Simple model for deriving sdg interacting boson model Hamiltonians: 150Nd example

NASA Astrophysics Data System (ADS)

Devi, Y. D.; Kota, V. K. B.

1993-07-01

A simple and yet useful model for deriving sdg interacting boson model (IBM) Hamiltonians is to assume that single-boson energies derive from identical particle (pp and nn) interactions and proton, neutron single-particle energies, and that the two-body matrix elements for bosons derive from pn interaction, with an IBM-2 to IBM-1 projection of the resulting p-n sdg IBM Hamiltonian. The applicability of this model in generating sdg IBM Hamiltonians is demonstrated, using a single-j-shell Otsuka-Arima-Iachello mapping of the quadrupole and hexadecupole operators in proton and neutron spaces separately and constructing a quadrupole-quadrupole plus hexadecupole-hexadecupole Hamiltonian in the analysis of the spectra, B(E2)'s, and E4 strength distribution in the example of 150Nd.

Weak quadrupole moments

NASA Astrophysics Data System (ADS)

Lackenby, B. G. C.; Flambaum, V. V.

2018-07-01

We introduce the weak quadrupole moment (WQM) of nuclei, related to the quadrupole distribution of the weak charge in the nucleus. The WQM produces a tensor weak interaction between the nucleus and electrons and can be observed in atomic and molecular experiments measuring parity nonconservation. The dominating contribution to the weak quadrupole is given by the quadrupole moment of the neutron distribution, therefore, corresponding experiments should allow one to measure the neutron quadrupoles. Using the deformed oscillator model and the Schmidt model we calculate the quadrupole distributions of neutrons, Q n , the WQMs, {Q}W(2), and the Lorentz invariance violating energy shifts in 9Be, 21Ne, 27Al, 131Xe, 133Cs, 151Eu, 153Eu, 163Dy, 167Er, 173Yb, 177Hf, 179Hf, 181Ta, 201Hg and 229Th.

The long-range non-additive three-body dispersion interactions for the rare gases, alkali, and alkaline-earth atoms

NASA Astrophysics Data System (ADS)

Tang, Li-Yan; Yan, Zong-Chao; Shi, Ting-Yun; Babb, James F.; Mitroy, J.

2012-03-01

The long-range non-additive three-body dispersion interaction coefficients Z111, Z112, Z113, and Z122 are computed for many atomic combinations using standard expressions. The atoms considered include hydrogen, the rare gases, the alkali atoms (up to Rb), and the alkaline-earth atoms (up to Sr). The term Z111 arising from three mutual dipole interactions is known as the Axilrod-Teller-Muto coefficient or the DDD (dipole-dipole-dipole) coefficient. Similarly, the terms Z112, Z113, and Z122 arise from the mutual combinations of dipole (1), quadrupole (2), and octupole (3) interactions between atoms and they are sometimes known, respectively, as dipole-dipole-quadrupole, dipole-dipole-octupole, and dipole-quadrupole-quadrupole coefficients. Results for the four Z coefficients are given for the homonuclear trimers, for the trimers involving two like-rare-gas atoms, and for the trimers with all combinations of the H, He, and Li atoms. An exhaustive compilation of all coefficients between all possible atomic combinations is presented as supplementary data.

Local correction of quadrupole errors at LHC interaction regions using action and phase jump analysis on turn-by-turn beam position data

NASA Astrophysics Data System (ADS)

Cardona, Javier Fernando; García Bonilla, Alba Carolina; Tomás García, Rogelio

2017-11-01

This article shows that the effect of all quadrupole errors present in an interaction region with low β * can be modeled by an equivalent magnetic kick, which can be estimated from action and phase jumps found on beam position data. This equivalent kick is used to find the strengths that certain normal and skew quadrupoles located on the IR must have to make an effective correction in that region. Additionally, averaging techniques to reduce noise on beam position data, which allows precise estimates of equivalent kicks, are presented and mathematically justified. The complete procedure is tested with simulated data obtained from madx and 2015-LHC experimental data. The analyses performed in the experimental data indicate that the strengths of the IR skew quadrupole correctors and normal quadrupole correctors can be estimated within a 10% uncertainty. Finally, the effect of IR corrections in the β* is studied, and a correction scheme that returns this parameter to its designed value is proposed.

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

Nesterov, V. A., E-mail: archerix@ukpost.ua

On the basis of the energy-density method, the effect of simultaneously taking into account the Pauli exclusion principle and the monopole and quadrupole polarizations of interacting nuclei on their interaction potential is considered for the example of the {sup 16}O + {sup 16}O system by using the wave function for the two-center shell model. The calculations performed in the adiabatic approximation reveal that the inclusion of the Pauli exclusion principle and the polarization of interacting nuclei, especially their quadrupole polarization, has a substantial effect on the potential of the nucleus-nucleus interaction.

Stability analysis of the Peregrine solution via squared eigenfunctions

NASA Astrophysics Data System (ADS)

Schober, C. M.; Strawn, M.

2017-10-01

A preliminary numerical investigation involving ensembles of perturbed initial data for the Peregrine soliton (the lowest order rational solution of the nonlinear Schrödinger equation) indicates that it is unstable [16]. In this paper we analytically investigate the linear stability of the Peregrine soliton, appealing to the fact that the Peregrine solution can be viewed as the singular limit of a single mode spatially periodic breathers (SPB). The "squared eigenfunction" connection between the Zakharov-Shabat (Z-S) system and the linearized NLS equation is employed in the stability analysis. Specifically, we determine the eigenfunctions of the Z-S system associated with the Peregrine soliton and construct a family of solutions of the associated linearized NLS (about the Peregrine) in terms of quadratic products of components of the eigenfunctions (i.e., the squared eigenfunction). We find there exist solutions of the linearization that grow exponentially in time, thus showing the Peregrine soliton is linearly unstable.

Measurements of the eigenfunction of reversed shear Alfvén eigenmodes that sweep downward in frequency

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

Heidbrink, W. W.; Austin, M. E.; Spong, D. A.

2013-08-15

Reversed shear Alfvén eigenmodes (RSAEs) usually sweep upward in frequency when the minimum value of the safety factor q{sub min} decreases in time. On rare occasions, RSAEs sweep downward prior to the upward sweep. Electron cyclotron emission measurements show that the radial eigenfunction during the downsweeping phase is similar to the eigenfunction of normal, upsweeping RSAEs.

Cranking Calculation in the sdg Interacting Boson Model

NASA Astrophysics Data System (ADS)

Wang, Baolin

1998-10-01

A self-consistent cranking calculation of the intrinsic states of the sdg interacting boson model is performed. The formulae of the moment of inertia are given in a general sdg IBM multipole Hamiltonian with one- and two-body terms. In the quadrupole interaction, the intrinsic states, the quadrupole and hexadecapole deformation and the moment of inertia are investigated in the large N limit. Using a simple Hamiltonian, the results of numerical calculations for 152, 154Sm and 154-160 Gd satisfactorily reproduce the experimental data.

Theory of elastic interaction between arbitrary colloidal particles in confined nematic liquid crystals.

PubMed

Tovkach, O M; Chernyshuk, S B; Lev, B I

2012-12-01

We develop the method proposed by Chernyshuk and Lev [Phys. Rev. E 81, 041701 (2010)] for theoretical investigation of elastic interactions between colloidal particles of arbitrary shape and chirality (polar as well as azimuthal anchoring) in the confined nematic liquid crystal (NLC). General expressions for six different types of multipole elastic interactions are obtained in the confined NLC: monopole-monopole (Coulomb type), monopole-dipole, monopole-quadrupole, dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole interactions. The obtained formulas remain valid in the presence of the external electric or magnetic fields. The exact equations are found for all multipole coefficients for the weak anchoring case. For the strong anchoring coupling, the connection between the symmetry of the shape or director and multipole coefficients is obtained, which enables us to predict which multipole coefficients vanish and which remain nonzero. The particles with azimuthal helicoid anchoring are considered as an example. Dipole-dipole interactions between helicoid cylinders and cones are found in the confined NLC. In addition, the banana-shaped particles in homeotropic and planar nematic cells are considered. It is found that the dipole-dipole interaction between banana-shaped particles differs greatly from the dipole-dipole interaction between the axially symmetrical particles in the nematic cell. There is a crossover from attraction to repulsion between banana particles along some directions in nematic cells. It is shown that monopoles do not "feel" the type of nematic cell: monopole-monopole interaction turns out to be the same in homeotropic and planar nematic cells and converges to the Coulomb law as thickness increases, L→∞.

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.

Eigenfunction Expansions and Lippmann-Schwinger Formulas

NASA Astrophysics Data System (ADS)

Gadella, M.; Kielanowski, P.

2011-12-01

In this paper we discuss in the mathematically precise way the definition of a resonance, that requires two Hamiltonians (free and perturbed), the notion of Gamow vectors, Lippmann-Schwinger equations and the analytic properties of their solutions in the context of the Gamow vectors. Next we discuss the eigenfunction expansions in the presence of resonances. In the case of the Friedrichs model, the precise form of these generalized eigenfunctions has been given in the literature. Although there are two families of eigenfunction expansions which are related through the time reversal operator, free and perturbed Hamiltonians are time invariant. On the other hand, PT symmetries play no role in this discussion. Our discussion clarifies the results of the paper [1], which contains imprecise or even wrong statements.

FAST TRACK COMMUNICATION: Two interacting atoms in a cavity: exact solutions, entanglement and decoherence

NASA Astrophysics Data System (ADS)

Torres, J. M.; Sadurní, E.; Seligman, T. H.

2010-05-01

We address the problem of two interacting atoms of different species inside a cavity and find the explicit solutions of the corresponding eigenvalues and eigenfunctions using a new variant. This model encompasses various commonly used models. By way of example we obtain closed expressions for concurrence and purity as a function of time for the case where the cavity is prepared in a number state. We discuss the behaviour of these quantities and their relative behaviour in the concurrence-purity plane.

Matter-wave solitons supported by quadrupole-quadrupole interactions and anisotropic discrete lattices

NASA Astrophysics Data System (ADS)

Zhong, Rong-Xuan; Huang, Nan; Li, Huang-Wu; He, He-Xiang; Lü, Jian-Tao; Huang, Chun-Qing; Chen, Zhao-Pin

2018-04-01

We numerically and analytically investigate the formations and features of two-dimensional discrete Bose-Einstein condensate solitons, which are constructed by quadrupole-quadrupole interactional particles trapped in the tunable anisotropic discrete optical lattices. The square optical lattices in the model can be formed by two pairs of interfering plane waves with different intensities. Two hopping rates of the particles in the orthogonal directions are different, which gives rise to a linear anisotropic system. We find that if all of the pairs of dipole and anti-dipole are perpendicular to the lattice panel and the line connecting the dipole and anti-dipole which compose the quadrupole is parallel to horizontal direction, both the linear anisotropy and the nonlocal nonlinear one can strongly influence the formations of the solitons. There exist three patterns of stable solitons, namely horizontal elongation quasi-one-dimensional discrete solitons, disk-shape isotropic pattern solitons and vertical elongation quasi-continuous solitons. We systematically demonstrate the relationships of chemical potential, size and shape of the soliton with its total norm and vertical hopping rate and analytically reveal the linear dispersion relation for quasi-one-dimensional discrete solitons.

Averages of Eigenfunctions Over Hypersurfaces

NASA Astrophysics Data System (ADS)

Canzani, Yaiza; Galkowski, Jeffrey; Toth, John A.

2018-06-01

Let ( M, g) be a compact, smooth, Riemannian manifold and φ_h an L 2-normalized sequence of Laplace eigenfunctions with defect measure {μ}. Let H be a smooth hypersurface with unit exterior normal ν. Our main result says that when μ is not concentrated conormally to H, the eigenfunction restrictions to H satisfy \\int_H φ_h dσ_H = o(1) \\quad and \\quad \\int_H h D_{ν} φ_h dσ_H = o(1), {h \\to 0^+}.

New method in muon-hadron absorption on Thx DUO2 nano material structure at 561 MHz quantum gyro-magnetic

NASA Astrophysics Data System (ADS)

Hardiyanto, M.; Ermawaty, I. R.

2018-01-01

We present an experimental of muan-hadron tunneling chain investigation with new methods of Thx DUO2 nano structure based on Josephson’s tunneling and Abrikosov-Balseiro-Russel (ABR) formulation with quantum quadrupole interacting with a strongly localized high gyro-magnetic optical field as encountered in high-resolution near-field optical microscopy for 1.2 nano meter lambda-function. The strong gradients of these localized gyro-magnetic fields suggest that higher-order multipolar interactions will affect the standard magnetic quadrupole transition rates in 1.8 x 103 currie/mm fuel energy in nuclear moderator pool and selection rules with quatum dot. For muan-hadron absorption in Josephson’s tunnelling quantum quadrupole in the strong confinement limit we calculated the inter band of gyro-magnetic quadrupole absorption rate and the associated selection rules. Founded that the magnetic quadrupole absorption rate is comparable with the absorption rate calculated in the gyro-magneticdipole approximation of ThxDUO2 nano material structure. This implies that near-field optical techniques can extend the range of spectroscopic measurements for 545 MHz at quantum gyro-magnetic field until 561 MHz deployment quantum field at B around 455-485 tesla beyond the standard dipole approximation. However, we also show that spatial resolution could be improved by the selective excitation of ABR formulation in quantum quadrupole transitions.

Quadrupole-Quadrupole Interactions to Control Plasmon-Induced Transparency

NASA Astrophysics Data System (ADS)

Rana, Goutam; Deshmukh, Prathmesh; Palkhivala, Shalom; Gupta, Abhishek; Duttagupta, S. P.; Prabhu, S. S.; Achanta, VenuGopal; Agarwal, G. S.

2018-06-01

Radiative dipolar resonance with Lorentzian line-shape induces the otherwise dark quadrupolar resonances resulting in electromagnetically induced transparency (EIT). The two interfering excitation pathways of the dipole are earlier shown to result in a Fano line shape with a high figure of merit suitable for sensing. In metamaterials made of metal nanorods or antennas, the plasmonic EIT (PIT) efficiency depends on the overlap of the dark and bright mode spectra as well as the asymmetry resulting from the separation between the monomer (dipole) and dimer (quadrupole) that governs the coupling strength. Increasing asymmetry in these structures leads to the reduction of the figure of merit due to a broadening of the Fano resonance. We demonstrate a PIT system in which the simultaneous excitation of two dipoles result in double PIT. The corresponding two quadrupoles interact and control the quality factor (Q ) of the PIT resonance. We show an antiresonancelike symmetric line shape with nonzero asymmetry factors. The PIT resonance vanishes due to quadrupole-quadrupole coupling. A Q factor of more than 100 at 0.977 THz is observed, which is limited by the experimental resolution of 6 GHz. From polarization-dependent studies we show that the broadening of the Lorentzian resonance is due to scattering-induced excitation of orthogonally oriented dipoles in the monomer and dimer bars in the terahertz regime. The high Q factors in the terahertz frequency region demonstrated here are interesting for sensing application.

A -cation control of magnetoelectric quadrupole order in A (TiO)Cu 4(PO4)4(A =Ba ,Sr, and Pb)

NASA Astrophysics Data System (ADS)

Kimura, K.; Toyoda, M.; Babkevich, P.; Yamauchi, K.; Sera, M.; Nassif, V.; Rønnow, H. M.; Kimura, T.

2018-04-01

Ferroic magnetic quadrupole order exhibiting macroscopic magnetoelectric activity is discovered in the novel compound A (TiO ) Cu4(PO4)4 with A = Pb, which is in contrast with antiferroic quadrupole order observed in the isostructural compounds with A = Ba and Sr. Unlike the famous lone-pair stereochemical activity which often triggers ferroelectricity as in PbTiO3, the Pb2 + cation in Pb (TiO ) Cu4(PO4)4 is stereochemically inactive but dramatically alters specific magnetic interactions and consequently switches the quadrupole order from antiferroic to ferroic. Our first-principles calculations uncover a positive correlation between the degree of A -O bond covalency and a stability of the ferroic quadrupole order.

Gravitational radiation quadrupole formula is valid for gravitationally interacting systems

NASA Technical Reports Server (NTRS)

Walker, M.; Will, C. M.

1980-01-01

An argument is presented for the validity of the quadrupole formula for gravitational radiation energy loss in the far field of nearly Newtonian (e.g., binary stellar) systems. This argument differs from earlier ones in that it determines beforehand the formal accuracy of approximation required to describe gravitationally self-interacting systems, uses the corresponding approximate equation of motion explicitly, and evaluates the appropriate asymptotic quantities by matching along the correct space-time light cones.

Communication: On the isotope anomaly of nuclear quadrupole coupling in molecules

NASA Astrophysics Data System (ADS)

Filatov, Michael; Zou, Wenli; Cremer, Dieter

2012-10-01

The dependence of the nuclear quadrupole coupling constants (NQCC) on the interaction between electrons and a nucleus of finite size is theoretically analyzed. A deviation of the ratio of the NQCCs obtained from two different isotopomers of a molecule from the ratio of the corresponding bare nuclear electric quadrupole moments, known as quadrupole anomaly, is interpreted in terms of the logarithmic derivatives of the electric field gradient at the nuclear site with respect to the nuclear charge radius. Quantum chemical calculations based on a Dirac-exact relativistic methodology suggest that the effect of the changing size of the Au nucleus in different isotopomers can be observed for Au-containing molecules, for which the predicted quadrupole anomaly reaches values of the order of 0.1%. This is experimentally detectable and provides an insight into the charge distribution of non-spherical nuclei.

Dynamical eigenfunction decomposition of turbulent channel flow

NASA Technical Reports Server (NTRS)

Ball, K. S.; Sirovich, L.; Keefe, L. R.

1991-01-01

The results of an analysis of low-Reynolds-number turbulent channel flow based on the Karhunen-Loeve (K-L) expansion are presented. The turbulent flow field is generated by a direct numerical simulation of the Navier-Stokes equations at a Reynolds number Re(tau) = 80 (based on the wall shear velocity and channel half-width). The K-L procedure is then applied to determine the eigenvalues and eigenfunctions for this flow. The random coefficients of the K-L expansion are subsequently found by projecting the numerical flow field onto these eigenfunctions. The resulting expansion captures 90 percent of the turbulent energy with significantly fewer modes than the original trigonometric expansion. The eigenfunctions, which appear either as rolls or shearing motions, possess viscous boundary layers at the walls and are much richer in harmonics than the original basis functions.

Quantum Ergodicity and L p Norms of Restrictions of Eigenfunctions

NASA Astrophysics Data System (ADS)

Hezari, Hamid

2018-02-01

We prove an analogue of Sogge's local L p estimates for L p norms of restrictions of eigenfunctions to submanifolds, and use it to show that for quantum ergodic eigenfunctions one can get improvements of the results of Burq-Gérard-Tzvetkov, Hu, and Chen-Sogge. The improvements are logarithmic on negatively curved manifolds (without boundary) and by o(1) for manifolds (with or without boundary) with ergodic geodesic flows. In the case of ergodic billiards with piecewise smooth boundary, we get o(1) improvements on L^∞ estimates of Cauchy data away from a shrinking neighborhood of the corners, and as a result using the methods of Ghosh et al., Jung and Zelditch, Jung and Zelditch, we get that the number of nodal domains of 2-dimensional ergodic billiards tends to infinity as λ \\to ∞. These results work only for a full density subsequence of any given orthonormal basis of eigenfunctions. We also present an extension of the L p estimates of Burq-Gérard-Tzvetkov, Hu, Chen-Sogge for the restrictions of Dirichlet and Neumann eigenfunctions to compact submanifolds of the interior of manifolds with piecewise smooth boundary. This part does not assume ergodicity on the manifolds.

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.

Multiple eigenmodes of the Rayleigh-Taylor instability observed for a fluid interface with smoothly varying density

NASA Astrophysics Data System (ADS)

Yu, C. X.; Xue, C.; Liu, J.; Hu, X. Y.; Liu, Y. Y.; Ye, W. H.; Wang, L. F.; Wu, J. F.; Fan, Z. F.

2018-01-01

In this article, multiple eigen-systems including linear growth rates and eigen-functions have been discovered for the Rayleigh-Taylor instability (RTI) by numerically solving the Sturm-Liouville eigen-value problem in the case of two-dimensional plane geometry. The system called the first mode has the maximal linear growth rate and is just extensively studied in literature. Higher modes have smaller eigen-values, but possess multi-peak eigen-functions which bring on multiple pairs of vortices in the vorticity field. A general fitting expression for the first four eigen-modes is presented. Direct numerical simulations show that high modes lead to appearances of multi-layered spike-bubble pairs, and lots of secondary spikes and bubbles are also generated due to the interactions between internal spikes and bubbles. The present work has potential applications in many research and engineering areas, e.g., in reducing the RTI growth during capsule implosions in inertial confinement fusion.

A Computer Program for the Computation of Running Gear Temperatures Using Green's Function

NASA Technical Reports Server (NTRS)

Koshigoe, S.; Murdock, J. W.; Akin, L. S.; Townsend, D. P.

1996-01-01

A new technique has been developed to study two dimensional heat transfer problems in gears. This technique consists of transforming the heat equation into a line integral equation with the use of Green's theorem. The equation is then expressed in terms of eigenfunctions that satisfy the Helmholtz equation, and their corresponding eigenvalues for an arbitrarily shaped region of interest. The eigenfunction are obtalned by solving an intergral equation. Once the eigenfunctions are found, the temperature is expanded in terms of the eigenfunctions with unknown time dependent coefficients that can be solved by using Runge Kutta methods. The time integration is extremely efficient. Therefore, any changes in the time dependent coefficients or source terms in the boundary conditions do not impose a great computational burden on the user. The method is demonstrated by applying it to a sample gear tooth. Temperature histories at representative surface locatons are given.

First Test Results of the 150 mm Aperture IR Quadrupole Models for the High Luminosity LHC

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

Ambrosio, G.; Chlachidze, G.; Wanderer, P.

2016-10-06

The High Luminosity upgrade of the LHC at CERN will use large aperture (150 mm) quadrupole magnets to focus the beams at the interaction points. The high field in the coils requires Nb3Sn superconductor technology, which has been brought to maturity by the LHC Accelerator Re-search Program (LARP) over the last 10 years. The key design targets for the new IR quadrupoles were established in 2012, and fabrication of model magnets started in 2014. This paper discusses the results from the first single short coil test and from the first short quadrupole model test. Remaining challenges and plans to addressmore » them are also presented and discussed.« less

CESR Upgrade: Plans and Recent Performance

NASA Astrophysics Data System (ADS)

Rogers, Joseph T.

1996-05-01

We are now in the second phase of a program to substantially upgrade the luminosity of the CESR e^+ e^- collider by increasing the number of stored bunches. In the first phase, completed in 1995, we progressed from collisions of beams of 7 bunches to beams of 9 trains of two bunches each, achieving a record luminosity of 3.2 × 10^32 cm-2s-1. To avoid unwanted collisions at each side of the interaction point, we electrostatically separate the beams on antisymmetric orbits, with a ± 2.1 mrad crossing angle at the interaction point. For the second phase we have altered the interaction region quadrupole magnets to increase the physical aperture and to reduce the maximum horizontal β in this region. We plan to store 9 trains of 3 bunches in the second phase, and anticipate a luminosity of 6 × 10^32 cm-2s-1. In the third phase installation, to begin in late 1997, we will replace the interaction region quadrupoles with a combination of a permanent magnet quadrupole and superconducting quadrupole pair on each side of the interaction point, which will further reduce the β functions throughout the interaction region and at the interaction point. To accomodate the higher currents we will replace each of the four 5-cell copper RF cavities with a single-cell superconducting cavity. In this phase we expect to achieve a luminosity in excess of 10^33 cm-2s-1 with 9 trains of 5 bunches. Recent development work includes the successful test of a superconducting RF cavity in CESR, installation of low-impedance electrostatic separators, upgrades to the vacuum system, a fast digital transverse feedback system, and new beam diagnostics. Recent studies have revealed the effects of collision at a crossing angle, the behavior of the long range beam-beam interaction at parasitic crossings, and the relationship of the dominant multibunch instability to photoemission in the beam chamber.

A nodal domain theorem for integrable billiards in two dimensions

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

Samajdar, Rhine; Jain, Sudhir R., E-mail: srjain@barc.gov.in

Eigenfunctions of integrable planar billiards are studied — in particular, the number of nodal domains, ν of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrödinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and non-separable integrable billiards, ν satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of mmodkn, given a particular k, for a set of quantum numbers, m,n. Further, we observe that the patterns in a familymore » are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations. - Highlights: • We find that the number of nodal domains of eigenfunctions of integrable, planar billiards satisfy a class of difference equations. • The eigenfunctions labelled by quantum numbers (m,n) can be classified in terms of mmodkn. • A theorem is presented, realising algebraic representations of geometrical patterns exhibited by the domains. • This work presents a connection between integrable systems and difference equations.« less

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

Gadella, M.; Negro, J.; Santander, M.

In this paper, we construct a Spectrum Generating Algebra (SGA) for a quantum system with purely continuous spectrum: the quantum free particle in a Lobachevski space with constant negative curvature. The SGA contains the geometrical symmetry algebra of the system plus a subalgebra of operators that give the spectrum of the system and connects the eigenfunctions of the Hamiltonian among themselves. In our case, the geometrical symmetry algebra is so(3,1) and the SGA is so(4,2). We start with a representation of so(4,2) by functions on a realization of the Lobachevski space given by a two-sheeted hyperboloid, where the Lie algebramore » commutators are the usual Poisson-Dirac brackets. Then, we introduce a quantized version of the representation in which functions are replaced by operators on a Hilbert space and Poisson-Dirac brackets by commutators. Eigenfunctions of the Hamiltonian are given and 'naive' ladder operators are identified. The previously defined 'naive' ladder operators shift the eigenvalues by a complex number so that an alternative approach is necessary. This is obtained by a non-self-adjoint function of a linear combination of the ladder operators, which gives the correct relation among the eigenfunctions of the Hamiltonian. We give an eigenfunction expansion of functions over the upper sheet of a two-sheeted hyperboloid in terms of the eigenfunctions of the Hamiltonian.« less

Quantum Spectra and Dynamics

NASA Astrophysics Data System (ADS)

Arce, Julio Cesar

1992-01-01

This work focuses on time-dependent quantum theory and methods for the study of the spectra and dynamics of atomic and molecular systems. Specifically, we have addressed the following two problems: (i) Development of a time-dependent spectral method for the construction of spectra of simple quantum systems--This includes the calculation of eigenenergies, the construction of bound and continuum eigenfunctions, and the calculation of photo cross-sections. Computational applications include the quadrupole photoabsorption spectra and dissociation cross-sections of molecular hydrogen from various vibrational states in its ground electronic potential -energy curve. This method is seen to provide an advantageous alternative, both from the computational and conceptual point of view, to existing standard methods. (ii) Explicit time-dependent formulation of photoabsorption processes --Analytical solutions of the time-dependent Schrodinger equation are constructed and employed for the calculation of probability densities, momentum distributions, fluxes, transition rates, expectation values and correlation functions. These quantities are seen to establish the link between the dynamics and the calculated, or measured, spectra and cross-sections, and to clarify the dynamical nature of the excitation, transition and ejection processes. Numerical calculations on atomic and molecular hydrogen corroborate and complement the previous results, allowing the identification of different regimes during the photoabsorption process.

Information technology in chemistry research and education: Part I. Ab initio studies on the hydrolysis of aromatic diazonium ions. Part II. Theoretical study and molecular modeling of non-covalent interactions. Part III. Applying information technology in chemistry education

NASA Astrophysics Data System (ADS)

Wu, Zhengyu

Part I of this dissertation studies the bonding in chemical reactions, while Part II studies the bonding related to inter- and intra-molecular interactions. Part III studies the application of IT technology in chemistry education. Part I of this dissertation (chapter 1 and chapter 2) focuses on the theoretical studies on the mechanism of the hydrolysis reactions of benzenediazonium ion and guaninediazonium ion. The major conclusion is that in hydrolysis reactions the "unimolecular mechanism" actually has to involve the reacting solvent molecule. Therefore, the unimolecular pathway can only serve as a conceptual model but will not happen in the reality. Chapter I concludes that the hydrolysis reaction of benzenediazonium ion takes the direct SN2Ar mechanism via a transition state but without going through a pre-coordination complex. Chapter 2 concludes that the formation of xanthine from the dediazoniation reaction of guaninediazonium ion in water takes the SN2Ar pathway without a transition state. And oxanine might come from an intermediate formed by the bimolecular deprotonation of the H atom on N3 of guaninediazonium ion synchronized with the pyrimidine ring opening reaction. Part II of this dissertation includes chapters 3, 4, and 5. Chapter 3 studies the quadrupole moment of benzene and quadrupole-quadrupole interactions. We concluded that the quadrupole-quadrupole interaction is important in the arene-arene interactions. Our study shows the most stable structure of benzene dimer is the point-to-face T-shaped structure. Chapter 4 studies the intermolecular interactions that result in the disorder of the crystal of 4-Chloroacetophenone-(4-methoxyphenylethylidene). We analyzed all the nearest neighbor interactions within that crystal and found that the crystal structure is determined by its thermo-dynamical properties. Our calculation perfectly reproduced the percentage of parallel-alignment of the crystal. Part III of this dissertation is focused on the application of database management system and computer technology on chemistry education. A database-supported webtool was developed to support the creation of news portfolio and peer reviews online. The responses to an in-class survey show that students embrace the use of this webtool for its conceptually clear design and its easiness of use.

Nuclear quadrupole resonance lineshape analysis for different motional models: Stochastic Liouville approach

NASA Astrophysics Data System (ADS)

Kruk, D.; Earle, K. A.; Mielczarek, A.; Kubica, A.; Milewska, A.; Moscicki, J.

2011-12-01

A general theory of lineshapes in nuclear quadrupole resonance (NQR), based on the stochastic Liouville equation, is presented. The description is valid for arbitrary motional conditions (particularly beyond the valid range of perturbation approaches) and interaction strengths. It can be applied to the computation of NQR spectra for any spin quantum number and for any applied magnetic field. The treatment presented here is an adaptation of the "Swedish slow motion theory," [T. Nilsson and J. Kowalewski, J. Magn. Reson. 146, 345 (2000), 10.1006/jmre.2000.2125] originally formulated for paramagnetic systems, to NQR spectral analysis. The description is formulated for simple (Brownian) diffusion, free diffusion, and jump diffusion models. The two latter models account for molecular cooperativity effects in dense systems (such as liquids of high viscosity or molecular glasses). The sensitivity of NQR slow motion spectra to the mechanism of the motional processes modulating the nuclear quadrupole interaction is discussed.

Dirac oscillator interacting with a topological defect

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

Carvalho, J.; Furtado, C.; Moraes, F.

In this work we study the interaction problem of a Dirac oscillator with gravitational fields produced by topological defects. The energy levels of the relativistic oscillator in the cosmic string and in the cosmic dislocation space-times are sensible to curvature and torsion associated to these defects and are important evidence of the influence of the topology on this system. In the presence of a localized magnetic field the energy levels acquire a term associated with the Aharonov-Bohm effect. We obtain the eigenfunctions and eigenvalues and see that in the nonrelativistic limit some results known in standard quantum mechanics are reached.

Eigenfunction fractality and pseudogap state near the superconductor-insulator transition.

PubMed

Feigel'man, M V; Ioffe, L B; Kravtsov, V E; Yuzbashyan, E A

2007-01-12

We develop a theory of a pseudogap state appearing near the superconductor-insulator (SI) transition in strongly disordered metals with an attractive interaction. We show that such an interaction combined with the fractal nature of the single-particle wave functions near the mobility edge leads to an anomalously large single-particle gap in the superconducting state near SI transition that persists and even increases in the insulating state long after the superconductivity is destroyed. We give analytic expressions for the value of the pseudogap in terms of the inverse participation ratio of the corresponding localization problem.

Performance of the first short model 150 mm aperture Nb$$_3$$Sn Quadrupole MQXFS for the High- Luminosity LHC upgrade

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

Chlachidze, G.; et al.

2016-08-30

The US LHC Accelerator Research Program (LARP) and CERN combined their efforts in developing Nb3Sn magnets for the High-Luminosity LHC upgrade. The ultimate goal of this collaboration is to fabricate large aperture Nb3Sn quadrupoles for the LHC interaction regions (IR). These magnets will replace the present 70 mm aperture NbTi quadrupole triplets for expected increase of the LHC peak luminosity by a factor of 5. Over the past decade LARP successfully fabricated and tested short and long models of 90 mm and 120 mm aperture Nb3Sn quadrupoles. Recently the first short model of 150 mm diameter quadrupole MQXFS was builtmore » with coils fabricated both by the LARP and CERN. The magnet performance was tested at Fermilab’s vertical magnet test facility. This paper reports the test results, including the quench training at 1.9 K, ramp rate and temperature dependence studies.« less

Influence of the Pauli exclusion principle and the polarization of nuclei on the nuclear part of the interaction potential in the 40Ca +40Ca system

NASA Astrophysics Data System (ADS)

Nesterov, V. O.

2018-06-01

In the framework of the energy density method with the use of the wave function of the two-center shell model, the influence of the simultaneous account for the Pauli exclusion principle and the monopole and quadrupole polarizations of nuclei on the nuclear part of the potential of their interaction by the example of the 40Ca +40Ca system is considered. The calculations performed in the framework of the adiabatic approximation show that the consideration of the Pauli exclusion principle and the polarization of nuclei, especially the quadrupole one, essentially affects the nucleus-nucleus interaction potential.

Improved Critical Eigenfunction Restriction Estimates on Riemannian Surfaces with Nonpositive Curvature

NASA Astrophysics Data System (ADS)

Xi, Yakun; Zhang, Cheng

2017-03-01

We show that one can obtain improved L 4 geodesic restriction estimates for eigenfunctions on compact Riemannian surfaces with nonpositive curvature. We achieve this by adapting Sogge's strategy in (Improved critical eigenfunction estimates on manifolds of nonpositive curvature, Preprint). We first combine the improved L 2 restriction estimate of Blair and Sogge (Concerning Toponogov's Theorem and logarithmic improvement of estimates of eigenfunctions, Preprint) and the classical improved {L^∞} estimate of Bérard to obtain an improved weak-type L 4 restriction estimate. We then upgrade this weak estimate to a strong one by using the improved Lorentz space estimate of Bak and Seeger (Math Res Lett 18(4):767-781, 2011). This estimate improves the L 4 restriction estimate of Burq et al. (Duke Math J 138:445-486, 2007) and Hu (Forum Math 6:1021-1052, 2009) by a power of {(log logλ)^{-1}}. Moreover, in the case of compact hyperbolic surfaces, we obtain further improvements in terms of {(logλ)^{-1}} by applying the ideas from (Chen and Sogge, Commun Math Phys 329(3):435-459, 2014) and (Blair and Sogge, Concerning Toponogov's Theorem and logarithmic improvement of estimates of eigenfunctions, Preprint). We are able to compute various constants that appeared in (Chen and Sogge, Commun Math Phys 329(3):435-459, 2014) explicitly, by proving detailed oscillatory integral estimates and lifting calculations to the universal cover H^2.

Nanofocusing of structured light for quadrupolar light-matter interactions.

PubMed

Sakai, Kyosuke; Yamamoto, Takeaki; Sasaki, Keiji

2018-05-17

The spatial structure of an electromagnetic field can determine the characteristics of light-matter interactions. A strong gradient of light in the near field can excite dipole-forbidden atomic transitions, e.g., electric quadrupole transitions, which are rarely observed under plane-wave far-field illumination. Structured light with a higher-order orbital angular momentum state may also modulate the selection rules in which an atom can absorb two quanta of angular momentum: one from the spin and another from the spatial structure of the beam. Here, we numerically demonstrate a strong focusing of structured light with a higher-order orbital angular momentum state in the near field. A quadrupole field was confined within a gap region of several tens of nanometres in a plasmonic tetramer structure. A plasmonic crystal surrounding the tetramer structure provides a robust antenna effect, where the incident structured light can be strongly coupled to the quadrupole field in the gap region with a larger alignment tolerance. The proposed system is expected to provide a platform for light-matter interactions with strong multipolar effects.

Compensation of orbit distortion due to quadrupole motion using feed-forward control at KEK ATF

NASA Astrophysics Data System (ADS)

Bett, D. R.; Charrondière, C.; Patecki, M.; Pfingstner, J.; Schulte, D.; Tomás, R.; Jeremie, A.; Kubo, K.; Kuroda, S.; Naito, T.; Okugi, T.; Tauchi, T.; Terunuma, N.; Burrows, P. N.; Christian, G. B.; Perry, C.

2018-07-01

The high luminosity requirement for a future linear collider sets a demanding limit on the beam quality at the Interaction Point (IP). One potential source of luminosity loss is the motion of the ground itself. The resulting misalignments of the quadrupole magnets cause distortions to the beam orbit and hence an increase in the beam emittance. This paper describes a technique for compensating this orbit distortion by using seismometers to monitor the misalignment of the quadrupole magnets in real-time. The first demonstration of the technique was achieved at the Accelerator Test Facility (ATF) at KEK in Japan. The feed-forward system consisted of a seismometer-based quadrupole motion monitoring system, an FPGA-based feed-forward processor and a stripline kicker plus associated electronics. Through the application of a kick calculated from the position of a single quadruple, the system was able to remove about 80% of the component of the beam jitter that was correlated to the motion of the quadrupole. As a significant fraction of the orbit jitter in the ATF final focus is due to sources other than quadrupole misalignment, this amounted to an approximately 15% reduction in the absolute beam jitter.

Nuclear deformation in the laboratory frame

NASA Astrophysics Data System (ADS)

Gilbreth, C. N.; Alhassid, Y.; Bertsch, G. F.

2018-01-01

We develop a formalism for calculating the distribution of the axial quadrupole operator in the laboratory frame within the rotationally invariant framework of the configuration-interaction shell model. The calculation is carried out using a finite-temperature auxiliary-field quantum Monte Carlo method. We apply this formalism to isotope chains of even-mass samarium and neodymium nuclei and show that the quadrupole distribution provides a model-independent signature of nuclear deformation. Two technical advances are described that greatly facilitate the calculations. The first is to exploit the rotational invariance of the underlying Hamiltonian to reduce the statistical fluctuations in the Monte Carlo calculations. The second is to determine quadruple invariants from the distribution of the axial quadrupole operator in the laboratory frame. This allows us to extract effective values of the intrinsic quadrupole shape parameters without invoking an intrinsic frame or a mean-field approximation.

Markov modeling of peptide folding in the presence of protein crowders

NASA Astrophysics Data System (ADS)

Nilsson, Daniel; Mohanty, Sandipan; Irbäck, Anders

2018-02-01

We use Markov state models (MSMs) to analyze the dynamics of a β-hairpin-forming peptide in Monte Carlo (MC) simulations with interacting protein crowders, for two different types of crowder proteins [bovine pancreatic trypsin inhibitor (BPTI) and GB1]. In these systems, at the temperature used, the peptide can be folded or unfolded and bound or unbound to crowder molecules. Four or five major free-energy minima can be identified. To estimate the dominant MC relaxation times of the peptide, we build MSMs using a range of different time resolutions or lag times. We show that stable relaxation-time estimates can be obtained from the MSM eigenfunctions through fits to autocorrelation data. The eigenfunctions remain sufficiently accurate to permit stable relaxation-time estimation down to small lag times, at which point simple estimates based on the corresponding eigenvalues have large systematic uncertainties. The presence of the crowders has a stabilizing effect on the peptide, especially with BPTI crowders, which can be attributed to a reduced unfolding rate ku, while the folding rate kf is left largely unchanged.

Refined and Microlocal Kakeya-Nikodym Bounds of Eigenfunctions in Higher Dimensions

NASA Astrophysics Data System (ADS)

Blair, Matthew D.; Sogge, Christopher D.

2017-12-01

We prove a Kakeya-Nikodym bound on eigenfunctions and quasimodes, which sharpens a result of the authors (Blair and Sogge in Anal PDE 8:747-764, 2015) and extends it to higher dimensions. As in the prior work, the key intermediate step is to prove a microlocal version of these estimates, which involves a phase space decomposition of these modes that is essentially invariant under the bicharacteristic/geodesic flow. In a companion paper (Blair and Sogge in J Differ Geom, 2015), it will be seen that these sharpened estimates yield improved L q ( M) bounds on eigenfunctions in the presence of nonpositive curvature when {2 < q < 2(d+1)/d-1}.

Electromagnetic Coupling of Negative Parity Nucleon Resonances N (1535) Based on Nonrelativistic Constituent Quark Model

NASA Astrophysics Data System (ADS)

Parsaei, Sara; Rajabi, Ali Akbar

2018-01-01

The electromagnetic transition between the nucleon and excited baryons has long been recognized as an important source of information for understanding strong interactions in the domain of quark confinement. We study the electromagnetic properties of the excitation of the negative parity the N*(1535) resonances in the nonrelativistic constituent quark model at large momentum transfers and have performed a calculation the longitudinal and transverse helicity amplitudes. Since the helicity amplitudes depend strongly on the quark wave function in this paper, we consider the baryon as a simple, non-relativistically three-body quark model and also consider a hypercentral potential scheme for the internal baryon structure, which makes three-body forces among three quarks. Since the hyper central potential depends only on the hyper radius, therefore, the Cornell potential which is a combination of the Coulombic-like term plus a linear confining term is considered as the potential for interaction between quarks. In our work, in solving the Schrodinger equation with the Cornell potential, the Nikiforov-Uvarov method employed, and the analytic eigen-energies and eigen-functions obtained. By using the obtained eigen-functions, the transition amplitudes calculated. We show that our results in the range {{{Q}}}2> 2 {{GeV}}2 lead to an overall better agreement with the experimental data in comparison with the other three non-relativistic quark models.

Wave functions of the Q .Q interaction in terms of unitary 9-j coefficients

NASA Astrophysics Data System (ADS)

Zamick, Larry; Harper, Matthew

2015-03-01

We obtain wave functions for two protons and two neutrons in the g9 /2 shell expressed as column vectors with amplitudes D (Jp,Jn) . When we use a quadrupole-quadrupole interaction (Q .Q ) we get, in many cases, a very strong overlap with wave functions given by a single set of unitary 9-j coefficients—U 9 j =<(jj ) 2 j(jjJB|(jj ) Jp(jj ) Jn) I> . Here JB=9 for even I T =0 states. For both even and odd T =1 states we take JB equal to 8 whilst for odd I ,T =0 we take JB to be 7. We compare the Q .Q results with those of a more realistic interaction.

Study of the 190Hg Nucleus: Testing the Existence of U(5) Symmetry

NASA Astrophysics Data System (ADS)

Jahangiri Tazekand, Z.; Mohseni, M.; Mohammadi, M. A.; Sabri, H.

2018-06-01

In this paper, we have considered the energy spectra, quadrupole transition probabilities, energy surface, charge radii, and quadrupole moment of the190Hg nucleus to describe the interplay between phase transitions and configuration mixing of intruder excitations. To this aim, we have used four different formalisms: (i) interacting boson model including configuration mixing, (ii) Z(5) critical symmetry, (iii) U(6)-based transitional Hamiltonian, and (iv) a transitional interacting boson model Hamiltonian in both interacting boson model (IBM)-1 and IBM-2 versions which are based on affine \\widehat{SU(1,1)} Lie algebra. Results show the advantages of configuration mixing and transitional Hamiltonians, in particular IBM-2 formalism, to reproduce the experimental counterparts when the weight of spherical symmetry increased.

Summary of Test Results of MQXFS1 - The First Short Model 150 mm Aperture $$Nb_3Sn$$ Quadrupole for the High-Luminosity

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

Stoynev, S.; et al.

The development ofmore » $$Nb_3Sn$$ quadrupole magnets for the High-Luminosity LHC upgrade is a joint venture between the US LHC Accelerator Research Program (LARP)* and CERN with the goal of fabricating large aperture quadrupoles for the LHC in-teraction regions (IR). The inner triplet (low-β) NbTi quadrupoles in the IR will be replaced by the stronger Nb3Sn magnets boosting the LHC program of having 10-fold increase in integrated luminos-ity after the foreseen upgrades. Previously LARP conducted suc-cessful tests of short and long models with up to 120 mm aperture. The first short 150 mm aperture quadrupole model MQXFS1 was assembled with coils fabricated by both CERN and LARP. The magnet demonstrated strong performance at the Fermilab’s verti-cal magnet test facility reaching the LHC operating limits. This paper reports the latest results from MQXFS1 tests with changed pre-stress levels. The overall magnet performance, including quench training and memory, ramp rate and temperature depend-ence, is also summarized.« less

Three-body Coulomb systems using generalized angular-momentum S states

NASA Technical Reports Server (NTRS)

Whitten, R. C.; Sims, J. S.

1974-01-01

An expansion of the three-body Coulomb potential in generalized angular-momentum eigenfunctions developed earlier by one of the authors is used to compute energy eigenvalues and eigenfunctions of bound S states of three-body Coulomb systems. The results for He, H(-), e(-)e(+)e(-), and pmu(-)p are compared with the results of other computational approaches.

Filter method without boundary-value condition for simultaneous calculation of eigenfunction and eigenvalue of a stationary Schrödinger equation on a grid.

PubMed

Nurhuda, M; Rouf, A

2017-09-01

The paper presents a method for simultaneous computation of eigenfunction and eigenvalue of the stationary Schrödinger equation on a grid, without imposing boundary-value condition. The method is based on the filter operator, which selects the eigenfunction from wave packet at the rate comparable to δ function. The efficacy and reliability of the method are demonstrated by comparing the simulation results with analytical or numerical solutions obtained by using other methods for various boundary-value conditions. It is found that the method is robust, accurate, and reliable. Further prospect of filter method for simulation of the Schrödinger equation in higher-dimensional space will also be highlighted.

Spectral properties of the massless relativistic quartic oscillator

NASA Astrophysics Data System (ADS)

Durugo, Samuel O.; Lőrinczi, József

2018-03-01

An explicit solution of the spectral problem of the non-local Schrödinger operator obtained as the sum of the square root of the Laplacian and a quartic potential in one dimension is presented. The eigenvalues are obtained as zeroes of special functions related to the fourth order Airy function, and closed formulae for the Fourier transform of the eigenfunctions are derived. These representations allow to derive further spectral properties such as estimates of spectral gaps, heat trace and the asymptotic distribution of eigenvalues, as well as a detailed analysis of the eigenfunctions. A subtle spectral effect is observed which manifests in an exponentially tight approximation of the spectrum by the zeroes of the dominating term in the Fourier representation of the eigenfunctions and its derivative.

Sturm-Liouville eigenproblems with an interior pole

NASA Technical Reports Server (NTRS)

Boyd, J. P.

1981-01-01

The eigenvalues and eigenfunctions of self-adjoint Sturm-Liouville problems with a simple pole on the interior of an interval are investigated. Three general theorems are proved, and it is shown that as n approaches infinity, the eigenfunctions more and more closely resemble those of an ordinary Sturm-Liouville problem. The low-order modes differ significantly from those of a nonsingular eigenproblem in that both eigenvalues and eigenfunctions are complex, and the eigenvalues for all small n may cluster about a common value in contrast to the widely separated eigenvalues of the corresponding nonsingular problem. In addition, the WKB is shown to be accurate for all n, and all eigenvalues of a normal one-dimensional Sturm-Liouville equation with nonperiodic boundary conditions are well separated.

HYPERFINE STRUCTURES AND NUCLEAR MOMENTS OF Lu$sup 176$m, Br$sup 80$, Br$sup 80$m, AND I$sup 132$ (thesis)

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

White, M.B.

1962-09-01

The method of atomic-beam radiofrequency spectroscopy was used to determine some nuclear and atomic properties of Lu/sup 176m/, Br/sup 80/, Br/sup 80m/, and I/sup 132/. Hyperfine structure me asurements were raade to determine the magnetic dipole interaction constants and the electric quadrupole interaction constants of all these isotopes. Also the nuclear spin and the electronic g/sub J/ factor were measured for Lu/sup 176m/, and the nuclear magnetic dipole moments and the electric quadrupole moments for the isotopes were calculated. All results are listed. 62 references. (auth)

The quadrupole moments of some even–even nuclei around the mass of A ~ 80: {sup 68−80}Ge on the neighborhood of {sup 76−84}Kr and {sup 76−84}Se isotopes

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

Yoruk, Abdulkadir, E-mail: yorukabdulkadir@hotmail.com; Turkan, Nureddin, E-mail: nureddin.turkan@medeniyet.edu.tr

2016-09-15

We have carried out the calculation of the quadrupole moments Q(2{sub 1}{sup +}) and electromagnetic transition rates B(E2) of some levels within the framework of the interacting boson model for even-mass Ge nuclei. The presented predictions of the quadrupole moments and B(E2) ratios for Ge nuclei are compared with the results of some previous experimental and theoretical ones along with those of the neighboring Kr and Se isotopes and then it was seen that they agree well with the previous experimental and theoretical ones.

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

Vidal, Luciano N., E-mail: lnvidal@utfpr.edu.br; Cappelli, Chiara, E-mail: chiara.cappelli@unipi.it; Egidi, Franco

A theoretical investigation on the origin dependence of the vibronic polarizabilities, isotropic and anisotropic rotational invariants, and scattering cross sections in Resonance Raman Optical Activity (RROA) spectroscopy is presented. Expressions showing the origin dependence of these polarizabilities were written in the resonance regime using the Franck-Condon (FC) and Herzberg-Teller (HT) approximations for the electronic transition moments. Differently from the far-from-resonance scattering regime, where the origin dependent terms cancel out when the rotational invariants are calculated, RROA spectrum can exhibit some origin dependence even for eigenfunctions of the electronic Hamiltonian. At the FC level, the RROA spectrum is completely origin invariantmore » if the polarizabilities are calculated using a single excited state or for a set of degenerate states. Otherwise, some origin effects can be observed in the spectrum. At the HT level, RROA spectrum is origin dependent even when the polarizabilities are evaluated from a single excited state but the origin effect is expected to be small in this case. Numerical calculations performed for (S)-methyloxirane, (2R,3R)-dimethyloxirane, and (R)-4-F-2-azetidinone at both FC and HT levels using the velocity representation of the electric dipole and quadrupole transition moments confirm the predictions of the theory and show the extent of origin effects and the effectiveness of suggested ways to remove them.« less

Virasoro symmetry of the constrained multicomponent Kadomtsev-Petviashvili hierarchy and its integrable discretization

NASA Astrophysics Data System (ADS)

Li, Chuanzhong; He, Jingsong

2016-06-01

We construct Virasoro-type additional symmetries of a kind of constrained multicomponent Kadomtsev-Petviashvili (KP) hierarchy and obtain the Virasoro flow equation for the eigenfunctions and adjoint eigenfunctions. We show that the algebraic structure of the Virasoro symmetry is retained under discretization from the constrained multicomponent KP hierarchy to the discrete constrained multicomponent KP hierarchy.

Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering

NASA Astrophysics Data System (ADS)

Pelinovsky, Dmitry E.; Sulem, Catherine

A complete set of eigenfunctions is introduced within the Riemann-Hilbert formalism for spectral problems associated to some solvable nonlinear evolution equations. In particular, we consider the time-independent and time-dependent Schrödinger problems which are related to the KdV and KPI equations possessing solitons and lumps, respectively. Non-standard scalar products, orthogonality and completeness relations are derived for these problems. The complete set of eigenfunctions is used for perturbation theory and bifurcation analysis of eigenvalues supported by the potentials under perturbations. We classify two different types of bifurcations of new eigenvalues and analyze their characteristic features. One type corresponds to thresholdless generation of solitons in the KdV equation, while the other predicts a threshold for generation of lumps in the KPI equation.

The Uniform Convergence of Eigenfunction Expansions of Schrödinger Operator in the Nikolskii Classes {H}_{p}^{\\alpha }(\\bar{\\Omega })

NASA Astrophysics Data System (ADS)

Jamaludin, N. A.; Ahmedov, A.

2017-09-01

Many boundary value problems in the theory of partial differential equations can be solved by separation methods of partial differential equations. When Schrödinger operator is considered then the influence of the singularity of potential on the solution of the partial differential equation is interest of researchers. In this paper the problems of the uniform convergence of the eigenfunction expansions of the functions from corresponding to the Schrödinger operator with the potential from classes of Sobolev are investigated. The spectral function corresponding to the Schrödinger operator is estimated in closed domain. The isomorphism of the Nikolskii classes is applied to prove uniform convergence of eigenfunction expansions of Schrödinger operator in closed domain.

The three-body problem with short-range interactions

NASA Astrophysics Data System (ADS)

Nielsen, E.; Fedorov, D. V.; Jensen, A. S.; Garrido, E.

2001-06-01

The quantum mechanical three-body problem is studied for general short-range interactions. We work in coordinate space to facilitate accurate computations of weakly bound and spatially extended systems. Hyperspherical coordinates are used in both the interpretation and as an integral part of the numerical method. Universal properties and model independence are discussed throughout the report. We present an overview of the hyperspherical adiabatic Faddeev equations. The wave function is expanded on hyperspherical angular eigenfunctions which in turn are found numerically using the Faddeev equations. We generalize the formalism to any dimension of space d greater or equal to two. We present two numerical techniques for solving the Faddeev equations on the hypersphere. These techniques are effective for short and intermediate/large distances including use for hard core repulsive potentials. We study the asymptotic limit of large hyperradius and derive the analytic behaviour of the angular eigenvalues and eigenfunctions. We discuss four applications of the general method. We first analyze the Efimov and Thomas effects for arbitrary angular momenta and for arbitrary dimensions d. Second we apply the method to extract the general behaviour of weakly bound three-body systems in two dimensions. Third we illustrate the method in three dimensions by structure computations of Borromean halo nuclei, the hypertriton and helium molecules. Fourth we investigate in three dimensions three-body continuum properties of Borromean halo nuclei and recombination reactions of helium atoms as an example of direct relevance for the stability of Bose-Einstein condensates.

Vision-Based Autonomous Sensor-Tasking in Uncertain Adversarial Environments

DTIC Science & Technology

2015-01-02

motion segmentation and change detection in crowd behavior. In particular we investigated Finite Time Lyapunov Exponents, Perron Frobenius Operator and...deformation tensor [11]. On the other hand, eigenfunctions of, the Perron Frobenius operator can be used to detect Almost Invariant Sets (AIS) which are... Perron Frobenius operator. Finally, Figure 1.12d shows the ergodic partitions (EP) obtained based on the eigenfunctions of the Koopman operator

FAST TRACK COMMUNICATION: Free form of the Foldy-Wouthuysen transformation in external electromagnetic fields

NASA Astrophysics Data System (ADS)

Murguía, Gabriela; Raya, Alfredo

2010-10-01

We derive the exact Foldy-Wouthuysen transformation for Dirac fermions in a time-independent external electromagnetic field in the basis of the Ritus eigenfunctions, namely the eigenfunctions of the operator (γ sdot Π)2, with Πμ = pμ - eAμ. On this basis, the transformation acquires a free form involving the dynamical quantum numbers induced by the field.

FIBER OPTICS: Method of calculation of the propagation constant for guided modes

NASA Astrophysics Data System (ADS)

Ardasheva, L. I.; Sadykov, Nail R.; Chernyakov, V. E.

1992-09-01

A new method of calculating the propagation constants and wave eigenfunctions of guided modes is proposed for axisymmetric translationally invariant fiber-optic waveguides with arbitrary refractive index profiles. The method is based on solving a parabolic scalar wave equation. A comparison is made between the numerical solution under steady-state conditions and the eigenfunctions of single-mode and multimode waveguides.

The Three-Component Defocusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions

NASA Astrophysics Data System (ADS)

Biondini, Gino; Kraus, Daniel K.; Prinari, Barbara

2016-12-01

We present a rigorous theory of the inverse scattering transform (IST) for the three-component defocusing nonlinear Schrödinger (NLS) equation with initial conditions approaching constant values with the same amplitude as {xto±∞}. The theory combines and extends to a problem with non-zero boundary conditions three fundamental ideas: (i) the tensor approach used by Beals, Deift and Tomei for the n-th order scattering problem, (ii) the triangular decompositions of the scattering matrix used by Novikov, Manakov, Pitaevski and Zakharov for the N-wave interaction equations, and (iii) a generalization of the cross product via the Hodge star duality, which, to the best of our knowledge, is used in the context of the IST for the first time in this work. The combination of the first two ideas allows us to rigorously obtain a fundamental set of analytic eigenfunctions. The third idea allows us to establish the symmetries of the eigenfunctions and scattering data. The results are used to characterize the discrete spectrum and to obtain exact soliton solutions, which describe generalizations of the so-called dark-bright solitons of the two-component NLS equation.

Modal element method for potential flow in non-uniform ducts: Combining closed form analysis with CFD

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Baumeister, Joseph F.

1994-01-01

An analytical procedure is presented, called the modal element method, that combines numerical grid based algorithms with eigenfunction expansions developed by separation of variables. A modal element method is presented for solving potential flow in a channel with two-dimensional cylindrical like obstacles. The infinite computational region is divided into three subdomains; the bounded finite element domain, which is characterized by the cylindrical obstacle and the surrounding unbounded uniform channel entrance and exit domains. The velocity potential is represented approximately in the grid based domain by a finite element solution and is represented analytically by an eigenfunction expansion in the uniform semi-infinite entrance and exit domains. The calculated flow fields are in excellent agreement with exact analytical solutions. By eliminating the grid surrounding the obstacle, the modal element method reduces the numerical grid size, employs a more precise far field boundary condition, as well as giving theoretical insight to the interaction of the obstacle with the mean flow. Although the analysis focuses on a specific geometry, the formulation is general and can be applied to a variety of problems as seen by a comparison to companion theories in aeroacoustics and electromagnetics.

Model for the dynamics of two interacting axisymmetric spherical bubbles undergoing small shape oscillations

PubMed Central

Kurihara, Eru; Hay, Todd A.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2011-01-01

Interaction between acoustically driven or laser-generated bubbles causes the bubble surfaces to deform. Dynamical equations describing the motion of two translating, nominally spherical bubbles undergoing small shape oscillations in a viscous liquid are derived using Lagrangian mechanics. Deformation of the bubble surfaces is taken into account by including quadrupole and octupole perturbations in the spherical-harmonic expansion of the boundary conditions on the bubbles. Quadratic terms in the quadrupole and octupole amplitudes are retained, and surface tension and shear viscosity are included in a consistent manner. A set of eight coupled second-order ordinary differential equations is obtained. Simulation results, obtained by numerical integration of the model equations, exhibit qualitative agreement with experimental observations by predicting the formation of liquid jets. Simulations also suggest that bubble-bubble interactions act to enhance surface mode instability. PMID:22088009

Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation.

PubMed

Hu, Xiao-Rui; Lou, Sen-Yue; Chen, Yong

2012-05-01

In nonlinear science, it is very difficult to find exact interaction solutions among solitons and other kinds of complicated waves such as cnoidal waves and Painlevé waves. Actually, even if for the most well-known prototypical models such as the Kortewet-de Vries (KdV) equation and the Kadomtsev-Petviashvili (KP) equation, this kind of problem has not yet been solved. In this paper, the explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetries which are related to Darboux transformation for the well-known KdV equation. The same approach also yields some other types of interaction solutions among different types of solutions such as solitary waves, rational solutions, Bessel function solutions, and/or general Painlevé II solutions.

Generation of coherent states of photon-added type via pathway of eigenfunctions

NASA Astrophysics Data System (ADS)

Górska, K.; Penson, K. A.; Duchamp, G. H. E.

2010-09-01

We obtain and investigate the regular eigenfunctions of simple differential operators xr dr + 1/dxr + 1, r = 1, 2, ..., with the eigenvalues equal to 1. With the help of these eigenfunctions, we construct a non-unitary analogue of a boson displacement operator which will be acting on the vacuum. In this way, we generate collective quantum states of the Fock space which are normalized and equipped with the resolution of unity with the positive weight functions that we obtain explicitly. These states are thus coherent states in the sense of Klauder. They span the truncated Fock space without first r lowest-lying basis states: |0rang, |1rang, ..., |r - 1rang. These states are squeezed, sub-Poissonian in nature and reminiscent of photon-added states in Agarwal and Tara (1991 Phys. Rev. A 43 492).

Accuracy of analytic energy level formulas applied to hadronic spectroscopy of heavy mesons

NASA Technical Reports Server (NTRS)

Badavi, Forooz F.; Norbury, John W.; Wilson, John W.; Townsend, Lawrence W.

