmon responses of both symmetric and antisymmetric oligomers on a conductive substrate under linear, azimuthal, and radial polarization excitations are analyzed numerically. By observing charge transfer plasmons under cylindrical vector beam (CVB) illumination for what we believe is the first time, we show that our studies open new horizons to induce significant charge transfer plasmons and antisymmetric Fano resonance lineshapes in metallic substrate-mediated plasmonic nanoclusters under both azimuthal and radial excitation as CVBs.

Phase-space quantum mechanics study of two identical particles in an external oscillatory potential

NASA Technical Reports Server (NTRS)

Nieto, Luis M.; Gadella, Manuel

1993-01-01

This simple example is used to show how the formalism of Moyal works when it is applied to systems of identical particles. The symmetric and antisymmetric Moyal propagators are evaluated for this case; from them, the correct energy levels of energy are obtained, as well as the Wigner functions for the symmetric and antisymmetric states of the two identical particle system. Finally, the solution of the Bloch equation is straightforwardly obtained from the expressions of the Moyal propagators.

Higher rank ABJM Wilson loops from matrix models

DOE PAGES

Cookmeyer, Jonathan; Liu, James T.; Pando Zayas, Leopoldo A.

2016-11-21

We compute the vacuum expectation values of 1/6 supersymmetric Wilson loops in higher dimensional representations of the gauge group in ABJM theory. We then present results for the m-symmetric and m-antisymmetric representations by exploiting standard matrix model techniques. At leading order, in the saddle point approximation, our expressions reproduce holographic results from both D6 and D2 branes corresponding to the antisymmetric and symmetric representations, respectively. We also compute 1/N corrections to the leading saddle point results.

A practical introduction to tensor networks: Matrix product states and projected entangled pair states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Orús, Román, E-mail: roman.orus@uni-mainz.de

This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas in the field, specially regarding the numerics. After a very general introduction we motivate the concept of tensor network and provide several examples. We then move on to explain some basics about Matrix Product States (MPS) and Projected Entangled Pair States (PEPS). Selected details on some of the associated numerical methods for 1d and 2d quantum lattice systems aremore » also discussed. - Highlights: • A practical introduction to selected aspects of tensor network methods is presented. • We provide analytical examples of MPS and 2d PEPS. • We provide basic aspects on several numerical methods for MPS and 2d PEPS. • We discuss a number of applications of tensor network methods from a broad perspective.« less

Fermionic topological quantum states as tensor networks

NASA Astrophysics Data System (ADS)

Wille, C.; Buerschaper, O.; Eisert, J.

2017-06-01

Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.

b matrix errors in echo planar diffusion tensor imaging

PubMed Central

Boujraf, Saïd; Luypaert, Robert; Osteaux, Michel

2001-01-01

Diffusion‐weighted magnetic resonance imaging (DW‐MRI) is a recognized tool for early detection of infarction of the human brain. DW‐MRI uses the signal loss associated with the random thermal motion of water molecules in the presence of magnetic field gradients to derive parameters that reflect the translational mobility of the water molecules in tissues. If diffusion‐weighted images with different values of b matrix are acquired during one individual investigation, it is possible to calculate apparent diffusion coefficient maps that are the elements of the diffusion tensor. The diffusion tensor elements represent the apparent diffusion coefficient of protons of water molecules in each pixel in the corresponding sample. The relation between signal intensity in the diffusion‐weighted images, diffusion tensor, and b matrix is derived from the Bloch equations. Our goal is to establish the magnitude of the error made in the calculation of the elements of the diffusion tensor when the imaging gradients are ignored. PACS number(s): 87.57. –s, 87.61.–c PMID:11602015

Steps to reconcile inflationary tensor and scalar spectra

NASA Astrophysics Data System (ADS)

Miranda, Vinícius; Hu, Wayne; Adshead, Peter

2014-05-01

The recent BICEP2 B-mode polarization determination of an inflationary tensor-scalar ratio r=0.2-0.05+0.07 is in tension with simple scale-free models of inflation due to a lack of a corresponding low multipole excess in the temperature power spectrum which places a limit of r0.002<0.11 (95% C.L.) on such models. Single-field inflationary models that reconcile these two observations, even those where the tilt runs substantially, introduce a scale into the scalar power spectrum. To cancel the tensor excess, and simultaneously remove the excess already present without tensors, ideally the model should introduce this scale as a relatively sharp transition in the tensor-scalar ratio around the horizon at recombination. We consider models which generate such a step in this quantity and find that they can improve the joint fit to the temperature and polarization data by up to 2ΔlnL≈-14 without changing cosmological parameters. Precision E-mode polarization measurements should be able to test this explanation.

Real-space mapping of the strongly coupled plasmons of nanoparticle dimers.

PubMed

Kim, Deok-Soo; Heo, Jinhwa; Ahn, Sung-Hyun; Han, Sang Woo; Yun, Wan Soo; Kim, Zee Hwan

2009-10-01

We carried out the near-field optical imaging of isolated and dimerized gold nanocubes to directly investigate the strong coupling between two adjacent nanoparticles. The high-resolution (approximately 10 nm) local field maps (intensities and phases) of self-assembled nanocube dimers reveal antisymmetric plasmon modes that are starkly different from a simple superposition of two monomeric dipole plasmons, which is fully reproduced by the electrodynamics simulations. The result decisively proves that, for the closely spaced pair of nanoparticles (interparticle distance/particle size approximately 0.04), the strong Coulombic attraction between the charges at the interparticle gap dominates over the intraparticle charge oscillations, resulting in a hybridized dimer plasmon mode that is qualitatively different from those expected from a simple dipole-dipole coupling model.

Surgical wound monitoring by MRI with a metamaterial-based implanted local coil

NASA Astrophysics Data System (ADS)

Kamel, Hanan; Syms, Richard R. A.; Kardoulaki, Evdokia M.; Rea, Marc

2018-03-01

An implantable sensor for monitoring surgical wounds after bowel reconstruction is proposed. The sensor consists of a coupled pair of 8-element magneto-inductive ring resonators, designed for mounting on a biofragmentable anastomosis ring to give a local increase in signal-to-noise ratio near an annular wound during 1H magnetic resonance imaging. Operation on an anti-symmetric spatial mode is used to avoid coupling to the B1 field during excitation, and a single wired connection is used for MRI signal output. The electrical response and field-of-view are estimated theoretically. Prototypes are constructed from flexible elements designed for operation at 1.5 T, electrical responses are characterized and local SNR enhancement is confirmed using agar gel phantoms.

New observations, new theoretical results and controversies regarding PC 3-5 waves

NASA Astrophysics Data System (ADS)

Takahashi, K.

Observations and theories of medium- to long-period (Pc 3-5) magnetic pulsations excited by magnetospheric particles are described. Satellite observations indicate that most pulsations can be classified into two groups according to their magnetic field polarization. One group has a transverse magnetic perturbation and the other strongly compressional perturbation. Despite this difference in polarization they share common characteristics, including large azimuthal wave number, westward propagation, and antisymmetric field-aligned structure. Recent theories describe these observations in a unified framework. It has been pointed out that trapped energetic ions play an important role in determining the instability threshold and the mode structure of the pulsations. Observations and theories of energetic particle response to the excited pulsations are also described.

Measurement of the β-asymmetry parameter of Cu67 in search for tensor-type currents in the weak interaction

NASA Astrophysics Data System (ADS)

Soti, G.; Wauters, F.; Breitenfeldt, M.; Finlay, P.; Herzog, P.; Knecht, A.; Köster, U.; Kraev, I. S.; Porobic, T.; Prashanth, P. N.; Towner, I. S.; Tramm, C.; Zákoucký, D.; Severijns, N.

2014-09-01

Background: Precision measurements at low energy search for physics beyond the standard model in a way complementary to searches for new particles at colliders. In the weak sector the most general β-decay Hamiltonian contains, besides vector and axial-vector terms, also scalar, tensor, and pseudoscalar terms. Current limits on the scalar and tensor coupling constants from neutron and nuclear β decay are on the level of several percent. Purpose: Extracting new information on tensor coupling constants by measuring the β-asymmetry parameter in the pure Gamow-Teller decay of Cu67, thereby testing the V-A structure of the weak interaction. Method: An iron sample foil into which the radioactive nuclei were implanted was cooled down to mK temperatures in a 3He-4He dilution refrigerator. An external magnetic field of 0.1 T, in combination with the internal hyperfine magnetic field, oriented the nuclei. The anisotropic β radiation was observed with planar high-purity germanium detectors operating at a temperature of about 10 K. An on-line measurement of the β asymmetry of Cu68 was performed as well for normalization purposes. Systematic effects were investigated using geant4 simulations. Results: The experimental value, Ã=0.587(14), is in agreement with the standard model value of 0.5991(2) and is interpreted in terms of physics beyond the standard model. The limits obtained on possible tensor-type charged currents in the weak interaction Hamiltonian are -0.045<(CT+CT')/CA<0.159 (90% C.L.). Conclusions: The obtained limits are comparable to limits from other correlation measurements in nuclear β decay and contribute to further constraining tensor coupling constants.

Mesoscopic model for the viscosities of nematic liquid crystals.

PubMed

Chrzanowska, A; Kröger, M; Sellers, S

1999-10-01

Based on the definition of the mesoscopic concept by Blenk et al. [Physica A 174, 119 (1991); J. Noneq. Therm. 16, 67 (1991); Mol. Cryst. Liq. Cryst. 204, 133 (1991)] an approach to calculate the Leslie viscosity coefficients for nematic liquid crystals is presented. The approach rests upon the mesoscopic stress tensor, whose structure is assumed similar to the macroscopic Leslie viscous stress. The proposed form is also the main dissipation part of the mesoscopic Navier-Stokes equation. On the basis of the correspondence between microscopic and mesoscopic scales a mean-field mesoscopic potential is introduced. It allows us to obtain the stress tensor angular velocity of the free rotating molecules with the help of the orientational Fokker-Planck equation. The macroscopic stress tensor is calculated as an average of the mesoscopic counterpart. Appropriate relations among mesoscopic viscosities have been found. The mesoscopic analysis results are shown to be consistent with the diffusional model of Kuzuu-Doi and Osipov-Terentjev with the exception of the shear viscosity alpha(4). In the nematic phase alpha(4) is shown to have two contributions: isotropic and nematic. There exists an indication that the influence of the isotropic part is dominant over the nematic part. The so-called microscopic stress tensor used in the microscopic theories is shown to be the mean-field potential-dependent representation of the mesoscopic stress tensor. In the limiting case of total alignment the Leslie coefficients are estimated for the diffusional and mesoscopic models. They are compared to the results of the affine transformation model of the perfectly ordered systems. This comparison shows disagreement concerning the rotational viscosity, whereas the coefficients characteristic for the symmetric part of the viscous stress tensor remain the same. The difference is caused by the hindered diffusion in the affine model case.

Dynamos driven by weak thermal convection and heterogeneous outer boundary heat flux

NASA Astrophysics Data System (ADS)

Sahoo, Swarandeep; Sreenivasan, Binod; Amit, Hagay

2016-01-01

We use numerical dynamo models with heterogeneous core-mantle boundary (CMB) heat flux to show that lower mantle lateral thermal variability may help support a dynamo under weak thermal convection. In our reference models with homogeneous CMB heat flux, convection is either marginally supercritical or absent, always below the threshold for dynamo onset. We find that lateral CMB heat flux variations organize the flow in the core into patterns that favour the growth of an early magnetic field. Heat flux patterns symmetric about the equator produce non-reversing magnetic fields, whereas anti-symmetric patterns produce polarity reversals. Our results may explain the existence of the geodynamo prior to inner core nucleation under a tight energy budget. Furthermore, in order to sustain a strong geomagnetic field, the lower mantle thermal distribution was likely dominantly symmetric about the equator.

Mechanical properties of non-centrosymmetric CePt3Si and CePt3B

NASA Astrophysics Data System (ADS)

Rogl, G.; Legut, D.; Sýkora, R.; Müller, P.; Müller, H.; Bauer, E.; Puchegger, S.; Zehetbauer, M.; Rogl, P.

2017-05-01

Elastic moduli, hardness (both at room temperature) and thermal expansion (4.2-670 K) have been experimentally determined for polycrystalline CePt3Si and its prototype compound CePt3B as well as for single-crystalline CePt3Si. Resonant ultrasound spectroscopy was used to determine elastic properties (Young’s modulus E and Poisson’s ratio ν) via the eigenfrequencies of the sample and the knowledge of sample mass and dimensions. Bulk and shear moduli were calculated from E and ν, and the respective Debye temperatures were derived. In addition, ab initio DFT calculations were carried out for both compounds. A comparison of parameters evaluated from DFT with those of experiments revealed, in general, satisfactory agreement. Positive and negative thermal expansion values obtained from CePt3Si single crystal data are fairly well explained in terms of the crystalline electric field model, using CEF parameters derived recently from inelastic neutron scattering. DFT calculations, in addition, demonstrate that the atomic vibrations keep almost unaffected by the antisymmetric spin-orbit coupling present in systems with crystal structures having no inversion symmetry. This is opposite to electronic properties, where the antisymmetric spin-orbit interaction has shown to distinctly influence features like the superconducting condensate of CePt3Si.

Modeling of a rotary motor driven by an anisotropic piezoelectric composite laminate.

PubMed

Zhu, M L; Lee, S R; Zhang, T Y; Tong, P

2000-01-01

This paper proposes an analytical model of a rotary motor driven by an anisotropic piezoelectric composite laminate. The driving element of the motor is a three-layer laminated plate. A piezoelectric layer is sandwiched between two anti-symmetric composite laminae. Because of the material anisotropy and the anti-symmetric configuration, torsional vibration can be induced through the inplane strain actuated by the piezoelectric layer. The advantages of the motor are its magnetic field immunity, simple structure, easy maintenance, low cost, and good low-speed performance. In this paper, the motor is considered to be a coupled dynamic system. The analytical model includes the longitudinal and torsional vibrations of the laminate and the rotating motion of the rotor under action of contact forces. The analytical model can predict the overall characteristics of the motor, including the modal frequency and the response of motion of the laminate, the rotating speed of the rotor, the input power, the output power, and the efficiency of the motor. The effects of the initial compressive force, the applied voltage, the moment of rotor inertia, and the frictional coefficient of the contact interface on the characteristics of the motor are simulated and discussed. A selection of the numerical results from the analytical model is confirmed by experimental data.

Solution of Einsteins Equation for Deformation of a Magnetized Neutron Star

NASA Astrophysics Data System (ADS)

Rizaldy, R.; Sulaksono, A.

2018-04-01

We studied the effect of very large and non-uniform magnetic field existed in the neutron star on the deformation of the neutron star. We used in our analytical calculation, multipole expansion of the tensor metric and the momentum-energy tensor in Legendre polynomial expansion up to the quadrupole order. In this way we obtain the solutions of Einstein’s equation with the correction factors due to the magnetic field are taken into account. We obtain from our numerical calculation that the degree of deformation (ellipticity) is increased when the the mass is decreased.

