Pepsi-SAXS: an adaptive method for rapid and accurate computation of small-angle X-ray scattering profiles.

PubMed

Grudinin, Sergei; Garkavenko, Maria; Kazennov, Andrei

2017-05-01

A new method called Pepsi-SAXS is presented that calculates small-angle X-ray scattering profiles from atomistic models. The method is based on the multipole expansion scheme and is significantly faster compared with other tested methods. In particular, using the Nyquist-Shannon-Kotelnikov sampling theorem, the multipole expansion order is adapted to the size of the model and the resolution of the experimental data. It is argued that by using the adaptive expansion order, this method has the same quadratic dependence on the number of atoms in the model as the Debye-based approach, but with a much smaller prefactor in the computational complexity. The method has been systematically validated on a large set of over 50 models collected from the BioIsis and SASBDB databases. Using a laptop, it was demonstrated that Pepsi-SAXS is about seven, 29 and 36 times faster compared with CRYSOL, FoXS and the three-dimensional Zernike method in SAStbx, respectively, when tested on data from the BioIsis database, and is about five, 21 and 25 times faster compared with CRYSOL, FoXS and SAStbx, respectively, when tested on data from SASBDB. On average, Pepsi-SAXS demonstrates comparable accuracy in terms of χ 2 to CRYSOL and FoXS when tested on BioIsis and SASBDB profiles. Together with a small allowed variation of adjustable parameters, this demonstrates the effectiveness of the method. Pepsi-SAXS is available at http://team.inria.fr/nano-d/software/pepsi-saxs.

Nonequilibrium electromagnetics: Local and macroscopic fields and constitutive relationships

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

Baker-Jarvis, James; Kabos, Pavel; Holloway, Christopher L.

We study the electrodynamics of materials using a Liouville-Hamiltonian-based statistical-mechanical theory. Our goal is to develop electrodynamics from an ensemble-average viewpoint that is valid for microscopic and nonequilibrium systems at molecular to submolecular scales. This approach is not based on a Taylor series expansion of the charge density to obtain the multipoles. Instead, expressions of the molecular multipoles are used in an inverse problem to obtain the averaging statistical-density function that is used to obtain the macroscopic fields. The advantages of this method are that the averaging function is constructed in a self-consistent manner and the molecules can either bemore » treated as point multipoles or contain more microstructure. Expressions for the local and macroscopic fields are obtained, and evolution equations for the constitutive parameters are developed. We derive equations for the local field as functions of the applied, polarization, magnetization, strain density, and macroscopic fields.« less

Comparison of FDTD numerical computations and analytical multipole expansion method for plasmonics-active nanosphere dimers.

PubMed

Dhawan, Anuj; Norton, Stephen J; Gerhold, Michael D; Vo-Dinh, Tuan

2009-06-08

This paper describes a comparative study of finite-difference time-domain (FDTD) and analytical evaluations of electromagnetic fields in the vicinity of dimers of metallic nanospheres of plasmonics-active metals. The results of these two computational methods, to determine electromagnetic field enhancement in the region often referred to as "hot spots" between the two nanospheres forming the dimer, were compared and a strong correlation observed for gold dimers. The analytical evaluation involved the use of the spherical-harmonic addition theorem to relate the multipole expansion coefficients between the two nanospheres. In these evaluations, the spacing between two nanospheres forming the dimer was varied to obtain the effect of nanoparticle spacing on the electromagnetic fields in the regions between the nanostructures. Gold and silver were the metals investigated in our work as they exhibit substantial plasmon resonance properties in the ultraviolet, visible, and near-infrared spectral regimes. The results indicate excellent correlation between the two computational methods, especially for gold nanosphere dimers with only a 5-10% difference between the two methods. The effect of varying the diameters of the nanospheres forming the dimer, on the electromagnetic field enhancement, was also studied.

Multipole expansions and Fock symmetry of the hydrogen atom

NASA Astrophysics Data System (ADS)

Meremianin, A. V.; Rost, J.-M.

2006-10-01

The main difficulty in utilizing the O(4) symmetry of the hydrogen atom in practical calculations is the dependence of the Fock stereographic projection on energy. This is due to the fact that the wavefunctions of the states with different energies are proportional to the hyperspherical harmonics (HSH) corresponding to different points on the hypersphere. Thus, the calculation of the matrix elements reduces to the problem of re-expanding HSH in terms of HSH depending on different points on the hypersphere. We solve this problem by applying the technique of multipole expansions for four-dimensional HSH. As a result, we obtain the multipole expansions whose coefficients are the matrix elements of the boost operator taken between hydrogen wavefunctions (i.e., hydrogen form factors). The explicit expressions for those coefficients are derived. It is shown that the hydrogen matrix elements can be presented as derivatives of an elementary function. Such an operator representation is convenient for the derivation of recurrence relations connecting matrix elements between states corresponding to different values of the quantum numbers n and l.

Gravitational scattering of electromagnetic radiation

NASA Technical Reports Server (NTRS)

Brooker, J. T.; Janis, A. I.

1980-01-01

The scattering of electromagnetic radiation by linearized gravitational fields is studied to second order in a perturbation expansion. The incoming electromagnetic radiation can be of arbitrary multipole structure, and the gravitational fields are also taken to be advanced fields of arbitrary multipole structure. All electromagnetic multipole radiation is found to be scattered by gravitational monopole and time-varying dipole fields. No case has been found, however, in which any electromagnetic multipole radiation is scattered by gravitational fields of quadrupole or higher-order multipole structure. This lack of scattering is established for infinite classes of special cases, and is conjectured to hold in general. The results of the scattering analysis are applied to the case of electromagnetic radiation scattered by a moving mass. It is shown how the mass and velocity may be determined by a knowledge of the incident and scattered radiation.

Fast algorithms for evaluating the stress field of dislocation lines in anisotropic elastic media

NASA Astrophysics Data System (ADS)

Chen, C.; Aubry, S.; Oppelstrup, T.; Arsenlis, A.; Darve, E.

2018-06-01

In dislocation dynamics (DD) simulations, the most computationally intensive step is the evaluation of the elastic interaction forces among dislocation ensembles. Because the pair-wise interaction between dislocations is long-range, this force calculation step can be significantly accelerated by the fast multipole method (FMM). We implemented and compared four different methods in isotropic and anisotropic elastic media: one based on the Taylor series expansion (Taylor FMM), one based on the spherical harmonics expansion (Spherical FMM), one kernel-independent method based on the Chebyshev interpolation (Chebyshev FMM), and a new kernel-independent method that we call the Lagrange FMM. The Taylor FMM is an existing method, used in ParaDiS, one of the most popular DD simulation softwares. The Spherical FMM employs a more compact multipole representation than the Taylor FMM does and is thus more efficient. However, both the Taylor FMM and the Spherical FMM are difficult to derive in anisotropic elastic media because the interaction force is complex and has no closed analytical formula. The Chebyshev FMM requires only being able to evaluate the interaction between dislocations and thus can be applied easily in anisotropic elastic media. But it has a relatively large memory footprint, which limits its usage. The Lagrange FMM was designed to be a memory-efficient black-box method. Various numerical experiments are presented to demonstrate the convergence and the scalability of the four methods.

Spherical-wave expansions of piston-radiator fields.

PubMed

Wittmann, R C; Yaghjian, A D

1991-09-01

Simple spherical-wave expansions of the continuous-wave fields of a circular piston radiator in a rigid baffle are derived. These expansions are valid throughout the illuminated half-space and are useful for efficient numerical computation in the near-field region. Multipole coefficients are given by closed-form expressions which can be evaluated recursively.

Studies of dispersion energy in hydrogen-bonded systems. H2O-HOH, H2O-HF, H3N-HF, HF-HF

NASA Astrophysics Data System (ADS)

Szcześniak, M. M.; Scheiner, Steve

1984-02-01

Dispersion energy is calculated in the systems H2O-HOH, H2O-HF, H3N-HF, and HF-HF as a function of the intermolecular separation using a variety of methods. M≂ller-Plesset perturbation theory to second and third orders is applied in conjunction with polarized basis sets of 6-311G** type and with an extended basis set including a second set of polarization functions (DZ+2P). These results are compared to a multipole expansion of the dispersion energy, based on the Unsöld approximation, carried out to the inverse tenth power of the intermolecular distance. Pairwise evaluation is also carried out using both atom-atom and bond-bond formulations. The MP3/6-311G** results are in generally excellent accord with the leading R-6 term of the multipole expansion. This expansion, if carried out to the R-10 term, reproduces extremely well previously reported dispersion energies calculated via variation-perturbation theory. Little damping of the expansion is required for intermolecular distances equal to or greater than the equilibrium separation. Although the asymptotic behavior of the MP2 dispersion energy is somewhat different than that of the other methods, augmentation of the basis set by a second diffuse set of d functions leads to quite good agreement in the vicinity of the minima. Both the atom-atom and bond-bond parametrization schemes are in good qualitative agreement with the other methods tested. All approaches produce similar dependence of the dispersion energy upon the angular orientation between the two molecules involved in the H bond.

Isotropic C6, C8 and C10 interaction coefficients for CH 4, C 2H 6, C 3H 8, n-C 4H 10 and cyclo- C3H 6

NASA Astrophysics Data System (ADS)

Thomas, Gerald F.; Mulder, Fred; Meath, William J.

1980-12-01

The non-empirical generalized Kirkwood, Unsöld, and the single-Δ Unsöld methods (with double-zeta quality SCF wave-functions) are used to calculate isotropic dispersion (and induction) energy coefficients C2n, with n ⩽ 5, for interactions involving ground state CH 4, C 2H 6, C 3H 8, n-C 4H 10 and cyclo-C 3H 6. Results are also given for the related multipole polarizabilities α l, multipole sums S1/(0) and S1(-1) which are evaluated using sum rules, and the permanent multipole moments. for l = 1 (dipole) to l = 3 (octupole). Estimates of the reliability of the non-empirical methods, for the type of molecules considered, are obtained by a comparison with accurate literature values of α 1S1(-1) and C6. This, and the asymptotic properties of the multipolar expansion of the dispersion energy, the use to discuss recommended representation for the isotropic long range interaction energies through R-10 where R is the intermolecular separation.

Lattice properties of the Phase I BNL x-ray lithography source obtained from fits to magnetic measurement data

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

Blumberg, L.N.; Murphy, J.B.; Reusch, M.F.

1991-01-01

The orbit, tune, chromaticity and {beta} values for the Phase 1 XLS ring were computed by numerical integration of equations of motion using fields obtained from the coefficients of the 3-dimensional solution of Laplace's Equation evaluated by fits to magnetic measurements. The results are in good agreement with available data. The method has been extended to higher order fits of TOSCA generated fields in planes normal to the reference axis using the coil configuration proposed for the Superconducting X-Ray Lithography Source. Agreement with results from numerical integration through fields given directly by TOSCA is excellent. The formulation of the normalmore » multipole expansion presented by Brown and Servranckx has been extended to include skew multipole terms. The method appears appropriate for analysis of magnetic measurements of the SXLS. 8 refs. , 2 figs., 2 tabs.« less

Structural analysis according to reduced data: VIII. Refinement of the extended model of aspherical atoms

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

Dudka, A. P.

A program for the refinement of the model of aspherical atoms within the Stewart-Hansen-Coppens formalism has been developed. Deformation scattering up to the 8th expansion order in multipoles has been taken into account for the first time. The program was tested for 11 crystals. The effect of the result of interpolation of radial scattering curves on the model parameters is considered. The importance of introduction of multipoles of high (5th-8th) orders into the model for a number of crystals is shown. The use of the extended multipole model for a silicon crystal revealed some new specific features of the electronicmore » structure: consideration of multipoles up to the 7th order makes it possible to explain the intensity of the forbidden 222 reflection.« less

A critical appraisal of the zero-multipole method: Structural, thermodynamic, dielectric, and dynamical properties of a water system.

PubMed

Wang, Han; Nakamura, Haruki; Fukuda, Ikuo

2016-03-21

We performed extensive and strict tests for the reliability of the zero-multipole (summation) method (ZMM), which is a method for estimating the electrostatic interactions among charged particles in a classical physical system, by investigating a set of various physical quantities. This set covers a broad range of water properties, including the thermodynamic properties (pressure, excess chemical potential, constant volume/pressure heat capacity, isothermal compressibility, and thermal expansion coefficient), dielectric properties (dielectric constant and Kirkwood-G factor), dynamical properties (diffusion constant and viscosity), and the structural property (radial distribution function). We selected a bulk water system, the most important solvent, and applied the widely used TIP3P model to this test. In result, the ZMM works well for almost all cases, compared with the smooth particle mesh Ewald (SPME) method that was carefully optimized. In particular, at cut-off radius of 1.2 nm, the recommended choices of ZMM parameters for the TIP3P system are α ≤ 1 nm(-1) for the splitting parameter and l = 2 or l = 3 for the order of the multipole moment. We discussed the origin of the deviations of the ZMM and found that they are intimately related to the deviations of the equilibrated densities between the ZMM and SPME, while the magnitude of the density deviations is very small.

Beyond Euler angles: exploiting the angle-axis parametrization in a multipole expansion of the rotation operator.

PubMed

Siemens, Mark; Hancock, Jason; Siminovitch, David

2007-02-01

Euler angles (alpha,beta,gamma) are cumbersome from a computational point of view, and their link to experimental parameters is oblique. The angle-axis {Phi, n} parametrization, especially in the form of quaternions (or Euler-Rodrigues parameters), has served as the most promising alternative, and they have enjoyed considerable success in rf pulse design and optimization. We focus on the benefits of angle-axis parameters by considering a multipole operator expansion of the rotation operator D(Phi, n), and a Clebsch-Gordan expansion of the rotation matrices D(MM')(J)(Phi, n). Each of the coefficients in the Clebsch-Gordan expansion is proportional to the product of a spherical harmonic of the vector n specifying the axis of rotation, Y(lambdamu)(n), with a fixed function of the rotation angle Phi, a Gegenbauer polynomial C(2J-lambda)(lambda+1)(cosPhi/2). Several application examples demonstrate that this Clebsch-Gordan expansion gives easy and direct access to many of the parameters of experimental interest, including coherence order changes (isolated in the Clebsch-Gordan coefficients), and rotation angle (isolated in the Gegenbauer polynomials).

Point Charges Optimally Placed to Represent the Multipole Expansion of Charge Distributions

PubMed Central

Onufriev, Alexey V.

2013-01-01

We propose an approach for approximating electrostatic charge distributions with a small number of point charges to optimally represent the original charge distribution. By construction, the proposed optimal point charge approximation (OPCA) retains many of the useful properties of point multipole expansion, including the same far-field asymptotic behavior of the approximate potential. A general framework for numerically computing OPCA, for any given number of approximating charges, is described. We then derive a 2-charge practical point charge approximation, PPCA, which approximates the 2-charge OPCA via closed form analytical expressions, and test the PPCA on a set of charge distributions relevant to biomolecular modeling. We measure the accuracy of the new approximations as the RMS error in the electrostatic potential relative to that produced by the original charge distribution, at a distance the extent of the charge distribution–the mid-field. The error for the 2-charge PPCA is found to be on average 23% smaller than that of optimally placed point dipole approximation, and comparable to that of the point quadrupole approximation. The standard deviation in RMS error for the 2-charge PPCA is 53% lower than that of the optimal point dipole approximation, and comparable to that of the point quadrupole approximation. We also calculate the 3-charge OPCA for representing the gas phase quantum mechanical charge distribution of a water molecule. The electrostatic potential calculated by the 3-charge OPCA for water, in the mid-field (2.8 Å from the oxygen atom), is on average 33.3% more accurate than the potential due to the point multipole expansion up to the octupole order. Compared to a 3 point charge approximation in which the charges are placed on the atom centers, the 3-charge OPCA is seven times more accurate, by RMS error. The maximum error at the oxygen-Na distance (2.23 Å ) is half that of the point multipole expansion up to the octupole order. PMID:23861790

Large-scale galactic motions: test of the Dipole Repeller model with the RFGC galaxies data

NASA Astrophysics Data System (ADS)

Parnovsky, S.

2017-06-01

The paper "The Dipole Repeller" in Nature Astronomy by Hoffman et al. state that the local large-scale galactic flow is dominated by a single attractor - associated with the Shapley Concentration - and a single previously unidentified repeller. We check this hypothesis using the data for 1459 galaxies from RFGC catalogue with distances up to 100 h-1 Mpc. We compared the models with multipole velocity field for pure Hubble expansion and dipole, quadrupole and octopole motion with the models with two attractors in the regions indicated by Hoffman et al with the multipole velocity field background. The results do not support the hypothesis, but does not contradict it. In any case, the inclusion of the following multipole is more effective than the addition of two attractors. Estimations of excess mass of attractors vary greatly, even changing their sign depending on the highest multipole used in model.

Methods for Boundary-Value Problems in Free-Surface Flows: The Third David W. Taylor Lecture, 27 August through 19 September 1974,

DTIC Science & Technology

1974-09-01

reduction arnd reflection, the method of Green functions, the method of multipole expansions, and, time permitting,* variational methods. I shall try to...depending upon the circumstances. If the motion is assumed to be harmonic in time with frequency 0, we may write cD(x,y,z,t) 4)1(x,y,z) cos at + • 2 (x,y,z... time , so that transient j motions associated with starting the wavemaker have died out and the fluid motion is also harmonic with frequency c. 1 Let

Multipole models of four-image gravitational lenses with anomalous flux ratios

NASA Astrophysics Data System (ADS)

Congdon, Arthur B.; Keeton, Charles R.

2005-12-01

It has been known for over a decade that many four-image gravitational lenses exhibit anomalous radio flux ratios. These anomalies can be explained by adding a clumpy cold dark matter (CDM) component to the background galactic potential of the lens. As an alternative, Evans & Witt (2003) recently suggested that smooth multipole perturbations provide a reasonable alternative to CDM substructure in some but not all cases. We generalize their method in two ways so as to determine whether multipole models can explain highly anomalous systems. We carry the multipole expansion to higher order, and also include external tidal shear as a free parameter. Fitting for the shear proves crucial to finding a physical (positive-definite density) model. For B1422+231, working to order kmax= 5 (and including shear) yields a model that is physical but implausible. Going to higher order (kmax>~ 9) reduces global departures from ellipticity, but at the cost of introducing small-scale wiggles in proximity to the bright images. These localized undulations are more pronounced in B2045+265, where kmax~ 17 multipoles are required to smooth out large-scale deviations from elliptical symmetry. Such modes surely cannot be taken at face value; they must indicate that the models are trying to reproduce some other sort of structure. Our formalism naturally finds models that fit the data exactly, but we use B0712+472 to show that measurement uncertainties have little effect on our results. Finally, we consider the system B1933+503, where two sources are lensed by the same foreground galaxy. The additional constraints provided by the images of the second source render the multipole model unphysical. We conclude that external shear must be taken into account to obtain plausible models, and that a purely smooth angular structure for the lens galaxy does not provide a viable alternative to the prevailing CDM clump hypothesis.

Windowed multipole for cross section Doppler broadening

NASA Astrophysics Data System (ADS)

Josey, C.; Ducru, P.; Forget, B.; Smith, K.

2016-02-01

This paper presents an in-depth analysis on the accuracy and performance of the windowed multipole Doppler broadening method. The basic theory behind cross section data is described, along with the basic multipole formalism followed by the approximations leading to windowed multipole method and the algorithm used to efficiently evaluate Doppler broadened cross sections. The method is tested by simulating the BEAVRS benchmark with a windowed multipole library composed of 70 nuclides. Accuracy of the method is demonstrated on a single assembly case where total neutron production rates and 238U capture rates compare within 0.1% to ACE format files at the same temperature. With regards to performance, clock cycle counts and cache misses were measured for single temperature ACE table lookup and for windowed multipole. The windowed multipole method was found to require 39.6% more clock cycles to evaluate, translating to a 7.9% performance loss overall. However, the algorithm has significantly better last-level cache performance, with 3 fewer misses per evaluation, or a 65% reduction in last-level misses. This is due to the small memory footprint of the windowed multipole method and better memory access pattern of the algorithm.

FMM-Yukawa: An adaptive fast multipole method for screened Coulomb interactions

NASA Astrophysics Data System (ADS)

Huang, Jingfang; Jia, Jun; Zhang, Bo

2009-11-01

A Fortran program package is introduced for the rapid evaluation of the screened Coulomb interactions of N particles in three dimensions. The method utilizes an adaptive oct-tree structure, and is based on the new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related packages are also available at http://www.fastmultipole.org/. This paper is a brief review of the program and its performance. Catalogue identifier: AEEQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL 2.0 No. of lines in distributed program, including test data, etc.: 12 385 No. of bytes in distributed program, including test data, etc.: 79 222 Distribution format: tar.gz Programming language: Fortran77 and Fortran90 Computer: Any Operating system: Any RAM: Depends on the number of particles, their distribution, and the adaptive tree structure Classification: 4.8, 4.12 Nature of problem: To evaluate the screened Coulomb potential and force field of N charged particles, and to evaluate a convolution type integral where the Green's function is the fundamental solution of the modified Helmholtz equation. Solution method: An adaptive oct-tree is generated, and a new version of fast multipole method is applied in which the "multipole-to-local" translation operator is diagonalized. Restrictions: Only three and six significant digits accuracy options are provided in this version. Unusual features: Most of the codes are written in Fortran77. Functions for memory allocation from Fortran90 and above are used in one subroutine. Additional comments: For supplementary information see http://www.fastmultipole.org/ Running time: The running time varies depending on the number of particles (denoted by N) in the system and their distribution. The running time scales linearly as a function of N for nearly uniform particle distributions. For three digits accuracy, the solver breaks even with direct summation method at about N = 750. References: [1] L. Greengard, J. Huang, A new version of the fast multipole method for screened Coulomb interactions in three dimensions, J. Comput. Phys. 180 (2002) 642-658.

Multipole moments in the effective fragment potential method

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

Bertoni, Colleen; Slipchenko, Lyudmila V.; Misquitta, Alston J.

In the effective fragment potential (EFP) method the Coulomb potential is represented using a set of multipole moments generated by the distributed multipole analysis (DMA) method. Misquitta, Stone, and Fazeli recently developed a basis space-iterated stockholder atom (BS-ISA) method to generate multipole moments. This study assesses the accuracy of the EFP interaction energies using sets of multipole moments generated from the BS-ISA method, and from several versions of the DMA method (such as analytic and numeric grid-based), with varying basis sets. Both methods lead to reasonable results, although using certain implementations of the DMA method can result in large errors.more » With respect to the CCSD(T)/CBS interaction energies, the mean unsigned error (MUE) of the EFP method for the S22 data set using BS-ISA–generated multipole moments and DMA-generated multipole moments (using a small basis set and the analytic DMA procedure) is 0.78 and 0.72 kcal/mol, respectively. Here, the MUE accuracy is on the same order as MP2 and SCS-MP2. The MUEs are lower than in a previous study benchmarking the EFP method without the EFP charge transfer term, demonstrating that the charge transfer term increases the accuracy of the EFP method. Regardless of the multipole moment method used, it is likely that much of the error is due to an insufficient short-range electrostatic term (i.e., charge penetration term), as shown by comparisons with symmetry-adapted perturbation theory.« less

Multipole moments in the effective fragment potential method

DOE PAGES

Bertoni, Colleen; Slipchenko, Lyudmila V.; Misquitta, Alston J.; ...

2017-02-17

In the effective fragment potential (EFP) method the Coulomb potential is represented using a set of multipole moments generated by the distributed multipole analysis (DMA) method. Misquitta, Stone, and Fazeli recently developed a basis space-iterated stockholder atom (BS-ISA) method to generate multipole moments. This study assesses the accuracy of the EFP interaction energies using sets of multipole moments generated from the BS-ISA method, and from several versions of the DMA method (such as analytic and numeric grid-based), with varying basis sets. Both methods lead to reasonable results, although using certain implementations of the DMA method can result in large errors.more » With respect to the CCSD(T)/CBS interaction energies, the mean unsigned error (MUE) of the EFP method for the S22 data set using BS-ISA–generated multipole moments and DMA-generated multipole moments (using a small basis set and the analytic DMA procedure) is 0.78 and 0.72 kcal/mol, respectively. Here, the MUE accuracy is on the same order as MP2 and SCS-MP2. The MUEs are lower than in a previous study benchmarking the EFP method without the EFP charge transfer term, demonstrating that the charge transfer term increases the accuracy of the EFP method. Regardless of the multipole moment method used, it is likely that much of the error is due to an insufficient short-range electrostatic term (i.e., charge penetration term), as shown by comparisons with symmetry-adapted perturbation theory.« less

Parallel Fast Multipole Method For Molecular Dynamics

DTIC Science & Technology

2007-06-01

Parallel Fast Multipole Method For Molecular Dynamics THESIS Reid G. Ormseth, Captain, USAF AFIT/GAP/ENP/07-J02 DEPARTMENT OF THE AIR FORCE AIR...the United States Government. AFIT/GAP/ENP/07-J02 Parallel Fast Multipole Method For Molecular Dynamics THESIS Presented to the Faculty Department of...has also been provided by ‘The Art of Molecular Dynamics Simulation ’ by Dennis Rapaport. This work is the clearest treatment of the Fast Multipole

Karhunen Loève approximation of random fields by generalized fast multipole methods

NASA Astrophysics Data System (ADS)

Schwab, Christoph; Todor, Radu Alexandru

2006-09-01

KL approximation of a possibly instationary random field a( ω, x) ∈ L2( Ω, d P; L∞( D)) subject to prescribed meanfield Ea(x)=∫a(ω,x) dP(ω) and covariance Va(x,x')=∫(a(ω,x)-Ea(x))(a(ω,x')-Ea(x')) dP(ω) in a polyhedral domain D⊂Rd is analyzed. We show how for stationary covariances Va( x, x') = ga(| x - x'|) with ga( z) analytic outside of z = 0, an M-term approximate KL-expansion aM( ω, x) of a( ω, x) can be computed in log-linear complexity. The approach applies in arbitrary domains D and for nonseparable covariances Ca. It involves Galerkin approximation of the KL eigenvalue problem by discontinuous finite elements of degree p ⩾ 0 on a quasiuniform, possibly unstructured mesh of width h in D, plus a generalized fast multipole accelerated Krylov-Eigensolver. The approximate KL-expansion aM( x, ω) of a( x, ω) has accuracy O(exp(- bM1/ d)) if ga is analytic at z = 0 and accuracy O( M- k/ d) if ga is Ck at zero. It is obtained in O( MN(log N) b) operations where N = O( h- d).

Exact e-e (exchange) correlations of 2-D quantum dots in magnetic field: Size extensive N = 3 , 4 , … , ‧ n ‧ -electron systems via multi-pole expansion

NASA Astrophysics Data System (ADS)

Aggarwal, Priyanka; Sharma, Shivalika; Singh, Sunny; Kaur, Harsimran; Hazra, Ram Kuntal

2017-04-01

Inclusion of coulomb interaction emerges with the complexity of either convergence of integrals or separation of variables of Schrödinger equations. For an N-electron system, interaction terms grow by N(N-1)/2 factors. Therefore, 2-e system stands as fundamental basic unit for generalized N-e systems. For the first time, we have evaluated e-e correlations in very simple and absolutely terminating finite summed hypergeometric series for 2-D double carrier parabolic quantum dot in both zero and arbitrary non-zero magnetic field (symmetric gauge) and have appraised these integrals in variational methods. The competitive role among confinement strength, magnetic field, mass of the carrier and dielectric constant of the medium on energy level diagram, level-spacing statistics, heat capacities (Cv at 1 K) and magnetization (T ∼ (0-1)K) is studied on systems spanning over wide range of materials (GaAs,Ge,CdS,SiO2 and He, etc). We have also constructed an exact theory for generalized correlated N-e 2-D quantum dots via multi-pole expansion but for the sake of compactness of the article we refrain from data.

On the dynamic toroidal multipoles from localized electric current distributions.

PubMed

Fernandez-Corbaton, Ivan; Nanz, Stefan; Rockstuhl, Carsten

2017-08-08

We analyze the dynamic toroidal multipoles and prove that they do not have an independent physical meaning with respect to their interaction with electromagnetic waves. We analytically show how the split into electric and toroidal parts causes the appearance of non-radiative components in each of the two parts. These non-radiative components, which cancel each other when both parts are summed, preclude the separate determination of each part by means of measurements of the radiation from the source or of its coupling to external electromagnetic waves. In other words, there is no toroidal radiation or independent toroidal electromagnetic coupling. The formal meaning of the toroidal multipoles is clear in our derivations. They are the higher order terms of an expansion of the multipolar coefficients of electric parity with respect to the electromagnetic size of the source.

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

Multipole-Based Cable Braid Electromagnetic Penetration Model: Electric Penetration Case

DOE PAGES

Campione, Salvatore; Warne, Larry K.; Langston, William L.; ...