1988-01-01

Linear and harmonic potential models are used in the nonrelativistic Schroedinger equation to obtain article mass spectra for mesons as bound states of quarks. The main emphasis is on the linear potential where exact solutions of the S-state eigenvalues and eigenfunctions and the asymptotic solution for the higher order partial wave are obtained. A study of the accuracy of two analytical energy level formulas as applied to heavy mesons is also included. Cornwall's formula is found to be particularly accurate and useful as a predictor of heavy quarkonium states. Exact solution for all partial waves of eigenvalues and eigenfunctions for a harmonic potential is also obtained and compared with the calculated discrete spectra of the linear potential. Detailed derivations of the eigenvalues and eigenfunctions of the linear and harmonic potentials are presented in appendixes.

On the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_1^\\alpha ({T^N})

NASA Astrophysics Data System (ADS)

Ahmedov, Anvarjon; Materneh, Ehab; Zainuddin, Hishamuddin

2017-09-01

The relevance of waves in quantum mechanics naturally implies that the decomposition of arbitrary wave packets in terms of monochromatic waves plays an important role in applications of the theory. When eigenfunction expansions does not converge, then the expansions of the functions with certain smoothness should be considered. Such functions gained prominence primarily through their application in quantum mechanics. In this work we study the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_p^α ({T^N}), related to the self-adjoint extension of the Laplace operator in torus TN . The sufficient conditions for summability is obtained using the modified Poisson formula. Isomorphism properties of the elliptic differential operators is applied in order to obtain estimation for the Fourier series of the functions from the classes of Liouville L_p^α .

Multicomponent integrable reductions in the Kadomtsev-Petviashvilli hierarchy

NASA Astrophysics Data System (ADS)

Sidorenko, Jurij; Strampp, Walter

1993-04-01

New types of reductions of the Kadomtsev-Petviashvili (KP) hierarchy are considered on the basis of Sato's approach. Within this approach the KP hierarchy is represented by infinite sets of equations for potentials u2,u3,..., of pseudodifferential operators and their eigenfunctions Ψ and adjoint eigenfunctions Ψ*. The KP hierarchy was studied under constraints of the following type (∑ni=1 ΨiΨ*i)x = Sκ,x where Sκ,x are symmetries for the KP equation and Ψi(λi), Ψ*i(λi) are eigenfunctions with eigenvalue λi. It is shown that for the first three cases κ=2,3,4 these constraints give rise to hierarchies of 1+1-dimensional commuting flows for the variables u2, Ψ1,...,Ψn, Ψ*1,...,Ψ*n. Bi-Hamiltonian structures for the new hierarchies are presented.

The Theory of Quantized Fields. III

DOE R&D Accomplishments Database

Schwinger, J.

1953-05-01

In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transformation probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the intra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.

Unified heat kernel regression for diffusion, kernel smoothing and wavelets on manifolds and its application to mandible growth modeling in CT images.

PubMed

Chung, Moo K; Qiu, Anqi; Seo, Seongho; Vorperian, Houri K

2015-05-01

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel method is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, the method is applied to characterize the localized growth pattern of mandible surfaces obtained in CT images between ages 0 and 20 by regressing the length of displacement vectors with respect to a surface template. Copyright © 2015 Elsevier B.V. All rights reserved.

Non-localization of eigenfunctions for Sturm-Liouville operators and applications

NASA Astrophysics Data System (ADS)

Liard, Thibault; Lissy, Pierre; Privat, Yannick

2018-02-01

In this article, we investigate a non-localization property of the eigenfunctions of Sturm-Liouville operators Aa = -∂xx + a (ṡ) Id with Dirichlet boundary conditions, where a (ṡ) runs over the bounded nonnegative potential functions on the interval (0 , L) with L > 0. More precisely, we address the extremal spectral problem of minimizing the L2-norm of a function e (ṡ) on a measurable subset ω of (0 , L), where e (ṡ) runs over all eigenfunctions of Aa, at the same time with respect to all subsets ω having a prescribed measure and all L∞ potential functions a (ṡ) having a prescribed essentially upper bound. We provide some existence and qualitative properties of the minimizers, as well as precise lower and upper estimates on the optimal value. Several consequences in control and stabilization theory are then highlighted.

Fission matrix-based Monte Carlo criticality analysis of fuel storage pools

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

Farlotti, M.; Ecole Polytechnique, Palaiseau, F 91128; Larsen, E. W.

2013-07-01

Standard Monte Carlo transport procedures experience difficulties in solving criticality problems in fuel storage pools. Because of the strong neutron absorption between fuel assemblies, source convergence can be very slow, leading to incorrect estimates of the eigenvalue and the eigenfunction. This study examines an alternative fission matrix-based Monte Carlo transport method that takes advantage of the geometry of a storage pool to overcome this difficulty. The method uses Monte Carlo transport to build (essentially) a fission matrix, which is then used to calculate the criticality and the critical flux. This method was tested using a test code on a simplemore » problem containing 8 assemblies in a square pool. The standard Monte Carlo method gave the expected eigenfunction in 5 cases out of 10, while the fission matrix method gave the expected eigenfunction in all 10 cases. In addition, the fission matrix method provides an estimate of the error in the eigenvalue and the eigenfunction, and it allows the user to control this error by running an adequate number of cycles. Because of these advantages, the fission matrix method yields a higher confidence in the results than standard Monte Carlo. We also discuss potential improvements of the method, including the potential for variance reduction techniques. (authors)« less

Whither HFI/NQI?

NASA Astrophysics Data System (ADS)

Bharuth-Ram, K.

2013-05-01

A brief review is given of the Hyperfine Interactions Conference series and, in particular, of the Joint meetings of the Hyperfine Interactions and Nuclear Quadrupole Interaction (HFI/NQI) Conferences, with respect to number of participants, contributed papers and participant countries. Trends are traced and recommendations are offered to attract a wider participation at future HFI/NQI conferences.

The effective way

NASA Astrophysics Data System (ADS)

Fruchart, Michel; Vitelli, Vincenzo

2018-03-01

A theoretical framework for the design of so-called perturbative metamaterials, based on weakly interacting unit cells, has led to the experimental demonstration of a quadrupole topological insulator.

Acoustics-turbulence interaction

NASA Technical Reports Server (NTRS)

Hussain, A. K. M. F.; Zaman, K. B. M. O.

1977-01-01

An investigation of the instability frequency was undertaken. Measurements revealed that the hot wire probe induces and sustains stable upstream oscillation of the free shear layer. The characteristics of the free shear layer tone are found to be different from the slit jet wedge edgetone phenomenon. The shear tone induced by a plane wedge in a plane free shear layer was then examined in order to further document the phenomenon. The eigenvalues and eigenfunctions of the tone fundamental show agreement with the spatial stability theory. A comprehensive summary of the results is also included.

Spin coherent states phenomena probed by quantum state tomography in Zeeman perturbed nuclear quadrupole resonance

NASA Astrophysics Data System (ADS)

Teles, João; Auccaise, Ruben; Rivera-Ascona, Christian; Araujo-Ferreira, Arthur G.; Andreeta, José P.; Bonagamba, Tito J.

2018-07-01

Recently, we reported an experimental implementation of quantum information processing (QIP) by nuclear quadrupole resonance (NQR). In this work, we present the first quantum state tomography (QST) experimental implementation in the NQR QIP context. Two approaches are proposed, employing coherence selection by temporal and spatial averaging. Conditions for reduction in the number of cycling steps are analyzed, which can be helpful for larger spin systems. The QST method was applied to the study of spin coherent states, where the alignment-to-orientation phenomenon and the evolution of squeezed spin states show the effect of the nonlinear quadrupole interaction intrinsic to the NQR system. The quantum operations were implemented using a single-crystal sample of KClO3 and observing ^{35}Cl nuclei, which posses spin 3/2.

Quadrupole collectivity beyond N = 50 in neutron- rich Se and Kr isotopes

NASA Astrophysics Data System (ADS)

Elman, Brandon; Gade, A.; Barofsky, D.; Bender, P. C.; Bowry, M.; Hjorth-Jensen, M.; Kemper, K. W.; Lipschutz, S.; Lunderberg, E.; Sachmpazidi, N.; Terpstra, N.; Walters, W. B.; Weisshaar, D.; Westerberg, A.; Williams, S. J.; Wimmer, K.

2017-09-01

We will present results on measuring the B (E 2 ;01+ ->2n+) strength for the neutron-rich 88,90Kr and 86Se isotopes from intermediate-energy Coulomb excitation. The electric quadrupole transition strengths to the first 2+ state complete, with considerably improved uncertainties, the evolution of quadrupole collectivity in the Kr and Se isotopes approaching N = 60 , for which 90Kr and 86Se had previously been the most uncertain. We also report significant excitation strength to several higher lying 2+ states in the krypton isotopes. The results confirm shell model calculations in the π (fpg) - ν (sdg) shell with only a minimally tuned shell model setup that is based on a nucleon-nucleon interaction derived from effective field theory with effective charges adjusted to 86Kr.

Support Structure Design of the $$\\hbox{Nb}_{3}\\hbox{Sn}$$ Quadrupole for the High Luminosity LHC

DOE PAGES

Juchno, M.; Ambrosio, G.; Anerella, M.; ...

2014-10-31

New low-β quadrupole magnets are being developed within the scope of the High Luminosity LHC (HL-LHC) project in collaboration with the US LARP program. The aim of the HLLHC project is to study and implement machine upgrades necessary for increasing the luminosity of the LHC. The new quadrupoles, which are based on the Nb₃Sn superconducting technology, will be installed in the LHC Interaction Regions and will have to generate a gradient of 140 T/m in a coil aperture of 150 mm. In this paper, we describe the design of the short model magnet support structure and discuss results of themore » detailed 3D numerical analysis performed in preparation for the first short model test.« less

Electrodynamical forbiddance of a strong quadrupole interaction in surface enhanced optical processes. Experimental confirmation of the existence in fullerene C{sub 60}

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

Polubotko, A. M., E-mail: alex.marina@mail.ioffe.ru; Chelibanov, V. P., E-mail: Chelibanov@gmail.com

2017-02-15

It is demonstrated that in the SERS and SEIRA spectra of the fullerene C{sub 60}, the lines, which are forbidden in usual Raman and IR spectra and allowed in SERS and SEIRA, are absent. In addition the enhancement SERS coefficient in a single molecule detection regime is ~10{sup 8} instead of the value 10{sup 14}–10{sup 15}, characteristic for this phenomenon. These results are explained by the existence of so-called electrodynamical forbiddance of a strong quadrupole light-molecule interaction, which arises because of belonging of C{sup 60} to the icosahedral symmetry group and due to the electrodynamical law divE = 0.

Control of Screening of a Charged Particle in Electrolytic Aqueous Paul Trap

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

Park, Jae Hyun nmn; Krstic, Predrag S

2011-01-01

Individual charged particles could be trapped and confined in the combined radio-frequency and DC quadrupole electric field of an aqueous Paul trap. Viscosity of water improves confinement and extends the range of the trap parameters which characterize the stability of the trap. Electrolyte, if present in aqueous solution, may screen the charged particle and thus partially or fully suppress electrophoretic interaction with the applied filed, possibly reducing it to a generally much weaker dielectrophoretic interaction with an induced dipole. Applying molecular dynamics simulation we show that the quadrupole field has a different affects at the electrolyte ions and at muchmore » heavier charged particle, effectively eliminating the screening effect and reinstating the electrophoretic confinement.« less

Control Of Screening Of A Charged Particle In Electrolytic Aqueous Paul Trap

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

Park, Jae Hyun; Krstic, Predrag S.

2011-06-01

Individual charged particles could be trapped and confined by the combined radio-frequency and DC quadrupole electric field of an aqueous Paul trap. Viscosity of water improves confinement and extends the range of the trap parameters which characterize the stability of the trap. Electrolyte, if present in aqueous solution, may screen the charged particle and thus partially or fully suppress electrophoretic interaction with the applied filed, possibly reducing it to a generally much weaker dielectrophoretic interaction with an induced dipole. Applying molecular dynamics simulation we show that the quadrupole field has a different effect at the electrolyte ions and at muchmore » heavier charged particle, effectively eliminating the screening by electrolyte ions and reinstating the electrophoretic confinement.« less

Calculation of yrast spectra in the doubly even cadmium isotopes

NASA Astrophysics Data System (ADS)

Khosa, S. K.; Mattu, P. K.

1991-02-01

The observed systematics of the low-lying states in 98-110Cd nuclei and the high-spin yrast spectra with Jπmax<=14+ are examined by carrying out Hartree-Fock-Bogoliubov calculations employing a pairing-plus-quadrupole-quadrupole effective interaction operating in a reasonably large valence space outside an inert 80Zr core. Our calculations reveal that the systematics of the low-lying yrast states in 98-110Cd are intricately linked with the deformation producing tendency of the n-p interaction when operating between spin-orbit-partner (SOP) orbits. Our results indicate that such systematics depend crucially on the simultaneous increase of relative occupation probabilities of the (d5/2)-proton and (d3/2)-neutron orbits in the 98-100Cd isotopes.

Higher-order electric multipole contributions to retarded non-additive three-body dispersion interaction energies between atoms: Equilateral triangle and collinear configurations

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

Salam, A., E-mail: salama@wfu.edu

2013-12-28

The theory of molecular quantum electrodynamics (QED) is used to calculate higher electric multipole contributions to the dispersion energy shift between three atoms or molecules arranged in a straight line or in an equilateral triangle configuration. As in two-body potentials, three-body dispersion interactions are viewed in the QED formalism to arise from exchange of virtual photons between coupled pairs of particles. By employing an interaction Hamiltonian that is quadratic in the electric displacement field means that third-order perturbation theory can be used to yield the energy shift for a particular combination of electric multipole polarizable species, with only six time-orderedmore » diagrams needing to be summed over. Specific potentials evaluated include dipole-dipole-quadrupole (DDQ), dipole-quadrupole-quadrupole (DQQ), and dipole-dipole-octupole (DDO) terms. For the geometries of interest, near-zone limiting forms are found to exhibit an R{sup −11} dependence on separation distance for the DDQ interaction, and an R{sup −13} behaviour for DQQ and DDO shifts, agreeing with an earlier semi-classical computation. Retardation weakens the potential in each case by R{sup −1} in the far-zone. It is found that by decomposing the octupole moment into its irreducible components of weights-1 and -3 that the former contribution to the DDO potential may be taken to be a higher-order correction to the leading triple dipole energy shift.« less

The shifted harmonic approximation and asymptotic SU(2) and SU(1,1) Clebsch-Gordan coefficients

NASA Astrophysics Data System (ADS)

Rowe, D. J.; de Guise, Hubert

2010-12-01

Clebsch-Gordan coefficients of SU(2) and SU(1,1) are defined as eigenfunctions of a linear operator acting on the tensor product of the Hilbert spaces for two irreps of these groups. The shifted harmonic approximation is then used to solve these equations in asymptotic limits in which these eigenfunctions approach harmonic oscillator wavefunctions and thereby derive asymptotic expressions for these Clebsch-Gordan coefficients.

Eigenfunctions and heat kernels of super Maass Laplacians on the super Poincaré upper half-plane

NASA Astrophysics Data System (ADS)

Oshima, Kazuto

1992-03-01

Heat kernels of ``super Maass Laplacians'' are explicitly constructed on super Poincaré upper half-plane by a serious treatment of a complete set of eigenfunctions. By component decomposition an explicit treatment can be done for arbitrary weight and a knowledge of classical Maass Laplacians becomes helpful. The result coincides with that of Aoki [Commun. Math. Phys. 117, 405 (1988)] which was obtained by solving differential equations.

Spin eigen-states of Dirac equation for quasi-two-dimensional electrons

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

Eremko, Alexander, E-mail: eremko@bitp.kiev.ua; Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua; Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua

Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shownmore » that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.« less

Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

PubMed Central

Chung, Moo K.; Qiu, Anqi; Seo, Seongho; Vorperian, Houri K.

2014-01-01

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface. PMID:25791435

Spatial modeling in ecology: the flexibility of eigenfunction spatial analyses.

PubMed

Griffith, Daniel A; Peres-Neto, Pedro R

2006-10-01

Recently, analytical approaches based on the eigenfunctions of spatial configuration matrices have been proposed in order to consider explicitly spatial predictors. The present study demonstrates the usefulness of eigenfunctions in spatial modeling applied to ecological problems and shows equivalencies of and differences between the two current implementations of this methodology. The two approaches in this category are the distance-based (DB) eigenvector maps proposed by P. Legendre and his colleagues, and spatial filtering based upon geographic connectivity matrices (i.e., topology-based; CB) developed by D. A. Griffith and his colleagues. In both cases, the goal is to create spatial predictors that can be easily incorporated into conventional regression models. One important advantage of these two approaches over any other spatial approach is that they provide a flexible tool that allows the full range of general and generalized linear modeling theory to be applied to ecological and geographical problems in the presence of nonzero spatial autocorrelation.

Photonuclear absorption cross sections

NASA Technical Reports Server (NTRS)

Norbury, John W.

1989-01-01

Neutron multiplicity in photonuclear reactions; invariance of classical electromagnetism; momentum transfer models in ion collisions; cosmic ray electromagnetic interactions; quadrupole excitations in nucleus-nucleus collisons and Y-89 interactions with relativistic nuclei; and the Weizsacker-Williams theory for nucleon emission via electromagnetic excitations in nucleus-nucleus collisions are discussed.

Chemical interaction between Lilium brownii and Rhizoma Anemarrhenae, the herbal constituents of Baihe Zhimu decoction, by liquid chromatography coupled to hybrid triple quadrupole linear ion trap mass spectrometer.

PubMed

Yang, Bo; Liu, Zhirui; Wang, Qian; Xia, Peiyuan

2018-03-01

During the course of decoction, the components of herbal formula interact with each other, such that chemical extraction characteristics are altered. The crude drugs, Lilium brownii (Baihe) and Rhizoma Anemarrhenae (Zhimu), are the herbal constituents of Baihe Zhimu decoction, a traditional herbal formula. To investigate the chemical interaction between Baihe and Zhimu when decocting together, eight marker components in Baihe Zhimu decoction were simultaneously characterized and quantified in one run by a hybrid triple quadrupole linear ion trap mass spectrometer in the multiple reactions monitoring-information dependent acquisition-enhanced product ion mode. The results showed that Zhimu significantly suppressed the extraction of phenolic glycosides (the components from Baihe) when co-decocting, and Baihe clearly suppressed the extraction of xanthones and steroidal saponins (the components from Zhimu). Overall, the presently developed method would be a preferred candidate for the investigation of the chemical interaction between herbal medicines. Copyright © 2017 John Wiley & Sons, Ltd.

Gyroscopic effect in low-energy classical capture of a rotating quadrupolar diatom by an ion.

PubMed

Dashevskaya, Elena; Litvin, Iliya; Nikitin, Evgueni

2006-03-09

The low-energy capture of homonuclear diatoms by ions is due mainly to the long-range part of the interpartner potential with leading terms that correspond to charge-quadrupole interaction and charge-induced dipole interaction. The capture dynamics is described by the perturbed-rotor adiabatic potentials and the Coriolis interaction between manifold of states that belong to a given value of the intrinsic angular momentum. When the latter is large enough, it can noticeably affect the capture cross section calculated in the adiabatic channel approximation due to the gyroscopic property of a rotating diatom. This paper presents the low-energy (low-temperature) state-selected partial and mean capture cross sections (rate coefficients) for the charge-quadrupole interaction that include the gyroscopic effect (decoupling of intrinsic angular momentum from the collision axis), quantum correction for the diatom rotation, and the correction for the charge-induced dipole interaction. These results complement recent studies on the gyroscopic effect in the quantum regime of diatom-ion capture (Dashevskaya, E. I.; Litvin, I.; Nikitin, E. E.; Troe, J. J. Chem. Phys. 2004, 120, 9989-9997).

Counting nodal domains on surfaces of revolution

NASA Astrophysics Data System (ADS)

Karageorge, Panos D.; Smilansky, Uzy

2008-05-01

We consider eigenfunctions of the Laplace-Beltrami operator on special surfaces of revolution. For this separable system, the nodal domains of the (real) eigenfunctions form a checkerboard pattern, and their number νn is proportional to the product of the angular and the 'surface' quantum numbers. Arranging the wavefunctions by increasing values of the Laplace-Beltrami spectrum, we obtain the nodal sequence, whose statistical properties we study. In particular, we investigate the distribution of the normalized counts \\frac{\

On Nonlinear Functionals of Random Spherical Eigenfunctions

NASA Astrophysics Data System (ADS)

Marinucci, Domenico; Wigman, Igor

2014-05-01

We prove central limit theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combines asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and total variation bounds for Gaussian subordinated fields. We discuss applications to geometric functionals like the defect and invariant statistics, e.g., polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.

The Uses and Abuses of the Acoustic Analogy in Helicopter Rotor Noise Prediction

NASA Technical Reports Server (NTRS)

Farassat, F.; Brentner, Kenneth S.

1987-01-01

This paper is theoretical in nature and addresses applications of the acoustic analogy in helicopter rotor noise prediction. It is argued that in many instances the acoustic analogy has not been used with care in rotor noise studies. By this it is meant that approximate or inappropriate formulations have been used. By considering various mechanisms of noise generation, such abuses are identified and the remedy is suggested. The mechanisms discussed are thickness, loading, quadrupole, and blade-vortex interaction noise. The quadrupole term of the Ffowcs Williams-Hawkings equation is written in a new form which separates the contributions of regions of high gradients such as shock surfaces. It is shown by order of magnitude studies that such regions are capable of producing noise with the same directivity as the thickness noise. The inclusion of this part of quadrupole sources in current acoustic codes is quite practical. Some of the difficulties with the use of loading noise formulations of the first author in predictions of blade-vortex interaction noise are discussed. It appears that there is a need for development of new theoretical results based on the acoustic analogy in this area. Because of the impulsive character of the blade surface pressure, a time scale of integration different from that used in loading and thickness computations must he used in a computer code for prediction of blade-vortex interaction noise.

Two charges on a plane in a magnetic field: hidden algebra, (particular) integrability, polynomial eigenfunctions

NASA Astrophysics Data System (ADS)

Turbiner, A. V.; Escobar-Ruiz, M. A.

2013-07-01

The quantum mechanics of two Coulomb charges on a plane (e1, m1) and (e2, m2) subject to a constant magnetic field B perpendicular to the plane is considered. Four integrals of motion are explicitly indicated. It is shown that for two physically important particular cases, namely that of two particles of equal Larmor frequencies, {e_c} \\propto \\frac{e_1}{m_1}-\\frac{e_2}{m_2}=0 (e.g. two electrons) and one of a neutral system (e.g. the electron-positron pair, hydrogen atom) at rest (the center-of-mass momentum is zero) some outstanding properties occur. They are the most visible in double polar coordinates in CMS (R, ϕ) and relative (ρ, φ) coordinate systems: (i) eigenfunctions are factorizable, all factors except one with the explicit ρ-dependence are found analytically, they have definite relative angular momentum, (ii) dynamics in the ρ-direction is the same for both systems, it corresponds to a funnel-type potential and it has hidden sl(2) algebra, at some discrete values of dimensionless magnetic fields b ⩽ 1, (iii) particular integral(s) occur, (iv) the hidden sl(2) algebra emerges in finite-dimensional representation, thus, the system becomes quasi-exactly-solvable and (v) a finite number of polynomial eigenfunctions in ρ appear. Nine families of eigenfunctions are presented explicitly.

Possibility of modifying the growth trajectory in Raeini Cashmere goat.

PubMed

Ghiasi, Heydar; Mokhtari, M S

2018-03-27

The objective of this study was to investigate the possibility of modifying the growth trajectory in Raeini Cashmere goat breed. In total, 13,193 records on live body weight collected from 4788 Raeini Cashmere goats were used. According to Akanke's information criterion (AIC), the sing-trait random regression model included fourth-order Legendre polynomial for direct and maternal genetic effect; maternal and individual permanent environmental effect was the best model for estimating (co)variance components. The matrices of eigenvectors for (co)variances between random regression coefficients of direct additive genetic were used to calculate eigenfunctions, and different eigenvector indices were also constructed. The obtained results showed that the first eigenvalue explained 79.90% of total genetic variance. Therefore, changing the body weights applying the first eigenfunction will be obtained rapidly. Selection based on the first eigenvector will cause favorable positive genetic gains for all body weight considered from birth to 12 months of age. For modifying the growth trajectory in Raeini Cashmere goat, the selection should be based on the second eigenfunction. The second eigenvalue accounted for 14.41% of total genetic variance for body weights that is low in comparison with genetic variance explained by the first eigenvalue. The complex patterns of genetic change in growth trajectory observed under the third and fourth eigenfunction and low amount of genetic variance explained by the third and fourth eigenvalues.

Three-level mixing model for nuclear chiral rotation: Role of the planar component

NASA Astrophysics Data System (ADS)

Chen, Q. B.; Starosta, K.; Koike, T.

2018-04-01

Three- and two-level mixing models are proposed to understand the doubling of states at the same spin and parity in triaxially deformed atomic nuclei with odd numbers of protons and neutrons. The particle-rotor model for such nuclei is solved using the newly proposed basis which couples angular momenta of two valence nucleons and the rotating triaxial mean field into left-handed |L > , right-handed |R > , and planar |P > configurations. The presence and impact of the planar component is investigated as a function of the total spin for mass A ≈130 nuclei with the valence h11 /2 proton particle, valence h11 /2 neutron hole, and the maximum difference between principal axes allowed by the quadrupole deformation of the mean field. It is concluded that at each spin value the higher energy member of a doublet of states is built on the antisymmetric combination of |L > and |R > and is free of the |P > component, indicating that it is of pure chiral geometry. For the lower energy member of the doublet, the contribution of the |P > component to the eigenfunction first decreases and then increases as a function of the total spin. This trend as well as the energy splitting between the doublet states are both determined by the Hamiltonian matrix elements between the planar (|P > ) and nonplanar (|L > and |R > ) subspaces of the full Hilbert space.

Magnetic Measurements of the First Nb 3Sn Model Quadrupole (MQXFS) for the High-Luminosity LHC

DOE PAGES

DiMarco, J.; Ambrosio, G.; Chlachidze, G.; ...

2016-12-12

The US LHC Accelerator Research Program (LARP) and CERN are developing high-gradient Nb 3Sn magnets for the High Luminosity LHC interaction regions. Magnetic measurements of the first 1.5 m long, 150 mm aperture model quadrupole, MQXFS1, were performed during magnet assembly at LBNL, as well as during cryogenic testing at Fermilab’s Vertical Magnet Test Facility. This paper reports on the results of these magnetic characterization measurements, as well as on the performance of new probes developed for the tests.

New ortho-para conversion mechanism in dense solid hydrogen.

PubMed

Strzhemechny, M A; Hemley, R J

2000-12-25

Analysis of recent measurements of striking changes in the rate of ortho-para conversion of solid H(2) up to 58 GPa shows that the conversion mechanism must differ from that at ambient pressure. A new conversion mechanism is identified in which the emerging excitations are coupled to the converting molecules via electric quadrupole-quadrupole rather than nuclear spin-spin interactions. The latter only initiates conversion while the coupling enhancement associated with the new mechanism is ensured by high compression and a gap closing, with the conversion energy diminishing strongly with increasing pressure.

LHC interaction region quadrupole cryostat design

NASA Astrophysics Data System (ADS)

Nicol, T. H.; Darve, Ch.; Huang, Y.; Page, T. M.

2002-05-01

The cryostat of a Large Hadron Collider (LHC) Interaction Region (IR) quadrupole magnet consists of all components of the inner triplet except the magnet assembly itself. It serves to support the magnet accurately and reliably within the vacuum vessel, to house all required cryogenic piping, and to insulate the cold mass from heat radiated and conducted from the environment. It must function reliably during storage, shipping and handling, normal magnet operation, quenches, and seismic excitations, and must be able to be manufactured at low cost. The major components of the cryostat are the vacuum vessel, thermal shield, multi-layer insulation system, cryogenic piping, and suspension system. The overall design of a cryostat for superconducting accelerator magnets requires consideration of fluid flow, proper selection of materials for their thermal and structural performance at both ambient and operating temperature, and knowledge of the environment to which the magnets will be subjected over the course of their expected operating lifetime. This paper describes the current LHC IR inner triplet quadrupole magnet cryostats being designed and manufactured at Fermilab as part of the US-LHC collaboration, and includes discussions on the structural and thermal considerations involved in the development of each of the major systems.

Theory of electronic structures and nuclear quadrupole interactions in molecular solids and semiconductor surfaces

NASA Astrophysics Data System (ADS)

Pati, Ranjit

We have investigated, using the Hartree-Fock Roothaan variational procedure, the electronic structures and associated nuclear quadrupole interactions (NQI) for the molecular solids, RDX (C3H6N6O6),/ /beta- HMX(C4H8N8O8), Cocaine (C17H21NO4), Cocaine Hydrochloride (C17H21NO4HCl) and Heroin (C21H23NO5) and for the (111) surface of silicon with adsorbed radioactive 111In atom and negative cadmium ion containing the excited nucleus 111Cd/* resulting from electron capture by lllIn. Our investigations indicate that for the ring 14N NQI parameters in RDX and β-HMX there is very good agreement between theory and experiment. For the peripheral 14N nuclei in NO2 groups, while the calculated electronic structures do explain the much weaker quadrupole coupling constants for these nuclei relative to the ring 14N nuclei, there are significant differences between theory and experiment. The influence of intermolecular interactions between adjacent molecules in the solid is invoked as a possible source for these differences. For the controlled substances, Cocaine and Heroin, again very good agreement is obtained between theory and experiment. For Cocaine Hydrochloride theory is able to explain the much smaller observed 14N nuclear quadrupole resonance frequency as compared to pure Cocaine. However there are significant differences between theory and experiment for the 14N and 35Cl quadrupole resonance frequencies. The influence of intermolecular interactions is one of the factors suggested to explain the difference. For the silicon (111) surface, the observed 111Cd/* NQI parameters, with the cadmium nucleus assumed to be located at the same site as the 111In nucleus from which it is generated, can be successfully explained by theory with the indium atom located at the two distinct sites available with the DAS model for the 7 x 7 reconstructed (111) surface. Some quantitative differences still remain, one of the main factor suggested for their explanation being a need for a thorough analysis of relaxation effects in the positions of silicon atoms associated with the presence of the indium atom. Applications of the Hartree-Fock Cluster theory to other related systems is suggested to subject the DAS model to additional tests at the microscopic level as in the system studied in the present thesis. (Abstract shortened by UMI.)

Analysis of the experimental level scheme of {sup 61}Cu using computational technique

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

Gupta, Anuradha, E-mail: annu1gupta1@gmail.com; Verma, Preeti, E-mail: preetiverma130587@gmail.com; Bharti, Arun, E-mail: arunbharti-2003@yahoo.co.in

2015-08-28

The high-spin structure in {sup 61}Cu nucleus is studied in terms of effective two body interaction. In order to take into account the deformed BCS basis, the basis states are expanded in terms of the core eigenfunctions. Yrast band with some other bands havew been obtained and back-bending in moment of inertia has also been calculated and compared with the available experimental data for {sup 61}Cu nucleus. On comparing the available experimental as well as other theoretical data, it is found that the treatment with PSM provides a satisfactory explanation of the available data.

Plane waves and structures in turbulent channel flow

NASA Technical Reports Server (NTRS)

Sirovich, L.; Ball, K. S.; Keefe, L. R.

1990-01-01

A direct simulation of turbulent flow in a channel is analyzed by the method of empirical eigenfunctions (Karhunen-Loeve procedure, proper orthogonal decomposition). This analysis reveals the presence of propagating plane waves in the turbulent flow. The velocity of propagation is determined by the flow velocity at the location of maximal Reynolds stress. The analysis further suggests that the interaction of these waves appears to be essential to the local production of turbulence via bursting or sweeping events in the turbulent boundary layer, with the additional suggestion that the fast acting plane waves act as triggers.

Nonlocal theory of beam-driven electron Bernstein waves

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

Jain, V.K.; Tripathi, V.K.

A nonlocal theory of electron Bernstein waves driven unstable by an axial beam (V = V/sub b/z-italic-circumflex) of finite width has been developed. Assuming a parabolic density profile for the background plasma, an equation describing the mode structure of the wave is obtained in the slab geometry. The eigenfunctions are found to be Hermite polynomials. Expressions for the growth rates of the instabilities caused by Cerenkov and slow cyclotron interactions are derived. The results of the theory are applied to explain some of the experimental observations of Jain and Christiansen (Phys. Lett. A 82, 127 (1981)).

LARP Long Quadrupole: A "Long" Step Toward an LHC

ScienceCinema

Giorgio Ambrosio

2017-12-09

The beginning of the development of Nb3Sn magnets for particle accelerators goes back to the 1960’s. But only very recently has this development begun to face the challenges of fabricating Nb3Sn magnets which can meet the requirements of modern particle accelerators. LARP (the LHC Accelerator Research Program) is leading this effort focusing on long models of the Interaction Region quadrupoles for a possible luminosity upgrade of the Large Hadron Collider. A major milestone in this development is to test, by the end of 2009, 4m-long quadrupole models, which will be the first Nb3Sn accelerator-type magnets approaching the length of real accelerator magnets. The Long Quadrupoles (LQ) are “Proof-of-Principle” magnets which are to demonstrate that Nb3Sn technology is sufficiently mature for use in high energy particle accelerators. Their design is based on the LARP Technological Quadrupole (TQ) models, under development at FNAL and LBNL, which have design gradients higher than 200 T/m and an aperture of 90 mm. Several challenges must be addressed for the successful fabrication of long Nb3Sn coils and magnets. These challenges and the solutions adopted will be presented together with the main features of the LQ magnets. Several R&D lines are participating to this effort and their contributions will be also presented.

Intermolecular configurations dominated by quadrupole-quadrupole electrostatic interactions: explicit correlation treatment of the five-dimensional potential energy surface and infrared spectra for the CO-N2 complex.

PubMed

Liu, Jing-Min; Zhai, Yu; Zhang, Xiao-Long; Li, Hui

2018-01-17

A thorough understanding of the intermolecular configurations of van der Waals complexes is a great challenge due to their weak interactions, floppiness and anharmonic nature. Although high-resolution microwave or infrared spectroscopy provides one of the most direct and precise pieces of experimental evidence, the origin and key role in determining such intermolecular configurations of a van der Waals system strongly depend on its highly accurate potential energy surface (PES) and a detailed analysis of its ro-vibrational wavefunctions. Here, a new five-dimensional potential energy surface for the van der Waals complex of CO-N 2 which explicitly incorporates the dependence on the stretch coordinate of the CO monomer is generated using the explicitly correlated couple cluster (CCSD(T)-F12) method in conjunction with a large basis set. Analytic four-dimensional PESs are obtained by the least-squares fitting of vibrationally averaged interaction energies for v = 0 and v = 1 to the Morse/Long-Range potential mode (V MLR ). These fits to 7966 points have root-mean-square deviations (RMSD) of 0.131 cm -1 and 0.129 cm -1 for v = 0 and v = 1, respectively, with only 315 parameters. Energy decomposition analysis is carried out, and it reveals that the dominant factor in controlling intermolecular configurations is quadrupole-quadrupole electrostatic interactions. Moreover, the rovibrational levels and wave functions are obtained for the first time. The predicted infrared transitions and intensities for the ortho-N 2 -CO complex as well as the calculated energy levels for para-N 2 -CO are in good agreement with the available experimental data with RMSD discrepancies smaller than 0.068 cm -1 . The calculated infrared band origin shift associated with the fundamental band frequency of CO is -0.721 cm -1 for ortho-N 2 -CO which is in excellent agreement with the experimental value of -0.739 cm -1 . The agreement with experimental values validates the high quality of the PESs and enhances our confidence to explain the observed mystery lines around 2163 cm -1 .

Rotational Parameters from Vibronic Eigenfunctions of Jahn-Teller Active Molecules

NASA Astrophysics Data System (ADS)

Garner, Scott M.; Miller, Terry A.

2017-06-01

The structure in rotational spectra of many free radical molecules is complicated by Jahn-Teller distortions. Understanding the magnitudes of these distortions is vital to determining the equilibrium geometric structure and details of potential energy surfaces predicted from electronic structure calculations. For example, in the recently studied {\\widetilde{A}^2E^{''} } state of the NO_3 radical, the magnitudes of distortions are yet to be well understood as results from experimental spectroscopic studies of its vibrational and rotational structure disagree with results from electronic structure calculations of the potential energy surface. By fitting either vibrationally resolved spectra or vibronic levels determined by a calculated potential energy surface, we obtain vibronic eigenfunctions for the system as linear combinations of basis functions from products of harmonic oscillators and the degenerate components of the electronic state. Using these vibronic eigenfunctions we are able to predict parameters in the rotational Hamiltonian such as the Watson Jahn-Teller distortion term, h_1, and compare with the results from the analysis of rotational experiments.

A variable-order laminated plate theory based on the variational-asymptotical method

NASA Technical Reports Server (NTRS)

Lee, Bok W.; Sutyrin, Vladislav G.; Hodges, Dewey H.

1993-01-01

The variational-asymptotical method is a mathematical technique by which the three-dimensional analysis of laminated plate deformation can be split into a linear, one-dimensional, through-the-thickness analysis and a nonlinear, two-dimensional, plate analysis. The elastic constants used in the plate analysis are obtained from the through-the-thickness analysis, along with approximate, closed-form three-dimensional distributions of displacement, strain, and stress. In this paper, a theory based on this technique is developed which is capable of approximating three-dimensional elasticity to any accuracy desired. The asymptotical method allows for the approximation of the through-the-thickness behavior in terms of the eigenfunctions of a certain Sturm-Liouville problem associated with the thickness coordinate. These eigenfunctions contain all the necessary information about the nonhomogeneities along the thickness coordinate of the plate and thus possess the appropriate discontinuities in the derivatives of displacement. The theory is presented in this paper along with numerical results for the eigenfunctions of various laminated plates.

Are neutron stars crushed? Gravitomagnetic tidal fields as a mechanism for binary-induced collapse

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

Favata, Marc

Numerical simulations of binary neutron stars by Wilson, Mathews, and Marronetti indicated that neutron stars that are stable in isolation can be made to collapse to black holes when placed in a binary. This claim was surprising as it ran counter to the Newtonian expectation that a neutron star in a binary should be more stable, not less. After correcting an error found by Flanagan, Wilson and Mathews found that the compression of the neutron stars was significantly reduced but not eliminated. This has motivated us to ask the following general question: Under what circumstances can general-relativistic tidal interactions causemore » an otherwise stable neutron star to be compressed? We have found that if a nonrotating neutron star possesses a current-quadrupole moment, interactions with a gravitomagnetic tidal field can lead to a compressive force on the star. If this current quadrupole is induced by the gravitomagnetic tidal field, it is related to the tidal field by an equation-of-state-dependent constant called the gravitomagnetic Love number. This is analogous to the Newtonian Love number that relates the strength of a Newtonian tidal field to the induced mass quadrupole moment of a star. The compressive force is almost never larger than the Newtonian tidal interaction that stabilizes the neutron star against collapse. In the case in which a current quadrupole is already present in the star (perhaps as an artifact of a numerical simulation), the compressive force can exceed the stabilizing one, leading to a net increase in the central density of the star. This increase is small (< or approx. 1%) but could, in principle, cause gravitational collapse in a star that is close to its maximum mass. This paper also reviews the history of the Wilson-Mathews-Marronetti controversy and, in an appendix, extends the discussion of tidally induced changes in the central density to rotating stars.« less

Spectroscopy of reflection-asymmetric nuclei with relativistic energy density functionals

NASA Astrophysics Data System (ADS)

Xia, S. Y.; Tao, H.; Lu, Y.; Li, Z. P.; Nikšić, T.; Vretenar, D.

2017-11-01

Quadrupole and octupole deformation energy surfaces, low-energy excitation spectra, and transition rates in 14 isotopic chains: Xe, Ba, Ce, Nd, Sm, Gd, Rn, Ra, Th, U, Pu, Cm, Cf, and Fm, are systematically analyzed using a theoretical framework based on a quadrupole-octupole collective Hamiltonian (QOCH), with parameters determined by constrained reflection-asymmetric and axially symmetric relativistic mean-field calculations. The microscopic QOCH model based on the PC-PK1 energy density functional and δ -interaction pairing is shown to accurately describe the empirical trend of low-energy quadrupole and octupole collective states, and predicted spectroscopic properties are consistent with recent microscopic calculations based on both relativistic and nonrelativistic energy density functionals. Low-energy negative-parity bands, average octupole deformations, and transition rates show evidence for octupole collectivity in both mass regions, for which a microscopic mechanism is discussed in terms of evolution of single-nucleon orbitals with deformation.

First determination of ground state electromagnetic moments of Fe 53

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

Miller, A. J.; Minamisono, K.; Rossi, D. M.

Here, the hyperfine coupling constants of neutron deficient 53Fe were deduced from the atomic hyperfine spectrum measured using the bunched-beam collinear laser spectroscopy technique. The low-energy 53Fe beam was produced by projectile-fragmentation reactions followed by gas stopping, and used for the first time for laser spectroscopy. Ground state magnetic-dipole and electric-quadrupole moments were determined as μ= –0.65(1)μ N and Q=+35(15)e 2fm 2, respectively. The multiconfiguration Dirac-Fock method was used to calculate the electric field gradient to deduce Q from the quadrupole hyperfine coupling constant, since the quadrupole coupling constant has not been determined for any Fe isotopes. Both experimental valuesmore » agree well with nuclear shell model calculations using the GXPF1A effective interaction performed in a full fp shell model space, which support the soft nature of the 56Ni nucleus.« less

Spontaneous structural distortion of the metallic Shastry-Sutherland system Dy B4 by quadrupole-spin-lattice coupling

NASA Astrophysics Data System (ADS)

Sim, Hasung; Lee, Seongsu; Hong, Kun-Pyo; Jeong, Jaehong; Zhang, J. R.; Kamiyama, T.; Adroja, D. T.; Murray, C. A.; Thompson, S. P.; Iga, F.; Ji, S.; Khomskii, D.; Park, Je-Geun

2016-11-01

Dy B4 has a two-dimensional Shastry-Sutherland (Sh-S) lattice with strong Ising character of the Dy ions. Despite the intrinsic frustrations, it undergoes two successive transitions: a magnetic ordering at TN=20 K and a quadrupole ordering at TQ=12.5 K . From high-resolution neutron and synchrotron x-ray powder diffraction studies, we have obtained full structural information on this material in all phases and demonstrate that structural modifications occurring at quadrupolar transition lead to the lifting of frustrations inherent in the Sh-S model. Our paper thus provides a complete experimental picture of how the intrinsic frustration of the Sh-S lattice can be lifted by the coupling to quadrupole moments. We show that two other factors, i.e., strong spin-orbit coupling and long-range Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in metallic Dy B4 , play an important role in this behavior.

First determination of ground state electromagnetic moments of Fe 53

DOE PAGES

Miller, A. J.; Minamisono, K.; Rossi, D. M.; ...

2017-11-16

Here, the hyperfine coupling constants of neutron deficient 53Fe were deduced from the atomic hyperfine spectrum measured using the bunched-beam collinear laser spectroscopy technique. The low-energy 53Fe beam was produced by projectile-fragmentation reactions followed by gas stopping, and used for the first time for laser spectroscopy. Ground state magnetic-dipole and electric-quadrupole moments were determined as μ= –0.65(1)μ N and Q=+35(15)e 2fm 2, respectively. The multiconfiguration Dirac-Fock method was used to calculate the electric field gradient to deduce Q from the quadrupole hyperfine coupling constant, since the quadrupole coupling constant has not been determined for any Fe isotopes. Both experimental valuesmore » agree well with nuclear shell model calculations using the GXPF1A effective interaction performed in a full fp shell model space, which support the soft nature of the 56Ni nucleus.« less

Connections between the dynamical symmetries in the microscopic shell model

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

Georgieva, A. I., E-mail: anageorg@issp.bas.bg; Drumev, K. P.

2016-03-25

The dynamical symmetries of the microscopic shell model appear as the limiting cases of a symmetry adapted Pairing-Plus-Quadrupole Model /PQM/, with a Hamiltonian containing isoscalar and isovector pairing and quadrupole interactions. We establish a correspondence between each of the three types of pairing bases and Elliott’s SU(3) basis, that describes collective rotation of nuclear systems with quadrupole deformation. It is derived from their complementarity to the same LS coupling chain of the shell model number conserving algebra. The probability distribution of the S U(3) basis states within the pairing eigenstates is also obtained through a numerical diagonalization of the PQMmore » Hamiltonian in each limit. We introduce control parameters, which define the phase diagram of the model and determine the role of each term of the Hamiltonian in the correct reproduction of the experimental data for the considered nuclei.« less

Ultrarelativistic bound states in the spherical well

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

Żaba, Mariusz; Garbaczewski, Piotr

2016-07-15

We address an eigenvalue problem for the ultrarelativistic (Cauchy) operator (−Δ){sup 1/2}, whose action is restricted to functions that vanish beyond the interior of a unit sphere in three spatial dimensions. We provide high accuracy spectral data for lowest eigenvalues and eigenfunctions of this infinite spherical well problem. Our focus is on radial and orbital shapes of eigenfunctions. The spectrum consists of an ordered set of strictly positive eigenvalues which naturally splits into non-overlapping, orbitally labelled E{sub (k,l)} series. For each orbital label l = 0, 1, 2, …, the label k = 1, 2, … enumerates consecutive lth seriesmore » eigenvalues. Each of them is 2l + 1-degenerate. The l = 0 eigenvalues series E{sub (k,0)} are identical with the set of even labeled eigenvalues for the d = 1 Cauchy well: E{sub (k,0)}(d = 3) = E{sub 2k}(d = 1). Likewise, the eigenfunctions ψ{sub (k,0)}(d = 3) and ψ{sub 2k}(d = 1) show affinity. We have identified the generic functional form of eigenfunctions of the spherical well which appear to be composed of a product of a solid harmonic and of a suitable purely radial function. The method to evaluate (approximately) the latter has been found to follow the universal pattern which effectively allows to skip all, sometimes involved, intermediate calculations (those were in usage, while computing the eigenvalues for l ≤ 3).« less

Effect of the magnetic dipole interaction on a spin-1 system

NASA Astrophysics Data System (ADS)

Hu, Fangqi; Jia, Wei; Zhao, Qing

2018-05-01

We consider a hybrid system composed of a spin-1 triplet coupled to a nuclear spin. We study the effect of the axisymmetric and the quadrupole term of the magnetic dipole interaction between the two electrons forming the triplet on the energy spectrum in a static magnetic field. The energy spectrum obtained by directly diagonalizing the Hamiltonian of the system shows that these two terms not only remove the special crossings that appear in the absence of the magnetic dipole interaction, but also produce new (avoided) crossings by lifting the relevant levels. Specially, the gaps between the avoided crossing levels increase with the strength of the quadrupole term. In order to accurately illustrate these effects, we present the results for the discriminant and von Neumann entropy of one electron interacting with the rest of the whole system. Finally, by numerically solving the time-dependent Schrödinger equations of the system, we discover that the polarization oscillation of electron and nuclear spin is in-phase and the total average longitudinal spin is not conserved at location of avoided crossing, but the two results are opposite beyond that.

The covalent interaction between dihydrogen and gold: A rotational spectroscopic study of H2-AuCl

NASA Astrophysics Data System (ADS)

Obenchain, Daniel A.; Frank, Derek S.; Grubbs, G. S.; Pickett, Herbert M.; Novick, Stewart E.

2017-05-01

The pure rotational transitions of H2-AuCl have been measured using a pulsed-jet cavity Fourier transform microwave spectrometer equipped with a laser ablation source. The structure was found to be T-shaped, with the H-H bond interacting with the gold atom. Both 35Cl and 37Cl isotopologues have been measured for both ortho and para states of H2. Rotational constants, quartic centrifugal distortion constants, and nuclear quadrupole coupling constants for gold and chlorine have been determined. The use of the nuclear spin-nuclear spin interaction terms Daa, Dbb, and Dcc for H2 were required to fit the ortho state of hydrogen, as well as a nuclear-spin rotation constant Caa. The values of the nuclear quadrupole coupling constant of gold are χa a=-817.9929 (35 ) MHz, χb b=504.0 (27 ) MHz, and χc c=314.0 (27 ) . This is large compared to the eQq of AuCl, 9.63 312(13) MHz, which indicates a strong, covalent interaction between gold and dihydrogen.

Wetting, meniscus structure, and capillary interactions of microspheres bound to a cylindrical liquid interface.

PubMed

Kim, Paul Y; Dinsmore, Anthony D; Hoagland, David A; Russell, Thomas P

2018-03-14

Wetting, meniscus structure, and capillary interactions for polystyrene microspheres deposited on constant curvature cylindrical liquid interfaces, constructed from nonvolatile ionic or oligomeric liquids, were studied by optical interferometry and optical microscopy. The liquid interface curvature resulted from the preferential wetting of finite width lines patterned onto planar silicon substrates. Key variables included sphere diameter, nominal (or average) contact angle, and deviatoric interfacial curvature. Menisci adopted the quadrupolar symmetry anticipated by theory, with interfacial deformation closely following predicted dependences on sphere diameter and nominal contact angle. Unexpectedly, the contact angle was not constant locally around the contact line, the nominal contact angle varied among seemingly identical spheres, and the maximum interface deviation did not follow the predicted dependence on deviatoric interfacial curvature. Instead, this deviation was up to an order-of-magnitude larger than predicted. Trajectories of neighboring microspheres visually manifested quadrupole-quadrupole interactions, eventually producing square sphere packings that foreshadow interfacial assembly as a potential route to hierarchical 2D particle structures.

Modeling the physisorption of graphene on metals

NASA Astrophysics Data System (ADS)

Tao, Jianmin; Tang, Hong; Patra, Abhirup; Bhattarai, Puskar; Perdew, John P.

2018-04-01

Many processes of technological and fundamental importance occur on surfaces. Adsorption is one of these phenomena that has received the most attention. However, it presents a great challenge to conventional density functional theory. Starting with the Lifshitz-Zaremba-Kohn second-order perturbation theory, here we develop a long-range van der Waals (vdW) correction for physisorption of graphene on metals. The model importantly includes quadrupole-surface interaction and screening effects. The results show that, when the vdW correction is combined with the Perdew-Burke-Enzerhof functional, it yields adsorption energies in good agreement with the random-phase approximation, significantly improving upon other vdW methods. We also find that, compared with the leading-order interaction, the higher-order quadrupole-surface correction accounts for about 25 % of the total vdW correction, suggesting the importance of the higher-order term.

Implementation of Magnetic Dipole Interaction in the Planewave-Basis Approach for Slab Systems

NASA Astrophysics Data System (ADS)

Oda, Tatsuki; Obata, Masao

2018-06-01

We implemented the magnetic dipole interaction (MDI) in a first-principles planewave-basis electronic structure calculation based on spin density functional theory. This implementation, employing the two-dimensional Ewald summation, enables us to obtain the total magnetic anisotropy energy of slab materials with contributions originating from both spin-orbit and magnetic dipole-dipole couplings on the same footing. The implementation was demonstrated using an iron square lattice. The result indicates that the magnetic anisotropy of the MDI is much less than that obtained from the atomic magnetic moment model due to the prolate quadrupole component of the spin magnetic moment density. We discuss the reduction in the anisotropy of the MDI in the case of modulation of the quadrupole component and the effect of magnetic field arising from the MDI on atomic scale.

Numerical investigation of non-perturbative kinetic effects of energetic particles on toroidicity-induced Alfvén eigenmodes in tokamaks and stellarators

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

Slaby, Christoph; Könies, Axel; Kleiber, Ralf

2016-09-15

The resonant interaction of shear Alfvén waves with energetic particles is investigated numerically in tokamak and stellarator geometry using a non-perturbative MHD-kinetic hybrid approach. The focus lies on toroidicity-induced Alfvén eigenmodes (TAEs), which are most easily destabilized by a fast-particle population in fusion plasmas. While the background plasma is treated within the framework of an ideal-MHD theory, the drive of the fast particles, as well as Landau damping of the background plasma, is modelled using the drift-kinetic Vlasov equation without collisions. Building on analytical theory, a fast numerical tool, STAE-K, has been developed to solve the resulting eigenvalue problem usingmore » a Riccati shooting method. The code, which can be used for parameter scans, is applied to tokamaks and the stellarator Wendelstein 7-X. High energetic-ion pressure leads to large growth rates of the TAEs and to their conversion into kinetically modified TAEs and kinetic Alfvén waves via continuum interaction. To better understand the physics of this conversion mechanism, the connections between TAEs and the shear Alfvén wave continuum are examined. It is shown that, when energetic particles are present, the continuum deforms substantially and the TAE frequency can leave the continuum gap. The interaction of the TAE with the continuum leads to singularities in the eigenfunctions. To further advance the physical model and also to eliminate the MHD continuum together with the singularities in the eigenfunctions, a fourth-order term connected to radiative damping has been included. The radiative damping term is connected to non-ideal effects of the bulk plasma and introduces higher-order derivatives to the model. Thus, it has the potential to substantially change the nature of the solution. For the first time, the fast-particle drive, Landau damping, continuum damping, and radiative damping have been modelled together in tokamak- as well as in stellarator geometry.« less

Crossing symmetry in alpha space

NASA Astrophysics Data System (ADS)

Hogervorst, Matthijs; van Rees, Balt C.

2017-11-01

We initiate the study of the conformal bootstrap using Sturm-Liouville theory, specializing to four-point functions in one-dimensional CFTs. We do so by decomposing conformal correlators using a basis of eigenfunctions of the Casimir which are labeled by a complex number α. This leads to a systematic method for computing conformal block decompositions. Analyzing bootstrap equations in alpha space turns crossing symmetry into an eigenvalue problem for an integral operator K. The operator K is closely related to the Wilson transform, and some of its eigenfunctions can be found in closed form.

Discriminating the structure of exo-2-aminonorbornane using nuclear quadrupole coupling interactions.

PubMed

Écija, Patricia; Cocinero, Emilio J; Lesarri, Alberto; Millán, Judith; Basterretxea, Francisco; Fernández, José A; Castaño, Fernando

2011-04-28

The intrinsic conformational and structural properties of the bicycle exo-2-aminonorbornane have been probed in a supersonic jet expansion using Fourier-transform microwave (FT-MW) spectroscopy and quantum chemical calculations. The rotational spectrum revealed two different conformers arising from the internal rotation of the amino group, exhibiting small (MHz) hyperfine patterns originated by the (14)N nuclear quadrupole coupling interaction. Complementary ab initio (MP2) and DFT (B3LYP and M05-2X) calculations provided comparative predictions for the structural properties, rotational and centrifugal distortion data, hyperfine parameters, and isomerization barriers. Due to the similarity of the rotational constants, the structural assignment of the observed rotamers and the calculation of the torsion angles of the amino group were based on the conformational dependence of the (14)N nuclear quadrupole coupling hyperfine tensor. In the most stable conformation (ss), the two amino N-H bonds are staggered with respect to the adjacent C-H bond. In the second conformer (st), only one of the N-H bonds is staggered and the other is trans. A third predicted conformer (ts) was not detected, consistent with a predicted conformational relaxation to conformer ss through a low barrier of 5.2 kJ mol(-1).

Manifestation of a strong quadrupole interaction and peculiarities in the SERS and SEHRS spectra of 4,4'-bipyridine

NASA Astrophysics Data System (ADS)

Golovin, A. V.; Polubotko, A. M.

2017-07-01

The paper analyzes Surface Enhanced Raman Scattering (SERS) and Surface Enhanced Hyper Raman Scattering (SEHRS) spectra of 4,4'-bypiridine molecule for two possible geometries, which are described by D 2 and D 2 h symmetry groups. It is pointed out on appearance of sufficiently strong lines, caused by vibrations with the unit irreducible representation for both possible configurations. Appearance of these lines in the SEHRS spectrum points out the existence of a strong quadrupole light-molecule interaction. In addition one observes the lines, caused by vibrations both with the unit irreducible representations A or A g and the irreducible representation B 1 or B 1 u . The last ones describe transformational properties of the d z component of the dipole moment, which is perpendicular to the surface. This property of the spectrum is caused by peculiarity of the geometry of the molecule, which consists of two benzene rings, which are weakly connected with each other. The linear combinations of the vibrations of the rings create two nearly degenerated symmetric and anti symmetrical states, which cannot be identified in the experimental spectra. The result is in a full agreement with the dipole-quadrupole theory of SERS and SEHRS.

Prediction of thermodynamic properties of coal derivatives. Progress report, September 1, 1981-August 31, 1982

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

Donohue, M.D.

It is the purpose of this research program to develop a model to predict the thermodynamic properties of coal derivatives. Unlike natural gas and petroleum, coal and its gasification and liquefaction products are predominantly aromatic and have substantial quadrupole moments. Because of these quadrupole forces, the numerous correlational techniques that have been developed for petroleum products cannot be used to predict the thermodynamic properties of coal derivatives. We are presently developing a correlation that will be useful in predicting the thermodynamic properties of coal derivatives. This theory is based on the Perturbed-Hard-Chain theory, but is different from PHCT in twomore » respects. First, PHCT uses a square-well to describe the intermolecular potential energy between two molecules. In our new theory, the Lennard-Jones potential energy function is used. The second difference is that we take into account the effect of quadrupole forces on the intermolecular potential energy. In PHCT these forces were ignored. In PHCT the contributions to the partition function (or equation of state) that arise from the attractive forces between molecules (regardless of whether these forces are treated as a square-well or by Lennard-Jones) are calculated by assuming that they are perturbations on a hard sphere. In calculating the contributions to the partition function that arise from the quadrupole-quadrupole interactions, we use a second order perturbation about the Lennard-Jones. For aromatic molecules, the effect of this additional perturbation is significant.« less

Interacting Boson Model and nucleons

NASA Astrophysics Data System (ADS)

Otsuka, Takaharu

2012-10-01

An overview on the recent development of the microscopic derivation of the Interacting Boson Model is presented with some remarks not found elsewhere. The OAI mapping is reviewed very briefly, including the basic correspondence from nucleon-pair to boson. The new fermionboson mapping method is introduced, where intrinsic states of nucleons and bosons for a wide variation of shapes play an important role. Nucleon intrinsic states are obtained from mean field models, which is Skyrme model in examples to be shown. This method generates IBM-2 Hamiltonian which can describe and predict various situations of quadrupole collective states, including U(5), SU(3), O(6) and E(5) limits. The method is extended so that rotational response (cranking) can be handled, which enables us to describe rotational bands of strongly deformed nuclei. Thus, we have obtained a unified framework for the microscopic derivation of the IBM covering all known situations of quadrupole collectivity at low energy.

Interaction of Strain and Nuclear Spins in Silicon: Quadrupolar Effects on Ionized Donors

NASA Astrophysics Data System (ADS)

Franke, David P.; Hrubesch, Florian M.; Künzl, Markus; Becker, Hans-Werner; Itoh, Kohei M.; Stutzmann, Martin; Hoehne, Felix; Dreher, Lukas; Brandt, Martin S.

2015-07-01

The nuclear spins of ionized donors in silicon have become an interesting quantum resource due to their very long coherence times. Their perfect isolation, however, comes at a price, since the absence of the donor electron makes the nuclear spin difficult to control. We demonstrate that the quadrupolar interaction allows us to effectively tune the nuclear magnetic resonance of ionized arsenic donors in silicon via strain and determine the two nonzero elements of the S tensor linking strain and electric field gradients in this material to S11=1.5 ×1022 V /m2 and S44=6 ×1022 V /m2 . We find a stronger benefit of dynamical decoupling on the coherence properties of transitions subject to first-order quadrupole shifts than on those subject to only second-order shifts and discuss applications of quadrupole physics including mechanical driving of magnetic resonance, cooling of mechanical resonators, and strain-mediated spin coupling.

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators.

PubMed

Bardhan, Jaydeep P; Knepley, Matthew G; Brune, Peter

2015-01-01

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson-Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators

PubMed Central

Bardhan, Jaydeep P.; Knepley, Matthew G.; Brune, Peter

2015-01-01

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood’s classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson–Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online. PMID:26273581

Methods in the study of discrete upper hybrid waves

NASA Astrophysics Data System (ADS)

Yoon, P. H.; Ye, S.; Labelle, J.; Weatherwax, A. T.; Menietti, J. D.