Nonassociative differential geometry and gravity with non-geometric fluxes

NASA Astrophysics Data System (ADS)

Aschieri, Paolo; Ćirić, Marija Dimitrijević; Szabo, Richard J.

2018-02-01

We systematically develop the metric aspects of nonassociative differential geometry tailored to the parabolic phase space model of constant locally non-geometric closed string vacua, and use it to construct preliminary steps towards a nonassociative theory of gravity on spacetime. We obtain explicit expressions for the torsion, curvature, Ricci tensor and Levi-Civita connection in nonassociative Riemannian geometry on phase space, and write down Einstein field equations. We apply this formalism to construct R-flux corrections to the Ricci tensor on spacetime, and comment on the potential implications of these structures in non-geometric string theory and double field theory.

The nonlocal elastomagnetoelectrostatics of disordered micropolar media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kabychenkov, A. F.; Lisiovskii, F. V., E-mail: lisf@rambler.ru

The interactions of electric, magnetic, and elastic subsystems in nonlinear disordered micropolar media that possess a bending–torsion tensor and an nonsymmetric strain tensor have been studied in the framework of phenomenological elastomagnetoelectrostatics. A system of nonlinear equations for determining the ground state of these media has been obtained by the variational method. It is shown that nonuniform external and internal rotations not only create elastic stresses, but also generate additional electric and magnetic fields, while nonuniform elastic stresses and external fields induce internal rotations. The nonlocal character of the micropolar media significantly influences elementary excitations and nonlinear dynamic processes.

Multipole plasmons in graphene nanoellipses

NASA Astrophysics Data System (ADS)

Wang, Weihua; Song, Zhengyong

2018-02-01

We study multipole plasmons in graphene nanoellipses under the quasi-static approximation. The graphene is characterized by a homogeneous surface conductivity, and two coupled differential and integral equations are solved self-consistently to investigate the plasmonic modes in nanoellipses with a fixed area. With respect to the major axis, the symmetric and antisymmetric modes originally doubly degenerate in nanodisks will show different behavior as the semi-major axis increases. The eigen frequencies of the symmetric modes decrease, while those of the antisymmetric modes increase. At the edges, the phase changes of the symmetric dipole modes are linear and independent on structural changes; the phase changes of antisymmetric modes deviate from linear relationship, and the deviation depends on the semi-major axis. As a very large aspect ratio, they exhibit sharp peaks at the endpoints of the minor axis and zero phase changes at the endpoints of the major axis. The non-degenerate breathing mode shows its hot spots at the endpoints of the minor axis, and its eigen frequency gradually increases as the semi-major axis increases.

Density functional theory calculations of 95Mo NMR parameters in solid-state compounds.

PubMed

Cuny, Jérôme; Furet, Eric; Gautier, Régis; Le Pollès, Laurent; Pickard, Chris J; d'Espinose de Lacaillerie, Jean-Baptiste

2009-12-21

The application of periodic density functional theory-based methods to the calculation of (95)Mo electric field gradient (EFG) and chemical shift (CS) tensors in solid-state molybdenum compounds is presented. Calculations of EFG tensors are performed using the projector augmented-wave (PAW) method. Comparison of the results with those obtained using the augmented plane wave + local orbitals (APW+lo) method and with available experimental values shows the reliability of the approach for (95)Mo EFG tensor calculation. CS tensors are calculated using the recently developed gauge-including projector augmented-wave (GIPAW) method. This work is the first application of the GIPAW method to a 4d transition-metal nucleus. The effects of ultra-soft pseudo-potential parameters, exchange-correlation functionals and structural parameters are precisely examined. Comparison with experimental results allows the validation of this computational formalism.

On squares of representations of compact Lie algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zeier, Robert, E-mail: robert.zeier@ch.tum.de; Zimborás, Zoltán, E-mail: zimboras@gmail.com

We study how tensor products of representations decompose when restricted from a compact Lie algebra to one of its subalgebras. In particular, we are interested in tensor squares which are tensor products of a representation with itself. We show in a classification-free manner that the sum of multiplicities and the sum of squares of multiplicities in the corresponding decomposition of a tensor square into irreducible representations has to strictly grow when restricted from a compact semisimple Lie algebra to a proper subalgebra. For this purpose, relevant details on tensor products of representations are compiled from the literature. Since the summore » of squares of multiplicities is equal to the dimension of the commutant of the tensor-square representation, it can be determined by linear-algebra computations in a scenario where an a priori unknown Lie algebra is given by a set of generators which might not be a linear basis. Hence, our results offer a test to decide if a subalgebra of a compact semisimple Lie algebra is a proper one without calculating the relevant Lie closures, which can be naturally applied in the field of controlled quantum systems.« less

Spatial distribution of F-net moment tensors for the 2005 West Off Fukuoka Prefecture Earthquake determined by the extended method of the NIED F-net routine

NASA Astrophysics Data System (ADS)

Matsumoto, Takumi; Ito, Yoshihiro; Matsubayashi, Hirotoshi; Sekiguchi, Shoji

2006-01-01

The 2005 West Off Fukuoka Prefecture Earthquake with a Japan Meteorological Agency (JMA) magnitude (MJMA) of 7.0 occurred on March 20, 2005. We determined moment tensor solutions, using a surface wave with an extended method of the NIED F-net routine processing. The horizontal distance to the station is rounded to the nearest interval of 1 km, and the variance reduction approach is applied to a focal depth from 2 km with an interval of 1 km. We obtain the moment tensors of 101 events with (MJMA) exceeding 3.0 and spatial distribution of these moment tensors. The focal mechanism of aftershocks is mainly of the strike-slip type. The alignment of the epicenters in the rupture zone of the main-shock is oriented between N110°E and N130°E, which is close to the strike of the main-shock's moment tensor solutions (N122°E). These moment tensor solutions of intermediatesized aftershocks around the focal region represent basic and important information concerning earthquakes in investigating regional tectonic stress fields, source mechanisms and so on.

A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lagos, Macarena; Baker, Tessa; Ferreira, Pedro G.

We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and ''Beyond Horndeski'' theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbationsmore » that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (à la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.« less

Reconstruction of primordial tensor power spectra from B -mode polarization of the cosmic microwave background

NASA Astrophysics Data System (ADS)

Hiramatsu, Takashi; Komatsu, Eiichiro; Hazumi, Masashi; Sasaki, Misao

2018-06-01

Given observations of the B -mode polarization power spectrum of the cosmic microwave background (CMB), we can reconstruct power spectra of primordial tensor modes from the early Universe without assuming their functional form such as a power-law spectrum. The shape of the reconstructed spectra can then be used to probe the origin of tensor modes in a model-independent manner. We use the Fisher matrix to calculate the covariance matrix of tensor power spectra reconstructed in bins. We find that the power spectra are best reconstructed at wave numbers in the vicinity of k ≈6 ×10-4 and 5 ×10-3 Mpc-1 , which correspond to the "reionization bump" at ℓ≲6 and "recombination bump" at ℓ≈80 of the CMB B -mode power spectrum, respectively. The error bar between these two wave numbers is larger because of the lack of the signal between the reionization and recombination bumps. The error bars increase sharply toward smaller (larger) wave numbers because of the cosmic variance (CMB lensing and instrumental noise). To demonstrate the utility of the reconstructed power spectra, we investigate whether we can distinguish between various sources of tensor modes including those from the vacuum metric fluctuation and SU(2) gauge fields during single-field slow-roll inflation, open inflation, and massive gravity inflation. The results depend on the model parameters, but we find that future CMB experiments are sensitive to differences in these models. We make our calculation tool available online.

Long-Lived Inverse Chirp Signals from Core-Collapse in Massive Scalar-Tensor Gravity

NASA Astrophysics Data System (ADS)

Sperhake, Ulrich; Moore, Christopher J.; Rosca, Roxana; Agathos, Michalis; Gerosa, Davide; Ott, Christian D.

2017-11-01

This Letter considers stellar core collapse in massive scalar-tensor theories of gravity. The presence of a mass term for the scalar field allows for dramatic increases in the radiated gravitational wave signal. There are several potential smoking gun signatures of a departure from general relativity associated with this process. These signatures could show up within existing LIGO-Virgo searches.

Chemical (knight) shift distortions of quadrupole-split deuteron powder spectra in solids

NASA Astrophysics Data System (ADS)

Torgeson, D. R.; Schoenberger, R. J.; Barnes, R. G.

In strong magnetic fields (e.g., 8 Tesla) anisotropy of the shift tensor (chemical or Knight shift) can alter the spacings of the features of quadrupole-split deuteron spectra of polycrystalline samples. Analysis of powder spectra yields both correct quadrupole coupling and symmetry parameters and all the components of the shift tensor. Synthetic and experimental examples are given to illustrate such behavior.

Irreducible structure, symmetry and average of Eshelby's tensor fields in isotropic elasticity

NASA Astrophysics Data System (ADS)

Zheng, Q.-S.; Zhao, Z.-H.; Du, D.-X.

2006-02-01

The strain field ɛ(x) in an infinitely large, homogenous, and isotropic elastic medium induced by a uniform eigenstrain ɛ0 in a domain ω depends linearly upon ɛ0 : ɛij(x)=Sijklω(x)ɛkl0. It has been a long-standing conjecture that the Eshelby's tensor field Sω(x) is uniform inside ω if and only if ω is ellipsoidally shaped. Because of the minor index symmetry Sijklω=Sjiklω=Sijlkω, Sω might have a maximum of 36 or nine independent components in three or two dimensions, respectively. In this paper, using the irreducible decomposition of Sω, we show that the isotropic part S of Sω vanishes outside ω and is uniform inside ω with the same value as the Eshelby's tensor S0 for 3D spherical or 2D circular domains. We further show that the anisotropic part Aω=Sω-S of Sω is characterized by a second- and a fourth-order deviatoric tensors and therefore have at maximum 14 or four independent components as characteristics of ω's geometry. Remarkably, the above irreducible structure of Sω is independent of ω's geometry (e.g., shape, orientation, connectedness, convexity, boundary smoothness, etc.). Interesting consequences have implication for a number of recently findings that, for example, both the values of Sω at the center of a 2D Cn(n⩾3,n≠4)-symmetric or 3D icosahedral ω and the average value of Sω over such a ω are equal to S0.

Anisoft - Advanced Treatment of Magnetic Anisotropy Data

NASA Astrophysics Data System (ADS)

Chadima, M.

2017-12-01

Since its first release, Anisoft (Anisotropy Data Browser) has gained a wide popularity in magnetic fabric community mainly due to its simple and user-friendly interface enabling very fast visualization of magnetic anisotropy tensors. Here, a major Anisoft update is presented transforming a rather simple data viewer into a platform offering an advanced treatment of magnetic anisotropy data. The updated software introduces new enlarged binary data format which stores both in-phase and out-of-phase (if measured) susceptibility tensors (AMS) or tensors of anisotropy of magnetic remanence (AMR) together with their respective confidence ellipses and values of F-tests for anisotropy. In addition to the tensor data, a whole array of specimen orientation angles, orientation of mesoscopic foliation(s) and lineation(s) is stored for each record enabling later editing or corrections. The input data may be directly acquired by AGICO Kappabridges (AMS) or Spinner Magnetometers (AMR); imported from various data formats, including the long-time standard binary ran-format; or manually created. Multiple anisotropy files can be combined together or split into several files by manual data selection or data filtering according to their values. Anisotropy tensors are conventionally visualized as principal directions (eigenvectors) in equal-area projection (stereoplot) together with a wide array of quantitative anisotropy parameters presented in histograms or in color-coded scatter plots showing mutual relationship of up to three quantitative parameters. When dealing with AMS in variable low fields, field-independent and field-dependent components of anisotropy can be determined (Hrouda 2009). For a group of specimens, individual principal directions can be contoured, or a mean tensor and respective confidence ellipses of its principal directions can be calculated using either the Hext-Jelinek (Jelinek 1978) statistics or the Bootstrap method (Constable & Tauxe 1990). Each graphical output can be exported into several vector or raster graphical formats or, via clipboard, pasted directly into a presentation or publication manuscript. Calculated principal directions or anisotropy parameters can be exported into various types of text files ready to be visualized or processed by any software of user's choice.

Research on third-order susceptibility tensor of silicon at telecom wavelength

NASA Astrophysics Data System (ADS)

Zhang, Yu-Hong; Liu, Hang; Chen, Zhan-Guo; Jia, Gang; Ren, Ce

2010-10-01

In this paper, the electro-induced birefringence based on Kerr effect and Franz-Keldysh effect in bulk silicon crystal at 1.3μm wavelengths has been measured. By using Kerr effect, the third-order susceptibility tensor of bulk crystalline silicon has been calculated.The two independent tensor of silicon X (3) susceptibility can be obtained by calculation (3) 6.22 (1 2.2%) 10 -20 m2 V2 and Xxyxy(3) = and xxxx(3) 9.13 (1 +/-2.2%) 10-20 m2 V 2 = m2/V2. The research can drive the silicon utility in the photo-electricity field.

Hydrogen Burning in Low Mass Stars Constrains Scalar-Tensor Theories of Gravity.

PubMed

Sakstein, Jeremy

2015-11-13

The most general scalar-tensor theories of gravity predict a weakening of the gravitational force inside astrophysical bodies. There is a minimum mass for hydrogen burning in stars that is set by the interplay of plasma physics and the theory of gravity. We calculate this for alternative theories of gravity and find that it is always significantly larger than the general relativity prediction. The observation of several low mass red dwarf stars therefore rules out a large class of scalar-tensor gravity theories and places strong constraints on the cosmological parameters appearing in the effective field theory of dark energy.

Laser pumping Cs atom magnetometer of theory research based on gradient tensor measuring

NASA Astrophysics Data System (ADS)

Yang, Zhang; Chong, Kang; Wang, Qingtao; Lei, Cheng; Zheng, Caiping

2011-02-01

At present, due to space exploration, military technology, geological exploration, magnetic navigation, medical diagnosis and biological magnetic fields study of the needs of research and development, the magnetometer is given strong driving force. In this paper, it will discuss the theoretical analysis and system design of laser pumping cesium magnetometer, cesium atomic energy level formed hyperfine structure with the I-J coupling, the hyperfine structure has been further split into Zeeman sublevels for the effects of magnetic field. To use laser pump and RF magnetic field make electrons transition in the hyperfine structure to produce the results of magneto-optical double resonance, and ultimately through the resonant frequency will be able to achieve accurate value of the external magnetic field. On this basis, we further have a discussion about magnetic gradient tensor measuring method. To a large extent, it increases the magnetic field measurement of information.

Influence of N-H...O and C-H...O hydrogen bonds on the 17O NMR tensors in crystalline uracil: computational study.