2017-07-11

In this paper, we investigate the electric penetration case of the first principles multipole-based cable braid electromagnetic penetration model reported in the Progress in Electromagnetics Research B 66, 63–89 (2016). We first analyze the case of a 1-D array of wires: this is a problem which is interesting on its own, and we report its modeling based on a multipole-conformal mapping expansion and extension by means of Laplace solutions in bipolar coordinates. We then compare the elastance (inverse of capacitance) results from our first principles cable braid electromagnetic penetration model to that obtained using the multipole-conformal mapping bipolar solution. Thesemore » results are found in a good agreement up to a radius to half spacing ratio of 0.6, demonstrating a robustness needed for many commercial cables. We then analyze realistic cable implementations without dielectrics and compare the results from our first principles braid electromagnetic penetration model to the semiempirical results reported by Kley in the IEEE Transactions on Electromagnetic Compatibility 35, 1–9 (1993). Finally, although we find results on the same order of magnitude of Kley's results, the full dependence on the actual cable geometry is accounted for only in our proposed multipole model which, in addition, enables us to treat perturbations from those commercial cables measured.« less

Multipole-Based Cable Braid Electromagnetic Penetration Model: Electric Penetration Case

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

Campione, Salvatore; Warne, Larry K.; Langston, William L.

In this paper, we investigate the electric penetration case of the first principles multipole-based cable braid electromagnetic penetration model reported in the Progress in Electromagnetics Research B 66, 63–89 (2016). We first analyze the case of a 1-D array of wires: this is a problem which is interesting on its own, and we report its modeling based on a multipole-conformal mapping expansion and extension by means of Laplace solutions in bipolar coordinates. We then compare the elastance (inverse of capacitance) results from our first principles cable braid electromagnetic penetration model to that obtained using the multipole-conformal mapping bipolar solution. Thesemore » results are found in a good agreement up to a radius to half spacing ratio of 0.6, demonstrating a robustness needed for many commercial cables. We then analyze realistic cable implementations without dielectrics and compare the results from our first principles braid electromagnetic penetration model to the semiempirical results reported by Kley in the IEEE Transactions on Electromagnetic Compatibility 35, 1–9 (1993). Finally, although we find results on the same order of magnitude of Kley's results, the full dependence on the actual cable geometry is accounted for only in our proposed multipole model which, in addition, enables us to treat perturbations from those commercial cables measured.« less

Traction reveals mechanisms of wall effects for microswimmers near boundaries

NASA Astrophysics Data System (ADS)

Shen, Xinhui; Marcos, Fu, Henry C.

2017-03-01

The influence of a plane boundary on low-Reynolds-number swimmers has frequently been studied using image systems for flow singularities. However, the boundary effect can also be expressed using a boundary integral representation over the traction on the boundary. We show that examining the traction pattern on the boundary caused by a swimmer can yield physical insights into determining when far-field multipole models are accurate. We investigate the swimming velocities and the traction of a three-sphere swimmer initially placed parallel to an infinite planar wall. In the far field, the instantaneous effect of the wall on the swimmer is well approximated by that of a multipole expansion consisting of a force dipole and a force quadrupole. On the other hand, the swimmer close to the wall must be described by a system of singularities reflecting its internal structure. We show that these limits and the transition between them can be independently identified by examining the traction pattern on the wall, either using a quantitative correlation coefficient or by visual inspection. Last, we find that for nonconstant propulsion, correlations between swimming stroke motions and internal positions are important and not captured by time-averaged traction on the wall, indicating that care must be taken when applying multipole expansions to study boundary effects in cases of nonconstant propulsion.

Traction reveals mechanisms of wall effects for microswimmers near boundaries.

PubMed

Shen, Xinhui; Marcos; Fu, Henry C

2017-03-01

The influence of a plane boundary on low-Reynolds-number swimmers has frequently been studied using image systems for flow singularities. However, the boundary effect can also be expressed using a boundary integral representation over the traction on the boundary. We show that examining the traction pattern on the boundary caused by a swimmer can yield physical insights into determining when far-field multipole models are accurate. We investigate the swimming velocities and the traction of a three-sphere swimmer initially placed parallel to an infinite planar wall. In the far field, the instantaneous effect of the wall on the swimmer is well approximated by that of a multipole expansion consisting of a force dipole and a force quadrupole. On the other hand, the swimmer close to the wall must be described by a system of singularities reflecting its internal structure. We show that these limits and the transition between them can be independently identified by examining the traction pattern on the wall, either using a quantitative correlation coefficient or by visual inspection. Last, we find that for nonconstant propulsion, correlations between swimming stroke motions and internal positions are important and not captured by time-averaged traction on the wall, indicating that care must be taken when applying multipole expansions to study boundary effects in cases of nonconstant propulsion.

Cluster-Based Multipolling Sequencing Algorithm for Collecting RFID Data in Wireless LANs

NASA Astrophysics Data System (ADS)

Choi, Woo-Yong; Chatterjee, Mainak

2015-03-01

With the growing use of RFID (Radio Frequency Identification), it is becoming important to devise ways to read RFID tags in real time. Access points (APs) of IEEE 802.11-based wireless Local Area Networks (LANs) are being integrated with RFID networks that can efficiently collect real-time RFID data. Several schemes, such as multipolling methods based on the dynamic search algorithm and random sequencing, have been proposed. However, as the number of RFID readers associated with an AP increases, it becomes difficult for the dynamic search algorithm to derive the multipolling sequence in real time. Though multipolling methods can eliminate the polling overhead, we still need to enhance the performance of the multipolling methods based on random sequencing. To that extent, we propose a real-time cluster-based multipolling sequencing algorithm that drastically eliminates more than 90% of the polling overhead, particularly so when the dynamic search algorithm fails to derive the multipolling sequence in real time.

Linearly scaling and almost Hamiltonian dielectric continuum molecular dynamics simulations through fast multipole expansions

NASA Astrophysics Data System (ADS)

Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul

2015-11-01

Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADES can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved—up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.

Local fields and effective conductivity tensor of ellipsoidal particle composite with anisotropic constituents

NASA Astrophysics Data System (ADS)

Kushch, Volodymyr I.; Sevostianov, Igor; Giraud, Albert

2017-11-01

An accurate semi-analytical solution of the conductivity problem for a composite with anisotropic matrix and arbitrarily oriented anisotropic ellipsoidal inhomogeneities has been obtained. The developed approach combines the superposition principle with the multipole expansion of perturbation fields of inhomogeneities in terms of ellipsoidal harmonics and reduces the boundary value problem to an infinite system of linear algebraic equations for the induced multipole moments of inhomogeneities. A complete full-field solution is obtained for the multi-particle models comprising inhomogeneities of diverse shape, size, orientation and properties which enables an adequate account for the microstructure parameters. The solution is valid for the general-type anisotropy of constituents and arbitrary orientation of the orthotropy axes. The effective conductivity tensor of the particulate composite with anisotropic constituents is evaluated in the framework of the generalized Maxwell homogenization scheme. Application of the developed method to composites with imperfect ellipsoidal interfaces is straightforward. Their incorporation yields probably the most general model of a composite that may be considered in the framework of analytical approach.

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

Higher-Order Binding Corrections to the Lamb Shift

NASA Astrophysics Data System (ADS)

Pachucki, K.

1993-08-01

In this work a new analytical method for calculating the one-loop self-energy correction to the Lamb shift is presented in detail. The technique relies on division into the low and the high energy parts. The low energy part is calculated using the multipole expansion and the high energy part is calculated by expanding the Dirac-Coulomb propagator in powers of the Coulomb field. The obtained results are in agreement with those previously known, but are more accurate. A new theoretical value of the Lamb shift is also given.

Multipolar electrostatics.

PubMed

Cardamone, Salvatore; Hughes, Timothy J; Popelier, Paul L A

2014-06-14

Atomistic simulation of chemical systems is currently limited by the elementary description of electrostatics that atomic point-charges offer. Unfortunately, a model of one point-charge for each atom fails to capture the anisotropic nature of electronic features such as lone pairs or π-systems. Higher order electrostatic terms, such as those offered by a multipole moment expansion, naturally recover these important electronic features. The question remains as to why such a description has not yet been widely adopted by popular molecular mechanics force fields. There are two widely-held misconceptions about the more rigorous formalism of multipolar electrostatics: (1) Accuracy: the implementation of multipole moments, compared to point-charges, offers little to no advantage in terms of an accurate representation of a system's energetics, structure and dynamics. (2) Efficiency: atomistic simulation using multipole moments is computationally prohibitive compared to simulation using point-charges. Whilst the second of these may have found some basis when computational power was a limiting factor, the first has no theoretical grounding. In the current work, we disprove the two statements above and systematically demonstrate that multipole moments are not discredited by either. We hope that this perspective will help in catalysing the transition to more realistic electrostatic modelling, to be adopted by popular molecular simulation software.

Design and Analysis of an Axisymmetric Phased Array Fed Gregorian Reflector System for Limited Scanning

DTIC Science & Technology

2016-01-22

Numerical electromagnetic simulations based on the multilevel fast multipole method (MLFMM) were used to analyze and optimize the antenna...and are not necessarily endorsed by the United States Government. numerical simulations with the multilevel fast multipole method (MLFMM...and optimized using numerical simulations conducted with the multilevel fast multipole method (MLFMM) using FEKO software (www.feko.info). The

Linearly scaling and almost Hamiltonian dielectric continuum molecular dynamics simulations through fast multipole expansions

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

Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul, E-mail: tavan@physik.uni-muenchen.de

2015-11-14

Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADESmore » can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved—up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.« less

Higher-order binding corrections to the Lamb shift

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

Pachucki, K.

1993-08-15

In this work a new analytical method for calculating the one-loop self-energy correction to the Lamb shift is presented in detail. The technique relies on division into the low and the high energy parts. The low energy part is calculated using the multipole expansion and the high energy part is calculated by expanding the Dirac-Coulomb propagator in powers of the Coulomb field. The obtained results are in agreement with those previously known, but are more accurate. A new theoretical value of the Lamb shift is also given. 47 refs., 2 figs., 1 tab.

Measuring the Symmetry of Supernova Remnants in the Radio

NASA Astrophysics Data System (ADS)

Stafford, Jennifer; Lopez, Laura A.

2017-01-01

Nearly 300 supernova remnants (SNRs) are known in the MIlky Way galaxy, and they offer an important means to study the explosions and interactions of supernovae at sub-pc scales. In this poster, we present analysis of the morphology of Galactic SNRs at radio wavelengths. Specifically, we measure the symmetry of several tens of SNRs in 6- and 20-cm Very Large Array images using a multipole expansion technique, the power-ratio method. We explore how the SNRs' morphology changes as a function of their size and estimated dynamical ages, with the aim of probing how SNR shapes evolve with time.

Exact formulas for multipole moments using Slater-type molecular orbitals

NASA Technical Reports Server (NTRS)

Jones, H. W.

1986-01-01

A triple infinite sum of formulas expressed as an expansion in Legendre polynomials is generated by use of computer algebra to represent the potential from the midpoint of two Slater-type orbitals; the charge density that determines the potential is given as the product of the two orbitals. An example using 1s orbitals shows that only a few terms are needed to obtain four-figure accuracy. Exact formulas are obtained for multipole moments by means of a careful study of expanded formulas, allowing an 'extrapolation to infinity'. This Loewdin alpha-function approach augmented by using a C matrix to characterize Slater-type orbitals can be readily generalized to all cases.

Dielectric metamaterials with toroidal dipolar response

DOE PAGES

Basharin, Alexey A.; Kafesaki, Maria; Economou, Eleftherios N.; ...

2015-03-27

Toroidal multipoles are the terms missing in the standard multipole expansion; they are usually overlooked due to their relatively weak coupling to the electromagnetic fields. Here, we propose and theoretically study all-dielectric metamaterials of a special class that represent a simple electromagnetic system supporting toroidal dipolar excitations in the THz part of the spectrum. In addition, we show that resonant transmission and reflection of such metamaterials is dominated by toroidal dipole scattering, the neglect of which would result in a misunderstanding interpretation of the metamaterials’ macroscopic response. Due to the unique field configuration of the toroidal mode, the proposed metamaterialsmore » could serve as a platform for sensing or enhancement of light absorption and optical nonlinearities.« less

Collisionless spectral-kinetic Simulation of the Multipole Resonance Probe

NASA Astrophysics Data System (ADS)

Dobrygin, Wladislaw; Szeremley, Daniel; Schilling, Christian; Oberrath, Jens; Eremin, Denis; Mussenbrock, Thomas; Brinkmann, Ralf Peter

2012-10-01

Plasma resonance spectroscopy is a well established plasma diagnostic method realized in several designs. One of these designs is the multipole resonance probe (MRP). In its idealized - geometrically simplified - version it consists of two dielectrically shielded, hemispherical electrodes to which an RF signal is applied. A numerical tool is under development, which is capable of simulating the dynamics of the plasma surrounding the MRP in electrostatic approximation. In the simulation the potential is separeted in an inner and a vacuum potential. The inner potential is influenced by the charged partilces and is calculated by a specialized Poisson solver. The vacuum potential fulfills Laplace's equetion and consists of the applied voltage of the probe as boundary condition. Both potentials are expanded in spherical harmonics. For a practical particle pusher implementation, the expansion must be appropriately truncated. Compared to a PIC simulation a grid is unnecessary to calculate the force on the particles. This work purpose is a collisionless kinetic simulation, which can be used to investigate kinetic effects on the resonance behavior of the MRP.[4pt] [1] M. Lapke et al., Appl. Phys. Lett. 93, 2008, 051502.

Perturbation of a Schwarzschild Black Hole Due to a Rotating Thin Disk

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

Čížek, P.; Semerák, O., E-mail: oldrich.semerak@mff.cuni.cz

Will, in 1974, treated the perturbation of a Schwarzschild black hole due to a slowly rotating, light, concentric thin ring by solving the perturbation equations in terms of a multipole expansion of the mass-and-rotation perturbation series. In the Schwarzschild background, his approach can be generalized to perturbation by a thin disk (which is more relevant astrophysically), but, due to rather bad convergence properties, the resulting expansions are not suitable for specific (numerical) computations. However, we show that Green’s functions, represented by Will’s result, can be expressed in closed form (without multipole expansion), which is more useful. In particular, they canmore » be integrated out over the source (a thin disk in our case) to yield good converging series both for the gravitational potential and for the dragging angular velocity. The procedure is demonstrated, in the first perturbation order, on the simplest case of a constant-density disk, including the physical interpretation of the results in terms of a one-component perfect fluid or a two-component dust in a circular orbit about the central black hole. Free parameters are chosen in such a way that the resulting black hole has zero angular momentum but non-zero angular velocity, as it is just carried along by the dragging effect of the disk.« less

Acoustic Interaction Forces and Torques Acting on Suspended Spheres in an Ideal Fluid.

PubMed

Lopes, J Henrique; Azarpeyvand, Mahdi; Silva, Glauber T

2016-01-01

In this paper, the acoustic interaction forces and torques exerted by an arbitrary time-harmonic wave on a set of N objects suspended in an inviscid fluid are theoretically analyzed. We utilize the partial-wave expansion method with translational addition theorem and re-expansion of multipole series to solve the related multiple scattering problem. We show that the acoustic interaction force and torque can be obtained using the farfield radiation force and torque formulas. To exemplify the method, we calculate the interaction forces exerted by an external traveling and standing plane wave on an arrangement of two and three olive-oil droplets in water. The droplets' radii are comparable to the wavelength (i.e., Mie scattering regime). The results show that the acoustic interaction forces present an oscillatory spatial distribution which follows the pattern formed by interference between the external and rescattered waves. In addition, acoustic interaction torques arise on the absorbing droplets whenever a nonsymmetric wavefront is formed by the external and rescattered waves' interference.

Cumulative atomic multipole moments complement any atomic charge model to obtain more accurate electrostatic properties

NASA Technical Reports Server (NTRS)

Sokalski, W. A.; Shibata, M.; Ornstein, R. L.; Rein, R.

1992-01-01

The quality of several atomic charge models based on different definitions has been analyzed using cumulative atomic multipole moments (CAMM). This formalism can generate higher atomic moments starting from any atomic charges, while preserving the corresponding molecular moments. The atomic charge contribution to the higher molecular moments, as well as to the electrostatic potentials, has been examined for CO and HCN molecules at several different levels of theory. The results clearly show that the electrostatic potential obtained from CAMM expansion is convergent up to R-5 term for all atomic charge models used. This illustrates that higher atomic moments can be used to supplement any atomic charge model to obtain more accurate description of electrostatic properties.

Multipole surface plasmons in metallic nanohole arrays

NASA Astrophysics Data System (ADS)

Nishida, Munehiro; Hatakenaka, Noriyuki; Kadoya, Yutaka

2015-06-01

The quasibound electromagnetic modes for the arrays of nanoholes perforated in thin gold film are analyzed both numerically by the rigorous coupled wave analysis (RCWA) method and semianalytically by the coupled mode method. It is shown that when the size of the nanohole occupies a large portion of the unit cell, the surface plasmon polaritons (SPPs) at both sides of the film are combined by the higher order waveguide modes of the holes to produce multipole surface plasmons: coupled surface plasmon modes with multipole texture on the elec-tric field distributions. Further, it is revealed that the multipole texture either enhances or suppresses the couplings between SPPs depending on their diffraction orders and also causes band inversion and reconstruction in the coupled SPP band structure. Due to the multipole nature of the quasibound modes, multiple dark modes coexist to produce a variety of Fano resonance structures on the transmission and reflection spectra.

First Higher-Multipole Model of Gravitational Waves from Spinning and Coalescing Black-Hole Binaries

NASA Astrophysics Data System (ADS)

London, Lionel; Khan, Sebastian; Fauchon-Jones, Edward; García, Cecilio; Hannam, Mark; Husa, Sascha; Jiménez-Forteza, Xisco; Kalaghatgi, Chinmay; Ohme, Frank; Pannarale, Francesco

2018-04-01

Gravitational-wave observations of binary black holes currently rely on theoretical models that predict the dominant multipoles (ℓ=2 ,|m |=2 ) of the radiation during inspiral, merger, and ringdown. We introduce a simple method to include the subdominant multipoles to binary black hole gravitational waveforms, given a frequency-domain model for the dominant multipoles. The amplitude and phase of the original model are appropriately stretched and rescaled using post-Newtonian results (for the inspiral), perturbation theory (for the ringdown), and a smooth transition between the two. No additional tuning to numerical-relativity simulations is required. We apply a variant of this method to the nonprecessing PhenomD model. The result, PhenomHM, constitutes the first higher-multipole model of spinning and coalescing black-hole binaries, and currently includes the (ℓ,|m |)=(2 ,2 ),(3 ,3 ),(4 ,4 ),(2 ,1 ),(3 ,2 ),(4 ,3 ) radiative moments. Comparisons with numerical-relativity waveforms demonstrate that PhenomHM is more accurate than dominant-multipole-only models for all binary configurations, and typically improves the measurement of binary properties.

First Higher-Multipole Model of Gravitational Waves from Spinning and Coalescing Black-Hole Binaries.

PubMed

London, Lionel; Khan, Sebastian; Fauchon-Jones, Edward; García, Cecilio; Hannam, Mark; Husa, Sascha; Jiménez-Forteza, Xisco; Kalaghatgi, Chinmay; Ohme, Frank; Pannarale, Francesco

2018-04-20

Gravitational-wave observations of binary black holes currently rely on theoretical models that predict the dominant multipoles (ℓ=2,|m|=2) of the radiation during inspiral, merger, and ringdown. We introduce a simple method to include the subdominant multipoles to binary black hole gravitational waveforms, given a frequency-domain model for the dominant multipoles. The amplitude and phase of the original model are appropriately stretched and rescaled using post-Newtonian results (for the inspiral), perturbation theory (for the ringdown), and a smooth transition between the two. No additional tuning to numerical-relativity simulations is required. We apply a variant of this method to the nonprecessing PhenomD model. The result, PhenomHM, constitutes the first higher-multipole model of spinning and coalescing black-hole binaries, and currently includes the (ℓ,|m|)=(2,2),(3,3),(4,4),(2,1),(3,2),(4,3) radiative moments. Comparisons with numerical-relativity waveforms demonstrate that PhenomHM is more accurate than dominant-multipole-only models for all binary configurations, and typically improves the measurement of binary properties.

SWIFT: SPH With Inter-dependent Fine-grained Tasking

NASA Astrophysics Data System (ADS)

Schaller, Matthieu; Gonnet, Pedro; Chalk, Aidan B. G.; Draper, Peter W.

2018-05-01

SWIFT runs cosmological simulations on peta-scale machines for solving gravity and SPH. It uses the Fast Multipole Method (FMM) to calculate gravitational forces between nearby particles, combining these with long-range forces provided by a mesh that captures both the periodic nature of the calculation and the expansion of the simulated universe. SWIFT currently uses a single fixed but time-variable softening length for all the particles. Many useful external potentials are also available, such as galaxy haloes or stratified boxes that are used in idealised problems. SWIFT implements a standard LCDM cosmology background expansion and solves the equations in a comoving frame; equations of state of dark-energy evolve with scale-factor. The structure of the code allows implementation for modified-gravity solvers or self-interacting dark matter schemes to be implemented. Many hydrodynamics schemes are implemented in SWIFT and the software allows users to add their own.

Some improvements in DNA interaction calculations

NASA Technical Reports Server (NTRS)

Egan, J. T.; Swissler, T. J.; Rein, R.

1974-01-01

Calculations are made on specific DNA-type complexes using refined expressions for electrostatic and polarization energies. Dispersion and repulsive terms are included in the evaluation of the total interaction energy. It is shown that the expansion of the electrostatic potential to include multipole moments up to octopole is necessary to achieve convergence of first-order energies. Polarization energies are not as sensitive to this expansion. The calculations also support the usefulness of the hard sphere model for DNA hydrogen bonds and indicate how stacking interactions are influenced by second-order energies.

Simulation of hydrodynamically interacting particles near a no-slip boundary

NASA Astrophysics Data System (ADS)

Swan, James W.; Brady, John F.

2007-11-01

The dynamics of spherical particles near a single plane wall are computed using an extension of the Stokesian dynamics method that includes long-range many-body and pairwise lubrication interactions between the spheres and the wall in Stokes flow. Extra care is taken to ensure that the mobility and resistance tensors are symmetric, positive, and definite—something which is ineluctable for particles in low-Reynolds-number flows. We discuss why two previous simulation methods for particles near a plane wall, one using multipole expansions and the other using the Rotne-Prager tensor, fail to produce symmetric resistance and mobility tensors. Additionally, we offer some insight on how the Stokesian dynamics paradigm might be extended to study the dynamics of particles in any confining geometry.

Beyond Point Charges: Dynamic Polarization from Neural Net Predicted Multipole Moments.

PubMed

Darley, Michael G; Handley, Chris M; Popelier, Paul L A

2008-09-09

Intramolecular polarization is the change to the electron density of a given atom upon variation in the positions of the neighboring atoms. We express the electron density in terms of multipole moments. Using glycine and N-methylacetamide (NMA) as pilot systems, we show that neural networks can capture the change in electron density due to polarization. After training, modestly sized neural networks successfully predict the atomic multipole moments from the nuclear positions of all atoms in the molecule. Accurate electrostatic energies between two atoms can be then obtained via a multipole expansion, inclusive of polarization effects. As a result polarization is successfully modeled at short-range and without an explicit polarizability tensor. This approach puts charge transfer and multipolar polarization on a common footing. The polarization procedure is formulated within the context of quantum chemical topology (QCT). Nonbonded atom-atom interactions in glycine cover an energy range of 948 kJ mol(-1), with an average energy difference between true and predicted energy of 0.2 kJ mol(-1), the largest difference being just under 1 kJ mol(-1). Very similar energy differences are found for NMA, which spans a range of 281 kJ mol(-1). The current proof-of-concept enables the construction of a new protein force field that incorporates electron density fragments that dynamically respond to their fluctuating environment.

Acoustic and elastic multiple scattering and radiation from cylindrical structures

NASA Astrophysics Data System (ADS)

Amirkulova, Feruza Abdukadirovna

Multiple scattering (MS) and radiation of waves by a system of scatterers is of great theoretical and practical importance and is required in a wide variety of physical contexts such as the implementation of "invisibility" cloaks, the effective parameter characterization, and the fabrication of dynamically tunable structures, etc. The dissertation develops fast, rapidly convergent iterative techniques to expedite the solution of MS problems. The formulation of MS problems reduces to a system of linear algebraic equations using Graf's theorem and separation of variables. The iterative techniques are developed using Neumann expansion and Block Toeplitz structure of the linear system; they are very general, and suitable for parallel computations and a large number of MS problems, i.e. acoustic, elastic, electromagnetic, etc., and used for the first time to solve MS problems. The theory is implemented in Matlab and FORTRAN, and the theoretical predictions are compared to computations obtained by COMSOL. To formulate the MS problem, the transition matrix is obtained by analyzing an acoustic and an elastic single scattering of incident waves by elastic isotropic and anisotropic solids. The mathematical model of wave scattering from multilayered cylindrical and spherical structures is developed by means of an exact solution of dynamic 3D elasticity theory. The recursive impedance matrix algorithm is derived for radially heterogeneous anisotropic solids. An explicit method for finding the impedance in piecewise uniform, transverse-isotropic material is proposed; the solution is compared to elasticity theory solutions involving Buchwald potentials. Furthermore, active exterior cloaking devices are modeled for acoustic and elastic media using multipole sources. A cloaking device can render an object invisible to some incident waves as seen by some external observer. The active cloak is generated by a discrete set of multipole sources that destructively interfere with an incident wave to produce zero total field over a finite spatial region. The approach precisely determines the necessary source amplitudes and enables a cloaked region to be determined using Graf's theorem. To apply the approach, the infinite series of multipole expansions are truncated, and the accuracy of cloaking is studied by modifying the truncation parameter.

AFMPB: An adaptive fast multipole Poisson-Boltzmann solver for calculating electrostatics in biomolecular systems

NASA Astrophysics Data System (ADS)

Lu, Benzhuo; Cheng, Xiaolin; Huang, Jingfang; McCammon, J. Andrew

2010-06-01

A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson-Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node-patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://lsec.cc.ac.cn/~lubz/afmpb.html and a mirror site at http://mccammon.ucsd.edu/. This paper is a brief summary of the program: the algorithms, the implementation and the usage. Program summaryProgram title: AFMPB: Adaptive fast multipole Poisson-Boltzmann solver Catalogue identifier: AEGB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL 2.0 No. of lines in distributed program, including test data, etc.: 453 649 No. of bytes in distributed program, including test data, etc.: 8 764 754 Distribution format: tar.gz Programming language: Fortran Computer: Any Operating system: Any RAM: Depends on the size of the discretized biomolecular system Classification: 3 External routines: Pre- and post-processing tools are required for generating the boundary elements and for visualization. Users can use MSMS ( http://www.scripps.edu/~sanner/html/msms_home.html) for pre-processing, and VMD ( http://www.ks.uiuc.edu/Research/vmd/) for visualization. Sub-programs included: An iterative Krylov subspace solvers package from SPARSKIT by Yousef Saad ( http://www-users.cs.umn.edu/~saad/software/SPARSKIT/sparskit.html), and the fast multipole methods subroutines from FMMSuite ( http://www.fastmultipole.org/). Nature of problem: Numerical solution of the linearized Poisson-Boltzmann equation that describes electrostatic interactions of molecular systems in ionic solutions. Solution method: A novel node-patch scheme is used to discretize the well-conditioned boundary integral equation formulation of the linearized Poisson-Boltzmann equation. Various Krylov subspace solvers can be subsequently applied to solve the resulting linear system, with a bounded number of iterations independent of the number of discretized unknowns. The matrix-vector multiplication at each iteration is accelerated by the adaptive new versions of fast multipole methods. The AFMPB solver requires other stand-alone pre-processing tools for boundary mesh generation, post-processing tools for data analysis and visualization, and can be conveniently coupled with different time stepping methods for dynamics simulation. Restrictions: Only three or six significant digits options are provided in this version. Unusual features: Most of the codes are in Fortran77 style. Memory allocation functions from Fortran90 and above are used in a few subroutines. Additional comments: The current version of the codes is designed and written for single core/processor desktop machines. Check http://lsec.cc.ac.cn/~lubz/afmpb.html and http://mccammon.ucsd.edu/ for updates and changes. Running time: The running time varies with the number of discretized elements ( N) in the system and their distributions. In most cases, it scales linearly as a function of N.