2007-11-01

Naturally occurring plasma waves characterized by fine frequency structure or discrete spectrum, detected by satellite, rocket-borne instruments, or ground-based receivers, can be interpreted as eigenmodes excited and trapped in field-aligned density structures. This paper overviews various theoretical methods to study such phenomena for a one-dimensional (1-D) density structure. Among the various methods are parabolic approximation, eikonal matching, eigenfunction matching, and full numerical solution based upon shooting method. Various approaches are compared against the full numerical solution. Among the analytic methods it is found that the eigenfunction matching technique best approximates the actual numerical solution. The analysis is further extended to 2-D geometry. A detailed comparative analysis between the eigenfunction matching and fully numerical methods is carried out for the 2-D case. Although in general the two methods compare favorably, significant differences are also found such that for application to actual observations it is prudent to employ the fully numerical method. Application of the methods developed in the present paper to actual geophysical problems will be given in a companion paper.

A low dimensional dynamical system for the wall layer

NASA Technical Reports Server (NTRS)

Aubry, N.; Keefe, L. R.

1987-01-01

Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging.

Electron transport near the Mott transition in n-GaAs and n-GaN

NASA Astrophysics Data System (ADS)

Romanets, P. N.; Sachenko, A. V.

2016-01-01

In this paper, we study the temperature dependence of the conductivity and the Hall coefficient near the metal-insulator phase transition. A theoretical investigation is performed within the effective mass approximation. The variational method is used to calculate the eigenvalues and eigenfunctions of the impurity states. Unlike previous studies, we have included nonlinear corrections to the screened impurity potential, because the Thomas-Fermi approximation is incorrect for the insulator phase. It is also shown that near the phase transition the exchange interaction is essential. The obtained temperature dependencies explain several experimental measurements in gallium arsenide (GaAs) and gallium nitride (GaN).

Systematic study of baryons in a three-body quark model

NASA Astrophysics Data System (ADS)

Aslanzadeh, M.; Rajabi, A. A.

2016-09-01

We investigated the structure of baryons within a three-body quark model based on hypercentral approach. We considered an SU(6)-invariant potential consisting of the well-known "Coulomb-plus-linear" potential plus some multipole interactions as V ( x) ∝ x - n with n > 2. Then, through an analytical solution, we obtained the energy eigenvalues and eigenfunctions of the three-body problem and evaluated some observables such as the mass spectrum of light baryons and both the electromagnetic elastic form factors, and the charge radii of nucleons. We compared our results with the experimental data and showed that the present model provides a good description of the observed resonances.

Dynamics of charged particles in a Paul radio-frequency quadrupole trap

NASA Technical Reports Server (NTRS)

Prestage, J. D.; Williams, A.; Maleki, L.; Djomehri, M. J.; Harabetian, E.

1991-01-01

A molecular-dynamics simulation of hundreds of ions confined in a Paul trap has been performed. The simulation includes the trapped particles' micromotion and interparticle Coulomb interactions. A random walk in velocity was implemented to bring the secular motion to a given temperature which was numerically measured. When the coupling Gamma is large the ions from concentric shells which undergo a quadrupole oscillation at the RF frequency, while the ions within a shell form a 2D hexagonal lattice. Ion clouds at 5 mK show no RF heating for q(z) less than about 0.6, whereas rapid heating is seen for qz = 0.8.

Laser ablated hydantoin: A high resolution rotational study.

PubMed

Alonso, Elena R; Kolesniková, Lucie; Alonso, José L

2017-09-28

Laser ablation techniques coupled with broadband and narrowband Fourier transform microwave spectroscopies have allowed the high resolution rotational study of solid hydantoin, an important target in astrochemistry as a possible precursor of glycine. The complicated hyperfine structure arising from the presence of two 14 N nuclei in non-equivalent positions has been resolved and interpreted in terms of the nuclear quadrupole coupling interactions. The results reported in this work provide a solid base for the interstellar searches of hydantoin in the astrophysical surveys. The values of the nuclear quadrupole coupling constants have been also discussed in terms of the electronic environment around the respective nitrogen atom.

Spectral transform and orthogonality relations for the Kadomtsev-Petviashvili I equation

NASA Astrophysics Data System (ADS)

Boiti, M.; Leon, J. J.-P.; Pempinelli, F.

1989-10-01

We define a new spectral transform r(k, l) of the potential u in the time dependent Schrödinger equation (associated to the KPI equation). Orthogonality relations for the sectionally holomorphic eigenfunctions of the Schrödinger equation are used to express the spectral transform f( k, l) previously introduced by Manakov and Fokas and Ablowitz in terms of r( k, l). The main advantage of the new spectral transform r( k, l) is that its definition does not require to introduce an additional nonanalytic eigenfunction N. Characterization equations for r( k, l) are also obtained.

The exact eigenfunctions and eigenvalues of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

NASA Technical Reports Server (NTRS)

Reimers, J. R.; Heller, E. J.

1985-01-01

Exact eigenfunctions for a two-dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eigenstates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a posteriori justification of the De Leon-Heller spectral quantization method.

Properties of natural frequencies and harmonic bending vibrations of a rod at one end of which is concentrated inertial load

NASA Astrophysics Data System (ADS)

Aliyev, Ziyatkhan S.; Guliyeva, Sevinc B.

2017-11-01

In this paper we consider a spectral problem that describes the bending vibrations of a homogeneous rod, in cross-sections of which the longitudinal force acts, the left end of which is fixed and on the right end an inertial mass is concentrated. We give a general characteristic of the location of the eigenvalues on the real axis, we study the structure of root spaces and oscillation properties of eigenfunctions, we investigate the basic properties in the space Lp, 1 < p < ∞, of the system of eigenfunctions of this problem.

Phase transition in 2-d system of quadrupoles on square lattice with anisotropic field

NASA Astrophysics Data System (ADS)

Sallabi, A. K.; Alkhttab, M.

2014-12-01

Monte Carlo method is used to study a simple model of two-dimensional interacting quadrupoles on ionic square lattice with anisotropic strength provided by the ionic lattice. Order parameter, susceptibility and correlation function data, show that this system form an ordered structure with p(2×1) symmetry at low temperature. The p(2×1) structure undergoes an order-disorder phase transition into disordered (1×1) phase at 8.3K. The two-point correlation function show exponential dependence on distance both above and below the transition temperature. At Tc the two-point correlation function shows a power law dependence on distance, e.g. C(r) ~ 1η. The value of the exponent η at Tc shows small deviation from the Ising value and indicates that this system falls into the same universality class as the XY model with cubic anisotropy. This model can be applied to prototypical quadrupoles physisorbed systems as N2 on NaCl(100).

Nuclear magnetic and nuclear quadrupole resonance parameters of β-carboline derivatives calculated using density functional theory

NASA Astrophysics Data System (ADS)

Ahmadinejad, Neda; Tari, Mostafa Talebi

2017-04-01

A density functional theory (DFT) calculations using B3LYP/6-311++G( d,p) method were carried out to investigate the relative stability of the molecules of β-carboline derivatives such as harmaline, harmine, harmalol, harmane and norharmane. Calculated nuclear quadrupole resonance (NQR) parameters were used to determine the 14N nuclear quadrupole coupling constant χ, asymmetry parameter η and EFG tensor ( q zz ). For better understanding of the electronic structure of β-carboline derivatives, natural bond orbital (NBO) analysis, isotropic and anisotropic NMR chemical shieldings were calculated for 14N nuclei using GIAO method for the optimized structures. The NBO analysis shows that pyrrole ring nitrogen (N9) atom has greater tendency than pyridine ring nitrogen (N2) atom to participate in resonance interactions and aromaticity development in the all of these structures. The NMR and NQR parameters were studied in order to find the correlations between electronic structure and the structural stability of the studied molecules.

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

Lackner, Friedrich; Ferracin, Paolo; Todesco, Ezio

The High luminosity LHC upgrade target is to increase the integrated luminosity by a factor 10, resulting in an integrated luminosity of 3000 fb-1. One major improvement foreseen is the reduction of the beam size at the collision points. This requires the development of 150 mm single aperture quadrupoles for the interaction regions. These quadrupoles are under development in a joint collaboration between CERN and the US-LHC Accelerator Research Program (LARP). The chosen approach for achieving a nominal quadrupole field gradient of 132.6 T/m is based on the Nb3Sn technology. The coils with a length of 7281 mm will bemore » the longest Nb3Sn coils fabricated so far for accelerator magnets. The production of the long coils was launched in 2016 based on practise coils made from copper. This paper provides a status of the production of the first low grade and full performance coils and describes the production process and applied quality control. Furthermore an outlook for the prototype assembly is provided.« less

Octupole deformations in high-K isomeric states of heavy and superheavy nuclei

NASA Astrophysics Data System (ADS)

Minkov, N.; Walker, P. M.

2016-01-01

We study the effects of quadrupole-octupole deformations on the energy and magnetic properties of high-K isomeric states in even-even heavy and superheavy nuclei. The neutron two-quasiparticle (2qp) isomeric energies and magnetic dipole moments are calculated within a deformed shell model with the Bardeen-Cooper- Schrieffer (BCS) pairing interaction over a wide range of quadrupole and octupole deformations. We found that in most cases the magnetic moments exhibit a pronounced sensitivity to the octupole deformation, while the 2qp energies indicate regions of nuclei in which the presence of high-K isomeric states may be associated with the presence of octupole softness or even with octupole deformation. In the present work we also examine the influence of the BCS pairing strength on the energy of the blocked isomer configuration. We show that the formation of 2qp energy minima in the space of quadrupole-octupole and eventually higher multipolarity deformations is a subtle effect depending on nuclear pairing correlations.

First determination of ground state electromagnetic moments of 53Fe

NASA Astrophysics Data System (ADS)

Miller, A. J.; Minamisono, K.; Rossi, D. M.; Beerwerth, R.; Brown, B. A.; Fritzsche, S.; Garand, D.; Klose, A.; Liu, Y.; Maaß, B.; Mantica, P. F.; Müller, P.; Nörtershäuser, W.; Pearson, M. R.; Sumithrarachchi, C.

2017-11-01

The hyperfine coupling constants of neutron deficient 53Fe were deduced from the atomic hyperfine spectrum of the 3 d64 s25D4↔3 d64 s 4 p 5F5 transition, measured using the bunched-beam collinear laser spectroscopy technique. The low-energy 53Fe beam was produced by projectile-fragmentation reactions followed by gas stopping, and used for the first time for laser spectroscopy. Ground state magnetic-dipole and electric-quadrupole moments were determined as μ =-0.65 (1 ) μN and Q =+35 (15 ) e2fm2 , respectively. The multiconfiguration Dirac-Fock method was used to calculate the electric field gradient to deduce Q from the quadrupole hyperfine coupling constant, since the quadrupole coupling constant has not been determined for any Fe isotopes. Both experimental values agree well with nuclear shell model calculations using the GXPF1A effective interaction performed in a full f p shell model space, which support the soft nature of the 56Ni nucleus.

Numerical simulation of NQR/NMR: Applications in quantum computing.

PubMed

Possa, Denimar; Gaudio, Anderson C; Freitas, Jair C C

2011-04-01

A numerical simulation program able to simulate nuclear quadrupole resonance (NQR) as well as nuclear magnetic resonance (NMR) experiments is presented, written using the Mathematica package, aiming especially applications in quantum computing. The program makes use of the interaction picture to compute the effect of the relevant nuclear spin interactions, without any assumption about the relative size of each interaction. This makes the program flexible and versatile, being useful in a wide range of experimental situations, going from NQR (at zero or under small applied magnetic field) to high-field NMR experiments. Some conditions specifically required for quantum computing applications are implemented in the program, such as the possibility of use of elliptically polarized radiofrequency and the inclusion of first- and second-order terms in the average Hamiltonian expansion. A number of examples dealing with simple NQR and quadrupole-perturbed NMR experiments are presented, along with the proposal of experiments to create quantum pseudopure states and logic gates using NQR. The program and the various application examples are freely available through the link http://www.profanderson.net/files/nmr_nqr.php. Copyright © 2011 Elsevier Inc. All rights reserved.

Isotropic–Nematic Phase Transitions in Gravitational Systems. II. Higher Order Multipoles

NASA Astrophysics Data System (ADS)

Takács, Ádám; Kocsis, Bence

2018-04-01

The gravitational interaction among bodies orbiting in a spherical potential leads to the rapid relaxation of the orbital planes’ distribution, a process called vector resonant relaxation. We examine the statistical equilibrium of this process for a system of bodies with similar semimajor axes and eccentricities. We extend the previous model of Roupas et al. by accounting for the multipole moments beyond the quadrupole, which dominate the interaction for radially overlapping orbits. Nevertheless, we find no qualitative differences between the behavior of the system with respect to the model restricted to the quadrupole interaction. The equilibrium distribution resembles a counterrotating disk at low temperature and a spherical structure at high temperature. The system exhibits a first-order phase transition between the disk and the spherical phase in the canonical ensemble if the total angular momentum is below a critical value. We find that the phase transition erases the high-order multipoles, i.e., small-scale structure in angular momentum space, most efficiently. The system admits a maximum entropy and a maximum energy, which lead to the existence of negative temperature equilibria.

UHB Engine Fan Broadband Noise Reduction Study

NASA Technical Reports Server (NTRS)

Gliebe, Philip R.; Ho, Patrick Y.; Mani, Ramani

1995-01-01

A study has been completed to quantify the contribution of fan broadband noise to advanced high bypass turbofan engine system noise levels. The result suggests that reducing fan broadband noise can produce 3 to 4 EPNdB in engine system noise reduction, once the fan tones are eliminated. Further, in conjunction with the elimination of fan tones and an increase in bypass ratio, a potential reduction of 7 to 10 EPNdB in system noise can be achieved. In addition, an initial assessment of engine broadband noise source mechanisms has been made, concluding that the dominant source of fan broadband noise is the interaction of incident inlet boundary layer turbulence with the fan rotor. This source has two contributors, i.e., unsteady life dipole response and steady loading quadrupole response. The quadrupole contribution was found to be the most important component, suggesting that broadband noise reduction can be achieved by the reduction of steady loading field-turbulence field quadrupole interaction. Finally, for a controlled experimental quantification and verification, the study recommends that further broadband noise tests be done on a simulated engine rig, such as the GE Aircraft Engine Universal Propulsion Simulator, rather than testing on an engine statically in an outdoor arena The rig should be capable of generating forward and aft propagating fan noise, and it needs to be tested in a large freejet or a wind tunnel.

Radiation drag in the field of a non-spherical source

NASA Astrophysics Data System (ADS)

Bini, D.; Geralico, A.; Passamonti, A.

2015-01-01

The motion of a test particle in the gravitational field of a non-spherical source endowed with both mass and mass quadrupole moment is investigated when a test radiation field is also present. The background is described by the Erez-Rosen solution, which is a static space-time belonging to the Weyl class of solutions to the vacuum Einstein's field equations, and reduces to the familiar Schwarzschild solution when the quadrupole parameter vanishes. The radiation flux has a fixed but arbitrary (non-zero) angular momentum. The interaction with the radiation field is assumed to be Thomson-like, i.e. the particles absorb and re-emit radiation, thus suffering for a friction-like drag force. Such an additional force is responsible for the Poynting-Robertson effect, which is well established in the framework of Newtonian gravity and has been recently extended to the general theory of relativity. The balance between gravitational attraction, centrifugal force and radiation drag leads to the occurrence of equilibrium circular orbits which are attractors for the surrounding matter for every fixed value of the interaction strength. The presence of the quadrupolar structure of the source introduces a further degree of freedom: there exists a whole family of equilibrium orbits parametrized by the quadrupole parameter, generalizing previous works. This scenario is expected to play a role in the context of accretion matter around compact objects.

UHB engine fan broadband noise reduction study

NASA Astrophysics Data System (ADS)

Gliebe, Philip R.; Ho, Patrick Y.; Mani, Ramani

1995-06-01

A study has been completed to quantify the contribution of fan broadband noise to advanced high bypass turbofan engine system noise levels. The result suggests that reducing fan broadband noise can produce 3 to 4 EPNdB in engine system noise reduction, once the fan tones are eliminated. Further, in conjunction with the elimination of fan tones and an increase in bypass ratio, a potential reduction of 7 to 10 EPNdB in system noise can be achieved. In addition, an initial assessment of engine broadband noise source mechanisms has been made, concluding that the dominant source of fan broadband noise is the interaction of incident inlet boundary layer turbulence with the fan rotor. This source has two contributors, i.e., unsteady life dipole response and steady loading quadrupole response. The quadrupole contribution was found to be the most important component, suggesting that broadband noise reduction can be achieved by the reduction of steady loading field-turbulence field quadrupole interaction. Finally, for a controlled experimental quantification and verification, the study recommends that further broadband noise tests be done on a simulated engine rig, such as the GE Aircraft Engine Universal Propulsion Simulator, rather than testing on an engine statically in an outdoor arena The rig should be capable of generating forward and aft propagating fan noise, and it needs to be tested in a large freejet or a wind tunnel.

Two charges on plane in a magnetic field I. “Quasi-equal” charges and neutral quantum system at rest cases

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

Escobar-Ruiz, M.A., E-mail: mauricio.escobar@nucleares.unam.mx; Turbiner, A.V., E-mail: turbiner@nucleares.unam.mx

Low-lying bound states for the problem of two Coulomb charges of finite masses on a plane subject to a constant magnetic field B perpendicular to the plane are considered. Major emphasis is given to two systems: two charges with the equal charge-to-mass ratio (quasi-equal charges) and neutral systems with concrete results for the hydrogen atom and two electrons (quantum dot). It is shown that for these two cases, when a neutral system is at rest (the center-of-mass momentum is zero), some outstanding properties occur: in double polar coordinates in CMS (R,ϕ) and relative (ρ,φ) coordinate systems (i) the eigenfunctions aremore » factorizable, all factors except for ρ-dependent are found analytically, they have definite relative angular momentum, (ii) dynamics in ρ-direction is the same for both systems being described by a funnel-type potential; (iii) at some discrete values of dimensionless magnetic fields b≤1 the system becomes quasi-exactly-solvable and a finite number of eigenfunctions in ρ are polynomials. The variational method is employed. Trial functions are based on combining for the phase of a wavefunction (a) the WKB expansion at large distances, (b) the perturbation theory at small distances (c) with a form of the known analytically (quasi-exactly-solvable) eigenfunctions. Such a form of trial function appears as a compact uniform approximation for lowest eigenfunctions. For the lowest states with relative magnetic quantum numbers s=0,1,2 this approximation gives not less than 7 s.d., 8 s.d., 9 s.d., respectively, for the total energy E(B) for magnetic fields 0.049a.u.« less

On the Aharonov-Bohm Operators with Varying Poles: The Boundary Behavior of Eigenvalues

NASA Astrophysics Data System (ADS)

Noris, Benedetta; Nys, Manon; Terracini, Susanna

2015-11-01

We consider a magnetic Schrödinger operator with magnetic field concentrated at one point (the pole) of a domain and half integer circulation, and we focus on the behavior of Dirichlet eigenvalues as functions of the pole. Although the magnetic field vanishes almost everywhere, it is well known that it affects the operator at the spectral level (the Aharonov-Bohm effect, Phys Rev (2) 115:485-491, 1959). Moreover, the numerical computations performed in (Bonnaillie-Noël et al., Anal PDE 7(6):1365-1395, 2014; Noris and Terracini, Indiana Univ Math J 59(4):1361-1403, 2010) show a rather complex behavior of the eigenvalues as the pole varies in a planar domain. In this paper, in continuation of the analysis started in (Bonnaillie-Noël et al., Anal PDE 7(6):1365-1395, 2014; Noris and Terracini, Indiana Univ Math J 59(4):1361-1403, 2010), we analyze the relation between the variation of the eigenvalue and the nodal structure of the associated eigenfunctions. We deal with planar domains with Dirichlet boundary conditions and we focus on the case when the singular pole approaches the boundary of the domain: then, the operator loses its singular character and the k-th magnetic eigenvalue converges to that of the standard Laplacian. We can predict both the rate of convergence and whether the convergence happens from above or from below, in relation with the number of nodal lines of the k-th eigenfunction of the Laplacian. The proof relies on the variational characterization of eigenvalues, together with a detailed asymptotic analysis of the eigenfunctions, based on an Almgren-type frequency formula for magnetic eigenfunctions and on the blow-up technique.

Numerical Aspects of Eigenvalue and Eigenfunction Computations for Chaotic Quantum Systems

NASA Astrophysics Data System (ADS)

Bäcker, A.

Summary: We give an introduction to some of the numerical aspects in quantum chaos. The classical dynamics of two-dimensional area-preserving maps on the torus is illustrated using the standard map and a perturbed cat map. The quantization of area-preserving maps given by their generating function is discussed and for the computation of the eigenvalues a computer program in Python is presented. We illustrate the eigenvalue distribution for two types of perturbed cat maps, one leading to COE and the other to CUE statistics. For the eigenfunctions of quantum maps we study the distribution of the eigenvectors and compare them with the corresponding random matrix distributions. The Husimi representation allows for a direct comparison of the localization of the eigenstates in phase space with the corresponding classical structures. Examples for a perturbed cat map and the standard map with different parameters are shown. Billiard systems and the corresponding quantum billiards are another important class of systems (which are also relevant to applications, for example in mesoscopic physics). We provide a detailed exposition of the boundary integral method, which is one important method to determine the eigenvalues and eigenfunctions of the Helmholtz equation. We discuss several methods to determine the eigenvalues from the Fredholm equation and illustrate them for the stadium billiard. The occurrence of spurious solutions is discussed in detail and illustrated for the circular billiard, the stadium billiard, and the annular sector billiard. We emphasize the role of the normal derivative function to compute the normalization of eigenfunctions, momentum representations or autocorrelation functions in a very efficient and direct way. Some examples for these quantities are given and discussed.

On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator

NASA Astrophysics Data System (ADS)

Korda, Milan; Mezić, Igor

2018-04-01

Extended dynamic mode decomposition (EDMD) (Williams et al. in J Nonlinear Sci 25(6):1307-1346, 2015) is an algorithm that approximates the action of the Koopman operator on an N-dimensional subspace of the space of observables by sampling at M points in the state space. Assuming that the samples are drawn either independently or ergodically from some measure μ , it was shown in Klus et al. (J Comput Dyn 3(1):51-79, 2016) that, in the limit as M→ ∞, the EDMD operator K_{N,M} converges to K_N, where K_N is the L_2(μ )-orthogonal projection of the action of the Koopman operator on the finite-dimensional subspace of observables. We show that, as N → ∞, the operator K_N converges in the strong operator topology to the Koopman operator. This in particular implies convergence of the predictions of future values of a given observable over any finite time horizon, a fact important for practical applications such as forecasting, estimation and control. In addition, we show that accumulation points of the spectra of K_N correspond to the eigenvalues of the Koopman operator with the associated eigenfunctions converging weakly to an eigenfunction of the Koopman operator, provided that the weak limit of the eigenfunctions is nonzero. As a by-product, we propose an analytic version of the EDMD algorithm which, under some assumptions, allows one to construct K_N directly, without the use of sampling. Finally, under additional assumptions, we analyze convergence of K_{N,N} (i.e., M=N), proving convergence, along a subsequence, to weak eigenfunctions (or eigendistributions) related to the eigenmeasures of the Perron-Frobenius operator. No assumptions on the observables belonging to a finite-dimensional invariant subspace of the Koopman operator are required throughout.

Corrections to atomic ground state energy due to interaction between atomic electric quadrupole and optical field

NASA Astrophysics Data System (ADS)

Hu, Jie; Chen, Yu; Bai, Yi-Xiu; He, Pei-Song; Sun, Qing; Ji, An-Chun

2018-04-01

Not Available Project supported by the National Natural Science Foundation of China (Grant Nos. 21503138, 11247324, 61405003, 11604225, 11404225, and 11474205) and the Fund from Beijing Education Committees, China (Grant No. KM201710028004).

Similarity-transformed perturbation theory on top of truncated local coupled cluster solutions: Theory and applications to intermolecular interactions

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

Azar, Richard Julian, E-mail: julianazar2323@berkeley.edu; Head-Gordon, Martin, E-mail: mhg@cchem.berkeley.edu

2015-05-28

Your correspondents develop and apply fully nonorthogonal, local-reference perturbation theories describing non-covalent interactions. Our formulations are based on a Löwdin partitioning of the similarity-transformed Hamiltonian into a zeroth-order intramonomer piece (taking local CCSD solutions as its zeroth-order eigenfunction) plus a first-order piece coupling the fragments. If considerations are limited to a single molecule, the proposed intermolecular similarity-transformed perturbation theory represents a frozen-orbital variant of the “(2)”-type theories shown to be competitive with CCSD(T) and of similar cost if all terms are retained. Different restrictions on the zeroth- and first-order amplitudes are explored in the context of large-computation tractability and elucidationmore » of non-local effects in the space of singles and doubles. To accurately approximate CCSD intermolecular interaction energies, a quadratically growing number of variables must be included at zeroth-order.« less

Mössbauer study of Brazilian soapstone

NASA Astrophysics Data System (ADS)

Gonçalves, M. A.; de Jesus Filho, M. F.; Garg, V. K.

1991-11-01

Steatite mineral rocks, soapstone, have been studied by X-ray diffraction, optical microscopic analysis (modal analysis), electron probe micro analysis and Mössbauer spectroscopy for characterization, mineral percentages and chemical composition. Mössbauer spectra show both, magnetic interactions corresponding to magnetite and doublets corresponding to talc. chlorite, dolomite and tremolite. The temperature dependence of the quadrupole splitting in dolomite has been explained in terms of crystal field interaction.

Propagation-invariant beams with quantum pendulum spectra: from Bessel beams to Gaussian beam-beams.

PubMed

Dennis, Mark R; Ring, James D

2013-09-01

We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly periodic Mathieu functions in azimuth, depend on a field strength parameter. When the parameter is zero, pendulum beams are Bessel beams, and as the parameter approaches infinity, they resemble transversely propagating one-dimensional Gaussian wave packets (Gaussian beam-beams). Pendulum beams are the eigenfunctions of an operator that interpolates between the squared angular momentum operator and the linear momentum operator. The analysis reveals connections with Mathieu beams, and insight into the paraxial approximation.

On the basis property of the system of eigenfunctions and associated functions of a one-dimensional Dirac operator

NASA Astrophysics Data System (ADS)

Savchuk, A. M.

2018-04-01

We study a one-dimensional Dirac system on a finite interval. The potential (a 2× 2 matrix) is assumed to be complex- valued and integrable. The boundary conditions are assumed to be regular in the sense of Birkhoff. It is known that such an operator has a discrete spectrum and the system \\{\\mathbf{y}_n\\}_1^∞ of its eigenfunctions and associated functions is a Riesz basis (possibly with brackets) in L_2\\oplus L_2. Our results concern the basis property of this system in the spaces L_μ\\oplus L_μ for μ\

A new approach to the Schrödinger equation with rational potentials

NASA Astrophysics Data System (ADS)

Dong, Ming-de; Chu, Jue-Hui

1984-04-01

A new analytic theory is established for the Schrödinger equation with a rational potential, including a complete classification of the regular eigenfunctions into three different types, an exact method of obtaining wavefunctions, an explicit formulation of the spectral equation (3 x 3 determinant) etc. All representations are exhibited in a unifying way via function-theoretic methods and therefore given in explicit form, in contrast to the prevailing discussion appealing to perturbation or variation methods or continued-fraction techniques. The irregular eigenfunctions at infinity can be obtained analogously and will be discussed separately as another solvable case for singular potentials.

Comment on "Calculations for the one-dimensional soft Coulomb problem and the hard Coulomb limit".

PubMed

Carrillo-Bernal, M A; Núñez-Yépez, H N; Salas-Brito, A L; Solis, Didier A

2015-02-01

In the referred paper, the authors use a numerical method for solving ordinary differential equations and a softened Coulomb potential -1/√[x(2)+β(2)] to study the one-dimensional Coulomb problem by approaching the parameter β to zero. We note that even though their numerical findings in the soft potential scenario are correct, their conclusions do not extend to the one-dimensional Coulomb problem (β=0). Their claims regarding the possible existence of an even ground state with energy -∞ with a Dirac-δ eigenfunction and of well-defined parity eigenfunctions in the one-dimensional hydrogen atom are questioned.

Quadratic Forms and Semiclassical Eigenfunction Hypothesis for Flat Tori

NASA Astrophysics Data System (ADS)

T. Sardari, Naser

2018-03-01

Let Q( X) be any integral primitive positive definite quadratic form in k variables, where {k≥4}, and discriminant D. For any integer n, we give an upper bound on the number of integral solutions of Q( X) = n in terms of n, k, and D. As a corollary, we prove a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given eigenspace of the Laplacian on the flat torus {T^d} for {d≥ 5}. This conjecture is motivated by the work of Berry [2,3] on the semiclassical eigenfunction hypothesis.

Expressive body movement responses to music are coherent, consistent, and low dimensional.

PubMed

Amelynck, Denis; Maes, Pieter-Jan; Martens, Jean Pierre; Leman, Marc

2014-12-01

Embodied music cognition stresses the role of the human body as mediator for the encoding and decoding of musical expression. In this paper, we set up a low dimensional functional model that accounts for 70% of the variability in the expressive body movement responses to music. With the functional principal component analysis, we modeled individual body movements as a linear combination of a group average and a number of eigenfunctions. The group average and the eigenfunctions are common to all subjects and make up what we call the commonalities. An individual performance is then characterized by a set of scores (the individualities), one score per eigenfunction. The model is based on experimental data which finds high levels of coherence/consistency between participants when grouped according to musical education. This shows an ontogenetic effect. Participants without formal musical education focus on the torso for the expression of basic musical structure (tempo). Musically trained participants decode additional structural elements in the music and focus on body parts having more degrees of freedom (such as the hands). Our results confirm earlier studies that different body parts move differently along with the music.

An eigenfunction method for reconstruction of large-scale and high-contrast objects.

PubMed

Waag, Robert C; Lin, Feng; Varslot, Trond K; Astheimer, Jeffrey P

2007-07-01

A multiple-frequency inverse scattering method that uses eigenfunctions of a scattering operator is extended to image large-scale and high-contrast objects. The extension uses an estimate of the scattering object to form the difference between the scattering by the object and the scattering by the estimate of the object. The scattering potential defined by this difference is expanded in a basis of products of acoustic fields. These fields are defined by eigenfunctions of the scattering operator associated with the estimate. In the case of scattering objects for which the estimate is radial, symmetries in the expressions used to reconstruct the scattering potential greatly reduce the amount of computation. The range of parameters over which the reconstruction method works well is illustrated using calculated scattering by different objects. The method is applied to experimental data from a 48-mm diameter scattering object with tissue-like properties. The image reconstructed from measurements has, relative to a conventional B-scan formed using a low f-number at the same center frequency, significantly higher resolution and less speckle, implying that small, high-contrast structures can be demonstrated clearly using the extended method.

Isolated rotor noise due to inlet distortion or turbulence

NASA Technical Reports Server (NTRS)

Mani, R.

1974-01-01

Theoretical formulation, analysis, and results are presented that are necessary to analyze quadrupole noise generated from a loaded, subsonic rotor because of its interaction with an inflow distortion or inlet turbulence. The ratio of quadrupole to dipole noise is largely a function of the axial Mach number, wheel tip Mach number, rotor solidity, and total pressure ratio across the rotor. It is relatively independent of the specific form of the inflow distortion or inlet turbulence. Comparisons with experimental data only succeed in predicting gross levels at a given speed and fail to predict the variation of noise at fixed speed with flow and pressure ratio. Likely sources of this discrepancy are discussed.

Covariant spectator theory of np scattering: Deuteron quadrupole moment

DOE PAGES

Gross, Franz

2015-01-26

The deuteron quadrupole moment is calculated using two CST model wave functions obtained from the 2007 high precision fits to np scattering data. Included in the calculation are a new class of isoscalar np interaction currents automatically generated by the nuclear force model used in these fits. The prediction for model WJC-1, with larger relativistic P-state components, is 2.5% smaller that the experiential result, in common with the inability of models prior to 2014 to predict this important quantity. However, model WJC-2, with very small P-state components, gives agreement to better than 1%, similar to the results obtained recently frommore » XEFT predictions to order N 3LO.« less

Decoupling correction system in RHIC

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

Trbojevic, D.; Tepikian, S.; Peggs, S.

A global linear decoupling in the Relativistic Heavy Ion Collider (RHIC) is going to be performed with the three families of skew quadrupoles. The operating horizontal and vertical betatron tunes in the RHIC will be separated by one unit [nu][sub x]=28.19 and [nu][sub y]=29.18. The linear coupling is corrected by minimizing the tune splitting [Delta][nu]-the off diagonal matrix [bold m] (defined by Edwards and Teng). The skew quadrupole correction system is located close to each of the six interaction regions. A detail study of the system is presented by the use of the TEAPOT accelerator physics code. [copyright] 1994 Americanmore » Institute of Physics« less

Diverse wave-particle interactions for energetic ions that traverse Alfvén eigenmodes on their first full orbit [Diverse nonlinear wave-particle interactions for energetic ions that traverse Alfvén eigenmodes on their first full orbit

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

Heidbrink, W. W.; Persico, E. A. D.; Austin, M. E.

2016-02-09

Here, neutral-beam ions that are deflected onto loss orbits by Alfvén eigenmodes (AE) on their first bounce orbit and are detected by a fast-ion loss detector (FILD) satisfy the “local resonance” condition. This theory qualitatively explains FILD observations for a wide variety of AE-particle interactions. When coherent losses are measured for multiple AE, oscillations at the sum and difference frequencies of the independent modes are often observed. The amplitudes of the sum and difference peaks correlate with the amplitudes of the fundamental loss-signal amplitudes but do not correlate with the measured mode amplitudes. In contrast to a simple uniform-plasma theorymore » of the interaction, the loss-signal amplitude at the sum frequency is often larger than the loss-signal amplitude at the difference frequency, indicating a more detailed computation of the orbital trajectories through the mode eigenfunctions is needed.« less

STM imaging ortho- and para-fluorothiophenol self-assembled monolayers on Au(111).

PubMed

Jiang, Peng; Deng, Ke; Fichou, Denis; Xie, Si-Shen; Nion, Aymeric; Wang, Chen

2009-05-05

Self-assembled monolayers (SAMs) of para- and ortho-fluorothiophenol (p- and o-FTP) spontaneously formed on Au(111) substrate have been contrasted through investigation by a scanning tunneling microscope (STM) at room temperature. High-resolution STM imaging reveals that p-FTP adopts a 6 x radical3R30 degrees molecule arrangement containing six molecules. Two different kinds of p-FTP molecule dimer line structures have been formed on Au(111) by intermolecular pi-pi stacking along 112 substrate directions, besides a single p-FTP molecule line. In contrast, o-FTP molecules self-assemble into a much looser wave-like SAM, which can be described as a 5 x 3 radical3R30 degrees structure containing two molecules. Periodic density functional theory (DFT) calculations for the two systems suggest that these kinds of FTP molecules preferentially take the asymmetrical positions between 3-fold face-centered cubic (fcc) hollow and bridge sites on Au(111), tilting from the substrate surface. Theoretical simulation gives apparent average tilted angles of 58 degrees and 68 degrees for p-FTP and o-FTP with respect to the surface normal, respectively. This simulation shows that o-FTP is more inclined to lie down toward the Au(111) surface compared to p-FTP. The difference between p-FTP and o-FTP SAM structures can be qualitatively understood in terms of the variation of intermolecular dipole-dipole orientation. This suggests that, besides well-known Au-S and pi-pi interactions, electrostatic interactions including dipole-dipole, quadrupole-quadrupole, and dipole-quadrupole interactions might also play an important role in influencing the SAM structures formed by aromatic thiols with a permanent dipole moment.

Measurement of the orientation of buffer-gas-cooled, electrostatically-guided ammonia molecules

NASA Astrophysics Data System (ADS)

Steer, Edward W.; Petralia, Lorenzo S.; Western, Colin M.; Heazlewood, Brianna R.; Softley, Timothy P.

2017-02-01

The extent to which the spatial orientation of internally and translationally cold ammonia molecules can be controlled as molecules pass out of a quadrupole guide and through different electric field regions is examined. Ammonia molecules are collisionally cooled in a buffer gas cell, and are subsequently guided by a three-bend electrostatic quadrupole into a detection chamber. The orientation of ammonia molecules is probed using (2 + 1) resonance-enhanced multiphoton ionisation (REMPI), with the laser polarisation axis aligned both parallel and perpendicular to the time-of-flight axis. Even with the presence of a near-zero field region, the ammonia REMPI spectra indicate some retention of orientation. Monte Carlo simulations propagating the time-dependent Schrödinger equation in a full basis set including the hyperfine interaction enable the orientation of ammonia molecules to be calculated - with respect to both the local field direction and a space-fixed axis - as the molecules pass through different electric field regions. The simulations indicate that the orientation of ∼95% of ammonia molecules in JK =11 could be achieved with the application of a small bias voltage (17 V) to the mesh separating the quadrupole and detection regions. Following the recent combination of the buffer gas cell and quadrupole guide apparatus with a linear Paul ion trap, this result could enable one to examine the influence of molecular orientation on ion-molecule reaction dynamics and kinetics.

Molecular near-field antenna effect in resonance hyper-Raman scattering: Intermolecular vibronic intensity borrowing of solvent from solute through dipole-dipole and dipole-quadrupole interactions

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

Shimada, Rintaro; Hamaguchi, Hiro-o, E-mail: hhama@nctu.edu.tw

2014-05-28

We quantitatively interpret the recently discovered intriguing phenomenon related to resonance Hyper-Raman (HR) scattering. In resonance HR spectra of all-trans-β-carotene (β-carotene) in solution, vibrations of proximate solvent molecules are observed concomitantly with the solute β-carotene HR bands. It has been shown that these solvent bands are subject to marked intensity enhancements by more than 5 orders of magnitude under the presence of β-carotene. We have called this phenomenon the molecular-near field effect. Resonance HR spectra of β-carotene in benzene, deuterated benzene, cyclohexane, and deuterated cyclohexane have been measured precisely for a quantitative analysis of this effect. The assignments of themore » observed peaks are made by referring to the infrared, Raman, and HR spectra of neat solvents. It has been revealed that infrared active and some Raman active vibrations are active in the HR molecular near-field effect. The observed spectra in the form of difference spectra (between benzene/deuterated benzene and cyclohexane/deuterated cyclohexane) are quantitatively analyzed on the basis of the extended vibronic theory of resonance HR scattering. The theory incorporates the coupling of excited electronic states of β-carotene with the vibrations of a proximate solvent molecule through solute–solvent dipole–dipole and dipole–quadrupole interactions. It is shown that the infrared active modes arise from the dipole–dipole interaction, whereas Raman active modes from the dipole–quadrupole interaction. It is also shown that vibrations that give strongly polarized Raman bands are weak in the HR molecular near-field effect. The observed solvent HR spectra are simulated with the help of quantum chemical calculations for various orientations and distances of a solvent molecule with respect to the solute. The observed spectra are best simulated with random orientations of the solvent molecule at an intermolecular distance of 10 Å.« less

A Study of the Momentum Distributions of the Final State Hadrons in Neutrino - Nucleus Interactions

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

Swider, Gregory M.

1980-12-01

In an experiment using the Fermilab 15-foot Bubble Chamber/Two-Plane EMI with a 47 percent (atomic) neon-in-hydrogen fill exposed to the quadrupole-triplet neutrino beam, we have identified some 9600 neutrino charged-current events....

Control of systematic uncertainties in the storage ring search for an electric dipole moment by measuring the electric quadrupole moment

NASA Astrophysics Data System (ADS)

Magiera, Andrzej

2017-09-01

Measurements of electric dipole moment (EDM) for light hadrons with use of a storage ring have been proposed. The expected effect is very small, therefore various subtle effects need to be considered. In particular, interaction of particle's magnetic dipole moment and electric quadrupole moment with electromagnetic field gradients can produce an effect of a similar order of magnitude as that expected for EDM. This paper describes a very promising method employing an rf Wien filter, allowing to disentangle that contribution from the genuine EDM effect. It is shown that both these effects could be separated by the proper setting of the rf Wien filter frequency and phase. In the EDM measurement the magnitude of systematic uncertainties plays a key role and they should be under strict control. It is shown that particles' interaction with field gradients offers also the possibility to estimate global systematic uncertainties with the precision necessary for an EDM measurement with the planned accuracy.

Influence of the electron density on the characteristics of terahertz waves generated under laser–cluster interaction

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

Frolov, A. A., E-mail: frolov@ihed.ras.ru

2016-12-15

A theory of generation of terahertz radiation under laser–cluster interaction, developed earlier for an overdense cluster plasma [A. A. Frolov, Plasma Phys. Rep. 42. 637 (2016)], is generalized for the case of arbitrary electron density. The spectral composition of radiation is shown to substantially depend on the density of free electrons in the cluster. For an underdense cluster plasma, there is a sharp peak in the terahertz spectrum at the frequency of the quadrupole mode of a plasma sphere. As the electron density increases to supercritical values, this spectral line vanishes and a broad maximum at the frequency comparable withmore » the reciprocal of the laser pulse duration appears in the spectrum. The dependence of the total energy of terahertz radiation on the density of free electrons is analyzed. The radiation yield is shown to increase significantly under resonance conditions, when the laser frequency is close to the eigenfrequency of the dipole or quadrupole mode of a plasma sphere.« less

Rapid Quantification of Four Anthocyanins in Red Grape Wine by Hydrophilic Interaction Liquid Chromatography/Triple Quadrupole Linear Ion Trap Mass Spectrometry.

PubMed

Sun, Yongming; Xia, Biqi; Chen, Xiangzhun; Duanmu, Chuansong; Li, Denghao; Han, Chao

2015-01-01

The identification and quantification of four anthocyanins (cyanidin-3-O-glucoside, peonidin-3-O-glucoside, delphinidin-3-O-glucoside, and malvidin-3-O-glucoside) in red grape wine were carried out by hydrophilic interaction liquid chromatography/triple quadrupole linear ion trap MS (HILIC/QTrap-MS/MS). Samples were diluted directly and separated on a Merck ZIC HILIC column with 20 mM ammonium acetate solution-acetonitrile mobile phase. Quantitative data acquisition was carried out in the multiple reaction monitoring mode. Additional identification and confirmation of target compounds were performed using the enhanced product ion mode of the linear ion trap. The LOQs were in the range 0.05-1.0 ng/mL. The average recoveries were in the range 94.6 to 104.5%. The HILIC/QTrap-MS/MS platform offers the best sensitivity and specificity for characterization and quantitative determination of the four anthocyanins in red grape wines and fulfills the quality criteria for routine laboratory application.

Superfluid quenching of the moment of inertia in a strongly interacting Fermi gas

NASA Astrophysics Data System (ADS)

Riedl, S.; Sánchez Guajardo, E. R.; Kohstall, C.; Hecker Denschlag, J.; Grimm, R.

2011-03-01

We report on the observation of a quenched moment of inertia resulting from superfluidity in a strongly interacting Fermi gas. Our method is based on setting the hydrodynamic gas in slow rotation and determining its angular momentum by detecting the precession of a radial quadrupole excitation. The measurements distinguish between the superfluid and collisional origins of hydrodynamic behavior, and show the phase transition.

The Distribution of Galaxies’ Gravitational Field Stemming from Their Tidal Interaction

NASA Astrophysics Data System (ADS)

Stephanovich, Vladimir; Godłowski, Włodzimierz

2015-09-01

We calculate the distribution function of astronomical objects’ (like galaxies and/or smooth halos of different kinds) gravitational fields due to their tidal interaction. For that we apply the statistical method of Chandrasekhar, used originally to calculate the famous Holtzmark distribution. We show that in our approach the distribution function is never Gaussian, its form being dictated by the potential of interaction between objects. This calculation permits us to perform a theoretical analysis of the relation between angular momentum and mass (richness) of the galaxy clusters. To do so, we follow the ideas of Catelan & Theuns and Heavens & Peacock. The main difference is that here we reduce the problem to a discrete many-body case, where all physical properties of the system are determined by the interaction potential V({{\\boldsymbol{r}}}{ij}). The essence of reduction is that we use the multipole (up to quadrupole here) expansion of Newtonian potential so that all hydrodynamic, “extended” characteristics of an object, such as its density mass, are “integrated out,” leaving its “point-like” characteristics, such as mass and quadrupole moment. In that sense we do not distinguish between galaxies and smooth components such as halos. We compare our theoretical results with observational data.

Theoretical study of the hyperfine-interaction constants and the isotope-shift factors for the 3 s21S0-3 s 3 p 3,1P1o transitions in Al+

NASA Astrophysics Data System (ADS)

Zhang, Tingxian; Xie, Luyou; Li, Jiguang; Lu, Zehuang

2017-07-01

We calculated the magnetic dipole and the electric quadrupole hyperfine interaction constants of 3 s 3 p 3,1P1o states and the isotope shift, including mass and field shift, factors for transitions from these two states to the ground state 3 s 2 1S0 in Al+ ions using the multiconfiguration Dirac-Hartree-Fock method. The effects of the electron correlations and the Breit interaction on these physical quantities were investigated in detail based on the active space approach. It is found that the core-core and the higher order correlations are considerable for evaluating the uncertainties of the atomic parameters concerned. The uncertainties of the hyperfine interaction constants in this work are less than 1.6%. Although the isotope shift factors are highly sensitive to the electron correlations, reasonable uncertainties were obtained by exploring the effects of the electron correlations. Moreover, we found that the relativistic nuclear recoil corrections to the mass shift factors are very small and insensitive to the electron correlations for Al+. These atomic parameters present in this work are valuable for extracting the nuclear electric quadrupole moments and the mean-square charge radii of Al isotopes.

Piriformospora indica Stimulates Root Metabolism of Arabidopsis thaliana.

PubMed

Strehmel, Nadine; Mönchgesang, Susann; Herklotz, Siska; Krüger, Sylvia; Ziegler, Jörg; Scheel, Dierk

2016-07-08

Piriformospora indica is a root-colonizing fungus, which interacts with a variety of plants including Arabidopsis thaliana. This interaction has been considered as mutualistic leading to growth promotion of the host. So far, only indolic glucosinolates and phytohormones have been identified as key players. In a comprehensive non-targeted metabolite profiling study, we analyzed Arabidopsis thaliana's roots, root exudates, and leaves of inoculated and non-inoculated plants by ultra performance liquid chromatography/electrospray ionization quadrupole-time-of-flight mass spectrometry (UPLC/(ESI)-QTOFMS) and gas chromatography/electron ionization quadrupole mass spectrometry (GC/EI-QMS), and identified further biomarkers. Among them, the concentration of nucleosides, dipeptides, oligolignols, and glucosinolate degradation products was affected in the exudates. In the root profiles, nearly all metabolite levels increased upon co-cultivation, like carbohydrates, organic acids, amino acids, glucosinolates, oligolignols, and flavonoids. In the leaf profiles, we detected by far less significant changes. We only observed an increased concentration of organic acids, carbohydrates, ascorbate, glucosinolates and hydroxycinnamic acids, and a decreased concentration of nitrogen-rich amino acids in inoculated plants. These findings contribute to the understanding of symbiotic interactions between plant roots and fungi of the order of Sebacinales and are a valid source for follow-up mechanistic studies, because these symbioses are particular and clearly different from interactions of roots with mycorrhizal fungi or dark septate endophytes.

Detection of Quadrupole Interactions by Muon Level Crossing Resonance

NASA Astrophysics Data System (ADS)

Cox, S. F. J.

1992-02-01

The positive muon proves to be a very versatile and sensitive magnetic resonance probe: implanted in virtually any material its polarisation may be monitored via the asymmetry in its radioactive decay, giving information on the sites occupied by the muon in lattices or molecules, and the local fields experienced at these sites. The scope of these experiments has been greatly extended by the development of a technique of cross relaxation or level crossing resonance which allows quadrupole splittings on nuclei adjacent to the muon to be measured. The principles of the technique and the conditions necessary for detection of the spectra are described, together with a number of applications. Of especial interest is the manner in which muons mimic the behaviour of protons in matter. In metal lattices, for instance, muons invariably adopt the same interstitial sites as do protons in the dilute hydride phases, so that they can be used to study problems of localisation and diffusion common to those of hydrogen in metals. Studies of the muon level crossing resonance in copper have given valuable information on the crystallographic site, electronic structure and low temperature mobility of the interstitial defect. In semiconductors, muons are expected to trap at other impurities - notably acceptors - in processes analogous to the passivation of dopants by hydrogen. Muon resonance offers the exciting prospect of spectroscopic study of these passivation complexes. In molecular materials, substitution of protons by muons can be thought of rather like deuteration. Muons implanted in ice produce a significant change in the quadrupole coupling constant of adjacent 17O nuclei which may be traced to the effects of the large muon zero point energy; the resonance spectrum also exhibits temperature dependent features which may be informative on the nature and lifetime of defects in the ice structure. Muon level crossing resonance has already been studied in an oxide superconductor and this relatively young field is now wide open for quadrupole interaction studies in other materials, using a variety of nuclei.

Atomistic simulations of CO2 and N2 within cage-type silica zeolites.

PubMed

Madison, Lindsey; Heitzer, Henry; Russell, Colin; Kohen, Daniela

2011-03-01

The behavior of CO(2) and N(2), both as single components and as binary mixtures, in two cage-type silica zeolites was studied using atomistic simulations. The zeolites considered, ITQ-3 and paradigm cage-type zeolite ZK4 (the all-silica analog of LTA), were chosen so that the principles illustrated can be generalized to other adsorbent/adsorbate systems with similar topology and types of interactions. N(2) was chosen both because of the potential uses of N(2)/CO(2) separations and because it differs from CO(2) most significantly in the magnitude of its Coulombic interactions with zeolites. Despite similarities between N(2) and CO(2) diffusion in other materials, we show here that the diffusion of CO(2) within cage-type zeolites is dominated by an energy barrier to diffusion located at the entrance to the narrow channels connecting larger cages. This barrier originates in Coulombic interactions between zeolites and CO(2)'s quadrupole and results in well-defined orientations for the diffusing molecules. Furthermore, CO(2)'s favorable electrostatic interactions with the zeolite framework result in preferential binding in the windows between cages. N(2)'s behavior, in contrast, is more consistent with that of molecules previously studied. Our analysis suggests that CO(2)'s behavior might be common for adsorbates with quadrupoles that interact strongly with a material that has narrow windows between cages.

Probing the Electronic Environment of Methylindoles using Internal Rotation and (14)N Nuclear Quadrupole Coupling.

PubMed

Gurusinghe, Ranil M; Tubergen, Michael J

2016-05-26

High-resolution rotational spectra were recorded in the 10.5-21.0 GHz frequency range for seven singly methylated indoles. (14)N nuclear quadrupole hyperfine structure and spectral splittings arising from tunneling along the internal rotation of the methyl group were resolved for all indole species. The nuclear quadrupole coupling constants were used to characterize the electronic environment of the nitrogen atom, and the program XIAM was used to fit the barrier to internal rotation to the measured transition frequencies. The best fit barriers were found to be 277.1(2), 374.32(4), 414.(5), 331.6(2), 126.8675(15), 121.413(4), and 426(3) cm(-1) for 1-methylindole through 7-methylindole, respectively. The fitted barriers were found to be in good agreement with barriers calculated at the ωB97XD/6-311++G(d,p) level. The complete set of experimental barriers is compared to theoretical investigations of the origins of methyl torsional barriers and confirms that the magnitude of these barriers is an overall effect of individual hyperconjugative and structural interactions of many bonding/antibonding orbitals.

Transition Quadrupole Collectivity of Ar and Cl Isotopes Near N = 28

NASA Astrophysics Data System (ADS)

Winkler, R.; Gade, A.; Brown, B. A.; Glasmacher, T.; Baugher, T. R.; Bazin, D.; Grinyer, G. F.; McDaniel, S.; Meharchand, R.; Ratkiewicz, A.; Stroberg, R.; Walsh, K.; Weisshaar, D.; Riley, L. A.

2010-11-01

Measurements of the reduced quadrupole transition strengths, B(E2; 0^+ -> 2^+) of even-even nuclei guide our understanding of the onset collectivity with the addition of valence nucleons beyond the known shell structure of the atomic nucleus. The study of the quadrupole collectivity of neutron-rich ^47,48Ar and ^45,46Cl via relativistic Coulomb excitation was performed using a cocktail of exotic beams produced by the coupled cyclotron facility at NSCL. Particle tracking and identification was achieved on an event-by-event basis using the S800 high-resolution spectrograph. Gamma rays emitted at the reaction target position in coincidence with the detection of scattered particles were observed with the segmented high-purity Germanium array SeGA, a vital tool for the Doppler reconstruction of each observed event. Results from the present work provide insight into the persistence of the N = 28 shell closure and will be discussed in the framework of the shell model utilizing modern effective interactions in the sdpf valence space. This work is supported by the National Science Foundation under Grants No. PHY-0606007 and PHY-0758099.

Characterization of goat colostrum oligosaccharides by nano-liquid chromatography on chip quadrupole time-of-flight mass spectrometry and hydrophilic interaction liquid chromatography-quadrupole mass spectrometry

PubMed Central

Martín-Ortiz, A.; Salcedo, J.; Barile, D.; Bunyatratchata, A.; Moreno, F.J.; Martin-García, I.; Clemente, A.; Sanz, M.L.; Ruiz-Matute, A.I.

2016-01-01

A detailed qualitative and quantitative characterization of goat colostrum oligosaccharides (GCO) has been carried out for the first time. Defatted and deproteinized colostrum samples, previously treated by size exclusion chromatography (SEC) to remove lactose, were analyzed by nanoflow liquid chromatography-quadrupole-time of flight mass spectrometry (Nano-LC-Chip-Q-TOF MS). Up to 78 oligosaccharides containing hexose, hexosamine, fucose, N-acetylneuraminic acid or N-glycolylneuraminic acid monomeric units were identified in the samples, some of them detected for the first time in goat colostra. As a second step, a hydrophilic interaction liquid chromatography coupled to mass spectrometry (HILIC-MS) methodology was developed for the separation and quantitation of the main GCO, both acidic and neutral carbohydrates. Among other experimental chromatographic conditions, mobile phase additives and column temperature were evaluated in terms of retention time, resolution, peak width and symmetry of target carbohydrates. Narrow peaks (wh: 0.2–0.6 min) and good symmetry (As: 0.8–1.4) were obtained for GCO using an acetonitrile:water gradient with 0.1% ammonium hydroxide at 40 °C. These conditions were selected to quantify the main oligosaccharides in goat colostrum samples. Values ranging from 140 to 315 mg L−1 for neutral oligosaccharides and from 83 to 251 mg L−1 for acidic oligosaccharides were found. The combination of both techniques resulted to be useful to achieve a comprehensive characterization of GCO. PMID:26427327

Resonance energy transfer: when a dipole fails.

PubMed

Andrews, David L; Leeder, Jamie M

2009-05-14

The Coulombic coupling of electric dipole (E1) transition moments is the most commonly studied and widely operative mechanism for energy migration in multichromophore systems. However a significant number of exceptions exist, in which donor decay and/or acceptor excitation processes are E1-forbidden. The alternative transfer mechanisms that can apply in such cases include roles for higher multipole transitions, exciton- or phonon-assisted interactions, and non-Coulombic interactions based on electron exchange. A quantum electrodynamical formulation provides a rigorous basis to assess the first of these, specifically addressing the relative significance of higher multipole contributions to the process of energy transfer in donor-acceptor systems where electric dipole transitions are precluded by symmetry. Working within the near-zone limit, where donor-acceptor separations are small in comparison to the chromophore scale, the analysis highlights the contributions of both electric quadrupole-electric quadrupole (E2-E2) coupling and the seldom considered second-order electric dipole-electric dipole (E1(2)-E1(2)) coupling. For both forms of interaction, experimentally meaningful rate equations are secured by the use of orientational averaging, and the mechanisms are analyzed with reference to systems in which E1-forbidden transitions are commonly reported.

Darboux theorems and Wronskian formulas for integrable systems I. Constrained KP flows

NASA Astrophysics Data System (ADS)

Oevel, W.

1993-05-01

Generalizations of the classical Darboux theorem are established for pseudo-differential scattering operators of the form L = limit∑i=0N u i∂ i + limitΣi=1m Φ i∂ -1limitΨi†i. Iteration of the Darboux transformations leads to a gauge transformed operator with coefficients given by Wronskian formulas involving a set of eigenfunctions of L. Nonlinear integrable partial differential equations are associated with the scattering operator L which arise as a symmetry reduction of the multicomponent KP hierarchy. With a suitable linear time evolution for the eigenfunctions the Darboux transformation is used to obtain solutions of the integrable equations in terms of Wronskian determinants.

Quench Protection of SC Quadrupole Magnets

NASA Astrophysics Data System (ADS)

Feher, S.; Bossert, R.; Dimarco, J.; Mitchell, D.; Lamm, M. J.; Limon, P. J.; Mazur, P.; Nobrega, F.; Orris, D.; Ozelis, J. P.; Strait, J. B.; Tompkins, J. C.; Zlobin, A. V.; McInturff, A. D.

1997-05-01

The energy stored in a superconducting accelerator magnet is dissipated after a quench in the coil normal zones, heating the coil and generating a turn to turn and coil to ground voltage drop. Quench heaters are used to protect the superconducting magnet by greatly increasing the coil normal zone thus allowing the energy to be dissipated over a larger conductor volume. Such heaters will be required for the Fermilab/LBNL design of the high gradient quads (HGQ) designed for the LHC interaction regions. As a first step, heaters were installed and tested in several Tevatron low-β superconducting quadrupoles. Experimental studies in normal and superfluid helium are presented which show the heater-induced quench response as a function of magnet excitation current, magnet temperature and peak heater energy density.

On a difficulty in eigenfunction expansion solutions for the start-up of fluid flow

NASA Astrophysics Data System (ADS)

Christov, Ivan C.

2015-11-01

Most mathematics and engineering textbooks describe the process of ``subtracting off'' the steady state of a linear parabolic partial differential equation as a technique for obtaining a boundary-value problem with homogeneous boundary conditions that can be solved by separation of variables (i.e., eigenfunction expansions). While this method produces the correct solution for the start-up of the flow of, e.g., a Newtonian fluid between parallel plates, it can lead to erroneous solutions to the corresponding problem for a class of non-Newtonian fluids. We show that the reason for this is the non-rigorous enforcement of the start-up condition in the textbook approach, which leads to a violation of the principle of causality. Nevertheless, these boundary-value problems can be solved correctly using eigenfunction expansions, and we present the formulation that makes this possible (in essence, an application of Duhamel's principle). The solutions obtained by this new approach are shown to agree identically with those obtained by using the Laplace transform in time only, a technique that enforces the proper start-up condition implicitly (hence, the same error cannot be committed). Supported, in part, by NSF Grant DMS-1104047 and the U.S. DOE (Contract No. DE-AC52-06NA25396) through the LANL/LDRD Program.

Waves propagating over a two-layer porous barrier on a seabed

NASA Astrophysics Data System (ADS)

Lin, Qiang; Meng, Qing-rui; Lu, Dong-qiang

2018-05-01

A research of wave propagation over a two-layer porous barrier, each layer of which is with different values of porosity and friction, is conducted with a theoretical model in the frame of linear potential flow theory. The model is more appropriate when the seabed consists of two different properties, such as rocks and breakwaters. It is assumed that the fluid is inviscid and incompressible and the motion is irrotational. The wave numbers in the porous region are complex ones, which are related to the decaying and propagating behaviors of wave modes. With the aid of the eigenfunction expansions, a new inner product of the eigenfunctions in the two-layer porous region is proposed to simplify the calculation. The eigenfunctions, under this new definition, possess the orthogonality from which the expansion coefficients can be easily deduced. Selecting the optimum truncation of the series, we derive a closed system of simultaneous linear equations for the same number of the unknown reflection and transmission coefficients. The effects of several physical parameters, including the porosity, friction, width, and depth of the porous barrier, on the dispersion relation, reflection and transmission coefficients are discussed in detail through the graphical representations of the solutions. It is concluded that these parameters have certain impacts on the reflection and transmission energy.