PubMed

Ida, Ramsey; De Clerk, Maurice; Wu, Gang

2006-01-26

We report a computational study for the 17O NMR tensors (electric field gradient and chemical shielding tensors) in crystalline uracil. We found that N-H...O and C-H...O hydrogen bonds around the uracil molecule in the crystal lattice have quite different influences on the 17O NMR tensors for the two C=O groups. The computed 17O NMR tensors on O4, which is involved in two strong N-H...O hydrogen bonds, show remarkable sensitivity toward the choice of cluster model, whereas the 17O NMR tensors on O2, which is involved in two weak C-H...O hydrogen bonds, show much smaller improvement when the cluster model includes the C-H...O hydrogen bonds. Our results demonstrate that it is important to have accurate hydrogen atom positions in the molecular models used for 17O NMR tensor calculations. In the absence of low-temperature neutron diffraction data, an effective way to generate reliable hydrogen atom positions in the molecular cluster model is to employ partial geometry optimization for hydrogen atom positions using a cluster model that includes all neighboring hydrogen-bonded molecules. Using an optimized seven-molecule model (a total of 84 atoms), we were able to reproduce the experimental 17O NMR tensors to a reasonably good degree of accuracy. However, we also found that the accuracy for the calculated 17O NMR tensors at O2 is not as good as that found for the corresponding tensors at O4. In particular, at the B3LYP/6-311++G(d,p) level of theory, the individual 17O chemical shielding tensor components differ by less than 10 and 30 ppm from the experimental values for O4 and O2, respectively. For the 17O quadrupole coupling constant, the calculated values differ by 0.30 and 0.87 MHz from the experimental values for O4 and O2, respectively.

Full moment tensors with uncertainties for the 2017 North Korea declared nuclear test and for a collocated, subsequent event

NASA Astrophysics Data System (ADS)

Alvizuri, C. R.; Tape, C.

2017-12-01

A seismic moment tensor is a 3×3 symmetric matrix that characterizes the far-field seismic radiation from a source, whether it be an earthquake, volcanic event, explosion. We estimate full moment tensors and their uncertainties for the North Korea declared nuclear test and for a collocated event that occurred eight minutes later. The nuclear test and the subsequent event occurred on September 3, 2017 at around 03:30 and 03:38 UTC time. We perform a grid search over the six-dimensional space of moment tensors, generating synthetic waveforms at each moment tensor grid point and then evaluating a misfit function between the observed and synthetic waveforms. The synthetic waveforms are computed using a 1-D structure model for the region; this approximation requires careful assessment of time shifts between data and synthetics, as well as careful choice of the bandpass for filtering. For each moment tensor we characterize its uncertainty in terms of waveform misfit, a probability function, and a confidence curve for the probability that the true moment tensor lies within the neighborhood of the optimal moment tensor. For each event we estimate its moment tensor using observed waveforms from all available seismic stations within a 2000-km radius. We use as much of the waveform as possible, including surface waves for all stations, and body waves above 1 Hz for some of the closest stations. Our preliminary magnitude estimates are Mw 5.1-5.3 for the first event and Mw 4.7 for the second event. Our results show a dominantly positive isotropic moment tensor for the first event, and a dominantly negative isotropic moment tensor for the subsequent event. As expected, the details of the probability density, waveform fit, and confidence curves are influenced by the structural model, the choice of filter frequencies, and the selection of stations.

Generalized reduced rank latent factor regression for high dimensional tensor fields, and neuroimaging-genetic applications

PubMed Central

Tao, Chenyang; Nichols, Thomas E.; Hua, Xue; Ching, Christopher R.K.; Rolls, Edmund T.; Thompson, Paul M.; Feng, Jianfeng

2017-01-01

We propose a generalized reduced rank latent factor regression model (GRRLF) for the analysis of tensor field responses and high dimensional covariates. The model is motivated by the need from imaging-genetic studies to identify genetic variants that are associated with brain imaging phenotypes, often in the form of high dimensional tensor fields. GRRLF identifies from the structure in the data the effective dimensionality of the data, and then jointly performs dimension reduction of the covariates, dynamic identification of latent factors, and nonparametric estimation of both covariate and latent response fields. After accounting for the latent and covariate effects, GRLLF performs a nonparametric test on the remaining factor of interest. GRRLF provides a better factorization of the signals compared with common solutions, and is less susceptible to overfitting because it exploits the effective dimensionality. The generality and the flexibility of GRRLF also allow various statistical models to be handled in a unified framework and solutions can be efficiently computed. Within the field of neuroimaging, it improves the sensitivity for weak signals and is a promising alternative to existing approaches. The operation of the framework is demonstrated with both synthetic datasets and a real-world neuroimaging example in which the effects of a set of genes on the structure of the brain at the voxel level were measured, and the results compared favorably with those from existing approaches. PMID:27666385

Two-point function of a quantum scalar field in the interior region of a Reissner-Nordstrom black hole

NASA Astrophysics Data System (ADS)

Lanir, Assaf; Levi, Adam; Ori, Amos; Sela, Orr

2018-01-01

We derive explicit expressions for the two-point function of a massless scalar field in the interior region of a Reissner-Nordstrom black hole, in both the Unruh and the Hartle-Hawking quantum states. The two-point function is expressed in terms of the standard l m ω modes of the scalar field (those associated with a spherical harmonic Yl m and a temporal mode e-i ω t), which can be conveniently obtained by solving an ordinary differential equation, the radial equation. These explicit expressions are the internal analogs of the well-known results in the external region (originally derived by Christensen and Fulling), in which the two-point function outside the black hole is written in terms of the external l m ω modes of the field. They allow the computation of ⟨Φ2⟩ren and the renormalized stress-energy tensor inside the black hole, after the radial equation has been solved (usually numerically). In the second part of the paper, we provide an explicit expression for the trace of the renormalized stress-energy tensor of a minimally coupled massless scalar field (which is nonconformal), relating it to the d'Alembertian of ⟨Φ2⟩ren . This expression proves itself useful in various calculations of the renormalized stress-energy tensor.

Lorentzian Goldstone modes shared among photons and gravitons

NASA Astrophysics Data System (ADS)

Chkareuli, J. L.; Jejelava, J.; Kepuladze, Z.

2018-02-01

It has long been known that photons and gravitons may appear as vector and tensor Goldstone modes caused by spontaneous Lorentz invariance violation (SLIV). Usually this approach is considered for photons and gravitons separately. We develop the emergent electrogravity theory consisting of the ordinary QED and the tensor-field gravity model which mimics the linearized general relativity in Minkowski spacetime. In this theory, Lorentz symmetry appears incorporated into higher global symmetries of the length-fixing constraints put on the vector and tensor fields involved, A_{μ }2=± MA2 and H_{μ ν }2=± MH2 (MA and MH are the proposed symmetry breaking scales). We show that such a SLIV pattern being related to breaking of global symmetries underlying these constraints induces the massless Goldstone and pseudo-Goldstone modes shared by photon and graviton. While for a vector field case the symmetry of the constraint coincides with Lorentz symmetry SO(1, 3) of the electrogravity Lagrangian, the tensor-field constraint itself possesses much higher global symmetry SO(7, 3), whose spontaneous violation provides a sufficient number of zero modes collected in a graviton. Accordingly, while the photon may only contain true Goldstone modes, the graviton appears at least partially to be composed of pseudo-Goldstone modes rather than of pure Goldstone ones. When expressed in terms of these modes, the theory looks essentially nonlinear and contains a variety of Lorentz and CPT violating couplings. However, all SLIV effects turn out to be strictly cancelled in the lowest order processes considered in some detail. How this emergent electrogravity theory could be observationally different from conventional QED and GR theories is also briefly discussed.

Toward an improved determination of Earth's lithospheric magnetic field from satellite observations

NASA Astrophysics Data System (ADS)

Kotsiaros, S.

2016-12-01

An analytical and numerical analysis of the spectral properties of the gradient tensor, initially performed by Rummel and van Gelderen (1992) for the gravity potential, shows that when the tensor elements are grouped into sets of semi-tangential and pure-tangential parts, they produce almost identical signal content as the normal element. Moreover, simple eigenvalue relations can be derived between these sets and the spherical harmonic expansion of the potential. This theoretical development generally applies to any potential field. First, the analysis of Rummel and van Gelderen (1992) is adapted to the magnetic field case and then the elements of the magnetic gradient tensor are estimated by 2 years of Swarm data and grouped into Γ(1) = {[∇B]rθ,[∇B]rφ} resp. Γ(2) = {[∇B]θθ-[∇B]φφ, 2[∇B]θφ}. It is shown that the estimated combinations Γ(1) and Γ(2) produce similar signal content as the theoretical radial gradient [∇B]rr. These results demonstrate the ability of multi-satellite missions such as Swarm, which cannot directly measure the radial gradient, to retrieve similar signal content by means of the horizontal gradients. Finally, lithospheric field models are derived using the gradient combinations Γ(1) and Γ(2) and compared with models derived from traditional vector and gradient data. The model resulting from Γ(1) leads to a very similar, and in particular cases improved, model compared to models retrieved by using approximately three times more data, i.e. a full set of vector, North-South and East-West gradients. ReferencesRummel, R., and M. van Gelderen (1992), Spectral analysis of the full gravity tensor, Geophysical Journal International, 111 (1), 159-169.

Black holes in vector-tensor theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic andmore » quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.« less

Effect of cosmological evolution on Solar System constraints and on the scalarization of neutron stars in massless scalar-tensor theories

NASA Astrophysics Data System (ADS)

Anderson, David; Yunes, Nicolás; Barausse, Enrico

2016-11-01

Certain scalar-tensor theories of gravity that generalize Jordan-Fierz-Brans-Dicke theory are known to predict nontrivial phenomenology for neutron stars. In these theories, first proposed by Damour and Esposito-Farèse, the scalar field has a standard kinetic term and couples conformally to the matter fields. The weak equivalence principle is therefore satisfied, but scalar effects may arise in strong-field regimes, e.g., allowing for violations of the strong equivalence principle in neutron stars ("spontaneous scalarization") or in sufficiently tight binary neutron-star systems ("dynamical/induced scalarization"). The original scalar-tensor theory proposed by Damour and Esposito-Farèse is in tension with Solar System constraints (for couplings that lead to scalarization), if one accounts for cosmological evolution of the scalar field and no mass term is included in the action. We extend here the conformal coupling of that theory, in order to ascertain if, in this way, Solar System tests can be passed, while retaining a nontrivial phenomenology for neutron stars. We find that, even with this generalized conformal coupling, it is impossible to construct a theory that passes both big bang nucleosynthesis and Solar System constraints, while simultaneously allowing for scalarization in isolated/binary neutron stars.

Scale invariance, conformality, and generalized free fields

DOE PAGES

Dymarsky, Anatoly; Farnsworth, Kara; Komargodski, Zohar; ...

2016-02-16

This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum fi eld theories with scale invariance but not conformal invariance. We present an important loophole in the arguments of Luty-Polchinski-Rattazzi and Dymarsky-Komargodski-Schwimmer-Theisen that is the trace of the energy-momentum tensor T could be a generalized free field. In this paper we rule out this possibility. The key ingredient is the observation that a unitary theory with scale but not conformal invariance necessarily has a non-vanishing anomaly for global scale transformations. We show that this anomaly cannot be reproduced if T is a generalized free field unlessmore » the theory also contains a dimension-2 scalar operator. In the special case where such an operator is present it can be used to redefine ("improve") the energy-momentum tensor, and we show that there is at least one energy-momentum tensor that is not a generalized free field. In addition, we emphasize that, in general, large momentum limits of correlation functions cannot be understood from the leading terms of the coordinate space OPE. This invalidates a recent argument by Farnsworth-Luty-Prilepina (FLP). Finally, despite the invalidity of the general argument of FLP, some of the techniques turn out to be useful in the present context.« less

Vacuum birefringence in strong magnetic fields: (II) Complex refractive index from the lowest Landau level

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hattori, Koichi, E-mail: khattori@yonsei.ac.kr; Itakura, Kazunori, E-mail: kazunori.itakura@kek.jp; Department of Particle and Nuclear Studies, Graduate University for Advanced Studies

2013-07-15

We compute the refractive indices of a photon propagating in strong magnetic fields on the basis of the analytic representation of the vacuum polarization tensor obtained in our previous paper. When the external magnetic field is strong enough for the fermion one-loop diagram of the polarization tensor to be approximated by the lowest Landau level, the propagating mode in parallel to the magnetic field is subject to modification: The refractive index deviates from unity and can be very large, and when the photon energy is large enough, the refractive index acquires an imaginary part indicating decay of a photon intomore » a fermion–antifermion pair. We study dependences of the refractive index on the propagating angle and the magnetic-field strength. It is also emphasized that a self-consistent treatment of the equation which defines the refractive index is indispensable for accurate description of the refractive index. This self-consistent treatment physically corresponds to consistently including the effects of back reactions of the distorted Dirac sea in response to the incident photon. -- Highlights: •Vacuum birefringence and photon decay are described by the complex refractive index. •Resummed photon vacuum polarization tensor in the lowest Landau level is used. •Back reactions from the distorted Dirac sea are self-consistently taken into account. •Self-consistent treatment drastically changes structure in photon energy dependence. •Dependences on photon propagation angle and magnetic-field strength are presented.« less

Charged Galileon black holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Babichev, Eugeny; Charmousis, Christos; Hassaine, Mokhtar, E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr, E-mail: hassaine@inst-mat.utalca.cl

We consider an Abelian gauge field coupled to a particular truncation of Horndeski theory. The Galileon field has translation symmetry and couples non minimally both to the metric and the gauge field. When the gauge-scalar coupling is zero the gauge field reduces to a standard Maxwell field. By taking into account the symmetries of the action, we construct charged black hole solutions. Allowing the scalar field to softly break symmetries of spacetime we construct black holes where the scalar field is regular on the black hole event horizon. Some of these solutions can be interpreted as the equivalent of Reissner-Nordstrommore » black holes of scalar tensor theories with a non trivial scalar field. A self tuning black hole solution found previously is extended to the presence of dyonic charge without affecting whatsoever the self tuning of a large positive cosmological constant. Finally, for a general shift invariant scalar tensor theory we demonstrate that the scalar field Ansatz and method we employ are mathematically compatible with the field equations. This opens up the possibility for novel searches of hairy black holes in a far more general setting of Horndeski theory.« less

Antisymmetric Amino-Wagging Band of Hydrazine up toK‧ = 13 Levels

NASA Astrophysics Data System (ADS)

Gulaczyk, Iwona; Kre, Marek; Valentin, Alain

1997-12-01

A newly recorded high-resolution infrared spectrum of hydrazine has been studied in the 729-1198 cm-1region (the ν12antisymmetric wagging band) with a resolution of 0.002 cm-1. About 1350 transitions withK‧ from 7 to 13 have been newly assigned and about 2350 transitions with lower values ofK‧ reanalyzed with the improved precision. The effective parameters have been calculated separately for each value ofK‧ using the Hougen-Ohashi hamiltonian for hydrazine. The extended assignment completes the analysis of the ν12band of hydrazine.

Antisymmetric Wilson loops in N = 4 SYM beyond the planar limit

NASA Astrophysics Data System (ADS)

Gordon, James

2018-01-01

We study the 1/2 -BPS circular Wilson loop in the totally antisymmetric representation of the gauge group in N = 4 supersymmetric Yang-Mills. This observable is captured by a Gaussian matrix model with appropriate insertion. We compute the first 1 /N correction at leading order in 't Hooft coupling by means of the matrix model loop equations. Disagreement with the 1-loop effective action of the holographically dual D5-brane suggests the need to account for gravitational backreaction on the string theory side.