Building better water models using the shape of the charge distribution of a water molecule

NASA Astrophysics Data System (ADS)

Dharmawardhana, Chamila Chathuranga; Ichiye, Toshiko

2017-11-01

The unique properties of liquid water apparently arise from more than just the tetrahedral bond angle between the nuclei of a water molecule since simple three-site models of water are poor at mimicking these properties in computer simulations. Four- and five-site models add partial charges on dummy sites and are better at modeling these properties, which suggests that the shape of charge distribution is important. Since a multipole expansion of the electrostatic potential describes a charge distribution in an orthogonal basis set that is exact in the limit of infinite order, multipoles may be an even better way to model the charge distribution. In particular, molecular multipoles up to the octupole centered on the oxygen appear to describe the electrostatic potential from electronic structure calculations better than four- and five-site models, and molecular multipole models give better agreement with the temperature and pressure dependence of many liquid state properties of water while retaining the computational efficiency of three-site models. Here, the influence of the shape of the molecular charge distribution on liquid state properties is examined by correlating multipoles of non-polarizable water models with their liquid state properties in computer simulations. This will aid in the development of accurate water models for classical simulations as well as in determining the accuracy needed in quantum mechanical/molecular mechanical studies and ab initio molecular dynamics simulations of water. More fundamentally, this will lead to a greater understanding of how the charge distribution of a water molecule leads to the unique properties of liquid water. In particular, these studies indicate that p-orbital charge out of the molecular plane is important.

Spectral Kinetic Simulation of the Ideal Multipole Resonance Probe

NASA Astrophysics Data System (ADS)

Gong, Junbo; Wilczek, Sebastian; Szeremley, Daniel; Oberrath, Jens; Eremin, Denis; Dobrygin, Wladislaw; Schilling, Christian; Friedrichs, Michael; Brinkmann, Ralf Peter

2015-09-01

The term Active Plasma Resonance Spectroscopy (APRS) denotes a class of diagnostic techniques which utilize the natural ability of plasmas to resonate on or near the electron plasma frequency ωpe: An RF signal in the GHz range is coupled into the plasma via an electric probe; the spectral response of the plasma is recorded, and a mathematical model is used to determine plasma parameters such as the electron density ne or the electron temperature Te. One particular realization of the method is the Multipole Resonance Probe (MRP). The ideal MRP is a geometrically simplified version of that probe; it consists of two dielectrically shielded, hemispherical electrodes to which the RF signal is applied. A particle-based numerical algorithm is described which enables a kinetic simulation of the interaction of the probe with the plasma. Similar to the well-known particle-in-cell (PIC), it contains of two modules, a particle pusher and a field solver. The Poisson solver determines, with the help of a truncated expansion into spherical harmonics, the new electric field at each particle position directly without invoking a numerical grid. The effort of the scheme scales linearly with the ensemble size N.

Efficient method of evaluation for Gaussian Hartree-Fock exchange operator for Gau-PBE functional

NASA Astrophysics Data System (ADS)

Song, Jong-Won; Hirao, Kimihiko

2015-07-01

We previously developed an efficient screened hybrid functional called Gaussian-Perdew-Burke-Ernzerhof (Gau-PBE) [Song et al., J. Chem. Phys. 135, 071103 (2011)] for large molecules and extended systems, which is characterized by the usage of a Gaussian function as a modified Coulomb potential for the Hartree-Fock (HF) exchange. We found that the adoption of a Gaussian HF exchange operator considerably decreases the calculation time cost of periodic systems while improving the reproducibility of the bandgaps of semiconductors. We present a distance-based screening scheme here that is tailored for the Gaussian HF exchange integral that utilizes multipole expansion for the Gaussian two-electron integrals. We found a new multipole screening scheme helps to save the time cost for the HF exchange integration by efficiently decreasing the number of integrals of, specifically, the near field region without incurring substantial changes in total energy. In our assessment on the periodic systems of seven semiconductors, the Gau-PBE hybrid functional with a new screening scheme has 1.56 times the time cost of a pure functional while the previous Gau-PBE was 1.84 times and HSE06 was 3.34 times.

Efficient method of evaluation for Gaussian Hartree-Fock exchange operator for Gau-PBE functional

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

Song, Jong-Won; Hirao, Kimihiko, E-mail: hirao@riken.jp

2015-07-14

We previously developed an efficient screened hybrid functional called Gaussian-Perdew–Burke–Ernzerhof (Gau-PBE) [Song et al., J. Chem. Phys. 135, 071103 (2011)] for large molecules and extended systems, which is characterized by the usage of a Gaussian function as a modified Coulomb potential for the Hartree-Fock (HF) exchange. We found that the adoption of a Gaussian HF exchange operator considerably decreases the calculation time cost of periodic systems while improving the reproducibility of the bandgaps of semiconductors. We present a distance-based screening scheme here that is tailored for the Gaussian HF exchange integral that utilizes multipole expansion for the Gaussian two-electron integrals.more » We found a new multipole screening scheme helps to save the time cost for the HF exchange integration by efficiently decreasing the number of integrals of, specifically, the near field region without incurring substantial changes in total energy. In our assessment on the periodic systems of seven semiconductors, the Gau-PBE hybrid functional with a new screening scheme has 1.56 times the time cost of a pure functional while the previous Gau-PBE was 1.84 times and HSE06 was 3.34 times.« less

Apparatus and method of dissociating ions in a multipole ion guide

DOEpatents

Webb, Ian K.; Tang, Keqi; Smith, Richard D.; Ibrahim, Yehia M.; Anderson, Gordon A.

2014-07-08

A method of dissociating ions in a multipole ion guide is disclosed. A stream of charged ions is supplied to the ion guide. A main RF field is applied to the ion guide to confine the ions through the ion guide. An excitation RF field is applied to one pair of rods of the ion guide. The ions undergo dissociation when the applied excitation RF field is resonant with a secular frequency of the ions. The multipole ion guide is, but not limited to, a quadrupole, a hexapole, and an octopole.

EEG-distributed inverse solutions for a spherical head model

NASA Astrophysics Data System (ADS)

Riera, J. J.; Fuentes, M. E.; Valdés, P. A.; Ohárriz, Y.

1998-08-01

The theoretical study of the minimum norm solution to the MEG inverse problem has been carried out in previous papers for the particular case of spherical symmetry. However, a similar study for the EEG is remarkably more difficult due to the very complicated nature of the expression relating the voltage differences on the scalp to the primary current density (PCD) even for this simple symmetry. This paper introduces the use of the electric lead field (ELF) on the dyadic formalism in the spherical coordinate system to overcome such a drawback using an expansion of the ELF in terms of longitudinal and orthogonal vector fields. This approach allows us to represent EEG Fourier coefficients on a 2-sphere in terms of a current multipole expansion. The choice of a suitable basis for the Hilbert space of the PCDs on the brain region allows the current multipole moments to be related by spatial transfer functions to the PCD spectral coefficients. Properties of the most used distributed inverse solutions are explored on the basis of these results. Also, a part of the ELF null space is completely characterized and those spherical components of the PCD which are possible silent candidates are discussed.

Multipole Algorithms for Molecular Dynamics Simulation on High Performance Computers.

NASA Astrophysics Data System (ADS)

Elliott, William Dewey

1995-01-01

A fundamental problem in modeling large molecular systems with molecular dynamics (MD) simulations is the underlying N-body problem of computing the interactions between all pairs of N atoms. The simplest algorithm to compute pair-wise atomic interactions scales in runtime {cal O}(N^2), making it impractical for interesting biomolecular systems, which can contain millions of atoms. Recently, several algorithms have become available that solve the N-body problem by computing the effects of all pair-wise interactions while scaling in runtime less than {cal O}(N^2). One algorithm, which scales {cal O}(N) for a uniform distribution of particles, is called the Greengard-Rokhlin Fast Multipole Algorithm (FMA). This work describes an FMA-like algorithm called the Molecular Dynamics Multipole Algorithm (MDMA). The algorithm contains several features that are new to N-body algorithms. MDMA uses new, efficient series expansion equations to compute general 1/r^{n } potentials to arbitrary accuracy. In particular, the 1/r Coulomb potential and the 1/r^6 portion of the Lennard-Jones potential are implemented. The new equations are based on multivariate Taylor series expansions. In addition, MDMA uses a cell-to-cell interaction region of cells that is closely tied to worst case error bounds. The worst case error bounds for MDMA are derived in this work also. These bounds apply to other multipole algorithms as well. Several implementation enhancements are described which apply to MDMA as well as other N-body algorithms such as FMA and tree codes. The mathematics of the cell -to-cell interactions are converted to the Fourier domain for reduced operation count and faster computation. A relative indexing scheme was devised to locate cells in the interaction region which allows efficient pre-computation of redundant information and prestorage of much of the cell-to-cell interaction. Also, MDMA was integrated into the MD program SIgMA to demonstrate the performance of the program over several simulation timesteps. One MD application described here highlights the utility of including long range contributions to Lennard-Jones potential in constant pressure simulations. Another application shows the time dependence of long range forces in a multiple time step MD simulation.

Polyakov loop correlator in perturbation theory

DOE PAGES

Berwein, Matthias; Brambilla, Nora; Petreczky, Péter; ...

2017-07-25

We study the Polyakov loop correlator in the weak coupling expansion and show how the perturbative series re-exponentiates into singlet and adjoint contributions. We calculate the order g 7 correction to the Polyakov loop correlator in the short distance limit. We show how the singlet and adjoint free energies arising from the re-exponentiation formula of the Polyakov loop correlator are related to the gauge invariant singlet and octet free energies that can be defined in pNRQCD, namely we find that the two definitions agree at leading order in the multipole expansion, but differ at first order in the quark-antiquark distance.

Solution of Einsteins Equation for Deformation of a Magnetized Neutron Star

NASA Astrophysics Data System (ADS)

Rizaldy, R.; Sulaksono, A.

2018-04-01

We studied the effect of very large and non-uniform magnetic field existed in the neutron star on the deformation of the neutron star. We used in our analytical calculation, multipole expansion of the tensor metric and the momentum-energy tensor in Legendre polynomial expansion up to the quadrupole order. In this way we obtain the solutions of Einstein’s equation with the correction factors due to the magnetic field are taken into account. We obtain from our numerical calculation that the degree of deformation (ellipticity) is increased when the the mass is decreased.

Polyakov loop correlator in perturbation theory

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

Berwein, Matthias; Brambilla, Nora; Petreczky, Péter

We study the Polyakov loop correlator in the weak coupling expansion and show how the perturbative series re-exponentiates into singlet and adjoint contributions. We calculate the order g 7 correction to the Polyakov loop correlator in the short distance limit. We show how the singlet and adjoint free energies arising from the re-exponentiation formula of the Polyakov loop correlator are related to the gauge invariant singlet and octet free energies that can be defined in pNRQCD, namely we find that the two definitions agree at leading order in the multipole expansion, but differ at first order in the quark-antiquark distance.

Electromagnetic field analysis and modeling of a relative position detection sensor for high speed maglev trains.

PubMed

Xue, Song; He, Ning; Long, Zhiqiang

2012-01-01

The long stator track for high speed maglev trains has a tooth-slot structure. The sensor obtains precise relative position information for the traction system by detecting the long stator tooth-slot structure based on nondestructive detection technology. The magnetic field modeling of the sensor is a typical three-dimensional (3-D) electromagnetic problem with complex boundary conditions, and is studied semi-analytically in this paper. A second-order vector potential (SOVP) is introduced to simplify the vector field problem to a scalar field one, the solution of which can be expressed in terms of series expansions according to Multipole Theory (MT) and the New Equivalent Source (NES) method. The coefficients of the expansions are determined by the least squares method based on the boundary conditions. Then, the solution is compared to the simulation result through Finite Element Analysis (FEA). The comparison results show that the semi-analytical solution agrees approximately with the numerical solution. Finally, based on electromagnetic modeling, a difference coil structure is designed to improve the sensitivity and accuracy of the sensor.

Electromagnetic Field Analysis and Modeling of a Relative Position Detection Sensor for High Speed Maglev Trains

PubMed Central

Xue, Song; He, Ning; Long, Zhiqiang

2012-01-01

The long stator track for high speed maglev trains has a tooth-slot structure. The sensor obtains precise relative position information for the traction system by detecting the long stator tooth-slot structure based on nondestructive detection technology. The magnetic field modeling of the sensor is a typical three-dimensional (3-D) electromagnetic problem with complex boundary conditions, and is studied semi-analytically in this paper. A second-order vector potential (SOVP) is introduced to simplify the vector field problem to a scalar field one, the solution of which can be expressed in terms of series expansions according to Multipole Theory (MT) and the New Equivalent Source (NES) method. The coefficients of the expansions are determined by the least squares method based on the boundary conditions. Then, the solution is compared to the simulation result through Finite Element Analysis (FEA). The comparison results show that the semi-analytical solution agrees approximately with the numerical solution. Finally, based on electromagnetic modeling, a difference coil structure is designed to improve the sensitivity and accuracy of the sensor. PMID:22778652

Reduced-rank approximations to the far-field transform in the gridded fast multipole method

NASA Astrophysics Data System (ADS)

Hesford, Andrew J.; Waag, Robert C.

2011-05-01

The fast multipole method (FMM) has been shown to have a reduced computational dependence on the size of finest-level groups of elements when the elements are positioned on a regular grid and FFT convolution is used to represent neighboring interactions. However, transformations between plane-wave expansions used for FMM interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of FMM computations when finest-level groups are large. The transformation operators, which are forward and inverse Fourier transforms with the wave space confined to the unit sphere, are smooth and well approximated using reduced-rank decompositions that further reduce the computational dependence of the FMM on finest-level group size. The adaptive cross approximation (ACA) is selected to represent the forward and adjoint far-field transformation operators required by the FMM. However, the actual error of the ACA is found to be greater than that predicted using traditional estimates, and the ACA generally performs worse than the approximation resulting from a truncated singular-value decomposition (SVD). To overcome these issues while avoiding the cost of a full-scale SVD, the ACA is employed with more stringent accuracy demands and recompressed using a reduced, truncated SVD. The results show a greatly reduced approximation error that performs comparably to the full-scale truncated SVD without degrading the asymptotic computational efficiency associated with ACA matrix assembly.

Reduced-Rank Approximations to the Far-Field Transform in the Gridded Fast Multipole Method.

PubMed

Hesford, Andrew J; Waag, Robert C

2011-05-10

The fast multipole method (FMM) has been shown to have a reduced computational dependence on the size of finest-level groups of elements when the elements are positioned on a regular grid and FFT convolution is used to represent neighboring interactions. However, transformations between plane-wave expansions used for FMM interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of FMM computations when finest-level groups are large. The transformation operators, which are forward and inverse Fourier transforms with the wave space confined to the unit sphere, are smooth and well approximated using reduced-rank decompositions that further reduce the computational dependence of the FMM on finest-level group size. The adaptive cross approximation (ACA) is selected to represent the forward and adjoint far-field transformation operators required by the FMM. However, the actual error of the ACA is found to be greater than that predicted using traditional estimates, and the ACA generally performs worse than the approximation resulting from a truncated singular-value decomposition (SVD). To overcome these issues while avoiding the cost of a full-scale SVD, the ACA is employed with more stringent accuracy demands and recompressed using a reduced, truncated SVD. The results show a greatly reduced approximation error that performs comparably to the full-scale truncated SVD without degrading the asymptotic computational efficiency associated with ACA matrix assembly.

Reduced-Rank Approximations to the Far-Field Transform in the Gridded Fast Multipole Method

PubMed Central

Hesford, Andrew J.; Waag, Robert C.

2011-01-01

The fast multipole method (FMM) has been shown to have a reduced computational dependence on the size of finest-level groups of elements when the elements are positioned on a regular grid and FFT convolution is used to represent neighboring interactions. However, transformations between plane-wave expansions used for FMM interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of FMM computations when finest-level groups are large. The transformation operators, which are forward and inverse Fourier transforms with the wave space confined to the unit sphere, are smooth and well approximated using reduced-rank decompositions that further reduce the computational dependence of the FMM on finest-level group size. The adaptive cross approximation (ACA) is selected to represent the forward and adjoint far-field transformation operators required by the FMM. However, the actual error of the ACA is found to be greater than that predicted using traditional estimates, and the ACA generally performs worse than the approximation resulting from a truncated singular-value decomposition (SVD). To overcome these issues while avoiding the cost of a full-scale SVD, the ACA is employed with more stringent accuracy demands and recompressed using a reduced, truncated SVD. The results show a greatly reduced approximation error that performs comparably to the full-scale truncated SVD without degrading the asymptotic computational efficiency associated with ACA matrix assembly. PMID:21552350

The fast multipole method and point dipole moment polarizable force fields.

PubMed

Coles, Jonathan P; Masella, Michel

2015-01-14

We present an implementation of the fast multipole method for computing Coulombic electrostatic and polarization forces from polarizable force-fields based on induced point dipole moments. We demonstrate the expected O(N) scaling of that approach by performing single energy point calculations on hexamer protein subunits of the mature HIV-1 capsid. We also show the long time energy conservation in molecular dynamics at the nanosecond scale by performing simulations of a protein complex embedded in a coarse-grained solvent using a standard integrator and a multiple time step integrator. Our tests show the applicability of fast multipole method combined with state-of-the-art chemical models in molecular dynamical systems.

Development of hardware accelerator for molecular dynamics simulations: a computation board that calculates nonbonded interactions in cooperation with fast multipole method.

PubMed

Amisaki, Takashi; Toyoda, Shinjiro; Miyagawa, Hiroh; Kitamura, Kunihiro

2003-04-15

Evaluation of long-range Coulombic interactions still represents a bottleneck in the molecular dynamics (MD) simulations of biological macromolecules. Despite the advent of sophisticated fast algorithms, such as the fast multipole method (FMM), accurate simulations still demand a great amount of computation time due to the accuracy/speed trade-off inherently involved in these algorithms. Unless higher order multipole expansions, which are extremely expensive to evaluate, are employed, a large amount of the execution time is still spent in directly calculating particle-particle interactions within the nearby region of each particle. To reduce this execution time for pair interactions, we developed a computation unit (board), called MD-Engine II, that calculates nonbonded pairwise interactions using a specially designed hardware. Four custom arithmetic-processors and a processor for memory manipulation ("particle processor") are mounted on the computation board. The arithmetic processors are responsible for calculation of the pair interactions. The particle processor plays a central role in realizing efficient cooperation with the FMM. The results of a series of 50-ps MD simulations of a protein-water system (50,764 atoms) indicated that a more stringent setting of accuracy in FMM computation, compared with those previously reported, was required for accurate simulations over long time periods. Such a level of accuracy was efficiently achieved using the cooperative calculations of the FMM and MD-Engine II. On an Alpha 21264 PC, the FMM computation at a moderate but tolerable level of accuracy was accelerated by a factor of 16.0 using three boards. At a high level of accuracy, the cooperative calculation achieved a 22.7-fold acceleration over the corresponding conventional FMM calculation. In the cooperative calculations of the FMM and MD-Engine II, it was possible to achieve more accurate computation at a comparable execution time by incorporating larger nearby regions. Copyright 2003 Wiley Periodicals, Inc. J Comput Chem 24: 582-592, 2003

The Analysis of Likert Scales Using State Multipoles: An Application of Quantum Methods to Behavioral Sciences Data

ERIC Educational Resources Information Center

Camparo, James; Camparo, Lorinda B.

2013-01-01

Though ubiquitous, Likert scaling's traditional mode of analysis is often unable to uncover all of the valid information in a data set. Here, the authors discuss a solution to this problem based on methodology developed by quantum physicists: the state multipole method. The authors demonstrate the relative ease and value of this method by…

Zero-multipole summation method for efficiently estimating electrostatic interactions in molecular system.

PubMed

Fukuda, Ikuo

2013-11-07

The zero-multipole summation method has been developed to efficiently evaluate the electrostatic Coulombic interactions of a point charge system. This summation prevents the electrically non-neutral multipole states that may artificially be generated by a simple cutoff truncation, which often causes large amounts of energetic noise and significant artifacts. The resulting energy function is represented by a constant term plus a simple pairwise summation, using a damped or undamped Coulombic pair potential function along with a polynomial of the distance between each particle pair. Thus, the implementation is straightforward and enables facile applications to high-performance computations. Any higher-order multipole moment can be taken into account in the neutrality principle, and it only affects the degree and coefficients of the polynomial and the constant term. The lowest and second moments correspond respectively to the Wolf zero-charge scheme and the zero-dipole summation scheme, which was previously proposed. Relationships with other non-Ewald methods are discussed, to validate the current method in their contexts. Good numerical efficiencies were easily obtained in the evaluation of Madelung constants of sodium chloride and cesium chloride crystals.

Electron beam control for barely separated beams

DOEpatents

Douglas, David R.; Ament, Lucas J. P.

2017-04-18

A method for achieving independent control of multiple beams in close proximity to one another, such as in a multi-pass accelerator where coaxial beams are at different energies, but moving on a common axis, and need to be split into spatially separated beams for efficient recirculation transport. The method for independent control includes placing a magnet arrangement in the path of the barely separated beams with the magnet arrangement including at least two multipole magnets spaced closely together and having a multipole distribution including at least one odd multipole and one even multipole. The magnetic fields are then tuned to cancel out for a first of the barely separated beams to allow independent control of the second beam with common magnets. The magnetic fields may be tuned to cancel out either the dipole component or tuned to cancel out the quadrupole component in order to independently control the separate beams.

Measurement of the generalized form factors near threshold via γ*p→nπ+ at high Q2

NASA Astrophysics Data System (ADS)

Park, K.; Gothe, R. W.; Adhikari, K. P.; Adikaram, D.; Anghinolfi, M.; Baghdasaryan, H.; Ball, J.; Battaglieri, M.; Batourine, V.; Bedlinskiy, I.; Bennett, R. P.; Biselli, A. S.; Bookwalter, C.; Boiarinov, S.; Branford, D.; Briscoe, W. J.; Brooks, W. K.; Burkert, V. D.; Carman, D. S.; Celentano, A.; Chandavar, S.; Charles, G.; Cole, P. L.; Contalbrigo, M.; Crede, V.; D'Angelo, A.; Daniel, A.; Dashyan, N.; De Vita, R.; De Sanctis, E.; Deur, A.; Djalali, C.; Doughty, D.; Dupre, R.; El Alaoui, A.; El Fassi, L.; Eugenio, P.; Fedotov, G.; Fradi, A.; Gabrielyan, M. Y.; Gevorgyan, N.; Gilfoyle, G. P.; Giovanetti, K. L.; Girod, F. X.; Goetz, J. T.; Gohn, W.; Golovatch, E.; Graham, L.; Griffioen, K. A.; Guidal, M.; Guo, L.; Hafidi, K.; Hakobyan, H.; Hanretty, C.; Heddle, D.; Hicks, K.; Holtrop, M.; Hyde, C. E.; Ilieva, Y.; Ireland, D. G.; Ishkhanov, B. S.; Isupov, E. L.; Jenkins, D.; Jo, H. S.; Joo, K.; Kalantarians, N.; Khandaker, M.; Khetarpal, P.; Kim, A.; Kim, W.; Klein, A.; Klein, F. J.; Kubarovsky, A.; Kubarovsky, V.; Kuhn, S. E.; Kuleshov, S. V.; Kvaltine, N. D.; Livingston, K.; Lu, H. Y.; MacGregor, I. J. D.; Markov, N.; Mayer, M.; McKinnon, B.; Mestayer, M. D.; Meyer, C. A.; Mineeva, T.; Mirazita, M.; Mokeev, V.; Moutarde, H.; Munevar, E.; Nadel-Turonski, P.; Nasseripour, R.; Niccolai, S.; Niculescu, G.; Niculescu, I.; Osipenko, M.; Ostrovidov, A. I.; Paolone, M.; Pappalardo, L.; Paremuzyan, R.; Park, S.; Pereira, S. Anefalos; Phelps, E.; Pisano, S.; Pogorelko, O.; Pozdniakov, S.; Price, J. W.; Procureur, S.; Prok, Y.; Ricco, G.; Rimal, D.; Ripani, M.; Ritchie, B. G.; Rosner, G.; Rossi, P.; Sabatié, F.; Saini, M. S.; Salgado, C.; Schott, D.; Schumacher, R. A.; Seraydaryan, H.; Sharabian, Y. G.; Smith, E. S.; Smith, G. D.; Sober, D. I.; Sokhan, D.; Stepanyan, S. S.; Stepanyan, S.; Stoler, P.; Strakovsky, I. I.; Strauch, S.; Taiuti, M.; Tang, W.; Taylor, C. E.; Tian, Y.; Tkachenko, S.; Trivedi, A.; Ungaro, M.; Vernarsky, B.; Vlassov, A. V.; Voutier, E.; Watts, D. P.; Weygand, D. P.; Wood, M. H.; Zachariou, N.; Zhao, B.; Zhao, Z. W.

2012-03-01

We report the first extraction of the pion-nucleon multipoles near the production threshold for the nπ+ channel at relatively high momentum transfer (Q2 up to 4.2 GeV2). The dominance of the s-wave transverse multipole (E0+), expected in this region, allowed us to access the generalized form factor G1 within the light-cone sum-rule (LCSR) framework as well as the axial form factor GA. The data analyzed in this work were collected by the nearly 4π CEBAF Large Acceptance Spectrometer (CLAS) using a 5.754-GeV electron beam on a proton target. The differential cross section and the π-N multipole E0+/GD were measured using two different methods, the LCSR and a direct multipole fit. The results from the two methods are found to be consistent and almost Q2 independent.

Systematic Improvement of Potential-Derived Atomic Multipoles and Redundancy of the Electrostatic Parameter Space.

PubMed

Jakobsen, Sofie; Jensen, Frank

2014-12-09

We assess the accuracy of force field (FF) electrostatics at several levels of approximation from the standard model using fixed partial charges to conformational specific multipole fits including up to quadrupole moments. Potential-derived point charges and multipoles are calculated using least-squares methods for a total of ∼1000 different conformations of the 20 natural amino acids. Opposed to standard charge fitting schemes the procedure presented in the current work employs fitting points placed on a single isodensity surface, since the electrostatic potential (ESP) on such a surface determines the ESP at all points outside this surface. We find that the effect of multipoles beyond partial atomic charges is of the same magnitude as the effect due to neglecting conformational dependency (i.e., polarizability), suggesting that the two effects should be included at the same level in FF development. The redundancy at both the partial charge and multipole levels of approximation is quantified. We present an algorithm which stepwise reduces or increases the dimensionality of the charge or multipole parameter space and provides an upper limit of the ESP error that can be obtained at a given truncation level. Thereby, we can identify a reduced set of multipole moments corresponding to ∼40% of the total number of multipoles. This subset of parameters provides a significant improvement in the representation of the ESP compared to the simple point charge model and close to the accuracy obtained using the complete multipole parameter space. The selection of the ∼40% most important multipole sites is highly transferable among different conformations, and we find that quadrupoles are of high importance for atoms involved in π-bonding, since the anisotropic electric field generated in such regions requires a large degree of flexibility.

Modeling super-resolution SERS using a T-matrix method to elucidate molecule-nanoparticle coupling and the origins of localization errors

NASA Astrophysics Data System (ADS)

Heaps, Charles W.; Schatz, George C.

2017-06-01

A computational method to model diffraction-limited images from super-resolution surface-enhanced Raman scattering microscopy is introduced. Despite significant experimental progress in plasmon-based super-resolution imaging, theoretical predictions of the diffraction limited images remain a challenge. The method is used to calculate localization errors and image intensities for a single spherical gold nanoparticle-molecule system. The light scattering is calculated using a modification of generalized Mie (T-matrix) theory with a point dipole source and diffraction limited images are calculated using vectorial diffraction theory. The calculation produces the multipole expansion for each emitter and the coherent superposition of all fields. Imaging the constituent fields in addition to the total field provides new insight into the strong coupling between the molecule and the nanoparticle. Regardless of whether the molecular dipole moment is oriented parallel or perpendicular to the nanoparticle surface, the anisotropic excitation distorts the center of the nanoparticle as measured by the point spread function by approximately fifty percent of the particle radius toward to the molecule. Inspection of the nanoparticle multipoles reveals that distortion arises from a weak quadrupole resonance interfering with the dipole field in the nanoparticle. When the nanoparticle-molecule fields are in-phase, the distorted nanoparticle field dominates the observed image. When out-of-phase, the nanoparticle and molecule are of comparable intensity and interference between the two emitters dominates the observed image. The method is also applied to different wavelengths and particle radii. At off-resonant wavelengths, the method predicts images closer to the molecule not because of relative intensities but because of greater distortion in the nanoparticle. The method is a promising approach to improving the understanding of plasmon-enhanced super-resolution experiments.

MEG (Magnetoencephalography) multipolar modeling of distributed sources using RAP-MUSIC (Recursively Applied and Projected Multiple Signal Characterization)

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

Mosher, J. C.; Baillet, S.; Jerbi, K.