Improved statistical power with a sparse shape model in detecting an aging effect in the hippocampus and amygdala

NASA Astrophysics Data System (ADS)

Chung, Moo K.; Kim, Seung-Goo; Schaefer, Stacey M.; van Reekum, Carien M.; Peschke-Schmitz, Lara; Sutterer, Matthew J.; Davidson, Richard J.

2014-03-01

The sparse regression framework has been widely used in medical image processing and analysis. However, it has been rarely used in anatomical studies. We present a sparse shape modeling framework using the Laplace- Beltrami (LB) eigenfunctions of the underlying shape and show its improvement of statistical power. Tradition- ally, the LB-eigenfunctions are used as a basis for intrinsically representing surface shapes as a form of Fourier descriptors. To reduce high frequency noise, only the first few terms are used in the expansion and higher frequency terms are simply thrown away. However, some lower frequency terms may not necessarily contribute significantly in reconstructing the surfaces. Motivated by this idea, we present a LB-based method to filter out only the significant eigenfunctions by imposing a sparse penalty. For dense anatomical data such as deformation fields on a surface mesh, the sparse regression behaves like a smoothing process, which will reduce the error of incorrectly detecting false negatives. Hence the statistical power improves. The sparse shape model is then applied in investigating the influence of age on amygdala and hippocampus shapes in the normal population. The advantage of the LB sparse framework is demonstrated by showing the increased statistical power.

Laplace-Beltrami Eigenvalues and Topological Features of Eigenfunctions for Statistical Shape Analysis

PubMed Central

Reuter, Martin; Wolter, Franz-Erich; Shenton, Martha; Niethammer, Marc

2009-01-01

This paper proposes the use of the surface based Laplace-Beltrami and the volumetric Laplace eigenvalues and -functions as shape descriptors for the comparison and analysis of shapes. These spectral measures are isometry invariant and therefore allow for shape comparisons with minimal shape pre-processing. In particular, no registration, mapping, or remeshing is necessary. The discriminatory power of the 2D surface and 3D solid methods is demonstrated on a population of female caudate nuclei (a subcortical gray matter structure of the brain, involved in memory function, emotion processing, and learning) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the Laplace-Beltrami eigenvalues and -functions are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann vs. the Dirichlet spectra in 3D. Furthermore, topological analyses employing the Morse-Smale complex (on the surfaces) and the Reeb graph (in the solids) are performed on selected eigenfunctions, yielding shape descriptors, that are capable of localizing geometric properties and detecting shape differences by indirectly registering topological features such as critical points, level sets and integral lines of the gradient field across subjects. The use of these topological features of the Laplace-Beltrami eigenfunctions in 2D and 3D for statistical shape analysis is novel. PMID:20161035

Algorithm for Stabilizing a POD-Based Dynamical System

NASA Technical Reports Server (NTRS)

Kalb, Virginia L.

2010-01-01

This algorithm provides a new way to improve the accuracy and asymptotic behavior of a low-dimensional system based on the proper orthogonal decomposition (POD). Given a data set representing the evolution of a system of partial differential equations (PDEs), such as the Navier-Stokes equations for incompressible flow, one may obtain a low-dimensional model in the form of ordinary differential equations (ODEs) that should model the dynamics of the flow. Temporal sampling of the direct numerical simulation of the PDEs produces a spatial time series. The POD extracts the temporal and spatial eigenfunctions of this data set. Truncated to retain only the most energetic modes followed by Galerkin projection of these modes onto the PDEs obtains a dynamical system of ordinary differential equations for the time-dependent behavior of the flow. In practice, the steps leading to this system of ODEs entail numerically computing first-order derivatives of the mean data field and the eigenfunctions, and the computation of many inner products. This is far from a perfect process, and often results in the lack of long-term stability of the system and incorrect asymptotic behavior of the model. This algorithm describes a new stabilization method that utilizes the temporal eigenfunctions to derive correction terms for the coefficients of the dynamical system to significantly reduce these errors.

Commensurability effects in one-dimensional Anderson localization: Anomalies in eigenfunction statistics

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

Kravtsov, V.E., E-mail: kravtsov@ictp.it; Landau Institute for Theoretical Physics, 2 Kosygina st., 117940 Moscow; Yudson, V.I., E-mail: yudson@isan.troitsk.ru

Highlights: > Statistics of normalized eigenfunctions in one-dimensional Anderson localization at E = 0 is studied. > Moments of inverse participation ratio are calculated. > Equation for generating function is derived at E = 0. > An exact solution for generating function at E = 0 is obtained. > Relation of the generating function to the phase distribution function is established. - Abstract: The one-dimensional (1d) Anderson model (AM), i.e. a tight-binding chain with random uncorrelated on-site energies, has statistical anomalies at any rational point f=(2a)/({lambda}{sub E}) , where a is the lattice constant and {lambda}{sub E} is the demore » Broglie wavelength. We develop a regular approach to anomalous statistics of normalized eigenfunctions {psi}(r) at such commensurability points. The approach is based on an exact integral transfer-matrix equation for a generating function {Phi}{sub r}(u, {phi}) (u and {phi} have a meaning of the squared amplitude and phase of eigenfunctions, r is the position of the observation point). This generating function can be used to compute local statistics of eigenfunctions of 1d AM at any disorder and to address the problem of higher-order anomalies at f=p/q with q > 2. The descender of the generating function P{sub r}({phi}){identical_to}{Phi}{sub r}(u=0,{phi}) is shown to be the distribution function of phase which determines the Lyapunov exponent and the local density of states. In the leading order in the small disorder we derived a second-order partial differential equation for the r-independent ('zero-mode') component {Phi}(u, {phi}) at the E = 0 (f=1/2 ) anomaly. This equation is nonseparable in variables u and {phi}. Yet, we show that due to a hidden symmetry, it is integrable and we construct an exact solution for {Phi}(u, {phi}) explicitly in quadratures. Using this solution we computed moments I{sub m} = N< vertical bar {psi} vertical bar {sup 2m}> (m {>=} 1) for a chain of the length N {yields} {infinity} and found an essential difference between their m-behavior in the center-of-band anomaly and for energies outside this anomaly. Outside the anomaly the 'extrinsic' localization length defined from the Lyapunov exponent coincides with that defined from the inverse participation ratio ('intrinsic' localization length). This is not the case at the E = 0 anomaly where the extrinsic localization length is smaller than the intrinsic one. At E = 0 one also observes an anomalous enhancement of large moments compatible with existence of yet another, much smaller characteristic length scale.« less

27 Al MAS NMR Studies of HBEA Zeolite at Low to High Magnetic Fields

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

Hu, Jian Zhi; Wan, Chuan; Vjunov, Aleksei

27Al single pulse (SP) MAS NMR spectra of HBEA zeolites with high Si/Al ratios of 71 and 75 were obtained at three magnetic field strengths of 7.05, 11.75 and 19.97 T. High field 27Al MAS NMR spectra acquired at 19.97 T show significantly improved spectral resolution, resulting in at least two well-resolved tetrahedral-Al NMR peaks. Based on the results obtained from 27Al MAS and MQMAS NMR acquired at 19.97 T, four different quadrupole peaks are used to deconvolute the 27Al SP MAS spectra acquired at vari-ous fields by using the same set of quadrupole coupling constants, asymmetric parameters and relativemore » integrated peak intensities for the tetrahedral Al peaks. The line shapes of individual peaks change from typical quadrupole line shape at low field to essentially symmetrical line shapes at high field. We demonstrate that for fully hydrated HBEA zeolites the effect of second order quadrupole interaction can be ignored and quantitative spectral analysis can be performed by directly fitting the high field spectra using mixed Gaussian/Lorentzian line shapes. Also, the analytical steps described in our work allow direct assignment of spectral intensity to individual Al tetrahedral sites (T-sites) of zeolite HBEA. Finally, the proposed concept is suggested generally applicable to other zeo-lite framework types, thus, allowing a direct probing of Al distributions by NMR spectroscopic methods in zeolites with high confi-dence.« less

Larp Nb3Sn Quadrupole Magnets for the Lhc Luminosity Upgrade

NASA Astrophysics Data System (ADS)

Ferracin, P.

2010-04-01

The US LHC Accelerator Research Program (LARP) is a collaboration between four US laboratories (BNL, FNAL, LBNL, and SLAC) aimed at contributing to the commissioning and operation of the LHC and conducting R&D on its luminosity upgrade. Within LARP, the Magnet Program's main goal is to demonstrate that Nb3Sn superconducting magnets are a viable option for a future upgrade of the LHC Interaction Regions. Over the past four years, LARP has successfully fabricated and tested several R&D magnets: 1) the subscale quadrupole magnet SQ, to perform technology studies with 300 mm long racetrack coils, 2) the technology quadrupole TQ, to investigate support structure behavior with 1 m long cos 2θ coils, and 3) the long racetrack magnet LR, to test 3.6 m long racetrack coils. The next milestone consists in the fabrication and test of the 3.7 m long quadrupole magnet LQ, with the goal of demonstrating that Nb3Sn technology is mature for use in high energy accelerators. After an overview of design features and test result of the LARP magnets fabricated so far, this paper focuses on the status of the fabrication of LQ: we describe the production of the 3.4 m long cos 2θ coils, and the of the qualification support structure. Finally, the status of the development of the next 1 m long model HQ, conceived to explore stress and field limits of Nb3Sn superconducting, magnets, is presented.

Theoretical design of twelve-band infrared metamaterial perfect absorber by combining the dipole, quadrupole, and octopole plasmon resonance modes of four different ring-strip resonators.

PubMed

Zhao, Lei; Liu, Han; He, Zhihong; Dong, Shikui

2018-05-14

Multiband metamaterial perfect absorbers (MPAs) have promising applications in many fields like microbolometers, infrared detection, biosensing, and thermal emitters. In general, the single resonator can only excite a fundamental mode and achieve single absorption band. The multiband MPA can be achieved by combining several different sized resonators together. However, it's still challenging to design the MPA with absorption bands of more than four and average absorptivity of more than 90% due to the interaction between differently sized resonators. In this paper, three absorption bands are successfully achieved with average absorptivity up to 98.5% only utilizing single one our designed ring-strip resonator, which can simultaneously excite a fundamental electric dipole mode, a higher-order electric quadrupole mode, and a higher-order electric octopole mode. As the biosensor, the sensing performance of the higher-order modes is higher than the fundamental modes. Then we try to increase the absorption bands by combining different sized ring-strip resonators together and make the average absorptivity above 90% by optimizing the geometry parameters. A six-band MPA is achieved by combining two different sized ring-strip resonators with average absorptivity up to 98.8%, which can excite two dipole modes, two quadrupole modes, and two octopole modes. A twelve-band MPA is achieved by combining four different sized ring-strip resonators with average absorptivity up to 93.7%, which can excite four dipole modes, four quadrupole modes, and four octopole modes.

Atomic electron energies including relativistic effects and quantum electrodynamic corrections

NASA Technical Reports Server (NTRS)

Aoyagi, M.; Chen, M. H.; Crasemann, B.; Huang, K. N.; Mark, H.

1977-01-01

Atomic electron energies have been calculated relativistically. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first order correction to the local approximation was thus included. Quantum-electrodynamic corrections were made. For all orbitals in all atoms with 2 less than or equal to Z less than or equal to 106, the following quantities are listed: total energies, electron kinetic energies, electron-nucleus potential energies, electron-electron potential energies consisting of electrostatic and Breit interaction (magnetic and retardation) terms, and vacuum polarization energies. These results will serve for detailed comparison of calculations based on other approaches. The magnitude of quantum electrodynamic corrections is exhibited quantitatively for each state.

FAST TRACK COMMUNICATION: SUSY transformations with complex factorization constants: application to spectral singularities

NASA Astrophysics Data System (ADS)

Samsonov, Boris F.

2010-10-01

Supersymmetric (SUSY) transformation operators with complex factorization constants are analyzed as operators acting in the Hilbert space of functions square integrable on the positive semiaxis. The obtained results are applied to Hamiltonians possessing spectral singularities which are non-Hermitian SUSY partners of self-adjoint operators. A new regularization procedure for the resolution of the identity operator in terms of a continuous biorthonormal set of the non-Hermitian Hamiltonian eigenfunctions is proposed. It is also argued that if the binorm of continuous spectrum eigenfunctions is interpreted in the same way as the norm of similar functions in the usual Hermitian case, then one can state that the function corresponding to a spectral singularity has zero binorm.

Nodal domains of a non-separable problem—the right-angled isosceles triangle

NASA Astrophysics Data System (ADS)

Aronovitch, Amit; Band, Ram; Fajman, David; Gnutzmann, Sven

2012-03-01

We study the nodal set of eigenfunctions of the Laplace operator on the right-angled isosceles triangle. A local analysis of the nodal pattern provides an algorithm for computing the number νn of nodal domains for any eigenfunction. In addition, an exact recursive formula for the number of nodal domains is found to reproduce all existing data. Eventually, we use the recursion formula to analyse a large sequence of nodal counts statistically. Our analysis shows that the distribution of nodal counts for this triangular shape has a much richer structure than the known cases of regular separable shapes or completely irregular shapes. Furthermore, we demonstrate that the nodal count sequence contains information about the periodic orbits of the corresponding classical ray dynamics.

Diverse wave-particle interactions for energetic ions that traverse Alfvén eigenmodes on their first full orbit

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

Heidbrink, W. W.; Persico, E. A. D.; Austin, M. E.

2016-02-15

Neutral-beam ions that are deflected onto loss orbits by Alfvén eigenmodes (AE) on their first bounce orbit and are detected by a fast-ion loss detector (FILD) satisfy the “local resonance” condition proposed by Zhang et al. [Nucl. Fusion 55, 22002 (2015)]. This theory qualitatively explains FILD observations for a wide variety of AE-particle interactions. When coherent losses are measured for multiple AE, oscillations at the sum and difference frequencies of the independent modes are often observed in the loss signal. The amplitudes of the sum and difference peaks correlate weakly with the amplitudes of the fundamental loss-signal amplitudes but domore » not correlate with the measured mode amplitudes. In contrast to a simple uniform-plasma theory of the interaction [Chen et al., Nucl. Fusion 54, 083005 (2014)], the loss-signal amplitude at the sum frequency is often larger than the loss-signal amplitude at the difference frequency, indicating a more detailed computation of the orbital trajectories through the mode eigenfunctions is needed.« less

Complementary π-π interactions induce multicomponent coassembly into functional fibrils.

PubMed

Ryan, Derek M; Doran, Todd M; Nilsson, Bradley L

2011-09-06

Noncovalent self-assembled materials inspired by amyloid architectures are useful for biomedical applications ranging from regenerative medicine to drug delivery. The selective coassembly of complementary monomeric units to provide ordered multicomponent fibrils is a possible strategy for enhancing the sophistication of these noncovalent materials. Herein we report that complementary π-π interactions can be exploited to promote the coassembly of phenylalanine (Phe) derivatives that possess complementary aromatic side-chain functionality. Specifically, equimolar mixtures of Fmoc-Phe and Fmoc-F(5)-Phe, which possess side-chain groups with complementary quadrupole electronics, readily coassemble to form two-component fibrils and hydrogels under conditions where Fmoc-Phe alone fails to self-assemble. In addition, it was found that equimolar mixtures of Fmoc-Phe with monohalogenated (F, Cl, and Br) Fmoc-Phe derivatives also coassembled into two-component fibrils. These results collectively indicate that face-to-face quadrupole stacking between benzyl side-chain groups does not account for the molecular recognition between Phe and halogenated Phe derivatives that promote cofibrillization but that coassembly is mediated by more subtle π-π effects arising from the halogenation of the benzyl side chain. The use of complementary π-π interactions to promote the coassembly of two distinct monomeric units into ordered two-component fibrils dramatically expands the repertoire of noncovalent interactions that can be used in the development of sophisticated noncovalent materials. © 2011 American Chemical Society

Development of MQXF: The Nb 3Sn low-β quadrupole for the HiLumi LHC

DOE PAGES

Ferracin, P.; G. Ambrosio; Anerella, M.; ...

2015-12-18

The High Luminosity (HiLumi) Large Hadron Collider (LHC) project has, as the main objective, to increase the LHC peak luminosity by a factor five and the integrated luminosity by a factor ten. This goal will be achieved mainly with a new interaction region layout, which will allow a stronger focusing of the colliding beams. The target will be to reduce the beam size in the interaction points by a factor of two, which requires doubling the aperture of the low-β (or inner triplet) quadrupole magnets. The use of Nb3Sn superconducting material and, as a result, the possibility of operating atmore » magnetic field levels in the windings higher than 11 T will limit the increase in length of these quadrupoles, called MQXF, to acceptable levels. After the initial design phase, where the key parameters were chosen and the magnet's conceptual design finalized, the MQXF project, a joint effort between the U.S. LHC Accelerator Research Program and the Conseil Europeen pour la Recherche Nucleaire (CERN), has now entered the construction and test phase of the short models. Concurrently, the preparation for the development of the full-length prototypes has been initiated. Lastly, this paper will provide an overview of the project status, describing and reporting on the performance of the superconducting material, the lessons learnt during the fabrication of superconducting coils and support structure, and the fine tuning of the magnet design in view of the start of the prototyping phase.« less

Characterization of goat colostrum oligosaccharides by nano-liquid chromatography on chip quadrupole time-of-flight mass spectrometry and hydrophilic interaction liquid chromatography-quadrupole mass spectrometry.

PubMed

Martín-Ortiz, A; Salcedo, J; Barile, D; Bunyatratchata, A; Moreno, F J; Martin-García, I; Clemente, A; Sanz, M L; Ruiz-Matute, A I

2016-01-08

A detailed qualitative and quantitative characterization of goat colostrum oligosaccharides (GCO) has been carried out for the first time. Defatted and deproteinized colostrum samples, previously treated by size exclusion chromatography (SEC) to remove lactose, were analyzed by nanoflow liquid chromatography-quadrupole-time of flight mass spectrometry (Nano-LC-Chip-Q-TOF MS). Up to 78 oligosaccharides containing hexose, hexosamine, fucose, N-acetylneuraminic acid or N-glycolylneuraminic acid monomeric units were identified in the samples, some of them detected for the first time in goat colostra. As a second step, a hydrophilic interaction liquid chromatography coupled to mass spectrometry (HILIC-MS) methodology was developed for the separation and quantitation of the main GCO, both acidic and neutral carbohydrates. Among other experimental chromatographic conditions, mobile phase additives and column temperature were evaluated in terms of retention time, resolution, peak width and symmetry of target carbohydrates. Narrow peaks (wh: 0.2-0.6min) and good symmetry (As: 0.8-1.4) were obtained for GCO using an acetonitrile:water gradient with 0.1% ammonium hydroxide at 40°C. These conditions were selected to quantify the main oligosaccharides in goat colostrum samples. Values ranging from 140 to 315mgL(-1) for neutral oligosaccharides and from 83 to 251mgL(-1) for acidic oligosaccharides were found. The combination of both techniques resulted to be useful to achieve a comprehensive characterization of GCO. Copyright © 2015 Elsevier B.V. All rights reserved.

Effects of the quadrupole wakefields in a passive streaker

DOE PAGES

Craievich, Paolo; Lutman, Alberto A.

2016-10-05

A novel method based on transverse wakefields has been recently proposed to characterize the temporal profile of a relativistic electron bunch. The electron bunch is streaked by the interaction with the transverse wakefield excited when the electrons travel off-axis in a device called the passive streaker. Furthermore, for the large transverse off-axis offsets required to effectively streak the electron bunch, higher order modes can be excited. The time-dependent quadrupole wakefield of the dielectric-lined structure can cause a significant enlargement of the transverse profile at the screen. Consequently, the measurement resolution is decreased also at the bunch tail. We report onmore » how the temporal profile can be effectively reconstructed also including the defocusing effect for a given transverse beam distribution at the passive streaker.« less

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

Yang, Chi; Arvapally, Ravi K.; Tekarli, Sammer M.

The trinuclear triangle-shaped system [tris{3,5-bis(heptafluoropropyl)-1,2,4-triazolatosilver(I)}] (1) and the multi-armed square-shaped metalloporphyrin PtOEP or the free porphyrin base H2OEP serve as excellent octopus hosts (OEP=2,3,7,8,12,13,17,18-octaethyl-21H,23H-porphine). Coupling of the fluorous/organic molecular octopi 1 and H2OEP or PtOEP by strong quadrupole-quadrupole and metal- interactions affords the supramolecular assemblies [1PtOEP] or [1H(2)OEP] (2a), which feature nanoscopic cavities surrounding the upper triangular and lower square cores. The fluorous/organic biphasic configuration of [1PtOEP] leads to an increase in the phosphorescence of PtOEP under ambient conditions. Guest molecules can be included in the biphasic double-octopus assembly in three different site-selective modes.

Isoscalar neutron-proton pairing and SU(4)-symmetry breaking in Gamow-Teller transitions

NASA Astrophysics Data System (ADS)

Kaneko, K.; Sun, Y.; Mizusaki, T.

2018-05-01

The isoscalar neutron-proton pairing is thought to be important for nuclei with equal number of protons and neutrons but its manifestation in structure properties remains to be understood. We investigate the Gamow-Teller (GT) transitions for the f7 /2-shell nuclei in large-scale shell-model calculations with the realistic Hamiltonian. We show that the isoscalar T =0 ,Jπ=1+ neutron-proton pairing interaction plays a decisive role for the concentration of GT strengths at the first-excited 11+ state in 42Sc, and that the suppression of these strengths in 46V, 50Mn, and 54Co is mainly caused by the spin-orbit force supplemented by the quadrupole-quadrupole interaction. Based on the good reproduction of the charge-exchange reaction data, we further analyze the interplay between the isoscalar and isovector pairing correlations. We conclude that even for the most promising A =42 nuclei where the SU(4) isoscalar-isovector-pairing symmetry is less broken, the probability of forming an isoscalar neutron-proton pairing condensation is less than 60% as compared to the expectation at the SU(4)-symmetry limit.

Energy levels, wavelengths, and transition rates of multipole transitions (E1, E2, M1, M2) in Au{sup 67+} and Au{sup 66+} ions

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

Hamasha, Safeia, E-mail: safeia@hu.edu.jo

2013-11-15

The fully relativistic configuration interaction method of the FAC code is used to calculate atomic data for multipole transitions in Mg-like Au (Au{sup 67+}) and Al-like Au (Au{sup 66+}) ions. Generated atomic data are important in the modeling of M-shell spectra for heavy Au ions and Au plasma diagnostics. Energy levels, oscillator strengths and transition rates are calculated for electric-dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) for transitions between excited and ground states 3l−nl{sup ′}, such that n=4,5,6,7. The local central potential is derived using the Dirac–Fock–Slater method. Correlation effects to all orders are consideredmore » by the configuration interaction expansion. All relativistic effects are included in the calculations. Calculated energy levels are compared against published values that were calculated using the multi-reference many body perturbation theory, which includes higher order QED effects. Favorable agreement was observed, with less than 0.15% difference.« less

Novel tunable green-red-emitting oxynitride phosphors co-activated with Ce3+, Tb3+, and Eu3+: photoluminescence and energy transfer.

PubMed

Huo, Jiansheng; Dong, Langping; Lü, Wei; Shao, Baiqi; You, Hongpeng

2017-07-14

A series of novel Ce 3+ , Tb 3+ and Eu 3+ ion doped Y 4 SiAlO 8 N-based oxynitride phosphors were synthesized by the solid-state method and characterized by X-ray powder diffraction, scanning electron microscopy, photoluminescence, lifetimes and thermo-luminescence. The excitation of the Ce 3+ /Tb 3+ co-doped and Ce 3+ /Tb 3+ /Eu 3+ tri-doped phosphor with near-UV radiation results in strong linear Tb 3+ green and Eu 3+ red emission. The occurrence of Ce 3+ -Tb 3+ and Ce 3+ -Tb 3+ -Eu 3+ energy transfer processes is responsible for the bright green or red luminescence. The Tb 3+ ion acting as an energy transfer bridge can alleviate MMCT quenching between the Ce 3+ -Eu 3+ ion pairs. The lifetime measurements demonstrated that the energy-transfer mechanisms of Ce 3+ → Tb 3+ and Tb 3+ → Eu 3+ are dipole-quadrupole and quadrupole-quadrupole interactions, respectively. The temperature dependent luminescence measurements showed that as-prepared green/red phosphors have good thermal stability against temperature quenching. The obtained results indicate that these phosphors might serve as promising candidates for n-UV LEDs.

Fabrication of First 4-m Coils for the LARP MQXFA Quadrupole and Assembly in Mirror Structure

DOE PAGES

Holik, Eddie Frank; Ambrosio, Giorgio; Anerella, Michael; ...

2017-01-23

The US LHC Accelerator Research Program is constructing prototype interaction region quadrupoles as part of the US in-kind contribution to the Hi-Lumi LHC project. The low-beta MQXFA Q1/Q3 coils have a 4-m length and a 150 mm bore. The design is first validated on short, one meter models (MQXFS) developed as part of the longstanding Nb3Sn quadrupole R&D by LARP in collaboration with CERN. In parallel, facilities and tooling are being developed and refined at BNL, LBNL, and FNAL to enable long coil production, assembly, and cold testing. Long length scale-up is based on the experience from the LARP 90more » mm aperture (TQ-LQ) and 120 mm aperture (HQ and Long HQ) programs. A 4-m long MQXF practice coil was fabricated, water jet cut and analyzed to verify procedures, parts, and tooling. In parallel, the first complete prototype coil (QXFP01a) was fabricated and assembled in a long magnetic mirror, MQXFPM1, to provide early feedback on coil design and fabrication following the successful experience of previous LARP mirror tests.« less

Mechanical Design Studies of the MQXF Long Model Quadrupole for the HiLumi LHC

DOE PAGES

Pan, Heng; Anderssen, Eric; Ambrosio, Giorgio; ...

2016-12-20

The Large Hadron Collider Luminosity upgrade (HiLumi) program requires new low-β triplet quadrupole magnets, called MQXF, in the Interaction Region (IR) to increase the LHC peak and integrated luminosity. The MQXF magnets, designed and fabricated in collaboration between CERN and the U.S. LARP, will all have the same cross section. The MQXF long model, referred as MQXFA, is a quadrupole using the Nb3Sn superconducting technology with 150 mm aperture and a 4.2 m magnetic length and is the first long prototype of the final MQXF design. The MQXFA magnet is based on the previous LARP HQ and MQXFS designs. Inmore » this paper we present the baseline design of the MQXFA structure with detailed 3D numerical analysis. A detailed tolerance analysis of the baseline case has been performed by using a 3D finite element model, which allows fast computation of structures modelled with actual tolerances. Tolerance sensitivity of each component is discussed to verify the actual tolerances to be achieved by vendors. In conclusion, tolerance stack-up analysis is presented in the end of this paper.« less

Field Tolerances for the Triplet Quadrupoles of the LHC High Luminosity Lattice

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

Nosochkov, Yuri; Cai, Y.; Jiao, Y.

2012-06-25

It has been proposed to implement the so-called Achromatic Telescopic Squeezing (ATS) scheme in the LHC high luminosity (HL) lattice to reduce beta functions at the Interaction Points (IP) up to a factor of 8. As a result, the nominal 4.5 km peak beta functions reached in the Inner Triplets (IT) at collision will be increased by the same factor. This, therefore, justifies the installation of new, larger aperture, superconducting IT quadrupoles. The higher beta functions will enhance the effects of the triplet quadrupole field errors leading to smaller beam dynamic aperture (DA). To maintain the acceptable DA, the effectsmore » of the triplet field errors must be re-evaluated, thus specifying new tolerances. Such a study has been performed for the so-called '4444' collision option of the HL-LHC layout version SLHCV3.01, where the IP beta functions are reduced by a factor of 4 in both planes with respect to a pre-squeezed value of 60 cm at two collision points. The dynamic aperture calculations were performed using SixTrack. The impact on the triplet field quality is presented.« less

A scale-bridging modeling approach for anisotropic organic molecules at patterned semiconductor surfaces

NASA Astrophysics Data System (ADS)

Kleppmann, Nicola; Klapp, Sabine H. L.

2015-02-01

Hybrid systems consisting of organic molecules at inorganic semiconductor surfaces are gaining increasing importance as thin film devices for optoelectronics. The efficiency of such devices strongly depends on the collective behavior of the adsorbed molecules. In the present paper, we propose a novel, coarse-grained model addressing the condensed phases of a representative hybrid system, that is, para-sexiphenyl (6P) at zinc-oxide (ZnO). Within our model, intermolecular interactions are represented via a Gay-Berne potential (describing steric and van-der-Waals interactions) combined with the electrostatic potential between two linear quadrupoles. Similarly, the molecule-substrate interactions include a coupling between a linear molecular quadrupole to the electric field generated by the line charges characterizing ZnO(10-10). To validate our approach, we perform equilibrium Monte Carlo simulations, where the lateral positions are fixed to a 2D lattice, while the rotational degrees of freedom are continuous. We use these simulations to investigate orientational ordering in the condensed state. We reproduce various experimentally observed features such as the alignment of individual molecules with the line charges on the surface, the formation of a standing uniaxial phase with a herringbone structure, as well as the formation of a lying nematic phase.

Inverse scattering transform for the KPI equation on the background of a one-line soliton*Inverse scattering transform for the KPI equation on the background of a one-line soliton

NASA Astrophysics Data System (ADS)

Fokas, A. S.; Pogrebkov, A. K.

2003-03-01

We study the initial value problem of the Kadomtsev-Petviashvili I (KPI) equation with initial data u(x1,x2,0) = u1(x1)+u2(x1,x2), where u1(x1) is the one-soliton solution of the Korteweg-de Vries equation evaluated at zero time and u2(x1,x2) decays sufficiently rapidly on the (x1,x2)-plane. This involves the analysis of the nonstationary Schrödinger equation (with time replaced by x2) with potential u(x1,x2,0). We introduce an appropriate sectionally analytic eigenfunction in the complex k-plane where k is the spectral parameter. This eigenfunction has the novelty that in addition to the usual jump across the real k-axis, it also has a jump across a segment of the imaginary k-axis. We show that this eigenfunction can be reconstructed through a linear integral equation uniquely defined in terms of appropriate scattering data. In turn, these scattering data are uniquely constructed in terms of u1(x1) and u2(x1,x2). This result implies that the solution of the KPI equation can be obtained through the above linear integral equation where the scattering data have a simple t-dependence.

Long range intermolecular interactions between the alkali diatomics Na2, K2, and NaK

NASA Astrophysics Data System (ADS)

Zemke, Warren T.; Byrd, Jason N.; Michels, H. Harvey; Montgomery, John A.; Stwalley, William C.

2010-06-01

Long range interactions between the ground state alkali diatomics Na2-Na2, K2-K2, Na2-K2, and NaK-NaK are examined. Interaction energies are first determined from ab initio calculations at the coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] level of theory, including counterpoise corrections. Long range energies calculated from diatomic molecular properties (polarizabilities and dipole and quadrupole moments) are then compared with the ab initio energies. A simple asymptotic model potential ELR=Eelec+Edisp+Eind is shown to accurately represent the intermolecular interactions for these systems at long range.

Long range intermolecular interactions between the alkali diatomics Na(2), K(2), and NaK.

PubMed

Zemke, Warren T; Byrd, Jason N; Michels, H Harvey; Montgomery, John A; Stwalley, William C

2010-06-28

Long range interactions between the ground state alkali diatomics Na(2)-Na(2), K(2)-K(2), Na(2)-K(2), and NaK-NaK are examined. Interaction energies are first determined from ab initio calculations at the coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] level of theory, including counterpoise corrections. Long range energies calculated from diatomic molecular properties (polarizabilities and dipole and quadrupole moments) are then compared with the ab initio energies. A simple asymptotic model potential E(LR)=E(elec)+E(disp)+E(ind) is shown to accurately represent the intermolecular interactions for these systems at long range.

[Some comments on ecological field].

PubMed

Wang, D

2000-06-01

Based on the data of plant ecological field studies, this paper reviewed the conception of ecological field, field eigenfunctions, graphs of ecological field and its application of ecological field theory in explaining plant interactions. It is suggested that the basic character of ecological field is material, and based on the current research level, it is not sure whether ecological field is a kind of specific field different from general physical field. The author gave some comments on the formula and estimation of parameters of basic field function-ecological potential model on ecological field. Both models have their own characteristics and advantages in specific conditions. The author emphasized that ecological field had even more meaning of ecological methodology, and applying ecological field theory in describing the types and processes of plant interactions had three characteristics: quantitative, synthetic and intuitionistic. Field graphing might provide a new way to ecological studies, especially applying the ecological field theory might give an appropriate quantitative explanation for the dynamic process of plant populations (coexistence and interference competition).

Proton-neutron sdg boson model and spherical-deformed phase transition

NASA Astrophysics Data System (ADS)

Otsuka, Takaharu; Sugita, Michiaki

1988-12-01

The spherical-deformed phase transition in nuclei is described in terms of the proton-neutron sdg interacting boson model. The sdg hamiltonian is introduced to model the pairing+quadrupole interaction. The phase transition is reproduced in this framework as a function of the boson number in the Sm isotopes, while all parameters in the hamiltonian are kept constant at values reasonable from the shell-model point of view. The sd IBM is derived from this model through the renormalization of g-boson effects.

Three-photon Gaussian-Gaussian-Laguerre-Gaussian excitation of a localized atom to a highly excited Rydberg state

NASA Astrophysics Data System (ADS)

Mashhadi, L.

2017-12-01

Optical vortices are currently one of the most intensively studied topics in light-matter interaction. In this work, a three-step axial Doppler- and recoil-free Gaussian-Gaussian-Laguerre-Gaussian (GGLG) excitation of a localized atom to the highly excited Rydberg state is presented. By assuming a large detuning for intermediate states, an effective quadrupole excitation related to the Laguerre-Gaussian (LG) excitation to the highly excited Rydberg state is obtained. This special excitation system radially confines the single highly excited Rydberg atom independently of the trapping system into a sharp potential landscape into the so-called ‘far-off-resonance optical dipole-quadrupole trap’ (FORDQT). The key parameters of the Rydberg excitation to the highly excited state, namely the effective Rabi frequency and the effective detuning including a position-dependent AC Stark shift, are calculated in terms of the basic parameters of the LG beam and of the polarization of the excitation lasers. It is shown that the obtained parameters can be tuned to have a precise excitation of a single atom to the desired Rydberg state as well. The features of transferring the optical orbital and spin angular momentum of the polarized LG beam to the atom via quadrupole Rydberg excitation offer a long-lived and controllable qudit quantum memory. In addition, in contrast to the Gaussian laser beam, the doughnut-shaped LG beam makes it possible to use a high intensity laser beam to increase the signal-to-noise ratio in quadrupole excitation with minimized perturbations coming from stray light broadening in the last Rydberg excitation process.

A technique for designing active control systems for astronomical telescope mirrors

NASA Technical Reports Server (NTRS)

Howell, W. E.; Creedon, J. F.

1973-01-01

The problem of designing a control system to achieve and maintain the required surface accuracy of the primary mirror of a large space telescope was considered. Control over the mirror surface is obtained through the application of a corrective force distribution by actuators located on the rear surface of the mirror. The design procedure is an extension of a modal control technique developed for distributed parameter plants with known eigenfunctions to include plants whose eigenfunctions must be approximated by numerical techniques. Instructions are given for constructing the mathematical model of the system, and a design procedure is developed for use with typical numerical data in selecting the number and location of the actuators. Examples of actuator patterns and their effect on various errors are given.

Singularities at the contact point of two kissing Neumann balls

NASA Astrophysics Data System (ADS)

Nazarov, Sergey A.; Taskinen, Jari

2018-02-01

We investigate eigenfunctions of the Neumann Laplacian in a bounded domain Ω ⊂Rd, where a cuspidal singularity is caused by a cavity consisting of two touching balls, or discs in the planar case. We prove that the eigenfunctions with all of their derivatives are bounded in Ω ‾, if the dimension d equals 2, but in dimension d ≥ 3 their gradients have a strong singularity O (| x - O|-α), α ∈ (0 , 2 -√{ 2 } ] at the point of tangency O. Our study is based on dimension reduction and other asymptotic procedures, as well as the Kondratiev theory applied to the limit differential equation in the punctured hyperplane R d - 1 ∖ O. We also discuss other shapes producing thinning gaps between touching cavities.

Eight piece quadrupole magnet, method for aligning quadrupole magent pole tips

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

Jaski, Mark S.; Liu, Jie; Donnelly, Aric T.

The invention provides an alternative to the standard 2-piece or 4-piece quadrupole. For example, an 8-piece and a 10-piece quadrupole are provided whereby the tips of each pole may be adjustable. Also provided is a method for producing a quadrupole using standard machining techniques but which results in a final tolerance accuracy of the resulting construct which is better than that obtained using standard machining techniques.

Dissymmetry effects on the laser spectroscopy of supersonically expanded rare gas/chiral arene heteroclusters.

PubMed

Filippi, Antonello; Giardini, Anna; Marcantoni, Enrico; Paladini, Alessandra; Piccirillo, Susanna; Renzi, Gabriele; Rondino, Flaminia; Roselli, Graziella; Satta, Mauro; Speranza, Maurizio

2007-04-14

The R2PI-TOF spectra of supersonically expanded rare gas/chiral arene heteroclusters have been rationalized in terms of the distortion of the pi-electron density reflecting the different dipole and quadrupole momenta induced in the rare gas atoms by interaction with the opposite pi-faces of the chiral arene itself.

Analytical solutions for the dynamics of two trapped interacting ultracold atoms

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

Idziaszek, Zbigniew; Calarco, Tommaso; CNR-INFM BEC Center, I-38050 Povo

2006-08-15

We discuss exact solutions of the Schroedinger equation for the system of two ultracold atoms confined in an axially symmetric harmonic potential. We investigate different geometries of the trapping potential, in particular we study the properties of eigenenergies and eigenfunctions for quasi-one-dimensional and quasi-two-dimensional traps. We show that the quasi-one-dimensional and the quasi-two-dimensional regimes for two atoms can be already realized in the traps with moderately large (or small) ratios of the trapping frequencies in the axial and the transverse directions. Finally, we apply our theory to Feshbach resonances for trapped atoms. Introducing in our description an energy-dependent scattering lengthmore » we calculate analytically the eigenenergies for two trapped atoms in the presence of a Feshbach resonance.« less

Transmission of singularities through a shock wave and the sound generation

NASA Technical Reports Server (NTRS)

Ting, L.

1974-01-01

The interaction of a plane shock wave of finite strength with a vortex line, point vortex, doublet or quadrupole of weak strength is studied. Based upon the physical condition that a free vortex line cannot support a pressure difference, rules are established which define the change of the linear intensity of the segment of the vortex line after its passage through the shock. The rules for point vortex, doublet, and quadrupole are then established as limiting cases. These rules can be useful for the construction of the solution of the entire flow field and for its physical interpretation. However, the solution can be obtained directly by the technique developed for shock diffraction problems. Explicit solutions and the associated sound generation are obtained for the passage of a point vortex through the shock wave.

Theoretical level energies and transition data for 4p64d4, 4p64d34f and 4p54d5 configurations of W34+ ion

NASA Astrophysics Data System (ADS)

Karpuškienė, R.; Bogdanovich, P.; Kisielius, R.

2017-05-01

The ab initio quasirelativistic approach developed specifically for the calculation of spectral parameters of highly charged ions was used to derive transition data for the tungsten ion W34+. The configuration interaction method was applied to include electron correlation effects. The relativistic effects were taken into account in the Breit-Pauli approximation. The level energies, radiative lifetimes τ, Landé g-factors are determined for the ground configuration 4p64d4 and two excited configurations 4p64d34f and 4p54d5. The radiative transition wavelengths λ and emission transition probabilities A for the electric dipole, electric quadrupole, electric octupole, magnetic dipole, and magnetic quadrupole transitions among the levels of these configurations are produced.

Multipole induced splitting of metal-cage vibrations in crystalline endohedral D2d-M2@C84 dimetallofullerenes.

PubMed

Krause, M; Popov, V N; Inakuma, M; Tagmatarchis, N; Shinohara, H; Georgi, P; Dunsch, L; Kuzmany, H

2004-01-22

Metal-carbon cage vibrations of crystalline endohedral D2d-M2@C84 (M=Sc,Y,Dy) dimetallofullerenes were analyzed by temperature dependent Raman scattering and a dynamical force field model. Three groups of metal-carbon cage modes were found at energies of 35-200 cm(-1) and assigned to metal-cage stretching and deformation vibrations. They exhibit a textbook example for the splitting of molecular vibrations in a crystal field. Induced dipole-dipole and quadrupole-quadrupole interactions account quantitatively for the observed mode splitting. Based on the metal-cage vibrational structure it is demonstrated that D2d-Y2@C84 dimetallofullerene retains a monoclinic crystal structure up to 550 K and undergoes a transition from a disordered to an ordered orientational state at a temperature of approximately 150 K.

Magnetic analysis of the Nb$$_3$$Sn low-beta quadrupole for the high luminosity LHC

DOE PAGES

Bermudez, Susana Izquierdo; Ambrosio, G.; Chlachidze, G.; ...

2017-01-10

As part of the Large Hadron Collider Luminosity upgrade (HiLumi-LHC) program, the US LARP collaboration and CERN are working together to design and build 150 mm aperture Nb 3Sn quadrupoles for the LHC interaction regions. A first series of 1.5 m long coils were fabricated, assembled and tested in the first short model. This paper presents the magnetic analysis, comparing magnetic field measurements with the expectations and the field quality requirements. The analysis is focused on the geometrical harmonics, iron saturation effect and cold-warm correlation. Three dimensional effects such as the variability of the field harmonics along the magnet axismore » and the contribution of the coil ends are also discussed. Furthemore, we present the influence of the conductor magnetization and the dynamic effects.« less

Energy levels and radiative rates for Ne-like ions from Cu to Ga

NASA Astrophysics Data System (ADS)

Singh, Narendra; Aggarwal, Sunny

2017-11-01

Energy levels, lifetimes and wave function compositions are computed for 127 fine structural levels in Ne-like ions (Z=29{-}31). Configuration interaction has been included among 51 configurations (generating 1016 levels) and multiconfigurational Dirac-Fock method is used to generate the wave functions. Similar calculations have also been performed using the fully relativistic flexible atomic code (FAC). Transition wavelength, oscillator strength, transition probabilities and line strength are reported for electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1) and magnetic quadrupole (M2) transitions from the ground level. We compared our calculated results with the available data in the literature. The calculated results are found to be in close agreement with the previous results. Further, we predict some new atomic data which may be important for plasma diagnostics.

A Vibrating Wire System For Quadrupole Fiducialization

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

Wolf, Zachary

2010-12-13

A vibrating wire system is being developed to fiducialize the quadrupoles between undulator segments in the LCLS. This note provides a detailed analysis of the system. The LCLS will have quadrupoles between the undulator segments to keep the electron beam focused. If the quadrupoles are not centered on the beam axis, the beam will receive transverse kicks, causing it to deviate from the undulator axis. Beam based alignment will be used to move the quadrupoles onto a straight line, but an initial, conventional alignment must place the quadrupole centers on a straight line to 100 {micro}m. In the fiducialization stepmore » of the initial alignment, the position of the center of the quadrupole is measured relative to tooling balls on the outside of the quadrupole. The alignment crews then use the tooling balls to place the magnet in the tunnel. The required error on the location of the quadrupole center relative to the tooling balls must be less than 25 {micro}m. In this note, we analyze a system under construction for the quadrupole fiducialization. The system uses the vibrating wire technique to position a wire onto the quadrupole magnetic axis. The wire position is then related to tooling balls using wire position detectors. The tooling balls on the wire position detectors are finally related to tooling balls on the quadrupole to perform the fiducialization. The total 25 {micro}m fiducialization error must be divided between these three steps. The wire must be positioned onto the quadrupole magnetic axis to within 10 {micro}m, the wire position must be measured relative to tooling balls on the wire position detectors to within 15 {micro}m, and tooling balls on the wire position detectors must be related to tooling balls on the quadrupole to within 10 {micro}m. The techniques used in these three steps will be discussed. The note begins by discussing various quadrupole fiducialization techniques used in the past and discusses why the vibrating wire technique is our method of choice. We then give an overview of the measurement system showing how the vibrating wire is positioned onto the quadrupole axis, how the wire position detectors locate the wire relative to tooling balls without touching the wire, and how the tooling ball positions are all measured. The novel feature of this system is the vibrating wire which we discuss in depth. We analyze the wire dynamics and calculate the expected sensitivity of the system. The note should be an aid in debugging the system by providing calculations to compare measurements to.« less

Multipolar Kondo effect in a S10-P32 mixture of 173Yb atoms

NASA Astrophysics Data System (ADS)

Kuzmenko, Igor; Kuzmenko, Tetyana; Avishai, Yshai; Jo, Gyu-Boong

2018-02-01

Whereas in the familiar Kondo effect the exchange interaction is dipolar, there are systems in which the exchange interaction is multipolar, as has been realized in a recent experiment. Here, we study multipolar Kondo effect in a Fermi gas of cold 173Yb atoms. Making use of different ac polarizabilities of the electronic ground state Yb (S10 ) and the long-lived metastable state Yb*(P32 ), it is suggested that the latter atoms can be localized and serve as a dilute concentration of magnetic impurities while the former ones remain itinerant. The exchange mechanism between the itinerant Yb and the localized Yb* atoms is analyzed and shown to be antiferromagnetic. The quadrupole and octupole interactions act to enhance the Kondo temperature TK that is found to be experimentally accessible. The bare exchange Hamiltonian needs to be decomposed into dipole (d), quadrupole (q), and octupole (o) interactions in order to retain its form under renormalization group (RG) analysis, in which the corresponding exchange constants (λd,λq, and λo) flow independently. Numerical solution of the RG scaling equations reveals a few finite fixed points. Arguments are presented that the Fermi-liquid fixed point at low temperature is unstable, indicating that the impurity is overscreened, which suggests a non-Fermi-liquid phase. The impurity contributions to the specific heat, entropy, and the magnetic susceptibility are calculated in the weak coupling regime (T ≫TK ), and are compared with the analogous results obtained for the standard case of dipolar exchange interaction (the s -d Hamiltonian).

Supersonic Quadrupole Noise Theory for High-Speed Helicopter Rotors

NASA Technical Reports Server (NTRS)

Farassat, F.; Brentner, Kenneth S.

1997-01-01

High-speed helicopter rotor impulsive noise prediction is an important problem of aeroacoustics. The deterministic quadrupoles have been shown to contribute significantly to high-speed impulsive (HSI) noise of rotors, particularly when the phenomenon of delocalization occurs. At high rotor-tip speeds, some of the quadrupole sources lie outside the sonic circle and move at supersonic speed. Brentner has given a formulation suitable for efficient prediction of quadrupole noise inside the sonic circle. In this paper, we give a simple formulation based on the acoustic analogy that is valid for both subsonic and supersonic quadrupole noise prediction. Like the formulation of Brentner, the model is exact for an observer in the far field and in the rotor plane and is approximate elsewhere. We give the full analytic derivation of this formulation in the paper. We present the method of implementation on a computer for supersonic quadrupoles using marching cubes for constructing the influence surface (Sigma surface) of an observer space- time variable (x; t). We then present several examples of noise prediction for both subsonic and supersonic quadrupoles. It is shown that in the case of transonic flow over rotor blades, the inclusion of the supersonic quadrupoles improves the prediction of the acoustic pressure signature. We show the equivalence of the new formulation to that of Brentner for subsonic quadrupoles. It is shown that the regions of high quadrupole source strength are primarily produced by the shock surface and the flow over the leading edge of the rotor. The primary role of the supersonic quadrupoles is to increase the width of a strong acoustic signal.

Electron configuration and hydrogen-bonding pattern in several thymine and uracil analogues studied by 1H-14N NQDR and DFT/QTAIM.

PubMed

Seliger, Janez; Žagar, Veselko; Latosińska, Magdalena; Latosińska, Jolanta Natalia

2012-08-02

Some thio- and aza-derivatives of natural nucleobases uracil and thymine: 2-thiouracil, 4-thiouracil, 6-methyl-2-thiouracil, 6-azauracil, and 6-aza-2-thiothymine have been studied experimentally in solid state by (1)H-(14)N NMR-NQR double resonance (NQDR) and theoretically by the Density Functional Theory (DFT)/Quantum Theory of Atoms in Molecules (QTAIM). The (14)N resonance frequencies have been measured at 173 and 295 K and assigned to particular nitrogen sites (-N═ and -NH-). The temperature factor has been found negligible. The changes in the molecular skeletons, electric charge distribution, intermolecular interactions pattern, and molecular aggregations caused by oxygen replacement with sulfur and carbon replacement with nitrogen are discussed in detail. Correlations between all the principal components of the (14)N quadrupole coupling tensor have been found helpful in the search for the experimental (14)N NQR frequencies, their assignment to a particular nitrogen positions and estimation of the strength of the inter- and intramolecular interactions. The variation in the NQR parameters have been mainly related to the variation in the population of π-electron orbital. For thiouracil derivatives a general trend is that the stronger the hydrogen bond is, the lower is the asymmetry parameter, while for thymine and 6-aza-2-thiotymine, the opposite relation holds. Differences in correlations of the principal components of the (14)N quadrupole coupling tensor at the amino and iminonitrogen positions in heterocyclic rings are discussed. The effect of C→H and C→N substitution at the amino nitrogen position and C→N substitution at the iminonitrogen position on the quadrupole coupling tensor is analyzed. This study also demonstrates the advantages of combining NQR and DFT/QTAIM to predict an unsolved crystalline structure of 4-thiouracil.

Evolution of the Carter constant for inspirals into a black hole: Effect of the black hole quadrupole

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

Flanagan, Eanna E.; Laboratory for Elementary Particle Physics, Cornell University, Ithaca, New York 14853; Hinderer, Tanja

2007-06-15

We analyze the effect of gravitational radiation reaction on generic orbits around a body with an axisymmetric mass quadrupole moment Q to linear order in Q, to the leading post-Newtonian order, and to linear order in the mass ratio. This system admits three constants of the motion in absence of radiation reaction: energy, angular momentum along the symmetry axis, and a third constant analogous to the Carter constant. We compute instantaneous and time-averaged rates of change of these three constants. For a point particle orbiting a black hole, Ryan has computed the leading order evolution of the orbit's Carter constant,more » which is linear in the spin. Our result, when combined with an interaction quadratic in the spin (the coupling of the black hole's spin to its own radiation reaction field), gives the next to leading order evolution. The effect of the quadrupole, like that of the linear spin term, is to circularize eccentric orbits and to drive the orbital plane towards antialignment with the symmetry axis. In addition we consider a system of two point masses where one body has a single mass multipole or current multipole of order l. To linear order in the mass ratio, to linear order in the multipole, and to the leading post-Newtonian order, we show that there does not exist an analog of the Carter constant for such a system (except for the cases of an l=1 current moment and an l=2 mass moment). Thus, the existence of the Carter constant in Kerr depends on interaction effects between the different multipoles. With mild additional assumptions, this result falsifies the conjecture that all vacuum, axisymmetric spacetimes possess a third constant of the motion for geodesic motion.« less

The influence of quadrupole sources in the boundary layer and wake of a blade on helicopter rotor noise

NASA Technical Reports Server (NTRS)

Farassat, F.; Brentner, Kenneth S.

1991-01-01

It is presently noted that, for an observer in or near the plane containing a helicopter rotor disk, and in the far field, part of the volume quadrupole sources, and the blade and wake surface quadrupole sources, completely cancel out. This suggests a novel quadrupole source description for the Ffowcs Williams-Hawkings equation which retain quadrupoles with axes parallel to the rotor disk; in this case, the volume and shock surface sourse terms are dominant.

Ab initio correlated calculations of rare-gas dimer quadrupoles

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

Donchev, Alexander G.

2007-10-15

This paper reports ab initio calculations of rare gas (RG=Kr, Ar, Ne, and He) dimer quadrupoles at the second order of Moeller-Plesset perturbation theory (MP2). The study reveals the crucial role of the dispersion contribution to the RG{sub 2} quadrupole in the neighborhood of the equilibrium dimer separation. The magnitude of the dispersion quadrupole is found to be much larger than that predicted by the approximate model of Hunt. As a result, the total MP2 quadrupole moment is significantly smaller than was assumed in virtually all previous related studies. An analytical model for the distance dependence of the RG{sub 2}more » quadrupole is proposed. The model is based on the effective-electron approach of Jansen, but replaces the original Gaussian approximation to the electron density in an RG atom by an exponential one. The role of the nonadditive contribution in RG{sub 3} quadrupoles is discussed.« less

The quadrupole moments of Cd and Zn isotopes - an apology

NASA Astrophysics Data System (ADS)

Haas, H.; Barbosa, M. B.; Correia, J. G.

2016-12-01

In 2010 we presented an update of the nuclear quadrupole moments (Q) for the Cd and Zn isotopes, based essentially on straightforward density functional (DF) calculations (H. Haas and J.G. Correia, Hyperfine Interact 198, 133-137 (2010)). It has been apparent for some years that the standard DF procedure obviously fails, however, to reproduce the known electric-field gradient (EFG) for various systems, typical cases being Cu2O, As and Sb, and the solid halogens. Recently a cure for this deficiency has been found in the hybrid DF technique. This method is now applied to solid Cd and Zn, and the resultant quadrupole moments are about 15 % smaller than in our earlier report. Also nuclear systematics, using the recently revised values of Q for the long-lived 11/2 isomers in111Cd to129Cd, together with earlier PAD data for107,109Cd, leads to the same conclusion. In addition, EFG calculations for the cadmium dimethyl molecule further support the new values: Q(111Cd, 5/2+) = .683(20) b, Q(67Zn, gs) = .132(5) b. This implies, that the value for the atomic EFG in the 3it {P}1 state of Zn must be revised, as it has been for Cd.

The quadrupole model for rigid-body gravity simulations

NASA Astrophysics Data System (ADS)

Dobrovolskis, Anthony R.; Korycansky, D. G.

2013-07-01

We introduce two new models for gravitational simulations of systems of non-spherical bodies, such as comets and asteroids. In both models, one body (the "primary") may be represented by any convenient means, to arbitrary accuracy. In our first model, all of the other bodies are represented by small gravitational "molecules" consisting of a few point masses, rigidly linked together. In our second model, all of the other bodies are treated as point quadrupoles, with gravitational potentials including spherical harmonic terms up to the third degree (rather than only the first degree, as for ideal spheres or point masses). This quadrupole formulation may be regarded as a generalization of MacCullagh's approximation. Both models permit the efficient calculation of the interaction energy, the force, and the torque acting on a small body in an arbitrary external gravitational potential. We test both models for the cases of a triaxial ellipsoid, a rectangular parallelepiped, and "duplex" combinations of two spheres, all in a point-mass potential. These examples were chosen in order to compare the accuracy of our technique with known analytical results, but the ellipsoid and duplex are also useful models for comets and asteroids. We find that both approaches show significant promise for more efficient gravitational simulations of binary asteroids, for example. An appendix also describes the duplex model in detail.

Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

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

Samin, Adib; Lahti, Erik; Zhang, Jinsuo, E-mail: zhang.3558@osu.edu

Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extendedmore » to cases that are more general and may be useful for benchmarking purposes.« less

Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method

NASA Astrophysics Data System (ADS)

Zhou, Zhenhuan; Li, Yuejie; Fan, Junhai; Rong, Dalun; Sui, Guohao; Xu, Chenghui

2018-05-01

A new Hamiltonian-based approach is presented for finding exact solutions for transverse vibrations of double-nanobeam-systems embedded in an elastic medium. The continuum model is established within the frameworks of the symplectic methodology and the nonlocal Euler-Bernoulli and Timoshenko beam beams. The symplectic eigenfunctions are obtained after expressing the governing equations in a Hamiltonian form. Exact frequency equations, vibration modes and displacement amplitudes are obtained by using symplectic eigenfunctions and end conditions. Comparisons with previously published work are presented to illustrate the accuracy and reliability of the proposed method. The comprehensive results for arbitrary boundary conditions could serve as benchmark results for verifying numerically obtained solutions. In addition, a study on the difference between the nonlocal beam and the nonlocal plate is also included.

Data-driven discovery of Koopman eigenfunctions using deep learning

NASA Astrophysics Data System (ADS)

Lusch, Bethany; Brunton, Steven L.; Kutz, J. Nathan

2017-11-01

Koopman operator theory transforms any autonomous non-linear dynamical system into an infinite-dimensional linear system. Since linear systems are well-understood, a mapping of non-linear dynamics to linear dynamics provides a powerful approach to understanding and controlling fluid flows. However, finding the correct change of variables remains an open challenge. We present a strategy to discover an approximate mapping using deep learning. Our neural networks find this change of variables, its inverse, and a finite-dimensional linear dynamical system defined on the new variables. Our method is completely data-driven and only requires measurements of the system, i.e. it does not require derivatives or knowledge of the governing equations. We find a minimal set of approximate Koopman eigenfunctions that are sufficient to reconstruct and advance the system to future states. We demonstrate the method on several dynamical systems.

Parallel momentum input by tangential neutral beam injections in stellarator and heliotron plasmas

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

Nishimura, S., E-mail: nishimura.shin@lhd.nifs.ac.jp; Nakamura, Y.; Nishioka, K.

The configuration dependence of parallel momentum inputs to target plasma particle species by tangentially injected neutral beams is investigated in non-axisymmetric stellarator/heliotron model magnetic fields by assuming the existence of magnetic flux-surfaces. In parallel friction integrals of the full Rosenbluth-MacDonald-Judd collision operator in thermal particles' kinetic equations, numerically obtained eigenfunctions are used for excluding trapped fast ions that cannot contribute to the friction integrals. It is found that the momentum inputs to thermal ions strongly depend on magnetic field strength modulations on the flux-surfaces, while the input to electrons is insensitive to the modulation. In future plasma flow studies requiringmore » flow calculations of all particle species in more general non-symmetric toroidal configurations, the eigenfunction method investigated here will be useful.« less

Wigner functions for fermions in strong magnetic fields

NASA Astrophysics Data System (ADS)

Sheng, Xin-li; Rischke, Dirk H.; Vasak, David; Wang, Qun

2018-02-01

We compute the covariant Wigner function for spin-(1/2) fermions in an arbitrarily strong magnetic field by exactly solving the Dirac equation at non-zero fermion-number and chiral-charge densities. The Landau energy levels as well as a set of orthonormal eigenfunctions are found as solutions of the Dirac equation. With these orthonormal eigenfunctions we construct the fermion field operators and the corresponding Wigner-function operator. The Wigner function is obtained by taking the ensemble average of the Wigner-function operator in global thermodynamical equilibrium, i.e., at constant temperature T and non-zero fermion-number and chiral-charge chemical potentials μ and μ_5, respectively. Extracting the vector and axial-vector components of the Wigner function, we reproduce the currents of the chiral magnetic and separation effect in an arbitrarily strong magnetic field.

Using Nested Contractions and a Hierarchical Tensor Format To Compute Vibrational Spectra of Molecules with Seven Atoms.

PubMed

Thomas, Phillip S; Carrington, Tucker

2015-12-31

We propose a method for solving the vibrational Schrödinger equation with which one can compute hundreds of energy levels of seven-atom molecules using at most a few gigabytes of memory. It uses nested contractions in conjunction with the reduced-rank block power method (RRBPM) described in J. Chem. Phys. 2014, 140, 174111. Successive basis contractions are organized into a tree, the nodes of which are associated with eigenfunctions of reduced-dimension Hamiltonians. The RRBPM is used recursively to compute eigenfunctions of nodes in bases of products of reduced-dimension eigenfunctions of nodes with fewer coordinates. The corresponding vectors are tensors in what is called CP-format. The final wave functions are therefore represented in a hierarchical CP-format. Computational efficiency and accuracy are significantly improved by representing the Hamiltonian in the same hierarchical format as the wave function. We demonstrate that with this hierarchical RRBPM it is possible to compute energy levels of a 64-D coupled-oscillator model Hamiltonian and also of acetonitrile (CH3CN) and ethylene oxide (C2H4O), for which we use quartic potentials. The most accurate acetonitrile calculation uses 139 MB of memory and takes 3.2 h on a single processor. The most accurate ethylene oxide calculation uses 6.1 GB of memory and takes 14 d on 63 processors. The hierarchical RRBPM shatters the memory barrier that impedes the calculation of vibrational spectra.