BOOK REVIEW: Nonlinear Continuum Mechanics for Finite Element Analysis

NASA Astrophysics Data System (ADS)

Bialek, James M.

1998-05-01

Nonlinear continuum mechanics of solids is a fascinating subject. All the assumptions inherited from an overexposure to linear behaviour and analysis must be re-examined. The standard definitions of strain designed for small deformation linear problems may be totally misleading when finite motion or large deformations are considered. Nonlinear behaviour includes phenomena like `snap-through', where bifurcation theory is applied to engineering design. Capabilities in this field are growing at a fantastic speed; for example, modern automobiles are presently being designed to crumple in the most energy absorbing manner in order to protect the occupants. The combination of nonlinear mechanics and the finite element method is a very important field. Most engineering designs encountered in the fusion effort are strictly limited to small deformation linear theory. In fact, fusion devices are usually kept in the low stress, long life regime that avoids large deformations, nonlinearity and any plastic behaviour. The only aspect of nonlinear continuum solid mechanics about which the fusion community now worries is that rare case where details of the metal forming process must be considered. This text is divided into nine sections: introduction, mathematical preliminaries, kinematics, stress and equilibrium, hyperelasticity, linearized equilibrium equations, discretization and solution, computer implementation and an appendix covering an introduction to large inelastic deformations. The authors have decided to use vector and tensor notation almost exclusively. This means that the usual maze of indicial equations is avoided, but most readers will therefore be stretched considerably to follow the presentation, which quickly proceeds to the heart of nonlinear behaviour in solids. With great speed the reader is led through the material (Lagrangian) and spatial (Eulerian) co-ordinates, the deformation gradient tensor (an example of a two point tensor), the right and left Cauchy-Green tensors, the Eulerian or Almansi strain tensor, distortional components, strain rate tensors, rate of deformation tensors, spin tensors and objectivity. The standard Cauchy stress tensor is mentioned in passing, and then virtual work and work conjugacy lead to alternative stress representations such as the Piola-Kirchoff representation. Chapter 5 concentrates on hyperelasticity (where stresses are derived from a stored energy function) and its subvarieties. Chapter 6 proceeds by linearizing the virtual work statement prior to discretization and Chapter 7 deals with approaches to solving the formulation. In Chapter 8 the FORTRAN finite element code written by Bonet (available via the world wide web) is described. In summary this book is written by experts, for future experts, and provides a very fast review of the field for people who already know the topic. The authors assume the reader is familiar with `elementary stress analysis' and has had some exposure to `the principle of the finite element method'. Their goals are summarized by the statement, `If the reader is prepared not to get too hung up on details, it is possible to use the book to obtain a reasonable overview of the subject'. This is a very nice summary of what is going on in the field but as a stand-alone text it is much too terse. The total bibliography is a page and a half. It would be an improvement if there were that much reference material for each chapter.

Symplectic Quantization of a Vector-Tensor Gauge Theory with Topological Coupling

NASA Astrophysics Data System (ADS)

Barcelos-Neto, J.; Silva, M. B. D.

We use the symplectic formalism to quantize a gauge theory where vectors and tensors fields are coupled in a topological way. This is an example of reducible theory and a procedure like of ghosts-of-ghosts of the BFV method is applied but in terms of Lagrange multipliers. Our final results are in agreement with the ones found in the literature by using the Dirac method.

Inversion of gravity gradient tensor data: does it provide better resolution?

NASA Astrophysics Data System (ADS)

Paoletti, V.; Fedi, M.; Italiano, F.; Florio, G.; Ialongo, S.

2016-04-01

The gravity gradient tensor (GGT) has been increasingly used in practical applications, but the advantages and the disadvantages of the analysis of GGT components versus the analysis of the vertical component of the gravity field are still debated. We analyse the performance of joint inversion of GGT components versus separate inversion of the gravity field alone, or of one tensor component. We perform our analysis by inspection of the Picard Plot, a Singular Value Decomposition tool, and analyse both synthetic data and gradiometer measurements carried out at the Vredefort structure, South Africa. We show that the main factors controlling the reliability of the inversion are algebraic ambiguity (the difference between the number of unknowns and the number of available data points) and signal-to-noise ratio. Provided that algebraic ambiguity is kept low and the noise level is small enough so that a sufficient number of SVD components can be included in the regularized solution, we find that: (i) the choice of tensor components involved in the inversion is not crucial to the overall reliability of the reconstructions; (ii) GGT inversion can yield the same resolution as inversion with a denser distribution of gravity data points, but with the advantage of using fewer measurement stations.

The beaming of subhalo accretion

NASA Astrophysics Data System (ADS)

Libeskind, Noam I.

2016-10-01

We examine the infall pattern of subhaloes onto hosts in the context of the large-scale structure. We find that the infall pattern is essentially driven by the shear tensor of the ambient velocity field. Dark matter subhaloes are preferentially accreted along the principal axis of the shear tensor which corresponds to the direction of weakest collapse. We examine the dependence of this preferential infall on subhalo mass, host halo mass and redshift. Although strongest for the most massive hosts and the most massive subhaloes at high redshift, the preferential infall of subhaloes is effectively universal in the sense that its always aligned with the axis of weakest collapse of the velocity shear tensor. It is the same shear tensor that dictates the structure of the cosmic web and hence the shear field emerges as the key factor that governs the local anisotropic pattern of structure formation. Since the small (sub-Mpc) scale is strongly correlated with the mid-range (~ 10 Mpc) scale - a scale accessible by current surveys of peculiar velocities - it follows that findings presented here open a new window into the relation between the observed large scale structure unveiled by current surveys of peculiar velocities and the preferential infall direction of the Local Group. This may shed light on the unexpected alignments of dwarf galaxies seen in the Local Group.

Influence of the Proton Pressure Tensor on the Turbulent Velocity Spectrum at Ion Kinetic Scales

NASA Astrophysics Data System (ADS)

Vasquez, B. J.; Markovskii, S.

2011-12-01

Numerical hybrid simulations with particle protons and fluid electrons are presented for turbulent fluctuations with spatial variations in a plane perpendicular to the background magnetic field. The steepened portion of the proton bulk velocity spectrum is found at smaller wavenumbers for larger background proton temperature. The velocity spectrum is determined, in part, by the proton pressure tensor. The proton pressure tensor is shown to possess non-gyrotropic and finite off-diagonal components in the places where the turbulent fluctuations have developed strong gradients. Proton demagnetization at these places is a factor in the departure from a Maxwellian velocity distribution function. How demagnetization could connect with both reversible and effectively irreversible aspects of the pressure tensor is considered. The effectively irreversible aspect corresponds to the net heating of the protons and to the dissipation of the turbulent energy cascade.

Off-shell supergravity in five dimensions and supersymmetric brane world scenarios

NASA Astrophysics Data System (ADS)

Zucker, M.

2003-09-01

We review the construction of off-shell Poincaré supergravity in five dimensions. We describe in detail the minimal multiplet, which is the basic building block, containing the propagating fields of supergravity. All matter multiplets containing (8 + 8) components, being the smallest matter multiplets in five dimensions, are constructed. Using these multiplets the complete tensor calculus for supergravity is developed. As expected it turns out, that there exist three distinct minimal (i.e. containing (48 + 48) field components) off-shell supergravities. The lagrangians for these theories and their gauged variants are given explicitly. These results are used in the second part to develop a tensor calculus on the orbifold . Gauged supergravity on the orbifold with additional cosmological constants at the fixpoints, is constructed. This generalizes the work of Randall-Sundrum to local supersymmetry. The developed tensor calculus is used to extend this model to include matter located at the fixpoints. Chiral and super Yang-Mills multiplets at the fixpoints are considered.

Strain, magnetic anisotropy, and anisotropic magnetoresistance in (Ga,Mn)As on high-index substrates: Application to (113)A -oriented layers

NASA Astrophysics Data System (ADS)

Dreher, L.; Donhauser, D.; Daeubler, J.; Glunk, M.; Rapp, C.; Schoch, W.; Sauer, R.; Limmer, W.

2010-06-01

Based on a detailed theoretical examination of the lattice distortion in high-index epilayers in terms of continuum mechanics, expressions are deduced that allow the calculation and experimental determination of the strain tensor for (hhl) -oriented (Ga,Mn)As layers. Analytical expressions are derived for the strain-dependent free-energy density and for the resistivity tensor for monoclinic and orthorhombic crystal symmetries, phenomenologically describing the magnetic anisotropy and anisotropic magnetoresistance by appropriate anisotropy and resistivity parameters, respectively. Applying the results to (113)A orientation with monoclinic crystal symmetry, the expressions are used to determine the strain tensor and the shear angle of a series of (113)A -oriented (Ga,Mn)As layers by high-resolution x-ray diffraction and to probe the magnetic anisotropy and anisotropic magnetoresistance at 4.2 K by means of angle-dependent magnetotransport. Whereas the transverse-resistivity parameters are nearly unaffected by the magnetic field, the parameters describing the longitudinal resistivity are strongly field dependent.

Dense lower crust elevates long-term earthquake rates in the New Madrid seismic zone

USGS Publications Warehouse

Levandowski, William Brower; Boyd, Oliver; Ramirez-Guzman, Leonardo

2016-01-01

Knowledge of the local state of stress is critical in appraising intraplate seismic hazard. Inverting earthquake moment tensors, we demonstrate that principal stress directions in the New Madrid seismic zone (NMSZ) differ significantly from those in the surrounding region. Faults in the NMSZ that are incompatible with slip in the regional stress field are favorably oriented relative to local stress. We jointly analyze seismic velocity, gravity, and topography to develop a 3-D crustal and upper mantle density model, revealing uniquely dense lower crust beneath the NMSZ. Finite element simulations then estimate the stress tensor due to gravitational body forces, which sums with regional stress. The anomalous lower crust both elevates gravity-derived stress at seismogenic depths in the NMSZ and rotates it to interfere more constructively with far-field stress, producing a regionally maximal deviatoric stress coincident with the highest concentration of modern seismicity. Moreover, predicted principal stress directions mirror variations (observed independently in moment tensors) at the NMSZ and across the region.

Natural Strain

NASA Technical Reports Server (NTRS)

Freed, Alan D.

1995-01-01

The purpose of this paper is to present a consistent and thorough development of the strain and strain-rate measures affiliated with Hencky. Natural measures for strain and strain-rate, as I refer to them, are first expressed in terms of of the fundamental body-metric tensors of Lodge. These strain and strain-rate measures are mixed tensor fields. They are mapped from the body to space in both the Eulerian and Lagrangian configurations, and then transformed from general to Cartesian fields. There they are compared with the various strain and strain-rate measures found in the literature. A simple Cartesian description for Hencky strain-rate in the Lagrangian state is obtained.

Self-consistent perturbed equilibrium with neoclassical toroidal torque in tokamaks

DOE PAGES

Park, Jong-Kyu; Logan, Nikolas C.

2017-03-01

Toroidal torque is one of the most important consequences of non-axisymmetric fields in tokamaks. The well-known neoclassical toroidal viscosity (NTV) is due to the second-order toroidal force from anisotropic pressure tensor in the presence of these asymmetries. This work shows that the first-order toroidal force originating from the same anisotropic pressure tensor, despite having no flux surface average, can significantly modify the local perturbed force balance and thus must be included in perturbed equilibrium self-consistent with NTV. The force operator with an anisotropic pressure tensor is not self-adjoint when the NTV torque is finite and thus is solved directly formore » each component. This approach yields a modified, non-self-adjoint Euler-Lagrange equation that can be solved using a variety of common drift-kinetic models in generalized tokamak geometry. The resulting energy and torque integral provides a unique way to construct a torque response matrix, which contains all the information of self-consistent NTV torque profiles obtainable by applying non-axisymmetric fields to the plasma. This torque response matrix can then be used to systematically optimize non-axisymmetric field distributions for desired NTV profiles. Published by AIP Publishing.« less

Probing Fe-V Bonding in a C3-Symmetric Heterobimetallic Complex.

PubMed

Greer, Samuel M; McKay, Johannes; Gramigna, Kathryn M; Thomas, Christine M; Stoian, Sebastian A; Hill, Stephen

2018-04-30

Direct metal-metal bonding of two distinct first-row transition metals remains relatively unexplored compared to their second- and third-row heterobimetallic counterparts. Herein, a recently reported Fe-V triply bonded species, [V( i PrNPPh 2 ) 3 FeI] (1; Kuppuswamy, S.; Powers, T. M.; Krogman, J. P.; Bezpalko, M. W.; Foxman, B. M.; Thomas, C. M. Vanadium-iron complexes featuring metal-metal multiple bonds. Chem. Sci. 2013, 4, 3557-3565), is investigated using high-frequency electron paramagnetic resonance, field- and temperature-dependent 57 Fe nuclear gamma resonance (Mössbauer) spectroscopy, and high-field electron-electron double resonance detected nuclear magnetic resonance. From the use of this suite of physical methods, we have assessed the electronic structure of 1. These studies allow us to establish the effective g̃ tensors as well as the Fe/V electro-nuclear hyperfine interaction tensors of the spin S = 1 / 2 ground state. We have rationalized these tensors in the context of ligand field theory supported by quantum chemical calculations. This theoretical analysis suggests that the S = 1 / 2 ground state originates from a single unpaired electron predominately localized on the Fe site.

Holographic stress-energy tensor near the Cauchy horizon inside a rotating black hole

NASA Astrophysics Data System (ADS)

Ishibashi, Akihiro; Maeda, Kengo; Mefford, Eric

2017-07-01

We investigate a stress-energy tensor for a conformal field theory (CFT) at strong coupling inside a small five-dimensional rotating Myers-Perry black hole with equal angular momenta by using the holographic method. As a gravitational dual, we perturbatively construct a black droplet solution by applying the "derivative expansion" method, generalizing the work of Haddad [Classical Quantum Gravity 29, 245001 (2012), 10.1088/0264-9381/29/24/245001] and analytically compute the holographic stress-energy tensor for our solution. We find that the stress-energy tensor is finite at both the future and past outer (event) horizons and that the energy density is negative just outside the event horizons due to the Hawking effect. Furthermore, we apply the holographic method to the question of quantum instability of the Cauchy horizon since, by construction, our black droplet solution also admits a Cauchy horizon inside. We analytically show that the null-null component of the holographic stress-energy tensor negatively diverges at the Cauchy horizon, suggesting that a singularity appears there, in favor of strong cosmic censorship.

Investigation of TbMn2O5 by polarized neutron diffraction

NASA Astrophysics Data System (ADS)

Zobkalo, I. A.; Gavrilov, S. V.; Sazonov, A.; Hutanu, V.