2001-01-01

We describe the use of truncated multipolar expansions for producing dynamic images of cortical neural activation from measurements of the magnetoencephalogram. We use a signal-subspace method to find the locations of a set of multipolar sources, each of which represents a region of activity in the cerebral cortex. Our method builds up an estimate of the sources in a recursive manner, i.e. we first search for point current dipoles, then magnetic dipoles, and finally first order multipoles. The dynamic behavior of these sources is then computed using a linear fit to the spatiotemporal data. The final step in the proceduremore » is to map each of the multipolar sources into an equivalent distributed source on the cortical surface. The method is illustrated through an application to epileptic interictal MEG data.« less

Large-scale 3D galaxy correlation function and non-Gaussianity

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

Raccanelli, Alvise; Doré, Olivier; Bertacca, Daniele

We investigate the properties of the 2-point galaxy correlation function at very large scales, including all geometric and local relativistic effects --- wide-angle effects, redshift space distortions, Doppler terms and Sachs-Wolfe type terms in the gravitational potentials. The general three-dimensional correlation function has a nonzero dipole and octupole, in addition to the even multipoles of the flat-sky limit. We study how corrections due to primordial non-Gaussianity and General Relativity affect the multipolar expansion, and we show that they are of similar magnitude (when f{sub NL} is small), so that a relativistic approach is needed. Furthermore, we look at how large-scalemore » corrections depend on the model for the growth rate in the context of modified gravity, and we discuss how a modified growth can affect the non-Gaussian signal in the multipoles.« less

The octapolic ellipsoidal term in magnetoencephalography

NASA Astrophysics Data System (ADS)

Dassios, George; Hadjiloizi, Demetra; Kariotou, Fotini

2009-01-01

The forward problem of magnetoencephalography (MEG) in ellipsoidal geometry has been studied by Dassios and Kariotou ["Magnetoencephalography in ellipsoidal geometry," J. Math. Phys. 44, 220 (2003)] using the theory of ellipsoidal harmonics. In fact, the analytic solution of the quadrupolic term for the magnetic induction field has been calculated in the case of a dipolar neuronal current. Nevertheless, since the quadrupolic term is only the leading nonvanishing term in the multipole expansion of the magnetic field, it contains not enough information for the construction of an effective algorithm to solve the inverse MEG problem, i.e., to recover the position and the orientation of a dipole from measurements of the magnetic field outside the head. For this task, the next multipole of the magnetic field is also needed. The present work provides exactly this octapolic contribution of the dipolar current to the expansion of the magnetic induction field. The octapolic term is expressed in terms of the ellipsoidal harmonics of the third degree, and therefore it provides the highest order terms that can be expressed in closed form using long but reasonable analytic and algebraic manipulations. In principle, the knowledge of the quadrupolic and the octapolic terms is enough to solve the inverse problem of identifying a dipole inside an ellipsoid. Nevertheless, a simple inversion algorithm for this problem is not yet known.

A Hierarchical Algorithm for Fast Debye Summation with Applications to Small Angle Scattering

PubMed Central

Gumerov, Nail A.; Berlin, Konstantin; Fushman, David; Duraiswami, Ramani

2012-01-01

Debye summation, which involves the summation of sinc functions of distances between all pair of atoms in three dimensional space, arises in computations performed in crystallography, small/wide angle X-ray scattering (SAXS/WAXS) and small angle neutron scattering (SANS). Direct evaluation of Debye summation has quadratic complexity, which results in computational bottleneck when determining crystal properties, or running structure refinement protocols that involve SAXS or SANS, even for moderately sized molecules. We present a fast approximation algorithm that efficiently computes the summation to any prescribed accuracy ε in linear time. The algorithm is similar to the fast multipole method (FMM), and is based on a hierarchical spatial decomposition of the molecule coupled with local harmonic expansions and translation of these expansions. An even more efficient implementation is possible when the scattering profile is all that is required, as in small angle scattering reconstruction (SAS) of macromolecules. We examine the relationship of the proposed algorithm to existing approximate methods for profile computations, and show that these methods may result in inaccurate profile computations, unless an error bound derived in this paper is used. Our theoretical and computational results show orders of magnitude improvement in computation complexity over existing methods, while maintaining prescribed accuracy. PMID:22707386

Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

DOE PAGES

Zhang, Bo; Lu, Benzhuo; Cheng, Xiaolin; ...

2013-01-01

This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. Lastly, the potential of the solver is demonstrated with preliminary numericalmore » results.« less

Measurement of the generalized form factors near threshold via γ *p → nπ + at high Q 2

DOE PAGES

Park, K.; Adhikari, K. P.; Adikaram, D.; ...

2012-03-26

We report the first extraction of the pion-nucleon multipoles near the production threshold for the nπ + channel at relatively high momentum transfer (Q 2 up to 4.2 GeV 2). The dominance of the s-wave transverse multipole (E 0+), expected in this region, allowed us to access the generalized form factor G 1 within the light-cone sum rule (LCSR) framework as well as the axial form factor G A. The data analyzed in this work were collected by the nearly 4π CEBAF Large Acceptance Spectrometer (CLAS) using a 5.754-GeV electron beam on a proton target. The differential cross section andmore » the π-N multipole E 0+/G D were measured using two different methods, the LCSR and a direct multipole fit. The results from the two methods are found to be consistent and almost Q 2 independent.« less

Hadronic transition {chi}{sub c1}{yields}{eta}{sub c}{pi}{pi} at the Beijing Spectrometer BES and the Cornell CLEO-c

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

Lu Qin; Kuang Yuping; CCAST

2007-03-01

Hadronic transitions of the {chi}{sub cj} states have not been studied yet. We calculate the rate of the hadronic transition {chi}{sub c1}{yields}{eta}{sub c}{pi}{pi} in the framework of QCD multipole expansion. We show that this process can be studied experimentally at the upgraded Beijing Spectrometer BES III and the Cornell CLEO-c.

Fast multipole method using Cartesian tensor in beam dynamic simulation

DOE PAGES

Zhang, He; Huang, He; Li, Rui; ...

2017-03-06

Here, the fast multipole method (FMM) using traceless totally symmetric Cartesian tensor to calculate the Coulomb interaction between charged particles will be presented. The Cartesian tensor-based FMM can be generalized to treat other non-oscillating interactions with the help of the differential algebra or the truncated power series algebra. Issues on implementation of the FMM in beam dynamic simulations are also discussed.

Calculations of the binding affinities of protein-protein complexes with the fast multipole method

NASA Astrophysics Data System (ADS)

Kim, Bongkeun; Song, Jiming; Song, Xueyu

2010-09-01

In this paper, we used a coarse-grained model at the residue level to calculate the binding free energies of three protein-protein complexes. General formulations to calculate the electrostatic binding free energy and the van der Waals free energy are presented by solving linearized Poisson-Boltzmann equations using the boundary element method in combination with the fast multipole method. The residue level model with the fast multipole method allows us to efficiently investigate how the mutations on the active site of the protein-protein interface affect the changes in binding affinities of protein complexes. Good correlations between the calculated results and the experimental ones indicate that our model can capture the dominant contributions to the protein-protein interactions. At the same time, additional effects on protein binding due to atomic details are also discussed in the context of the limitations of such a coarse-grained model.

Utilizing fast multipole expansions for efficient and accurate quantum-classical molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Schwörer, Magnus; Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul

2015-03-01

Recently, a novel approach to hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations has been suggested [Schwörer et al., J. Chem. Phys. 138, 244103 (2013)]. Here, the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 103-105 molecules as negative gradients of a DFT/PMM hybrid Hamiltonian. The electrostatic interactions are efficiently described by a hierarchical fast multipole method (FMM). Adopting recent progress of this FMM technique [Lorenzen et al., J. Chem. Theory Comput. 10, 3244 (2014)], which particularly entails a strictly linear scaling of the computational effort with the system size, and adapting this revised FMM approach to the computation of the interactions between the DFT and PMM fragments of a simulation system, here, we show how one can further enhance the efficiency and accuracy of such DFT/PMM-MD simulations. The resulting gain of total performance, as measured for alanine dipeptide (DFT) embedded in water (PMM) by the product of the gains in efficiency and accuracy, amounts to about one order of magnitude. We also demonstrate that the jointly parallelized implementation of the DFT and PMM-MD parts of the computation enables the efficient use of high-performance computing systems. The associated software is available online.

System and method for trapping and measuring a charged particle in a liquid

DOEpatents

Reed, Mark A; Krstic, Predrag S; Guan, Weihua; Zhao, Xiongce

2013-07-23

A system and method for trapping a charged particle is disclosed. A time-varying periodic multipole electric potential is generated in a trapping volume. A charged particle under the influence of the multipole electric field is confined to the trapping volume. A three electrode configuration giving rise to a 3D Paul trap and a four planar electrode configuration giving rise to a 2D Paul trap are disclosed.

System and method for trapping and measuring a charged particle in a liquid

DOEpatents

Reed, Mark A; Krstic, Predrag S; Guan, Weihua; Zhao, Xiongce

2012-10-23

A system and method for trapping a charged particle is disclosed. A time-varying periodic multipole electric potential is generated in a trapping volume. A charged particle under the influence of the multipole electric field is confined to the trapping volume. A three electrode configuration giving rise to a 3D Paul trap and a four planar electrode configuration giving rise to a 2D Paul trap are disclosed.

Analytical transition-matrix treatment of electric multipole polarizabilities of hydrogen-like atoms

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

Kharchenko, V.F., E-mail: vkharchenko@bitp.kiev.ua

2015-04-15

The direct transition-matrix approach to the description of the electric polarization of the quantum bound system of particles is used to determine the electric multipole polarizabilities of the hydrogen-like atoms. It is shown that in the case of the bound system formed by the Coulomb interaction the corresponding inhomogeneous integral equation determining an off-shell scattering function, which consistently describes virtual multiple scattering, can be solved exactly analytically for all electric multipole polarizabilities. Our method allows to reproduce the known Dalgarno–Lewis formula for electric multipole polarizabilities of the hydrogen atom in the ground state and can also be applied to determinemore » the polarizability of the atom in excited bound states. - Highlights: • A new description for electric polarization of hydrogen-like atoms. • Expression for multipole polarizabilities in terms of off-shell scattering functions. • Derivation of integral equation determining the off-shell scattering function. • Rigorous analytic solving the integral equations both for ground and excited states. • Study of contributions of virtual multiple scattering to electric polarizabilities.« less

Localized surface plasmon mediated energy transfer in the vicinity of core-shell nanoparticle

NASA Astrophysics Data System (ADS)

Shishodia, Manmohan Singh; Juneja, Soniya

2016-05-01

Multipole spectral expansion based theory of energy transfer interactions between a donor and an acceptor molecule in the vicinity of a core-shell (nanoshell or core@shell) based plasmonic nanostructure is developed. In view of the diverse applications and rich plasmonic features such as tuning capability of surface plasmon (SP) frequencies, greater sensitivity to the change of dielectric environment, controllable redirection of electromagnetic radiation, closed form expressions for Energy Transfer Rate Enhancement Factor (ETREF) near core-shell particle are reported. The dependence of ETREF on different parameters is established through fitting equations, perceived to be of key importance for developing appropriate designs. The theoretical approach developed in the present work is capable of treating higher order multipoles, which, in turn, are also shown to play a crucial role in the present context. Moreover, closed form expressions derived in the present work can directly be used as formula, e.g., for designing SP based biosensors and estimating energy exchange between proteins and excitonic interactions in quantum dots.

Factorization of laser-pulse ionization probabilities in the multiphotonic regime

NASA Astrophysics Data System (ADS)

Della Picca, R.; Fiol, J.; Fainstein, P. D.

2013-09-01

We present a detailed study of the ionization probability of H and H_{2}^{+} induced by a short intense laser pulse. Starting from a Coulomb-Volkov description of the process we derive a multipole-like expansion where each term is factored into two contributions: one that accounts for the effect of the electromagnetic field on the free-electron final state and a second factor that depends only on the target structure. Such a separation may be valuable to solve complex atomic or molecular systems as well as to interpret the dynamics of the process in simpler terms. We show that the series expansion converges rapidly, and thus the inclusion of the first few terms is sufficient to produce accurate results.

Strong Evidence for Nucleon Resonances near 1900 MeV

DOE PAGES

Anisovich, A. V.; Burkert, V.; Hadžimehmedović, M.; ...

2017-08-11

Data on the reaction yp→K +A from the CLAS experiments are used to derive the leading multipoles, E 0+, M 1-, E 1+, and M 1+, from the production threshold to 2180 MeV in 24 slices of the invariant mass. The four multipoles are determined without any constraints. The multipoles are fitted using a multichannel L+P model that allows us to search for singularities and to extract the positions of poles on the complex energy plane in an almost model-independent method. The multipoles are also used as additional constraints in an energy-dependent analysis of a large body of pion andmore » photoinduced reactions within the Bonn-Gatchina partial wave analysis. The study confirms the existence of poles due to nucleon resonances with spin parity J P=1/2 -, 1/2 +, and 3/2 + in the region at about 1.9 GeV.« less

Multipole correction of atomic monopole models of molecular charge distribution. I. Peptides

NASA Technical Reports Server (NTRS)

Sokalski, W. A.; Keller, D. A.; Ornstein, R. L.; Rein, R.

1993-01-01

The defects in atomic monopole models of molecular charge distribution have been analyzed for several model-blocked peptides and compared with accurate quantum chemical values. The results indicate that the angular characteristics of the molecular electrostatic potential around functional groups capable of forming hydrogen bonds can be considerably distorted within various models relying upon isotropic atomic charges only. It is shown that these defects can be corrected by augmenting the atomic point charge models by cumulative atomic multipole moments (CAMMs). Alternatively, sets of off-center atomic point charges could be automatically derived from respective multipoles, providing approximately equivalent corrections. For the first time, correlated atomic multipoles have been calculated for N-acetyl, N'-methylamide-blocked derivatives of glycine, alanine, cysteine, threonine, leucine, lysine, and serine using the MP2 method. The role of the correlation effects in the peptide molecular charge distribution are discussed.

Strong Evidence for Nucleon Resonances near 1900 MeV

NASA Astrophysics Data System (ADS)

Anisovich, A. V.; Burkert, V.; Hadžimehmedović, M.; Ireland, D. G.; Klempt, E.; Nikonov, V. A.; Omerović, R.; Osmanović, H.; Sarantsev, A. V.; Stahov, J.; Švarc, A.; Thoma, U.

2017-08-01

Data on the reaction γ p →K+Λ from the CLAS experiments are used to derive the leading multipoles, E0 +, M1 -, E1 +, and M1 +, from the production threshold to 2180 MeV in 24 slices of the invariant mass. The four multipoles are determined without any constraints. The multipoles are fitted using a multichannel L +P model that allows us to search for singularities and to extract the positions of poles on the complex energy plane in an almost model-independent method. The multipoles are also used as additional constraints in an energy-dependent analysis of a large body of pion and photoinduced reactions within the Bonn-Gatchina partial wave analysis. The study confirms the existence of poles due to nucleon resonances with spin parity JP=1 /2- , 1 /2+ , and 3 /2+ in the region at about 1.9 GeV.

Rare-Earth Fourth-Order Multipole Moment in Cubic ErCo2 Probed by Linear Dichroism in Core-Level Photoemission

NASA Astrophysics Data System (ADS)

Abozeed, Amina A.; Kadono, Toshiharu; Sekiyama, Akira; Fujiwara, Hidenori; Higashiya, Atsushi; Yamasaki, Atsushi; Kanai, Yuina; Yamagami, Kohei; Tamasaku, Kenji; Yabashi, Makina; Ishikawa, Tetsuya; Andreev, Alexander V.; Wada, Hirofumi; Imada, Shin

2018-03-01

We developed a method to experimentally quantify the fourth-order multipole moment of the rare-earth 4f orbital. Linear dichroism (LD) in the Er 3d5/2 core-level photoemission spectra of cubic ErCo2 was measured using bulk-sensitive hard X-ray photoemission spectroscopy. Theoretical calculation reproduced the observed LD, and the result showed that the observed result does not contradict the suggested Γ 83 ground state. Theoretical calculation further showed a linear relationship between the LD size and the size of the fourth-order multipole moment of the Er3+ ion, which is proportional to the expectation value < O40 + 5O44> , where Onm are the Stevens operators. These analyses indicate that the LD in 3d photoemission spectra can be used to quantify the average fourth-order multipole moment of rare-earth atoms in a cubic crystal electric field.

Multipoles and Force on External Points for a Two-layered Spheroidal Liquid Mass Rotating Differentialy

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

Cisneros-Parra, Joel U.; Martinez-Herrera, Francisco J.; Montalvo-Castro, J. Daniel

We recently reported on a series of equilibrium figures for a self-gravitating heterogeneous liquid body, consisting of two concentric distorted spheroids, “nucleus” and “atmosphere,” each endowed with its own internal motion of differential rotation. In our current work, we calculate the body’s force at external points and obtain a multipolar expansion of the potential. We also give an account of figures with prolate nuclei, which remained unnoticed by us in our former paper.

RichMol: A general variational approach for rovibrational molecular dynamics in external electric fields

NASA Astrophysics Data System (ADS)

Owens, Alec; Yachmenev, Andrey

2018-03-01

In this paper, a general variational approach for computing the rovibrational dynamics of polyatomic molecules in the presence of external electric fields is presented. Highly accurate, full-dimensional variational calculations provide a basis of field-free rovibrational states for evaluating the rovibrational matrix elements of high-rank Cartesian tensor operators and for solving the time-dependent Schrödinger equation. The effect of the external electric field is treated as a multipole moment expansion truncated at the second hyperpolarizability interaction term. Our fully numerical and computationally efficient method has been implemented in a new program, RichMol, which can simulate the effects of multiple external fields of arbitrary strength, polarization, pulse shape, and duration. Illustrative calculations of two-color orientation and rotational excitation with an optical centrifuge of NH3 are discussed.

Boundary integral equation analysis for suspension of spheres in Stokes flow

NASA Astrophysics Data System (ADS)

Corona, Eduardo; Veerapaneni, Shravan

2018-06-01

We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical expressions for evaluating the operators away from the boundary. When two particle are located close to each other, we use a truncated series expansion to compute the hydrodynamic interaction. On the other hand, we use the standard spectrally accurate quadrature scheme to evaluate smooth integrals on the far-field, and accelerate the resulting discrete sums using the fast multipole method (FMM). We employ this discretization scheme to analyze several boundary integral formulations of interest including those arising in porous media flow, active matter and magneto-hydrodynamics of rigid particles. We provide numerical results verifying the accuracy and scaling of their evaluation.

Real-time digital signal recovery for a multi-pole low-pass transfer function system.

PubMed

Lee, Jhinhwan

2017-08-01

In order to solve the problems of waveform distortion and signal delay by many physical and electrical systems with multi-pole linear low-pass transfer characteristics, a simple digital-signal-processing (DSP)-based method of real-time recovery of the original source waveform from the distorted output waveform is proposed. A mathematical analysis on the convolution kernel representation of the single-pole low-pass transfer function shows that the original source waveform can be accurately recovered in real time using a particular moving average algorithm applied on the input stream of the distorted waveform, which can also significantly reduce the overall delay time constant. This method is generalized for multi-pole low-pass systems and has noise characteristics of the inverse of the low-pass filter characteristics. This method can be applied to most sensors and amplifiers operating close to their frequency response limits to improve the overall performance of data acquisition systems and digital feedback control systems.

Atomic Forces for Geometry-Dependent Point Multipole and Gaussian Multipole Models

PubMed Central

Elking, Dennis M.; Perera, Lalith; Duke, Robert; Darden, Thomas; Pedersen, Lee G.

2010-01-01

In standard treatments of atomic multipole models, interaction energies, total molecular forces, and total molecular torques are given for multipolar interactions between rigid molecules. However, if the molecules are assumed to be flexible, two additional multipolar atomic forces arise due to 1) the transfer of torque between neighboring atoms, and 2) the dependence of multipole moment on internal geometry (bond lengths, bond angles, etc.) for geometry-dependent multipole models. In the current study, atomic force expressions for geometry-dependent multipoles are presented for use in simulations of flexible molecules. The atomic forces are derived by first proposing a new general expression for Wigner function derivatives ∂Dlm′m/∂Ω. The force equations can be applied to electrostatic models based on atomic point multipoles or Gaussian multipole charge density. Hydrogen bonded dimers are used to test the inter-molecular electrostatic energies and atomic forces calculated by geometry-dependent multipoles fit to the ab initio electrostatic potential (ESP). The electrostatic energies and forces are compared to their reference ab initio values. It is shown that both static and geometry-dependent multipole models are able to reproduce total molecular forces and torques with respect to ab initio, while geometry-dependent multipoles are needed to reproduce ab initio atomic forces. The expressions for atomic force can be used in simulations of flexible molecules with atomic multipoles. In addition, the results presented in this work should lead to further development of next generation force fields composed of geometry-dependent multipole models. PMID:20839297

Testing statistical isotropy in cosmic microwave background polarization maps

NASA Astrophysics Data System (ADS)

Rath, Pranati K.; Samal, Pramoda Kumar; Panda, Srikanta; Mishra, Debesh D.; Aluri, Pavan K.

2018-04-01

We apply our symmetry based Power tensor technique to test conformity of PLANCK Polarization maps with statistical isotropy. On a wide range of angular scales (l = 40 - 150), our preliminary analysis detects many statistically anisotropic multipoles in foreground cleaned full sky PLANCK polarization maps viz., COMMANDER and NILC. We also study the effect of residual foregrounds that may still be present in the Galactic plane using both common UPB77 polarization mask, as well as the individual component separation method specific polarization masks. However, some of the statistically anisotropic modes still persist, albeit significantly in NILC map. We further probed the data for any coherent alignments across multipoles in several bins from the chosen multipole range.

New Distributed Multipole Methods for Accurate Electrostatics for Large-Scale Biomolecular Simultations

NASA Astrophysics Data System (ADS)

Sagui, Celeste

2006-03-01

An accurate and numerically efficient treatment of electrostatics is essential for biomolecular simulations, as this stabilizes much of the delicate 3-d structure associated with biomolecules. Currently, force fields such as AMBER and CHARMM assign ``partial charges'' to every atom in a simulation in order to model the interatomic electrostatic forces, so that the calculation of the electrostatics rapidly becomes the computational bottleneck in large-scale simulations. There are two main issues associated with the current treatment of classical electrostatics: (i) how does one eliminate the artifacts associated with the point-charges (e.g., the underdetermined nature of the current RESP fitting procedure for large, flexible molecules) used in the force fields in a physically meaningful way? (ii) how does one efficiently simulate the very costly long-range electrostatic interactions? Recently, we have dealt with both of these challenges as follows. In order to improve the description of the molecular electrostatic potentials (MEPs), a new distributed multipole analysis based on localized functions -- Wannier, Boys, and Edminston-Ruedenberg -- was introduced, which allows for a first principles calculation of the partial charges and multipoles. Through a suitable generalization of the particle mesh Ewald (PME) and multigrid method, one can treat electrostatic multipoles all the way to hexadecapoles all without prohibitive extra costs. The importance of these methods for large-scale simulations will be discussed, and examplified by simulations from polarizable DNA models.

From dipolar to multipolar interactions between ultracold Feshbach molecules

NASA Astrophysics Data System (ADS)

Quéméner, Goulven; Lepers, Maxence; Luc-Koenig, Eliane; Dulieu, Olivier

2016-05-01

Using the multipolar expansion of electrostatic and magnetostatic potential energies, we characterize the long-range interactions between two weakly-bound diatomic molecules, taking as an example the paramagnetic Er2 Feshbach molecules which were produced recently. The interaction between atomic magnetic dipoles gives rise to the usual R-3 leading term of the multipolar expansion, where R is the intermolecular distance. We show that additional terms scaling as R-5, R-7 and so on also appear, which are strongly anisotropic with respect to the orientation of the molecules. These terms can be seen as effective molecular multipole moments reflecting the spatial extension of the molecules which is non-negligible compared to R. We acknowledge the financial support of the COPOMOL project (ANR-13-IS04-0004) from Agence Nationale de la Recherche.

Geometry and solid angle corrections for accurate measurement of multipole and parity mixing ratios using nuclear orientation

NASA Astrophysics Data System (ADS)

Roccia, S.; Gaulard, C.; Étilé, A.; Chakma, R.

2017-07-01

In the context of nuclear orientation, we propose a new method to correct the multipole mixing ratios for asymmetries in the geometry of the setup but also in the detection system. This method is also robust against temperature fluctuations, beam intensity fluctuations and uncertainties in the nuclear structure of the nuclei. Additionally, this method provides a natural way to combine data from different detectors and make good use of all available statistics. We could use this method to demonstrate the accuracy that can be reached with the PolarEx setup now installed at the ALTO facility.

Global Aspects of Charged Particle Motion in Axially Symmetric Multipole Magnetic Fields

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2003-01-01

The motion of a single charged particle in the space outside of a compact region of steady currents is investigated. The charged particle is assumed to produce negligible electromagnetic radiation, so that its energy is conserved. The source of the magnetic field is represented as a point multipole. After a general description, attention is focused on magnetic fields with axial symmetry. Lagrangian dynamical theory is utilized to identify constants of the motion as well as the equations of motion themselves. The qualitative method of Stonner is used to examine charged particle motion in axisymmetric multipole fields of all orders. Although the equations of motion generally have no analytical solutions and must be integrated numerically to produce a specific orbit, a topological examination of dynamics is possible, and can be used, d la Stonner, to completely describe the global aspects of the motion of a single charged particle in a space with an axisymmetric multipole magnetic field.

3D Lagrangian VPM: simulations of the near-wake of an actuator disc and horizontal axis wind turbine

NASA Astrophysics Data System (ADS)

Berdowski, T.; Ferreira, C.; Walther, J.

2016-09-01

The application of a 3-dimensional Lagrangian vortex particle method has been assessed for modelling the near-wake of an axisymmetrical actuator disc and 3-bladed horizontal axis wind turbine with prescribed circulation from the MEXICO (Model EXperiments In COntrolled conditions) experiment. The method was developed in the framework of the open- source Parallel Particle-Mesh library for handling the efficient data-parallelism on a CPU (Central Processing Unit) cluster, and utilized a O(N log N)-type fast multipole method for computational acceleration. Simulations with the actuator disc resulted in a wake expansion, velocity deficit profile, and induction factor that showed a close agreement with theoretical, numerical, and experimental results from literature. Also the shear layer expansion was present; the Kelvin-Helmholtz instability in the shear layer was triggered due to the round-off limitations of a numerical method, but this instability was delayed to beyond 1 diameter downstream due to the particle smoothing. Simulations with the 3-bladed turbine demonstrated that a purely 3-dimensional flow representation is challenging to model with particles. The manifestation of local complex flow structures of highly stretched vortices made the simulation unstable, but this was successfully counteracted by the application of a particle strength exchange scheme. The axial and radial velocity profile over the near wake have been compared to that of the original MEXICO experiment, which showed close agreement between results.

Towards an accurate representation of electrostatics in classical force fields: Efficient implementation of multipolar interactions in biomolecular simulations

NASA Astrophysics Data System (ADS)

Sagui, Celeste; Pedersen, Lee G.; Darden, Thomas A.

2004-01-01

The accurate simulation of biologically active macromolecules faces serious limitations that originate in the treatment of electrostatics in the empirical force fields. The current use of "partial charges" is a significant source of errors, since these vary widely with different conformations. By contrast, the molecular electrostatic potential (MEP) obtained through the use of a distributed multipole moment description, has been shown to converge to the quantum MEP outside the van der Waals surface, when higher order multipoles are used. However, in spite of the considerable improvement to the representation of the electronic cloud, higher order multipoles are not part of current classical biomolecular force fields due to the excessive computational cost. In this paper we present an efficient formalism for the treatment of higher order multipoles in Cartesian tensor formalism. The Ewald "direct sum" is evaluated through a McMurchie-Davidson formalism [L. McMurchie and E. Davidson, J. Comput. Phys. 26, 218 (1978)]. The "reciprocal sum" has been implemented in three different ways: using an Ewald scheme, a particle mesh Ewald (PME) method, and a multigrid-based approach. We find that even though the use of the McMurchie-Davidson formalism considerably reduces the cost of the calculation with respect to the standard matrix implementation of multipole interactions, the calculation in direct space remains expensive. When most of the calculation is moved to reciprocal space via the PME method, the cost of a calculation where all multipolar interactions (up to hexadecapole-hexadecapole) are included is only about 8.5 times more expensive than a regular AMBER 7 [D. A. Pearlman et al., Comput. Phys. Commun. 91, 1 (1995)] implementation with only charge-charge interactions. The multigrid implementation is slower but shows very promising results for parallelization. It provides a natural way to interface with continuous, Gaussian-based electrostatics in the future. It is hoped that this new formalism will facilitate the systematic implementation of higher order multipoles in classical biomolecular force fields.