Cd-binding to model membranes

NASA Astrophysics Data System (ADS)

Geszner, R.; Saibene, S.; Butz, T.; Lerf, A.

1990-08-01

The binding of Cd2+ to the model membranes Di-myristoyl L-α-phosphatidic acid (DMPA) and Di-myristoyl L-α-phosphatidylcholine (DMPC) was studied by time differential perturbed angular correlation (TDPAC) on111mCd, via its nuclear quadrupole interaction. Whereas Cd2+ does not bind to the neutral DMPC, it binds to charged DMPA up to a 0.8∶1 Cd/lipid ratio.

Fluorine Scan of Inhibitors of the Cysteine Protease Human Cathepsin L: Dipolar and Quadrupolar Effects in the π-Stacking of Fluorinated Phenyl Rings on Peptide Amide Bonds.

PubMed

Giroud, Maude; Harder, Michael; Kuhn, Bernd; Haap, Wolfgang; Trapp, Nils; Schweizer, W Bernd; Schirmeister, Tanja; Diederich, François

2016-05-19

The π-stacking of fluorinated benzene rings on protein backbone amide groups was investigated, using a dual approach comprising enzyme-ligand binding studies complemented by high-level quantum chemical calculations. In the experimental study, the phenyl substituent of triazine nitrile inhibitors of human cathepsin L (hCatL), which stacks onto the peptide amide bond Gly67-Gly68 at the entrance of the S3 pocket, was systematically fluorinated, and differences in inhibitory potency were measured in a fluorimetric assay. Binding affinity is influenced by lipophilicity (clog P), the dipole and quadrupole moments of the fluorinated rings, but also by additional interactions of the introduced fluorine atoms with the local environment of the pocket. Generally, the higher the degree of fluorination, the better the binding affinities. Gas phase calculations strongly support the contributions of the molecular quadrupole moments of the fluorinated phenyl rings to the π-stacking interaction with the peptide bond. These findings provide useful guidelines for enhancing π-stacking on protein amide fragments. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Calculations with spectroscopic accuracy for energies, transition rates, hyperfine interaction constants, and Landé gJ-factors in nitrogen-like Kr XXX

NASA Astrophysics Data System (ADS)

Wang, K.; Li, S.; Jönsson, P.; Fu, N.; Dang, W.; Guo, X. L.; Chen, C. Y.; Yan, J.; Chen, Z. B.; Si, R.

2017-01-01

Extensive self-consistent multi-configuration Dirac-Fock (MCDF) calculations and second-order many-body perturbation theory (MBPT) calculations are performed for the lowest 272 states belonging to the 2s22p3, 2s2p4, 2p5, 2s22p23l, and 2s2p33l (l=s, p, d) configurations of N-like Kr XXX. Complete and consistent data sets of level energies, wavelengths, line strengths, oscillator strengths, lifetimes, AJ, BJ hyperfine interaction constants, Landé gJ-factors, and electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), magnetic quadrupole (M2) transition rates among all these levels are given. The present MCDF and MBPT results are compared with each other and with other available experimental and theoretical results. The mean relative difference between our two sets of level energies is only about 0.003% for these 272 levels. The accuracy of the present calculations are high enough to facilitate identification of many observed spectral lines. These accurate data can be served as benchmark for other calculations and can be useful for fusion plasma research and astrophysical applications.

Hydrophilic interaction ultra-performance liquid chromatography coupled with triple-quadrupole tandem mass spectrometry for highly rapid and sensitive analysis of underivatized amino acids in functional foods.

PubMed

Zhou, Guisheng; Pang, Hanqing; Tang, Yuping; Yao, Xin; Mo, Xuan; Zhu, Shaoqing; Guo, Sheng; Qian, Dawei; Qian, Yefei; Su, Shulan; Zhang, Li; Jin, Chun; Qin, Yong; Duan, Jin-ao

2013-05-01

This work presented a new analytical methodology based on hydrophilic interaction ultra-performance liquid chromatography coupled with triple-quadrupole tandem mass spectrometry in multiple-reaction monitoring mode for analysis of 24 underivatized free amino acids (FAAs) in functional foods. The proposed method was first reported and validated by assessing the matrix effects, linearity, limit of detections and limit of quantifications, precision, repeatability, stability and recovery of all target compounds, and it was used to determine the nutritional substances of FAAs in ginkgo seeds and further elucidate the nutritional value of this functional food. The result showed that ginkgo seed turned out to be a good source of FAAs with high levels of several essential FAAs and to have a good nutritional value. Furthermore, the principal component analysis was performed to classify the ginkgo seed samples on the basis of 24 FAAs. As a result, the samples could be mainly clustered into three groups, which were similar to areas classification. Overall, the presented method would be useful for the investigation of amino acids in edible plants and agricultural products.

Comparison of conventional and novel quadrupole drift tube magnets inspired by Klaus Halbach

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

Feinberg, B.

1995-02-01

Quadrupole drift tube magnets for a heavy-ion linac provide a demanding application of magnet technology. A comparison is made of three different solutions to the problem of providing an adjustable high-field-strength quadrupole magnet in a small volume. A conventional tape-wound electromagnet quadrupole magnet (conventional) is compared with an adjustable permanent-magnet/iron quadrupole magnet (hybrid) and a laced permanent-magnet/iron/electromagnet (laced). Data is presented from magnets constructed for the SuperHILAC heavy-ion linear accelerator, and conclusions are drawn for various applications.

Quantum phases of quadrupolar Fermi gases in coupled one-dimensional systems

NASA Astrophysics Data System (ADS)

Huang, Wen-Min; Lahrz, M.; Mathey, L.

2014-01-01

Following the recent proposal to create quadrupolar gases [Bhongale et al., Phys. Rev. Lett. 110, 155301 (2013), 10.1103/PhysRevLett.110.155301], we investigate what quantum phases can be created in these systems in one dimension. We consider a geometry of two coupled one-dimensional (1D) systems, and derive the quantum phase diagram of ultracold fermionic atoms interacting via quadrupole-quadrupole interactions within a Tomonaga-Luttinger-liquid framework. We map out the phase diagram as a function of the distance between the two tubes and the angle between the direction of the tubes and the quadrupolar moments. The latter can be controlled by an external field. We show that there are two magic angles θB,1c and θB,2c between 0 and π /2, where the intratube quadrupolar interactions vanish and change signs. Adopting a pseudospin language with regard to the two 1D systems, the system undergoes a spin-gap transition and displays a zigzag density pattern, above θB,2c and below θB,1c. Between the two magic angles, we show that polarized triplet superfluidity and a planar spin-density-wave order compete with each other. The latter corresponds to a bond-order solid in higher dimensions. We demonstrate that this order can be further stabilized by applying a commensurate periodic potential along the tubes.

Excitation of transverse dipole and quadrupole modes in a pure ion plasma in a linear Paul trap to study collective processes in intense beams

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

Gilson, Erik P.; Davidson, Ronald C.; Efthimion, Philip C.

Transverse dipole and quadrupole modes have been excited in a one-component cesium ion plasma trapped in the Paul Trap Simulator Experiment (PTSX) in order to characterize their properties and understand the effect of their excitation on equivalent long-distance beam propagation. The PTSX device is a compact laboratory Paul trap that simulates the transverse dynamics of a long, intense charge bunch propagating through an alternating-gradient transport system by putting the physicist in the beam's frame of reference. A pair of arbitrary function generators was used to apply trapping voltage waveform perturbations with a range of frequencies and, by changing which electrodesmore » were driven with the perturbation, with either a dipole or quadrupole spatial structure. The results presented in this paper explore the dependence of the perturbation voltage's effect on the perturbation duration and amplitude. Perturbations were also applied that simulate the effect of random lattice errors that exist in an accelerator with quadrupole magnets that are misaligned or have variance in their field strength. The experimental results quantify the growth in the equivalent transverse beam emittance that occurs due to the applied noise and demonstrate that the random lattice errors interact with the trapped plasma through the plasma's internal collective modes. Coherent periodic perturbations were applied to simulate the effects of magnet errors in circular machines such as storage rings. The trapped one component plasma is strongly affected when the perturbation frequency is commensurate with a plasma mode frequency. The experimental results, which help to understand the physics of quiescent intense beam propagation over large distances, are compared with analytic models.« less

Large-scale shell-model calculations for 32-39P isotopes

NASA Astrophysics Data System (ADS)

Srivastava, P. C.; Hirsch, J. G.; Ermamatov, M. J.; Kota, V. K. B.

2012-10-01

In this work, the structure of 32-39P isotopes is described in the framework of stateof-the-art large-scale shell-model calculations, employing the code ANTOINE with three modern effective interactions: SDPF-U, SDPF-NR and the extended pairing plus quadrupole-quadrupoletype forces with inclusion of monopole interaction (EPQQM). Protons are restricted to fill the sd shell, while neutrons are active in the sd - pf valence space. Results for positive and negative level energies and electromagnetic observables are compared with the available experimental data.

Hexadecapolar Colloids

DOE PAGES

Senyuk, Bohdan; Puls, Owen; Tovkach, Oleh M.; ...

2016-02-11

Outermost occupied electron shells of chemical elements can have symmetries resembling that of monopoles, dipoles, quadrupoles and octupoles corresponding to filled s-, p-, d- and forbitals. Theoretically, elements with hexadecapolar outer shells could also exist, but none of the known elements have filled g-orbitals. On the other hand, the research paradigm of ‘colloidal atoms’ displays complexity of particle behaviour exceeding that of atomic counterparts, which is driven by DNA functionalization, geometric shape and topology and weak external stimuli. We describe elastic hexadecapoles formed by polymer microspheres dispersed in a liquid crystal, a nematic fluid of orientationally ordered molecular rods. Becausemore » of conically degenerate boundary conditions, the solid microspheres locally perturb the alignment of the nematic host, inducing hexadecapolar distortions that drive anisotropic colloidal interactions. We uncover physical underpinnings of formation of colloidal elastic hexadecapoles and report the ensuing bonding inaccessible to elastic dipoles, quadrupoles and other nematic colloids studied previously.« less

Higher-order dielectrophoretic effects: levitation at a field null.

PubMed

Washizu, M; Jones, T B; Kaler, K V

1993-08-20

Experiments with certain new micro-electrode structures used to achieve passive dielectrophoretic levitation of small particles and biological cells reveal a pronounced size-dependent effect not anticipated by the conventional dipole-based model. The conventional theory fails to predict this size effect because it neglects higher-order moments such as the quadrupole, hexapole, and octupole. These higher-order moments are in fact responsible for the levitation force achieved by azimuthally periodic electrode structures because, in such geometries, the electric field is zero along the axis so that the induced dipole moment must be zero. For example, the planar quadrupole levitates particles passively along the central axis through the interaction of its field with the induced quadrupolar moment of the particle. The size effect reported with this structure is readily explained in terms of this quadrupolar component of the ponderomotive force exerted on the particle.

Formation of a Fluorous/Organic Biphasic Supramolecular Octopus Assembly for Enhanced Porphyrin Phosphorescence in Air

DOE PAGES

Yang, Chi; Arvapally, Ravi K.; Tekarli, Sammer M.; ...

2015-03-03

The trinuclear triangle-shaped system [tris{3,5-bis(heptafluoropropyl)-1,2,4-triazolatosilver(I)}] (1) and the multi-armed square-shaped metalloporphyrin PtOEP or the free porphyrin base H2OEP serve as excellent octopus hosts (OEP=2,3,7,8,12,13,17,18-octaethyl-21H,23H-porphine). Coupling of the fluorous/organic molecular octopi 1 and H2OEP or PtOEP by strong quadrupole-quadrupole and metal- interactions affords the supramolecular assemblies [1PtOEP] or [1H(2)OEP] (2a), which feature nanoscopic cavities surrounding the upper triangular and lower square cores. The fluorous/organic biphasic configuration of [1PtOEP] leads to an increase in the phosphorescence of PtOEP under ambient conditions. Guest molecules can be included in the biphasic double-octopus assembly in three different site-selective modes.

Fourier transform microwave spectroscopy of the SiCl+ ion

NASA Astrophysics Data System (ADS)

Tanaka, Keiichi; Harada, Kensuke; Cabezas, Carlos; Endo, Yasuki

2018-03-01

Fourier transform microwave spectra for the J = 1 ← 0 and 2 ← 1 rotational transitions of the SiCl+ ion were observed for two isotopologues (35 Cl and 37 Cl) in the ground and the first excited vibrational states of the ground 1Σ+ electronic state. Thanks to the high resolution of the FTMW spectrometer, hyperfine structures due to the quadrupole moment of the chlorine nucleus and the nuclear spin-rotation interaction were fully resolved. The observed FTMW spectra were combined with previously reported MMW and diode laser spectra in an analysis to determine the mass-independent Dunham coefficients Uk,l as well as a mass scaling parameter Δ01Cl = - 0.856 (30) . The equilibrium bond length of SiCl+ determined is re = 1.9439729 (10) Å and the nuclear quadrupole coupling constant of Si35 Cl+ is eQqe = - 11.8788 (23) MHz.

Benchmarking Atomic Data for Astrophysics: Be-like Ions between B II and Ne VII

NASA Astrophysics Data System (ADS)

Wang, Kai; Chen, Zhan Bin; Zhang, Chun Yu; Si, Ran; Jönsson, Per; Hartman, Henrik; Gu, Ming Feng; Chen, Chong Yang; Yan, Jun

2018-02-01

Large-scale self-consistent multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction calculations are reported for the n≤slant 6 levels in Be-like ions from B II to Ne VII. Effects from electron correlation are taken into account by means of large expansions in terms of a basis of configuration state functions, and a complete and accurate data set of excitation energies; lifetimes; wavelengths; electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole line strengths; transition rates; and oscillator strengths for these levels is provided for each ion. Comparisons are made with available experimental and theoretical results. The uncertainty of excitation energies is assessed to be 0.01% on average, which makes it possible to find and rule out misidentifications and aid new line identifications involving high-lying levels in astrophysical spectra. The complete data set is also useful for modeling and diagnosing astrophysical plasmas.

Measuring the Magnetic Center Behavior of an ILC Superconducting Quadrupole Prototype

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

Spencer, Cherrill M.; Adolphsen, Chris; Berndt, Martin

2011-02-07

The main linacs of the proposed International Linear Collider (ILC) consist of superconducting cavities operated at 2K. The accelerating cavities are contained in a contiguous series of cryogenic modules that also house the main linac quadrupoles, thus the quadrupoles also need to be superconducting. In an early ILC design, these magnets are about 0.6 m long, have cos (2{theta}) coils, and operate at constant field gradients up to 60 T/m. In order to preserve the small beam emittances in the ILC linacs, the e+ and e- beams need to traverse the quadrupoles near their magnetic centers. A quadrupole shunting techniquemore » is used to measure the quadrupole alignment with the beams; this process requires the magnetic centers move by no more than about 5 micrometers when their strength is changed. To determine if such tight stability is achievable in a superconducting quadrupole, we at SLAC measured the magnetic center motions in a prototype ILC quadrupole built at CIEMAT in Spain. A rotating coil technique was used with a better than 0.1 micrometer precision in the relative field center position, and less than a 2 micrometer systematic error over 30 minutes. This paper describes the warm-bore cryomodule that houses the quadrupole in its Helium vessel, the magnetic center measurement system, the measured center data and strength and harmonics magnetic data.« less

Miniature micromachined quadrupole mass spectrometer array and method of making the same

NASA Technical Reports Server (NTRS)

Chutjian, Ara (Inventor); Brennen, Reid A. (Inventor); Hecht, Michael (Inventor); Wiberg, Dean (Inventor); Orient, Otto (Inventor)

2001-01-01

The present invention provides a quadrupole mass spectrometer and an ion filter for use in the quadrupole mass spectrometer. The ion filter includes a thin patterned layer including a two-dimensional array of poles forming one or more quadrupoles. The patterned layer design permits the use of very short poles and with a very dense spacing of the poles, so that the ion filter may be made very small. Also provided is a method for making the ion filter and the quadrupole mass spectrometer. The method involves forming the patterned layer of the ion filter in such a way that as the poles of the patterned layer are formed, they have the relative positioning and alignment for use in a final quadrupole mass spectrometer device.

Miniature micromachined quadrupole mass spectrometer array and method of making the same

NASA Technical Reports Server (NTRS)

Fuerstenau, Stephen D. (Inventor); Yee, Karl Y. (Inventor); Chutjian, Ara (Inventor); Orient, Otto J. (Inventor); Rice, John T. (Inventor)

2002-01-01

The present invention provides a quadrupole mass spectrometer and an ion filter, or pole array, for use in the quadrupole mass spectrometer. The ion filter includes a thin patterned layer including a two-dimensional array of poles forming one or more quadrupoles. The patterned layer design permits the use of very short poles and with a very dense spacing of the poles, so that the ion filter may be made very small. Also provided is a method for making the ion filter and the quadrupole mass spectrometer. The method involves forming the patterned layer of the ion filter in such a way that as the poles of the patterned layer are formed, they have the relative positioning and alignment for use in a final quadrupole mass spectrometer device.

Miniature micromachined quadrupole mass spectrometer array and method of making the same

NASA Technical Reports Server (NTRS)

Chutjian, Ara (Inventor); Rice, John T. (Inventor); Fuerstenau, Stephen D. (Inventor); Orient, Otto J. (Inventor); Yee, Karl Y. (Inventor)

2000-01-01

The present invention provides a quadrupole mass spectrometer and an ion filter, or pole array, for use in the quadrupole mass spectrometer. The ion filter includes a thin patterned layer including a two-dimensional array of poles forming one or more quadrupoles. The patterned layer design permits the use of very short poles and with a very dense spacing of the poles, so that the ion filter may be made very small. Also provided is a method for making the ion filter and the quadrupole mass spectrometer. The method involves forming the patterned layer of the ion filter in such a way that as the poles of the patterned layer are formed, they have the relative positioning and alignment for use in a final quadrupole mass spectrometer device.

Miniature micromachined quadrupole mass spectrometer array and method of making the same

NASA Technical Reports Server (NTRS)

Yee, Karl Y. (Inventor); Fuerstenau, Stephen D. (Inventor); Orient, Otto J. (Inventor); Rice, John T. (Inventor); Chutjian, Ara (Inventor)

2001-01-01

The present invention provides a quadrupole mass spectrometer and an ion filter, or pole array, for use in the quadrupole mass spectrometer. The ion filter includes a thin patterned layer including a two-dimensional array of poles forming one or more quadrupoles. The patterned layer design permits the use of very short poles and with a very dense spacing of the poles, so that the ion filter may be made very small. Also provided is a method for making the ion filter and the quadrupole mass spectrometer. The method involves forming the patterned layer of the ion filter in such a way that as the poles of the patterned layer are formed, they have the relative positioning and alignment for use in a final quadrupole mass spectrometer device.

Miniature micromachined quadrupole mass spectrometer array and method of making the same

NASA Technical Reports Server (NTRS)

Hecht, Michael (Inventor); Wiberg, Dean (Inventor); Orient, Otto (Inventor); Brennen, Reid A. (Inventor); Chutjian, Ara (Inventor)

2001-01-01

The present invention provides a quadrupole mass spectrometer and an ion filter for use in the quadrupole mass spectrometer. The ion filter includes a thin patterned layer including a two-dimensional array of poles forming one or more quadrupoles. The patterned layer design permits the use of very short poles and with a very dense spacing of the poles, so that the ion filter may be made very small. Also provided is a method for making the ion filter and the quadrupole mass spectrometer. The method involves forming the patterned layer of the ion filter in such a way that as the poles of the patterned layer are formed, they have the relative positioning and aligrnent for use in a final quadrupole mass spectrometer device.

Miniature micromachined quadrupole mass spectrometer array and method of making the same

NASA Technical Reports Server (NTRS)

Orient, Otto (Inventor); Wiberg, Dean (Inventor); Brennen, Reid A. (Inventor); Hecht, Michael (Inventor); Chutjian, Ara (Inventor)

2000-01-01

The present invention provides a quadrupole mass spectrometer and an ion filter for use in the quadrupole mass spectrometer. The ion filter includes a thin patterned layer including a two-dimensional array of poles forming one or more quadrupoles. The patterned layer design permits the use of very short poles and with a very dense spacing of the poles, so that the ion filter may be made very small. Also provided is a method for making the ion filter and the quadrupole mass spectrometer. The method involves forming the patterned layer of the ion filter in such a way that as the poles of the patterned layer are formed, they have the relative positioning and alignment for use in a final quadrupole mass spectrometer device.

Two-dimensional quantum ring in a graphene layer in the presence of a Aharonov–Bohm flux

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

Amaro Neto, José; Bueno, M.J.; Furtado, Claudio, E-mail: furtado@fisica.ufpb.br

2016-10-15

In this paper we study the relativistic quantum dynamics of a massless fermion confined in a quantum ring. We use a model of confining potential and introduce the interaction via Dirac oscillator coupling, which provides ring confinement for massless Dirac fermions. The energy levels and corresponding eigenfunctions for this model in graphene layer in the presence of Aharonov–Bohm flux in the centre of the ring and the expression for persistent current in this model are derived. We also investigate the model for quantum ring in graphene layer in the presence of a disclination and a magnetic flux. The energy spectrummore » and wave function are obtained exactly for this case. We see that the persistent current depends on parameters characterizing the topological defect.« less

Transverse-rapidity yt dependence of the nonjet azimuth quadrupole from 62- and 200-GeV Au-Au collisions

NASA Astrophysics Data System (ADS)

Kettler, David T.; Prindle, Duncan J.; Trainor, Thomas A.

2015-06-01

Previous measurements of a quadrupole component of azimuth correlations denoted by symbol v2 have been interpreted to represent elliptic flow, a hydrodynamic phenomenon conjectured to play a major role in noncentral nucleus-nucleus collisions. v2 measurements provide the main support for conclusions that a "perfect liquid" is formed in heavy-ion collisions at the Relativistic Heavy Ion Collider. However, conventional v2 methods based on one-dimensional (1D) azimuth correlations give inconsistent results and may include a jet contribution. In some cases the data trends appear to be inconsistent with hydrodynamic interpretations. In this study we distinguish several components of 2D angular correlations and isolate a nonjet (NJ) azimuth quadrupole denoted by v2{2D} . We establish systematic variations of the NJ quadrupole on yt, centrality, and collision energy. We adopt transverse-rapidity yt as both a velocity measure and a logarithmic alternative to transverse momentum pt. Based on NJ-quadrupole trends, we derive a completely factorized universal parametrization of quantity v2{2D} (yt,b ,√{sN N}) which describes the centrality, yt, and energy dependence. From yt-differential v2(yt) data we isolate a quadrupole spectrum and infer a quadrupole source boost having unexpected properties. NJ quadrupole v2 trends obtained with 2D model fits are remarkably simple. The centrality trend appears to be uncorrelated with a sharp transition in jet-related structure that may indicate rapid change of Au-Au medium properties. The lack of correspondence suggests that the NJ quadrupole may be insensitive to such a medium. Several quadrupole trends have interesting implications for hydro interpretations.

Reduced dynamical model of the vibrations of a metal plate

NASA Astrophysics Data System (ADS)

Moreno, D.; Barrientos, Bernardino; Perez-Lopez, Carlos; Mendoza-Santoyo, Fernando; Guerrero, J. A.; Funes, M.

2005-02-01

The Proper Orthogonal Decomposition (POD) method is applied to the vibrations analysis of a metal plate. The data obtained from the metal plate under vibrations were measured with a laser vibrometer. The metal plate was subject to vibrations with an electrodynamical shaker in a range of frequencies from 100 to 5000 Hz. The deformation measurements were taken on a quarter of the plate in a rectangular grid of 7 x 8 points. The plate deformation measurements were used to calculate the eigenfunctions and the eigenvalues. It was found that a large fraction of the total energy of the deformation is contained within the first six POD modes. The essential features of the deformation are thus described by only the six first eigenfunctions. A reduced order model for the dynamical behavior is then constructed using Galerkin projection of the equation of motion for the vertical displacement of a plate.

Using Peano Curves to Construct Laplacians on Fractals

NASA Astrophysics Data System (ADS)

Molitor, Denali; Ott, Nadia; Strichartz, Robert

2015-12-01

We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia sets. The Peano curve allows us to visualize eigenfunctions of the Laplacian by graphing the pullback to the circle. We study in detail three fractals: the pentagasket, the octagasket and the magic carpet. We also use the method for two nonfractal self-similar sets, the torus and the equilateral triangle, obtaining appealing new visualizations of eigenfunctions on the triangle. In contrast to the many familiar pictures of approximations to standard Peano curves, that do no show self-intersections, our descriptions of approximations to the Peano curves have self-intersections that play a vital role in constructing graph approximations to the fractal with explicit graph Laplacians that give the fractal Laplacian in the limit.

Boundary Concentration for Eigenvalue Problems Related to the Onset of Superconductivity

NASA Astrophysics Data System (ADS)

del Pino, Manuel; Felmer, Patricio L.; Sternberg, Peter

We examine the asymptotic behavior of the eigenvalue μ(h) and corresponding eigenfunction associated with the variational problem in the regime h>>1. Here A is any vector field with curl equal to 1. The problem arises within the Ginzburg-Landau model for superconductivity with the function μ(h) yielding the relationship between the critical temperature vs. applied magnetic field strength in the transition from normal to superconducting state in a thin mesoscopic sample with cross-section Ω 2. We first carry out a rigorous analysis of the associated problem on a half-plane and then rigorously justify some of the formal arguments of [BS], obtaining an expansion for μ while also proving that the first eigenfunction decays to zero somewhere along the sample boundary when Ω is not a disc. For interior decay, we demonstrate that the rate is exponential.

Disconjugacy, regularity of multi-indexed rationally extended potentials, and Laguerre exceptional polynomials

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

Grandati, Y.; Quesne, C.

2013-07-15

The power of the disconjugacy properties of second-order differential equations of Schrödinger type to check the regularity of rationally extended quantum potentials connected with exceptional orthogonal polynomials is illustrated by re-examining the extensions of the isotonic oscillator (or radial oscillator) potential derived in kth-order supersymmetric quantum mechanics or multistep Darboux-Bäcklund transformation method. The function arising in the potential denominator is proved to be a polynomial with a nonvanishing constant term, whose value is calculated by induction over k. The sign of this term being the same as that of the already known highest degree term, the potential denominator has themore » same sign at both extremities of the definition interval, a property that is shared by the seed eigenfunction used in the potential construction. By virtue of disconjugacy, such a property implies the nodeless character of both the eigenfunction and the resulting potential.« less

Diskoseismology: Probing accretion disks. II - G-modes, gravitational radiation reaction, and viscosity

NASA Technical Reports Server (NTRS)

Nowak, Michael A.; Wagoner, Robert V.

1992-01-01

A scalar potential is used to derive a single partial differential equation governing the oscillation of a disk. The eigenfunctions and eigenfrequencies of a variety of disk models are found to fall into two main classes which are analogous to the p-modes and g-modes in the sun. Specifically, the eigenfunctions and eigenfrequencies of isothermal disks are computed, and the way in which these results can be generalized to other disk models is indicated. The (assumed) relatively small rates of growth or damping of the modes due to various mechanisms, in particular gravitational radiation reaction and parameterized models of viscosity are also computed. It is found that for certain parameters the p-modes are unstable to gravitational radiation reaction (CFS instability), while both the p-modes and g-modes are unstable to viscosity unless highly anisotropic viscosity models are considered.

Vibrational treatment of the formic acid double minimum case in valence coordinates

NASA Astrophysics Data System (ADS)

Richter, Falk; Carbonnière, P.

2018-02-01

One single full dimensional valence coordinate HCOOH ground state potential energy surface accurate for both cis and trans conformers for all levels up to 6000 cm-1 relative to trans zero point energy has been generated at CCSD(T)-F12a/aug-cc-pVTZ level. The fundamentals and a set of eigenfunctions complete up to about 3120 and 2660 cm-1 for trans- and cis-HCOOH, respectively, have been calculated and assigned using the improved relaxation method of the Heidelberg multi-configuration time-dependent Hartree package and an exact expression for the kinetic energy in valence coordinates generated by the TANA program. The calculated trans fundamental transition frequencies agree with experiment to within 5 cm-1. A few reassignments are suggested. Our results discard any cis trans delocalization effects for vibrational eigenfunctions up to 3640 cm-1 relative to trans zero point energy.

Generalized Ince Gaussian beams

NASA Astrophysics Data System (ADS)

Bandres, Miguel A.; Gutiérrez-Vega, Julio C.

2006-08-01

In this work we present a detailed analysis of the tree families of generalized Gaussian beams, which are the generalized Hermite, Laguerre, and Ince Gaussian beams. The generalized Gaussian beams are not the solution of a Hermitian operator at an arbitrary z plane. We derived the adjoint operator and the adjoint eigenfunctions. Each family of generalized Gaussian beams forms a complete biorthonormal set with their adjoint eigenfunctions, therefore, any paraxial field can be described as a superposition of a generalized family with the appropriate weighting and phase factors. Each family of generalized Gaussian beams includes the standard and elegant corresponding families as particular cases when the parameters of the generalized families are chosen properly. The generalized Hermite Gaussian and Laguerre Gaussian beams correspond to limiting cases of the generalized Ince Gaussian beams when the ellipticity parameter of the latter tends to infinity or to zero, respectively. The expansion formulas among the three generalized families and their Fourier transforms are also presented.

Analytical bound-state solutions of the Schrödinger equation for the Manning-Rosen plus Hulthén potential within SUSY quantum mechanics

NASA Astrophysics Data System (ADS)

Ahmadov, A. I.; Naeem, Maria; Qocayeva, M. V.; Tarverdiyeva, V. A.

2018-01-01

In this paper, the bound-state solution of the modified radial Schrödinger equation is obtained for the Manning-Rosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any l≠0 angular momentum case via the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary l states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.

Vortex knots in tangled quantum eigenfunctions

PubMed Central

Taylor, Alexander J.; Dennis, Mark R.

2016-01-01

Tangles of string typically become knotted, from macroscopic twine down to long-chain macromolecules such as DNA. Here, we demonstrate that knotting also occurs in quantum wavefunctions, where the tangled filaments are vortices (nodal lines/phase singularities). The probability that a vortex loop is knotted is found to increase with its length, and a wide gamut of knots from standard tabulations occur. The results follow from computer simulations of random superpositions of degenerate eigenstates of three simple quantum systems: a cube with periodic boundaries, the isotropic three-dimensional harmonic oscillator and the 3-sphere. In the latter two cases, vortex knots occur frequently, even in random eigenfunctions at relatively low energy, and are constrained by the spatial symmetries of the modes. The results suggest that knotted vortex structures are generic in complex three-dimensional wave systems, establishing a topological commonality between wave chaos, polymers and turbulent Bose–Einstein condensates. PMID:27468801

Vibrational modes of thin oblate clouds of charge

NASA Astrophysics Data System (ADS)

Jenkins, Thomas G.; Spencer, Ross L.

2002-07-01

A numerical method is presented for finding the eigenfunctions (normal modes) and mode frequencies of azimuthally symmetric non-neutral plasmas confined in a Penning trap whose axial thickness is much smaller than their radial size. The plasma may be approximated as a charged disk in this limit; the normal modes and frequencies can be found if the surface charge density profile σ(r) of the disk and the trap bounce frequency profile ωz(r) are known. The dependence of the eigenfunctions and equilibrium plasma shapes on nonideal components of the confining Penning trap fields is discussed. The results of the calculation are compared with the experimental data of Weimer et al. [Phys. Rev. A 49, 3842 (1994)] and it is shown that the plasma in this experiment was probably hollow and had mode displacement functions that were concentrated near the center of the plasma.

Adaptive eigenspace method for inverse scattering problems in the frequency domain

NASA Astrophysics Data System (ADS)

Grote, Marcus J.; Kray, Marie; Nahum, Uri

2017-02-01

A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method.

Nuclear Quadrupole Moments and Nuclear Shell Structure

DOE R&D Accomplishments Database

Townes, C. H.; Foley, H. M.; Low, W.

1950-06-23

Describes a simple model, based on nuclear shell considerations, which leads to the proper behavior of known nuclear quadrupole moments, although predictions of the magnitudes of some quadrupole moments are seriously in error.

Coulomb-like elastic interaction induced by symmetry breaking in nematic liquid crystal colloids.

PubMed

Lee, Beom-Kyu; Kim, Sung-Jo; Kim, Jong-Hyun; Lev, Bohdan

2017-11-21

It is generally thought that colloidal particles in a nematic liquid crystal do not generate the first multipole term called deformation elastic charge as it violates the mechanical equilibrium. Here, we demonstrate theoretically and experimentally that this is not the case, and deformation elastic charges, as well as dipoles and quadrupoles, can be induced through anisotropic boundary conditions. We report the first direct observation of Coulomb-like elastic interactions between colloidal particles in a nematic liquid crystal. The behaviour of two spherical colloidal particles with asymmetric anchoring conditions induced by asymmetric alignment is investigated experimentally; the interaction of two particles located at the boundary of twist and parallel aligned regions is observed. We demonstrate that such particles produce deformation elastic charges and interact by Coulomb-like interactions.

Means and method for the focusing and acceleration of parallel beams of charged particles

DOEpatents

Maschke, Alfred W.

1983-07-05

A novel apparatus and method for focussing beams of charged particles comprising planar arrays of electrostatic quadrupoles. The quadrupole arrays may comprise electrodes which are shared by two or more quadrupoles. Such quadrupole arrays are particularly adapted to providing strong focussing forces for high current, high brightness, beams of charged particles, said beams further comprising a plurality of parallel beams, or beamlets, each such beamlet being focussed by one quadrupole of the array. Such arrays may be incorporated in various devices wherein beams of charged particles are accelerated or transported, such as linear accelerators, klystron tubes, beam transport lines, etc.

Noise reduction in negative-ion quadrupole mass spectrometry

DOEpatents

Chastagner, P.

1993-04-20

A quadrupole mass spectrometer (QMS) system is described having an ion source, quadrupole mass filter, and ion collector/recorder system. A weak, transverse magnetic field and an electron collector are disposed between the quadrupole and ion collector. When operated in negative ion mode, the ion source produces a beam of primarily negatively-charged particles from a sample, including electrons as well as ions. The beam passes through the quadrupole and enters the magnetic field, where the electrons are deflected away from the beam path to the electron collector. The negative ions pass undeflected to the ion collector where they are detected and recorded as a mass spectrum.

Noise reduction in negative-ion quadrupole mass spectrometry

DOEpatents

Chastagner, Philippe

1993-01-01

A quadrupole mass spectrometer (QMS) system having an ion source, quadrupole mass filter, and ion collector/recorder system. A weak, transverse magnetic field and an electron collector are disposed between the quadrupole and ion collector. When operated in negative ion mode, the ion source produces a beam of primarily negatively-charged particles from a sample, including electrons as well as ions. The beam passes through the quadrupole and enters the magnetic field, where the electrons are deflected away from the beam path to the electron collector. The negative ions pass undeflected to the ion collector where they are detected and recorded as a mass spectrum.

Particle beam injector system and method

DOEpatents

Guethlein, Gary

2013-06-18

Methods and devices enable coupling of a charged particle beam to a radio frequency quadrupole accelerator. Coupling of the charged particle beam is accomplished, at least in-part, by relying on of sensitivity of the input phase space acceptance of the radio frequency quadrupole to the angle of the input charged particle beam. A first electric field across a beam deflector deflects the particle beam at an angle that is beyond the acceptance angle of the radio frequency quadrupole. By momentarily reversing or reducing the established electric field, a narrow portion of the charged particle beam is deflected at an angle within the acceptance angle of the radio frequency quadrupole. In another configuration, beam is directed at an angle within the acceptance angle of the radio frequency quadrupole by the first electric field and is deflected beyond the acceptance angle of the radio frequency quadrupole due to the second electric field.

Klystron having electrostatic quadrupole focusing arrangement

DOEpatents

Maschke, Alfred W.

1983-08-30

A klystron includes a source for emitting at least one electron beam, and an accelerator for accelarating the beam in a given direction through a number of drift tube sections successively aligned relative to one another in the direction of the beam. A number of electrostatic quadrupole arrays are successively aligned relative to one another along at least one of the drift tube sections in the beam direction for focusing the electron beam. Each of the electrostatic quadrupole arrays forms a different quadrupole for each electron beam. Two or more electron beams can be maintained in parallel relationship by the quadrupole arrays, thereby enabling space charge limitations encountered with conventional single beam klystrons to be overcome.

Klystron having electrostatic quadrupole focusing arrangement

DOEpatents

Maschke, A.W.

1983-08-30

A klystron includes a source for emitting at least one electron beam, and an accelerator for accelerating the beam in a given direction through a number of drift tube sections successively aligned relative to one another in the direction of the beam. A number of electrostatic quadrupole arrays are successively aligned relative to one another along at least one of the drift tube sections in the beam direction for focusing the electron beam. Each of the electrostatic quadrupole arrays forms a different quadrupole for each electron beam. Two or more electron beams can be maintained in parallel relationship by the quadrupole arrays, thereby enabling space charge limitations encountered with conventional single beam klystrons to be overcome. 4 figs.

A modified quadrupole mass spectrometer with custom RF link rods driver for remote operation

NASA Technical Reports Server (NTRS)

Tashbar, P. W.; Nisen, D. B.; Moore, W. W., Jr.

1973-01-01

A commercial quadrupole residual gas analyzer system has been upgraded for operation at extended cable lengths. Operation inside a vacuum chamber for the standard quadrupole nude head is limited to approximately 2 m from its externally located rf/dc generator because of the detuning of the rf oscillator circuits by the coaxial cable reactance. The advance of long distance remote operation inside a vacuum chamber for distances of 45 and 60 m was made possible without altering the quadrupole's rf/dc generator circuit by employing an rf link to drive the quadrupole rods. Applications of the system have been accomplished for in situ space simulation thermal/vacuum testing of sophisticated payloads.

Relativistic many-body bound systems: electromagnetic properties. Monograph report

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

Danos, M.; Gillet, V.

1977-04-01

The formulae for the calculation of the electron scattering form factors, and of the static magnetic dipole and electric quadrupole moments, of relativistic many-body bound systems are derived. The framework, given in NBS Monograph 147, is relativistic quantum field theory in the Schrodinger picture; the physical particles, i.e., the solutions of the interacting fields, are given as linear combinations of the solutions of the free fields, called the parton fields. The parton--photon interaction is taken as given by minimal coupling. In addition, the contribution of the photon--vector meson vertex of the vector dominance model is derived.

HZEFRG1: An energy-dependent semiempirical nuclear fragmentation model

NASA Technical Reports Server (NTRS)

Townsend, Lawrence W.; Wilson, John W.; Tripathi, Ram K.; Norbury, John W.; Badavi, Francis F.; Khan, Ferdous

1993-01-01

Methods for calculating cross sections for the breakup of high-energy heavy ions by the combined nuclear and coulomb fields of the interacting nuclei are presented. The nuclear breakup contributions are estimated with an abrasion-ablation model of heavy ion fragmentation that includes an energy-dependent, mean free path. The electromagnetic dissociation contributions arising from the interacting coulomb fields are estimated by using Weizsacker-Williams theory extended to include electric dipole and electric quadrupole contributions. The complete computer code that implements the model is included as an appendix. Extensive comparisons of cross section predictions with available experimental data are made.

Quantized discrete space oscillators

NASA Technical Reports Server (NTRS)

Uzes, C. A.; Kapuscik, Edward

1993-01-01

A quasi-canonical sequence of finite dimensional quantizations was found which has canonical quantization as its limit. In order to demonstrate its practical utility and its numerical convergence, this formalism is applied to the eigenvalue and 'eigenfunction' problem of several harmonic and anharmonic oscillators.

Tunable Luminescence in Sr2MgSi2O7:Tb3+, Eu3+Phosphors Based on Energy Transfer

PubMed Central

Li, Minhong; Wang, Lili; Ran, Weiguang; Deng, Zhihan; Shi, Jinsheng; Ren, Chunyan

2017-01-01

A series of Tb3+, Eu3+-doped Sr2MgSi2O7 (SMSO) phosphors were synthesized by high temperature solid-state reaction. X-ray diffraction (XRD) patterns, Rietveld refinement, photoluminescence spectra (PL), and luminescence decay curves were utilized to characterize each sample’s properties. Intense green emission due to Tb3+ 5D4→7F5 transition was observed in the Tb3+ single-doped SMSO sample, and the corresponding concentration quenching mechanism was demonstrated to be a diople-diople interaction. A wide overlap between Tb3+ emission and Eu3+ excitationspectraresults in energy transfer from Tb3+ to Eu3+. This has been demonstrated by the emission spectra and decay curves of Tb3+ in SMSO:Tb3+, Eu3+ phosphors. Energy transfer mechanism was determined to be a quadrupole-quadrupole interaction. And critical distance of energy transfer from Tb3+ to Eu3+ ions is calculated to be 6.7 Å on the basis of concentration quenching method. Moreover, white light emission was generated via adjusting concentration ratio of Tb3+ and Eu3+ in SMSO:Tb3+, Eu3+ phosphors. All the results indicate that SMSO:Tb3+, Eu3+ is a promising single-component white light emitting phosphor. PMID:28772587

Damping of spin-dipole mode and generation of quadrupole mode excitations in a spin-orbit coupled Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Li, Chuan-Hsun; Blasing, David; Chen, Yong

2017-04-01

In cold atom systems, spin excitations have been shown to be a sensitive probe of interactions and quantum statistical effects, and can be used to study spin transport in both Fermi and Bose gases. In particular, spin-dipole mode (SDM) is a type of excitation that can generate a spin current without a net mass current. We present recent measurements and analysis of SDM in a disorder-free, interacting three-dimensional (3D) 87Rb Bose-Einstein condensate (BEC) by applying spin-dependent synthetic electric fields to actuate head-on collisions between two BECs of different spin states. We experimentally study and compare the behaviors of the system following SDM excitations in the presence as well as absence of synthetic 1D spin-orbit coupling (SOC). We find that in the absence of SOC, SDM is relatively weakly damped, accompanied with collision-induced thermalization which heats up the atomic cloud. However, in the presence of SOC, we find that SDM is more strongly damped with reduced thermalization, and observe excitation of a quadrupole mode that exhibits BEC shape oscillation even after SDM is damped out. Such a mode conversion bears analogies with the Beliaev coupling process or the parametric frequency down conversion of light in nonlinear optics.

Characterization of the ELIMED prototype permanent magnet quadrupole system

NASA Astrophysics Data System (ADS)

Russo, A. D.; Schillaci, F.; Pommarel, L.; Romano, F.; Amato, A.; Amico, A. G.; Calanna, A.; Cirrone, G. A. P.; Costa, M.; Cuttone, G.; Amato, C.; De Luca, G.; Flacco, F. A.; Gallo, G.; Giove, D.; Grmek, A.; La Rosa, G.; Leanza, R.; Maggiore, M.; Malka, V.; Milluzzo, G.; Petringa, G.; Pipek, J.; Scuderi, V.; Vauzour, B.; Zappalà, E.

2017-01-01

The system described in this work is meant to be a prototype of a more performing one that will be installed at ELI-Beamlines in Prague for the collection of ions produced after the interaction Laser-target, [1]. It has been realized by the researchers of INFN-LNS (Laboratori Nazionali del Sud of the Instituto Nazionale di Fisica Nucleare) and SIGMAPHI, a French company, using a system of Permanent Magnet Quadrupoles (PMQs), [2]. The final system that will be installed in Prague is designed for protons and carbons up to 60 MeV/u, around 10 times more than the energies involved in the present work. The prototype, shown in this work, has been tested in collaboration with the SAPHIR experimental facility group at LOA (Laboratoire d'Optique Appliqueé) in Paris using a 200 TW Ti:Sapphire laser system. The purpose of this work is to validate the design and the performances of this large and compact bore system and to characterize the beam produced after the interaction laser-target and its features. Moreover, the optics simulations have been compared with a real beam shape on a GAFChromic film. The procedure used during the experimental campaign and the most relevant results are reported here demonstrating a good agreement with the simulations and a good control on the beam optics.

Some aspects of self-consistent higher-order interactions

NASA Astrophysics Data System (ADS)

Sakamoto, Hideo

2018-05-01

After a brief review of the formalism of the self-consistent higher-order interactions, applications of a ([Q 3 Q 3](2) · Q 2) type of three-body interaction to the quadrupole moment of the 3‑ state in 208Pb and the energy splitting of the septuplet of states (h 9/23‑)I with I = 3/2, 5/2, …, 15/2 in 209Bi are discussed. It is shown that if the contribution of the three-body interaction is included, the theoretical value of the Qel (3‑) moment becomes rather small compared to the experiment, but the observed small energy splitting of the septuplet can essentially be understood within the particle-vibration coupling model. Roles of non-linear field couplings provided by the self-consistent higher-order interactions are also discussed.

Classification of three-state Hamiltonians solvable by the coordinate Bethe ansatz

NASA Astrophysics Data System (ADS)

Crampé, N.; Frappat, L.; Ragoucy, E.

2013-10-01

We classify ‘all’ Hamiltonians with rank 1 symmetry and nearest-neighbour interactions, acting on a periodic three-state spin chain, and solvable through (generalization of) the coordinate Bethe ansatz (CBA). In this way we obtain four multi-parametric extensions of the known 19-vertex Hamiltonians (such as Zamolodchikov-Fateev, Izergin-Korepin and Bariev Hamiltonians). Apart from the 19-vertex Hamiltonians, there exist 17-vertex and 14-vertex Hamiltonians that cannot be viewed as subcases of the 19-vertex ones. In the case of 17-vertex Hamiltonians, we get a generalization of the genus 5 special branch found by Martins, plus three new ones. We also get two 14-vertex Hamiltonians. We solve all these Hamiltonians using CBA, and provide their spectrum, eigenfunctions and Bethe equations. Special attention is given to provide the specifications of our multi-parametric Hamiltonians that give back known Hamiltonians.

Neutral-atom electron binding energies from relaxed-orbital relativistic Hartree-Fock-Slater calculations for Z between 2 and 106

NASA Technical Reports Server (NTRS)

Huang, K.-N.; Aoyagi, M.; Mark, H.; Chen, M. H.; Crasemann, B.

1976-01-01

Electron binding energies in neutral atoms have been calculated relativistically, with the requirement of complete relaxation. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order correction to the local approximation was thus included. Quantum-electrodynamic corrections were made. For all elements with atomic numbers ranging from 2 to 106, the following quantities are listed: total energies, electron kinetic energies, electron-nucleus potential energies, electron-electron potential energies consisting of electrostatic and Breit interaction (magnetic and retardation) terms, and vacuum polarization energies. Binding energies including relaxation are listed for all electrons in all atoms over the indicated range of atomic numbers. A self-energy correction is included for the 1s, 2s, and 2p(1/2) levels. Results for selected atoms are compared with energies calculated by other methods and with experimental values.

Determination of nuclear quadrupole moments – An example of the synergy of ab initio calculations and microwave spectroscopy

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

Kellö, Vladimir

Highly correlated scalar relativistic calculations of electric field gradients at nuclei in diatomic molecules in combination with accurate nuclear quadrupole coupling constants obtained from microwave spectroscopy are used for determination of nuclear quadrupole moments.

Dunkl-Darboux differential-difference operators

NASA Astrophysics Data System (ADS)

Khekalo, S. P.

2017-02-01

Using a natural generalization, we construct and study analogues of Dunkl differential-difference operators on the line. These analogues turn out to be closely connected with the so-called Burchnall- Chaundy-Adler-Moser polynomials and, therefore, with Darboux transforms. We find the eigenfunctions of these operators.

Induced Angular Momentum

ERIC Educational Resources Information Center

Parker, G. W.

1978-01-01

Discusses, classically and quantum mechanically, the angular momentum induced in the bound motion of an electron by an external magnetic field. Calculates the current density and its magnetic moment, and then uses two methods to solve the first-order perturbation theory equation for the required eigenfunction. (Author/GA)

Unusual Enhancement of Magnetization by Pressure in the Antiferro-Quadrupole-Ordered Phase in CeB6

NASA Astrophysics Data System (ADS)

Ikeda, Suguru; Sera, Masafumi; Hane, Shingo; Uwatoko, Yoshiya; Kosaka, Masashi; Kunii, Satoru

2007-06-01

The effect of pressure on CeB6 was investigated by the measurement of the magnetization (M) under pressure, and we obtained the following results. The effect of pressure on M in phase I is very small. By applying pressure, TQ is enhanced, but TN and the critical field from the antiferromagnetic (AFM) phase III to the antiferro-quadrupole (AFQ) phase II (HcIII--II) are suppressed, as previously reported. The magnetization curve in phase III shows the characteristic shoulder at H˜ HcIII--II/2 at ambient pressure. This shoulder becomes much more pronounced by applying pressure. Both HcIII--II and the magnetic field, where a shoulder is seen in the magnetization curve in phase III, are largely suppressed by pressure. In phase II, the M-T curve at a low magnetic field exhibits an unusual concave temperature dependence below TQ down to TN. Thus, we found that the lower the magnetic field, the larger the enhancement of M in both phases III and II. To clarify the origin of the unusual pressure effect of M, we performed a mean-field calculation for the 4-sublattice model using the experimental results of dTQ/dP>0 and dTN/dP<0 and assuming the positive pressure dependence of the Txyz-antiferro-octupole (AFO) interaction. The characteristic features of the pressure effect of M obtained by the experiments could be reproduced well by the mean-field calculation. We found that the origin of the characteristic effect of pressure on CeB6 is the change in the subtle balance between the AFM interaction and the magnetic field-induced-effective FM interaction induced by the coexistence of the Oxy-AFQ and Txyz-AFO interactions under pressure.

Morphological evolution of Jinshan Trough in Hangzhou Bay (China) from 1960 to 2011

NASA Astrophysics Data System (ADS)

Liu, Yifei; Xia, Xiaoming; Chen, Shenliang; Jia, Jianjun; Cai, Tinglu

2017-11-01

An extensive system of tidal channels, starting with Jinshan Trough in the east, is located along the north shore of Hangzhou Bay, China. This contribution investigates the morphological evolution of Jinshan Trough by using 17 bathymetric charts from a series covering a period of 51 years from 1960 to 2011. Three stages of evolution during this period are distinguishable based on the morphology and annual mean volume data. The first stage (1960-1987) is characterized by extension of the trough; the second stage (1987-1996) is a relatively stable period with some adjustments in the trough morphology; the third stage (1996-2011) is marked by the processes of erosion and deposition in the beginning of the period and a subsequent slow erosion process. Spatio-temporal variability of the trough was evaluated by using empirical orthogonal function (EOF) analysis. The first eigenfunction indicates that erosion is the main evolution process and there exists three stages similar to those distinguished from volume variations. The second eigenfunction mainly reflects erosion and deposition in the northwest part of the trough located in the flood tidal current shadow area of the artificial headland in Jinshan. The third eigenfunction mainly reflects annual fluctuations of erosion and deposition in the side slope at the artificial headland in Jinshan. A particularly intense erosion process occurred between 1996 and 1998. The major effects on morphological evolution in Jinshan Trough from 1960 to 2011 were investigated and tentative conclusions were presented. Continuous coastal reclamations in Jinshan had the most pronounced effect on the morphological evolution during the first and the second stages. The storm surge had a pronounced effect on the evolution at the beginning of the third stage.

Wave chaos in a randomly inhomogeneous waveguide: spectral analysis of the finite-range evolution operator.

PubMed

Makarov, D V; Kon'kov, L E; Uleysky, M Yu; Petrov, P S

2013-01-01

The problem of sound propagation in a randomly inhomogeneous oceanic waveguide is considered. An underwater sound channel in the Sea of Japan is taken as an example. Our attention is concentrated on the domains of finite-range ray stability in phase space and their influence on wave dynamics. These domains can be found by means of the one-step Poincare map. To study manifestations of finite-range ray stability, we introduce the finite-range evolution operator (FREO) describing transformation of a wave field in the course of propagation along a finite segment of a waveguide. Carrying out statistical analysis of the FREO spectrum, we estimate the contribution of regular domains and explore their evanescence with increasing length of the segment. We utilize several methods of spectral analysis: analysis of eigenfunctions by expanding them over modes of the unperturbed waveguide, approximation of level-spacing statistics by means of the Berry-Robnik distribution, and the procedure used by A. Relano and coworkers [Relano et al., Phys. Rev. Lett. 89, 244102 (2002); Relano, Phys. Rev. Lett. 100, 224101 (2008)]. Comparing the results obtained with different methods, we find that the method based on the statistical analysis of FREO eigenfunctions is the most favorable for estimating the contribution of regular domains. It allows one to find directly the waveguide modes whose refraction is regular despite the random inhomogeneity. For example, it is found that near-axial sound propagation in the Sea of Japan preserves stability even over distances of hundreds of kilometers due to the presence of a shearless torus in the classical phase space. Increasing the acoustic wavelength degrades scattering, resulting in recovery of eigenfunction localization near periodic orbits of the one-step Poincaré map.

Conformational study of 2-phenylethylamine by molecular-beam Fourier transform microwave spectroscopy.

PubMed

López, Juan C; Cortijo, Vanessa; Blanco, Susana; Alonso, Jose L

2007-08-28

The conformational preferences of the simplest amine neurotransmitter 2-phenylethylamine have been investigated using molecular beam Fourier transform microwave (MB-FTMW) spectroscopy. Two new conformers have been observed together with the two previously reported by Godfrey et al. [J. Am. Chem. Soc., 1995, 117, 8204]. The (14)N nuclear quadrupole hyperfine structure has been resolved for all four conformers. Comparison of the experimental rotational and quadrupole coupling constants with those calculated theoretically provides a conclusive test for the identification of all conformers. The two most stable conformers present a gauche (folded) disposition of the alkyl-amine chain and are stabilised by a weak NH...pi interaction between the amino group and the aromatic ring. The other two conformers show an anti (extended) arrangement of the alkyl-amine chain. Tunnelling splittings have been observed in the spectrum of one of the anti conformers. The post expansion relative abundances in the supersonic jet have been also investigated and related to the conformer energies.

Reexamining the nuclear structure of 154Gd in the dynamic pairing plus quadrupole model

NASA Astrophysics Data System (ADS)

Gupta, J. B.; Hamilton, J. H.

2017-05-01

In a previous study of the collective multiphonon bands in 154Gd, using the microscopic dynamic pairing plus quadrupole model, data for eight K bands were analyzed. In the last four decades, its decay scheme is significantly revised and the nuclear theory has undergone a significant change. Special focus is on new weak intensity transitions in several bands and on the reassigned levels in its decay scheme. The present study represents a detailed revised analysis of the collective even parity bands below 2.1 MeV. Also, a discussion is given on the nature of the Kπ=0+ excited bands, validity of band mixing approach, and of the assumption of shape coexistence of β band with ground band. Comparison is made with the X (5) analytical symmetry and the algebraic interacting boson model predictions. Discussion of the 2 n transfer reactions is given. The validity of the multiphonon view of the Kπ=4+ and 22+ bands is also studied.

A microscopic explanation of the isotonic multiplet at N=90

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

Gupta, J. B., E-mail: jbgupta2011@gmail.com

2014-08-14

The shape phase transition from spherical to soft deformed at N=88-90 was observed long ago. After the prediction of the X(5) symmetry, for which analytical solution of the nuclear Hamiltonian is given [1], good examples of X(5) nuclei were identified in the N=90 isotones of Nd, Sm, Gd and Dy, in the recent works. The N=90 isotones have almost the similar deformed level structure, forming the isotonic multiplet in Z=50-66, N=82-104 quadrant. This is explained microscopically in terms of the Nilsson level diagram. Using the Dynamic Pairing-Plus-Quadrupole model of Kumar-Baranger, the quadrupole deformation and the occupancies of the neutrons andmore » protons in these nuclei have been calculated, which support the formation of N=88, 90 isotonic multiplets. The existence of F-spin multiplets in Z=66-82, N=82-104 quadrant, identified in earlier works on the Interacting Boson Model, is also explained in our study.« less

Second-generation coil design of the Nb 3Sn low-β quadrupole for the high luminosity LHC

DOE PAGES

Bermudez, S. Izquierdo; Ambrosio, G.; Ballarino, A.; ...

2016-01-18

As part of the Large Hadron Collider Luminosity upgrade (HiLumi-LHC) program, the US LARP collaboration and CERN are working together to design and build a 150 mm aperture Nb 3Sn quadrupole for the LHC interaction regions. A first series of 1.5 m long coils were fabricated and assembled in a first short model. A detailed visual inspection of the coils was carried out to investigate cable dimensional changes during heat treatment and the position of the windings in the coil straight section and in the end region. The analyses allow identifying a set of design changes which, combined with amore » fine tune of the cable geometry and a field quality optimization, were implemented in a new, second-generation, coil design. In this study, we review the main characteristics of the first generation coils, describe the modification in coil lay-out, and discuss their impact on parts design and magnet analysis.« less

Non-target screening of Allura Red AC photodegradation products in a beverage through ultra high performance liquid chromatography coupled with hybrid triple quadrupole/linear ion trap mass spectrometry.

PubMed

Gosetti, Fabio; Chiuminatto, Ugo; Mazzucco, Eleonora; Calabrese, Giorgio; Gennaro, Maria Carla; Marengo, Emilio

2013-01-15

The study deals with the identification of the degradation products formed by simulated sunlight photoirradiation in a commercial beverage that contains Allura Red AC dye. An UHPLC-MS/MS method, that makes use of hybrid triple quadrupole/linear ion trap, was developed. In the identification step the software tool information dependent acquisition (IDA) was used to automatically obtain information about the species present and to build a multiple reaction monitoring (MRM) method with the MS/MS fragmentation pattern of the species considered. The results indicate that the identified degradation products are formed from side-reactions and/or interactions among the dye and other ingredients present in the beverage (ascorbic acid, citric acid, sucrose, aromas, strawberry juice, and extract of chamomile flowers). The presence of aromatic amine or amide functionalities in the chemical structures proposed for the degradation products might suggest potential hazards to consumer health. Copyright © 2012 Elsevier Ltd. All rights reserved.

The ab initio Calculation of Electric Field Gradient at the Site of P Impurity in α-Al3O2

NASA Astrophysics Data System (ADS)

Zhang, Qiao-Li; Yuan, Da-Qing; Zhang, Huan-Qiao; Fan, Ping; Zuo, Yi; Zheng, Yong-Nan; Masuta, K.; Fukuda, M.; Mihara, M.; Minamisono, T.; Kitagawa, A.; Zhu, Sheng-Yun

2012-09-01

An ab initio calculation of the electric-field gradient (EFG) at the site of a phosphorous impurity substituting an Al atom in α-Al2O3 is carried out using the WIEN2k code with the full-potential linearized augmented plane wave plus local orbital method (LAPW+lo) in the frame of density functional theory. The atomic lattice relaxations caused by the implanted impurities were calculated for two different charged states to well describe the electronic structure of the doped system. The EFG at the site of the phosphorous impurity in the charged supercell calculated with the exchange-correlation potential of the Wu-Cohen generalized gradient approximation (WC-GGA) is 0.573 × 1021 V/m2. Then, the nuclear quadrupole moment of the I = 3 state in 28P is deduced to be 137 mb from the quadrupole interaction frequency of 190 kHz measured recently by the β-NQR method.

Differentially pumped dual linear quadrupole ion trap mass spectrometer

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

Owen, Benjamin C.; Kenttamaa, Hilkka I.

The present disclosure provides a new tandem mass spectrometer and methods of using the same for analyzing charged particles. The differentially pumped dual linear quadrupole ion trap mass spectrometer of the present disclose includes a combination of two linear quadrupole (LQIT) mass spectrometers with differentially pumped vacuum chambers.

Quantum correction to classical gravitational interaction between two polarizable objects

NASA Astrophysics Data System (ADS)

Wu, Puxun; Hu, Jiawei; Yu, Hongwei

2016-12-01

When gravity is quantized, there inevitably exist quantum gravitational vacuum fluctuations which induce quadrupole moments in gravitationally polarizable objects and produce a quantum correction to the classical Newtonian interaction between them. Here, based upon linearized quantum gravity and the leading-order perturbation theory, we study, from a quantum field-theoretic prospect, this quantum correction between a pair of gravitationally polarizable objects treated as two-level harmonic oscillators. We find that the interaction potential behaves like r-11 in the retarded regime and r-10 in the near regime. Our result agrees with what were recently obtained in different approaches. Our study seems to indicate that linearized quantum gravity is robust in dealing with quantum gravitational effects at low energies.