2018-05-01

In order to make a new approach to the elucidation of the microscopic mechanisms of multiferroicity in the RMn2O5 family, experiments with different methods of polarized neutrons scattering were performed on a TbMn2O5 single crystal. We employed three different techniques of polarized neutron diffraction without the analysis after scattering, the XYZ-polarization analysis, and technique of spherical neutron polarimetry (SNP). Measurements with SNP were undertaken both with and without external electric field. A characteristic difference in the population of ‘right’ and ‘left’ helix domains in all magnetically ordered phases of TbMn2O5, was observed. This difference can be controlled by an external electric field in the field-cooled mode. The analysis of the results gives an evidence that antisymmetric Dzyaloshinsky-Moria exchange is effective in all the magnetic phases in TbMn2O5.

Strong field control of the interatomic Coulombic decay process in quantum dots

NASA Astrophysics Data System (ADS)

Haller, Anika; Chiang, Ying-Chih; Menger, Maximilian; Aziz, Emad F.; Bande, Annika

2017-01-01

In recent years the laser-induced interatomic Coulombic decay (ICD) process in paired quantum dots has been predicted (Bande, 2013). In this work we target the enhancement of ICD by scanning over a range of strong-field laser intensities. The GaAs quantum dots are modeled by a one-dimensional double-well potential in which simulations are done with the space-resolved multi-configuration time-dependent Hartree method including antisymmetrization to account for the fermions. As a novelty a complementary state-resolved ansatz is developed to consolidate the interpretation of transient state populations, widths obtained for the ICD and the competing direct ionization channel, and Fano peak profiles in the photoelectron spectra. The major results are that multi-photon processes are unimportant even for the strongest fields. Further, below- π to π pulses display the highest ICD efficiency while the direct ionization becomes less dominant.

AC current rectification in Nb films with or without symmetrical Nb/Ni periodic pinning arrays in perpendicular magnetic field

NASA Astrophysics Data System (ADS)

Pryadun, Vladimir

2005-03-01

Rectification of AC current has been observed in plain superconducting Nb films and in Nb/Ni films with symmetric periodic pinning centers. The rectified DC voltage appears for various sample geometries (cross or strip) both along and transverse to the alternating current direction, is nearly anti-symmetric with perpendicular magnetic field and strongly dependent on temperature below Tc. Analyses of the data at different temperatures, drive frequencies from 100kHz to 150MHz and at the different sample sides [1] shows that not far below Tc the rectification phenomena can be understood in terms of generation of electric fields due to local excess of critical current. Further below Tc anisotropic pinning effects could also contribute to the rectification. [1] F.G.Aliev, et al., Cond. Mat.405656. Supported by Comunidad Autonoma de Madrid -CAM/07N/0050/2002

How tetraquarks can generate a second chiral phase transition

DOE PAGES

Pisarski, Robert D.; Skokov, Vladimir V.

2016-09-09

We consider how tetraquarks can affect the chiral phase transition in theories like QCD, with light quarks coupled to three colors. For two flavors the tetraquark field is an isosinglet, and its effect is minimal. For three flavors, however, the tetraquark field transforms in the same representation of the chiral symmetry group as the usual chiral order parameter, and so for very light quarks there may be two chiral phase transitions, which are both of first order. In QCD, results from the lattice indicate that any transition from the tetraquark condensate is a smooth crossover. In the plane of temperature,more » T, and quark chemical potential, μ, though, a crossover line for the tetraquark condensate is naturally related to the transition line for color superconductivity. For four flavors we suggest that a triquark field, antisymmetric in both flavor and color, combine to form hexaquarks.« less

The stability of nonlinear dynamos and the limited role of kinematic growth rates

NASA Astrophysics Data System (ADS)

Brandenburg, A.; Krause, F.; Meinel, R.; Moss, D.; Tuominen, I.

1989-04-01

The growth rate behavior of several kinematic dynamo models was investigated in the context of the observation that, as a rule, a magnetic field of a single symmetry dominates in the sun and other cosmic objects. For all dynamo models considered, it is shown that, as the dynamo numbers increase, the kinematic growth rates of fields of different parities are asymptotically equal, indicating that growth rates do not dominate the final state of the field. The possibility that the stability of different solutions of nonlinear dynamos determines the final state was then investigated. Dynamo models in spherical geometry were found in which both symmetric and antisymmetric solutions are stable. The kind of symmetry finally established depends in these cases on the initial conditions, i.e., on the history of the object. It is noted that the basic mechanism stabilizing or destabilizing different solutions is not well understood.

Investigation of TbMn2O5 by polarized neutron diffraction.

PubMed

Zobkalo, I A; Gavrilov, S V; Sazonov, A; Hutanu, V

2018-05-23

In order to make a new approach to the elucidation of the microscopic mechanisms of multiferroicity in the RMn 2 O 5 family, experiments with different methods of polarized neutrons scattering were performed on a TbMn 2 O 5 single crystal. We employed three different techniques of polarized neutron diffraction without the analysis after scattering, the XYZ-polarization analysis, and technique of spherical neutron polarimetry (SNP). Measurements with SNP were undertaken both with and without external electric field. A characteristic difference in the population of 'right' and 'left' helix domains in all magnetically ordered phases of TbMn 2 O 5 , was observed. This difference can be controlled by an external electric field in the field-cooled mode. The analysis of the results gives an evidence that antisymmetric Dzyaloshinsky-Moria exchange is effective in all the magnetic phases in TbMn 2 O 5 .

Quantum field theory in spaces with closed time-like curves

NASA Astrophysics Data System (ADS)

Boulware, D. G.

Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27(pi). A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.

Atomic spectral-product representations of molecular electronic structure: metric matrices and atomic-product composition of molecular eigenfunctions.

PubMed

Ben-Nun, M; Mills, J D; Hinde, R J; Winstead, C L; Boatz, J A; Gallup, G A; Langhoff, P W

2009-07-02

Recent progress is reported in development of ab initio computational methods for the electronic structures of molecules employing the many-electron eigenstates of constituent atoms in spectral-product forms. The approach provides a universal atomic-product description of the electronic structure of matter as an alternative to more commonly employed valence-bond- or molecular-orbital-based representations. The Hamiltonian matrix in this representation is seen to comprise a sum over atomic energies and a pairwise sum over Coulombic interaction terms that depend only on the separations of the individual atomic pairs. Overall electron antisymmetry can be enforced by unitary transformation when appropriate, rather than as a possibly encumbering or unnecessary global constraint. The matrix representative of the antisymmetrizer in the spectral-product basis, which is equivalent to the metric matrix of the corresponding explicitly antisymmetric basis, provides the required transformation to antisymmetric or linearly independent states after Hamiltonian evaluation. Particular attention is focused in the present report on properties of the metric matrix and on the atomic-product compositions of molecular eigenstates as described in the spectral-product representations. Illustrative calculations are reported for simple but prototypically important diatomic (H(2), CH) and triatomic (H(3), CH(2)) molecules employing algorithms and computer codes devised recently for this purpose. This particular implementation of the approach combines Slater-orbital-based one- and two-electron integral evaluations, valence-bond constructions of standard tableau functions and matrices, and transformations to atomic eigenstate-product representations. The calculated metric matrices and corresponding potential energy surfaces obtained in this way elucidate a number of aspects of the spectral-product development, including the nature of closure in the representation, the general redundancy or linear dependence of its explicitly antisymmetrized form, the convergence of the apparently disparate atomic-product and explicitly antisymmetrized atomic-product forms to a common invariant subspace, and the nature of a chemical bonding descriptor provided by the atomic-product compositions of molecular eigenstates. Concluding remarks indicate additional studies in progress and the prognosis for performing atomic spectral-product calculations more generally and efficiently.

Magnetization reversal in mixed ferrite-chromite perovskites with non magnetic cation on the A-site.

PubMed

Billoni, Orlando V; Pomiro, Fernando; Cannas, Sergio A; Martin, Christine; Maignan, Antoine; Carbonio, Raul E

2016-11-30

In this work, we have performed Monte Carlo simulations in a classical model for RFe1-x Cr x O3 with R  =  Y and Lu, comparing the numerical simulations with experiments and mean field calculations. In the analyzed compounds, the antisymmetric exchange or Dzyaloshinskii-Moriya (DM) interaction induced a weak ferromagnetism due to a canting of the antiferromagnetically ordered spins. This model is able to reproduce the magnetization reversal (MR) observed experimentally in a field cooling process for intermediate x values and the dependence with x of the critical temperatures. We also analyzed the conditions for the existence of MR in terms of the strength of DM interactions between Fe(3+) and Cr(3+) ions with the x values variations.

The structure and Gel'fand patterns inherent in the Heisenberg supergenerator algebra of dual Liouville-space ||kq{K-tilde.}(k1 - kn)[lambda- tilde],scriptn>> tensors and the Cayley algebra of scalar invariants over a (k1 - kn) field

NASA Astrophysics Data System (ADS)

Temme, F. P.

1991-06-01

For many-body spin cluster problems, dual-symmetry recoupled tensors over Liouville space provide suitable bases for a generalized torque formalism using the Sn-adapted density operator in which to discuss NMR and related techniques. The explicit structure of such tensors is considered in the context of the Cayley algebra of scalar invariants over a field, specified by the inner ki rank labels of the Tkq(kl-kn)s. The pertinence of both lexical combinatorial architectures over inner rank sets and SU2 propagative topologies in specifying the structure of dual recoupling tensors is considered in the context of the Sn partitional aspects of spin clusters. The form of Heisenberg superoperator generators whose algebra underlies the Gel'fand pattern algebra of SU(2) and SU(2)×Sn tensor bases over Liouville space is presented together with both the related s-boson algebras and a description of the associated {||2k 0>>} pattern sets of CF29H carrier space under the appropriate symmetry. These concepts are correlated with recent work on SU(2)×Sn induced symmetry hierarchies over Liouville spin space. The pertinence of this theoretical work to an understanding of multiquantum NMR in Liouville space formalisms is stressed in a discussion of the nature of pathways for intracluster J coupling, which also gives a valuable physical insight into the nature of coherence transfer in more general spin-1/2 systems.

Scalar-tensor linear inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Artymowski, Michał; Racioppi, Antonio, E-mail: Michal.Artymowski@uj.edu.pl, E-mail: Antonio.Racioppi@kbfi.ee

2017-04-01

We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f (φ) R /2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead tomore » linear inflation in the strong coupling limit.« less

Scalar-tensor extension of the ΛCDM model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Algoner, W.C.; Velten, H.E.S.; Zimdahl, W., E-mail: w.algoner@cosmo-ufes.org, E-mail: velten@pq.cnpq.br, E-mail: winfried.zimdahl@pq.cnpq.br

2016-11-01

We construct a cosmological scalar-tensor-theory model in which the Brans-Dicke type scalar Φ enters the effective (Jordan-frame) Hubble rate as a simple modification of the Hubble rate of the ΛCDM model. This allows us to quantify differences between the background dynamics of scalar-tensor theories and general relativity (GR) in a transparent and observationally testable manner in terms of one single parameter. Problems of the mapping of the scalar-field degrees of freedom on an effective fluid description in a GR context are discused. Data from supernovae, the differential age of old galaxies and baryon acoustic oscillations are shown to strongly limitmore » potential deviations from the standard model.« less

Gravitational wave memory in an expanding universe

NASA Astrophysics Data System (ADS)

Tolish, Alexander; Wald, Robert

2016-03-01

We investigate the gravitational wave memory effect in an expanding FLRW spacetime. We find that if the gravitational field is decomposed into gauge-invariant scalar, vector, and tensor modes after the fashion of Bardeen, only the tensor mode gives rise to memory, and this memory can be calculated using the retarded Green's function associated with the tensor wave equation. If locally similar radiation source events occur on flat and FLRW backgrounds, we find that the resulting memories will differ only by a redshift factor, and we explore whether or not this factor depends on the expansion history of the FLRW universe. We compare our results to related work by Bieri, Garfinkle, and Yau.

NIED seismic moment tensor catalogue for regional earthquakes around Japan: quality test and application

NASA Astrophysics Data System (ADS)

Kubo, Atsuki; Fukuyama, Eiichi; Kawai, Hiroyuki; Nonomura, Ken'ichi

2002-10-01

We have examined the quality of the National Research Institute for Earth Science and Disaster Prevention (NIED) seismic moment tensor (MT) catalogue obtained using a regional broadband seismic network (FREESIA). First, we examined using synthetic waveforms the robustness of the solutions with regard to data noise as well as to errors in the velocity structure and focal location. Then, to estimate the reliability, robustness and validity of the catalogue, we compared it with the Harvard centroid moment tensor (CMT) catalogue as well as the Japan Meteorological Agency (JMA) focal mechanism catalogue. We found out that the NIED catalogue is consistent with Harvard and JMA catalogues within the uncertainty of 0.1 in moment magnitude, 10 km in depth, and 15° in direction of the stress axes. The NIED MT catalogue succeeded in reducing to 3.5 the lower limit of moment magnitude above which the moment tensor could be reliably estimated. Finally, we estimated the stress tensors in several different regions by using the NIED MT catalogue. This enables us to elucidate the stress/deformation field in and around the Japanese islands to understand the mode of deformation and applied stress. Moreover, we identified a region of abnormal stress in a swarm area from stress tensor estimates.

Reversible and dissipative macroscopic contributions to the stress tensor: active or passive?

PubMed

Brand, H R; Pleiner, H; Svenšek, D

2014-09-01

The issue of dynamic contributions to the macroscopic stress tensor has been of high interest in the field of bio-inspired active systems over the last few years. Of particular interest is a direct coupling ("active term") of the stress tensor with the order parameter, the latter describing orientational order induced by active processes. Here we analyze more generally possible reversible and irreversible dynamic contributions to the stress tensor for various passive and active macroscopic systems. This includes systems with tetrahedral/octupolar order, polar and non-polar (chiral) nematic and smectic liquid crystals, as well as active fluids with a dynamic preferred (polar or non-polar) direction. We show that it cannot a priori be seen, neither from the symmetry properties of the macroscopic variables involved, nor from the structure of the cross-coupling contributions to the stress tensor, whether the system studied is active or passive. Rather, that depends on whether the variables that give rise to those cross-couplings in the stress tensor are driven or not. We demonstrate that several simplified descriptions of active systems in the literature that neglect the necessary counter term to the active term violate linear irreversible thermodynamics and lead to an unphysical contribution to the entropy production.

The theory of spherically symmetric thin shells in conformal gravity

NASA Astrophysics Data System (ADS)

Berezin, Victor; Dokuchaev, Vyacheslav; Eroshenko, Yury

The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy-momentum tensor of the thin shell is proportional to Diracs delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl-Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in detail the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless ( = massless) shell, it is shown that their dynamics cannot be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl-Einstein gravity, the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.