Radical-Driven Silicon Surface Passivation for Organic-Inorganic Hybrid Photovoltaics

NASA Astrophysics Data System (ADS)

Chandra, Nitish

The advent of metamaterials has increased the complexity of possible light-matter interactions, creating gaps in knowledge and violating various commonly used approximations and rendering some common mathematical frameworks incomplete. Our forward scattering experiments on metallic shells and cavities have created a need for a rigorous geometry-based analysis of scattering problems and more rigorous current distribution descriptions in the volume of the scattering object. In order to build an accurate understanding of these interactions, we have revisited the fundamentals of Maxwell's equations, electromagnetic potentials and boundary conditions to build a bottom-up geometry-based analysis of scattering. Individual structures or meta-atoms can be designed to localize the incident electromagnetic radiation in order to create a change in local constitutive parameters and possible nonlinear responses. Hence, in next generation engineered materials, an accurate determination of current distribution on the surface and in the structure's volume play an important role in describing and designing desired properties. Multipole expansions of the exact current distribution determined using principles of differential geometry provides an elegant way to study these local interactions of meta-atoms. The dynamics of the interactions can be studied using the behavior of the polarization and magnetization densities generated by localized current densities interacting with the electromagnetic potentials associated with the incident waves. The multipole method combined with propagation of electromagnetic potentials can be used to predict a large variety of linear and nonlinear physical phenomena. This has been demonstrated in experiments that enable the analog detection of sources placed at subwavelength separation by using time reversal of observed signals. Time reversal is accomplished by reversing the direction of the magnetic dipole in bianisotropic metasurfaces while simultaneously providing a method to reduce the losses often observed when light interacts with meta-structures.

Alignments of parity even/odd-only multipoles in CMB

NASA Astrophysics Data System (ADS)

Aluri, Pavan K.; Ralston, John P.; Weltman, Amanda

2017-12-01

We compare the statistics of parity even and odd multipoles of the cosmic microwave background (CMB) sky from Planck full mission temperature measurements. An excess power in odd multipoles compared to even multipoles has previously been found on large angular scales. Motivated by this apparent parity asymmetry, we evaluate directional statistics associated with even compared to odd multipoles, along with their significances. Primary tools are the Power tensor and Alignment tensor statistics. We limit our analysis to the first 60 multipoles i.e. l = [2, 61]. We find no evidence for statistically unusual alignments of even parity multipoles. More than one independent statistic finds evidence for alignments of anisotropy axes of odd multipoles, with a significance equivalent to ∼2σ or more. The robustness of alignment axes is tested by making Galactic cuts and varying the multipole range. Very interestingly, the region spanned by the (a)symmetry axes is found to broadly contain other parity (a)symmetry axes previously observed in the literature.

Stray field signatures of Néel textured skyrmions in Ir/Fe/Co/Pt multilayer films

NASA Astrophysics Data System (ADS)

Yagil, A.; Almoalem, A.; Soumyanarayanan, Anjan; Tan, Anthony K. C.; Raju, M.; Panagopoulos, C.; Auslaender, O. M.

2018-05-01

Skyrmions are nanoscale spin configurations with topological properties that hold great promise for spintronic devices. Here, we establish their Néel texture, helicity, and size in Ir/Fe/Co/Pt multilayer films by constructing a multipole expansion to model their stray field signatures and applying it to magnetic force microscopy images. Furthermore, the demonstrated sensitivity to inhomogeneity in skyrmion properties, coupled with a unique capability to estimate the pinning force governing dynamics, portend broad applicability in the burgeoning field of topological spin textures.

First Principles Model of Electric Cable Braid Penetration with Dielectrics

DOE PAGES

Campione, Salvatore; Warne, Larry Kevin; Langston, William L.; ...

2018-01-01

In this study, we report the formulation to account for dielectrics in a first principles multipole-based cable braid electromagnetic penetration model. To validate our first principles model, we consider a one-dimensional array of wires, which can be modeled analytically with a multipole-conformal mapping expansion for the wire charges; however, the first principles model can be readily applied to realistic cable geometries. We compare the elastance (i.e. the inverse of the capacitance) results from the first principles cable braid electromagnetic penetration model to those obtained using the analytical model. The results are found in good agreement up to a radius tomore » half spacing ratio of 0.5-0.6, depending on the permittivity of the dielectric used, within the characteristics of many commercial cables. We observe that for typical relative permittivities encountered in braided cables, the transfer elastance values are essentially the same as those of free space; the self-elastance values are also approximated by the free space solution as long as the dielectric discontinuity is taken into account for the planar mode.« less

Localized surface plasmon mediated energy transfer in the vicinity of core-shell nanoparticle

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

Shishodia, Manmohan Singh, E-mail: manmohan@gbu.ac.in; Juneja, Soniya

2016-05-28

Multipole spectral expansion based theory of energy transfer interactions between a donor and an acceptor molecule in the vicinity of a core-shell (nanoshell or core@shell) based plasmonic nanostructure is developed. In view of the diverse applications and rich plasmonic features such as tuning capability of surface plasmon (SP) frequencies, greater sensitivity to the change of dielectric environment, controllable redirection of electromagnetic radiation, closed form expressions for Energy Transfer Rate Enhancement Factor (ETREF) near core-shell particle are reported. The dependence of ETREF on different parameters is established through fitting equations, perceived to be of key importance for developing appropriate designs. Themore » theoretical approach developed in the present work is capable of treating higher order multipoles, which, in turn, are also shown to play a crucial role in the present context. Moreover, closed form expressions derived in the present work can directly be used as formula, e.g., for designing SP based biosensors and estimating energy exchange between proteins and excitonic interactions in quantum dots.« less

A 5 x 40 cm rectangular-beam multipole ion source

NASA Technical Reports Server (NTRS)

Robinson, R. S.; Kaufman, H. R.; Haynes, C. M.

1981-01-01

A rectangular ion source particularly suited for the continuous sputter processing of materials over a wide area is discussed. A multipole magnetic field configuration was used to design an ion source with a 5 x 40 cm beam area, while a three-grid ion optics system was used to maximize ion current density at the design ion energy of 500 eV. An average extracted current density of about 4 mA/sq cm could be obtained from 500 eV Ar ions. The difference between the experimental performance and the design value of 6 mA/sq cm is attributed to grid misalignment due to thermal expansion. The discharge losses at typical operating conditions ranged from about 600 to 1000 eV/ion, in reasonable agreement with the design value of 800 eV/ion. The use of multiple rectangular-beam ion sources to process wider areas than would be possible with a single source was also studied, and the most uniform coverage was found to be obtainable with a 0 to 2 cm overlap.

First Principles Model of Electric Cable Braid Penetration with Dielectrics

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

Campione, Salvatore; Warne, Larry Kevin; Langston, William L.

In this study, we report the formulation to account for dielectrics in a first principles multipole-based cable braid electromagnetic penetration model. To validate our first principles model, we consider a one-dimensional array of wires, which can be modeled analytically with a multipole-conformal mapping expansion for the wire charges; however, the first principles model can be readily applied to realistic cable geometries. We compare the elastance (i.e. the inverse of the capacitance) results from the first principles cable braid electromagnetic penetration model to those obtained using the analytical model. The results are found in good agreement up to a radius tomore » half spacing ratio of 0.5-0.6, depending on the permittivity of the dielectric used, within the characteristics of many commercial cables. We observe that for typical relative permittivities encountered in braided cables, the transfer elastance values are essentially the same as those of free space; the self-elastance values are also approximated by the free space solution as long as the dielectric discontinuity is taken into account for the planar mode.« less

HPAM: Hirshfeld Partitioned Atomic Multipoles

PubMed Central

Elking, Dennis M.; Perera, Lalith; Pedersen, Lee G.

2011-01-01

An implementation of the Hirshfeld (HD) and Hirshfeld-Iterated (HD-I) atomic charge density partitioning schemes is described. Atomic charges and atomic multipoles are calculated from the HD and HD-I atomic charge densities for arbitrary atomic multipole rank lmax on molecules of arbitrary shape and size. The HD and HD-I atomic charges/multipoles are tested by comparing molecular multipole moments and the electrostatic potential (ESP) surrounding a molecule with their reference ab initio values. In general, the HD-I atomic charges/multipoles are found to better reproduce ab initio electrostatic properties over HD atomic charges/multipoles. A systematic increase in precision for reproducing ab initio electrostatic properties is demonstrated by increasing the atomic multipole rank from lmax = 0 (atomic charges) to lmax = 4 (atomic hexadecapoles). Both HD and HD-I atomic multipoles up to rank lmax are shown to exactly reproduce ab initio molecular multipole moments of rank L for L ≤ lmax. In addition, molecular dipole moments calculated by HD, HD-I, and ChelpG atomic charges only (lmax = 0) are compared with reference ab initio values. Significant errors in reproducing ab initio molecular dipole moments are found if only HD or HD-I atomic charges used. PMID:22140274

An efficient blocking M2L translation for low-frequency fast multipole method in three dimensions

NASA Astrophysics Data System (ADS)

Takahashi, Toru; Shimba, Yuta; Isakari, Hiroshi; Matsumoto, Toshiro

2016-05-01

We propose an efficient scheme to perform the multipole-to-local (M2L) translation in the three-dimensional low-frequency fast multipole method (LFFMM). Our strategy is to combine a group of matrix-vector products associated with M2L translation into a matrix-matrix product in order to diminish the memory traffic. For this purpose, we first developed a grouping method (termed as internal blocking) based on the congruent transformations (rotational and reflectional symmetries) of M2L-translators for each target box in the FMM hierarchy (adaptive octree). Next, we considered another method of grouping (termed as external blocking) that was able to handle M2L translations for multiple target boxes collectively by using the translational invariance of the M2L translation. By combining these internal and external blockings, the M2L translation can be performed efficiently whilst preservingthe numerical accuracy exactly. We assessed the proposed blocking scheme numerically and applied it to the boundary integral equation method to solve electromagnetic scattering problems for perfectly electrical conductor. From the numerical results, it was found that the proposed M2L scheme achieved a few times speedup compared to the non-blocking scheme.

Point charge representation of multicenter multipole moments in calculation of electrostatic properties

NASA Technical Reports Server (NTRS)

Sokalski, W. A.; Shibata, M.; Ornstein, R. L.; Rein, R.

1993-01-01

Distributed Point Charge Models (PCM) for CO, (H2O)2, and HS-SH molecules have been computed from analytical expressions using multi-center multipole moments. The point charges (set of charges including both atomic and non-atomic positions) exactly reproduce both molecular and segmental multipole moments, thus constituting an accurate representation of the local anisotropy of electrostatic properties. In contrast to other known point charge models, PCM can be used to calculate not only intermolecular, but also intramolecular interactions. Comparison of these results with more accurate calculations demonstrated that PCM can correctly represent both weak and strong (intramolecular) interactions, thus indicating the merit of extending PCM to obtain improved potentials for molecular mechanics and molecular dynamics computational methods.

Revision of FMM-Yukawa: An adaptive fast multipole method for screened Coulomb interactions

NASA Astrophysics Data System (ADS)

Zhang, Bo; Huang, Jingfang; Pitsianis, Nikos P.; Sun, Xiaobai

2010-12-01

FMM-YUKAWA is a mathematical software package primarily for rapid evaluation of the screened Coulomb interactions of N particles in three dimensional space. Since its release, we have revised and re-organized the data structure, software architecture, and user interface, for the purpose of enabling more flexible, broader and easier use of the package. The package and its documentation are available at http://www.fastmultipole.org/, along with a few other closely related mathematical software packages. New version program summaryProgram title: FMM-Yukawa Catalogue identifier: AEEQ_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEQ_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL 2.0 No. of lines in distributed program, including test data, etc.: 78 704 No. of bytes in distributed program, including test data, etc.: 854 265 Distribution format: tar.gz Programming language: FORTRAN 77, FORTRAN 90, and C. Requires gcc and gfortran version 4.4.3 or later Computer: All Operating system: Any Classification: 4.8, 4.12 Catalogue identifier of previous version: AEEQ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 2331 Does the new version supersede the previous version?: Yes Nature of problem: To evaluate the screened Coulomb potential and force field of N charged particles, and to evaluate a convolution type integral where the Green's function is the fundamental solution of the modified Helmholtz equation. Solution method: The new version of fast multipole method (FMM) that diagonalizes the multipole-to-local translation operator is applied with the tree structure adaptive to sample particle locations. Reasons for new version: To handle much larger particle ensembles, to enable the iterative use of the subroutines in a solver, and to remove potential contention in assignments for parallelization. Summary of revisions: The software package FMM-Yukawa has been revised and re-organized in data structure, software architecture, programming methods, and user interface. The revision enables more flexible use of the package and economic use of memory resources. It consists of five stages. The initial stage (stage 1) determines, based on the accuracy requirement and FMM theory, the length of multipole expansions and the number of quadrature points for diagonalization, and loads the quadrature nodes and weights that are computed off line. Stage 2 constructs the oct-tree and interaction lists, with adaptation to the sparsity or density of particles and employing a dynamic memory allocation scheme at every tree level. Stage 3 executes the core FMM subroutine for numerical calculation of the particle interactions. The subroutine can now be used iteratively as in a solver, while the particle locations remain the same. Stage 4 releases the memory allocated in Stage 2 for the adaptive tree and interaction lists. The user can modify the iterative routine easily. When the particle locations are changed such as in a molecular dynamics simulation, stage 2 to 4 can also be used together repeatedly. The final stage releases the memory space used for the quadrature and other remaining FMM parameters. Programs at the stage level and at the user interface are re-written in the C programming language, while most of the translation and interaction operations remain in FORTRAN. As a result of the change in data structures and memory allocation, the revised package can accommodate much larger particle ensembles while maintaining the same accuracy-efficiency performance. The new version is also developed as an important precursor to its parallel counterpart on multi-core or many core processors in a shared memory programming environment. Particularly, in order to ensure mutual exclusion in concurrent updates without incurring extra latency, we have replaced all the assignment statements at a source box that put its data to multiple target boxes with assignments at every target box that gather data from source boxes. This amounts to replacing the column version of matrix-vector multiplication with the row version. The matrix here, however, is in compressive representation. Sufficient care is taken in the revision not to alter the algorithmic complexity or numerical behavior, as concurrent writing potentially takes place in the upward calculation of the multipole expansion coefficients, interactions at every level of the FMM tree, and downward calculation of the local expansion coefficients. The software modules and their compositions are also organized according to the stages they are used. Demonstration files and makefiles for merging the user routines and the library routines are provided. Restrictions: Accuracy requirement is described in terms of three or six digits. Higher multiples of three digits will be allowed in a later version. Finer decimation in digits for accuracy specification may or may not be necessary. Unusual features: Ready and friendly for customized use and instrumental in expression of concurrency and dependency for efficient parallelization. Running time: The running time depends linearly on the number N of particles, and varies with the distribution characteristics of the particle distribution. It also depends on the accuracy requirement, a higher accuracy requirement takes relatively longer time. The code outperforms the direct summation method when N⩾750.

A spectral Poisson solver for kinetic plasma simulation

NASA Astrophysics Data System (ADS)

Szeremley, Daniel; Obberath, Jens; Brinkmann, Ralf

2011-10-01

Plasma resonance spectroscopy is a well established plasma diagnostic method, realized in several designs. One of these designs is the multipole resonance probe (MRP). In its idealized - geometrically simplified - version it consists of two dielectrically shielded, hemispherical electrodes to which an RF signal is applied. A numerical tool is under development which is capable of simulating the dynamics of the plasma surrounding the MRP in electrostatic approximation. In this contribution we concentrate on the specialized Poisson solver for that tool. The plasma is represented by an ensemble of point charges. By expanding both the charge density and the potential into spherical harmonics, a largely analytical solution of the Poisson problem can be employed. For a practical implementation, the expansion must be appropriately truncated. With this spectral solver we are able to efficiently solve the Poisson equation in a kinetic plasma simulation without the need of introducing a spatial discretization.

Method and apparatus for efficient photodetachment and purification of negative ion beams

DOEpatents

Beene, James R [Oak Ridge, TN; Liu, Yuan [Knoxville, TN; Havener, Charles C [Knoxville, TN

2008-02-26

Methods and apparatus are described for efficient photodetachment and purification of negative ion beams. A method of purifying an ion beam includes: inputting the ion beam into a gas-filled multipole ion guide, the ion beam including a plurality of ions; increasing a laser-ion interaction time by collisional cooling the plurality of ions using the gas-filled multipole ion guide, the plurality of ions including at least one contaminant; and suppressing the at least one contaminant by selectively removing the at least one contaminant from the ion beam by electron photodetaching at least a portion of the at least one contaminant using a laser beam.

Development of Fast Algorithms Using Recursion, Nesting and Iterations for Computational Electromagnetics

NASA Technical Reports Server (NTRS)

Chew, W. C.; Song, J. M.; Lu, C. C.; Weedon, W. H.

1995-01-01

In the first phase of our work, we have concentrated on laying the foundation to develop fast algorithms, including the use of recursive structure like the recursive aggregate interaction matrix algorithm (RAIMA), the nested equivalence principle algorithm (NEPAL), the ray-propagation fast multipole algorithm (RPFMA), and the multi-level fast multipole algorithm (MLFMA). We have also investigated the use of curvilinear patches to build a basic method of moments code where these acceleration techniques can be used later. In the second phase, which is mainly reported on here, we have concentrated on implementing three-dimensional NEPAL on a massively parallel machine, the Connection Machine CM-5, and have been able to obtain some 3D scattering results. In order to understand the parallelization of codes on the Connection Machine, we have also studied the parallelization of 3D finite-difference time-domain (FDTD) code with PML material absorbing boundary condition (ABC). We found that simple algorithms like the FDTD with material ABC can be parallelized very well allowing us to solve within a minute a problem of over a million nodes. In addition, we have studied the use of the fast multipole method and the ray-propagation fast multipole algorithm to expedite matrix-vector multiplication in a conjugate-gradient solution to integral equations of scattering. We find that these methods are faster than LU decomposition for one incident angle, but are slower than LU decomposition when many incident angles are needed as in the monostatic RCS calculations.

Multipolar electrostatics for proteins: atom-atom electrostatic energies in crambin.

PubMed

Yuan, Yongna; Mills, Matthew J L; Popelier, Paul L A

2014-02-15

Accurate electrostatics necessitates the use of multipole moments centered on nuclei or extra point charges centered away from the nuclei. Here, we follow the former alternative and investigate the convergence behavior of atom-atom electrostatic interactions in the pilot protein crambin. Amino acids are cut out from a Protein Data Bank structure of crambin, as single amino acids, di, or tripeptides, and are then capped with a peptide bond at each side. The atoms in the amino acids are defined through Quantum Chemical Topology (QCT) as finite volume electron density fragments. Atom-atom electrostatic energies are computed by means of a multipole expansion with regular spherical harmonics, up to a total interaction rank of L = ℓA+ ℓB + 1 = 10. The minimum internuclear distance in the convergent region of all the 15 possible types of atom-atom interactions in crambin that were calculated based on single amino acids are close to the values calculated from di and tripeptides. Values obtained at B3LYP/aug-cc-pVTZ and MP2/aug-cc-pVTZ levels are only slightly larger than those calculated at HF/6-31G(d,p) level. This convergence behavior is transferable to the well-known amyloid beta polypeptide Aβ1-42. Moreover, for a selected central atom, the influence of its neighbors on its multipole moments is investigated, and how far away this influence can be ignored is also determined. Finally, the convergence behavior of AMBER becomes closer to that of QCT with increasing internuclear distance. Copyright © 2013 Wiley Periodicals, Inc.

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

Gniewek, Piotr, E-mail: pgniewek@tiger.chem.uw.edu.pl; Jeziorski, Bogumił, E-mail: jeziorsk@chem.uw.edu.pl

The exchange splitting J of the interaction energy of the hydrogen atom with a proton is calculated using the conventional surface-integral formula J{sub surf}[Φ], the volume-integral formula of the symmetry-adapted perturbation theory J{sub SAPT}[Φ], and a variational volume-integral formula J{sub var}[Φ]. The calculations are based on the multipole expansion of the wave function Φ, which is divergent for any internuclear distance R. Nevertheless, the resulting approximations to the leading coefficient j{sub 0} in the large-R asymptotic series J(R) = 2e{sup −R−1}R(j{sub 0} + j{sub 1}R{sup −1} + j{sub 2}R{sup −2} + ⋯) converge with the rate corresponding to the convergencemore » radii equal to 4, 2, and 1 when the J{sub var}[Φ], J{sub surf}[Φ], and J{sub SAPT}[Φ] formulas are used, respectively. Additionally, we observe that also the higher j{sub k} coefficients are predicted correctly when the multipole expansion is used in the J{sub var}[Φ] and J{sub surf}[Φ] formulas. The symmetry adapted perturbation theory formula J{sub SAPT}[Φ] predicts correctly only the first two coefficients, j{sub 0} and j{sub 1}, gives a wrong value of j{sub 2}, and diverges for higher j{sub n}. Since the variational volume-integral formula can be easily generalized to many-electron systems and evaluated with standard basis-set techniques of quantum chemistry, it provides an alternative for the determination of the exchange splitting and the exchange contribution of the interaction potential in general.« less

An accurate metric for the spacetime around rotating neutron stars

NASA Astrophysics Data System (ADS)

Pappas, George

2017-04-01

The problem of having an accurate description of the spacetime around rotating neutron stars is of great astrophysical interest. For astrophysical applications, one needs to have a metric that captures all the properties of the spacetime around a rotating neutron star. Furthermore, an accurate appropriately parametrized metric, I.e. a metric that is given in terms of parameters that are directly related to the physical structure of the neutron star, could be used to solve the inverse problem, which is to infer the properties of the structure of a neutron star from astrophysical observations. In this work, we present such an approximate stationary and axisymmetric metric for the exterior of rotating neutron stars, which is constructed using the Ernst formalism and is parametrized by the relativistic multipole moments of the central object. This metric is given in terms of an expansion on the Weyl-Papapetrou coordinates with the multipole moments as free parameters and is shown to be extremely accurate in capturing the physical properties of a neutron star spacetime as they are calculated numerically in general relativity. Because the metric is given in terms of an expansion, the expressions are much simpler and easier to implement, in contrast to previous approaches. For the parametrization of the metric in general relativity, the recently discovered universal 3-hair relations are used to produce a three-parameter metric. Finally, a straightforward extension of this metric is given for scalar-tensor theories with a massless scalar field, which also admit a formulation in terms of an Ernst potential.

Method of reducing multipole content in a conductor assembly during manufacture

DOEpatents

Meinke, Rainer [Melbourne, FL

2011-08-09

A method for manufacture of a conductor assembly. The assembly is of the type which, when conducting current, generates a magnetic field or in which, in the presence of a changing magnetic field, a voltage is induced. In an example embodiment one or more first coil rows are formed. The assembly has multiple coil rows about an axis with outer coil rows formed about inner coil rows. A determination is made of deviations from specifications associated with the formed one or more first coil rows. One or more deviations correspond to a magnitude of a multipole field component which departs from a field specification. Based on the deviations, one or more wiring patterns are generated for one or more second coil rows to be formed about the one or more first coil rows. The one or more second coil rows are formed in the assembly. The magnitude of each multipole field component that departs from the field specification is offset.

Method of reducing multipole content in a conductor assembly during manufacture

DOEpatents

Meinke, Rainer

2013-08-20

A method for manufacture of a conductor assembly. The assembly is of the type which, when conducting current, generates a magnetic field or in which, in the presence of a changing magnetic field, a voltage is induced. In an example embodiment one or more first coil rows are formed. The assembly has multiple coil rows about an axis with outer coil rows formed about inner coil rows. A determination is made of deviations from specifications associated with the formed one or more first coil rows. One or more deviations correspond to a magnitude of a multipole field component which departs from a field specification. Based on the deviations, one or more wiring patterns are generated for one or more second coil rows to be formed about the one or more first coil rows. The one or more second coil rows are formed in the assembly. The magnitude of each multipole field component that departs from the field specification is offset.

Characterization of the International Linear Collider damping ring optics

NASA Astrophysics Data System (ADS)

Shanks, J.; Rubin, D. L.; Sagan, D.

2014-10-01

A method is presented for characterizing the emittance dilution and dynamic aperture for an arbitrary closed lattice that includes guide field magnet errors, multipole errors and misalignments. This method, developed and tested at the Cornell Electron Storage Ring Test Accelerator (CesrTA), has been applied to the damping ring lattice for the International Linear Collider (ILC). The effectiveness of beam based emittance tuning is limited by beam position monitor (BPM) measurement errors, number of corrector magnets and their placement, and correction algorithm. The specifications for damping ring magnet alignment, multipole errors, number of BPMs, and precision in BPM measurements are shown to be consistent with the required emittances and dynamic aperture. The methodology is then used to determine the minimum number of position monitors that is required to achieve the emittance targets, and how that minimum depends on the location of the BPMs. Similarly, the maximum tolerable multipole errors are evaluated. Finally, the robustness of each BPM configuration with respect to random failures is explored.

Design study of beam position monitors for measuring second-order moments of charged particle beams

NASA Astrophysics Data System (ADS)

Yanagida, Kenichi; Suzuki, Shinsuke; Hanaki, Hirofumi

2012-01-01

This paper presents a theoretical investigation on the multipole moments of charged particle beams in two-dimensional polar coordinates. The theoretical description of multipole moments is based on a single-particle system that is expanded to a multiparticle system by superposition, i.e., summing over all single-particle results. This paper also presents an analysis and design method for a beam position monitor (BPM) that detects higher-order (multipole) moments of a charged particle beam. To calculate the electric fields, a numerical analysis based on the finite difference method was created and carried out. Validity of the numerical analysis was proven by comparing the numerical with the analytical results for a BPM with circular cross section. Six-electrode BPMs with circular and elliptical cross sections were designed for the SPring-8 linac. The results of the numerical calculations show that the second-order moment can be detected for beam sizes ≧420μm (circular) and ≧550μm (elliptical).

The Atacama Cosmology Telescope: Calibration with the Wilkinson Microwave Anisotropy Probe Using Cross-Correlations

NASA Technical Reports Server (NTRS)

Hajian, Amir; Acquaviva, Viviana; Ade, Peter A. R.; Aguirre, Paula; Amiri, Mandana; Appel, John William; Barrientos, L. Felipe; Battistelli, Elia S.; Bond, John R.; Brown, Ben;

Generalization of the Gaussian electrostatic model: Extension to arbitrary angular momentum, distributed multipoles, and speedup with reciprocal space methods

NASA Astrophysics Data System (ADS)

Cisneros, G. Andrés; Piquemal, Jean-Philip; Darden, Thomas A.

2006-11-01

The simulation of biological systems by means of current empirical force fields presents shortcomings due to their lack of accuracy, especially in the description of the nonbonded terms. We have previously introduced a force field based on density fitting termed the Gaussian electrostatic model-0 (GEM-0) J.-P. Piquemal et al. [J. Chem. Phys. 124, 104101 (2006)] that improves the description of the nonbonded interactions. GEM-0 relies on density fitting methodology to reproduce each contribution of the constrained space orbital variation (CSOV) energy decomposition scheme, by expanding the electronic density of the molecule in s-type Gaussian functions centered at specific sites. In the present contribution we extend the Coulomb and exchange components of the force field to auxiliary basis sets of arbitrary angular momentum. Since the basis functions with higher angular momentum have directionality, a reference molecular frame (local frame) formalism is employed for the rotation of the fitted expansion coefficients. In all cases the intermolecular interaction energies are calculated by means of Hermite Gaussian functions using the McMurchie-Davidson [J. Comput. Phys. 26, 218 (1978)] recursion to calculate all the required integrals. Furthermore, the use of Hermite Gaussian functions allows a point multipole decomposition determination at each expansion site. Additionally, the issue of computational speed is investigated by reciprocal space based formalisms which include the particle mesh Ewald (PME) and fast Fourier-Poisson (FFP) methods. Frozen-core (Coulomb and exchange-repulsion) intermolecular interaction results for ten stationary points on the water dimer potential-energy surface, as well as a one-dimensional surface scan for the canonical water dimer, formamide, stacked benzene, and benzene water dimers, are presented. All results show reasonable agreement with the corresponding CSOV calculated reference contributions, around 0.1 and 0.15kcal/mol error for Coulomb and exchange, respectively. Timing results for single Coulomb energy-force calculations for (H2O)n, n =64, 128, 256, 512, and 1024, in periodic boundary conditions with PME and FFP at two different rms force tolerances are also presented. For the small and intermediate auxiliaries, PME shows faster times than FFP at both accuracies and the advantage of PME widens at higher accuracy, while for the largest auxiliary, the opposite occurs.

Generalization of the Gaussian electrostatic model: Extension to arbitrary angular momentum, distributed multipoles, and speedup with reciprocal space methods

PubMed Central

Cisneros, G. Andrés; Piquemal, Jean-Philip; Darden, Thomas A.