Elasticity solutions for a class of composite laminate problems with stress singularities

NASA Technical Reports Server (NTRS)

Wang, S. S.

1983-01-01

A study on the fundamental mechanics of fiber-reinforced composite laminates with stress singularities is presented. Based on the theory of anisotropic elasticity and Lekhnitskii's complex-variable stress potentials, a system of coupled governing partial differential equations are established. An eigenfunction expansion method is introduced to determine the orders of stress singularities in composite laminates with various geometric configurations and material systems. Complete elasticity solutions are obtained for this class of singular composite laminate mechanics problems. Homogeneous solutions in eigenfunction series and particular solutions in polynomials are presented for several cases of interest. Three examples are given to illustrate the method of approach and the basic nature of the singular laminate elasticity solutions. The first problem is the well-known laminate free-edge stress problem, which has a rather weak stress singularity. The second problem is the important composite delamination problem, which has a strong crack-tip stress singularity. The third problem is the commonly encountered bonded composite joints, which has a complex solution structure with moderate orders of stress singularities.

Quadratic Zeeman effect in hydrogen Rydberg states: Rigorous error estimates for energy eigenvalues, energy eigenfunctions, and oscillator strengths

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

Falsaperla, P.; Fonte, G.

1994-10-01

A variational method, based on some results due to T. Kato [Proc. Phys. Soc. Jpn. 4, 334 (1949)], and previously discussed is here applied to the hydrogen atom in uniform magnetic fields of tesla in order to calculate, with a rigorous error estimate, energy eigenvalues, energy eigenfunctions, and oscillator strengths relative to Rydberg states up to just below the field-free ionization threshold. Making use of a basis (parabolic Sturmian basis) with a size varying from 990 up to 5050, we obtain, over the energy range of [minus]190 to [minus]24 cm[sup [minus]1], all of the eigenvalues and a good part ofmore » the oscillator strengths with a remarkable accuracy. This, however, decreases with increasing excitation energy and, thus, above [similar to][minus]24 cm[sup [minus]1], we obtain results of good accuracy only for eigenvalues ranging up to [similar to][minus]12 cm[sup [minus]1].« less

Matrix eigenvalue method for free-oscillations modelling of spherical elastic bodies

NASA Astrophysics Data System (ADS)

Zábranová, E.; Hanyk, L.; Matyska, C.

2017-11-01

Deformations and changes of the gravitational potential of pre-stressed self-gravitating elastic bodies caused by free oscillations are described by means of the momentum and Poisson equations and the constitutive relation. For spherically symmetric bodies, the equations and boundary conditions are transformed into ordinary differential equations of the second order by the spherical harmonic decomposition and further discretized by highly accurate pseudospectral difference schemes on Chebyshev grids; we pay special attention to the conditions at the centre of the models. We thus obtain a series of matrix eigenvalue problems for eigenfrequencies and eigenfunctions of the free oscillations. Accuracy of the presented numerical approach is tested by means of the Rayleigh quotients calculated for the eigenfrequencies up to 500 mHz. Both the modal frequencies and eigenfunctions are benchmarked against the output from the Mineos software package based on shooting methods. The presented technique is a promising alternative to widely used methods because it is stable and with a good capability up to high frequencies.

Sum rules and other properties involving resonance projection operators. [for optical potential description of electron scattering from atoms and ions

NASA Technical Reports Server (NTRS)

Berk, A.; Temkin, A.

1985-01-01

A sum rule is derived for the auxiliary eigenvalues of an equation whose eigenspectrum pertains to projection operators which describe electron scattering from multielectron atoms and ions. The sum rule's right-hand side depends on an integral involving the target system eigenfunctions. The sum rule is checked for several approximations of the two-electron target. It is shown that target functions which have a unit eigenvalue in their auxiliary eigenspectrum do not give rise to well-defined projection operators except through a limiting process. For Hylleraas target approximations, the auxiliary equations are shown to contain an infinite spectrum. However, using a Rayleigh-Ritz variational principle, it is shown that a comparatively simple aproximation can exhaust the sum rule to better than five significant figures. The auxiliary Hylleraas equation is greatly simplified by conversion to a square root equation containing the same eigenfunction spectrum and from which the required eigenvalues are trivially recovered by squaring.

Analytical Solutions of the Schrödinger Equation for the Manning-Rosen plus Hulthén Potential Within SUSY Quantum Mechanics

NASA Astrophysics Data System (ADS)

Ahmadov, A. I.; Naeem, Maria; Qocayeva, M. V.; Tarverdiyeva, V. A.

2018-02-01

In this paper, the bound state solution of the modified radial Schrödinger equation is obtained for the Manning-Rosen plus Hulthén potential by implementing the novel improved scheme to surmount the centrifugal term. The energy eigenvalues and corresponding radial wave functions are defined for any l ≠ 0 angular momentum case via the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSYQM) methods. By using these two different methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary l states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.

Bi-orthogonality relations for fluid-filled elastic cylindrical shells: Theory, generalisations and application to construct tailored Green's matrices

NASA Astrophysics Data System (ADS)

Ledet, Lasse S.; Sorokin, Sergey V.

2018-03-01

The paper addresses the classical problem of time-harmonic forced vibrations of a fluid-filled cylindrical shell considered as a multi-modal waveguide carrying infinitely many waves. The forced vibration problem is solved using tailored Green's matrices formulated in terms of eigenfunction expansions. The formulation of Green's matrix is based on special (bi-)orthogonality relations between the eigenfunctions, which are derived here for the fluid-filled shell. Further, the relations are generalised to any multi-modal symmetric waveguide. Using the orthogonality relations the transcendental equation system is converted into algebraic modal equations that can be solved analytically. Upon formulation of Green's matrices the solution space is studied in terms of completeness and convergence (uniformity and rate). Special features and findings exposed only through this modal decomposition method are elaborated and the physical interpretation of the bi-orthogonality relation is discussed in relation to the total energy flow which leads to derivation of simplified equations for the energy flow components.

Aharonov–Anandan quantum phases and Landau quantization associated with a magnetic quadrupole moment

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

Fonseca, I.C.; Bakke, K., E-mail: kbakke@fisica.ufpb.br

The arising of geometric quantum phases in the wave function of a moving particle possessing a magnetic quadrupole moment is investigated. It is shown that an Aharonov–Anandan quantum phase (Aharonov and Anandan, 1987) can be obtained in the quantum dynamics of a moving particle with a magnetic quadrupole moment. In particular, it is obtained as an analogue of the scalar Aharonov–Bohm effect for a neutral particle (Anandan, 1989). Besides, by confining the quantum particle to a hard-wall confining potential, the dependence of the energy levels on the geometric quantum phase is discussed and, as a consequence, persistent currents can arisemore » from this dependence. Finally, an analogue of the Landau quantization is discussed. -- Highlights: •Scalar Aharonov–Bohm effect for a particle possessing a magnetic quadrupole moment. •Aharonov–Anandan quantum phase for a particle with a magnetic quadrupole moment. •Dependence of the energy levels on the Aharonov–Anandan quantum phase. •Landau quantization associated with a particle possessing a magnetic quadrupole moment.« less

Curvature-induced capillary interaction of spherical particles at a liquid interface.

PubMed

Würger, Alois

2006-10-01

We consider a liquid interface with different principal curvatures +/-c and find that the mere presence of a spherical particle leads to a deformation field of quadrupolar symmetry; the corresponding "capillary quadrupole moment" is given by the ratio of the particle size and the curvature radius. The resulting pair interaction of nearby particles is anisotropic and favors the formation of aggregates of cubic symmetry. Since the single-particle trapping energy depends quadratically on curvature with a negative prefactor, a curvature gradient induces a lateral force that pushes the particles towards strongly curved regions of the interface. As an illustration we discuss the effects occurring on a catenoid.

The interaction of O(plus) ions with the interior surface of a copper chamber

NASA Technical Reports Server (NTRS)

Siegel, M. W.; Boring, J. W.

1971-01-01

Modulated beams of 0(+), Ar(+), and Kr(+) in the 100-300 eV range are directed into a copper box simulating the ante-chamber of an orbiting mass spectrometer. An RF quadrupole mass spectrometer and phase sensitive detection extract the component of the internal mass spectrum correlated with the beam. Intense Ar and Kr signals are observed; however, no O or O2 is detectable, indicating loss of the primary O(+) beam to surface interactions. All four primary ions stimulate sizeable signals at masses 26 and 28. The relevance of these experiments to the interpretation of mass spectra obtained by orbiting satellites is discussed.

Nonuniform radiation damage in permanent magnet quadrupoles.

PubMed

Danly, C R; Merrill, F E; Barlow, D; Mariam, F G

2014-08-01

We present data that indicate nonuniform magnetization loss due to radiation damage in neodymium-iron-boron Halbach-style permanent magnet quadrupoles. The proton radiography (pRad) facility at Los Alamos uses permanent-magnet quadrupoles for magnifying lenses, and a system recently commissioned at GSI-Darmsdadt uses permanent magnets for its primary lenses. Large fluences of spallation neutrons can be produced in close proximity to these magnets when the proton beam is, intentionally or unintentionally, directed into the tungsten beam collimators; imaging experiments at LANL's pRad have shown image degradation with these magnetic lenses at proton beam doses lower than those expected to cause damage through radiation-induced reduction of the quadrupole strength alone. We have observed preferential degradation in portions of the permanent magnet quadrupole where the field intensity is highest, resulting in increased high-order multipole components.

Exact cancellation of emittance growth due to coupled transverse dynamics in solenoids and rf couplers

NASA Astrophysics Data System (ADS)

Dowell, David H.; Zhou, Feng; Schmerge, John

2018-01-01

Weak, rotated magnetic and radio frequency quadrupole fields in electron guns and injectors can couple the beam's horizontal with vertical motion, introduce correlations between otherwise orthogonal transverse momenta, and reduce the beam brightness. This paper discusses two important sources of coupled transverse dynamics common to most electron injectors. The first is quadrupole focusing followed by beam rotation in a solenoid, and the second coupling comes from a skewed high-power rf coupler or cavity port which has a rotated rf quadrupole field. It is shown that a dc quadrupole field can correct for both types of couplings and exactly cancel their emittance growths. The degree of cancellation of the rf skew quadrupole emittance is limited by the electron bunch length. Analytic expressions are derived and compared with emittance simulations and measurements.

Characterization, stoichiometry, and stability of salivary protein-tannin complexes by ESI-MS and ESI-MS/MS.

PubMed

Canon, Francis; Paté, Franck; Meudec, Emmanuelle; Marlin, Thérèse; Cheynier, Véronique; Giuliani, Alexandre; Sarni-Manchado, Pascale

2009-12-01

Numerous protein-polyphenol interactions occur in biological and food domains particularly involving proline-rich proteins, which are representative of the intrinsically unstructured protein group (IUP). Noncovalent protein-ligand complexes are readily detected by electrospray ionization mass spectrometry (ESI-MS), which also gives access to ligand binding stoichiometry. Surprisingly, the study of interactions between polyphenolic molecules and proteins is still an area where ESI-MS has poorly benefited, whereas it has been extensively applied to the detection of noncovalent complexes. Electrospray ionization mass spectrometry has been applied to the detection and the characterization of the complexes formed between tannins and a human salivary proline-rich protein (PRP), namely IB5. The study of the complex stability was achieved by low-energy collision-induced dissociation (CID) measurements, which are commonly implemented using triple quadrupole, hybrid quadrupole time-of-flight, or ion trap instruments. Complexes composed of IB5 bound to a model polyphenol EgCG have been detected by ESI-MS and further analyzed by MS/MS. Mild ESI interface conditions allowed us to observe intact noncovalent PRP-tannin complexes with stoichiometries ranging from 1:1 to 1:5. Thus, ESI-MS shows its efficiency for (1) the study of PRP-tannin interactions, (2) the determination of stoichiometry, and (3) the study of complex stability. We were able to establish unambiguously both their stoichiometries and their overall subunit architecture via tandem mass spectrometry and solution disruption experiments. Our results prove that IB5.EgCG complexes are maintained intact in the gas phase.

Rotationally adiabatic pair interactions of para- and ortho-hydrogen with the halogen molecules F2, Cl2, and Br2.

PubMed

Berg, Matthias; Accardi, Antonio; Paulus, Beate; Schmidt, Burkhard

2014-08-21

The present work is concerned with the weak interactions between hydrogen and halogen molecules, i.e., the interactions of pairs H2-X2 with X = F, Cl, Br, which are dominated by dispersion and quadrupole-quadrupole forces. The global minimum of the four-dimensional (4D) coupled cluster with singles and doubles and perturbative triples (CCSD(T)) pair potentials is always a T shaped structure where H2 acts as the hat of the T, with well depths (De) of 1.3, 2.4, and 3.1 kJ/mol for F2, Cl2, and Br2, respectively. MP2/AVQZ results, in reasonable agreement with CCSD(T) results extrapolated to the basis set limit, are used for detailed scans of the potentials. Due to the large difference in the rotational constants of the monomers, in the adiabatic approximation, one can solve the rotational Schrödinger equation for H2 in the potential of the X2 molecule. This yields effective two-dimensional rotationally adiabatic potential energy surfaces where pH2 and oH2 are point-like particles. These potentials for the H2-X2 complexes have global and local minima for effective linear and T-shaped complexes, respectively, which are separated by 0.4-1.0 kJ/mol, where oH2 binds stronger than pH2 to X2, due to higher alignment to minima structures of the 4D-pair potential. Further, we provide fits of an analytical function to the rotationally adiabatic potentials.

Pauli energy spectrum for twist-deformed spacetime

NASA Astrophysics Data System (ADS)

Daszkiewicz, Marcin

2018-04-01

In this paper, we define the Pauli Hamiltonian function for the twist-deformed N-enlarged Newton-Hooke spacetime provided by M. Daszkiewicz [Mod. Phys. Lett. A 27, 1250083 (2012)]. Further, we derive its energy spectrum, i.e. we find the corresponding eigenvalues as well as the proper eigenfunctions.

On the Time-Dependent Analysis of Gamow Decay

ERIC Educational Resources Information Center

Durr, Detlef; Grummt, Robert; Kolb, Martin

2011-01-01

Gamow's explanation of the exponential decay law uses complex "eigenvalues" and exponentially growing "eigenfunctions". This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wavefunctions. Observing that the time evolution of any…

Electrostatic quadrupole focused particle accelerating assembly with laminar flow beam

DOEpatents

Maschke, A.W.

1984-04-16

A charged particle accelerating assembly provided with a predetermined ratio of parametric structural characteristics and with related operating voltages applied to each of its linearly spaced focusing and accelerating quadrupoles, thereby to maintain a particle beam traversing the electrostatic fields of the quadrupoles in the assembly in an essentially laminar flow through the assembly.

Electrostatic quadrupole focused particle accelerating assembly with laminar flow beam

DOEpatents

Maschke, Alfred W.

1985-01-01

A charged particle accelerating assembly provided with a predetermined ratio of parametric structural characteristics and with related operating voltages applied to each of its linearly spaced focusing and accelerating quadrupoles, thereby to maintain a particle beam traversing the electrostatic fields of the quadrupoles in the assembly in an essentially laminar flow throughout the assembly.

Building 1D resonance broadened quasilinear (RBQ) code for fast ions Alfvénic relaxations

NASA Astrophysics Data System (ADS)

Gorelenkov, Nikolai; Duarte, Vinicius; Berk, Herbert

2016-10-01

The performance of the burning plasma is limited by the confinement of superalfvenic fusion products, e.g. alpha particles, which are capable of resonating with the Alfvénic eigenmodes (AEs). The effect of AEs on fast ions is evaluated using a resonance line broadened diffusion coefficient. The interaction of fast ions and AEs is captured for cases where there are either isolated or overlapping modes. A new code RBQ1D is being built which constructs diffusion coefficients based on realistic eigenfunctions that are determined by the ideal MHD code NOVA. The wave particle interaction can be reduced to one-dimensional dynamics where for the Alfvénic modes typically the particle kinetic energy is nearly constant. Hence to a good approximation the Quasi-Linear (QL) diffusion equation only contains derivatives in the angular momentum. The diffusion equation is then one dimensional that is efficiently solved simultaneously for all particles with the equation for the evolution of the wave angular momentum. The evolution of fast ion constants of motion is governed by the QL diffusion equations which are adapted to find the ion distribution function.

The Columbia University Sub-micron Charged Particle Beam

PubMed Central

Randers-Pehrson, Gerhard; Johnson, Gary W.; Marino, Stephen A.; Xu, Yanping; Dymnikov, Alexander D.; Brenner, David J.

2009-01-01

A lens system consisting of two electrostatic quadrupole triplets has been designed and constructed at the Radiological Research Accelerator Facility (RARAF) of Columbia University. The lens system has been used to focus 6-MeV 4He ions to a beam spot in air with a diameter of 0.8 µm. The quadrupole electrodes can withstand voltages high enough to focus 4He ions up to 10 MeV and protons up to 5 MeV. The quadrupole triplet design is novel in that alignment is made through precise construction and the relative strengths of the quadrupoles are accomplished by the lengths of the elements, so that the magnitudes of the voltages required for focusing are nearly identical. The insulating sections between electrodes have had ion implantation to improve the voltage stability of the lens. The lens design employs Russian symmetry for the quadrupole elements. PMID:20161365

Exact cancellation of emittance growth due to coupled transverse dynamics in solenoids and rf couplers

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

Dowell, David H.; Zhou, Feng; Schmerge, John

Weak, rotated magnetic and radio frequency quadrupole fields in electron guns and injectors can couple the beam’s horizontal with vertical motion, introduce correlations between otherwise orthogonal transverse momenta, and reduce the beam brightness. This paper discusses two important sources of coupled transverse dynamics common to most electron injectors. The first is quadrupole focusing followed by beam rotation in a solenoid, and the second coupling comes from a skewed high-power rf coupler or cavity port which has a rotated rf quadrupole field. It is shown that a dc quadrupole field can correct for both types of couplings and exactly cancel theirmore » emittance growths. The degree of cancellation of the rf skew quadrupole emittance is limited by the electron bunch length. Analytic expressions are derived and compared with emittance simulations and measurements.« less

Exact cancellation of emittance growth due to coupled transverse dynamics in solenoids and rf couplers

DOE PAGES

Dowell, David H.; Zhou, Feng; Schmerge, John

2018-01-17

Weak, rotated magnetic and radio frequency quadrupole fields in electron guns and injectors can couple the beam’s horizontal with vertical motion, introduce correlations between otherwise orthogonal transverse momenta, and reduce the beam brightness. This paper discusses two important sources of coupled transverse dynamics common to most electron injectors. The first is quadrupole focusing followed by beam rotation in a solenoid, and the second coupling comes from a skewed high-power rf coupler or cavity port which has a rotated rf quadrupole field. It is shown that a dc quadrupole field can correct for both types of couplings and exactly cancel theirmore » emittance growths. The degree of cancellation of the rf skew quadrupole emittance is limited by the electron bunch length. Analytic expressions are derived and compared with emittance simulations and measurements.« less

High spin states of 72-74Kr

NASA Astrophysics Data System (ADS)

Kaushik, M.; Kumawat, M.; Singh, U. K.; Saxena, G.

2018-05-01

A theoretical investigation has made on the structure of high spin states of 72-74Kr within the framework of cranked Hartree-Fock-Bogoliubov (CHFB) theory employing a pairing + quadrupole + hexadecapole model interaction. Dependence of shape with the spin, excitation energy, alignment of proton as well as neutron 0g9/2 orbital along with backbending phenomenon are discussed upto a high spin J = 26. We found reasonable agreement with the experimental values and other theoretical calculations.

Synthesis and energy transfer studies of LaMgAl{sub 11}O{sub 19}:Cr{sup 3+}, Nd{sup 3+} phosphors

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

Zhu, Jicheng; Xia, Zhiguo; Liu, Quanlin, E-mail: qlliu@ustb.edu.cn

2016-02-15

Highlights: • Cr{sup 3+}/Nd{sup 3+} co-doped LaMgAl{sub 11}O{sub 19} phosphors were synthesized. • The energy transfer mechanism is ascribed to the dipole–quadrupole interaction. • The materials can convert the UV–vis light into near-infrared emission. - Abstract: Cr{sup 3+}/Nd{sup 3+} co-activated LaMgAl{sub 11}O{sub 19} phosphors have been synthesized by high temperature solid-state method. In the LaMgAl{sub 11}O{sub 19}:Cr{sup 3+}/Nd{sup 3+} system, Cr{sup 3+} can absorb the UV–vis photons (350–650 nm), and then energy transfer takes place between Cr{sup 3+} and Nd{sup 3+}, and finally the samples give near infrared emission originated from Nd{sup 3+}. Energy transfer from Cr{sup 3+} to Nd{supmore » 3+} is discussed via the variations of the lifetime values of Cr{sup 3+}, and the mechanism has been ascribed to the dipole–quadrupole interaction. The absorption of Cr{sup 3+} in the visible region and the following energy transfer from Cr{sup 3+} to Nd{sup 3+} indicated that the material can potentially serve as spectral convertors to improve the photovoltaic conversion efficiency of silicon-based solar cell.« less

Distal and proximal ligand interactions in heme proteins: Correlations between C-O and Fe-C vibrational frequencies, oxygen-17 and carbon-13 nuclear magnetic resonance chemical shifts, and oxygen-17 nuclear quadrupole coupling constants in C sup 17 O- and sup 13 CO-labeled species

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

Ki Deok Park; Guo, K.; Adebodun, F.

1991-03-05

The authors have obtained the oxygen-17 nuclear magnetic resonance (NMR) spectra of a variety of C{sup 17}O-labeled heme proteins, including sperm whale (Physeter catodon) myoglobin, two synthetic sperm whale myoglobin mutants (His E7 {yields} Val E7; His E7 {yields} Phe E7), adult human hemoglobin, rabbit (Oryctolagus cuniculus) hemoglobin, horseradish (Cochlearia armoracia) peroxidase isoenzymes A and C, and Caldariomyces fumago chloroperoxidase, in some cases as a function of pH, and have determined their isotropic {sup 17}O NMR chemical shifts, {delta}{sub i}, and spin-lattice relaxation times, T{sub 1}. They have also obtained similar results on a picket fence prophyrin. The results showmore » an excellent correlation between the infrared C-O vibrational frequencies, {nu}(C-O), and {delta}{sub i}, between {nu}(C-O) and the {sup 17}O nuclear quadrupole coupling constant, and as expected between e{sup 2}qQ/h and {delta}{sub i}. The results suggest the IR and NMR measurements reflect the same interaction, which is thought to be primarily the degree of {pi}-back-bonding from Fe d to CO {pi}* orbitals, as outlined previously.« less

Interaction of Fast Ions with Global Plasma Modes in the C-2 Field Reversed Configuration Experiment

NASA Astrophysics Data System (ADS)

Smirnov, Artem; Dettrick, Sean; Clary, Ryan; Korepanov, Sergey; Thompson, Matthew; Trask, Erik; Tuszewski, Michel

2012-10-01

A high-confinement operating regime [1] with plasma lifetimes significantly exceeding past empirical scaling laws was recently obtained by combining plasma gun edge biasing and tangential Neutral Beam Injection (NBI) in the C-2 field-reversed configuration (FRC) experiment [2, 3]. We present experimental and computational results on the interaction of fast ions with the n=2 rotational and n=1 wobble modes in the C-2 FRC. It is found that the n=2 mode is similar to quadrupole magnetic fields in its detrimental effect on the fast ion transport due to symmetry breaking. The plasma gun generates an inward radial electric field, thus stabilizing the n=2 rotational instability without applying the quadrupole magnetic fields. The resultant FRCs are nearly axisymmetric, which enables fast ion confinement. The NBI further suppresses the n=2 mode, improves the plasma confinement characteristics, and increases the plasma configuration lifetime [4]. The n=1 wobble mode has relatively little effect on the fast ion transport, likely due to the approximate axisymmetry about the displaced plasma column. [4pt] [1] M. Tuszewski et al., Phys. Rev. Lett. 108, 255008 (2012).[0pt] [2] M. Binderbauer et al., Phys. Rev. Lett. 105, 045003 (2010).[0pt] [3] H.Y. Guo et al., Phys. Plasmas 18, 056110 (2011).[0pt] [4] M. Tuszewski et al., Phys. Plasmas 19, 056108 (2012)

Pseudospectra in non-Hermitian quantum mechanics

NASA Astrophysics Data System (ADS)

Krejčiřík, D.; Siegl, P.; Tater, M.; Viola, J.

2015-10-01

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

Completeness of the Coulomb Wave Functions in Quantum Mechanics

ERIC Educational Resources Information Center

Mukunda, N.

1978-01-01

Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)

The infinite well and Dirac delta function potentials as pedagogical, mathematical and physical models in quantum mechanics

NASA Astrophysics Data System (ADS)

Belloni, M.; Robinett, R. W.

2014-07-01

The infinite square well and the attractive Dirac delta function potentials are arguably two of the most widely used models of one-dimensional bound-state systems in quantum mechanics. These models frequently appear in the research literature and are staples in the teaching of quantum theory on all levels. We review the history, mathematical properties, and visualization of these models, their many variations, and their applications to physical systems. For the ISW and the attractive DDF potentials, Eq. (4) implies, as expected, that energy eigenfunctions will have a kink-a discontinuous first derivative at the location of the infinite jump(s) in the potentials. However, the large |p| behavior of the momentum-space energy eigenfunction given by Eq. (5) will be |ϕ(p)|∝1/p2. Therefore for the ISW and the attractive DDF potentials, expectation value of p will be finite, but even powers of p higher than 2 will not lead to convergent integrals. This analysis proves that despite the kinks in the ISW and attractive DDF eigenfunctions, is finite, and therefore yield appropriate solutions to the Schrödinger equation.The existence of power-law ‘tails’ of a momentum distribution as indicated in Eq. (5) in the case of ‘less than perfect’ potentials [41], including a 1/p2 power-law dependence for a singular potential (such as the DDF form) may seem a mathematical artifact, but we note two explicit realizations of exactly this type of behavior in well-studied quantum systems.As noted below (in Section 6.2) the momentum-space energy eigenfunction of the ground state of one of the most familiar (and singular) potentials, namely that of the Coulomb problem, is given by ϕ1,0,0(p)=√{8p0/π}p0/2 where p0=ħ/a0 with a0 the Bohr radius. This prediction for the p-dependence of the hydrogen ground state momentum-space distribution was verified by Weigold [42] and collaborators with measurements taken out to p-values beyond 1.4p0; well out onto the power-law ‘tail’.More recently, Tan [43] and others [44,45] have noted that for condensed matter or atomic systems with a large scattering length, so that the short-range interactions can actually be modeled as singular δ-functions, the momentum distribution also exhibits a large momentum ‘tail’ which falls off as C/k4. The constant of proportionality, C (or contact as it has come to be known), encodes important information on the microscopic physics, in much the way that the constants in Eq. (5) are related to the details of the 1D potential. In fact, in one review [46] of these developments, this connection has been described as “How the tail wags the dog in ultracold atomic gases”. Just as with the H-atom momentum distribution, experiments have verified this power-law behavior for both fermion [47,48] and more recently Bose systems [49].It is these connections, namely of exemplary results derived in simpler one-dimensional systems such as the ISW and DDF potentials which find parallels in more fundamental physical realizations, that motivate us to review many of the basic mathematical and physical results of these two ‘benchmark’ model potentials. We hope that both students and instructors alike involved in advanced undergraduate and graduate courses in quantum mechanics will find this survey useful. We trust that it will aid readers in exploring a wide array of physical effects, using rigorous mathematical methods, in the context of familiar one-dimensional systems, making use of otherwise hard-to-find results.

Photoionization of Ne8+

NASA Astrophysics Data System (ADS)

Pindzola, M. S.; Abdel-Naby, Sh. A.; Robicheaux, F.; Colgan, J.

2014-05-01

Single and double photoionization cross sections for Ne8+ are calculated using a non-perturbative fully relativistic time-dependent close-coupling method. A Bessel function expansion is used to include both dipole and quadrupole effects in the radiation field interaction and the repulsive interaction between electrons includes both the Coulomb and Gaunt interactions. The fully correlated ground state of Ne8+ is obtained by solving a time-independent inhomogeneous set of close-coupled equations. Propagation of the time-dependent close-coupled equations yields single and double photoionization cross sections for Ne8+ at energies easily accessible at advanced free electron laser facilities. This work was supported in part by grants from NSF and US DoE. Computational work was carried out at NERSC in Oakland, California, NICS in Knoxville, Tennessee, and OLCF in Oak Ridge, Tennessee.

Leakage of power from dipole to higher multipoles due to non-symmetric beam shape of the CMB missions

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

Das, Santanu; Souradeep, Tarun, E-mail: santanud@iucaa.ernet.in, E-mail: tarun@iucaa.ernet.in

2015-05-01

A number of studies of WMAP and Planck claimed the low multipole (specially quadrupole) power deficiency in CMB power spectrum. Anomaly in the orientations of the low multipoles have also been claimed. There is a possibility that the power deficiency at low multipoles may not be of primordial origin and is only an observation artifact coming from the scan procedure adapted in the WMAP or Planck satellites. Therefore, it is always important to investigate all the observational artifacts that can mimic them. The CMB dipole which is much higher than the quadrupole can leak to the higher multipoles due tomore » the non-symmetric beam shape of the WMAP or Planck. We observe that a non-negligible amount of power from the dipole can get transferred to the quadrupole and the higher multipoles due to the non-symmetric beam shapes and contaminate the observed measurements. The orientation of the quadrupole generated by this power transfer is surprisingly very close to the quadrupole observed from the WMAP and Planck maps. However, our analysis shows that the orientation of the quadrupole can not be explained using only the dipole power leakage. In this paper we calculate the amount of quadrupole power leakage for different WMAP bands. For Planck we present the results in terms of upper limits on asymmetric beam parameters that can lead to significant amount of power leakage.« less

Permanent magnet edge-field quadrupole

DOEpatents

Tatchyn, R.O.

1997-01-21

Planar permanent magnet edge-field quadrupoles for use in particle accelerating machines and in insertion devices designed to generate spontaneous or coherent radiation from moving charged particles are disclosed. The invention comprises four magnetized rectangular pieces of permanent magnet material with substantially similar dimensions arranged into two planar arrays situated to generate a field with a substantially dominant quadrupole component in regions close to the device axis. 10 figs.

Permanent magnet edge-field quadrupole

DOEpatents

Tatchyn, Roman O.

1997-01-01

Planar permanent magnet edge-field quadrupoles for use in particle accelerating machines and in insertion devices designed to generate spontaneous or coherent radiation from moving charged particles are disclosed. The invention comprises four magnetized rectangular pieces of permanent magnet material with substantially similar dimensions arranged into two planar arrays situated to generate a field with a substantially dominant quadrupole component in regions close to the device axis.

Investigating a Quadrant Surface Coil Array for NQR Remote Sensing

DTIC Science & Technology

2014-10-23

UNCLASSIFIED 1  Abstract—this paper is on the design and fabrication of a surface coil array in a quadrant layout for NQR (Nuclear Quadrupole...coupling and SNR (Signal-to-Noise Ratio) at standoff distances perpendicular from each coil. Index Terms— Nuclear Quadrupole Resonance, NQR ...Coil Array, probe, Nuclear Magnetic Resonance, tuning, decoupling, RLC, mutual coupling, RLC I. INTRODUCTION N Nuclear quadrupole resonance ( NQR

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.

The Effect of Global-Scale, Steady-State Convection and Elastic-Gravitational Asphericities on Helioseismic Oscillations

NASA Astrophysics Data System (ADS)

Lavely, Eugene M.; Ritzwoller, Michael H.

1992-06-01

In this paper we derive a theory, based on quasi-degenerate perturbation theory, that governs the effect of global-scale, steady-state convection and associated static asphericities in the elastic-gravitational variables (adiabatic bulk modulus kappa , density ρ , and gravitational potential φ ) on helioseismic eigenfrequencies and eigenfunctions and present a formalism with which this theory can be applied computationally. The theory rests on three formal assumptions: (1) that convection is temporally steady in a frame corotating with the Sun, (2) that accurate eigenfrequencies and eigenfunctions can be determined by retaining terms in the seismically perturbed equations of motion only to first order in p-mode displacement, and (3) that we are justified in retaining terms only to first order in convective velocity (this is tantamount to assuming that the convective flow is anelastic). The most physically unrealistic assumption is (1), and we view the results of this paper as the first step toward a more general theory governing the seismic effects of time-varying fields. Although the theory does not govern the seismic effects of non-stationary flows, it can be used to approximate the effects of unsteady flows on the acoustic wavefield if the flow is varying smoothly in time. The theory does not attempt to model seismic modal amplitudes since these are governed, in part, by the exchange of energy between convection and acoustic motions which is not a part of this theory. However, we show how theoretical wavefields can be computed given a description of the stress field produced by a source process such as turbulent convection. The basic reference model that will be perturbed by rotation, convection, structural asphericities, and acoustic oscillations is a spherically symmetric, non-rotating, non-magnetic, isotropic, static solar model that, when subject to acoustic oscillations, oscillates adiabatically. We call this the SNRNMAIS model. An acoustic mode of the SNRNMAIS model is denoted by k = (n,l,m), where n is the radial order, l is the harmonic degree, and m is the azimuthal order of the mode. The main result of the paper is the general matrix element Hn'n,l'lm'm for steady-state convection satisfying the anelastic condition with static structural asphericities. It is written in terms of the radial, scalar eigenfunctions of the SNRNMAIS model, resulting in equations (90)-(110). We prove Rayleigh's principle in our derivation of quasi-degenerate perturbation theory which, as a by-product, yields the general matrix element. Within this perturbative method, modes need not be exactly degenerate in the SNRNMAIS solar model to couple, only nearly so. General matrix elements compose the hermitian supermatrix Z. The eigenvalues of the supermatrix are the eigenfrequency perturbations of the convecting, aspherical model and the eigenvector components of Z are the expansion coefficients in the linear combination forming the eigenfunctions in which the eigenfunctions of the SNRNMAIS solar model act as basis functions. The properties of the Wigner 3j symbols and the reduced matrix elements composing Hn'n,l'lm' produce selection rules governing the coupling of SNRNMAIS modes that hold even for time-varying flows. We state selection rules for both quasi-degenerate and degenerate perturbation theories. For example, within degenerate perturbation theory, only odd-degree s toroidal flows and even degree structural asphericities, both with s <= 2l, will couple and/or split acoustic modes with harmonic degree l. In addition, the frequency perturbations caused by a toroidal flow display odd symmetry with respect to the degenerate frequency when ordered from the minimum to the maximum frequency perturbation. We consider the special case of differential rotation, the odd-degree, axisymmetric, toroidal component of general convection, and present the general matrix element and selection rules under quasi-degenerate perturbation theory. We argue that due to the spacing of modes that satisfy the selection rules, quasi-degenerate coupling can, for all practical purposes, be neglected in modelling the effect of low-degree differential rotation on helioseismic data. In effect, modes that can couple through low-degree differential rotation are too far separated in frequency to couple strongly. This is not the case for non-axisymmetric flows and asphericities where near degeneracies will regularly occur, and couplings can be relatively strong especially among SNRNMAIS modes within the same multiplet. All derivations are performed and all solutions are presented in a frame corotating with the mean solar angular rotation rate. Equation (18) shows how to transform the eigenfrequencies and eigenfunctions in the corotating frame into an inertial frame. The transformation has the effect that each eigenfunction in the inertial frame is itself time varying. That is, a mode of oscillation, which is defined to have a single frequency in the corotating frame, becomes multiply periodic in the inertial frame.

Are the low-lying isovector 1 + states scissors vibrations?

NASA Astrophysics Data System (ADS)

Faessler, A.

At the Technische Hochschule in Darmstadt the group of Richter and coworkers found in 1983/84 in deformed rare earth nuclei low-lying isovector 1 + states. Such states have been predicted in the generalized Bohr-Mottelson model and in the interacting boson model no. 2 (IBA2). In the generalized Bohr-Mottelson model one allows for proton and neutron quadrupole deformations separately. If one includes only static proton and neutron deformations the generalized Bohr-Mottelson model reduces to the two rotor model. It describes the excitation energy of these states in good agreement with the data but overestimates the magnetic dipole transition probabilities by a factor 5. In the interacting boson model (IBA2) where only the outermost nucleons participate in the excitation the magnetic dipole transition probability is only overestimated by a factor 2. The too large collectivity in both models results from the fact that they concentrate the whole strength of the scissors vibrations into one state. A microscopic description is needed to describe the spreading of the scissors strength over several states. For a microscopic determination of these scissors states one uses the Quasi-particle Random Phase Approximation (QRPA). But this approach has a serious difficulty. Since one rotates for the calculation the nucleus into the intrinsic system the state corresponding to the rotation of the whole nucleus is a spurious state. The usual procedure to remove this spuriosity is to use the Thouless theorem which says that a spurious state created by an operator which commutes with the total hamiltonian (here the total angular momentum, corresponding to a rotation of the whole system) produces the spurious state if applied to the ground state. It says further the energy of this spurious state lies at zero excitation energy (it is degenerate with the ground state) and is orthogonal to all physical states. Thus the usual approach is to vary the quadrupole-quadrupole force strength so that a state lies at zero excitation energy and to identify that with the spuríous state. This procedure assumes that a total angular momentum commutes with a total hamiltonian. But this is not the case since the total hamiltonian contains a deformed Saxon-Woods potential. Thus one has to take care explicitly that the spurious state is removed. This we do in our approach by introducing Lagrange multipliers for each excited states and requesting that these states are orthogonal to the spurious state which is explicitly constructed by applying the total angular momentum operator to the ground state. To reduce the number of free parameters in the hamiltonian we take the Saxon-Woods potential for the deformed nuclei from the literature (with minor adjustments) and determine the proton-proton, neutron-neutron and the proton-neutron quadrupole force constant by requesting that the hamiltonian commutes with the total angular momentum in the (QRPA) ground state. This yields equations fixing all three coupling constants for the quadrupole-quadrupole force allowing even for isospin symmetry violation. The spin-spin force is taken from the Reid soft core potential. A possible spin-quadrupole force has been taken from the work of Soloviev but it turns out that this is not important. The calculation shows that the strength of the scissors vibrations are spread over many states. The main 1 + state at around 3 MeV has an overlap of the order of 14 % of the scissors state. 50% of that state are spread over the physical states up to an excitation energy of 6 MeV. The rest is distributed over higher lying states. The expectation value of the many-body hamiltonian in the scissors vibrational state shows roughly an excitation energy of 7 MeV above the ground state. The results also support the experimental findings that these states are mainly orbital excitations. States are not very collective. Normally only a proton and neutron particle-hole pair are with a large amplitude participating in forming these states. But those protons and neutrons which are excited perform scissors type vibrations.

Energetic ion mass analysis using a radio-frequency quadrupole filter.

PubMed

Medley, S S

1978-06-01

In conventional applications of the radio-frequency quadrupole mass analyzer, the ion injection energy is usually limited to less than the order of 100 eV due to constraints on the dimensions and power supply of the device. However, requirements often arise, for example in fusion plasma ion diagnostics, for mass analysis of much more energetic ions. A technique easily adaptable to any conventional quadrupole analyzer which circumvents the limitation on injection energy is documented in this paper. Briefly, a retarding potential applied to the pole assembly is shown to facilitate mass analysis of multikiloelectron volt ions without altering the salient characteristics of either the quadrupole filter or the ion beam.

An overview of the evaluation of oxygen interaction with materials-third phase (EOIM-III) experiment - Space Shuttle Mission 46

NASA Technical Reports Server (NTRS)

Leger, Lubert J.; Koontz, Steven L.; Visentine, James T.; Hunton, Donald

1993-01-01

An overview of EOIM-III, designed to produce benchmark atomic oxygen reactivity data is presented. Ambient density measurements are conducted using a quadrupole mass spectrometer calibrated for atomic oxygen measurements in a unique ground-based test facility. The combination of these data with the predictions of ambient density models permits an assessment of the accuracy of measured reaction rates on a variety of materials, many of which have never been tested in LEO previously.

Pocket formula for nuclear deformations of actinides

NASA Astrophysics Data System (ADS)

Manjunatha, H. C.; Sridhar, K. N.

2018-06-01

We have formulated a pocket formula for quadrupole (β2), octupole (β3), hexadecapole (β4) and hexacontatetrapole (β6) deformation of the nuclear ground state of all isotopes of actinide nuclei (89 < Z < 103). This formula is first of its kind and produces a nuclear deformation of all isotopes actinide nuclei 89 < Z < 103 with simple inputs of Z and A. Hence, this formula is useful in the fields of nuclear physics to study the structure and interaction of nuclei.

Phase transitions in the sdg interacting boson model

NASA Astrophysics Data System (ADS)

Van Isacker, P.; Bouldjedri, A.; Zerguine, S.

2010-05-01

A geometric analysis of the sdg interacting boson model is performed. A coherent state is used in terms of three types of deformation: axial quadrupole ( β), axial hexadecapole ( β) and triaxial ( γ). The phase-transitional structure is established for a schematic sdg Hamiltonian which is intermediate between four dynamical symmetries of U(15), namely the spherical U(5)⊗U(9), the (prolate and oblate) deformed SU(3) and the γ-soft SO(15) limits. For realistic choices of the Hamiltonian parameters the resulting phase diagram has properties close to what is obtained in the sd version of the model and, in particular, no transition towards a stable triaxial shape is found.

Machine detector interface studies: Layout and synchrotron radiation estimate in the future circular collider interaction region

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

Boscolo, Manuela; Burkhardt, Helmut; Sullivan, Michael

The interaction region layout for the e +e – future circular collider FCC-ee is presented together with a preliminary estimate of synchrotron radiation that affects this region. We describe in this paper the main guidelines of this design and the estimate of synchrotron radiation coming from the last bending magnets and from the final focus quadrupoles, with the software tools developed for this purpose. Here, the design follows the asymmetric optics layout as far as incoming bend radiation is concerned with the maximum foreseen beam energy of 175 GeV and we present a feasible initial layout with an indication ofmore » tolerable synchrotron radiation.« less

Machine detector interface studies: Layout and synchrotron radiation estimate in the future circular collider interaction region

DOE PAGES

Boscolo, Manuela; Burkhardt, Helmut; Sullivan, Michael

2017-01-27

The interaction region layout for the e +e – future circular collider FCC-ee is presented together with a preliminary estimate of synchrotron radiation that affects this region. We describe in this paper the main guidelines of this design and the estimate of synchrotron radiation coming from the last bending magnets and from the final focus quadrupoles, with the software tools developed for this purpose. Here, the design follows the asymmetric optics layout as far as incoming bend radiation is concerned with the maximum foreseen beam energy of 175 GeV and we present a feasible initial layout with an indication ofmore » tolerable synchrotron radiation.« less

Sources of sound in fluid flows

NASA Technical Reports Server (NTRS)

Williams, J. E. F.

1974-01-01

Some features of a flow that produce acoustic radiation, particularly when the flow is turbulent and interacting with solid surfaces such as turbine or compressor blades are discussed. Early theoretical ideas on the subject are reviewed and are shown to be inadequate at high Mach number. Some recent theoretical developments that form the basis of a description of sound generation by supersonic flows interacting with surfaces are described. At high frequencies the problem is treated as one of describing the surface-induced diffraction field of adjacent aerodynamic quadrupole sources. This approach has given rise to distinctly new features of the problem that seem to have bearing on the radiating properties of relatively large aerodynamic surfaces.

Higher Order Multipole Potentials and Electrostatic Screening Effects on Cohesive Energy and Bulk Modulus of Metallic Nanoparticles

NASA Astrophysics Data System (ADS)

Barakat, T.

2011-12-01

Higher order multipole potentials and electrostatic screening effects are introduced to incorporate the dangling bonds on the surface of a metallic nanopaticle and to modify the coulomb like potential energy terms, respectively. The total interaction energy function for any metallic nanoparticle is represented in terms of two- and three-body potentials. The two-body part is described by dipole-dipole interaction potential, and in the three-body part, triple-dipole (DDD) and dipole-dipole-quadrupole (DDQ) terms are included. The size-dependent cohesive energy and bulk modulus are observed to decrease with decreasing sizes, a result which is in good agreement with the experimental values of Mo and W nanoparticles.

An energy-filtering device coupled to a quadrupole mass spectrometer for soft-landing molecular ions on surfaces with controlled energy

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

Bodin, A.; Laloo, R.; Abeilhou, P.

2013-09-15

We have developed an energy-filtering device coupled to a quadrupole mass spectrometer to deposit ionized molecules on surfaces with controlled energy in ultra high vacuum environment. Extensive numerical simulations as well as direct measurements show that the ion beam flying out of a quadrupole exhibits a high-energy tail decreasing slowly up to several hundred eV. This energy distribution renders impossible any direct soft-landing deposition of molecular ions. To remove this high-energy tail by energy filtering, a 127° electrostatic sector and a specific triplet lenses were designed and added after the last quadrupole of a triple quadrupole mass spectrometer. The resultsmore » obtained with this energy-filtering device show clearly the elimination of the high-energy tail. The ion beam that impinges on the sample surface satisfies now the soft-landing criterion for molecular ions, opening new research opportunities in the numerous scientific domains involving charges adsorbed on insulating surfaces.« less

Evaluating Mass Analyzers as Candidates for Small, Portable, Rugged Single Point Mass Spectrometers for Analysis of Permanent Gases

NASA Technical Reports Server (NTRS)

Arkin, C. Richard; Ottens, Andrew K.; Diaz, Jorge A.; Griffin, Timothy P.; Follestein, Duke; Adams, Fredrick; Steinrock, T. (Technical Monitor)

2001-01-01

For Space Shuttle launch safety, there is a need to monitor the concentration Of H2, He, O2, and Ar around the launch vehicle. Currently a large mass spectrometry system performs this task, using long transport lines to draw in samples. There is great interest in replacing this stationary system with several miniature, portable, rugged mass spectrometers which act as point sensors which can be placed at the sampling point. Five commercial and two non-commercial analyzers are evaluated. The five commercial systems include the Leybold Inficon XPR-2 linear quadrupole, the Stanford Research (SRS-100) linear quadrupole, the Ferran linear quadrupole array, the ThermoQuest Polaris-Q quadrupole ion trap, and the IonWerks Time-of-Flight (TOF). The non-commercial systems include a compact double focusing sector (CDFMS) developed at the University of Minnesota, and a quadrupole ion trap (UF-IT) developed at the University of Florida.

Triple Quadrupole Versus High Resolution Quadrupole-Time-of-Flight Mass Spectrometry for Quantitative LC-MS/MS Analysis of 25-Hydroxyvitamin D in Human Serum

NASA Astrophysics Data System (ADS)

Geib, Timon; Sleno, Lekha; Hall, Rabea A.; Stokes, Caroline S.; Volmer, Dietrich A.

2016-08-01

We describe a systematic comparison of high and low resolution LC-MS/MS assays for quantification of 25-hydroxyvitamin D3 in human serum. Identical sample preparation, chromatography separations, electrospray ionization sources, precursor ion selection, and ion activation were used; the two assays differed only in the implemented final mass analyzer stage; viz. high resolution quadrupole-quadrupole-time-of-flight (QqTOF) versus low resolution triple quadrupole instruments. The results were assessed against measured concentration levels from a routine clinical chemiluminescence immunoassay. Isobaric interferences prevented the simple use of TOF-MS spectra for extraction of accurate masses and necessitated the application of collision-induced dissociation on the QqTOF platform. The two mass spectrometry assays provided very similar analytical figures of merit, reflecting the lack of relevant isobaric interferences in the MS/MS domain, and were successfully applied to determine the levels of 25-hydroxyvitamin D for patients with chronic liver disease.

Production and installation of the LHC low-beta triplets

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

Feher, S.; Bossert, R.; DiMarco, J.

2005-09-01

The LHC performance depends critically on the low-{beta}, triplets, located on either side of the four interaction points. Each triplet consists of four superconducting quadrupole magnets, which must operate reliably at up to 215 T/m, sustain extremely high heat loads and have an excellent field quality. A collaboration of CERN, Fermilab and KEK was formed in 1996 to design and build the triplet systems, and after nine years of joint effort the production has been completed in 2005. We retrace the main events of the project and present the design features and performance of the low-{beta} quadrupoles, built by KEKmore » and Fermilab, as well as of other vital elements of the triplet. The tunnel installation of the first triplet and plans for commissioning in the LHC are also presented. Apart from the excellent technical results, the construction of the LHC low-{beta} triplets has been a highly enriching experience combining harmoniously the different competences and approaches to engineering in a style reminiscent of high energy physics experiment collaborations, and rarely before achieved in construction of an accelerator.« less

Energy levels, lifetimes, and transition rates for the selenium isoelectronic sequence Pd XIII-Te XIX, Xe XXI-Nd XXVII, W XLI

NASA Astrophysics Data System (ADS)

Wang, K.; Yang, X.; Chen, Z. B.; Si, R.; Chen, C. Y.; Yan, J.; Zhao, X. H.; Dang, W.

2017-09-01

Energy levels, wavelengths, lifetimes, oscillator strengths, and electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), magnetic quadrupole (M2) transition rates among the 46 fine structure levels belonging to the ([ Ar ] 3d10) 4s2 4p4, ([ Ar ] 3d10) 4s2 4p3 4 d, and ([ Ar ] 3d10) 4 s 4p5 configurations for the selenium isoelectronic sequence Pd XIII-Te XIX, Xe XXI-Nd XXVII, W XLI are reported. These data are determined in the multi-configuration Dirac-Fock (MCDF) approach, in which relativistic effects, main electron correlations within the n = 7 complex, Breit interaction (BI), and quantum electrodynamic (QED) corrections are included. The many-body perturbation theory (MBPT) method is also employed as an independent calculation to confirm the present accuracy, taking W XLI as an example. Comparisons and analysis are made between the present results and available experimental and theoretical ones, and good agreements are obtained. These accurate data are expected to be useful in nuclear fusion research and astrophysical applications.

Ultrahigh-resolution γ-ray spectroscopy of 156Gd: a test of tetrahedral symmetry.

PubMed

Jentschel, M; Urban, W; Krempel, J; Tonev, D; Dudek, J; Curien, D; Lauss, B; de Angelis, G; Petkov, P

2010-06-04

Tetrahedral symmetry in strongly interacting systems would establish a new class of quantum effects at subatomic scale. Excited states in 156Gd that could carry the information about the tetrahedral symmetry were populated in the 155Gd(n,γ)156Gd reaction and studied using the GAMS4/5 Bragg spectrometers at the Institut Laue-Langevin. We have identified the 5(1)- → 3(1)- transition of 131.983(12) keV in 156Gd and determined its intensity to be 1.9(3)x10(-6) per neutron capture. The lifetime τ=220(-30)(+180) fs of the 5(1)- state in 156Gd has been measured using the GRID technique. The resulting B(E2)=293(-134)(+6) Weisskopf unit rate of the 131.983 keV transition provides the intrinsic quadrupole moment of the 5(1)- state in 156Gd to be Q0=7.1(-1.6)(+0.7) b. This large value, comparable to the quadrupole moment of the ground state in 156Gd, gives strong evidence against tetrahedral symmetry in the lowest odd-spin, negative-parity band of 156Gd.

Comprehensive two-dimensional gas chromatography in combination with rapid scanning quadrupole mass spectrometry in perfume analysis.

PubMed

Mondello, Luigi; Casillia, Alessandro; Tranchida, Peter Quinto; Dugo, Giovanni; Dugo, Paola

2005-03-04

Single column gas chromatography (GC) in combination with a flame ionization detector (FID) and/or a mass spectrometer is routinely employed in the determination of perfume profiles. The latter are to be considered medium to highly complex matrices and, as such, can only be partially separated even on long capillaries. Inevitably, several monodimensional peaks are the result of two or more overlapping components, often hindering reliable identification and quantitation. The present investigation is based on the use of a comprehensive GC (GC x GC) method, in vacuum outlet conditions, for the near to complete resolution of a complex perfume sample. A rapid scanning quadrupole mass spectrometry (qMS) system, employed for the assignment of GC x GC peaks, supplied high quality mass spectra. The validity of the three-dimensional (3D) GC x GC-qMS application was measured and compared to that of GC-qMS analysis on the same matrix. Peak identification, in all applications, was achieved through MS spectra library matching and the interactive use of linear retention indices (LRI).

Nature of isomerism of solid isothiourea salts, inhibitors of nitric oxide synthases, as studied by 1H-14N nuclear quadrupole double resonance, X-ray, and density functional theory/quantum theory of atoms in molecules.

PubMed

Latosińska, J N; Latosińska, M; Seliger, J; Žagar, V; Maurin, J K; Kazimierczuk, Z

2012-02-09

Isothioureas, inhibitors of nitric oxide synthases, have been studied experimentally in solid state by nuclear quadrupole double resonance (NQDR) and X-ray methods and theoretically by the quantum theory of atoms in molecules/density functional theory. Resonance frequencies on (14)N have been detected and assigned to particular nitrogen sites in each molecule. The crystal packings of (S)-3,4-dichlorobenzyl-N-methylisothiouronium chloride with the disordered chlorine positions in benzene ring and (S)-butyloisothiouronium bromide have been resolved in X-ray diffraction studies. (14)N NQDR spectra have been found good indicators of isomer type and strength of intra- or intermolecular N-H···X (X = Cl, Br) interactions. From among all salts studied, only for (S)-2,3,4,5,6-pentabromobenzylisothiouronium chloride are both nitrogen sites equivalent, which has been explained by the slow exchange. This unique structural feature can be a key factor in the high biological activity of (S)-2,3,4,5,6-pentabromobenzylisothiouronium salts.

CFD Modelling of a Quadrupole Vortex Inside a Cylindrical Channel for Research into Advanced Hybrid Rocket Designs

NASA Astrophysics Data System (ADS)

Godfrey, B.; Majdalani, J.

2014-11-01

This study relies on computational fluid dynamics (CFD) tools to analyse a possible method for creating a stable quadrupole vortex within a simulated, circular-port, cylindrical rocket chamber. A model of the vortex generator is created in a SolidWorks CAD program and then the grid is generated using the Pointwise mesh generation software. The non-reactive flowfield is simulated using an open source computational program, Stanford University Unstructured (SU2). Subsequent analysis and visualization are performed using ParaView. The vortex generation approach that we employ consists of four tangentially injected monopole vortex generators that are arranged symmetrically with respect to the center of the chamber in such a way to produce a quadrupole vortex with a common downwash. The present investigation focuses on characterizing the flow dynamics so that future investigations can be undertaken with increasing levels of complexity. Our CFD simulations help to elucidate the onset of vortex filaments within the monopole tubes, and the evolution of quadrupole vortices downstream of the injection faceplate. Our results indicate that the quadrupole vortices produced using the present injection pattern can become quickly unstable to the extent of dissipating soon after being introduced into simulated rocket chamber. We conclude that a change in the geometrical configuration will be necessary to produce more stable quadrupoles.

1H NMR relaxometry and quadrupole relaxation enhancement as a sensitive probe of dynamical properties of solids—[C(NH2)3]3Bi2I9 as an example

NASA Astrophysics Data System (ADS)

Florek-Wojciechowska, M.; Wojciechowski, M.; Jakubas, R.; Brym, Sz.; Kruk, D.

2016-02-01

1H nuclear magnetic resonance relaxometry has been applied to reveal information on dynamics and structure of Gu3Bi2I9 ([Gu = C(NH2)3] denotes guanidinium cation). The data have been analyzed in terms of a theory of quadrupole relaxation enhancement, which has been extended here by including effects associated with quadrupole (14N) spin relaxation caused by a fast fluctuating component of the electric field gradient tensor. Two motional processes have been identified: a slow one occurring on a timescale of about 8 × 10-6 s which has turned out to be (almost) temperature independent, and a fast process in the range of 10-9 s. From the 1H-14N relaxation contribution (that shows "quadrupole peaks") the quadrupole parameters, which are a fingerprint of the arrangement of the anionic network, have been determined. It has been demonstrated that the magnitude of the quadrupole coupling considerably changes with temperature and the changes are not caused by phase transitions. At the same time, it has been shown that there is no evidence of abrupt changes in the cationic dynamics and the anionic substructure upon the phase transitions.

A code for analysis of the fine structure in near-rigid weakly-bonded open-shell complexes that consist of a diatomic radical in a Σ3 state and a closed-shell molecule

NASA Astrophysics Data System (ADS)

Fawzy, Wafaa M.

2010-10-01

A FORTRAN code is developed for simulation and fitting the fine structure of a planar weakly-bonded open-shell complex that consists of a diatomic radical in a Σ3 electronic state and a diatomic or a polyatomic closed-shell molecule. The program sets up the proper total Hamiltonian matrix for a given J value and takes account of electron-spin-electron-spin, electron-spin rotation interactions, and the quartic and sextic centrifugal distortion terms within the complex. Also, R-dependence of electron-spin-electron-spin and electron-spin rotation couplings are considered. The code does not take account of effects of large-amplitude internal rotation of the diatomic radical within the complex. It is assumed that the complex has a well defined equilibrium geometry so that effects of large amplitude motion are negligible. Therefore, the computer code is suitable for a near-rigid rotor. Numerical diagonalization of the matrix provides the eigenvalues and the eigenfunctions that are necessary for calculating energy levels, frequencies, relative intensities of infrared or microwave transitions, and expectation values of the quantum numbers within the complex. Goodness of all the quantum numbers, with exception of J and parity, depends on relative sizes of the product of the rotational constants and quantum numbers (i.e. BJ, CJ, and AK), electron-spin-electron-spin, and electron-spin rotation couplings, as well as the geometry of the complex. Therefore, expectation values of the quantum numbers are calculated in the eigenfunctions basis of the complex. The computational time for the least squares fits has been significantly reduced by using the Hellman-Feynman theory for calculating the derivatives. The computer code is useful for analysis of high resolution infrared and microwave spectra of a planar near-rigid weakly-bonded open-shell complex that contains a diatomic fragment in a Σ3 electronic state and a closed-shell molecule. The computer program was successfully applied to analysis and fitting the observed high resolution infrared spectra of the O 2sbnd HF/O 2sbnd DF and O 2sbnd N 2O complexes. Test input file for simulation and fitting the high resolution infrared spectrum of the O 2sbnd DF complex is provided. Program summaryProgram title: TSIG_COMP Catalogue identifier: AEGM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGM_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 10 030 No. of bytes in distributed program, including test data, etc.: 51 663 Distribution format: tar.gz Programming language: Fortran 90, free format Computer: SGI Origin 3400, workstations and PCs Operating system: Linux, UNIX and Windows (see Restrictions below) RAM: Case dependent Classification: 16.2 Nature of problem: TSIG_COMP calculates frequencies, relative intensities, and expectation values of the various quantum numbers and parities of bound states involved in allowed ro-vibrational transitions in semi-rigid planar weakly-bonded open-shell complexes. The complexes of interest contain a free radical in a Σ3 state and a closed-shell partner, where the electron-spin-electron-spin interaction, electron-spin rotation interaction, and centrifugal forces significantly modify the spectral patterns. To date, ab initio methods are incapable of taking these effects into account to provide accurate predictions for the ro-vibrational energy levels of the complexes of interest. In the TSIG_COMP program, the problem is solved by using the proper effective Hamiltonian and molecular basis set. Solution method: The program uses a Hamiltonian operator that takes into account vibration, end-over-end rotation, electron-spin-electron-spin and electron-spin rotation interactions as well as the various centrifugal distortion terms. The Hamiltonian operator and the molecular basis set are used to set up the Hamiltonian matrix in the inertial axis system of the complex of interest. Diagonalization of the Hamiltonian matrix provides the eigenvalues and the eigenfunctions for the bound ro-vibrational states. These eigenvalues and eigenfunctions are used to calculate frequencies and relative intensities of the allowed infrared or microwave transitions as well as expectation values of all the quantum numbers and parities of states involved in the transitions. The program employs the method of least squares fits to fit the observed frequencies to the calculated frequencies to provide the molecular parameters that determine the geometry of the complex of interest. Restrictions: The number of transitions and parameters included in the fits is limited to 80 parameters and 200 transitions. However, these numbers can be increased by adjusting dimensions of the arrays (not recommended). Running the program under MS windows is recommended for simulations of any number of transitions and for fitting a relatively small number of parameters and transitions (maximum 15 parameters and 82 transitions), for fitting larger number of parameters run time error may occur. Because spectra of weakly bonded complexes are recorded at low temperatures, in most of cases fittings can be performed under MS windows. Running time: Problem-dependent. The provided test input for Linux fits 82 transitions and 21 parameters, the actual run time is 62 minutes. The provided test input file for MS windows fits 82 transitions and 15 parameters; the actual runtime is 5 minutes.