Q-space trajectory imaging for multidimensional diffusion MRI of the human brain

PubMed Central

Westin, Carl-Fredrik; Knutsson, Hans; Pasternak, Ofer; Szczepankiewicz, Filip; Özarslan, Evren; van Westen, Danielle; Mattisson, Cecilia; Bogren, Mats; O’Donnell, Lauren; Kubicki, Marek; Topgaard, Daniel; Nilsson, Markus

2016-01-01

This work describes a new diffusion MR framework for imaging and modeling of microstructure that we call q-space trajectory imaging (QTI). The QTI framework consists of two parts: encoding and modeling. First we propose q-space trajectory encoding, which uses time-varying gradients to probe a trajectory in q-space, in contrast to traditional pulsed field gradient sequences that attempt to probe a point in q-space. Then we propose a microstructure model, the diffusion tensor distribution (DTD) model, which takes advantage of additional information provided by QTI to estimate a distributional model over diffusion tensors. We show that the QTI framework enables microstructure modeling that is not possible with the traditional pulsed gradient encoding as introduced by Stejskal and Tanner. In our analysis of QTI, we find that the well-known scalar b-value naturally extends to a tensor-valued entity, i.e., a diffusion measurement tensor, which we call the b-tensor. We show that b-tensors of rank 2 or 3 enable estimation of the mean and covariance of the DTD model in terms of a second order tensor (the diffusion tensor) and a fourth order tensor. The QTI framework has been designed to improve discrimination of the sizes, shapes, and orientations of diffusion microenvironments within tissue. We derive rotationally invariant scalar quantities describing intuitive microstructural features including size, shape, and orientation coherence measures. To demonstrate the feasibility of QTI on a clinical scanner, we performed a small pilot study comparing a group of five healthy controls with five patients with schizophrenia. The parameter maps derived from QTI were compared between the groups, and 9 out of the 14 parameters investigated showed differences between groups. The ability to measure and model the distribution of diffusion tensors, rather than a quantity that has already been averaged within a voxel, has the potential to provide a powerful paradigm for the study of complex tissue architecture. PMID:26923372

Einstein's physical strategy, energy conservation, symmetries, and stability: "But Grossmann & I believed that the conservation laws were not satisfied"

NASA Astrophysics Data System (ADS)

Pitts, J. Brian

2016-05-01

Recent work on the history of General Relativity by Renn et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex(es) did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? How did his work relate to emerging knowledge (1911-1914) of the canonical energy-momentum tensor and its translation-induced conservation? After initially using energy-momentum tensors hand-crafted from the gravitational field equations, Einstein used an identity from his assumed linear coordinate covariance xμ‧ = Mνμ xν to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell's theory (which avoids negative-energies but gets an asymmetric canonical tensor as a result) as on a scalar theory (the Newtonian limit). Einstein's theory thus has a symmetric canonical energy-momentum tensor. But as a result, it also has 3 negative-energy field degrees of freedom (later called "ghosts" in particle physics). Thus the Entwurf theory fails a 1920s-1930s a priori particle physics stability test with antecedents in Lagrange's and Dirichlet's stability work; one might anticipate possible gravitational instability. This critique of the Entwurf theory can be compared with Einstein's 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury's perihelion right. One can live with absolute rotation but cannot live with instability. Particle physics also can be useful in the historiography of gravity and space-time, both in assessing the growth of objective knowledge and in suggesting novel lines of inquiry to see whether and how Einstein faced the substantially mathematical issues later encountered in particle physics. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like. Future work will show how the history of General Relativity, especially Noether's work, sheds light on particle physics.

A strategy for optical properties investigation in ABe2BO3F2 (A=K, Rb, Cs) using finite field methods

NASA Astrophysics Data System (ADS)

Mushahali, Hahaer; Mu, Baoxia; Wang, Qian; Mamat, Mamatrishat; Cao, Haibin; Yang, Guang; Jing, Qun

2018-07-01

The finite-field methods can be used to intuitively learn about the optical response and find out the atomic contributions to the birefringence and SHG tensors. In this paper, the linear and second-order nonlinear optical properties of ABe2BO3F2 family (A = K, Rb, Cs) compounds are investigated using the finite-field methods within different exchange-correlation functionals. The results show that the obtained birefringence and SHG tensors are in good agreement with the experimental values. The atomic contribution to the total birefringence was further investigated using the variation of the atomic charges, and the Born effective charges. The results show that the boron-oxygen groups give main contribution to the anisotropic birefringence.

Quantum phase transitions in a two-dimensional quantum XYX model: ground-state fidelity and entanglement.

PubMed

Li, Bo; Li, Sheng-Hao; Zhou, Huan-Qiang

2009-06-01

A systematic analysis is performed for quantum phase transitions in a two-dimensional anisotropic spin-1/2 antiferromagnetic XYX model in an external magnetic field. With the help of an innovative tensor network algorithm, we compute the fidelity per lattice site to demonstrate that the field-induced quantum phase transition is unambiguously characterized by a pinch point on the fidelity surface, marking a continuous phase transition. We also compute an entanglement estimator, defined as a ratio between the one-tangle and the sum of squared concurrences, to identify both the factorizing field and the critical point, resulting in a quantitative agreement with quantum Monte Carlo simulation. In addition, the local order parameter is "derived" from the tensor network representation of the system's ground-state wave functions.

Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories

NASA Astrophysics Data System (ADS)

Dong, Xi

2016-06-01

We develop a framework for studying the well-known universal term in the Rényi entropy for an arbitrary entangling region in four-dimensional conformal field theories that are holographically dual to gravitational theories. The shape dependence of the Rényi entropy Sn is described by two coefficients: fb(n ) for traceless extrinsic curvature deformations and fc(n ) for Weyl tensor deformations. We provide the first calculation of the coefficient fb(n ) in interacting theories by relating it to the stress tensor one-point function in a deformed hyperboloid background. The latter is then determined by a straightforward holographic calculation. Our results show that a previous conjecture fb(n )=fc(n ), motivated by surprising evidence from a variety of free field theories and studies of conical defects, fails holographically.

Mapping Magnetic Susceptibility Anisotropies of White Matter in vivo in the Human Brain at 7 Tesla

PubMed Central

Li, Xu; Vikram, Deepti S; Lim, Issel Anne L; Jones, Craig K; Farrell, Jonathan A.D.; van Zijl, Peter C. M.

2012-01-01

High-resolution magnetic resonance phase- or frequency- shift images acquired at high field show contrast related to magnetic susceptibility differences between tissues. Such contrast varies with the orientation of the organ in the field, but the development of quantitative susceptibility mapping (QSM) has made it possible to reproducibly image the intrinsic tissue susceptibility contrast. However, recent studies indicate that magnetic susceptibility is anisotropic in brain white matter and, as such, needs to be described by a symmetric second-rank tensor (χ¯¯). To fully determine the elements of this tensor, it would be necessary to acquire frequency data at six or more orientations. Assuming cylindrical symmetry of the susceptibility tensor in myelinated white matter fibers, we propose a simplified method to reconstruct the susceptibility tensor in terms of a mean magnetic susceptibility, MMS = (χ∥ + 2χ⊥)/3 and a magnetic susceptibility anisotropy, MSA = χ∥ − χ⊥, where χ∥ and χ⊥ are susceptibility parallel and perpendicular to the white matter fiber direction, respectively. Computer simulations show that with a practical head rotation angle of around 20°–30°, four head orientations suffice to reproducibly reconstruct the tensor with good accuracy. We tested this approach on whole brain 1×1×1 mm3 frequency data acquired from five healthy subjects at 7 T. The frequency information from phase images collected at four head orientations was combined with the fiber direction information extracted from diffusion tensor imaging (DTI) to map the white matter susceptibility tensor. The MMS and MSA were quantified for regions in several large white matter fiber structures, including the corona radiata, posterior thalamic radiation and corpus callosum. MMS ranged from −0.037 to −0.053 ppm (referenced to CSF being about zero). MSA values could be quantified without the need for a reference and ranged between 0.004 and 0.029 ppm, in line with the expectation that the susceptibility perpendicular to the fiber is more diamagnetic than the one parallel to it. PMID:22561358

Geometrically nonlinear transient vibrations of actively damped anti-symmetric angle ply laminated composite shallow shell using active fibre composite (AFC) actuators

NASA Astrophysics Data System (ADS)

Ashok, M. H.; Shivakumar, J.; Nandurkar, Santosh; Khadakbhavi, Vishwanath; Pujari, Sanjay

2018-02-01

In present work, the thin laminated composite shallow shell as smart structure with AFC material’s ACLD treatment is analyzed for geometrically nonlinear transient vibrations. The AFC material is used to make the constraining layer of the ACLD treatment. Golla-Hughes-McTavish (GHM) is used to model the constrained viscoelastic layer of the ACLD treatment in time domain. Along with a simple first-order shear deformation theory the Von Kármán type non-linear strain displacement relations are used for deriving this electromechanical coupled problem. A 3-dimensional finite element model of smart composite panels integrated with the ACLD treated patches has been modelled to reveal the performance of ACLD treated patches on improving the damping properties of slender anti-symmetric angle-ply laminated shallow shell, in controlling the transient vibrations which are geometrically nonlinear. The mathematical results explain that the ACLD treated patches considerably enhance the damping properties of anti-symmetric angle-ply panels undergoing geometrically nonlinear transient vibrations.

Improving sensitivity to magnetic fields and electric dipole moments by using measurements of individual magnetic sublevels

NASA Astrophysics Data System (ADS)

Tang, Cheng; Zhang, Teng; Weiss, David S.

2018-03-01

We explore ways to use the ability to measure the populations of individual magnetic sublevels to improve the sensitivity of magnetic field measurements and measurements of atomic electric dipole moments (EDMs). When atoms are initialized in the m =0 magnetic sublevel, the shot-noise-limited uncertainty of these measurements is 1 /√{2 F (F +1 ) } smaller than that of a Larmor precession measurement. When the populations in the even (or odd) magnetic sublevels are combined, we show that these measurements are independent of the tensor Stark shift and the second order Zeeman shift. We discuss the complicating effect of a transverse magnetic field and show that when the ratio of the tensor Stark shift to the transverse magnetic field is sufficiently large, an EDM measurement with atoms initialized in the superposition of the stretched states can reach the optimal sensitivity.

General equilibrium second-order hydrodynamic coefficients for free quantum fields

NASA Astrophysics Data System (ADS)

Buzzegoli, M.; Grossi, E.; Becattini, F.

2017-10-01

We present a systematic calculation of the corrections of the stress-energy tensor and currents of the free boson and Dirac fields up to second order in thermal vorticity, which is relevant for relativistic hydrodynamics. These corrections are non-dissipative because they survive at general thermodynamic equilibrium with non vanishing mean values of the conserved generators of the Lorentz group, i.e. angular momenta and boosts. Their equilibrium nature makes it possible to express the relevant coefficients by means of correlators of the angular-momentum and boost operators with stress-energy tensor and current, thus making simpler to determine their so-called "Kubo formulae". We show that, at least for free fields, the corrections are of quantum origin and we study several limiting cases and compare our results with previous calculations. We find that the axial current of the free Dirac field receives corrections proportional to the vorticity independently of the anomalous term.

Quantum transport in antidot arrays in magnetic fields

NASA Astrophysics Data System (ADS)

Ishizaka, Satoshi; Nihey, Fumiyuki; Nakamura, Kazuo; Sone, Jun' Ichi; Ando, Tsuneya

1995-04-01

Transport in antidot arrays in magnetic fields is studied numerically. We calculate the density of states and conductivity tensor by the self-consistent Born approximation. Although peak positions of the density of states agree well with the quantization condition for several short periodic orbits, the behavior of the conductivity tensor is very complicated. Coupling among the periodic orbits causes an oscillation in the Hall conductivity in magnetic fields around the localized peak. In low magnetic fields, the skipping orbit, which runs from an antidot to its neighboring antidot, plays a crucial role for diagonal conductivity, and its coupling with the periodic orbits causes an oscillation in the diagonal conductivity. The resulting magnetoresistance oscillates with a period near one magnetic flux quantum as observed in recent experiments. Furthermore, the oscillation due to the manifestation of Hofstadter's butterfly is present in both the diagonal conductivity and the Hall conductivity.

Hybrid Natural Inflation

NASA Astrophysics Data System (ADS)

Ross, Graham G.; Germán, Gabriel; Vázquez, J. Alberto

2016-05-01

We construct two simple effective field theory versions of Hybrid Natural Inflation (HNI) that illustrate the range of its phenomenological implications. The resulting inflationary sector potential, V = Δ4(1 + acos( ϕ/f)), arises naturally, with the inflaton field a pseudo-Nambu-Goldstone boson. The end of inflation is triggered by a waterfall field and the conditions for this to happen are determined. Also of interest is the fact that the slow-roll parameter ɛ (and hence the tensor r) is a non-monotonic function of the field with a maximum where observables take universal values that determines the maximum possible tensor to scalar ratio r. In one of the models the inflationary scale can be as low as the electroweak scale. We explore in detail the associated HNI phenomenology, taking account of the constraints from Black Hole production, and perform a detailed fit to the Planck 2015 temperature and polarisation data.

Emergent odd-parity multipoles and magnetoelectric effects on a diamond structure: Implication for the 5 d transition metal oxides A OsO4 (A =K ,Rb, and Cs)

NASA Astrophysics Data System (ADS)

Hayami, Satoru; Kusunose, Hiroaki; Motome, Yukitoshi

2018-01-01

We report our theoretical predictions on the linear magnetoelectric (ME) effects originating from odd-parity multipoles associated with spontaneous spin and orbital ordering on a diamond structure. We derive a two-orbital model for d electrons in eg orbitals by including the effective spin-orbit coupling which arises from the mixing between eg and t2 g orbitals. We show that the model acquires a net antisymmetric spin-orbit coupling once staggered spin and orbital orders occur spontaneously. The staggered orders are accompanied by odd-parity multipoles: magnetic monopole, quadrupoles, and toroidal dipoles. We classify the types of the odd-parity multipoles according to the symmetry of the spin and orbital orders. Furthermore, by computing the ME tensor using the linear response theory, we show that the staggered orders induce a variety of the linear ME responses. We elaborate all possible ME responses for each staggered order, which are useful to identify the order parameter and to detect the odd-parity multipoles by measuring the ME effects. We also elucidate the effect of lowering symmetry by a tetragonal distortion, which leads to richer ME responses. The implications of our results are discussed for the 5 d transition metal oxides, A OsO4 (A =K,Rb, and Cs) , in which the order parameters are not fully identified.

Quantum Sets and Clifford Algebras

NASA Astrophysics Data System (ADS)

Finkelstein, David

1982-06-01

The mathematical language presently used for quantum physics is a high-level language. As a lowest-level or basic language I construct a quantum set theory in three stages: (1) Classical set theory, formulated as a Clifford algebra of “ S numbers” generated by a single monadic operation, “bracing,” Br = {…}. (2) Indefinite set theory, a modification of set theory dealing with the modal logical concept of possibility. (3) Quantum set theory. The quantum set is constructed from the null set by the familiar quantum techniques of tensor product and antisymmetrization. There are both a Clifford and a Grassmann algebra with sets as basis elements. Rank and cardinality operators are analogous to Schroedinger coordinates of the theory, in that they are multiplication or “ Q-type” operators. “ P-type” operators analogous to Schroedinger momenta, in that they transform the Q-type quantities, are bracing (Br), Clifford multiplication by a set X, and the creator of X, represented by Grassmann multiplication c( X) by the set X. Br and its adjoint Br* form a Bose-Einstein canonical pair, and c( X) and its adjoint c( X)* form a Fermi-Dirac or anticanonical pair. Many coefficient number systems can be employed in this quantization. I use the integers for a discrete quantum theory, with the usual complex quantum theory as limit. Quantum set theory may be applied to a quantum time space and a quantum automaton.