2007-01-01

The simulation of biological systems by means of current empirical force fields presents shortcomings due to their lack of accuracy, especially in the description of the nonbonded terms. We have previously introduced a force field based on density fitting termed the Gaussian electrostatic model-0 (GEM-0) J.-P. Piquemal et al. [J. Chem. Phys. 124, 104101 (2006)] that improves the description of the nonbonded interactions. GEM-0 relies on density fitting methodology to reproduce each contribution of the constrained space orbital variation (CSOV) energy decomposition scheme, by expanding the electronic density of the molecule in s-type Gaussian functions centered at specific sites. In the present contribution we extend the Coulomb and exchange components of the force field to auxiliary basis sets of arbitrary angular momentum. Since the basis functions with higher angular momentum have directionality, a reference molecular frame (local frame) formalism is employed for the rotation of the fitted expansion coefficients. In all cases the intermolecular interaction energies are calculated by means of Hermite Gaussian functions using the McMurchie-Davidson [J. Comput. Phys. 26, 218 (1978)] recursion to calculate all the required integrals. Furthermore, the use of Hermite Gaussian functions allows a point multipole decomposition determination at each expansion site. Additionally, the issue of computational speed is investigated by reciprocal space based formalisms which include the particle mesh Ewald (PME) and fast Fourier-Poisson (FFP) methods. Frozen-core (Coulomb and exchange-repulsion) intermolecular interaction results for ten stationary points on the water dimer potential-energy surface, as well as a one-dimensional surface scan for the canonical water dimer, formamide, stacked benzene, and benzene water dimers, are presented. All results show reasonable agreement with the corresponding CSOV calculated reference contributions, around 0.1 and 0.15 kcal/mol error for Coulomb and exchange, respectively. Timing results for single Coulomb energy-force calculations for (H2O)n, n=64, 128, 256, 512, and 1024, in periodic boundary conditions with PME and FFP at two different rms force tolerances are also presented. For the small and intermediate auxiliaries, PME shows faster times than FFP at both accuracies and the advantage of PME widens at higher accuracy, while for the largest auxiliary, the opposite occurs. PMID:17115732

Non-Gaussian structure of B-mode polarization after delensing

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

Namikawa, Toshiya; Nagata, Ryo, E-mail: namikawa@slac.stanford.edu, E-mail: rnagata@post.kek.jp

2015-10-01

The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. Inmore » this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. As a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.« less

Non-Gaussian structure of B-mode polarization after delensing

NASA Astrophysics Data System (ADS)

Namikawa, Toshiya; Nagata, Ryo

2015-10-01

The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. In this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. As a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.

Non-Gaussian structure of B-mode polarization after delensing

DOE PAGES

Namikawa, Toshiya; Nagata, Ryo

2015-10-01

The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. Inmore » this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. Furthermore, as a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.« less

Multiscale estimation of excess mass from gravity data

NASA Astrophysics Data System (ADS)

Castaldo, Raffaele; Fedi, Maurizio; Florio, Giovanni

2014-06-01

We describe a multiscale method to estimate the excess mass of gravity anomaly sources, based on the theory of source moments. Using a multipole expansion of the potential field and considering only the data along the vertical direction, a system of linear equations is obtained. The choice of inverting data along a vertical profile can help us to reduce the interference effects due to nearby anomalies and will allow a local estimate of the source parameters. A criterion is established allowing the selection of the optimal highest altitude of the vertical profile data and truncation order of the series expansion. The inversion provides an estimate of the total anomalous mass and of the depth to the centre of mass. The method has several advantages with respect to classical methods, such as the Gauss' method: (i) we need just a 1-D inversion to obtain our estimates, being the inverted data sampled along a single vertical profile; (ii) the resolution may be straightforward enhanced by using vertical derivatives; (iii) the centre of mass is also estimated, besides the excess mass; (iv) the method is very robust versus noise; (v) the profile may be chosen in such a way to minimize the effects from interfering anomalies or from side effects due to the a limited area extension. The multiscale estimation of excess mass method can be successfully used in various fields of application. Here, we analyse the gravity anomaly generated by a sulphide body in the Skelleftea ore district, North Sweden, obtaining source mass and volume estimates in agreement with the known information. We show also that these estimates are substantially improved with respect to those obtained with the classical approach.

Fast multipole methods on a cluster of GPUs for the meshless simulation of turbulence

NASA Astrophysics Data System (ADS)

Yokota, R.; Narumi, T.; Sakamaki, R.; Kameoka, S.; Obi, S.; Yasuoka, K.

2009-11-01

Recent advances in the parallelizability of fast N-body algorithms, and the programmability of graphics processing units (GPUs) have opened a new path for particle based simulations. For the simulation of turbulence, vortex methods can now be considered as an interesting alternative to finite difference and spectral methods. The present study focuses on the efficient implementation of the fast multipole method and pseudo-particle method on a cluster of NVIDIA GeForce 8800 GT GPUs, and applies this to a vortex method calculation of homogeneous isotropic turbulence. The results of the present vortex method agree quantitatively with that of the reference calculation using a spectral method. We achieved a maximum speed of 7.48 TFlops using 64 GPUs, and the cost performance was near 9.4/GFlops. The calculation of the present vortex method on 64 GPUs took 4120 s, while the spectral method on 32 CPUs took 4910 s.

Magnetic field of longitudinal gradient bend

NASA Astrophysics Data System (ADS)

Aiba, Masamitsu; Böge, Michael; Ehrlichman, Michael; Streun, Andreas

2018-06-01

The longitudinal gradient bend is an effective method for reducing the natural emittance in light sources. It is, however, not a common element. We have analyzed its magnetic field and derived a set of formulae. Based on the derivation, we discuss how to model the longitudinal gradient bend in accelerator codes that are used for designing electron storage rings. Strengths of multipole components can also be evaluated from the formulae, and we investigate the impact of higher order multipole components in a very low emittance lattice.

Microscopic Description of Electric and Magnetic Toroidal Multipoles in Hybrid Orbitals

NASA Astrophysics Data System (ADS)

Hayami, Satoru; Kusunose, Hiroaki

2018-03-01

We derive the quantum-mechanical operator expressions of multipoles under the space-time inversion group. We elucidate that electric and magnetic toroidal multipoles, in addition to ordinary non-toroidal ones, are fundamental pieces to express arbitrary electronic degrees of freedom. We show that electric (magnetic) toroidal multipoles higher than the dipole (monopole) can become active in a hybridized-orbital system. We also demonstrate emergent cross-correlated couplings between the electric, magnetic, and elastic degrees of freedom, such as magneto-electric and magneto(electro)-elastic coupling, under toroidal multipole orders.

Mass independent kinetic energy reducing inlet system for vacuum environment

DOEpatents

Reilly, Peter T.A.

2014-05-13

A particle inlet system comprises a first chamber having a limiting orifice for an incoming gas stream and a micrometer controlled expansion slit. Lateral components of the momentum of the particles are substantially cancelled due to symmetry of the configuration once the laminar flow converges at the expansion slit. The particles and flow into a second chamber, which is maintained at a lower pressure than the first chamber, and then moves into a third chamber including multipole guides for electromagnetically confining the particle. The vertical momentum of the particles descending through the center of the third chamber is minimized as an upward stream of gases reduces the downward momentum of the particles. The translational kinetic energy of the particles is near-zero irrespective of the mass of the particles at an exit opening of the third chamber, which may be advantageously employed to provide enhanced mass resolution in mass spectrometry.

Mass independent kinetic energy reducing inlet system for vacuum environment

DOEpatents

Reilly, Peter T. A. [Knoxville, TN

2010-12-14

A particle inlet system comprises a first chamber having a limiting orifice for an incoming gas stream and a micrometer controlled expansion slit. Lateral components of the momentum of the particles are substantially cancelled due to symmetry of the configuration once the laminar flow converges at the expansion slit. The particles and flow into a second chamber, which is maintained at a lower pressure than the first chamber, and then moves into a third chamber including multipole guides for electromagnetically confining the particle. The vertical momentum of the particles descending through the center of the third chamber is minimized as an upward stream of gases reduces the downward momentum of the particles. The translational kinetic energy of the particles is near-zero irrespective of the mass of the particles at an exit opening of the third chamber, which may be advantageously employed to provide enhanced mass resolution in mass spectrometry.

Mass independent kinetic energy reducing inlet system for vacuum environment

DOEpatents

Reilly, Peter T.A.

2013-12-03

A particle inlet system comprises a first chamber having a limiting orifice for an incoming gas stream and a micrometer controlled expansion slit. Lateral components of the momentum of the particles are substantially cancelled due to symmetry of the configuration once the laminar flow converges at the expansion slit. The particles and flow into a second chamber, which is maintained at a lower pressure than the first chamber, and then moves into a third chamber including multipole guides for electromagnetically confining the particle. The vertical momentum of the particles descending through the center of the third chamber is minimized as an upward stream of gases reduces the downward momentum of the particles. The translational kinetic energy of the particles is near-zero irrespective of the mass of the particles at an exit opening of the third chamber, which may be advantageously employed to provide enhanced mass resolution in mass spectrometry.

Gay-Berne and electrostatic multipole based coarse-grain potential in implicit solvent

NASA Astrophysics Data System (ADS)

Wu, Johnny; Zhen, Xia; Shen, Hujun; Li, Guohui; Ren, Pengyu

2011-10-01

A general, transferable coarse-grain (CG) framework based on the Gay-Berne potential and electrostatic point multipole expansion is presented for polypeptide simulations. The solvent effect is described by the Generalized Kirkwood theory. The CG model is calibrated using the results of all-atom simulations of model compounds in solution. Instead of matching the overall effective forces produced by atomic models, the fundamental intermolecular forces such as electrostatic, repulsion-dispersion, and solvation are represented explicitly at a CG level. We demonstrate that the CG alanine dipeptide model is able to reproduce quantitatively the conformational energy of all-atom force fields in both gas and solution phases, including the electrostatic and solvation components. Replica exchange molecular dynamics and microsecond dynamic simulations of polyalanine of 5 and 12 residues reveal that the CG polyalanines fold into "alpha helix" and "beta sheet" structures. The 5-residue polyalanine displays a substantial increase in the "beta strand" fraction relative to the 12-residue polyalanine. The detailed conformational distribution is compared with those reported from recent all-atom simulations and experiments. The results suggest that the new coarse-graining approach presented in this study has the potential to offer both accuracy and efficiency for biomolecular modeling.

Revised Parameters for the AMOEBA Polarizable Atomic Multipole Water Model.

PubMed

Laury, Marie L; Wang, Lee-Ping; Pande, Vijay S; Head-Gordon, Teresa; Ponder, Jay W

2015-07-23

A set of improved parameters for the AMOEBA polarizable atomic multipole water model is developed. An automated procedure, ForceBalance, is used to adjust model parameters to enforce agreement with ab initio-derived results for water clusters and experimental data for a variety of liquid phase properties across a broad temperature range. The values reported here for the new AMOEBA14 water model represent a substantial improvement over the previous AMOEBA03 model. The AMOEBA14 model accurately predicts the temperature of maximum density and qualitatively matches the experimental density curve across temperatures from 249 to 373 K. Excellent agreement is observed for the AMOEBA14 model in comparison to experimental properties as a function of temperature, including the second virial coefficient, enthalpy of vaporization, isothermal compressibility, thermal expansion coefficient, and dielectric constant. The viscosity, self-diffusion constant, and surface tension are also well reproduced. In comparison to high-level ab initio results for clusters of 2-20 water molecules, the AMOEBA14 model yields results similar to AMOEBA03 and the direct polarization iAMOEBA models. With advances in computing power, calibration data, and optimization techniques, we recommend the use of the AMOEBA14 water model for future studies employing a polarizable water model.

Chaotic dynamical aperture

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

Lee, S.Y.; Tepikian, S.

1985-01-01

Nonlinear magnetic forces become more important for particles in the modern large accelerators. These nonlinear elements are introduced either intentionally to control beam dynamics or by uncontrollable random errors. Equations of motion in the nonlinear Hamiltonian are usually non-integrable. Because of the nonlinear part of the Hamiltonian, the tune diagram of accelerators is a jungle. Nonlinear magnet multipoles are important in keeping the accelerator operation point in the safe quarter of the hostile jungle of resonant tunes. Indeed, all the modern accelerator designs have taken advantages of nonlinear mechanics. On the other hand, the effect of the uncontrollable random multipolesmore » should be evaluated carefully. A powerful method of studying the effect of these nonlinear multipoles is using a particle tracking calculation, where a group of test particles are tracing through these magnetic multipoles in the accelerator hundreds to millions of turns in order to test the dynamical aperture of the machine. These methods are extremely useful in the design of a large accelerator such as SSC, LEP, HERA and RHIC. These calculations unfortunately take a tremendous amount of computing time. In this review the method of determining chaotic orbit and applying the method to nonlinear problems in accelerator physics is discussed. We then discuss the scaling properties and effect of random sextupoles.« less

On the completeness and the linear dependence of the Cartesian multipole series in representing the solution to the Helmholtz equation.

PubMed

Liu, Yangfan; Bolton, J Stuart

2016-08-01

The (Cartesian) multipole series, i.e., the series comprising monopole, dipoles, quadrupoles, etc., can be used, as an alternative to the spherical or cylindrical wave series, in representing sound fields in a wide range of problems, such as source radiation, sound scattering, etc. The proofs of the completeness of the spherical and cylindrical wave series in these problems are classical results, and it is also generally agreed that the Cartesian multipole series spans the same space as the spherical waves: a rigorous mathematical proof of that statement has, however, not been presented. In the present work, such a proof of the completeness of the Cartesian multipole series, both in two and three dimensions, is given, and the linear dependence relations among different orders of multipoles are discussed, which then allows one to easily extract a basis from the multipole series. In particular, it is concluded that the multipoles comprising the two highest orders in the series form a basis of the whole series, since the multipoles of all the lower source orders can be expressed as a linear combination of that basis.

A unified formulation of dichroic signals using the Borrmann effect and twisted photon beams.

PubMed

Collins, Stephen P; Lovesey, Stephen W

2018-05-21

Dichroic X-ray signals derived from the Borrmann effect and a twisted photon beam with topological charge l = 1 are formulated with an effective wavevector. The unification applies for non-magnetic and magnetic materials. Electronic degrees of freedom associated with an ion are encapsulated in multipoles previously used to interpret conventional dichroism and Bragg diffraction enhanced by an atomic resonance. A dichroic signal exploiting the Borrmann effect with a linearly polarized beam presents charge-like multipoles that include a hexadecapole. A difference between dichroic signals obtained with a twisted beam carrying spin polarization (circular polarization) and opposite winding numbers presents charge-like atomic multipoles, whereas a twisted beam carrying linear polarization alone presents magnetic (time-odd) multipoles. Charge-like multipoles include a quadrupole, and magnetic multipoles include a dipole and an octupole. We discuss the practicalities and relative merits of spectroscopy exploiting the two remarkably closely-related processes. Signals using beams with topological charges l ≥ 2 present additional atomic multipoles.

TMFF-A Two-Bead Multipole Force Field for Coarse-Grained Molecular Dynamics Simulation of Protein.

PubMed

Li, Min; Liu, Fengjiao; Zhang, John Z H

2016-12-13

Coarse-grained (CG) models are desirable for studying large and complex biological systems. In this paper, we propose a new two-bead multipole force field (TMFF) in which electric multipoles up to the quadrupole are included in the CG force field. The inclusion of electric multipoles in the proposed CG force field enables a more realistic description of the anisotropic electrostatic interactions in the protein system and, thus, provides an improvement over the standard isotropic two-bead CG models. In order to test the accuracy of the new CG force field model, extensive molecular dynamics simulations were carried out for a series of benchmark protein systems. These simulation studies showed that the TMFF model can realistically reproduce the structural and dynamical properties of proteins, as demonstrated by the close agreement of the CG results with those from the corresponding all-atom simulations in terms of root-mean-square deviations (RMSDs) and root-mean-square fluctuations (RMSFs) of the protein backbones. The current two-bead model is highly coarse-grained and is 50-fold more efficient than all-atom method in MD simulation of proteins in explicit water.

A hybrid method for solutes in complex solvents: Density functional theory combined with empirical force fields

NASA Astrophysics Data System (ADS)

Eichinger, M.; Tavan, P.; Hutter, J.; Parrinello, M.

1999-06-01

We present a hybrid method for molecular dynamics simulations of solutes in complex solvents as represented, for example, by substrates within enzymes. The method combines a quantum mechanical (QM) description of the solute with a molecular mechanics (MM) approach for the solvent. The QM fragment of a simulation system is treated by ab initio density functional theory (DFT) based on plane-wave expansions. Long-range Coulomb interactions within the MM fragment and between the QM and the MM fragment are treated by a computationally efficient fast multipole method. For the description of covalent bonds between the two fragments, we introduce the scaled position link atom method (SPLAM), which removes the shortcomings of related procedures. The various aspects of the hybrid method are scrutinized through test calculations on liquid water, the water dimer, ethane and a small molecule related to the retinal Schiff base. In particular, the extent to which vibrational spectra obtained by DFT for the solute can be spoiled by the lower quality force field of the solvent is checked, including cases in which the two fragments are covalently joined. The results demonstrate that our QM/MM hybrid method is especially well suited for the vibrational analysis of molecules in condensed phase.

Efficient Broadband Simulation of Fluid-Structure Coupling for Membrane-Type Acoustic Transducer Arrays Using the Multilevel Fast Multipole Algorithm.

PubMed

Shieh, Bernard; Sabra, Karim G; Degertekin, F Levent

2016-11-01

A boundary element model provides great flexibility for the simulation of membrane-type micromachined ultrasonic transducers (MUTs) in terms of membrane shape, actuating mechanism, and array layout. Acoustic crosstalk is accounted for through a mutual impedance matrix that captures the primary crosstalk mechanism of dispersive-guided modes generated at the fluid-solid interface. However, finding the solution to the fully populated boundary element matrix equation using standard techniques requires computation time and memory usage that scales by the cube and by the square of the number of nodes, respectively, limiting simulation to a small number of membranes. We implement a solver with improved speed and efficiency through the application of a multilevel fast multipole algorithm (FMA). By approximating the fields of collections of nodes using multipole expansions of the free-space Green's function, an FMA solver can enable the simulation of hundreds of thousands of nodes while incurring an approximation error that is controllable. Convergence is drastically improved using a problem-specific block-diagonal preconditioner. We demonstrate the solver's capabilities by simulating a 32-element 7-MHz 1-D capacitive MUT (CMUT) phased array with 2880 membranes. The array is simulated using 233280 nodes for a very wide frequency band up to 50 MHz. For a simulation with 15210 nodes, the FMA solver performed ten times faster and used 32 times less memory than a standard solver based on LU decomposition. We investigate the effects of mesh density and phasing on the predicted array response and find that it is necessary to use about seven nodes over the width of the membrane to observe convergence of the solution-even below the first membrane resonance frequency-due to the influence of higher order membrane modes.

A non-JKL density matrix functional for intergeminal correlation between closed-shell geminals from analysis of natural orbital configuration interaction expansions

NASA Astrophysics Data System (ADS)

van Meer, R.; Gritsenko, O. V.; Baerends, E. J.

2018-03-01

Almost all functionals that are currently used in density matrix functional theory have been created by some a priori ansatz that generates approximations to the second-order reduced density matrix (2RDM). In this paper, a more consistent approach is used: we analyze the 2RDMs (in the natural orbital basis) of rather accurate multi-reference configuration interaction expansions for several small molecules (CH4, NH3, H2O, FH, and N2) and use the knowledge gained to generate new functionals. The analysis shows that a geminal-like structure is present in the 2RDMs, even though no geminal theory has been applied from the onset. It is also shown that the leading non-geminal dynamical correlation contributions are generated by a specific set of double excitations. The corresponding determinants give rise to non-JKL (non Coulomb/Exchange like) multipole-multipole dispersive attractive terms between geminals. Due to the proximity of the geminals, these dispersion terms are large and cannot be omitted, proving pure JKL functionals to be essentially deficient. A second correction emerges from the observation that the "normal" geminal-like exchange between geminals breaks down when one breaks multiple bonds. This problem can be fixed by doubling the exchange between bond broken geminals, effectively restoring the often physically correct high-spin configurations on the bond broken fragments. Both of these corrections have been added to the commonly used antisymmetrized product of strongly orthogonal geminals functional. The resulting non-JKL functional Extended Löwdin-Shull Dynamical-Multibond is capable of reproducing complete active space self-consistent field curves, in which one active orbital is used for each valence electron.

Born-Oppenheimer approximation in an effective field theory language

NASA Astrophysics Data System (ADS)

Brambilla, Nora; Krein, Gastão; Tarrús Castellà, Jaume; Vairo, Antonio

2018-01-01

The Born-Oppenheimer approximation is the standard tool for the study of molecular systems. It is founded on the observation that the energy scale of the electron dynamics in a molecule is larger than that of the nuclei. A very similar physical picture can be used to describe QCD states containing heavy quarks as well as light-quarks or gluonic excitations. In this work, we derive the Born-Oppenheimer approximation for QED molecular systems in an effective field theory framework by sequentially integrating out degrees of freedom living at energies above the typical energy scale where the dynamics of the heavy degrees of freedom occurs. In particular, we compute the matching coefficients of the effective field theory for the case of the H2+ diatomic molecule that are relevant to compute its spectrum up to O (m α5). Ultrasoft photon loops contribute at this order, being ultimately responsible for the molecular Lamb shift. In the effective field theory the scaling of all the operators is homogeneous, which facilitates the determination of all the relevant contributions, an observation that may become useful for high-precision calculations. Using the above case as a guidance, we construct under some conditions an effective field theory for QCD states formed by a color-octet heavy quark-antiquark pair bound with a color-octet light-quark pair or excited gluonic state, highlighting the similarities and differences between the QED and QCD systems. Assuming that the multipole expansion is applicable, we construct the heavy-quark potential up to next-to-leading order in the multipole expansion in terms of nonperturbative matching coefficients to be obtained from lattice QCD.

Accurate van der Waals coefficients from density functional theory

PubMed Central

Tao, Jianmin; Perdew, John P.; Ruzsinszky, Adrienn

2012-01-01

The van der Waals interaction is a weak, long-range correlation, arising from quantum electronic charge fluctuations. This interaction affects many properties of materials. A simple and yet accurate estimate of this effect will facilitate computer simulation of complex molecular materials and drug design. Here we develop a fast approach for accurate evaluation of dynamic multipole polarizabilities and van der Waals (vdW) coefficients of all orders from the electron density and static multipole polarizabilities of each atom or other spherical object, without empirical fitting. Our dynamic polarizabilities (dipole, quadrupole, octupole, etc.) are exact in the zero- and high-frequency limits, and exact at all frequencies for a metallic sphere of uniform density. Our theory predicts dynamic multipole polarizabilities in excellent agreement with more expensive many-body methods, and yields therefrom vdW coefficients C6, C8, C10 for atom pairs with a mean absolute relative error of only 3%. PMID:22205765

Computational electromagnetics: the physics of smooth versus oscillatory fields.

PubMed

Chew, W C

2004-03-15

This paper starts by discussing the difference in the physics between solutions to Laplace's equation (static) and Maxwell's equations for dynamic problems (Helmholtz equation). Their differing physical characters are illustrated by how the two fields convey information away from their source point. The paper elucidates the fact that their differing physical characters affect the use of Laplacian field and Helmholtz field in imaging. They also affect the design of fast computational algorithms for electromagnetic scattering problems. Specifically, a comparison is made between fast algorithms developed using wavelets, the simple fast multipole method, and the multi-level fast multipole algorithm for electrodynamics. The impact of the physical characters of the dynamic field on the parallelization of the multi-level fast multipole algorithm is also discussed. The relationship of diagonalization of translators to group theory is presented. Finally, future areas of research for computational electromagnetics are described.

Convergence of highly parallel stray field calculation using the fast multipole method on irregular meshes

NASA Astrophysics Data System (ADS)

Palmesi, P.; Abert, C.; Bruckner, F.; Suess, D.

2018-05-01

Fast stray field calculation is commonly considered of great importance for micromagnetic simulations, since it is the most time consuming part of the simulation. The Fast Multipole Method (FMM) has displayed linear O(N) parallelization behavior on many cores. This article investigates the error of a recent FMM approach approximating sources using linear—instead of constant—finite elements in the singular integral for calculating the stray field and the corresponding potential. After measuring performance in an earlier manuscript, this manuscript investigates the convergence of the relative L2 error for several FMM simulation parameters. Various scenarios either calculating the stray field directly or via potential are discussed.

AN EFFICIENT HIGHER-ORDER FAST MULTIPOLE BOUNDARY ELEMENT SOLUTION FOR POISSON-BOLTZMANN BASED MOLECULAR ELECTROSTATICS

PubMed Central

Bajaj, Chandrajit; Chen, Shun-Chuan; Rand, Alexander

2011-01-01

In order to compute polarization energy of biomolecules, we describe a boundary element approach to solving the linearized Poisson-Boltzmann equation. Our approach combines several important features including the derivative boundary formulation of the problem and a smooth approximation of the molecular surface based on the algebraic spline molecular surface. State of the art software for numerical linear algebra and the kernel independent fast multipole method is used for both simplicity and efficiency of our implementation. We perform a variety of computational experiments, testing our method on a number of actual proteins involved in molecular docking and demonstrating the effectiveness of our solver for computing molecular polarization energy. PMID:21660123

Electrostatic contribution to the persistence length of a semiflexible dipolar chain.

PubMed

Podgornik, Rudi

2004-09-01

We investigate the electrostatic contribution to the persistence length of a semiflexible polymer chain whose segments interact via a screened Debye-Hückel dipolar interaction potential. We derive the expressions for the renormalized persistence length on the level of a 1/D-expansion method already successfully used in other contexts of polyelectrolye physics. We investigate different limiting forms of the renormalized persistence length of the dipolar chain and show that, in, general, it depends less strongly on the screening length than in the context of a monopolar chain. We show that for a dipolar chain the electrostatic persistence length in the same regime of the parameter phase space as the original Odijk-Skolnick-Fixman (OSF) form for a monopolar chain depends logarithmically on the screening length rather than quadratically. This can be understood solely on the basis of a swifter decay of the dipolar interactions with separation compared to the monopolar electrostatic interactions. We comment also on the general contribution of higher multipoles to the electrostatic renormalization of the bending rigidity.

Spin dephasing in a magnetic dipole field.

PubMed

Ziener, C H; Kampf, T; Reents, G; Schlemmer, H-P; Bauer, W R

2012-05-01

Transverse relaxation by dephasing in an inhomogeneous field is a general mechanism in physics, for example, in semiconductor physics, muon spectroscopy, or nuclear magnetic resonance. In magnetic resonance imaging the transverse relaxation provides information on the properties of several biological tissues. Since the dipole field is the most important part of the multipole expansion of the local inhomogeneous field, dephasing in a dipole field is highly important in relaxation theory. However, there have been no analytical solutions which describe the dephasing in a magnetic dipole field. In this work we give a complete analytical solution for the dephasing in a magnetic dipole field which is valid over the whole dynamic range.

The electron-spin--nuclear-spin interaction studied by polarized neutron scattering.

PubMed

Stuhrmann, Heinrich B

2007-11-01

Dynamic nuclear spin polarization (DNP) is mediated by the dipolar interaction of paramagnetic centres with nuclear spins. This process is most likely to occur near paramagnetic centres at an angle close to 45 degrees with respect to the direction of the external magnetic field. The resulting distribution of polarized nuclear spins leads to an anisotropy of the polarized neutron scattering pattern, even with randomly oriented radical molecules. The corresponding cross section of polarized coherent neutron scattering in terms of a multipole expansion is derived for radical molecules in solution. An application using data of time-resolved polarized neutron scattering from an organic chromium(V) molecule is tested.

Prediction of conformationally dependent atomic multipole moments in carbohydrates

PubMed Central

Cardamone, Salvatore

2015-01-01

The conformational flexibility of carbohydrates is challenging within the field of computational chemistry. This flexibility causes the electron density to change, which leads to fluctuating atomic multipole moments. Quantum Chemical Topology (QCT) allows for the partitioning of an “atom in a molecule,” thus localizing electron density to finite atomic domains, which permits the unambiguous evaluation of atomic multipole moments. By selecting an ensemble of physically realistic conformers of a chemical system, one evaluates the various multipole moments at defined points in configuration space. The subsequent implementation of the machine learning method kriging delivers the evaluation of an analytical function, which smoothly interpolates between these points. This allows for the prediction of atomic multipole moments at new points in conformational space, not trained for but within prediction range. In this work, we demonstrate that the carbohydrates erythrose and threose are amenable to the above methodology. We investigate how kriging models respond when the training ensemble incorporating multiple energy minima and their environment in conformational space. Additionally, we evaluate the gains in predictive capacity of our models as the size of the training ensemble increases. We believe this approach to be entirely novel within the field of carbohydrates. For a modest training set size of 600, more than 90% of the external test configurations have an error in the total (predicted) electrostatic energy (relative to ab initio) of maximum 1 kJ mol−1 for open chains and just over 90% an error of maximum 4 kJ mol−1 for rings. © 2015 Wiley Periodicals, Inc. PMID:26547500

Prediction of conformationally dependent atomic multipole moments in carbohydrates.