An Introduction to Multilinear Formula Score Theory. Measurement Series 84-4.

ERIC Educational Resources Information Center

Levine, Michael V.

Formula score theory (FST) associates each multiple choice test with a linear operator and expresses all of the real functions of item response theory as linear combinations of the operator's eigenfunctions. Hard measurement problems can then often be reformulated as easier, standard mathematical problems. For example, the problem of estimating…

An Isoperimetric Inequality for Fundamental Tones of Free Plates

ERIC Educational Resources Information Center

Chasman, Laura

2009-01-01

We establish an isoperimetric inequality for the fundamental tone (first nonzero eigenvalue) of the free plate of a given area, proving the ball is maximal. Given tau greater than 0, the free plate eigenvalues omega and eigenfunctions upsilon are determined by the equation Delta Delta upsilon - tau Delta upsilon = omega upsilon together with…

Alternative Form of the Hydrogenic Wave Functions for an Extended, Uniformly Charged Nucleus.

ERIC Educational Resources Information Center

Ley-Koo, E.; And Others

1980-01-01

Presented are forms of harmonic oscillator attraction and Coulomb wave functions which can be explicitly constructed and which lead to numerical results for the energy eigenvalues and eigenfunctions of the atomic system. The Schrodinger equation and its solution and specific cases of muonic atoms illustrating numerical calculations are included.…

Teaching Qualitative Energy-Eigenfunction Shape with Physlets

ERIC Educational Resources Information Center

Belloni, Mario; Christian, Wolfgang; Cox, Anne J.

2007-01-01

More than 35 years ago, French and Taylor outlined an approach to teach students and teachers alike how to understand "qualitative plots of bound-state wave functions." They described five fundamental statements based on the quantum-mechanical concepts of probability and energy (total and potential), which could be used to deduce the shape of…

A High Frequency Model of Cascade Noise

NASA Technical Reports Server (NTRS)

Envia, Edmane

1998-01-01

Closed form asymptotic expressions for computing high frequency noise generated by an annular cascade in an infinite duct containing a uniform flow are presented. There are two new elements in this work. First, the annular duct mode representation does not rely on the often-used Bessel function expansion resulting in simpler expressions for both the radial eigenvalues and eigenfunctions of the duct. In particular, the new representation provides an explicit approximate formula for the radial eigenvalues obviating the need for solutions of the transcendental annular duct eigenvalue equation. Also, the radial eigenfunctions are represented in terms of exponentials eliminating the numerical problems associated with generating the Bessel functions on a computer. The second new element is the construction of an unsteady response model for an annular cascade. The new construction satisfies the boundary conditions on both the cascade and duct walls simultaneously adding a new level of realism to the noise calculations. Preliminary results which demonstrate the effectiveness of the new elements are presented. A discussion of the utility of the asymptotic formulas for calculating cascade discrete tone as well as broadband noise is also included.

Quantum integrable systems from conformal blocks

NASA Astrophysics Data System (ADS)

Chen, Heng-Yu; Qualls, Joshua D.

2017-05-01

In this note, we extend the striking connections between quantum integrable systems and conformal blocks recently found in [M. Isachenkov and V. Schomerus, Phys. Rev. Lett. 117, 071602 (2016), 10.1103/PhysRevLett.117.071602] in several directions. First, we explicitly demonstrate that the action of the quartic conformal Casimir operator on general d-dimensional scalar conformal blocks can be expressed in terms of certain combinations of commuting integrals of motions of the two particle hyperbolic BC2 Calogero-Sutherland system. The permutation and reflection properties of the underlying Dunkl operators play crucial roles in establishing such a connection. Next, we show that the scalar superconformal blocks in superconformal field theories (SCFTs) with four and eight supercharges and suitable chirality constraints can also be identified with the eigenfunctions of the same Calogero-Sutherland system; this demonstrates the universality of such a connection. Finally, we observe that the so-called "seed" conformal blocks for constructing four point functions for operators with arbitrary space-time spins in four-dimensional CFTs can also be linearly expanded in terms of Calogero-Sutherland eigenfunctions.

Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

NASA Astrophysics Data System (ADS)

Guarnieri, F.; Moon, W.; Wettlaufer, J. S.

2017-09-01

Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with a negative constant drift, described by a Fokker-Planck equation with a potential V (x ) =-[b ln(x ) +a x ] , for b >0 and a <0 . The problem belongs to a family of Fokker-Planck equations with logarithmic potentials closely related to the Bessel process that has been extensively studied for its applications in physics, biology, and finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schrödinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a constant negative drift. We conclude with a comparison to other analytical methods and with numerical solutions.

A photometric mode identification method, including an improved non-adiabatic treatment of the atmosphere

NASA Astrophysics Data System (ADS)

Dupret, M.-A.; De Ridder, J.; De Cat, P.; Aerts, C.; Scuflaire, R.; Noels, A.; Thoul, A.

2003-02-01

We present an improved version of the method of photometric mode identification of Heynderickx et al. (\\cite{hey}). Our new version is based on the inclusion of precise non-adiabatic eigenfunctions determined in the outer stellar atmosphere according to the formalism recently proposed by Dupret et al. (\\cite{dup}). Our improved photometric mode identification technique is therefore no longer dependent on ad hoc parameters for the non-adiabatic effects. It contains the complete physical conditions of the outer atmosphere of the star, provided that rotation does not play a key role. We apply our method to the two slowly pulsating B stars HD 74560 and HD 138764 and to the beta Cephei star EN (16) Lac. Besides identifying the degree l of the pulsating stars, our method is also a tool for improving the knowledge of stellar interiors and atmospheres, by imposing constraints on parameters such as the metallicity and the mixing-length parameter alpha (a procedure we label non-adiabatic asteroseismology). The non-adiabatic eigenfunctions needed for the mode identification are available upon request from the authors.

Extraction and prediction of indices for monsoon intraseasonal oscillations: an approach based on nonlinear Laplacian spectral analysis

NASA Astrophysics Data System (ADS)

Sabeerali, C. T.; Ajayamohan, R. S.; Giannakis, Dimitrios; Majda, Andrew J.

2017-11-01

An improved index for real-time monitoring and forecast verification of monsoon intraseasonal oscillations (MISOs) is introduced using the recently developed nonlinear Laplacian spectral analysis (NLSA) technique. Using NLSA, a hierarchy of Laplace-Beltrami (LB) eigenfunctions are extracted from unfiltered daily rainfall data from the Global Precipitation Climatology Project over the south Asian monsoon region. Two modes representing the full life cycle of the northeastward-propagating boreal summer MISO are identified from the hierarchy of LB eigenfunctions. These modes have a number of advantages over MISO modes extracted via extended empirical orthogonal function analysis including higher memory and predictability, stronger amplitude and higher fractional explained variance over the western Pacific, Western Ghats, and adjoining Arabian Sea regions, and more realistic representation of the regional heat sources over the Indian and Pacific Oceans. Real-time prediction of NLSA-derived MISO indices is demonstrated via extended-range hindcasts based on NCEP Coupled Forecast System version 2 operational output. It is shown that in these hindcasts the NLSA MISO indices remain predictable out to ˜3 weeks.

Instability of rectangular jets

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Thies, Andrew T.

1993-01-01

The instability of rectangular jets is investigated using a vortex-sheet model. It is shown that such jets support four linearly independent families of instability waves. Within each family there are infinitely many modes. A way to classify these modes according to the characteristics of their mode shapes or eigenfunctions is proposed. It is demonstrated that the boundary element method can be used to calculate the dispersion relations and eigenfunctions of these instability wave modes. The method is robust and efficient. A parametric study of the instability wave characteristics has been carried out. A sample of the numerical results is reported here. It is found that the first and third modes of each instability wave family are corner modes. The pressure fluctuations associated with these instability waves are localized near the corners of the jet. The second mode, however, is a center mode with maximum fluctuations concentrated in the central portion of the jet flow. The center mode has the largest spatial growth rate. It is anticipated that as the instability waves propagate downstream the center mode would emerge as the dominant instability of the jet.

Quantum finance Hamiltonian for coupon bond European and barrier options.

PubMed

Baaquie, Belal E

2008-03-01

Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier option for a financial instrument is "knocked out" (terminated with zero value) if the price of the underlying instrument exceeds or falls below preset limits; the barrier option is realized by imposing boundary conditions on the eigenfunctions of the forward interest rates' Hamiltonian. The price of the European coupon bond option and the zero coupon bond barrier option are calculated. It is shown that, is general, the constraint function for a coupon bond barrier option can -- to a good approximation -- be linearized. A calculation using an overcomplete set of eigenfunctions yields an approximate price for the coupon bond barrier option, which is given in the form of an integral of a factor that results from the barrier condition times another factor that arises from the payoff function.

Numerical operator calculus in higher dimensions.

PubMed

Beylkin, Gregory; Mohlenkamp, Martin J

2002-08-06

When an algorithm in dimension one is extended to dimension d, in nearly every case its computational cost is taken to the power d. This fundamental difficulty is the single greatest impediment to solving many important problems and has been dubbed the curse of dimensionality. For numerical analysis in dimension d, we propose to use a representation for vectors and matrices that generalizes separation of variables while allowing controlled accuracy. Basic linear algebra operations can be performed in this representation using one-dimensional operations, thus bypassing the exponential scaling with respect to the dimension. Although not all operators and algorithms may be compatible with this representation, we believe that many of the most important ones are. We prove that the multiparticle Schrödinger operator, as well as the inverse Laplacian, can be represented very efficiently in this form. We give numerical evidence to support the conjecture that eigenfunctions inherit this property by computing the ground-state eigenfunction for a simplified Schrödinger operator with 30 particles. We conjecture and provide numerical evidence that functions of operators inherit this property, in which case numerical operator calculus in higher dimensions becomes feasible.

Quantum self-organization and nuclear collectivities

NASA Astrophysics Data System (ADS)

Otsuka, T.; Tsunoda, Y.; Togashi, T.; Shimizu, N.; Abe, T.

2018-02-01

The quantum self-organization is introduced as one of the major underlying mechanisms of the quantum many-body systems. In the case of atomic nuclei as an example, two types of the motion of nucleons, single-particle states and collective modes, dominate the structure of the nucleus. The outcome of the collective mode is determined basically by the balance between the effect of the mode-driving force (e.g., quadrupole force for the ellipsoidal deformation) and the resistance power against it. The single-particle energies are one of the sources to produce such resistance power: a coherent collective motion is more hindered by larger gaps between relevant single particle states. Thus, the single-particle state and the collective mode are “enemies” each other. However, the nuclear forces are demonstrated to be rich enough so as to enhance relevant collective mode by reducing the resistance power by changing singleparticle energies for each eigenstate through monopole interactions. This will be verified with the concrete example taken from Zr isotopes. Thus, when the quantum self-organization occurs, single-particle energies can be self-organized, being enhanced by (i) two quantum liquids, e.g., protons and neutrons, (ii) two major force components, e.g., quadrupole interaction (to drive collective mode) and monopole interaction (to control resistance). In other words, atomic nuclei are not necessarily like simple rigid vases containing almost free nucleons, in contrast to the naïve Fermi liquid picture. Type II shell evolution is considered to be a simple visible case involving excitations across a (sub)magic gap. The quantum self-organization becomes more important in heavier nuclei where the number of active orbits and the number of active nucleons are larger. The quantum self-organization is a general phenomenon, and is expected to be found in other quantum systems.

Exploring the Angstrom Excursion of Au Nanoparticles Excited away from a Metal Surface by an Impulsive Acoustic Perturbation.

PubMed

Kim, Ji-Wan; Kovalenko, Oleksandr; Liu, Yu; Bigot, Jean-Yves

2016-12-27

We report the anharmonic angstrom dynamics of self-assembled Au nanoparticles (Au:NPs) away from a nickel surface on top of which they are coupled by their near-field interaction. The deformation and the oscillatory excursion away from the surface are induced by picosecond acoustic pulses and probed at the surface plasmon resonance with femtosecond laser pulses. The overall dynamics are due to an efficient transfer of translational momentum from the Ni surface to the Au:NPs, therefore avoiding usual thermal effects and energy redistribution among the electronic states. Two modes are clearly revealed by the oscillatory shift of the Au:NPs surface plasmon resonance-the quadrupole deformation mode due to the transient ellipsoid shape and the excursion mode when the Au:NPs bounce away from the surface. We find that, contrary to the quadrupole mode, the excursion mode is sensitive to the distance between Au:NPs and Ni. Importantly, the excursion dynamics display a nonsinusoidal motion that cannot be explained by a standard harmonic potential model. A detailed modeling of the dynamics using a Hamaker-type Lennard-Jones potential between two media is performed, showing that each Au:NPs coherently evolves in a nearly one-dimensional anharmonic potential with a total excursion of ∼1 Å. This excursion induces a shift of the surface plasmon resonance detectable because of the strong near-field interaction. This general method of observing the spatiotemporal dynamics with angstrom and picosecond resolutions can be directly transposed to many nanostructures or biosystems to reveal the interaction and contact mechanism with their surrounding medium while remaining in their fundamental electronic states.

Scissors Modes and Spin Excitations in Light Nuclei Including ΔN=2 Excitations: Behaviour of 8Be and 10Be

NASA Astrophysics Data System (ADS)

Fayache, M. S.; Sharma, S. Shelley; Zamick, L.

1996-10-01

Shell model calculations are performed for magnetic dipole excitations in8Be and10Be, first with a quadrupole-quadrupole interaction (Q·Q) and then with a realistic interaction. The calculations are performed both in a 0pspace and in a large space which includes all 2ℏωexcitations. In the 0pwithQ·Qwe have an analytic expression for the energies of all states. In this limit we find that in10Be theL=1S=0 scissors mode with isospinT=1 is degenerate with that ofT=2. By projection from an intrinsic state we can obtain simple expressions forB(M1) to the scissors modes in8Be and10Be. We plot cumulative sums for energy-weighted isovector orbital transitions fromJ=0+ground states to the 1+excited states. These have the structure of a low-energy plateau and a steep rise to a high-energy plateau. The relative magnitudes of these plateaux are discussed. By comparing8Be and10Be we find that contrary to the behaviour in heavy deformed nuclei,B(M1)orbitalis not proportional toB(E2). On the other hand, a sum rule which relatesB(M1) to the difference (B(E2)isoscalar-B(E2)isovector) succeeds in describing the difference in behaviours in the two nuclei. The results forQ·Qand the realistic interactions are compared, as are the results in the 0pspace and the large (0p+2ℏω) space. The Wigner supermultiplet scheme is a very useful guide in analyzing the shell model results.

Mass resolution of linear quadrupole ion traps with round rods.

PubMed

Douglas, D J; Konenkov, N V

2014-11-15

Auxiliary dipole excitation is widely used to eject ions from linear radio-frequency quadrupole ion traps for mass analysis. Linear quadrupoles are often constructed with round rod electrodes. The higher multipoles introduced to the electric potential by round rods might be expected to change the ion ejection process. We have therefore investigated the optimum ratio of rod radius, r, to field radius, r0, for excitation and ejection of ions. Trajectory calculations are used to determine the excitation contour, S(q), the fraction of ions ejected when trapped at q values close to the ejection (or excitation) q. Initial conditions are randomly selected from Gaussian distributions of the x and y coordinates and a thermal distribution of velocities. The N = 6 (12 pole) and N = 10 (20 pole) multipoles are added to the quadrupole potential. Peak shapes and resolution were calculated for ratios r/r0 from 1.09 to 1.20 with an excitation time of 1000 cycles of the trapping radio-frequency. Ratios r/r0 in the range 1.140 to 1.160 give the highest resolution and peaks with little tailing. Ratios outside this range give lower resolution and peaks with tails on either the low-mass side or the high-mass side of the peaks. This contrasts with the optimum ratio of 1.126-1.130 for a quadrupole mass filter operated conventionally at the tip of the first stability region. With the optimum geometry the resolution is 2.7 times greater than with an ideal quadrupole field. Adding only a 2.0% hexapole field to a quadrupole field increases the resolution by a factor of 1.6 compared with an ideal quadrupole field. Addition of a 2.0% octopole lowers resolution and degrades peak shape. With the optimum value of r/r0 , the resolution increases with the ejection time (measured in cycles of the trapping rf, n) approximately as R0.5 = 6.64n, in contrast to a pure quadrupole field where R0.5 = 1.94n. Adding weak nonlinear fields to a quadrupole field can improve the resolution with mass-selective ejection of ions by up to a factor of 2.7. The optimum ratio r/r0 is 1.14 to 1.16, which differs from the optimum ratio for a mass filter of 1.128-1.130. Copyright © 2014 John Wiley & Sons, Ltd.

Design and fabrication of a basic mass analyzer and vacuum system

NASA Technical Reports Server (NTRS)

Judson, C. M.; Josias, C.; Lawrence, J. L., Jr.

1977-01-01

A two-inch hyperbolic rod quadrupole mass analyzer with a mass range of 400 to 200 amu and a sensitivity exceeding 100 packs per billion has been developed and tested. This analyzer is the basic hardware portion of a microprocessor-controlled quadrupole mass spectrometer for a Gas Analysis and Detection System (GADS). The development and testing of the hyperbolic-rod quadrupole mass spectrometer and associated hardware are described in detail.

Ellipsoidal universe can solve the cosmic microwave background quadrupole problem.

PubMed

Campanelli, L; Cea, P; Tedesco, L

2006-09-29

The recent 3 yr Wilkinson Microwave Anisotropy Probe data have confirmed the anomaly concerning the low quadrupole amplitude compared to the best-fit Lambda-cold dark matter prediction. We show that by allowing the large-scale spatial geometry of our universe to be plane symmetric with eccentricity at decoupling or order 10(-2), the quadrupole amplitude can be drastically reduced without affecting higher multipoles of the angular power spectrum of the temperature anisotropy.

Stability of an aqueous quadrupole micro-trap

DOE PAGES

Park, Jae Hyun; Krstić, Predrag S.

2012-03-30

Recently demonstrated functionality of an aqueous quadrupole micro- or nano-trap opens a new avenue for applications of the Paul traps, like is confinement of a charged biomolecule which requires water environment for its chemical stability. Besides strong viscosity forces, motion of a charged particle in the aqueous trap is subject to dielectrophoretic and electrophoretic forces. In this study, we describe the general conditions for stability of a charged particle in an aqueous quadrupole trap. We find that for the typical micro-trap parameters, effects of both dielectrophoresis and electrophoresis significantly influence the trap stability. In particular, the aqueous quadrupole trap couldmore » play of a role of a synthetic virtual nanopore for the 3rd generation of DNA sequencing technology.« less

Simple Model for the Benzene Hexafluorobenzene Interaction

DOE PAGES

Tillack, Andreas F.; Robinson, Bruce H.

2017-06-05

While the experimental intermolecular distance distribution functions of pure benzene and pure hexafluorobenzene are well described by transferable all-atom force fields, the interaction between the two molecules (in a 1:1 mixture) is not well simulated. We demonstrate that the parameters of the transferable force fields are adequate to describe the intermolecular distance distribution if the charges are replaced by a set of charges that are not located at the atoms. Here, the simplest model that well describes the experimental distance distribution, between benzene and hexafluorobenzene, is that of a single ellipsoid for each molecule, representing the van der Waals interactions,more » and a set of three point charges (on the axis perpendicular to the arene plane) which give the same quadrupole moment as do the all atom charges from the transferable force fields.« less

Twisted-Light-Ion Interaction: The Role of Longitudinal Fields

NASA Astrophysics Data System (ADS)

Quinteiro, G. F.; Schmidt-Kaler, Ferdinand; Schmiegelow, Christian T.

2017-12-01

The propagation of light beams is well described using the paraxial approximation, where field components along the propagation direction are usually neglected. For strongly inhomogeneous or shaped light fields, however, this approximation may fail, leading to intriguing variations of the light-matter interaction. This is the case of twisted light having opposite orbital and spin angular momenta. We compare experimental data for the excitation of a quadrupole transition in a single trapped 40Ca+ ion from Schmiegelow et al. [Nat. Commun. 7, 12998 (2016), 10.1038/ncomms12998] with a complete model where longitudinal components of the electric field are taken into account. Our model matches the experimental data and excludes by 11 standard deviations the approximation of a complete transverse field. This demonstrates the relevance of all field components for the interaction of twisted light with matter.

Simple Model for the Benzene Hexafluorobenzene Interaction

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

Tillack, Andreas F.; Robinson, Bruce H.

While the experimental intermolecular distance distribution functions of pure benzene and pure hexafluorobenzene are well described by transferable all-atom force fields, the interaction between the two molecules (in a 1:1 mixture) is not well simulated. We demonstrate that the parameters of the transferable force fields are adequate to describe the intermolecular distance distribution if the charges are replaced by a set of charges that are not located at the atoms. Here, the simplest model that well describes the experimental distance distribution, between benzene and hexafluorobenzene, is that of a single ellipsoid for each molecule, representing the van der Waals interactions,more » and a set of three point charges (on the axis perpendicular to the arene plane) which give the same quadrupole moment as do the all atom charges from the transferable force fields.« less

Geometry and mechanics of two-dimensional defects in amorphous materials

PubMed Central

Moshe, Michael; Levin, Ido; Aharoni, Hillel; Kupferman, Raz; Sharon, Eran

2015-01-01

We study the geometry of defects in amorphous materials and their elastic interactions. Defects are defined and characterized by deviations of the material’s intrinsic metric from a Euclidian metric. This characterization makes possible the identification of localized defects in amorphous materials, the formulation of a corresponding elastic problem, and its solution in various cases of physical interest. We present a multipole expansion that covers a large family of localized 2D defects. The dipole term, which represents a dislocation, is studied analytically and experimentally. Quadrupoles and higher multipoles correspond to fundamental strain-carrying entities. The interactions between those entities, as well as their interaction with external stress fields, are fundamental to the inelastic behavior of solids. We develop analytical tools to study those interactions. The model, methods, and results presented in this work are all relevant to the study of systems that involve a distribution of localized sources of strain. Examples are plasticity in amorphous materials and mechanical interactions between cells on a flexible substrate. PMID:26261331

Extension of the quasistatic far-wing line shape theory to multicomponent anisotropic potentials

NASA Technical Reports Server (NTRS)

Ma, Q.; Tipping, R. H.

1994-01-01

The formalism developed previously for the calculation of the far-wing line shape function and the corresponding absorption coefficient using a single-component anisotropic interaction term and the binary collision and quasistatic approximations is generalized to multicomponent anisotropic potential functions. Explicit expressions are presented for several common cases, including the long-range dipole-dipole plus dipole-quadrupole interaction and a linear molecule interacting with a perturber atom. After determining the multicomponent functional representation for the interaction between the CO2 and Ar from previously published data, we calculate the theoretical line shape function and the corresponding absorption due to the nu(sub 3) band of CO2 in the frequency range 2400-2580 cm(exp -1) and compare our results with previous calculations carried out using a single-component anisotropic interaction, and with the results obtained assuming Lorentzian line shapes. The principal uncertainties in the present results, possible refinements of the theoretical formalism, and the applicability to other systems are discussed briefly.

23Na and 35/37Cl as NMR probes of growth and shape of sodium taurodeoxycholate micellar aggregates in the presence of NaCl.

PubMed

Asaro, Fioretta; Feruglio, Luigi; Galantini, Luciano; Nardelli, Alessia

2013-02-15

The growth of the aggregates of the dihydroxylated bile salt sodium taurodeoxycholate (NaTDC) upon NaCl addition and the involvement of the counterion were investigated by NMR spectroscopy of monoatomic ionic species. (23)Na T(1) values from 0.015, 0.100, and 0.200 mol kg(-1) NaTDC solutions in D(2)O, at variable NaCl content, proved to be sensitive to the transition from primary to secondary aggregates, which occurs in the former sample, and to intermicellar interaction. Some (79)Br NMR measurements were performed on a 0.100 mol kg(-1) NaTDC sample added by NaBr in place of NaCl for comparison purposes. The (23)Na, (35)Cl, and (37)Cl double quantum filtered (DQF) patterns, from the 0.100 mol kg(-1) NaTDC sample, and (23)Na ones also from the 0.200 mol kg(-1) NaTDC one, in the presence of 0.750 mol kg(-1) NaCl, are a clear manifestation of motional anisotropy. Moreover, the DQF spectra of (23)Na and (37)Cl, which possess close quadrupole moments, display a striking similarity. The DQF lineshapes were simulated exploiting the Scilab environment to obtain an estimate of the residual quadrupole splitting magnitude. These results support the description of NaTDC micelles as cylindrical aggregates, strongly interacting at high ionic strengths, and capable of association with added electrolytes. Copyright © 2012 Elsevier Inc. All rights reserved.

[Determination of hydroxyproline in liver tissue by hydrophilic interaction chromatography-quadrupole/electrostatic field orbitrap high resolution mass spectrometry].

PubMed

Liu, Wei; Qi, Shenglan; Xu, Ying; Xiao, Zhun; Fu, Yadong; Chen, Jiamei; Yang, Tao; Liu, Ping

2017-12-08

A method for the determination of hydroxyproline (Hyp) in liver tissue of mice by hydrophilic interaction chromatography-quadrupole/electrostatic field orbitrap high resolution mass spectrometry (HILIC-HRMS) was developed. The liver tissue samples of normal mice and liver fibrosis mice induced by carbon tetrachloride were hydrolyzed by concentrated hydrochloric acid. After filtrated and diluted by solution, the diluent was separated on an Hypersil GOLD HILIC column (100 mm×2.1 mm, 3 μm). Water-acetonitrile (28:72, v/v)were used as the mobile phases with isocratic elution. Finally, the target analytes were detected in positive model by HRMS equipped with an electrospray ionization source. The linear range of hydroxyproline was from 0.78 to 100.00 μg/L with the correlation coefficient ( R 2 ) of 0.9983. The limit of quantification was 0.78 μg/L. By detecting the spiked samples, the recoveries were in the range of 97.4%-100.9% with the relative standard deviations (RSDs) between 1.4% and 2.0%. In addition, comparison of the measurement results by this method and the chloramine T method was proceeded. It was found that the linear correlation between the two methods was very good, and the Pearson correlation coefficient was 0.927. And this method had simpler operation procedure and higher accuracy than chloramine T method. This method can be used for the quick determination of hydroxyproline in liver tissue samples.

Clustering fossil from primordial gravitational waves in anisotropic inflation

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

Emami, Razieh; Firouzjahi, Hassan, E-mail: emami@ipm.ir, E-mail: firouz@ipm.ir

2015-10-01

Inflationary models can correlate small-scale density perturbations with the long-wavelength gravitational waves (GW) in the form of the Tensor-Scalar-Scalar (TSS) bispectrum. This correlation affects the mass-distribution in the Universe and leads to the off-diagonal correlations of the density field modes in the form of the quadrupole anisotropy. Interestingly, this effect survives even after the tensor mode decays when it re-enters the horizon, known as the fossil effect. As a result, the off-diagonal correlation function between different Fourier modes of the density fluctuations can be thought as a way to probe the large-scale GW and the mechanism of inflation behind themore » fossil effect. Models of single field slow roll inflation generically predict a very small quadrupole anisotropy in TSS while in models of multiple fields inflation this effect can be observable. Therefore this large scale quadrupole anisotropy can be thought as a spectroscopy for different inflationary models. In addition, in models of anisotropic inflation there exists quadrupole anisotropy in curvature perturbation power spectrum. Here we consider TSS in models of anisotropic inflation and show that the shape of quadrupole anisotropy is different than in single field models. In fact, in these models, quadrupole anisotropy is projected into the preferred direction and its amplitude is proportional to g{sub *} N{sub e} where N{sub e} is the number of e-folds and g{sub *} is the amplitude of quadrupole anisotropy in curvature perturbation power spectrum. We use this correlation function to estimate the large scale GW as well as the preferred direction and discuss the detectability of the signal in the galaxy surveys like Euclid and 21 cm surveys.« less

On the inter-instrument and the inter-laboratory transferability of a tandem mass spectral reference library: 2. Optimization and characterization of the search algorithm.

PubMed

Oberacher, Herbert; Pavlic, Marion; Libiseller, Kathrin; Schubert, Birthe; Sulyok, Michael; Schuhmacher, Rainer; Csaszar, Edina; Köfeler, Harald C

2009-04-01

A sophisticated matching algorithm developed for highly efficient identity search within tandem mass spectral libraries is presented. For the optimization of the search procedure a collection of 410 tandem mass spectra corresponding to 22 compounds was used. The spectra were acquired in three different laboratories on four different instruments. The following types of tandem mass spectrometric instruments were used: quadrupole-quadrupole-time-of-flight (QqTOF), quadrupole-quadrupole-linear ion trap (QqLIT), quadrupole-quadrupole-quadrupole (QqQ), and linear ion trap-Fourier transform ion cyclotron resonance mass spectrometer (LIT-FTICR). The obtained spectra were matched to an established MS/MS-spectral library that contained 3759 MS/MS-spectra corresponding to 402 different reference compounds. All 22 test compounds were part of the library. A dynamic intensity cut-off, the search for neutral losses, and optimization of the formula used to calculate the match probability were shown to significantly enhance the performance of the presented library search approach. With the aid of these features the average number of correct assignments was increased to 98%. For statistical evaluation of the match reliability the set of fragment ion spectra was extended with 300 spectra corresponding to 100 compounds not included in the reference library. Performance was checked with the aid of receiver operating characteristic (ROC) curves. Using the magnitude of the match probability as well as the precursor ion mass as benchmarks to rate the obtained top hit, overall correct classification of a compound being included or not included in the mass spectrometric library, was obtained in more than 95% of cases clearly indicating a high predictive accuracy of the established matching procedure. Copyright (c) 2009 John Wiley & Sons, Ltd.

Electrostatic design and beam transport for a folded tandem electrostatic quadrupole accelerator facility for accelerator-based boron neutron capture therapy.

PubMed

Vento, V Thatar; Bergueiro, J; Cartelli, D; Valda, A A; Kreiner, A J

2011-12-01

Within the frame of an ongoing project to develop a folded Tandem-Electrostatic-Quadrupole (TESQ) accelerator facility for Accelerator-Based Boron Neutron Capture Therapy (AB-BNCT), we discuss here the electrostatic design of the machine, including the accelerator tubes with electrostatic quadrupoles and the simulations for the transport and acceleration of a high intensity beam. Copyright © 2011 Elsevier Ltd. All rights reserved.

Higher order parametric excitation modes for spaceborne quadrupole mass spectrometers

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

Gershman, D. J.; Block, B. P.; Rubin, M.

This paper describes a technique to significantly improve upon the mass peak shape and mass resolution of spaceborne quadrupole mass spectrometers (QMSs) through higher order auxiliary excitation of the quadrupole field. Using a novel multiresonant tank circuit, additional frequency components can be used to drive modulating voltages on the quadrupole rods in a practical manner, suitable for both improved commercial applications and spaceflight instruments. Auxiliary excitation at frequencies near twice that of the fundamental quadrupole RF frequency provides the advantages of previously studied parametric excitation techniques, but with the added benefit of increased sensed excitation amplitude dynamic range and themore » ability to operate voltage scan lines through the center of upper stability islands. Using a field programmable gate array, the amplitudes and frequencies of all QMS signals are digitally generated and managed, providing a robust and stable voltage control system. These techniques are experimentally verified through an interface with a commercial Pfeiffer QMG422 quadrupole rod system. When operating through the center of a stability island formed from higher order auxiliary excitation, approximately 50% and 400% improvements in 1% mass resolution and peak stability were measured, respectively, when compared with traditional QMS operation. Although tested with a circular rod system, the presented techniques have the potential to improve the performance of both circular and hyperbolic rod geometry QMS sensors.« less

{sup 1}H NMR relaxometry and quadrupole relaxation enhancement as a sensitive probe of dynamical properties of solids—[C(NH{sub 2}){sub 3}]{sub 3}Bi{sub 2}I{sub 9} as an example

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

Florek-Wojciechowska, M.; Wojciechowski, M.; Brym, Sz.

{sup 1}H nuclear magnetic resonance relaxometry has been applied to reveal information on dynamics and structure of Gu{sub 3}Bi{sub 2}I{sub 9} ([Gu = C(NH{sub 2}){sub 3}] denotes guanidinium cation). The data have been analyzed in terms of a theory of quadrupole relaxation enhancement, which has been extended here by including effects associated with quadrupole ({sup 14}N) spin relaxation caused by a fast fluctuating component of the electric field gradient tensor. Two motional processes have been identified: a slow one occurring on a timescale of about 8 × 10{sup −6} s which has turned out to be (almost) temperature independent, andmore » a fast process in the range of 10{sup −9} s. From the {sup 1}H-{sup 14}N relaxation contribution (that shows “quadrupole peaks”) the quadrupole parameters, which are a fingerprint of the arrangement of the anionic network, have been determined. It has been demonstrated that the magnitude of the quadrupole coupling considerably changes with temperature and the changes are not caused by phase transitions. At the same time, it has been shown that there is no evidence of abrupt changes in the cationic dynamics and the anionic substructure upon the phase transitions.« less

Induced CMB quadrupole from pointing offsets

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

Moss, Adam; Scott, Douglas; Sigurdson, Kris, E-mail: adammoss@phas.ubc.ca, E-mail: dscott@phas.ubc.ca, E-mail: krs@phas.ubc.ca

2011-01-01

Recent claims in the literature have suggested that the WMAP quadrupole is not primordial in origin, and arises from an aliasing of the much larger dipole field because of incorrect satellite pointing. We attempt to reproduce this result and delineate the key physics leading to the effect. We find that, even if real, the induced quadrupole would be smaller than the WMAP value. We discuss reasons why the WMAP data are unlikely to suffer from this particular systematic effect, including the implications for observations of point sources. Given this evidence against the reality of the effect, the similarity between themore » pointing-offset-induced signal and the actual quadrupole then appears to be quite puzzling. However, we find that the effect arises from a convolution between the gradient of the dipole field and anisotropic coverage of the scan direction at each pixel. There is something of a directional conspiracy here — the dipole signal lies close to the Ecliptic Plane, and its direction, together with the WMAP scan strategy, results in a strong coupling to the Y{sub 2,−1} component in Ecliptic co-ordinates. The dominant strength of this component in the measured quadrupole suggests that one should exercise increased caution in interpreting its estimated amplitude. The Planck satellite has a different scan strategy which does not so directly couple the dipole and quadrupole in this way and will soon provide an independent measurement.« less

An efficient and robust method for predicting helicopter rotor high-speed impulsive noise

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.

1996-01-01

A new formulation for the Ffowcs Williams-Hawkings quadrupole source, which is valid for a far-field in-plane observer, is presented. The far-field approximation is new and unique in that no further approximation of the quadrupole source strength is made and integrands with r(exp -2) and r(exp -3) dependence are retained. This paper focuses on the development of a retarded-time formulation in which time derivatives are analytically taken inside the integrals to avoid unnecessary computational work when the observer moves with the rotor. The new quadrupole formulation is similar to Farassat's thickness and loading formulation 1A. Quadrupole noise prediction is carried out in two parts: a preprocessing stage in which the previously computed flow field is integrated in the direction normal to the rotor disk, and a noise computation stage in which quadrupole surface integrals are evaluated for a particular observer position. Preliminary predictions for hover and forward flight agree well with experimental data. The method is robust and requires computer resources comparable to thickness and loading noise prediction.

Measurements of the microwave spectrum, Re-H bond length, and Re quadrupole coupling for HRe(CO)5

NASA Astrophysics Data System (ADS)

Kukolich, Stephen G.; Sickafoose, Shane M.

1993-11-01

Rotational transition frequencies for rhenium pentacarbonyl hydride were measured in the 4-10 GHz range using a Flygare-Balle type microwave spectrometer. The rotational constants and Re nuclear quadrupole coupling constants for the four isotopomers, (1) H187Re(CO)5, (2) H185Re(CO)5, (3) D187Re(CO)5, and (4) D185Re(CO)5, were obtained from the spectra. For the most common isotopomer, B(1)=818.5464(2) MHz and eq Q(187Re)=-900.13(3) MHz. The Re-H bond length (r0) determined by fitting the rotational constants is 1.80(1) Å. Although the Re atom is located at a site of near-octahedral symmetry, the quadrupole coupling is large due to the large Re nuclear moments. A 2.7% increase in Re quadrupole coupling was observed for D-substituted isotopomers, giving a rather large isotope effect on the quadrupole coupling. The Cax-Re-Ceq angle is 96(1)°, when all Re-C-O angles are constrained to 180°.

The exact solution of the monoenergetic transport equation for critical cylinders

NASA Technical Reports Server (NTRS)

Westfall, R. M.; Metcalf, D. R.

1972-01-01

An analytic solution for the critical, monoenergetic, bare, infinite cylinder is presented. The solution is obtained by modifying a previous development based on a neutron density transform and Case's singular eigenfunction method. Numerical results for critical radii and the neutron density as a function of position are included and compared with the results of other methods.

On Superstability of Semigroups

NASA Technical Reports Server (NTRS)

Balakrishnan. A. V.

1997-01-01

This paper presents a brief report on superstable semigroups - abstract theory and some applications thereof. The notion of super stability is a strengthening of exponential stability and occurs in Timoshenko models of structures with self-straining material using pure (idealized) rate feed- back. It is also relevant to the problem of Riesz bases of eigenfunctions of infinitesimal generators under perturbation.

A Complete Set for the Maass Laplacians on the Pseudosphere

NASA Astrophysics Data System (ADS)

Oshima, K.

1989-02-01

We obtain a completeness relation from eigenfunctions of the Maass laplacians in terms of the pseudospherical polar coordinates. We derive addition theorems of ``generalized'' associated Legendre functions. With the help of the addition theorems, we get a simple path integral picture for a charged particle on the Poincaré upper half plane with a constant magnetic field.

The Rhic Azimuth Quadrupole:. "perfect Liquid" or Gluonic Radiation?

NASA Astrophysics Data System (ADS)

Trainor, Thomas A.

Large elliptic flow at RHIC seems to indicate that ideal hydrodynamics provides a good description of Au-Au collisions, at least at the maximum RHIC energy. The medium formed has been interpreted as a nearly perfect (low-viscosity) liquid, and connections have been made to gravitation through string theory. Recently, claimed observations of large flow fluctuations comparable to participant eccentricity fluctuations seem to confirm the ideal hydro scenario. However, determination of the azimuth quadrupole with 2D angular autocorrelations, which accurately distinguish "flow" (quadrupole) from "nonflow" (minijets), contradicts conventional interpretations. Centrality trends may depend only on the initial parton geometry, and methods used to isolate flow fluctuations are sensitive instead mainly to minijet correlations. The results presented in this paper suggest that the azimuth quadrupole may be a manifestation of gluonic multipole radiation.

Test results of the LARP Nb$$_3$$Sn quadrupole HQ03a

DOE PAGES

DiMarco, J.; G. Ambrosio; Chlachidze, G.; ...

2016-03-09

The US LHC Accelerator Research Program (LARP) has been developingmore » $$Nb_3Sn$$ quadrupoles of progressively increasing performance for the high luminosity upgrade of the Large Hadron Collider. The 120 mm aperture High-field Quadrupole (HQ) models are the last step in the R&D phase supporting the development of the new IR Quadrupoles (MQXF). Three series of HQ coils were fabricated and assembled in a shell-based support structure, progressively optimizing the design and fabrication process. The final set of coils consistently applied the optimized design solutions, and was assembled in the HQ03a model. Furthermore, this paper reports a summary of the HQ03a test results, including training, mechanical performance, field quality and quench studies.« less

Dynamical quadrupole structure factor of frustrated ferromagnetic chain

NASA Astrophysics Data System (ADS)

Onishi, Hiroaki

2018-05-01

We investigate the dynamical quadrupole structure factor of a spin-1/2 J1-J2 Heisenberg chain with competing ferromagnetic J1 and antiferromagnetic J2 in a magnetic field by exploiting density-matrix renormalization group techniques. In a field-induced spin nematic regime, we observe gapless excitations at q = π according to quasi-long-range antiferro-quadrupole correlations. The gapless excitation mode has a quadratic form at the saturation, while it changes into a linear dispersion as the magnetization decreases.

Nuclear Quadrupole Resonance (NQR) Method and Probe for Generating RF Magnetic Fields in Different Directions to Distinguish NQR from Acoustic Ringing Induced in a Sample

DTIC Science & Technology

1997-08-01

77,719 TITLE OF THE INVENTION NUCLEAR QUADRUPOLE RESONANCE ( NQR ) METHOD AND PROBE FOR GENERATING RF MAGNETIC FIELDS IN DIFFERENT DIRECTIONS TO...DISTINGUISH NQR FROM ACOUSTIC RINGING INDUCED IN A SAMPLE BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a...nuclear quadrupole 15 resonance ( NQR ) method and probe for generating RF magnetic fields in different directions towards a sample. More specifically

γ-unstable nuclei in the sdg boson model

NASA Astrophysics Data System (ADS)

Kuyucak, S.; Lac, V.-S.; Morrison, I.; Barrett, B. R.

1991-07-01

Following the recent Pt(p, p‧) experiments which indicated the need for g bosons to reproduce the E4 data, we have extended the O(6) limit of the sd boson model to include g bosons. It is shown that a γ-unstable hamiltonian in the sdg model consisting of a quadrupole interaction and a g boson energy leads to results that are very similar to the O(6) limit. Deviations from the empirical energy spectrum that stem from the γ-unstable nature of the hamiltonian can be improved by including a consistent hexadecapole interaction which induces triaxiality. The same hexadecapole operator can also account for the strong E4 transitions. Applications are made to the Xe and Pt isotopes.

Where's water? The many binding sites of hydantoin.

PubMed

Gruet, Sébastien; Pérez, Cristóbal; Steber, Amanda L; Schnell, Melanie

2018-02-21

Prebiotic hydantoin and its complexes with one and two water molecules are investigated using high-resolution broadband rotational spectroscopy in the 2-8 GHz frequency range. The hyperfine structure due to the nuclear quadrupole coupling of the two 14 N atoms is analysed for the monomer and the complexes. This characteristic hyperfine structure will support a definitive assignment from low frequency radioastronomy data. Experiments with H 2 18 O provide accurate experimental information on the preferred binding sites of water, which are compared with quantum-chemically calculated coordinates. In the 2-water complexes, the water molecules bind to hydantoin as a dimer instead of individually, indicating the strong water-water interactions. This information provides first insight on how hydantoin interacts with water on the molecular level.

Structure and orientational ordering in a fluid of elongated quadrupolar molecules

NASA Astrophysics Data System (ADS)

Singh, Ram Chandra

2013-01-01

A second-order density-functional theory is used to study the effect of quadrupolar interactions on the isotropic-nematic transition in a system of fluids of elongated molecules interacting via the Gay-Berne potential. The direct pair-correlation functions of the coexisting isotropic fluid that enter in the theory as input information are obtained by solving the Ornstein-Zernike equation using the Percus-Yevick integral equation theory in the (reduced) temperature range of 1.6≤T∗≤3.0 for different densities, temperatures and quadrupole moments. Using the harmonic coefficients of the direct pair-correlation functions, isotropic-nematic phase coexistence and thermodynamic parameters have been calculated. The theoretical results have been compared with the available computer simulation results.

Open sd-shell nuclei from first principles

DOE PAGES

Jansen, Gustav R.; Signoracci, Angelo J.; Hagen, Gaute; ...

2016-07-05

We extend the ab initio coupled-cluster effective interaction (CCEI) method to open-shell nuclei with protons and neutrons in the valence space, and compute binding energies and excited states of isotopes of neon and magnesium. We employ a nucleon-nucleon and three-nucleon interaction from chiral effective field theory evolved to a lower cutoff via a similarity renormalization group transformation. We find good agreement with experiment for binding energies and spectra, while charge radii of neon isotopes are underestimated. For the deformed nuclei 20Ne and 24Mg we reproduce rotational bands and electric quadrupole transitions within uncertainties estimated from an effective field theory formore » deformed nuclei, thereby demonstrating that collective phenomena in sd-shell nuclei emerge from complex ab initio calculations.« less

Open sd-shell nuclei from first principles

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

Jansen, Gustav R.; Signoracci, Angelo J.; Hagen, Gaute

We extend the ab initio coupled-cluster effective interaction (CCEI) method to open-shell nuclei with protons and neutrons in the valence space, and compute binding energies and excited states of isotopes of neon and magnesium. We employ a nucleon-nucleon and three-nucleon interaction from chiral effective field theory evolved to a lower cutoff via a similarity renormalization group transformation. We find good agreement with experiment for binding energies and spectra, while charge radii of neon isotopes are underestimated. For the deformed nuclei 20Ne and 24Mg we reproduce rotational bands and electric quadrupole transitions within uncertainties estimated from an effective field theory formore » deformed nuclei, thereby demonstrating that collective phenomena in sd-shell nuclei emerge from complex ab initio calculations.« less

Characterization of the hyperfine interaction of the excited D50 state of Eu3 +:Y2SiO5

NASA Astrophysics Data System (ADS)

Cruzeiro, Emmanuel Zambrini; Etesse, Jean; Tiranov, Alexey; Bourdel, Pierre-Antoine; Fröwis, Florian; Goldner, Philippe; Gisin, Nicolas; Afzelius, Mikael

2018-03-01

We characterize the europium (Eu3 +) hyperfine interaction of the excited state (D50) and determine its effective spin Hamiltonian parameters for the Zeeman and quadrupole tensors. An optical free induction decay method is used to measure all hyperfine splittings under a weak external magnetic field (up to 10 mT) for various field orientations. On the basis of the determined Hamiltonian, we discuss the possibility to predict optical transition probabilities between hyperfine levels for the F70⟷D50 transition. The obtained results provide necessary information to realize an optical quantum memory scheme which utilizes long spin coherence properties of 3 + 151Eu :Y2SiO5 material under external magnetic fields.

High-resolution molecular-beam spectroscopy of NaCN and Na 13CN

NASA Astrophysics Data System (ADS)

van Vaals, J. J.; Meerts, W. Leo; Dymanus, A.

The sodium cyanide molecule was studied by molecular-beam electric-resonance spectroscopy in the microwave region. We used the seeded-beam technique to produce a supersonic beam with strong translational, rotational and vibrational cooling. In the frequency range 9.5-40 GHz we observed and identified for NaCN 186 and for Na 13CN 107 hyperfine transitions in 20 and 16 rotational transitions, respectively, all in the ground vibrational state. The rotational, the five quartic and three sextic centrifugal distortion constants of NaCN are: A″ = 57921.954(7) MHz; B″ = 8369.312(2) MHz, C″ = 7272.712(2) MHz. All quadrupole and several spin-rotation coupling constants for the hyperfine interaction were evaluated. The quadrupole coupling constants (in MHz) for NaCN are: eQq12(Na) = -5.344(5), eQq12 = 2.397(7). eQq12(N) = 2.148(4), eQq12(N) = -4.142(5). From these constants and those of Na 13CN we have determined the principal components of the quadrupole coupling tensor for potassium and nitrogen. The structure of sodium cyanide evaluated from the rotational constants of NaCN and Na 13CN was found to be T shaped, similar to the structure of KCN but completely different from the linear isocyanide configuration of LiNC. The effective structural parameters for sodium cyanide in the ground vibrational state are: rCN = 1.170(4) Å, rNaC = 2.379(15) Å, rN12N = 2.233(15) Å, in gratifying agreement with ab initio calculations. Both the geometrical structure and the hyperfine coupling justify the conclusion that the CN group in gaseous sodium cyanide approximately can be considered as a free CN - ion.

Elastic and transition form factors of the Δ(1232)

DOE PAGES

Segovia, Jorge; Chen, Chen; Cloet, Ian C.; ...

2013-12-10

Predictions obtained with a confining, symmetry-preserving treatment of a vector Ⓧ vector contact interaction at leading-order in a widely used truncation of QCD’s Dyson–Schwinger equations are presented for Δ and Ω baryon elastic form factors and the γN → Δ transition form factors. This simple framework produces results that are practically indistinguishable from the best otherwise available, an outcome which highlights that the key to describing many features of baryons and unifying them with the properties of mesons is a veracious expression of dynamical chiral symmetry breaking in the hadron bound-state problem. The following specific results are of particular interest.more » The Δ elastic form factors are very sensitive to m Δ. Hence, given that the parameters which define extant simulations of lattice-regularised QCD produce Δ-resonance masses that are very large, the form factors obtained therewith are a poor guide to properties of the Δ(1232). Considering the Δ-baryon’s quadrupole moment, whilst all computations produce a negative value, the conflict between theoretical predictions entails that it is currently impossible to reach a sound conclusion on the nature of the Δ-baryon’s deformation in the infinite momentum frame. Furthermore, results for analogous properties of the Ω baryon are less contentious. In connection with the N → Δ transition, the Ash-convention magnetic transition form factor falls faster than the neutron’s magnetic form factor and nonzero values for the associated quadrupole ratios reveal the impact of quark orbital angular momentum within the nucleon and Δ; and, furthermore, these quadrupole ratios do slowly approach their anticipated asymptotic limits.« less

High energy proton induced radiation damage of rare earth permanent magnet quadrupoles

NASA Astrophysics Data System (ADS)

Schanz, M.; Endres, M.; Löwe, K.; Lienig, T.; Deppert, O.; Lang, P. M.; Varentsov, D.; Hoffmann, D. H. H.; Gutfleisch, O.

2017-12-01

Permanent magnet quadrupoles (PMQs) are an alternative to common electromagnetic quadrupoles especially for fixed rigidity beam transport scenarios at particle accelerators. Using those magnets for experimental setups can result in certain scenarios, in which a PMQ itself may be exposed to a large amount of primary and secondary particles with a broad energy spectrum, interacting with the magnetic material and affecting its magnetic properties. One specific scenario is proton microscopy, where a proton beam traverses an object and a collimator in which a part of the beam is scattered and deflected into PMQs used as part of a diagnostic system. During the commissioning of the PRIOR (Proton Microscope for Facility for Antiproton and Ion Research) high energy proton microscope facility prototype at Gesellschaft für Schwerionenforschung in 2014, a significant reduction of the image quality was observed which was partially attributed to the demagnetization of the used PMQ lenses and the corresponding decrease of the field quality. In order to study this phenomenon, Monte Carlo simulations were carried out and spare units manufactured from the same magnetic material—single wedges and a fully assembled PMQ module—were deliberately irradiated by a 3.6 GeV intense proton beam. The performed investigations have shown that in proton radiography applications the above described scattering may result in a high irradiation dose in the PMQ magnets. This did not only decrease the overall magnetic strength of the PMQs but also caused a significant degradation of the field quality of an assembled PMQ module by increasing the parasitic multipole field harmonics which effectively makes PMQs impractical for proton radiography applications or similar scenarios.

High energy proton induced radiation damage of rare earth permanent magnet quadrupoles.

PubMed

Schanz, M; Endres, M; Löwe, K; Lienig, T; Deppert, O; Lang, P M; Varentsov, D; Hoffmann, D H H; Gutfleisch, O

2017-12-01

Permanent magnet quadrupoles (PMQs) are an alternative to common electromagnetic quadrupoles especially for fixed rigidity beam transport scenarios at particle accelerators. Using those magnets for experimental setups can result in certain scenarios, in which a PMQ itself may be exposed to a large amount of primary and secondary particles with a broad energy spectrum, interacting with the magnetic material and affecting its magnetic properties. One specific scenario is proton microscopy, where a proton beam traverses an object and a collimator in which a part of the beam is scattered and deflected into PMQs used as part of a diagnostic system. During the commissioning of the PRIOR (Proton Microscope for Facility for Antiproton and Ion Research) high energy proton microscope facility prototype at Gesellschaft für Schwerionenforschung in 2014, a significant reduction of the image quality was observed which was partially attributed to the demagnetization of the used PMQ lenses and the corresponding decrease of the field quality. In order to study this phenomenon, Monte Carlo simulations were carried out and spare units manufactured from the same magnetic material-single wedges and a fully assembled PMQ module-were deliberately irradiated by a 3.6 GeV intense proton beam. The performed investigations have shown that in proton radiography applications the above described scattering may result in a high irradiation dose in the PMQ magnets. This did not only decrease the overall magnetic strength of the PMQs but also caused a significant degradation of the field quality of an assembled PMQ module by increasing the parasitic multipole field harmonics which effectively makes PMQs impractical for proton radiography applications or similar scenarios.

The 57Fe hyperfine interactions in human liver ferritin and its iron-polymaltose analogues: the heterogeneous iron core model

NASA Astrophysics Data System (ADS)

Oshtrakh, M. I.; Alenkina, I. V.; Semionkin, V. A.

2016-12-01

Human liver ferritin and its iron-polymaltose pharmaceutical analogues Ferrum Lek, Maltofer® and Ferrifol® were studied using Mössbauer spectroscopy at 295 and 90 K. The Mössbauer spectra were fitted on the basis of a new model of heterogeneous iron core structure using five quadrupole doublets. These components were related to the corresponding more or less close-packed iron core layers/regions demonstrating some variations in the 57Fe hyperfine parameters for the studied samples.

NMR spectrum analysis for CrAs at ambient pressure

NASA Astrophysics Data System (ADS)

Kotegawa, H.; Nakahara, S.; Matsushima, K.; Tou, H.; Matsuoka, E.; Sugawara, H.; Harima, H.

2018-05-01

We report NMR spectrum analysis for CrAs, which was recently reported to be superconducting under pressure. The NMR spectrum obtained by the powdered single crystals shows a typical powder pattern reproduced by the electric field gradient (EFG) parameters and isotropic Knight shift, indicating anisotropy of Knight shift is not remarkable in CrAs. For the oriented sample, the spectrum can be understood by considering that the crystals are aligned for H ∥ b . The temperature dependence of Knight shift was successfully obtained from NMR spectrum with large nuclear quadrupole interaction.

Structure of the Lightest Tin Isotopes

NASA Astrophysics Data System (ADS)

Morris, T. D.; Simonis, J.; Stroberg, S. R.; Stumpf, C.; Hagen, G.; Holt, J. D.; Jansen, G. R.; Papenbrock, T.; Roth, R.; Schwenk, A.

2018-04-01

We link the structure of nuclei around 100Sn, the heaviest doubly magic nucleus with equal neutron and proton numbers (N =Z =50 ), to nucleon-nucleon (N N ) and three-nucleon (N N N ) forces constrained by data of few-nucleon systems. Our results indicate that 100Sn is doubly magic, and we predict its quadrupole collectivity. We present precise computations of 101Sn based on three-particle-two-hole excitations of 100Sn, and we find that one interaction accurately reproduces the small splitting between the lowest Jπ=7 /2+ and 5 /2+ states.

Spin temperature concept verified by optical magnetometry of nuclear spins

NASA Astrophysics Data System (ADS)

Vladimirova, M.; Cronenberger, S.; Scalbert, D.; Ryzhov, I. I.; Zapasskii, V. S.; Kozlov, G. G.; Lemaître, A.; Kavokin, K. V.

2018-01-01

We develop a method of nonperturbative optical control over adiabatic remagnetization of the nuclear spin system and apply it to verify the spin temperature concept in GaAs microcavities. The nuclear spin system is shown to exactly follow the predictions of the spin temperature theory, despite the quadrupole interaction that was earlier reported to disrupt nuclear spin thermalization. These findings open a way for the deep cooling of nuclear spins in semiconductor structures, with the prospect of realizing nuclear spin-ordered states for high-fidelity spin-photon interfaces.

Mass spectra stimulated by O+ and Ar+ interacting with a surface.

NASA Technical Reports Server (NTRS)

Siegel, M. W.; Krauss, R. H.; Boring, J. W.

1972-01-01

Beams of O(+) and Ar(+) in the energy range from 100 to 300 eV were directed into an aperture in one face of a copper box. The mass spectrum from a similar aperture in an adjacent face was observed with the aid of a commercial RF quadrupole spectrometer. On the basis of the results obtained it is reported that O(+) beams at about 200 eV may be essentially lost after a few collisions with a surface, in agreement with similar conclusions about atomic oxygen at thermal energies.

Hyperfine-Structure-Induced Depolarization of Impulsively Aligned I2 Molecules

NASA Astrophysics Data System (ADS)

Thomas, Esben F.; Søndergaard, Anders A.; Shepperson, Benjamin; Henriksen, Niels E.; Stapelfeldt, Henrik

2018-04-01

A moderately intense 450 fs laser pulse is used to create rotational wave packets in gas phase I2 molecules. The ensuing time-dependent alignment, measured by Coulomb explosion imaging with a delayed probe pulse, exhibits the characteristic revival structures expected for rotational wave packets but also a complex nonperiodic substructure and decreasing mean alignment not observed before. A quantum mechanical model attributes the phenomena to coupling between the rotational angular momenta and the nuclear spins through the electric quadrupole interaction. The calculated alignment trace agrees very well with the experimental results.

Mössbauer Study of Hexavalent Iron Compounds

NASA Astrophysics Data System (ADS)

Dedushenko, S. K.; Perfiliev, Yu. D.; Goldfeld, M. G.; Tsapin, A. I.

2001-11-01

Six crystalline ferrates(VI): K3Na(FeO4)2, K2FeO4, Rb2FeO4, Cs2FeO4, K2Sr(FeO4)2 and BaFeO4, were studied by Mössbauer spectroscopy. Room-temperature spectra of potassium, rubidium and cesium ferrates are single lines, but spectra of barium, potassium strontium and potassium sodium ferrates show a presence of quadrupole interactions. Most of these salts display an antiferromagnetic transition with a Néel temperature within 2 to 8 K range.

Comprehensive analysis of a multidimensional liquid chromatography mass spectrometry dataset acquired on a quadrupole selecting, quadrupole collision cell, time-of-flight mass spectrometer: I. How much of the data is theoretically interpretable by search engines?

PubMed

Chalkley, Robert J; Baker, Peter R; Hansen, Kirk C; Medzihradszky, Katalin F; Allen, Nadia P; Rexach, Michael; Burlingame, Alma L

2005-08-01

An in-depth analysis of a multidimensional chromatography-mass spectrometry dataset acquired on a quadrupole selecting, quadrupole collision cell, time-of-flight (QqTOF) geometry instrument was carried out. A total of 3269 CID spectra were acquired. Through manual verification of database search results and de novo interpretation of spectra 2368 spectra could be confidently determined as predicted tryptic peptides. A detailed analysis of the non-matching spectra was also carried out, highlighting what the non-matching spectra in a database search typically are composed of. The results of this comprehensive dataset study demonstrate that QqTOF instruments produce information-rich data of which a high percentage of the data is readily interpretable.