Mid-Crustal Stress Magnitude and Rotation Transients Related to the Seismic Cycle

NASA Astrophysics Data System (ADS)

Nüchter, J. A.; Ellis, S.

2008-12-01

Seismic slip causes a stress drop in the upper crust, and a major stress increase at the lower termination of the fault in the middle crust. Previous numerical models show how these stresses relax during an episode of postseismic creep. Natural evidence for postseismic stress and strain transients at depth is provided by 1) the geological record of exhumed metamorphic rocks, and 2) from postseismic surface deformation transients. In the present study, we use numerical models to investigate the changes in the geometry of the mid-crustal stress field caused by seismic slip along normal faults within an extensional tectonic setting. We model a 100x30km crustal section, with a fault reaching down to 20km and dipping at 60°. A non-linear thermal gradient and constant elastic parameters are applied. Thermally activated creep is described by values derived from laboratory creep experiments on wet quartzite. The crust is loaded by horizontal extension at a constant rate, and earthquakes are triggered by a short term decrease in the frictional coefficient of the fault. During the interseismic period, this coefficient is set to high values to lock the fault. A sequence of 30 earthquakes with a constant recurrence interval of 500y is simulated, and the results for the last seismic cycle are analyzed. In such a tectonic setting, the Anderson theory predicts that the maximum principal stress is vertical. A stress field consistent to this theory is reached after an initial stage of 15ka extension without earthquake activity. The results for the 30th seismic cycle imply that seismic slip causes a major stress increase of at least 50MPa at a depth level below the brittle ductile transition, which is in accordance to reports on seismic stress increase derived from the record of metamorphic rocks. In the hanging wall, the stress increase results mainly from an increase in the maximum principal stress and the stress tensor rotates counter-clockwise by 10-30°. In the footwall the stress increase results mainly from a drop in the minimum principal stress, and the stress tensor rotates clockwise by 45-60°. A change in the magnitude of differential stress can be addressed by the addition of an incremental stress tensor resulting from elastic strain to the preexisting stress tensor. In an isotropic medium, the orientation of the maximum and the minimum principal stress changes are controlled by the directions of maximum compression and maximum extension, respectively. The magnitude and the orientation of the resulting stress tensor depend: 1) on the absolute magnitudes and on the ratio of the magnitudes of pre-existing stress and incremental change in the stress tensor; and 2) on the mis-orientation between existing stress and stress change principal directions. The zone of coseismic loading correlates to the interval in which seismic slip tapers off with depth. For a normal fault, the crust here is subjected to fault-parallel compression in the hanging wall, and to extension in the footwall. The resulting orientation of the seismic principal compressive stress change parallel to the fault in the hanging wall and normal to the fault in the footwall causes the particular deflection of the resulting stress tensor . During the interseismic period, the stress peak relaxes by thermally activated creep, while the deflection of the stress tensor is persistent. We show that significant mis- orientations of the stress tensor can be preserved over timescales typical for a seismic cycle, in dependence on the far field extension rate. We conclude that seismic activity causes 1) a non-steady state mid-crustal stress field, and 2) a persistent deflection of the stress tensor orientation from the predictions of the Anderson theory.

3D polarisation speckle as a demonstration of tensor version of the van Cittert-Zernike theorem for stochastic electromagnetic beams

NASA Astrophysics Data System (ADS)

Ma, Ning; Zhao, Juan; Hanson, Steen G.; Takeda, Mitsuo; Wang, Wei

2016-10-01

Laser speckle has received extensive studies of its basic properties and associated applications. In the majority of research on speckle phenomena, the random optical field has been treated as a scalar optical field, and the main interest has been concentrated on their statistical properties and applications of its intensity distribution. Recently, statistical properties of random electric vector fields referred to as Polarization Speckle have come to attract new interest because of their importance in a variety of areas with practical applications such as biomedical optics and optical metrology. Statistical phenomena of random electric vector fields have close relevance to the theories of speckles, polarization and coherence theory. In this paper, we investigate the correlation tensor for stochastic electromagnetic fields modulated by a depolarizer consisting of a rough-surfaced retardation plate. Under the assumption that the microstructure of the scattering surface on the depolarizer is as fine as to be unresolvable in our observation region, we have derived a relationship between the polarization matrix/coherency matrix for the modulated electric fields behind the rough-surfaced retardation plate and the coherence matrix under the free space geometry. This relation is regarded as entirely analogous to the van Cittert-Zernike theorem of classical coherence theory. Within the paraxial approximation as represented by the ABCD-matrix formalism, the three-dimensional structure of the generated polarization speckle is investigated based on the correlation tensor, indicating a typical carrot structure with a much longer axial dimension than the extent in its transverse dimension.

On the cosmology of scalar-tensor-vector gravity theory

NASA Astrophysics Data System (ADS)

Jamali, Sara; Roshan, Mahmood; Amendola, Luca

2018-01-01

We consider the cosmological consequences of a special scalar-tensor-vector theory of gravity, known as MOG (for MOdified Gravity), proposed to address the dark matter problem. This theory introduces two scalar fields G(x) and μ(x), and one vector field phiα(x), in addition to the metric tensor. We set the corresponding self-interaction potentials to zero, as in the standard form of MOG. Then using the phase space analysis in the flat Friedmann-Robertson-Walker background, we show that the theory possesses a viable sequence of cosmological epochs with acceptable time dependency for the cosmic scale factor. We also investigate MOG's potential as a dark energy model and show that extra fields in MOG cannot provide a late time accelerated expansion. Furthermore, using a dynamical system approach to solve the non-linear field equations numerically, we calculate the angular size of the sound horizon, i.e. θs, in MOG. We find that 8× 10‑3rad<θs<8.2× 10‑3 rad which is way outside the current observational bounds. Finally, we generalize MOG to a modified form called mMOG, and we find that mMOG passes the sound-horizon constraint. However, mMOG also cannot be considered as a dark energy model unless one adds a cosmological constant, and more importantly, the matter dominated era is still slightly different from the standard case.

ESR modes in a Strong-Leg Ladder in the Tomonaga-Luttinger Liquid Phase

NASA Astrophysics Data System (ADS)

Zvyagin, S.; Ozerov, M.; Maksymenko, M.; Wosnitza, J.; Honecker, A.; Landee, C. P.; Turnbull, M.; Furuya, S. C.; Giamarchi, T.

Magnetic excitations in the strong-leg quantum spin ladder compound (C7H10N)2CuBr4 (known as DIMPY) in the field-induced Tomonaga-Luttinger spin liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual non-linear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a fingerprint of the spin dynamics in a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder and owe its ESR observability to the uniform Dzyaloshinskii-Moriya interaction. This work was partially supported by the DFG and Helmholtz Gemeinschaft (Germany), Swiss SNF under Division II, and ERC synergy UQUAM project. We acknowledge the support of the HLD at HZDR, member of the European Magnetic Field Laboratory (EMFL).

Drift of Phase Fluctuations in the ABC Model

NASA Astrophysics Data System (ADS)

Bertini, Lorenzo; Buttà, Paolo

2013-07-01

In a recent work, Bodineau and Derrida analyzed the phase fluctuations in the ABC model. In particular, they computed the asymptotic variance and, on the basis of numerical simulations, they conjectured the presence of a drift, which they guessed to be an antisymmetric function of the three densities. By assuming the validity of the fluctuating hydrodynamic approximation, we prove the presence of such a drift, providing an analytical expression for it. This expression is then shown to be an antisymmetric function of the three densities. The antisymmetry of the drift can also be inferred from a symmetry property of the underlying microscopic dynamics.

Lattice study of planar equivalence: The quark condensate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Armoni, Adi; Lucini, Biagio; Patella, Agostino

2008-08-15

We study quenched SU(N) gauge theories with fermions in the two-index symmetric, antisymmetric and the adjoint representations. Our main motivation is to check whether at large number of colors those theories become nonperturbatively equivalent. We prove the equivalence assuming that the charge-conjugation symmetry is not broken in pure Yang-Mills theory. We then carry out a quenched lattice simulation of the quark condensate in the symmetric, antisymmetric and the adjoint representations for SU(2), SU(3), SU(4), SU(6), and SU(8). We show that the data support the equivalence and discuss the size of subleading corrections.

Detecting Lamb waves with broadband acousto-ultrasonic signals in composite structures

NASA Technical Reports Server (NTRS)

Kautz, Harold E.

1992-01-01

Lamb waves can be produced and detected in ceramic matrix composites (CMC) and metal matrix composites (MMC) plates using the acousto-ultrasonic configuration employing broadband transducers. Experimental dispersion curves of lowest symmetric and lowest antisymmetric modes behave in a manner analogous to the graphite/polymer theoretical curves. In this study a basis has been established for analyzing Lamb wave velocities for characterizing composite plates. Lamb wave disperison curves and group velocities were correlated with variations in axial stiffness and shear stiffness in MMC and CMC. For CMCs, interfacial shear strength was also correlated with the first antisymmetric Lamb mode.

Detecting Lamb waves with broad-band acousto-ultrasonic signals in composite structures

NASA Technical Reports Server (NTRS)

Kautz, Harold E.

1992-01-01

Lamb waves can be produced and detected in ceramic matrix composites (CMC) and metal matrix composites (MMC) plates using the acousto-ultrasonic configuration employing broadband transducers. Experimental dispersion curves of lowest symmetric and antisymmetric modes behave in a manner analogous to the graphite/polymer theoretical curves. In this study a basis has been established for analyzing Lamb wave velocities for characterizing composite plates. Lamb wave dispersion curves and group velocities were correlated with variations in axial stiffness and shear stiffness in MMC and CMC. For CMC, interfacial shear strength was also correlated with the first antisymmetric Lamb mode.

Invariant quantities in the scalar-tensor theories of gravitation

NASA Astrophysics Data System (ADS)

Järv, Laur; Kuusk, Piret; Saal, Margus; Vilson, Ott

2015-01-01

We consider the general scalar-tensor gravity without derivative couplings. By rescaling of the metric and reparametrization of the scalar field, the theory can be presented in different conformal frames and parametrizations. In this work we argue that while due to the freedom to transform the metric and the scalar field, the scalar field itself does not carry a physical meaning (in a generic parametrization), there are functions of the scalar field and its derivatives which remain invariant under the transformations. We put forward a scheme to construct these invariants, discuss how to formulate the theory in terms of the invariants, and show how the observables like parametrized post-Newtonian parameters and characteristics of the cosmological solutions can be neatly expressed in terms of the invariants. In particular, we describe the scalar field solutions in Friedmann-Lemaître-Robertson-Walker cosmology in Einstein and Jordan frames and explain their correspondence despite the approximate equations turning out to be linear and nonlinear in different frames.

On the equivalence among stress tensors in a gauge-fluid system

NASA Astrophysics Data System (ADS)

Mitra, Arpan Krishna; Banerjee, Rabin; Ghosh, Subir

2017-12-01

In this paper, we bring out the subtleties involved in the study of a first-order relativistic field theory with auxiliary field variables playing an essential role. In particular, we discuss the nonisentropic Eulerian (or Hamiltonian) fluid model. Interactions are introduced by coupling the fluid to a dynamical Maxwell (U(1)) gauge field. This dynamical nature of the gauge field is crucial in showing the equivalence, on the physical subspace, of the stress tensor derived from two definitions, i.e. the canonical (Noether) one and the symmetric one. In the conventional equal-time formalism, we have shown that the generators of the space-time transformations obtained from these two definitions agree modulo the Gauss constraint. This equivalence in the physical sector has been achieved only because of the dynamical nature of the gauge fields. Subsequently, we have explicitly demonstrated the validity of the Schwinger condition. A detailed analysis of the model in lightcone formalism has also been done where several interesting features are revealed.

Tensor network state correspondence and holography

NASA Astrophysics Data System (ADS)

Singh, Sukhwinder

2018-01-01

In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"—a correspondence between quantum many-body states mediated by tensor networks as we describe—to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.

Moment tensor clustering: a tool to monitor mining induced seismicity

NASA Astrophysics Data System (ADS)

Cesca, Simone; Dahm, Torsten; Tolga Sen, Ali

2013-04-01

Automated moment tensor inversion routines have been setup in the last decades for the analysis of global and regional seismicity. Recent developments could be used to analyse smaller events and larger datasets. In particular, applications to microseismicity, e.g. in mining environments, have then led to the generation of large moment tensor catalogues. Moment tensor catalogues provide a valuable information about the earthquake source and details of rupturing processes taking place in the seismogenic region. Earthquake focal mechanisms can be used to discuss the local stress field, possible orientations of the fault system or to evaluate the presence of shear and/or tensile cracks. Focal mechanism and moment tensor solutions are typically analysed for selected events, and quick and robust tools for the automated analysis of larger catalogues are needed. We propose here a method to perform cluster analysis for large moment tensor catalogues and identify families of events which characterize the studied microseismicity. Clusters include events with similar focal mechanisms, first requiring the definition of distance between focal mechanisms. Different metrics are here proposed, both for the case of pure double couple, constrained moment tensor and full moment tensor catalogues. Different clustering approaches are implemented and discussed. The method is here applied to synthetic and real datasets from mining environments to demonstrate its potential: the proposed cluserting techniques prove to be able to automatically recognise major clusters. An important application for mining monitoring concerns the early identification of anomalous rupture processes, which is relevant for the hazard assessment. This study is funded by the project MINE, which is part of the R&D-Programme GEOTECHNOLOGIEN. The project MINE is funded by the German Ministry of Education and Research (BMBF), Grant of project BMBF03G0737.

Method to compute the stress-energy tensor for a quantum field outside a black hole that forms from collapse

NASA Astrophysics Data System (ADS)

Anderson, Paul; Evans, Charles

2017-01-01

A method to compute the stress-energy tensor for a quantized massless minimally coupled scalar field outside the event horizon of a 4-D black hole that forms from the collapse of a spherically symmetric null shell is given. The method is illustrated in the corresponding 2-D case which is mathematically similar but is simple enough that the calculations can be done analytically. The approach to the Unruh state at late times is discussed. National Science Foundation Grant No. PHY-1505875 to Wake Forest University and National Science Foundation Grant No. PHY-1506182 to the University of North Carolina, Chapel Hill

Quantum gravitational corrections from the Wheeler–DeWitt equation for scalar–tensor theories

NASA Astrophysics Data System (ADS)

Steinwachs, Christian F.; van der Wild, Matthijs L.

2018-07-01

We perform the canonical quantization of a general scalar–tensor theory and derive the first quantum gravitational corrections following from a semiclassical expansion of the Wheeler–DeWitt equation. The non-minimal coupling of the scalar field to gravity induces a derivative coupling between the scalar field and the gravitational degrees of freedom, which prevents a direct application of the expansion scheme. We address this technical difficulty by transforming the theory from the Jordan frame to the Einstein frame. We find that a large non-minimal coupling can have strong effects on the quantum gravitational correction terms. We briefly discuss these effects in the context of the specific model of Higgs inflation.