PubMed

Cardamone, Salvatore; Popelier, Paul L A

2015-12-15

The conformational flexibility of carbohydrates is challenging within the field of computational chemistry. This flexibility causes the electron density to change, which leads to fluctuating atomic multipole moments. Quantum Chemical Topology (QCT) allows for the partitioning of an "atom in a molecule," thus localizing electron density to finite atomic domains, which permits the unambiguous evaluation of atomic multipole moments. By selecting an ensemble of physically realistic conformers of a chemical system, one evaluates the various multipole moments at defined points in configuration space. The subsequent implementation of the machine learning method kriging delivers the evaluation of an analytical function, which smoothly interpolates between these points. This allows for the prediction of atomic multipole moments at new points in conformational space, not trained for but within prediction range. In this work, we demonstrate that the carbohydrates erythrose and threose are amenable to the above methodology. We investigate how kriging models respond when the training ensemble incorporating multiple energy minima and their environment in conformational space. Additionally, we evaluate the gains in predictive capacity of our models as the size of the training ensemble increases. We believe this approach to be entirely novel within the field of carbohydrates. For a modest training set size of 600, more than 90% of the external test configurations have an error in the total (predicted) electrostatic energy (relative to ab initio) of maximum 1 kJ mol(-1) for open chains and just over 90% an error of maximum 4 kJ mol(-1) for rings. © 2015 Wiley Periodicals, Inc.

Multipolar response of nonspherical silicon nanoparticles in the visible and near-infrared spectral ranges

NASA Astrophysics Data System (ADS)

Terekhov, Pavel D.; Baryshnikova, Kseniia V.; Artemyev, Yuriy A.; Karabchevsky, Alina; Shalin, Alexander S.; Evlyukhin, Andrey B.

2017-07-01

Spectral multipole resonances of parallelepiped-, pyramid-, and cone-like shaped silicon nanoparticles excited by linearly polarized light waves are theoretically investigated. The numerical finite element method is applied for the calculations of the scattering cross sections as a function of the nanoparticles geometrical parameters. The roles of multipole moments (up to the third order) in the scattering process are analyzed using the semianalytical multipole decomposition approach. The possibility of scattering pattern configuration due to the tuning of the multipole contributions to the total scattered waves is discussed and demonstrated. It is shown that cubic nanoparticles can provide a strong isotropic side scattering with minimization of the scattering in forward and backward directions. In the case of the pyramidal and conical nanoparticles the total suppression of the side scattering can be obtained. It was found that due to the shape factor of the pyramidal and conical nanoparticles their electric toroidal dipole resonance can be excited in the spectral region of the first electric and magnetic dipole resonances. The influence of the incident light directions on the optical response of the pyramidal and conical nanoparticles is discussed. The obtained results provide important information that can be used for the development of nanoantennas with improved functionality due to the directional scattering effects.

Multipole Vectors: Decomposing Functions on a Sphere

NASA Astrophysics Data System (ADS)

Copi, C. J.; Huterer, D.; Starkman, G. D.

2011-09-01

We propose a novel representation of cosmic microwave anisotropy maps, where each multipole order l is represented by l unit vectors pointing in directions on the sky and an overall magnitude. These "multipole vectors and scalars" transform as vectors under rotations. Like the usual spherical harmonics, multipole vectors form an irreducible representation of the proper rotation group SO(3). However, they are related to the familiar spherical harmonic coefficients, alm, in a nonlinear way, and are therefore sensitive to different aspects of the CMB anisotropy. Nevertheless, it is straightforward to determine the multipole vectors for a given CMB map and we present an algorithm to compute them. Using the WMAP full-sky maps, we perform several tests of the hypothesis that the CMB anisotropy is statistically isotropic and Gaussian random. We find that the result from comparing the oriented area of planes defined by these vectors between multipole pairs 2<=l1!=l2<=8 is inconsistent with the isotropic Gaussian hypothesis at the 99.4% level for the ILC map and at 98.9% level for the cleaned map of Tegmark et al. A particular correlation is suggested between the l=3 and l=8 multipoles, as well as several other pairs. This effect is entirely different from the now familiar planarity and alignment of the quadrupole and octupole: while the aforementioned is fairly unlikely, the multipole vectors indicate correlations not expected in Gaussian random skies that make them unusually likely. The result persists after accounting for pixel noise and after assuming a residual 10% dust contamination in the cleaned WMAP map. While the definitive analysis of these results will require more work, we hope that multipole vectors will become a valuable tool for various cosmological tests, in particular those of cosmic isotropy.

Complexity Reduction in Large Quantum Systems: Fragment Identification and Population Analysis via a Local Optimized Minimal Basis

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

Mohr, Stephan; Masella, Michel; Ratcliff, Laura E.

We present, within Kohn-Sham Density Functional Theory calculations, a quantitative method to identify and assess the partitioning of a large quantum mechanical system into fragments. We then introduce a simple and efficient formalism (which can be written as generalization of other well-known population analyses) to extract, from first principles, electrostatic multipoles for these fragments. The corresponding fragment multipoles can in this way be seen as reliable (pseudo-) observables. By applying our formalism within the code BigDFT, we show that the usage of a minimal set of in-situ optimized basis functions is of utmost importance for having at the same timemore » a proper fragment definition and an accurate description of the electronic structure. With this approach it becomes possible to simplify the modeling of environmental fragments by a set of multipoles, without notable loss of precision in the description of the active quantum mechanical region. Furthermore, this leads to a considerable reduction of the degrees of freedom by an effective coarsegraining approach, eventually also paving the way towards efficient QM/QM and QM/MM methods coupling together different levels of accuracy.« less

Quantum crystallographic charge density of urea

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

Wall, Michael E.

Standard X-ray crystallography methods use free-atom models to calculate mean unit-cell charge densities. Real molecules, however, have shared charge that is not captured accurately using free-atom models. To address this limitation, a charge density model of crystalline urea was calculated using high-level quantum theory and was refined against publicly available ultra-high-resolution experimental Bragg data, including the effects of atomic displacement parameters. The resulting quantum crystallographic model was compared with models obtained using spherical atom or multipole methods. Despite using only the same number of free parameters as the spherical atom model, the agreement of the quantum model with the datamore » is comparable to the multipole model. The static, theoretical crystalline charge density of the quantum model is distinct from the multipole model, indicating the quantum model provides substantially new information. Hydrogen thermal ellipsoids in the quantum model were very similar to those obtained using neutron crystallography, indicating that quantum crystallography can increase the accuracy of the X-ray crystallographic atomic displacement parameters. Lastly, the results demonstrate the feasibility and benefits of integrating fully periodic quantum charge density calculations into ultra-high-resolution X-ray crystallographic model building and refinement.« less

Quantum crystallographic charge density of urea

DOE PAGES

Wall, Michael E.

2016-06-08

Standard X-ray crystallography methods use free-atom models to calculate mean unit-cell charge densities. Real molecules, however, have shared charge that is not captured accurately using free-atom models. To address this limitation, a charge density model of crystalline urea was calculated using high-level quantum theory and was refined against publicly available ultra-high-resolution experimental Bragg data, including the effects of atomic displacement parameters. The resulting quantum crystallographic model was compared with models obtained using spherical atom or multipole methods. Despite using only the same number of free parameters as the spherical atom model, the agreement of the quantum model with the datamore » is comparable to the multipole model. The static, theoretical crystalline charge density of the quantum model is distinct from the multipole model, indicating the quantum model provides substantially new information. Hydrogen thermal ellipsoids in the quantum model were very similar to those obtained using neutron crystallography, indicating that quantum crystallography can increase the accuracy of the X-ray crystallographic atomic displacement parameters. Lastly, the results demonstrate the feasibility and benefits of integrating fully periodic quantum charge density calculations into ultra-high-resolution X-ray crystallographic model building and refinement.« less

Complexity Reduction in Large Quantum Systems: Fragment Identification and Population Analysis via a Local Optimized Minimal Basis

DOE PAGES

Mohr, Stephan; Masella, Michel; Ratcliff, Laura E.; ...

2017-07-21

We present, within Kohn-Sham Density Functional Theory calculations, a quantitative method to identify and assess the partitioning of a large quantum mechanical system into fragments. We then introduce a simple and efficient formalism (which can be written as generalization of other well-known population analyses) to extract, from first principles, electrostatic multipoles for these fragments. The corresponding fragment multipoles can in this way be seen as reliable (pseudo-) observables. By applying our formalism within the code BigDFT, we show that the usage of a minimal set of in-situ optimized basis functions is of utmost importance for having at the same timemore » a proper fragment definition and an accurate description of the electronic structure. With this approach it becomes possible to simplify the modeling of environmental fragments by a set of multipoles, without notable loss of precision in the description of the active quantum mechanical region. Furthermore, this leads to a considerable reduction of the degrees of freedom by an effective coarsegraining approach, eventually also paving the way towards efficient QM/QM and QM/MM methods coupling together different levels of accuracy.« less

Revised Parameters for the AMOEBA Polarizable Atomic Multipole Water Model

PubMed Central

Pande, Vijay S.; Head-Gordon, Teresa; Ponder, Jay W.

2016-01-01

A set of improved parameters for the AMOEBA polarizable atomic multipole water model is developed. The protocol uses an automated procedure, ForceBalance, to adjust model parameters to enforce agreement with ab initio-derived results for water clusters and experimentally obtained data for a variety of liquid phase properties across a broad temperature range. The values reported here for the new AMOEBA14 water model represent a substantial improvement over the previous AMOEBA03 model. The new AMOEBA14 water model accurately predicts the temperature of maximum density and qualitatively matches the experimental density curve across temperatures ranging from 249 K to 373 K. Excellent agreement is observed for the AMOEBA14 model in comparison to a variety of experimental properties as a function of temperature, including the 2nd virial coefficient, enthalpy of vaporization, isothermal compressibility, thermal expansion coefficient and dielectric constant. The viscosity, self-diffusion constant and surface tension are also well reproduced. In comparison to high-level ab initio results for clusters of 2 to 20 water molecules, the AMOEBA14 model yields results similar to the AMOEBA03 and the direct polarization iAMOEBA models. With advances in computing power, calibration data, and optimization techniques, we recommend the use of the AMOEBA14 water model for future studies employing a polarizable water model. PMID:25683601

Gay-Berne and electrostatic multipole based coarse-grain potential in implicit solvent

PubMed Central

Wu, Johnny; Zhen, Xia; Shen, Hujun; Li, Guohui; Ren, Pengyu

2011-01-01

A general, transferable coarse-grain (CG) framework based on the Gay-Berne potential and electrostatic point multipole expansion is presented for polypeptide simulations. The solvent effect is described by the Generalized Kirkwood theory. The CG model is calibrated using the results of all-atom simulations of model compounds in solution. Instead of matching the overall effective forces produced by atomic models, the fundamental intermolecular forces such as electrostatic, repulsion-dispersion, and solvation are represented explicitly at a CG level. We demonstrate that the CG alanine dipeptide model is able to reproduce quantitatively the conformational energy of all-atom force fields in both gas and solution phases, including the electrostatic and solvation components. Replica exchange molecular dynamics and microsecond dynamic simulations of polyalanine of 5 and 12 residues reveal that the CG polyalanines fold into “alpha helix” and “beta sheet” structures. The 5-residue polyalanine displays a substantial increase in the “beta strand” fraction relative to the 12-residue polyalanine. The detailed conformational distribution is compared with those reported from recent all-atom simulations and experiments. The results suggest that the new coarse-graining approach presented in this study has the potential to offer both accuracy and efficiency for biomolecular modeling. PMID:22029338

Electromagnetic multipole moments of elementary spin-1/2, 1, and 3/2 particles

NASA Astrophysics Data System (ADS)

Delgado-Acosta, E. G.; Kirchbach, M.; Napsuciale, M.; Rodríguez, S.

2012-06-01

We study multipole decompositions of the electromagnetic currents of spin-1/2, 1, and 3/2 particles described in terms of representation-specific wave equations which are second order in the momenta and which emerge within the recently elaborated Poincaré covariant-projector method, where the respective Lagrangians explicitly depend on the Lorentz group generators of the representations of interest. The currents are then the ordinary linear Noether currents related to phase invariance, and present themselves always as two-terms motion-plus spin-magnetization currents. The spin-magnetization currents appear weighted by the gyromagnetic ratio g, a free parameter in the method which we fix either by unitarity of forward Compton scattering amplitudes in the ultraviolet for spin-1 and spin-3/2, or in the spin-1/2 case, by their asymptotic vanishing, thus ending up in all three cases with the universal g value of g=2. Within the method under discussion, we calculate the electric multipoles of the above spins for the spinor, the four-vector, and the four-vector-spinor representations, and find it favorable in some aspects, specifically in comparison with the conventional Proca and Rarita-Schwinger frameworks. We furthermore attend to the most general non-Lagrangian spin-3/2 currents, which are allowed by Lorentz invariance to be up to third order in the momenta and construct the linear-current equivalent of identical multipole moments of one of them. We conclude that nonlinear non-Lagrangian spin-3/2 currents are not necessarily more general and more advantageous than the linear spin-3/2 Lagrangian current emerging within the covariant-projector formalism. Finally, we test the representation dependence of the multipoles by placing spin-1 and spin-3/2 in the respective (1,0)⊕(0,1) and (3/2,0)⊕(0,3/2) single-spin representations. We observe representation independence of the charge monopoles and the magnetic dipoles, in contrast to the higher multipoles, which turn out to be representation-dependent. In particular, we find the bi-vector (1,0)⊕(0,1) to be characterized by an electric quadrupole moment of opposite sign to the one found in (1/2,1/2), and consequently to the W boson. This observation allows us to explain the positive electric quadrupole moment of the ρ meson extracted from recent analyses of the ρ meson electric form factor. Our finding points toward the possibility that the ρ-meson could transform as part of an antisymmetric tensor with an a1 mesonlike state as its representation companion, a possibility consistent with the empirically established ρ and a1 vector meson dominance of the hadronic vector and axial-vector currents.

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

Bahrdt, J.; Frentrup, W.; Gaupp, A.

BESSY plans to go to topping up operation in the near future. A high injection efficiency is essential to avoid particle losses inside the undulator magnets and to ensure a low radiation background in the beamlines. Dynamic and static multipoles of the insertion devices have to be minimized to accomplish this requirement. APPLE II devices show strong dynamic multipoles in the elliptical and vertical polarization mode. Measurements before and after shimming of these multipoles are presented. The static multipoles of the BESSY UE56-2 which are due to systematic block inhomgeneities have successfully been shimmed recovering the full dynamic aperture.

The active site of hen egg-white lysozyme: flexibility and chemical bonding

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

Held, Jeanette, E-mail: jeanette.netzel@uni-bayreuth.de; Smaalen, Sander van

Chemical bonding at the active site of lysozyme is analyzed on the basis of a multipole model employing transferable multipole parameters from a database. Large B factors at low temperatures reflect frozen-in disorder, but therefore prevent a meaningful free refinement of multipole parameters. Chemical bonding at the active site of hen egg-white lysozyme (HEWL) is analyzed on the basis of Bader’s quantum theory of atoms in molecules [QTAIM; Bader (1994 ▶), Atoms in Molecules: A Quantum Theory. Oxford University Press] applied to electron-density maps derived from a multipole model. The observation is made that the atomic displacement parameters (ADPs) ofmore » HEWL at a temperature of 100 K are larger than ADPs in crystals of small biological molecules at 298 K. This feature shows that the ADPs in the cold crystals of HEWL reflect frozen-in disorder rather than thermal vibrations of the atoms. Directly generalizing the results of multipole studies on small-molecule crystals, the important consequence for electron-density analysis of protein crystals is that multipole parameters cannot be independently varied in a meaningful way in structure refinements. Instead, a multipole model for HEWL has been developed by refinement of atomic coordinates and ADPs against the X-ray diffraction data of Wang and coworkers [Wang et al. (2007), Acta Cryst. D63, 1254–1268], while multipole parameters were fixed to the values for transferable multipole parameters from the ELMAM2 database [Domagala et al. (2012), Acta Cryst. A68, 337–351] . Static and dynamic electron densities based on this multipole model are presented. Analysis of their topological properties according to the QTAIM shows that the covalent bonds possess similar properties to the covalent bonds of small molecules. Hydrogen bonds of intermediate strength are identified for the Glu35 and Asp52 residues, which are considered to be essential parts of the active site of HEWL. Furthermore, a series of weak C—H⋯O hydrogen bonds are identified by means of the existence of bond critical points (BCPs) in the multipole electron density. It is proposed that these weak interactions might be important for defining the tertiary structure and activity of HEWL. The deprotonated state of Glu35 prevents a distinction between the Phillips and Koshland mechanisms.« less

The Gaussian streaming model and convolution Lagrangian effective field theory

DOE PAGES

Vlah, Zvonimir; Castorina, Emanuele; White, Martin

2016-12-05

We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM tomore » a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.« less

The Gaussian streaming model and convolution Lagrangian effective field theory

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

Vlah, Zvonimir; Castorina, Emanuele; White, Martin, E-mail: zvlah@stanford.edu, E-mail: ecastorina@berkeley.edu, E-mail: mwhite@berkeley.edu

We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM tomore » a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.« less

Flexibly imposing periodicity in kernel independent FMM: A multipole-to-local operator approach

NASA Astrophysics Data System (ADS)

Yan, Wen; Shelley, Michael

2018-02-01

An important but missing component in the application of the kernel independent fast multipole method (KIFMM) is the capability for flexibly and efficiently imposing singly, doubly, and triply periodic boundary conditions. In most popular packages such periodicities are imposed with the hierarchical repetition of periodic boxes, which may give an incorrect answer due to the conditional convergence of some kernel sums. Here we present an efficient method to properly impose periodic boundary conditions using a near-far splitting scheme. The near-field contribution is directly calculated with the KIFMM method, while the far-field contribution is calculated with a multipole-to-local (M2L) operator which is independent of the source and target point distribution. The M2L operator is constructed with the far-field portion of the kernel function to generate the far-field contribution with the downward equivalent source points in KIFMM. This method guarantees the sum of the near-field & far-field converge pointwise to results satisfying periodicity and compatibility conditions. The computational cost of the far-field calculation observes the same O (N) complexity as FMM and is designed to be small by reusing the data computed by KIFMM for the near-field. The far-field calculations require no additional control parameters, and observes the same theoretical error bound as KIFMM. We present accuracy and timing test results for the Laplace kernel in singly periodic domains and the Stokes velocity kernel in doubly and triply periodic domains.

An optimal FFT-based anisotropic power spectrum estimator

NASA Astrophysics Data System (ADS)

Hand, Nick; Li, Yin; Slepian, Zachary; Seljak, Uroš

2017-07-01

Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a moving line-of-sight, can be accelerated using Fast Fourier Transforms (FFTs) by decomposing the Legendre polynomials into products of Cartesian vectors. Here, we present a faster, optimal means of using FFTs for this measurement. We avoid redundancy present in the Cartesian decomposition by using a spherical harmonic decomposition of the Legendre polynomials. With this method, a given multipole of order l requires only 2l+1 FFTs rather than the (l+1)(l+2)/2 FFTs of the Cartesian approach. For the hexadecapole (l = 4), this translates to 40% fewer FFTs, with increased savings for higher l. The reduction in wall-clock time enables the calculation of finely-binned wedges in P(k,μ), obtained by computing multipoles up to a large lmax and combining them. This transformation has a number of advantages. We demonstrate that by using non-uniform bins in μ, we can isolate plane-of-sky (angular) systematics to a narrow bin at 0μ simeq while eliminating the contamination from all other bins. We also show that the covariance matrix of clustering wedges binned uniformly in μ becomes ill-conditioned when combining multipoles up to large values of lmax, but that the problem can be avoided with non-uniform binning. As an example, we present results using lmax=16, for which our procedure requires a factor of 3.4 fewer FFTs than the Cartesian method, while removing the first μ bin leads only to a 7% increase in statistical error on f σ8, as compared to a 54% increase with lmax=4.

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

Hand, Nick; Seljak, Uroš; Li, Yin

Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a moving line-of-sight, can be accelerated using Fast Fourier Transforms (FFTs) by decomposing the Legendre polynomials into products of Cartesian vectors. Here, we present a faster, optimal means of using FFTs for this measurement. We avoid redundancy present in the Cartesian decomposition by using a spherical harmonic decomposition of the Legendre polynomials. With this method, a given multipole of order ℓ requires only 2ℓ+1 FFTs rather than the (ℓ+1)(ℓ+2)/2 FFTsmore » of the Cartesian approach. For the hexadecapole (ℓ = 4), this translates to 40% fewer FFTs, with increased savings for higher ℓ. The reduction in wall-clock time enables the calculation of finely-binned wedges in P ( k ,μ), obtained by computing multipoles up to a large ℓ{sub max} and combining them. This transformation has a number of advantages. We demonstrate that by using non-uniform bins in μ, we can isolate plane-of-sky (angular) systematics to a narrow bin at 0μ ≅ while eliminating the contamination from all other bins. We also show that the covariance matrix of clustering wedges binned uniformly in μ becomes ill-conditioned when combining multipoles up to large values of ℓ{sub max}, but that the problem can be avoided with non-uniform binning. As an example, we present results using ℓ{sub max}=16, for which our procedure requires a factor of 3.4 fewer FFTs than the Cartesian method, while removing the first μ bin leads only to a 7% increase in statistical error on f σ{sub 8}, as compared to a 54% increase with ℓ{sub max}=4.« less

Reconstruction of real-space linear matter power spectrum from multipoles of BOSS DR12 results

NASA Astrophysics Data System (ADS)

Lee, Seokcheon

2018-02-01

Recently, the power spectrum (PS) multipoles using the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 (DR12) sample are analyzed [1]. The based model for the analysis is the so-called TNS quasi-linear model and the analysis provides the multipoles up to the hexadecapole [2]. Thus, one might be able to recover the real-space linear matter PS by using the combinations of multipoles to investigate the cosmology [3]. We provide the analytic form of the ratio of quadrupole (hexadecapole) to monopole moments of the quasi-linear PS including the Fingers-of-God (FoG) effect to recover the real-space PS in the linear regime. One expects that observed values of the ratios of multipoles should be consistent with those of the linear theory at large scales. Thus, we compare the ratios of multipoles of the linear theory, including the FoG effect with the measured values. From these, we recover the linear matter power spectra in real-space. These recovered power spectra are consistent with the linear matter power spectra.

Multipole analysis of {sup 2}H({gamma},p)n in the {Delta} resonance region

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

Whisnant, C.S.; Mize, W.K.; Pomarede, D.

1998-07-01

An energy-dependent multipole analysis of the photodisintegration of deuterium has been performed for photon energies between 187 and 314 MeV using recent data taken with linearly polarized photons. A good fit is obtained with 11 free parameters determining eight multipoles. A wide variety of multipole solutions has been examined and in all cases the cross section with photon polarization parallel to the reaction plane is dominated by electric transitions, with E2{bold {center_dot}}E1 interference responsible for the observed forward-backward angular asymmetry. The cross sections observed in perpendicular kinematics are dominated by magnetic multipoles. Several recent N{Delta}/NN coupled-channel calculations have predicted amore » pronounced 90{degree} dip in the cross section that is absent from the data. This dip can be reproduced by changing the M2 strength distribution in our fit. A comparison is made with multipoles calculated by Wilhelm and Arenh{umlt o}vel at 300 MeV. {copyright} {ital 1998} {ital The American Physical Society}« less

Polynomial interpretation of multipole vectors

NASA Astrophysics Data System (ADS)

Katz, Gabriel; Weeks, Jeff

2004-09-01

Copi, Huterer, Starkman, and Schwarz introduced multipole vectors in a tensor context and used them to demonstrate that the first-year Wilkinson microwave anisotropy probe (WMAP) quadrupole and octopole planes align at roughly the 99.9% confidence level. In the present article, the language of polynomials provides a new and independent derivation of the multipole vector concept. Bézout’s theorem supports an elementary proof that the multipole vectors exist and are unique (up to rescaling). The constructive nature of the proof leads to a fast, practical algorithm for computing multipole vectors. We illustrate the algorithm by finding exact solutions for some simple toy examples and numerical solutions for the first-year WMAP quadrupole and octopole. We then apply our algorithm to Monte Carlo skies to independently reconfirm the estimate that the WMAP quadrupole and octopole planes align at the 99.9% level.

Extinction cross-section cancellation of a cylindrical radiating active source near a rigid corner and acoustic invisibility

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2017-11-01

Active cloaking in its basic form requires that the extinction cross-section (or energy efficiency) from a radiating body vanishes. In this analysis, this physical effect is demonstrated for an active cylindrically radiating acoustic source in a non-viscous fluid, undergoing periodic axisymmetric harmonic vibrations near a rigid corner (i.e., quarter-space). The rigorous multipole expansion method in cylindrical coordinates, the method of images, and the addition theorem of cylindrical wave functions are used to derive closed-form mathematical expressions for the radiating, amplification, and extinction cross-sections of the active source. Numerical computations are performed assuming monopole and dipole modal oscillations of the circular source. The results reveal some of the situations where the extinction energy efficiency factor of the active source vanishes depending on its size and location with respect to the rigid corner, thus, achieving total invisibility. Moreover, the extinction energy efficiency factor varies between positive or negative values. These effects also occur for higher-order modal oscillations of the active source. The results find potential applications in the development of acoustic cloaking devices and invisibility in underwater acoustics or other areas.

Preparing the BESSY APPLE Undulators for Top-Up Operation

NASA Astrophysics Data System (ADS)

Bahrdt, J.; Frentrup, W.; Gaupp, A.; Scheer, M.

2007-01-01

BESSY plans to go to topping up operation in the near future. A high injection efficiency is essential to avoid particle losses inside the undulator magnets and to ensure a low radiation background in the beamlines. Dynamic and static multipoles of the insertion devices have to be minimized to accomplish this requirement. APPLE II devices show strong dynamic multipoles in the elliptical and vertical polarization mode. Measurements before and after shimming of these multipoles are presented. The static multipoles of the BESSY UE56-2 which are due to systematic block inhomgeneities have successfully been shimmed recovering the full dynamic aperture.

Searching the Force Field Electrostatic Multipole Parameter Space.

PubMed

Jakobsen, Sofie; Jensen, Frank

2016-04-12

We show by tensor decomposition analyses that the molecular electrostatic potential for amino acid peptide models has an effective rank less than twice the number of atoms. This rank indicates the number of parameters that can be derived from the electrostatic potential in a statistically significant way. Using this as a guideline, we investigate different strategies for deriving a reduced set of atomic charges, dipoles, and quadrupoles capable of reproducing the reference electrostatic potential with a low error. A full combinatorial search of selected parameter subspaces for N-methylacetamide and a cysteine peptide model indicates that there are many different parameter sets capable of providing errors close to that of the global minimum. Among the different reduced multipole parameter sets that have low errors, there is consensus that atoms involved in π-bonding require higher order multipole moments. The possible correlation between multipole parameters is investigated by exhaustive searches of combinations of up to four parameters distributed in all possible ways on all possible atomic sites. These analyses show that there is no advantage in considering combinations of multipoles compared to a simple approach where the importance of each multipole moment is evaluated sequentially. When combined with possible weighting factors related to the computational efficiency of each type of multipole moment, this may provide a systematic strategy for determining a computational efficient representation of the electrostatic component in force field calculations.

The chaotic dynamical aperture

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

Lee, S.Y.; Tepikian, S.