Tidal coupling of a Schwarzschild black hole and circularly orbiting moon

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

Fang Hua; Lovelace, Geoffrey

2005-12-15

We describe the possibility of using the laser interferometer space antenna (LISA) 's gravitational-wave observations to study, with high precision, the response of a massive central body (e.g. a black hole or a soliton star) to the tidal gravitational pull of an orbiting, compact, small-mass object (a white dwarf, neutron star, or small-mass black hole). Motivated by this LISA application, we use first-order perturbation theory to study tidal coupling for a special, idealized case: a Schwarzschild black hole of mass M, tidally perturbed by a 'moon' with mass {mu}<>M with orbital angularmore » velocity {omega}. We investigate the details of how the tidal deformation of the hole gives rise to an induced quadrupole moment I{sub ij} in the hole's external gravitational field at large radii, including the vicinity of the moon. In the limit that the moon is static, we find, in Schwarzschild coordinates and Regge-Wheeler gauge, the surprising result that there is no induced quadrupole moment. We show that this conclusion is gauge dependent and that the static, induced quadrupole moment for a black hole is inherently ambiguous, and we contrast this with an earlier result of Suen, which gave, in a very different gauge, a nonzero static induced quadrupole moment with a sign opposite to what one would get for a fluid central body. For the orbiting moon and the central Schwarzschild hole, we find (in agreement with a recent result of Poisson) a time-varying induced quadrupole moment that is proportional to the time derivative of the moon's tidal field, I{sub ij}=(32/45)M{sup 6}E{sub ij} and that therefore is out of phase with the tidal field by a spatial angle {pi}/4 and by a temporal phase shift {pi}/2. This induced quadrupole moment produces a gravitational force on the moon that reduces its orbital energy and angular momentum at the same rate as the moon's tidal field sends energy and angular momentum into the hole's horizon. As a partial analog of a result derived long ago by Hartle for a spinning hole and a static distant companion, we show that the orbiting moon's tidal field induces a tidal bulge on the hole's horizon, and that the rate of change of the horizon shape (i.e. the horizon shear) leads the perturbing tidal field at the horizon by an angle 4M{omega}. We prefer to avoid introducing an ingoing null geodesic, as Hartle did in his definition of the phase shift, because the moon is in the central body's near zone (b<<1/{omega}) and thus should interact with the horizon instantaneously, not causally. We discuss the implications of these results for LISA's future observations of tidal coupling, including the inappropriateness of using the concepts of tidal polarizability and tidal lag or lead angle, for the massive central body, when discussing LISA's observations.« less

Testing the Binary Black Hole Nature of a Compact Binary Coalescence

NASA Astrophysics Data System (ADS)

Krishnendu, N. V.; Arun, K. G.; Mishra, Chandra Kant

2017-09-01

We propose a novel method to test the binary black hole nature of compact binaries detectable by gravitational wave (GW) interferometers and, hence, constrain the parameter space of other exotic compact objects. The spirit of the test lies in the "no-hair" conjecture for black holes where all properties of a Kerr black hole are characterized by its mass and spin. The method relies on observationally measuring the quadrupole moments of the compact binary constituents induced due to their spins. If the compact object is a Kerr black hole (BH), its quadrupole moment is expressible solely in terms of its mass and spin. Otherwise, the quadrupole moment can depend on additional parameters (such as the equation of state of the object). The higher order spin effects in phase and amplitude of a gravitational waveform, which explicitly contains the spin-induced quadrupole moments of compact objects, hence, uniquely encode the nature of the compact binary. Thus, we argue that an independent measurement of the spin-induced quadrupole moment of the compact binaries from GW observations can provide a unique way to distinguish binary BH systems from binaries consisting of exotic compact objects.

17O nuclear quadrupole coupling constants of water bound to a metal ion: A gadolinium(III) case study

NASA Astrophysics Data System (ADS)

Yazyev, Oleg V.; Helm, Lothar

2006-08-01

Rotational correlation times of metal ion aqua complexes can be determined from O17 NMR relaxation rates if the quadrupole coupling constant of the bound water oxygen-17 nucleus is known. The rotational correlation time is an important parameter for the efficiency of Gd3+ complexes as magnetic resonance imaging contrast agents. Using a combination of density functional theory with classical and Car-Parrinello molecular dynamics simulations we performed a computational study of the O17 quadrupole coupling constants in model aqua ions and the [Gd(DOTA)(H2O)]- complex used in clinical diagnostics. For the inner sphere water molecule in the [Gd(DOTA)(H2O)]- complex the determined quadrupole coupling parameter χ√1+η2/3 of 8.7MHz is very similar to that of the liquid water (9.0MHz ). Very close values were also predicted for the the homoleptic aqua ions of Gd3+ and Ca2+. We conclude that the O17 quadrupole coupling parameters of water molecules coordinated to closed shell and lanthanide metal ions are similar to water molecules in the liquid state.

The importance of quadrupole sources in prediction of transonic tip speed propeller noise

NASA Technical Reports Server (NTRS)

Hanson, D. B.; Fink, M. R.

1978-01-01

A theoretical analysis is presented for the harmonic noise of high speed, open rotors. Far field acoustic radiation equations based on the Ffowcs-Williams/Hawkings theory are derived for a static rotor with thin blades and zero lift. Near the plane of rotation, the dominant sources are the volume displacement and the rho U(2) quadrupole, where u is the disturbance velocity component in the direction blade motion. These sources are compared in both the time domain and the frequency domain using two dimensional airfoil theories valid in the subsonic, transonic, and supersonic speed ranges. For nonlifting parabolic arc blades, the two sources are equally important at speeds between the section critical Mach number and a Mach number of one. However, for moderately subsonic or fully supersonic flow over thin blade sections, the quadrupole term is negligible. It is concluded for thin blades that significant quadrupole noise radiation is strictly a transonic phenomenon and that it can be suppressed with blade sweep. Noise calculations are presented for two rotors, one simulating a helicopter main rotor and the other a model propeller. For the latter, agreement with test data was substantially improved by including the quadrupole source term.

Testing the Binary Black Hole Nature of a Compact Binary Coalescence.

PubMed

Krishnendu, N V; Arun, K G; Mishra, Chandra Kant

2017-09-01

We propose a novel method to test the binary black hole nature of compact binaries detectable by gravitational wave (GW) interferometers and, hence, constrain the parameter space of other exotic compact objects. The spirit of the test lies in the "no-hair" conjecture for black holes where all properties of a Kerr black hole are characterized by its mass and spin. The method relies on observationally measuring the quadrupole moments of the compact binary constituents induced due to their spins. If the compact object is a Kerr black hole (BH), its quadrupole moment is expressible solely in terms of its mass and spin. Otherwise, the quadrupole moment can depend on additional parameters (such as the equation of state of the object). The higher order spin effects in phase and amplitude of a gravitational waveform, which explicitly contains the spin-induced quadrupole moments of compact objects, hence, uniquely encode the nature of the compact binary. Thus, we argue that an independent measurement of the spin-induced quadrupole moment of the compact binaries from GW observations can provide a unique way to distinguish binary BH systems from binaries consisting of exotic compact objects.

Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Brody, Dorje C.

2018-04-01

The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads to a challenging open problem concerning the formulation of the eigenvalue problem in the momentum space. The WKB analysis gives the exact asymptotic behavior of the eigenfunction.

Simple One-Dimensional Quantum-Mechanical Model for a Particle Attached to a Surface

ERIC Educational Resources Information Center

Fernandez, Francisco M.

2010-01-01

We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schrodinger equation for a harmonic oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships…

On Closed Shells in Nuclei. II

DOE R&D Accomplishments Database

Mayer, M. G.

1949-04-01

Discussion on the use of spins and magnetic moments of the even-odd nuclei by Feenberg and Nordheim to determine the angular momentum of the eigenfunction of the odd particle; discussion of prevalence of isomerism in certain regions of the isotope chart; tabulated data on levels of square well potential, spectroscopic levels, spin term, number of states, shells and known spins and orbital assignments.

The Application of a Boundary Integral Equation Method to the Prediction of Ducted Fan Engine Noise

NASA Technical Reports Server (NTRS)

Dunn, M. H.; Tweed, J.; Farassat, F.

1999-01-01

The prediction of ducted fan engine noise using a boundary integral equation method (BIEM) is considered. Governing equations for the BIEM are based on linearized acoustics and describe the scattering of incident sound by a thin, finite-length cylindrical duct in the presence of a uniform axial inflow. A classical boundary value problem (BVP) is derived that includes an axisymmetric, locally reacting liner on the duct interior. Using potential theory, the BVP is recast as a system of hypersingular boundary integral equations with subsidiary conditions. We describe the integral equation derivation and solution procedure in detail. The development of the computationally efficient ducted fan noise prediction program TBIEM3D, which implements the BIEM, and its utility in conducting parametric noise reduction studies are discussed. Unlike prediction methods based on spinning mode eigenfunction expansions, the BIEM does not require the decomposition of the interior acoustic field into its radial and axial components which, for the liner case, avoids the solution of a difficult complex eigenvalue problem. Numerical spectral studies are presented to illustrate the nexus between the eigenfunction expansion representation and BIEM results. We demonstrate BIEM liner capability by examining radiation patterns for several cases of practical interest.

THEORETICAL p-MODE OSCILLATION FREQUENCIES FOR THE RAPIDLY ROTATING {delta} SCUTI STAR {alpha} OPHIUCHI

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

Deupree, Robert G., E-mail: bdeupree@ap.smu.ca

2011-11-20

A rotating, two-dimensional stellar model is evolved to match the approximate conditions of {alpha} Oph. Both axisymmetric and nonaxisymmetric oscillation frequencies are computed for two-dimensional rotating models which approximate the properties of {alpha} Oph. These computed frequencies are compared to the observed frequencies. Oscillation calculations are made assuming the eigenfunction can be fitted with six Legendre polynomials, but comparison calculations with eight Legendre polynomials show the frequencies agree to within about 0.26% on average. The surface horizontal shape of the eigenfunctions for the two sets of assumed number of Legendre polynomials agrees less well, but all calculations show significant departuresmore » from that of a single Legendre polynomial. It is still possible to determine the large separation, although the small separation is more complicated to estimate. With the addition of the nonaxisymmetric modes with |m| {<=} 4, the frequency space becomes sufficiently dense that it is difficult to comment on the adequacy of the fit of the computed to the observed frequencies. While the nonaxisymmetric frequency mode splitting is no longer uniform, the frequency difference between the frequencies for positive and negative values of the same m remains 2m times the rotation rate.« less

Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator

NASA Astrophysics Data System (ADS)

Karthiga, S.; Chithiika Ruby, V.; Senthilvelan, M.; Lakshmanan, M.

2017-10-01

In position dependent mass (PDM) problems, the quantum dynamics of the associated systems have been understood well in the literature for particular orderings. However, no efforts seem to have been made to solve such PDM problems for general orderings to obtain a global picture. In this connection, we here consider the general ordered quantum Hamiltonian of an interesting position dependent mass problem, namely, the Mathews-Lakshmanan oscillator, and try to solve the quantum problem for all possible orderings including Hermitian and non-Hermitian ones. The other interesting point in our study is that for all possible orderings, although the Schrödinger equation of this Mathews-Lakshmanan oscillator is uniquely reduced to the associated Legendre differential equation, their eigenfunctions cannot be represented in terms of the associated Legendre polynomials with integral degree and order. Rather the eigenfunctions are represented in terms of associated Legendre polynomials with non-integral degree and order. We here explore such polynomials and represent the discrete and continuum states of the system. We also exploit the connection between associated Legendre polynomials with non-integral degree with other orthogonal polynomials such as Jacobi and Gegenbauer polynomials.

Estimating amplitude ratios in boundary layer stability theory: a comparison between two approaches

NASA Astrophysics Data System (ADS)

Govindarajan, Rama; Narasimha, R.

2001-07-01

We first demonstrate that, if the contributions of higher-order mean flow are ignored, the parabolized stability equations (Bertolotti et al. 1992) and the ‘full’ non-parallel equation of Govindarajan & Narasimha (1995, hereafter GN95) are both equivalent to order R[minus sign]1 in the local Reynolds number R to Gaster's (1974) equation for the stability of spatially developing boundary layers. It is therefore of some concern that a detailed comparison between Gaster (1974) and GN95 reveals a small difference in the computed amplitude ratios. Although this difference is not significant in practical terms in Blasius flow, it is traced here to the approximation, in Gaster's method, of neglecting the change in eigenfunction shape due to flow non-parallelism. This approximation is not justified in the critical and the wall layers, where the neglected term is respectively O(R[minus sign]2/3) and O(R[minus sign]1) compared to the largest term. The excellent agreement of GN95 with exact numerical simulations, on the other hand, suggests that the effect of change in eigenfunction is accurately taken into account in that paper.

Mathematical modeling of two phase stratified flow in a microchannel with curved interface

NASA Astrophysics Data System (ADS)

Dandekar, Rajat; Picardo, Jason R.; Pushpavanam, S.

2017-11-01

Stratified or layered two-phase flows are encountered in several applications of microchannels, such as solvent extraction. Assuming steady, unidirectional creeping flow, it is possible to solve the Stokes equations by the method of eigenfunctions, provided the interface is flat and meets the wall with a 90 degree contact angle. However, in reality the contact angle depends on the pair of liquids and the material of the channel, and differs significantly from 90 degrees in many practical cases. For unidirectional flow, this implies that the interface is a circular arc (of constant curvature). We solve this problem within the framework of eigenfunctions, using the procedure developed by Shankar. We consider two distinct cases: (a) the interface meets the wall with the equilibrium contact angle; (b) the interface is pinned by surface treatment of the walls, so that the flow rates determine the apparent contact angle. We show that the contact angle appreciably affects the velocity profile and the volume fractions of the liquids, while limiting the range of flow rates that can be sustained without the interface touching the top/bottom walls. Non-intuitively, we find that the pressure drop is reduced when the more viscous liquid wets the wall.

Electromagnetic and scalar diffraction by a right-angled wedge with a uniform surface impedance

NASA Technical Reports Server (NTRS)

Hwang, Y. M.

1974-01-01

The diffraction of an electromagnetic wave by a perfectly-conducting right-angled wedge with one surface covered by a dielectric slab or absorber is considered. The effect of the coated surface is approximated by a uniform surface impedance. The solution of the normally incident electromagnetic problem is facilitated by introducing two scalar fields which satisfy a mixed boundary condition on one surface of the wedge and a Neumann of Dirichlet boundary condition on the other. A functional transformation is employed to simplify the boundary conditions so that eigenfunction expansions can be obtained for the resulting Green's functions. The eigenfunction expansions are transformed into the integral representations which then are evaluated asymptotically by the modified Pauli-Clemmow method of steepest descent. A far zone approximation is made to obtain the scattered field from which the diffraction coefficient is found for scalar plane, cylindrical or sperical wave incident on the edge. With the introduction of a ray-fixed coordinate system, the dyadic diffraction coefficient for plane or cylindrical EM waves normally indicent on the edge is reduced to the sum of two dyads which can be written alternatively as a 2 X 2 diagonal matrix.

Numerical operator calculus in higher dimensions

PubMed Central

Beylkin, Gregory; Mohlenkamp, Martin J.

2002-01-01

When an algorithm in dimension one is extended to dimension d, in nearly every case its computational cost is taken to the power d. This fundamental difficulty is the single greatest impediment to solving many important problems and has been dubbed the curse of dimensionality. For numerical analysis in dimension d, we propose to use a representation for vectors and matrices that generalizes separation of variables while allowing controlled accuracy. Basic linear algebra operations can be performed in this representation using one-dimensional operations, thus bypassing the exponential scaling with respect to the dimension. Although not all operators and algorithms may be compatible with this representation, we believe that many of the most important ones are. We prove that the multiparticle Schrödinger operator, as well as the inverse Laplacian, can be represented very efficiently in this form. We give numerical evidence to support the conjecture that eigenfunctions inherit this property by computing the ground-state eigenfunction for a simplified Schrödinger operator with 30 particles. We conjecture and provide numerical evidence that functions of operators inherit this property, in which case numerical operator calculus in higher dimensions becomes feasible. PMID:12140360

An analysis of the vertical structure equation for arbitrary thermal profiles

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.; Dee, Dick P.

1989-01-01

The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations.

An analysis of the vertical structure equation for arbitrary thermal profiles

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.; Dee, Dick P.

1987-01-01

The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations.

The construction of partner potential from the general potential Rosen-Morse and Manning Rosen in 4 dimensional Schrodinger system

NASA Astrophysics Data System (ADS)

Nathalia Wea, Kristiana; Suparmi, A.; Cari, C.; Wahyulianti

2017-11-01

The solution of the Schrodinger equation with physical potential is the important part in quantum physics. Many methods have been developed to resolve the Schrodinger equation. The Nikiforov-Uvarov method and supersymmetric method are the most methods that interesting to be explored. The supersymmetric method not only used to solve the Schrodinger equation but also used to construct the partner potential from a general potential. In this study, the Nikiforov-Uvarov method was used to solve the Schrodinger equation while the supersymmetric method was used to construction partner potential. The study about the construction of the partner potential from general potential Rosen-Morse and Manning Rosen in D-dimensional Schrodinger system has been done. The partner potential was obtained are solvable. By using the Nikiforov-Uvarov method the eigenfunction of the Schrodinger equation in D-dimensional system with general potential Rosen-Morse and Manning Rosen and the Schrodinger equation in D-dimensional system with partner potential Rosen-Morse and Manning Rosen are determined. The eigenfunctions are different between the Schrodinger equation with general potential and the Schrodinger potential with the partner potential.

Population of collective modes in light scattering by many atoms

NASA Astrophysics Data System (ADS)

Guerin, William; Kaiser, Robin

2017-05-01

The interaction of light with an atomic sample containing a large number of particles gives rise to many collective (or cooperative) effects, such as multiple scattering, superradiance, and subradiance, even if the atomic density is low and the incident optical intensity weak (linear optics regime). Tracing over the degrees of freedom of the light field, the system can be well described by an effective atomic Hamiltonian, which contains the light-mediated dipole-dipole interaction between atoms. This long-range interaction is at the origin of the various collective effects, or of collective excitation modes of the system. Even though an analysis of the eigenvalues and eigenfunctions of these collective modes does allow distinguishing superradiant modes, for instance, from other collective modes, this is not sufficient to understand the dynamics of a driven system, as not all collective modes are significantly populated. Here, we study how the excitation parameters, i.e., the driving field, determines the population of the collective modes. We investigate in particular the role of the laser detuning from the atomic transition, and demonstrate a simple relation between the detuning and the steady-state population of the modes. This relation allows understanding several properties of cooperative scattering, such as why superradiance and subradiance become independent of the detuning at large enough detuning without vanishing, and why superradiance, but not subradiance, is suppressed near resonance. We also show that the spatial properties of the collective modes allow distinguishing diffusive modes, responsible for radiation trapping, from subradiant modes.

Mechanical performance of short models for MQXF, the Nb3Sn low-β quadrupole for the Hi-Lumi LHC

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

Vallone, Giorgio; Ambrosio, Giorgio; Anderssen, Eric

In the framework of the Hi-Lumi LHC Project, CERN and U.S. LARP are jointly developing MQXF, a 150-mm aperture high-field Nb3Sn quadrupole for the upgrade of the inner triplet of the low-beta interaction regions. The magnet is supported by a shell-based structure, providing the preload by means of bladder-key technology and differential thermal contraction of the various components. Two short models have been produced using the same cross section currently considered for the final magnet. The structures were preliminarily tested replacing the superconducting coils with blocks of aluminum. This procedure allows for model validation and calibration, and also to setmore » performance goals for the real magnet. Strain gauges were used to monitor the behavior of the structure during assembly, cool down and also excitation in the case of the magnets. The various structures differ for the shell partitioning strategies adopted and for the presence of thick or thin laminations. This study presents the results obtained and discusses the mechanical performance of all the short models produced up to now.« less

Blue and white light emission in Tm3+ and Tm3+/Dy3+ doped zinc phosphate glasses upon UV light excitation

NASA Astrophysics Data System (ADS)

Meza-Rocha, A. N.; Speghini, A.; Lozada-Morales, R.; Caldiño, U.

2016-08-01

A spectroscopic study based on photoluminescence spectra and decay time profiles in Tm3+ and Tm3+/Dy3+ doped Zn(PO3)2 glasses is reported. The Tm3+ doped Zn(PO3)2 glass, upon 357 nm excitation, exhibits blue emission with CIE1931 chromaticity coordinates, x = 0.157 and y = 0.030, and color purity of about 96%. Under excitations at 348, 352 and 363 nm, which match with the emissions of AlGaN and GaN based LEDs, the Tm3+/Dy3+ co-doped Zn(PO3)2 glass displays natural white, bluish white and cool white overall emissions, with correlated color temperature values of 4523, 10700 and 7788 K, respectively, depending strongly on the excitation wavelength. The shortening of the Dy3+ emission decay time in presence of Tm3+ suggests that Dy3+→Tm3+ non-radiative energy transfer occurs. By using the Inokuti-Hirayama model, it is inferred that an electric quadrupole-quadrupole interaction might be the dominant mechanism involved in the energy transfer. The efficiency and probability of this energy transfer are 0.12 and 126.70 s-1, respectively.

Mechanical qualification of the support structure for MQXF, the Nb 3Sn low-β quadrupole for the high luminosity LHC

DOE PAGES

Juchno, M.; Ambrosio, G.; Anerella, M.; ...

2016-01-26

Within the scope of the High Luminosity LHC project, the collaboration between CERN and U.S. LARP is developing new low-β quadrupoles using the Nb 3Sn superconducting technology for the upgrade of the LHC interaction regions. The magnet support structure of the first short model was designed and two units were fabricated and tested at CERN and at LBNL. The structure provides the preload to the collars-coils subassembly by an arrangement of outer aluminum shells pre-tensioned with water-pressurized bladders. For the mechanical qualification of the structure and the assembly procedure, superconducting coils were replaced with solid aluminum “dummy coils”, the structuremore » was preloaded at room temperature, and then cooled-down to 77 K. Mechanical behavior of the magnet structure was monitored with the use of strain gauges installed on the aluminum shells, the dummy coils and the axial preload system. As a result, this paper reports on the outcome of the assembly and the cool-down tests with dummy coils, which were performed at CERN and at LBNL, and presents the strain gauge measurements compared to the 3D finite element model predictions.« less

Mechanical performance of short models for MQXF, the Nb3Sn low-β quadrupole for the Hi-Lumi LHC

DOE PAGES

Vallone, Giorgio; Ambrosio, Giorgio; Anderssen, Eric; ...

2016-12-23

In the framework of the Hi-Lumi LHC Project, CERN and U.S. LARP are jointly developing MQXF, a 150-mm aperture high-field Nb3Sn quadrupole for the upgrade of the inner triplet of the low-beta interaction regions. The magnet is supported by a shell-based structure, providing the preload by means of bladder-key technology and differential thermal contraction of the various components. Two short models have been produced using the same cross section currently considered for the final magnet. The structures were preliminarily tested replacing the superconducting coils with blocks of aluminum. This procedure allows for model validation and calibration, and also to setmore » performance goals for the real magnet. Strain gauges were used to monitor the behavior of the structure during assembly, cool down and also excitation in the case of the magnets. The various structures differ for the shell partitioning strategies adopted and for the presence of thick or thin laminations. This study presents the results obtained and discusses the mechanical performance of all the short models produced up to now.« less

Selective Isobar Suppression for Accelerator Mass Spectrometry and Radioactive Ion Beam Science

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

Galindo-Uribarri, Alfredo; Havener, Charles C; Lewis, Thomas L.

2010-01-01

Several applications of AMS will benefit from pushing further the detection limits of AMS isotopes. A new method of selective isobar suppression by photodetachment in a radio-frequency quadrupole ion cooler is being developed at HRIBF with a two-fold purpose: (1) increasing the AMS sensitivity for certain isotopes of interest and (2) purifying radioactive ion beams for nuclear science. The potential of suppressing the 36S contaminants in a 36Cl beam using this method has been explored with stable S- and Cl- ions and a Nd:YLF laser. In the study, the laser beam was directed along the experiment's beam line and throughmore » a RF quadrupole ion cooler. Negative 32S and 35Cl ions produced by a Cs sputter ion source were focused into the ion cooler where they were slowed by collisions with He buffer gas; this increased the interaction time between the negative ion beam and the laser beam. As a result, suppression of S- by a factor of 3000 was obtained with about 2.5 W average laser power in the cooler while no reduction in Cl- current was observed.« less

Modeling Aerodynamically Generated Sound of Helicopter Rotors

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.; Farassat, F.

2002-01-01

A great deal of progress has been made in the modeling of aerodynamically generated sound of rotors over the past decade. Although the modeling effort has focused on helicopter main rotors, the theory is generally valid for a wide range of rotor configurations. The Ffowcs Williams Hawkings (FW-H) equation has been the foundation for much of the development. The monopole and dipole source terms of the FW-H equation account for the thickness and loading noise, respectively. Bladevortex-interaction noise and broadband noise are important types of loading noise, hence much research has been directed toward the accurate modeling of these noise mechanisms. Both subsonic and supersonic quadrupole noise formulations have been developed for the prediction of high-speed impulsive noise. In an effort to eliminate the need to compute the quadrupole contribution, the FW-H equation has also been utilized on permeable surfaces surrounding all physical noise sources. Comparisons of the Kirchhoff formulation for moving surfaces with the FW-H equation have shown that the Kirchhoff formulation for moving surfaces can give erroneous results for aeroacoustic problems. Finally, significant progress has been made incorporating the rotor noise models into full vehicle noise prediction tools.

Instrumentation status of the low-b magnet systems at the Large Hadron Collider (LHC)

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

Darve, C.; /Fermilab; Balle, C.

2011-05-01

The low-{beta} magnet systems are located in the Large Hadron Collider (LHC) insertion regions around the four interaction points. They are the key elements in the beams focusing/defocusing process allowing proton collisions at luminosity up to 10{sup 34}cm{sup -2}s{sup -1}. Those systems are a contribution of the US-LHC Accelerator project. The systems are mainly composed of the quadrupole magnets (triplets), the separation dipoles and their respective electrical feed-boxes (DFBX). The low-{beta} magnet systems operate in an environment of extreme radiation, high gradient magnetic field and high heat load to the cryogenic system due to the beam dynamic effect. Due tomore » the severe environment, the robustness of the diagnostics is primordial for the operation of the triplets. The hardware commissioning phase of the LHC was completed in February 2010. In the sake of a safer and more user-friendly operation, several consolidations and instrumentation modifications were implemented during this commissioning phase. This paper presents the instrumentation used to optimize the engineering process and operation of the final focusing/defocusing quadrupole magnets for the first years of operation.« less

CALCULATIONS WITH SPECTROSCOPIC ACCURACY: ENERGIES AND TRANSITION RATES IN THE NITROGEN ISOELECTRONIC SEQUENCE FROM Ar XII TO Zn XXIV

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

Wang, K.; Dang, W.; Si, R.

2016-03-15

Combined relativistic configuration interaction and many-body perturbation calculations are performed for the 359 fine-structure levels of the 2s{sup 2} 2p{sup 3}, 2 s2p{sup 4}, 2p{sup 5}, 2s{sup 2} 2p{sup 2} 3l, 2 s2p{sup 3} 3l, 2p{sup 4} 3l, and 2s{sup 2} 2p{sup 2} 4l configurations in N-like ions from Ar xii to Zn xxiv. Complete and consistent data sets of energies, wavelengths, radiative rates, oscillator strengths, and line strengths for all possible electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole transitions among the 359 levels are given for each ion. The present work significantly increases the amount of accuratemore » data for ions in the nitrogen-like sequence, and the accuracy of the energy levels is high enough to enable the identification and interpretation of observed spectra involving the n = 3, 4 levels, for which experimental values are largely scarce. Meanwhile, the results should be of great help for modeling and diagnosing astrophysical and fusion plasmas.« less

Characterization of magnetic nanoparticles using programmed quadrupole magnetic field-flow fractionation

PubMed Central

Williams, P. Stephen; Carpino, Francesca; Zborowski, Maciej

2010-01-01

Quadrupole magnetic field-flow fractionation is a relatively new technique for the separation and characterization of magnetic nanoparticles. Magnetic nanoparticles are often of composite nature having a magnetic component, which may be a very finely divided material, and a polymeric or other material coating that incorporates this magnetic material and stabilizes the particles in suspension. There may be other components such as antibodies on the surface for specific binding to biological cells, or chemotherapeutic drugs for magnetic drug delivery. Magnetic field-flow fractionation (MgFFF) has the potential for determining the distribution of the magnetic material among the particles in a given sample. MgFFF differs from most other forms of field-flow fractionation in that the magnetic field that brings about particle separation induces magnetic dipole moments in the nanoparticles, and these potentially can interact with one another and perturb the separation. This aspect is examined in the present work. Samples of magnetic nanoparticles were analysed under different experimental conditions to determine the sensitivity of the method to variation of conditions. The results are shown to be consistent and insensitive to conditions, although magnetite content appeared to be somewhat higher than expected. PMID:20732895

Multiple shadows from distorted static black holes

NASA Astrophysics Data System (ADS)

Grover, Jai; Kunz, Jutta; Nedkova, Petya; Wittig, Alexander; Yazadjiev, Stoytcho

2018-04-01

We study the local shadow of the Schwarzschild black hole with a quadrupole distortion and the influence of the external gravitational field on the photon dynamics. The external matter sources modify the light ring structure and lead to the appearance of multiple shadow images. In the case of negative quadrupole moments we identify the most prominent mechanism causing multiple shadow formation. Furthermore, we obtain a condition under which this mechanism can be realized. This condition depends on the quadrupole moment, but also on the position of the observer and the celestial sphere.

The nuclear electric quadrupole moment of copper.

PubMed

Santiago, Régis Tadeu; Teodoro, Tiago Quevedo; Haiduke, Roberto Luiz Andrade

2014-06-21

The nuclear electric quadrupole moment (NQM) of the (63)Cu nucleus was determined from an indirect approach by combining accurate experimental nuclear quadrupole coupling constants (NQCCs) with relativistic Dirac-Coulomb coupled cluster calculations of the electric field gradient (EFG). The data obtained at the highest level of calculation, DC-CCSD-T, from 14 linear molecules containing the copper atom give rise to an indicated NQM of -198(10) mbarn. Such result slightly deviates from the previously accepted standard value given by the muonic method, -220(15) mbarn, although the error bars are superimposed.

A Superstrong Adjustable Permanent Magnet for the Final Focus Quadrupole in a Linear Collider

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

Mihara, T.

A super strong permanent magnet quadrupole (PMQ) was fabricated and tested. It has an integrated strength of 28.5T with overall length of 10 cm and a 7mm bore radius. The final focus quadrupole of a linear collider needs a variable focal length. This can be obtained by slicing the magnet into pieces along the beamline direction and rotating these slices. But this technique may lead to movement of the magnetic center and introduction of a skew quadrupole component when the strength is varied. A ''double ring structure'' can ease these effects. A second prototype PMQ, containing thermal compensation materials andmore » with a double ring structure, has been fabricated. Worm gear is selected as the mechanical rotating scheme because the double ring structure needs a large torque to rotate magnets. The structure of the second prototype PMQ is shown.« less

Study of a micro chamber quadrupole mass spectrometer

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

Wang Jinchan; Zhang Xiaobing; Mao Fuming

The design of a micro chamber quadrupole mass spectrometer (MCQMS) having a small total volume of only 20 cm{sup 3}, including Faraday cup ion detector and ion source, is described. This MCQMS can resist a vacuum baking temperature of 400-500 deg. C. The quadrupole elements with a hyperbolic surface are made of a ceramic material and coated with a thin metal layer. The quadrupole mass filter has a field radius of 3 mm and a length of 100 mm. Prototypes of this new MCQMS can detect a minimum partial pressure of 10{sup -8} Pa, have a peak width of {delta}M=1more » at 10% peak height from mass number 1 to 60, and show an excellent long-term stability. The new MCQMS is intended to be used in residual gas analyses of electron devices during a mutual pumping and baking process.« less

Mass peak shape improvement of a quadrupole mass filter when operating with a rectangular wave power supply.

PubMed

Luo, Chan; Jiang, Dan; Ding, Chuan-Fan; Konenkov, Nikolai V

2009-09-01

Numeric experiments were performed to study the first and second stability regions and find the optimal configurations of a quadrupole mass filter constructed of circular quadrupole rods with a rectangular wave power supply. The ion transmission contours were calculated using ion trajectory simulations. For the first stability region, the optimal rod set configuration and the ratio r/r(0) is 1.110-1.115; for the second stability region, it is 1.128-1.130. Low-frequency direct current (DC) modulation with the parameters of m = 0.04-0.16 and nu = omega/Omega = 1/8-1/14 improves the mass peak shape of the circular rod quadrupole mass filter at the optimal r/r(0) ratio of 1.130. The amplitude modulation does not improve mass peak shape. Copyright (c) 2009 John Wiley & Sons, Ltd.

Development of a GC/Quadrupole-Orbitrap Mass Spectrometer, Part I: Design and Characterization

PubMed Central

2015-01-01

Identification of unknown compounds is of critical importance in GC/MS applications (metabolomics, environmental toxin identification, sports doping, petroleomics, and biofuel analysis, among many others) and remains a technological challenge. Derivation of elemental composition is the first step to determining the identity of an unknown compound by MS, for which high accuracy mass and isotopomer distribution measurements are critical. Here, we report on the development of a dedicated, applications-grade GC/MS employing an Orbitrap mass analyzer, the GC/Quadrupole-Orbitrap. Built from the basis of the benchtop Orbitrap LC/MS, the GC/Quadrupole-Orbitrap maintains the performance characteristics of the Orbitrap, enables quadrupole-based isolation for sensitive analyte detection, and includes numerous analysis modalities to facilitate structural elucidation. We detail the design and construction of the instrument, discuss its key figures-of-merit, and demonstrate its performance for the characterization of unknown compounds and environmental toxins. PMID:25208235

Microfluidic quadrupole and floating concentration gradient.

PubMed

Qasaimeh, Mohammad A; Gervais, Thomas; Juncker, David

2011-09-06

The concept of fluidic multipoles, in analogy to electrostatics, has long been known as a particular class of solutions of the Navier-Stokes equation in potential flows; however, experimental observations of fluidic multipoles and of their characteristics have not been reported yet. Here we present a two-dimensional microfluidic quadrupole and a theoretical analysis consistent with the experimental observations. The microfluidic quadrupole was formed by simultaneously injecting and aspirating fluids from two pairs of opposing apertures in a narrow gap formed between a microfluidic probe and a substrate. A stagnation point was formed at the centre of the microfluidic quadrupole, and its position could be rapidly adjusted hydrodynamically. Following the injection of a solute through one of the poles, a stationary, tunable, and movable-that is, 'floating'-concentration gradient was formed at the stagnation point. Our results lay the foundation for future combined experimental and theoretical exploration of microfluidic planar multipoles including convective-diffusive phenomena.

Reconstruction of CMB temperature anisotropies with primordial CMB induced polarization in galaxy clusters

NASA Astrophysics Data System (ADS)

Liu, Guo-Chin; Ichiki, Kiyotomo; Tashiro, Hiroyuki; Sugiyama, Naoshi

2016-07-01

Scattering of cosmic microwave background (CMB) radiation in galaxy clusters induces polarization signals determined by the quadrupole anisotropy in the photon distribution at the location of clusters. This `remote quadrupole' derived from the measurements of the induced polarization in galaxy clusters provides an opportunity to reconstruct local CMB temperature anisotropies. In this Letter, we develop an algorithm of the reconstruction through the estimation of the underlying primordial gravitational potential, which is the origin of the CMB temperature and polarization fluctuations and CMB induced polarization in galaxy clusters. We found a nice reconstruction for the quadrupole and octopole components of the CMB temperature anisotropies with the assistance of the CMB induced polarization signals. The reconstruction can be an important consistency test on the puzzles of CMB anomalies, especially for the low-quadrupole and axis-of-evil problems reported in Wilkinson Microwave Anisotropy Probe and Planck data.

Physical origin of the quadrupole out-of-plane magnetic field in Hall-magnetohydrodynamic reconnection

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

Uzdensky, Dmitri A.; Kulsrud, Russell M.

2006-06-15

A quadrupole pattern of the out-of-plane component of the magnetic field inside a reconnection region is seen as an important signature of the Hall-magnetohydrodynamic regime of reconnection. It has been first observed in numerical simulations and just recently confirmed in the Magnetic Reconnection Experiment [Y. Ren, M. Yamada, S. Gerhardt, H. Ji, R. Kulsrud, and A. Kuritsin, Phys. Rev. Lett. 95, 055003 (2005)] and also seen in spacecraft observations of Earth's magnetosphere. In this study, the physical origin of the quadrupole field is analyzed and traced to a current of electrons that flows along the lines in and out ofmore » the inner reconnection region to maintain charge neutrality. The role of the quadrupole magnetic field in the overall dynamics of the reconnection process is discussed. In addition, the bipolar poloidal electric field is estimated and its effect on ion motions is emphasized.« less

Modulated magnetic structure of F e3P O7 as seen by 57Fe Mössbauer spectroscopy

NASA Astrophysics Data System (ADS)

Sobolev, A. V.; Akulenko, A. A.; Glazkova, I. S.; Pankratov, D. A.; Presniakov, I. A.

2018-03-01

The paper reports results of the 57Fe Mössbauer measurements on an F e3P O4O3 powder sample recorded at various temperatures, including the point of magnetic phase transition TN≈163 K . The spectra measured above TN consist of a quadrupole doublet with high quadrupole splitting of Δ300 K≈1.10 mm /s , emphasizing that F e3 + ions are located in crystal positions with a strong electric-field gradient (EFG). To predict the sign and orientation of the main components of the EFG tensor, we calculated the EFG using the density-functional-theory approach. In the temperature range T

Influence of Pt substitution on magnetic properties of multipolar ordering compounds Ce(Pd,Pt)3S4

NASA Astrophysics Data System (ADS)

Michimura, S.; Nishikawa, Ushio; Shimizu, Akihide; Kosaka, Masashi; Numakura, Ryosuke; Iizuka, Ryosuke; Katano, Susumu

2018-05-01

We have studied the magnetic properties of the multipolar ordering compounds Ce(Pd1-xPtx) 3S4 with 0.00 ≤ x ≤ 0.53 by means of magnetic susceptibility and magnetization measurements. In CePd3S4 , a simultaneous phase transition of the antiferro quadrupolar (AFQ) ordering and ferro magnetic (FM) ordering has been observed at 6.3 K. It has been suggested that the primary order parameter of CePd3S4 is the quadrupole moments, and it has not been understood why the FM ordering occurs at very high temperature which is almost the same magnetic transition temperature of GdPd3S4 . GdPd3S4 shows an antiferromagnetic (AFM) transition at 5.8 K. With increasing Pt substitution in CePd3S4 , the FM transition temperature TC (x) is rapidly suppressed to 2.4 K for x ≃ 0.3 and approaches asymptotically to 1.9 K (x = 0.53) . The results of magnetization curve suggest that the ordered state below TC (x) remains FM and AFQ ordered state for the whole range of x. For x ≥ 0.29 , TC (x) reaches at around 2 K, a new AFM transition was observed at TN (x) ≃ 7 K . We determined the T - x phase diagram, and discuss the phase transitions at TC (x) and TN (x) . The results suggest the possibility of the presence of the correlation between the magnetic interaction and the quadrupole interaction, and the correlation is not understood based on the previous multipolar model.

Removal of two large-scale cosmic microwave background anomalies after subtraction of the integrated Sachs-Wolfe effect

NASA Astrophysics Data System (ADS)

Rassat, A.; Starck, J.-L.; Dupé, F.-X.

2013-09-01

Context. Although there is currently a debate over the significance of the claimed large-scale anomalies in the cosmic microwave background (CMB), their existence is not totally dismissed. In parallel to the debate over their statistical significance, recent work has also focussed on masks and secondary anisotropies as potential sources of these anomalies. Aims: In this work we investigate simultaneously the impact of the method used to account for masked regions as well as the impact of the integrated Sachs-Wolfe (ISW) effect, which is the large-scale secondary anisotropy most likely to affect the CMB anomalies. In this sense, our work is an update of previous works. Our aim is to identify trends in CMB data from different years and with different mask treatments. Methods: We reconstruct the ISW signal due to 2 Micron All-Sky Survey (2MASS) and NRAO VLA Sky Survey (NVSS) galaxies, effectively reconstructing the low-redshift ISW signal out to z ~ 1. We account for regions of missing data using the sparse inpainting technique. We test sparse inpainting of the CMB, large scale structure and ISW and find that it constitutes a bias-free reconstruction method suitable to study large-scale statistical isotropy and the ISW effect. Results: We focus on three large-scale CMB anomalies: the low quadrupole, the quadrupole/octopole alignment, and the octopole planarity. After sparse inpainting, the low quadrupole becomes more anomalous, whilst the quadrupole/octopole alignment becomes less anomalous. The significance of the low quadrupole is unchanged after subtraction of the ISW effect, while the trend amongst the CMB maps is that both the low quadrupole and the quadrupole/octopole alignment have reduced significance, yet other hypotheses remain possible as well (e.g. exotic physics). Our results also suggest that both of these anomalies may be due to the quadrupole alone. While the octopole planarity significance is reduced after inpainting and after ISW subtraction, however, we do not find that it was very anomalous to start with. In the spirit of participating in reproducible research, we make all codes and resulting products which constitute main results of this paper public here: http://www.cosmostat.org/anomaliesCMB.html

Gamma-unstable nuclei in the sdg boson model

NASA Astrophysics Data System (ADS)

Kuyucak, S.; Lac, V.-S.; Morrison, I.; Barret, B. R.

Following the recent Pt(p,p') experiments which indicated the need for high angular momentum (g) bosons to reproduce the E4 data, we have extended the O(6) limit of the sd boson model to the sdg bosons. It is shown that a gamma-unstable Hamiltonian in the sdg model consisting of a quadrupole interaction and a g boson energy leads to results that are very similar to the O(6) limit. Deviations from the empirical energy spectrum that stem from the gamma-unstable nature of the Hamiltonian can be improved by including a consistent hexadecapole interaction which induces triaxiality. The same hexadecapole operator can also account for the strong E4 transitions to the 4(sup +) states presumed to be g boson states. Specific applications are made to the Xe and Pt isotopes.

New General Relativistic Contribution to Mercury's Perihelion Advance

NASA Astrophysics Data System (ADS)

Will, Clifford M.

2018-05-01

We point out the existence of a new general relativistic contribution to the perihelion advance of Mercury that, while smaller than the contributions arising from the solar quadrupole moment and angular momentum, is 100 times larger than the second-post-Newtonian contribution. It arises in part from relativistic "crossterms" in the post-Newtonian equations of motion between Mercury's interaction with the Sun and with the other planets, and in part from an interaction between Mercury's motion and the gravitomagnetic field of the moving planets. At a few parts in 1 06 of the leading general relativistic precession of 42.98 arcseconds per century, these effects are likely to be detectable by the BepiColombo mission to place and track two orbiters around Mercury, scheduled for launch around 2018.

New General Relativistic Contribution to Mercury's Perihelion Advance.

PubMed

Will, Clifford M

2018-05-11

We point out the existence of a new general relativistic contribution to the perihelion advance of Mercury that, while smaller than the contributions arising from the solar quadrupole moment and angular momentum, is 100 times larger than the second-post-Newtonian contribution. It arises in part from relativistic "crossterms" in the post-Newtonian equations of motion between Mercury's interaction with the Sun and with the other planets, and in part from an interaction between Mercury's motion and the gravitomagnetic field of the moving planets. At a few parts in 10^{6} of the leading general relativistic precession of 42.98 arcseconds per century, these effects are likely to be detectable by the BepiColombo mission to place and track two orbiters around Mercury, scheduled for launch around 2018.

Microscopic derivation of IBM and structural evolution in nuclei

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

Nomura, Kosuke

A Hamiltonian of the interacting boson model (IBM) is derived based on the mean-field calculations with nuclear energy density functionals (EDFs). The multi-nucleon dynamics of the surface deformation is simulated in terms of the boson degrees of freedom. The interaction strengths of the IBM Hamiltonian are determined by mapping the potential energy surfaces (PESs) of a given EDF with quadrupole degrees of freedom onto the corresponding PES of IBM. A fermion-to-boson mapping for a rotational nucleus is discussed in terms of the rotational response, which reflects a specific time-dependent feature. Ground-state correlation energy is evaluated as a signature of structuralmore » evolution. Some examples resulting from the present spectroscopic calculations are shown for neutron-rich Pt, Os and W isotopes including exotic ones.« less

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

Owen, Benjamin C.; Kenttamaa, Hilkka I.

The present disclosure provides a new tandem mass spectrometer and methods of using the same for analyzing charged particles. The differentially pumped dual linear quadrupole ion trap mass spectrometer of the present disclose includes a combination of two linear quadrupole (LQIT) mass spectrometers with differentially pumped vacuum chambers.

The nuclear electric quadrupole moment of antimony from the molecular method.

PubMed

Haiduke, Roberto L A; da Silva, Albérico B F; Visscher, Lucas

2006-08-14

Relativistic Dirac-Coulomb (DC) Hartree-Fock calculations are employed to obtain the analytic electric field gradient (EFG) on the antimony nucleus in the SbN, SbP, SbF, and SbCl molecules. The electronic correlation contribution to the EFGs is included with the DC-CCSD(T) and DC-CCSD-T approaches, also in the four-component framework, using a finite-difference method. The total EFG results, along with the experimental nuclear quadrupole coupling constants from microwave spectroscopy, allow to derive the nuclear quadrupole moments of (121)Sb and (123)Sb, respectively, as -543(11) and -692(14) mb.

Observation of Excited Quadrupole-Bound States in Cold Anions

NASA Astrophysics Data System (ADS)

Zhu, Guo-Zhu; Liu, Yuan; Wang, Lai-Sheng

2017-07-01

We report the first observation of an excited quadrupole-bound state (QBS) in an anion. High-resolution photoelectron imaging of cryogenically cooled 4-cyanophenoxide (4 CP- ) anions yields an electron detachment threshold of 24 927 cm-1 . The photodetachment spectrum reveals a resonant transition 20 cm-1 below the detachment threshold, which is attributed to an excited QBS of 4 CP- because neutral 4CP has a large quadrupole moment with a negligible dipole moment. The QBS is confirmed by observation of seventeen above-threshold resonances due to autodetachment from vibrational levels of the QBS.

Method and apparatus for measuring the gas permeability of a solid sample

DOEpatents

Carstens, D.H.W.

1984-01-27

The disclosure is directed to an apparatus and method for measuring the permeability of a gas in a sample. The gas is allowed to reach a steady flow rate through the sample. A measurable amount of the gas is collected during a given time period and then delivered to a sensitive quadrupole. The quadrupole signal, adjusted for background, is proportional to the amount of gas collected during the time period. The quadrupole can be calibrated with a standard helium leak. The gas can be deuterium and the sample can be polyvinyl alcohol.

Charge Dependence and Electric Quadrupole Effects on Single-Nucleon Removal in Relativistic and Intermediate Energy Nuclear Collisions

NASA Technical Reports Server (NTRS)

Norbury, John W.

1992-01-01

Single nucleon removal in relativistic and intermediate energy nucleus-nucleus collisions is studied using a generalization of Weizsacker-Williams theory that treats each electromagnetic multipole separately. Calculations are presented for electric dipole and quadrupole excitations and incorporate a realistic minimum impact parameter, Coulomb recoil corrections, and the uncertainties in the input photonuclear data. Discrepancies are discussed. The maximum quadrupole effect to be observed in future experiments is estimated and also an analysis of the charge dependence of the electromagnetic cross sections down to energies as low as 100 MeV/nucleon is made.

Charge dependence and electric quadrupole effects on single-nucleon removal in relativistic and intermediate energy nuclear collisions

NASA Technical Reports Server (NTRS)

Norbury, J. W.; Townsend, L. W. (Principal Investigator)

1990-01-01

Single-nucleon removal in relativistic and intermediate energy nucleus-nucleus collisions is studied using a generalization of Weizsacker-Williams theory that treats each electromagnetic multipole separately. Calculations are presented for electric dipole and quadrupole excitations and incorporate a realistic minimum impact parameter, Coulomb recoil corrections, and the uncertainties in the input photonuclear data. Discrepancies are discussed. The maximum quadrupole effect to be observed in future experiments is estimated and also an analysis of the charge dependence of the electromagnetic cross sections down to energies as low as 100 MeV/nucleon is made.

Electron cloud generation and trapping in a quadrupole magnet at the Los Alamos proton storage ring

NASA Astrophysics Data System (ADS)

Macek, Robert J.; Browman, Andrew A.; Ledford, John E.; Borden, Michael J.; O'Hara, James F.; McCrady, Rodney C.; Rybarcyk, Lawrence J.; Spickermann, Thomas; Zaugg, Thomas J.; Pivi, Mauro T. F.

2008-01-01

Recent beam physics studies on the two-stream e-p instability at the LANL proton storage ring (PSR) have focused on the role of the electron cloud generated in quadrupole magnets where primary electrons, which seed beam-induced multipacting, are expected to be largest due to grazing angle losses from the beam halo. A new diagnostic to measure electron cloud formation and trapping in a quadrupole magnet has been developed, installed, and successfully tested at PSR. Beam studies using this diagnostic show that the “prompt” electron flux striking the wall in a quadrupole is comparable to the prompt signal in the adjacent drift space. In addition, the “swept” electron signal, obtained using the sweeping feature of the diagnostic after the beam was extracted from the ring, was larger than expected and decayed slowly with an exponential time constant of 50 to 100μs. Other measurements include the cumulative energy spectra of prompt electrons and the variation of both prompt and swept electron signals with beam intensity. Experimental results were also obtained which suggest that a good fraction of the electrons observed in the adjacent drift space for the typical beam conditions in the 2006 run cycle were seeded by electrons ejected from the quadrupole.

Variable energy constant current accelerator structure

DOEpatents

Anderson, Oscar A.

1990-01-01

A variable energy, constant current ion beam accelerator structure is disclosed comprising an ion source capable of providing the desired ions, a pre-accelerator for establishing an initial energy level, a matching/pumping module having means for focusing means for maintaining the beam current, and at least one main accelerator module for continuing beam focus, with means capable of variably imparting acceleration to the beam so that a constant beam output current is maintained independent of the variable output energy. In a preferred embodiment, quadrupole electrodes are provided in both the matching/pumping module and the one or more accelerator modules, and are formed using four opposing cylinder electrodes which extend parallel to the beam axis and are spaced around the beam at 90.degree. intervals with opposing electrodes maintained at the same potential. Adjacent cylinder electrodes of the quadrupole structure are maintained at different potentials to thereby reshape the cross section of the charged particle beam to an ellipse in cross section at the mid point along each quadrupole electrode unit in the accelerator modules. The beam is maintained in focus by alternating the major axis of the ellipse along the x and y axis respectively at adjacent quadrupoles. In another embodiment, electrostatic ring electrodes may be utilized instead of the quadrupole electrodes.

Tuneable complementary metamaterial structures based on graphene for single and multiple transparency windows

PubMed Central

Ding, Jun; Arigong, Bayaner; Ren, Han; Zhou, Mi; Shao, Jin; Lu, Meng; Chai, Yang; Lin, Yuankun; Zhang, Hualiang

2014-01-01

Novel graphene-based tunable plasmonic metamaterials featuring single and multiple transparency windows are numerically studied in this paper. The designed structures consist of a graphene layer perforated with quadrupole slot structures and dolmen-like slot structures printed on a substrate. Specifically, the graphene-based quadrupole slot structure can realize a single transparency window, which is achieved without breaking the structure symmetry. Further investigations have shown that the single transparency window in the proposed quadrupole slot structure is more likely originated from the quantum effect of Autler-Townes splitting. Then, by introducing a dipole slot to the quadrupole slot structure to form the dolmen-like slot structure, an additional transmission dip could occur in the transmission spectrum, thus, a multiple-transparency-window system can be achieved (for the first time for graphene-based devices). More importantly, the transparency windows for both the quadrupole slot and the dolmen-like slot structures can be dynamically controlled over a broad frequency range by varying the Fermi energy levels of the graphene layer (through electrostatic gating). The proposed slot metamaterial structures with tunable single and multiple transparency windows could find potential applications in many areas such as multiple-wavelength slow-light devices, active plasmonic switching, and optical sensing. PMID:25146672

Tuneable complementary metamaterial structures based on graphene for single and multiple transparency windows.

PubMed

Ding, Jun; Arigong, Bayaner; Ren, Han; Zhou, Mi; Shao, Jin; Lu, Meng; Chai, Yang; Lin, Yuankun; Zhang, Hualiang

2014-08-22

Novel graphene-based tunable plasmonic metamaterials featuring single and multiple transparency windows are numerically studied in this paper. The designed structures consist of a graphene layer perforated with quadrupole slot structures and dolmen-like slot structures printed on a substrate. Specifically, the graphene-based quadrupole slot structure can realize a single transparency window, which is achieved without breaking the structure symmetry. Further investigations have shown that the single transparency window in the proposed quadrupole slot structure is more likely originated from the quantum effect of Autler-Townes splitting. Then, by introducing a dipole slot to the quadrupole slot structure to form the dolmen-like slot structure, an additional transmission dip could occur in the transmission spectrum, thus, a multiple-transparency-window system can be achieved (for the first time for graphene-based devices). More importantly, the transparency windows for both the quadrupole slot and the dolmen-like slot structures can be dynamically controlled over a broad frequency range by varying the Fermi energy levels of the graphene layer (through electrostatic gating). The proposed slot metamaterial structures with tunable single and multiple transparency windows could find potential applications in many areas such as multiple-wavelength slow-light devices, active plasmonic switching, and optical sensing.

Electrostatic Properties of Aqueous Salt Solution Interfaces: A Comparison of Polarizable and Non-Polarizable Ion Models

PubMed Central

Warren, G. Lee; Patel, Sandeep

2014-01-01

The effects of ion force field polarizability on the interfacial electrostatic properties of ~1 M aqueous solutions of NaCl, CsCl and NaI are investigated using molecular dynamics simulations employing both non-polarizable and Drude-polarizable ion sets. Differences in computed depth-dependent orientational distributions, “permanent” and induced dipole and quadrupole moment profiles, and interfacial potentials are obtained for both ion sets to further elucidate how ion polarizability affects interfacial electrostatic properties among the various salts relative to pure water. We observe that the orientations and induced dipoles of water molecules are more strongly perturbed in the presence of polarizable ions via a stronger ionic double layer effect arising from greater charge separation. Both anions and cations exhibit enhanced induced dipole moments and strong z alignment in the vicinity of the Gibbs dividing surface (GDS) with the magnitude of the anion induced dipoles being nearly an order of magnitude larger than those of the cations and directed into the vapor phase. Depth-dependent profiles for the trace and zz components of the water molecular quadrupole moment tensors reveal 40% larger quadrupole moments in the bulk phase relative to the vapor mimicking a similar observed 40% increase in the average water dipole moment. Across the GDS, the water molecular quadrupole moments increase non-monotonically (in contrast to the water dipoles) and exhibit a locally reduced contribution just below the surface due to both orientational and polarization effects. Computed interfacial potentials for the non-polarizable salts yield values 20 to 60 mV more positive than pure water and increase by an additional 30 to 100 mV when ion polarizability is included. A rigorous decomposition of the total interfacial potential into ion monopole, water and ion dipole, and water quadrupole components reveals that a very strong, positive ion monopole contribution is offset by negative contributions from all other potential sources. Water quadrupole components modulated by the water density contribute significantly to the observed interfacial potential increments and almost entirely explain observed differences in the interfacial potentials for the two chloride salts. By lumping all remaining non-quadrupole interfacial potential contributions into a single “effective” dipole potential, we observe that the ratio of quadrupole to “effective” dipole contributions range from 2:1 in CsCl to 1:1.5 in NaI suggesting that both contributions are comparably important in determining the interfacial potential increments. We also find that oscillations in the quadrupole potential in the double layer region are opposite in sign and partially cancel those of the “effective” dipole potential. PMID:18712908

Student Solution Manual for Essential Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-02-01

1. Matrices and vector spaces; 2. Vector calculus; 3. Line, surface and volume integrals; 4. Fourier series; 5. Integral transforms; 6. Higher-order ODEs; 7. Series solutions of ODEs; 8. Eigenfunction methods; 9. Special functions; 10. Partial differential equations; 11. Solution methods for PDEs; 12. Calculus of variations; 13. Integral equations; 14. Complex variables; 15. Applications of complex variables; 16. Probability; 17. Statistics.

Essential Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-02-01

1. Matrices and vector spaces; 2. Vector calculus; 3. Line, surface and volume integrals; 4. Fourier series; 5. Integral transforms; 6. Higher-order ODEs; 7. Series solutions of ODEs; 8. Eigenfunction methods; 9. Special functions; 10. Partial differential equations; 11. Solution methods for PDEs; 12. Calculus of variations; 13. Integral equations; 14. Complex variables; 15. Applications of complex variables; 16. Probability; 17. Statistics; Appendices; Index.

A semi-inverse variational method for generating the bound state energy eigenvalues in a quantum system: the Dirac Coulomb type-equation

NASA Astrophysics Data System (ADS)

Libarir, K.; Zerarka, A.

2018-05-01

Exact eigenspectra and eigenfunctions of the Dirac quantum equation are established using the semi-inverse variational method. This method improves of a considerable manner the efficiency and accuracy of results compared with the other usual methods much argued in the literature. Some applications for different state configurations are proposed to concretize the method.

Control of Spatially Inhomogeneous Shear Flows

DTIC Science & Technology

2009-11-27

vectors fi with unit norm represent the eigenfunctions of H∗H, i.e. H∗ Hfi = σ 2i fi , (3.11) then the output energy will be given by the square of the so...modes, it is convenient to show that φoci are the eigenmodes of PQ; multiplying (3.11) with Lc yields LcH∗ Hfi = PQφoci = σ 2i φoci . (3.18) The

The Convergence Problems of Eigenfunction Expansions of Elliptic Differential Operators

NASA Astrophysics Data System (ADS)

Ahmedov, Anvarjon

2018-03-01

In the present research we investigate the problems concerning the almost everywhere convergence of multiple Fourier series summed over the elliptic levels in the classes of Liouville. The sufficient conditions for the almost everywhere convergence problems, which are most difficult problems in Harmonic analysis, are obtained. The methods of approximation by multiple Fourier series summed over elliptic curves are applied to obtain suitable estimations for the maximal operator of the spectral decompositions. Obtaining of such estimations involves very complicated calculations which depends on the functional structure of the classes of functions. The main idea on the proving the almost everywhere convergence of the eigenfunction expansions in the interpolation spaces is estimation of the maximal operator of the partial sums in the boundary classes and application of the interpolation Theorem of the family of linear operators. In the present work the maximal operator of the elliptic partial sums are estimated in the interpolation classes of Liouville and the almost everywhere convergence of the multiple Fourier series by elliptic summation methods are established. The considering multiple Fourier series as an eigenfunction expansions of the differential operators helps to translate the functional properties (for example smoothness) of the Liouville classes into Fourier coefficients of the functions which being expanded into such expansions. The sufficient conditions for convergence of the multiple Fourier series of functions from Liouville classes are obtained in terms of the smoothness and dimensions. Such results are highly effective in solving the boundary problems with periodic boundary conditions occurring in the spectral theory of differential operators. The investigations of multiple Fourier series in modern methods of harmonic analysis incorporates the wide use of methods from functional analysis, mathematical physics, modern operator theory and spectral decomposition. New method for the best approximation of the square-integrable function by multiple Fourier series summed over the elliptic levels are established. Using the best approximation, the Lebesgue constant corresponding to the elliptic partial sums is estimated. The latter is applied to obtain an estimation for the maximal operator in the classes of Liouville.

Organization of model helical peptides in lipid bilayers: insight into the behavior of single-span protein transmembrane domains.

PubMed Central

Sharpe, Simon; Barber, Kathryn R; Grant, Chris W M; Goodyear, David; Morrow, Michael R

2002-01-01

Selectively deuterated transmembrane peptides comprising alternating leucine-alanine subunits were examined in fluid bilayer membranes by solid-state nuclear magnetic resonance (NMR) spectroscopy in an effort to gain insight into the behavior of membrane proteins. Two groups of peptides were studied: 21-mers having a 17-amino-acid hydrophobic domain calculated to be close in length to the hydrophobic thickness of 1-palmitoyl-2-oleoyl phosphatidylcholine and 26-mers having a 22-amino-acid hydrophobic domain calculated to exceed the membrane hydrophobic thickness. (2)H NMR spectral features similar to ones observed for transmembrane peptides from single-span receptors of higher animal cells were identified which apparently correspond to effectively monomeric peptide. Spectral observations suggested significant distortion of the transmembrane alpha-helix, and/or potential for restriction of rotation about the tilted helix long axis for even simple peptides. Quadrupole splittings arising from the 26-mer were consistent with greater peptide "tilt" than were those of the analogous 21-mer. Quadrupole splittings associated with monomeric peptide were relatively insensitive to concentration and temperature over the range studied, indicating stable average conformations, and a well-ordered rotation axis. At high peptide concentration (6 mol% relative to phospholipid) it appeared that the peptide predicted to be longer than the membrane thickness had a particular tendency toward reversible peptide-peptide interactions occurring on a timescale comparable with or faster than approximately 10(-5) s. This interaction may be direct or lipid-mediated and was manifest as line broadening. Peptide rotational diffusion rates within the membrane, calculated from quadrupolar relaxation times, T(2e), were consistent with such interactions. In the case of the peptide predicted to be equal to the membrane thickness, at low peptide concentration spectral lineshape indicated the additional presence of a population of peptide having rotational motion that was restricted on a timescale of 10(-5) s. PMID:12080125