Source characterization of underground explosions from hydrodynamic-to-elastic coupling simulations

NASA Astrophysics Data System (ADS)

Chiang, A.; Pitarka, A.; Ford, S. R.; Ezzedine, S. M.; Vorobiev, O.

2017-12-01

A major improvement in ground motion simulation capabilities for underground explosion monitoring during the first phase of the Source Physics Experiment (SPE) is the development of a wave propagation solver that can propagate explosion generated non-linear near field ground motions to the far-field. The calculation is done using a hybrid modeling approach with a one-way hydrodynamic-to-elastic coupling in three dimensions where near-field motions are computed using GEODYN-L, a Lagrangian hydrodynamics code, and then passed to WPP, an elastic finite-difference code for seismic waveform modeling. The advancement in ground motion simulation capabilities gives us the opportunity to assess moment tensor inversion of a realistic volumetric source with near-field effects in a controlled setting, where we can evaluate the recovered source properties as a function of modeling parameters (i.e. velocity model) and can provide insights into previous source studies on SPE Phase I chemical shots and other historical nuclear explosions. For example the moment tensor inversion of far-field SPE seismic data demonstrated while vertical motions are well-modeled using existing velocity models large misfits still persist in predicting tangential shear wave motions from explosions. One possible explanation we can explore is errors and uncertainties from the underlying Earth model. Here we investigate the recovered moment tensor solution, particularly on the non-volumetric component, by inverting far-field ground motions simulated from physics-based explosion source models in fractured material, where the physics-based source models are based on the modeling of SPE-4P, SPE-5 and SPE-6 near-field data. The hybrid modeling approach provides new prospects in modeling explosion source and understanding the uncertainties associated with it.

Metal foil method for noncontact measurement of lateral vibrations of a nonmetallic cylinder by a solenoid

NASA Astrophysics Data System (ADS)

Han, Soon Woo; Bang, Young Bong; Kim, Yoon Young

2006-10-01

This investigation shows that if a solenoid encircles a metal foil loop wound around a nonmetallic cylinder vibrating laterally, an electromotive force is induced in the solenoid. The induction is possible only when the foil loop is complete and an antisymmetric magnetic field is applied to the foil. In this work, stationary permanent magnets were used. Because the solenoid is the sensing element, no physical contact between the element and a test specimen is required. The effects of the metal foil thickness and width on the measurement sensitivity were studied and vibration modal testing of an acryl cylinder was performed.

Radiative processes of uniformly accelerated entangled atoms

NASA Astrophysics Data System (ADS)

Menezes, G.; Svaiter, N. F.

2016-05-01

We study radiative processes of uniformly accelerated entangled atoms, interacting with an electromagnetic field prepared in the Minkowski vacuum state. We discuss the structure of the rate of variation of the atomic energy for two atoms traveling in different hyperbolic world lines. We identify the contributions of vacuum fluctuations and radiation reaction to the generation of entanglement as well as to the decay of entangled states. Our results resemble the situation in which two inertial atoms are coupled individually to two spatially separated cavities at different temperatures. In addition, for equal accelerations we obtain that one of the maximally entangled antisymmetric Bell state is a decoherence-free state.

Waves in a plane graphene - dielectric waveguide structure

NASA Astrophysics Data System (ADS)

Evseev, Dmitry A.; Eliseeva, Svetlana V.; Sementsov, Dmitry I.

2017-10-01

The features of the guided TE modes propagation have been investigated on the basis of computer simulations in a planar structure consisting of a set of alternating layers of dielectric and graphene. Within the framework of the effective medium approximation, the dispersion relations have been received for symmetric and antisymmetric waveguide modes, determined by the frequency range of their existence. The wave field distribution by structure, frequency dependences of the constants of propagation and transverse components of the wave vectors, as well as group and phase velocities of waveguide modes have been obtained, the effect of the graphene part in a structure on the waveguide mode behavior has been shown.

Relative-observer definition of the Simon tensor

NASA Astrophysics Data System (ADS)

Bini, Donato; Geralico, Andrea

2018-05-01

The definition of the Simon tensor, originally given only in Kerr spacetime and associated with the static family of observers, is generalized to any spacetime and to any possible observer family. Such generalization is obtained by a standard ‘3  +  1’ splitting of the Bianchi identities, which are rewritten here as a ‘balance equation’ between various spatial fields, associated with the kinematical properties of the observer congruence and representing the spacetime curvature.

Geometric phase of cosmological scalar and tensor perturbations in f(R) gravity

NASA Astrophysics Data System (ADS)

Balajany, Hamideh; Mehrafarin, Mohammad

2018-05-01

By using the conformal equivalence of f(R) gravity in vacuum and the usual Einstein theory with scalar-field matter, we derive the Hamiltonian of the linear cosmological scalar and tensor perturbations in f(R) gravity in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes as a Lewis-Riesenfeld phase.

Inflation in anisotropic scalar-tensor theories

NASA Technical Reports Server (NTRS)

Pimentel, Luis O.; Stein-Schabes, Jaime

1988-01-01

The existence of an inflationary phase in anisotropic Scalar-Tensor Theories is investigated by means of a conformal transformation that allows us to rewrite these theories as gravity minimally coupled to a scalar field with a nontrivial potential. The explicit form of the potential is then used and the No Hair Theorem concludes that there is an inflationary phase in all open or flat anisotropic spacetimes in these theories. Several examples are constructed where the effect becomes manifest.

Turbulence Modeling Effects on the Prediction of Equilibrium States of Buoyant Shear Flows

NASA Technical Reports Server (NTRS)

Zhao, C. Y.; So, R. M. C.; Gatski, T. B.

2001-01-01

The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated. The velocity field models used include a two-equation closure, a Reynolds-stress closure assuming two different pressure-strain models and three different dissipation rate tensor models. As for the thermal field closure models, two different pressure-scrambling models and nine different temperature variance dissipation rate, Epsilon(0) equations were considered. The emphasis of this paper is focused on the effects of the Epsilon(0)-equation, of the dissipation rate models, of the pressure-strain models and of the pressure-scrambling models on the prediction of the approach to equilibrium turbulence. Equilibrium turbulence is defined by the time rate (if change of the scaled Reynolds stress anisotropic tensor and heat flux vector becoming zero. These conditions lead to the equilibrium state parameters. Calculations show that the Epsilon(0)-equation has a significant effect on the prediction of the approach to equilibrium turbulence. For a particular Epsilon(0)-equation, all velocity closure models considered give an equilibrium state if anisotropic dissipation is accounted for in one form or another in the dissipation rate tensor or in the Epsilon(0)-equation. It is further found that the models considered for the pressure-strain tensor and the pressure-scrambling vector have little or no effect on the prediction of the approach to equilibrium turbulence.

Natural chemical shielding analysis of nuclear magnetic resonance shielding tensors from gauge-including atomic orbital calculations

NASA Astrophysics Data System (ADS)

Bohmann, Jonathan A.; Weinhold, Frank; Farrar, Thomas C.

1997-07-01

Nuclear magnetic shielding tensors computed by the gauge including atomic orbital (GIAO) method in the Hartree-Fock self-consistent-field (HF-SCF) framework are partitioned into magnetic contributions from chemical bonds and lone pairs by means of natural chemical shielding (NCS) analysis, an extension of natural bond orbital (NBO) analysis. NCS analysis complements the description provided by alternative localized orbital methods by directly calculating chemical shieldings due to delocalized features in the electronic structure, such as bond conjugation and hyperconjugation. Examples of NCS tensor decomposition are reported for CH4, CO, and H2CO, for which a graphical mnemonic due to Cornwell is used to illustrate the effect of hyperconjugative delocalization on the carbon shielding.

Superconducting tensor gravity gradiometer

NASA Technical Reports Server (NTRS)

Paik, H. J.

1981-01-01

The employment of superconductivity and other material properties at cryogenic temperatures to fabricate sensitive, low-drift, gravity gradiometer is described. The device yields a reduction of noise of four orders of magnitude over room temperature gradiometers, and direct summation and subtraction of signals from accelerometers in varying orientations are possible with superconducting circuitry. Additional circuits permit determination of the linear and angular acceleration vectors independent of the measurement of the gravity gradient tensor. A dewar flask capable of maintaining helium in a liquid state for a year's duration is under development by NASA, and a superconducting tensor gravity gradiometer for the NASA Geodynamics Program is intended for a LEO polar trajectory to measure the harmonic expansion coefficients of the earth's gravity field up to order 300.

Normal stress differences and beyond-Navier-Stokes hydrodynamics

NASA Astrophysics Data System (ADS)

Alam, Meheboob; Saha, Saikat

2017-06-01

A recently proposed beyond-Navier-Stokes order hydrodynamic theory for dry granular fluids is revisited by focussing on the behaviour of the stress tensor and the scaling of related transport coefficients in the dense limit. For the homogeneous shear flow, it is shown that the eigen-directions of the second-moment tensor and those of the shear tensor become co-axial, thus making the first normal stress difference (N1) to zero in the same limit. In contrast, the origin of the second normal stress difference (N2) is tied to the `excess' temperature along the mean-vorticity direction and the imposed shear field, respectively, in the dilute and dense flows. The scaling relations for transport coefficients are suggested based on the present theory.

An Ap-Structure with Finslerian Flavor II:. Torsion, Curvature and Other Objects

NASA Astrophysics Data System (ADS)

Wanas, M. I.; Kamal, Mona M.

An absolute parallelism (AP-) space having Finslerian properties is called FAP-space. This FAP-structure is wider than both conventional AP and Finsler structures. In the present work, more geometric objects as curvature and torsion tensors are derived in the context of this structure. Also second order tensors, usually needed for physical applications, are derived and studied. Furthermore, the anti-curvature and the W-tensor are defined for the FAP-structure. Relations between Riemannian, AP, Finsler and FAP structures are given. These relations facilitate comparison between results of applications carried out in the framework of these structures. We hope that the use of the FAP-structure, in applications may throw some light on some of the problems facing geometric field theories.

Differential Geometry and Lie Groups for Physicists

NASA Astrophysics Data System (ADS)

Fecko, Marián.

2006-10-01

Introduction; 1. The concept of a manifold; 2. Vector and tensor fields; 3. Mappings of tensors induced by mappings of manifolds; 4. Lie derivative; 5. Exterior algebra; 6. Differential calculus of forms; 7. Integral calculus of forms; 8. Particular cases and applications of Stoke's Theorem; 9. Poincaré Lemma and cohomologies; 10. Lie Groups - basic facts; 11. Differential geometry of Lie Groups; 12. Representations of Lie Groups and Lie Algebras; 13. Actions of Lie Groups and Lie Algebras on manifolds; 14. Hamiltonian mechanics and symplectic manifolds; 15. Parallel transport and linear connection on M; 16. Field theory and the language of forms; 17. Differential geometry on TM and T*M; 18. Hamiltonian and Lagrangian equations; 19. Linear connection and the frame bundle; 20. Connection on a principal G-bundle; 21. Gauge theories and connections; 22. Spinor fields and Dirac operator; Appendices; Bibliography; Index.

Differential Geometry and Lie Groups for Physicists

NASA Astrophysics Data System (ADS)

Fecko, Marián.

2011-03-01

Introduction; 1. The concept of a manifold; 2. Vector and tensor fields; 3. Mappings of tensors induced by mappings of manifolds; 4. Lie derivative; 5. Exterior algebra; 6. Differential calculus of forms; 7. Integral calculus of forms; 8. Particular cases and applications of Stoke's Theorem; 9. Poincaré Lemma and cohomologies; 10. Lie Groups - basic facts; 11. Differential geometry of Lie Groups; 12. Representations of Lie Groups and Lie Algebras; 13. Actions of Lie Groups and Lie Algebras on manifolds; 14. Hamiltonian mechanics and symplectic manifolds; 15. Parallel transport and linear connection on M; 16. Field theory and the language of forms; 17. Differential geometry on TM and T*M; 18. Hamiltonian and Lagrangian equations; 19. Linear connection and the frame bundle; 20. Connection on a principal G-bundle; 21. Gauge theories and connections; 22. Spinor fields and Dirac operator; Appendices; Bibliography; Index.

Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories.

PubMed

Dong, Xi

2016-06-24

We develop a framework for studying the well-known universal term in the Rényi entropy for an arbitrary entangling region in four-dimensional conformal field theories that are holographically dual to gravitational theories. The shape dependence of the Rényi entropy S_{n} is described by two coefficients: f_{b}(n) for traceless extrinsic curvature deformations and f_{c}(n) for Weyl tensor deformations. We provide the first calculation of the coefficient f_{b}(n) in interacting theories by relating it to the stress tensor one-point function in a deformed hyperboloid background. The latter is then determined by a straightforward holographic calculation. Our results show that a previous conjecture f_{b}(n)=f_{c}(n), motivated by surprising evidence from a variety of free field theories and studies of conical defects, fails holographically.

Effect of gas mixing on physical properties of warm collisional helicon plasmas

NASA Astrophysics Data System (ADS)

Kabir, M.; Niknam, A. R.

2017-10-01

The effect of inert gas mixing on the physical properties of a helicon plasma source with a Nagoya type III antenna is analytically investigated by taking into account the thermal and collisional effects. The dielectric permittivity tensor of this mixed gas plasma is obtained by using the Bhatnagar-Gross- Krook kinetic theory. Considering the dielectric tensor of mixed gas plasma and solving the electromagnetic field equations, the profiles of electromagnetic fields and plasma resistance are plotted and discussed. The results show that the plasma resistance peaks decrease with increasing Xe fraction in Ar-Xe plasma, and increase with the He fraction in Ar-He plasma. It is also shown that by increasing the xenon filling fraction, the electromagnetic field amplitudes are lowered, and by increasing the helium filling fraction, they are increased.

Trifocal Tensor-Based Adaptive Visual Trajectory Tracking Control of Mobile Robots.

PubMed

Chen, Jian; Jia, Bingxi; Zhang, Kaixiang

2017-11-01

In this paper, a trifocal tensor-based approach is proposed for the visual trajectory tracking task of a nonholonomic mobile robot equipped with a roughly installed monocular camera. The desired trajectory is expressed by a set of prerecorded images, and the robot is regulated to track the desired trajectory using visual feedback. Trifocal tensor is exploited to obtain the orientation and scaled position information used in the control system, and it works for general scenes owing to the generality of trifocal tensor. In the previous works, the start, current, and final images are required to share enough visual information to estimate the trifocal tensor. However, this requirement can be easily violated for perspective cameras with limited field of view. In this paper, key frame strategy is proposed to loosen this requirement, extending the workspace of the visual servo system. Considering the unknown depth and extrinsic parameters (installing position of the camera), an adaptive controller is developed based on Lyapunov methods. The proposed control strategy works for almost all practical circumstances, including both trajectory tracking and pose regulation tasks. Simulations are made based on the virtual experimentation platform (V-REP) to evaluate the effectiveness of the proposed approach.

The simplicial Ricci tensor

NASA Astrophysics Data System (ADS)

Alsing, Paul M.; McDonald, Jonathan R.; Miller, Warner A.

2011-08-01

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincarè conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area—an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.