1985-10-01

Nonlinear magnetic forces become more important for particles in the modern large accelerators. These nonlinear elements are introduced either intentionally to control beam dynamics or by uncontrollable random errors. Equations of motion in the nonlinear Hamiltonian are usually non-integrable. Because of the nonlinear part of the Hamiltonian, the tune diagram of accelerators is a jungle. Nonlinear magnet multipoles are important in keeping the accelerator operation point in the safe quarter of the hostile jungle of resonant tunes. Indeed, all the modern accelerator design have taken advantages of nonlinear mechanics. On the other hand, the effect of the uncontrollable random multipolesmore » should be evaluated carefully. A powerful method of studying the effect of these nonlinear multipoles is using a particle tracking calculation, where a group of test particles are tracing through these magnetic multipoles in the accelerator hundreds to millions of turns in order to test the dynamical aperture of the machine. These methods are extremely useful in the design of a large accelerator such as SSC, LEP, HERA and RHIC. These calculations unfortunately take tremendous amount of computing time. In this paper, we try to apply the existing method in the nonlinear dynamics to study the possible alternative solution. When the Hamiltonian motion becomes chaotic, the tune of the machine becomes undefined. The aperture related to the chaotic orbit can be identified as chaotic dynamical aperture. We review the method of determining chaotic orbit and apply the method to nonlinear problems in accelerator physics. We then discuss the scaling properties and effect of random sextupoles.« less

Intrinsic acoustical cross sections in the multiple scattering by a pair of rigid cylindrical particles in 2D

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2017-08-01

The multiple scattering effects occurring between two scatterers are described based upon the multipole expansion formalism as well as the addition theorem of cylindrical wave functions. An original approach is presented in which an effective incident acoustic field on a particular object, which includes both the primary and re-scattered waves from the other particle is determined first, and then used with the scattered field to derive closed-form analytical expressions for the inherent (i.e. intrinsic) cross-sections based on the far-field scattering. This method does not introduce any approximation in the calculation of the intrinsic cross-sections since the procedure is reduced to the one-body problem. The mathematical expressions for the intrinsic cross-sections are formulated in partial-wave series expansions (PWSEs) in cylindrical coordinates involving the angle of incidence, the addition theorem for the cylindrical wave functions, and the expansion coefficients of the scatterers. Numerical examples illustrate the analysis for two rigid circular cylindrical cross-sections with different radii immersed in a non-viscous fluid. Computations for the dimensionless extrinsic and intrinsic extinction cross-section factors are evaluated with particular emphasis on varying the angle of incidence, the interparticle distance, as well as the sizes of the particles. A symmetric behavior is observed for the dimensionless extrinsic extinction cross-section, while asymmetry arises for the intrinsic extinction cross-section of each particle with respect to the angle of incidence. The present analysis provides a complete analytical and computational method for the prediction of the intrinsic (local) scattering, absorption and extinction cross-sections in the multiple acoustic scatterings of plane progressive waves of arbitrary incidence by a pair of scatterers. The results and computational analyses can be used as a priori information for future applications to guide the direct or inverse characterization of multiple scattering systems in acoustically-engineered metamaterials, cloaking devices, particle dynamics, levitation, manipulation and handling, and other areas.

Multilevel fast multipole method based on a potential formulation for 3D electromagnetic scattering problems.

PubMed

Fall, Mandiaye; Boutami, Salim; Glière, Alain; Stout, Brian; Hazart, Jerome

2013-06-01

A combination of the multilevel fast multipole method (MLFMM) and boundary element method (BEM) can solve large scale photonics problems of arbitrary geometry. Here, MLFMM-BEM algorithm based on a scalar and vector potential formulation, instead of the more conventional electric and magnetic field formulations, is described. The method can deal with multiple lossy or lossless dielectric objects of arbitrary geometry, be they nested, in contact, or dispersed. Several examples are used to demonstrate that this method is able to efficiently handle 3D photonic scatterers involving large numbers of unknowns. Absorption, scattering, and extinction efficiencies of gold nanoparticle spheres, calculated by the MLFMM, are compared with Mie's theory. MLFMM calculations of the bistatic radar cross section (RCS) of a gold sphere near the plasmon resonance and of a silica coated gold sphere are also compared with Mie theory predictions. Finally, the bistatic RCS of a nanoparticle gold-silver heterodimer calculated with MLFMM is compared with unmodified BEM calculations.

Acoustic coupled fluid-structure interactions using a unified fast multipole boundary element method.

PubMed

Wilkes, Daniel R; Duncan, Alec J

2015-04-01

This paper presents a numerical model for the acoustic coupled fluid-structure interaction (FSI) of a submerged finite elastic body using the fast multipole boundary element method (FMBEM). The Helmholtz and elastodynamic boundary integral equations (BIEs) are, respectively, employed to model the exterior fluid and interior solid domains, and the pressure and displacement unknowns are coupled between conforming meshes at the shared boundary interface to achieve the acoustic FSI. The low frequency FMBEM is applied to both BIEs to reduce the algorithmic complexity of the iterative solution from O(N(2)) to O(N(1.5)) operations per matrix-vector product for N boundary unknowns. Numerical examples are presented to demonstrate the algorithmic and memory complexity of the method, which are shown to be in good agreement with the theoretical estimates, while the solution accuracy is comparable to that achieved by a conventional finite element-boundary element FSI model.

Mean-field theory for multipole ordering in f-electron systems on the basis of a j-j coupling scheme

NASA Astrophysics Data System (ADS)

Yamamura, Ryosuke; Hotta, Takashi

2018-05-01

We develop a microscopic theory for multipole ordering, applicable to the system with plural numbers of f electrons per ion, from an itinerant picture on the basis of a j-j coupling scheme. For the purpose, by introducing the Γ8 Hubbard Hamiltonian as the minimum model to discuss the multipole ordering in f-electron systems, we describe the mean-field approximation in terms of the multipole operators. For the case of n = 2 , where n denotes the average f-electron number per ion, we analyze the model on a simple cubic lattice to obtain the multipole phase diagram. In particular, we find the order of non-Kramers Γ3 quadrupoles, O20 and O22 , with different ordering vectors. We attempt to explain the phase diagram from the discussion on the interaction energy.

First-principles Theory of Magnetic Multipoles in Condensed Matter Systems

NASA Astrophysics Data System (ADS)

Suzuki, Michi-To; Ikeda, Hiroaki; Oppeneer, Peter M.

2018-04-01

The multipole concept, which characterizes the spacial distribution of scalar and vector objects by their angular dependence, has already become widely used in various areas of physics. In recent years it has become employed to systematically classify the anisotropic distribution of electrons and magnetization around atoms in solid state materials. This has been fuelled by the discovery of several physical phenomena that exhibit unusual higher rank multipole moments, beyond that of the conventional degrees of freedom as charge and magnetic dipole moment. Moreover, the higher rank electric/magnetic multipole moments have been suggested as promising order parameters in exotic hidden order phases. While the experimental investigations of such anomalous phases have provided encouraging observations of multipolar order, theoretical approaches have developed at a slower pace. In particular, a materials' specific theory has been missing. The multipole concept has furthermore been recognized as the key quantity which characterizes the resultant configuration of magnetic moments in a cluster of atomic moments. This cluster multipole moment has then been introduced as macroscopic order parameter for a noncollinear antiferromagnetic structure in crystals that can explain unusual physical phenomena whose appearance is determined by the magnetic point group symmetry. It is the purpose of this review to discuss the recent developments in the first-principles theory investigating multipolar degrees of freedom in condensed matter systems. These recent developments exemplify that ab initio electronic structure calculations can unveil detailed insight in the mechanism of physical phenomena caused by the unconventional, multipole degree of freedom.

A wideband FMBEM for 2D acoustic design sensitivity analysis based on direct differentiation method

NASA Astrophysics Data System (ADS)

Chen, Leilei; Zheng, Changjun; Chen, Haibo

2013-09-01

This paper presents a wideband fast multipole boundary element method (FMBEM) for two dimensional acoustic design sensitivity analysis based on the direct differentiation method. The wideband fast multipole method (FMM) formed by combining the original FMM and the diagonal form FMM is used to accelerate the matrix-vector products in the boundary element analysis. The Burton-Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The strongly singular and hypersingular integrals in the sensitivity equations can be evaluated explicitly and directly by using the piecewise constant discretization. The iterative solver GMRES is applied to accelerate the solution of the linear system of equations. A set of optimal parameters for the wideband FMBEM design sensitivity analysis are obtained by observing the performances of the wideband FMM algorithm in terms of computing time and memory usage. Numerical examples are presented to demonstrate the efficiency and validity of the proposed algorithm.

Electronic structure of an anticancer drug DC81 and its interaction with DNA base pairs

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

Tiwari, Gargi, E-mail: gargi.tiwari@rediffmail.com; Sharma, Dipendra, E-mail: d-11sharma@rediffmail.com; Dwivedi, K. K., E-mail: dwivedikarunesh4@gmail.com

The drug, 8-Hydroxy-7-methoxy-pyrrolo-[2,1-c][1,4] benzodiazepine-5-one, commonly christened as DC81 belongs to the pyrrolo-[2,1-c][1,4]benzodiazepine (PBDs) family. It is a member of the group of naturally occurring antitumour antibiotics produced by various Streptomyces species. The antitumour activity of DC81 is attributed to its sequence specific interaction with G-C rich DNA region in particular, for Pu-G-Pu motifs. In the present paper, physico-chemical properties DC81 have been carried out using an ab-initio method, HF/6-31G(d,p) with GAMESS program. MEP, HOMO and LUMO surfaces have been scanned. Ionization potential, electron affinity, electronegativity, global hardness and softness of the drug have been calculated. Further, drug-DNA interactions have beenmore » examined using modified second order perturbation theory along with multicentred-multipole expansion technique. Results have been discussed in the light of other theoretical and experimental observations. Efforts have been made to elucidate the binding patterns and thereby biological properties of the drug.« less

Self-diffusion in MgO--a density functional study.

PubMed

Runevall, Odd; Sandberg, Nils

2011-08-31

Density functional theory calculations have been performed to study self-diffusion in magnesium oxide, a model material for a wide range of ionic compounds. Formation energies and entropies of Schottky defects and divacancies were obtained by means of total energy and phonon calculations in supercell configurations. Transition state theory was used to estimate defect migration rates, with migration energies taken from static calculations, and the corresponding frequency factors estimated from the phonon spectrum. In all static calculations we corrected for image effects using either a multipole expansion or an extrapolation to the low concentration limit. It is shown that both methods give similar results. The results for self-diffusion of Mg and O confirm the previously established picture, namely that in materials of nominal purity, Mg diffuses extrinsically by a single vacancy mechanism, while O diffuses intrinsically by a divacancy mechanism. Quantitatively, the current results are in very good agreement with experiments concerning O diffusion, while for Mg the absolute diffusion rate is generally underestimated by a factor of 5-10. The reason for this discrepancy is discussed.

Electronic structure of an anticancer drug DC81 and its interaction with DNA base pairs

NASA Astrophysics Data System (ADS)

Tiwari, Gargi; Sharma, Dipendra; Dwivedi, K. K.; Dwivedi, M. K.

2016-05-01

The drug, 8-Hydroxy-7-methoxy-pyrrolo-[2,1-c][1,4] benzodiazepine-5-one, commonly christened as DC81 belongs to the pyrrolo-[2,1-c][1,4]benzodiazepine (PBDs) family. It is a member of the group of naturally occurring antitumour antibiotics produced by various Streptomyces species. The antitumour activity of DC81 is attributed to its sequence specific interaction with G-C rich DNA region in particular, for Pu-G-Pu motifs. In the present paper, physico-chemical properties DC81 have been carried out using an ab-initio method, HF/6-31G(d,p) with GAMESS program. MEP, HOMO and LUMO surfaces have been scanned. Ionization potential, electron affinity, electronegativity, global hardness and softness of the drug have been calculated. Further, drug-DNA interactions have been examined using modified second order perturbation theory along with multicentred-multipole expansion technique. Results have been discussed in the light of other theoretical and experimental observations. Efforts have been made to elucidate the binding patterns and thereby biological properties of the drug.

Resolution of identity approximation for the Coulomb term in molecular and periodic systems.

PubMed

Burow, Asbjörn M; Sierka, Marek; Mohamed, Fawzi

2009-12-07

A new formulation of resolution of identity approximation for the Coulomb term is presented, which uses atom-centered basis and auxiliary basis functions and treats molecular and periodic systems of any dimensionality on an equal footing. It relies on the decomposition of an auxiliary charge density into charged and chargeless components. Applying the Coulomb metric under periodic boundary conditions constrains the explicit form of the charged part. The chargeless component is determined variationally and converged Coulomb lattice sums needed for its determination are obtained using chargeless linear combinations of auxiliary basis functions. The lattice sums are partitioned in near- and far-field portions which are treated through an analytical integration scheme employing two- and three-center electron repulsion integrals and multipole expansions, respectively, operating exclusively in real space. Our preliminary implementation within the TURBOMOLE program package demonstrates consistent accuracy of the method across molecular and periodic systems. Using common auxiliary basis sets the errors of the approximation are small, in average about 20 muhartree per atom, for both molecular and periodic systems.

Resolution of identity approximation for the Coulomb term in molecular and periodic systems

NASA Astrophysics Data System (ADS)

Burow, Asbjörn M.; Sierka, Marek; Mohamed, Fawzi

2009-12-01

A new formulation of resolution of identity approximation for the Coulomb term is presented, which uses atom-centered basis and auxiliary basis functions and treats molecular and periodic systems of any dimensionality on an equal footing. It relies on the decomposition of an auxiliary charge density into charged and chargeless components. Applying the Coulomb metric under periodic boundary conditions constrains the explicit form of the charged part. The chargeless component is determined variationally and converged Coulomb lattice sums needed for its determination are obtained using chargeless linear combinations of auxiliary basis functions. The lattice sums are partitioned in near- and far-field portions which are treated through an analytical integration scheme employing two- and three-center electron repulsion integrals and multipole expansions, respectively, operating exclusively in real space. Our preliminary implementation within the TURBOMOLE program package demonstrates consistent accuracy of the method across molecular and periodic systems. Using common auxiliary basis sets the errors of the approximation are small, in average about 20 μhartree per atom, for both molecular and periodic systems.

A field-cancellation algorithm for constructing economical planar permanent magnet (PM) multipoles with large high-quality field apertures

NASA Astrophysics Data System (ADS)

Tatchyn, Roman

1997-05-01

In recent years studies have been initiated on a new class of multipole field generators consisting of cuboid planar permanent magnet (PM) pieces arranged in bi-planar arrays of 2-fold rotational symmetry(R. Tatchyn, "Planar Permanent Magnet Multipoles: for Particle Accelerator and Storage Ring Applications ," IEEE Trans. Mag. 30, 5050(1994).)(T. Cremer, R. Tatchyn, "Planar Permanent Magnet Multipoles: Measurements and Configurations," in Proceedings of the 1995 Particle Accelerator Conference, IEEE Catalog No. 95CH35843, paper FAQ-20.). These structures, first introduced for Free Electron Laser (FEL) applications(R. Tatchyn, "Selected applications of planar permanent magnet multipoles in FEL insertion device design," NIM A341, 449(1994).), are based on reducing the rotational symmetry of conventional N-pole field generators from N-fold to 2-fold. One consequence of this reduction is a large higher-multipole content in a planar PM multipole's field at distances relatively close to the structure's axis, making it generally unsuitable for applications requiring a large high-quality field aperture. In this paper we outline an economical field-cancellation algorithm that can substantially decrease the harmonic content of a planar PM's field without breaking its biplanar geometry or 2-fold rotational symmetry. This will enable planar PM multipoles to be employed in a broader range of applications than heretofore possible, in particular as distributed focusing elements installed in insertion device gaps on synchrotron storage rings. This accomplishment is expected to remove the conventional restriction of an insertion device's length to the scale of the local focusing beta, enabling short-period, small-gap undulators to be installed and operated as high-brightness sources on lower-energy storage rings(R. Tatchyn, P. Csonka, A. Toor, "Perspectives on micropole undulators in synchrotron radiation technology," Rev. Sci. Instrum. 60(7), 1796(1989).). Operation as ordinary focusing elements in storage ring magnetic lattices, as well as the performance of other high-quality multipole applications, should also becomes possible with the realization of the proposed structures.

Multipole vectors: A new representation of the CMB sky and evidence for statistical anisotropy or non-Gaussianity at 2⩽l⩽8

NASA Astrophysics Data System (ADS)

Copi, Craig J.; Huterer, Dragan; Starkman, Glenn D.

2004-08-01

We propose a novel representation of cosmic microwave anisotropy maps, where each multipole order l is represented by l unit vectors pointing in directions on the sky and an overall magnitude. These “multipole vectors and scalars” transform as vectors under rotations. Like the usual spherical harmonics, multipole vectors form an irreducible representation of the proper rotation group SO(3). However, they are related to the familiar spherical harmonic coefficients alm in a nonlinear way and are therefore sensitive to different aspects of the cosmic microwave background (CMB) anisotropy. Nevertheless, it is straightforward to determine the multipole vectors for a given CMB map and we present an algorithm to compute them. A code implementing this algorithm is available at http://www.phys.cwru.edu/projects/mpvectors/. Using the Wilkinson Microwave Anisotropy Probe (WMAP) full-sky maps, we perform several tests of the hypothesis that the CMB anisotropy is statistically isotropic and Gaussian random. We find that the result from comparing the oriented area of planes defined by these vectors between multipole pairs 2⩽l1≠l2⩽8 is inconsistent with the isotropic Gaussian hypothesis at the 99.4% level for the internal linear combination map and at 98.9% level for the cleaned map of Tegmark et al. A particular correlation is suggested between the l=3 and l=8 multipoles, as well as several other pairs. This effect is entirely different from the now familiar planarity and alignment of the quadrupole and octupole: while the aforementioned is fairly unlikely, the multipole vectors indicate correlations not expected in Gaussian random skies that make them unusually likely. The result persists after accounting for pixel noise and after assuming a residual 10% dust contamination in the cleaned WMAP map. While the definitive analysis of these results will require more work, we hope that multipole vectors will become a valuable tool for various cosmological tests, in particular those of cosmic isotropy.

Parallel fast multipole boundary element method applied to computational homogenization

NASA Astrophysics Data System (ADS)

Ptaszny, Jacek

2018-01-01

In the present work, a fast multipole boundary element method (FMBEM) and a parallel computer code for 3D elasticity problem is developed and applied to the computational homogenization of a solid containing spherical voids. The system of equation is solved by using the GMRES iterative solver. The boundary of the body is dicretized by using the quadrilateral serendipity elements with an adaptive numerical integration. Operations related to a single GMRES iteration, performed by traversing the corresponding tree structure upwards and downwards, are parallelized by using the OpenMP standard. The assignment of tasks to threads is based on the assumption that the tree nodes at which the moment transformations are initialized can be partitioned into disjoint sets of equal or approximately equal size and assigned to the threads. The achieved speedup as a function of number of threads is examined.

Nonlinear gravitational self-force: Field outside a small body

NASA Astrophysics Data System (ADS)

Pound, Adam

2012-10-01

A small extended body moving through an external spacetime gαβ creates a metric perturbation hαβ, which forces the body away from geodesic motion in gαβ. The foundations of this effect, called the gravitational self-force, are now well established, but concrete results have mostly been limited to linear order. Accurately modeling the dynamics of compact binaries requires proceeding to nonlinear orders. To that end, I show how to obtain the metric perturbation outside the body at all orders in a class of generalized wave gauges. In a small buffer region surrounding the body, the form of the perturbation can be found analytically as an expansion for small distances r from a representative worldline. Given only a specification of the body’s multipole moments, the field obtained in the buffer region suffices to find the metric everywhere outside the body via a numerical puncture scheme. Following this procedure at first and second order, I calculate the field in the buffer region around an arbitrarily structured compact body at sufficiently high order in r to numerically implement a second-order puncture scheme, including effects of the body’s spin. I also define nth-order (local) generalizations of the Detweiler-Whiting singular and regular fields and show that in a certain sense, the body can be viewed as a skeleton of multipole moments.

Reconfigurable lateral optical force achieved by selectively exciting plasmonic dark modes near Fano resonance

NASA Astrophysics Data System (ADS)

Chen, Huajin; Ye, Qian; Zhang, Yiwen; Shi, Lei; Liu, Shiyang; Jian, Zi; Lin, Zhifang

2017-08-01

We demonstrate a reconfigurable lateral optical force (OF) on a plasmonic nanoparticle immersed in a simple optical field invariant along the lateral direction and formed by two interfering plane waves. This lateral OF is shown, from the multipolar expansion technique, attributed to several coupling channels established between multiple multipoles excited on a plasmonic nanoparticle, in particular, the adjacent electric multipole modes that bring about the Fano interferences, which can substantially enhance the lateral scattering asymmetry, leading to an augmented lateral OF comparable to the longitudinal OF. More importantly, by engineering Fano interference either intrinsically through particle size or extrinsically through selectively exciting narrow plasmonic dark modes the direction of the lateral OF is reversibly switchable. The lateral OF can even be modulated continuously from positive to negative by controlling the incident angle of the interfering plane waves due to the variation of relative phase of the excited plasmonic dark modes near Fano resonance, facilitating the plasmonic nanoparticle as a controllable conveyor as well as the optical selection and separation. Besides, a fundamental and counterintuitive physical consequence emerges in that the simple proportional relation between the lateral OF and the Belinfante spin momentum derived in the small particle limit breaks down when the Fano interference comes into play, in particular, a negative lateral OF opposite the Belinfante spin momentum can be induced by properly controlling the selective excitation.

Calculations of molecular multipole electric moments of a series of exo-insaturated four-membered heterocycles, Y = CCH2CH2X

NASA Astrophysics Data System (ADS)

Romero, Angel H.

2017-10-01

The influence of ring puckering angle on the multipole moments of sixteen four-membered heterocycles (1-16) was theoretically estimated using MP2 and different DFTs in combination with the 6-31+G(d,p) basis set. To obtain an accurate evaluation, CCSD/cc-pVDZ level and, the MP2 and PBE1PBE methods in combination with the aug-cc-pVDZ and aug-cc-pVTZ basis sets were performed on the planar geometries of 1-16. In general, the DFT and MP2 approaches provided an identical dependence of the electrical properties with the puckering angle for 1-16. Quantitatively, the quality of the level of theory and basis sets affects significant the predictions of the multipole moments, in particular for the heterocycles containing C=O and C=S bonds. Convergence basis sets within the MP2 and PBE1PBE approximations are reached in the dipole moment calculations when the aug-cc-pVTZ basis set is used, while the quadrupole and octupole moment computations require a larger basis set than aug-cc-pVTZ. On the other hand, the multipole moments showed a strong dependence with the molecular geometry and the nature of the carbon-heteroatom bonds. Specifically, the C-X bond determines the behavior of the μ(ϕ), θ(ϕ) and Ώ(ϕ) functions, while the C=Y bond plays an important role in the magnitude of the studied properties.

Interactions of molecules and the properties of crystals

NASA Astrophysics Data System (ADS)

McConnell, Thomas Daniel Leigh

In this thesis the basic theory of the lattice dynamics of molecular crystals is considered, with particular reference to the specific case of linear molecules. The objective is to carry out a critical investigation of a number of empirical potentials as models for real systems. Suitable coordinates are introduced, in particular vibrational coordinates which are used to describe the translational and rotational modes of the free molecule. The Taylor expansion of the intermolecular potential is introduced and its terms considered, in particular the (first-order) equilibrium conditions for such a system and the (second-order) lattice vibrations. The elastic properties are also considered, in particular with reference to the specific case of rhombohedral crystals. The compressibility and a number of conditions for elastic stability are introduced. The total intermolecular interaction potential is divided into three components using perturbation methods, the electrostatic energy, the repulsion energy and the dispersion energy. A number of models are introduced for these various components. The induction energy is neglected. The electrostatic interaction is represented by atomic multipole and molecular multipole models. The repulsion and dispersion energies are modelled together in a central interaction potential, either the Lennard-Jones atom-atom potential or the anisotropic Berne-Pechukas molecule-molecule potential. In each case, the Taylor expansion coefficients, used to calculate the various molecular properties, are determined. An algorithm is described which provides a relatively simple method for calculating cartesian tensors, which are found in the Taylor expansion coefficients of the multipolar potentials. This proves to be particularly useful from a computational viewpoint, both in terms of programming and calculating efficiency. The model system carbonyl sulphide is introduced and its lattice properties are described. Suitable parameters for potentials used to model the system are discussed and the simplifications to the Taylor expansion coefficients due to crystal symmetry are detailed. Four potential parameters are chosen to be fitted to four lattice properties, representing zero, first and second order Taylor expansion coefficients. The supplementary tests of a given fitted potential are detailed. A number of forms for the electrostatic interaction of carbonyl sulphide are considered, each combined with a standard atom-atom potential. The success of the molecular octupole model is considered and the inability of more complex electrostatic potentials to improve on this simple model is noted. The anisotropic Berne-Pechukas potential, which provides an increased estimate of the compressibility is considered as being an improvement on the various atom-atom potentials. The effect of varying the exponents in the atom-atom (or molecule-molecule) potential, representing a systematic variation of the repulsion and dispersion energy models, is examined and a potential which is able to reproduce all of the given lattice properties for carbonyl sulphide is obtained. The molecular crystal of cyanogen iodide is investigated. Superficially it is similar to the crystal of carbonyl sulphide and the potentials used with success for the latter are applied to cyanogen iodide to determine whether they are equally as effective models for this molecule. These potentials are found to be far less successful, in all cases yielding a number of unrealistic results. Reasons for the failure of the model are considered, in particular the 3 differences between the electrostatic properties of the two molecules are discussed. It is concluded that some of the simplifications which proved satisfactory for carbonyl sulphide are invalid for simple extension to the case of cyanogen iodide. A first estimate of the differences in the electrostatic properties is attempted, calculating the induction energies of the two molecules. The assumption that the induction energy may be neglected is justified for the case of carbonyl sulphide but found to be far less satisfactory for cyanogen iodide. Finally details of ab initio calculations are outlined. The amount of experimental data available for the electrostatic properties of the two molecules under consideration is relatively small and the experimental data which is available is supplemented by values obtained from these calculations.

Robust Diagnosis Method Based on Parameter Estimation for an Interturn Short-Circuit Fault in Multipole PMSM under High-Speed Operation.

PubMed

Lee, Jewon; Moon, Seokbae; Jeong, Hyeyun; Kim, Sang Woo

2015-11-20

This paper proposes a diagnosis method for a multipole permanent magnet synchronous motor (PMSM) under an interturn short circuit fault. Previous works in this area have suffered from the uncertainties of the PMSM parameters, which can lead to misdiagnosis. The proposed method estimates the q-axis inductance (Lq) of the faulty PMSM to solve this problem. The proposed method also estimates the faulty phase and the value of G, which serves as an index of the severity of the fault. The q-axis current is used to estimate the faulty phase, the values of G and Lq. For this reason, two open-loop observers and an optimization method based on a particle-swarm are implemented. The q-axis current of a healthy PMSM is estimated by the open-loop observer with the parameters of a healthy PMSM. The Lq estimation significantly compensates for the estimation errors in high-speed operation. The experimental results demonstrate that the proposed method can estimate the faulty phase, G, and Lq besides exhibiting robustness against parameter uncertainties.

A Wideband Fast Multipole Method for the two-dimensional complex Helmholtz equation

NASA Astrophysics Data System (ADS)

Cho, Min Hyung; Cai, Wei

2010-12-01

A Wideband Fast Multipole Method (FMM) for the 2D Helmholtz equation is presented. It can evaluate the interactions between N particles governed by the fundamental solution of 2D complex Helmholtz equation in a fast manner for a wide range of complex wave number k, which was not easy with the original FMM due to the instability of the diagonalized conversion operator. This paper includes the description of theoretical backgrounds, the FMM algorithm, software structures, and some test runs. Program summaryProgram title: 2D-WFMM Catalogue identifier: AEHI_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHI_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.: 4636 No. of bytes in distributed program, including test data, etc.: 82 582 Distribution format: tar.gz Programming language: C Computer: Any Operating system: Any operating system with gcc version 4.2 or newer Has the code been vectorized or parallelized?: Multi-core processors with shared memory RAM: Depending on the number of particles N and the wave number k Classification: 4.8, 4.12 External routines: OpenMP ( http://openmp.org/wp/) Nature of problem: Evaluate interaction between N particles governed by the fundamental solution of 2D Helmholtz equation with complex k. Solution method: Multilevel Fast Multipole Algorithm in a hierarchical quad-tree structure with cutoff level which combines low frequency method and high frequency method. Running time: Depending on the number of particles N, wave number k, and number of cores in CPU. CPU time increases as N log N.

An improved fast multipole method for electrostatic potential calculations in a class of coarse-grained molecular simulations

NASA Astrophysics Data System (ADS)

Poursina, Mohammad; Anderson, Kurt S.

2014-08-01

This paper presents a novel algorithm to approximate the long-range electrostatic potential field in the Cartesian coordinates applicable to 3D coarse-grained simulations of biopolymers. In such models, coarse-grained clusters are formed via treating groups of atoms as rigid and/or flexible bodies connected together via kinematic joints. Therefore, multibody dynamic techniques are used to form and solve the equations of motion of such coarse-grained systems. In this article, the approximations for the potential fields due to the interaction between a highly negatively/positively charged pseudo-atom and charged particles, as well as the interaction between clusters of charged particles, are presented. These approximations are expressed in terms of physical and geometrical properties of the bodies such as the entire charge, the location of the center of charge, and the pseudo-inertia tensor about the center of charge of the clusters. Further, a novel substructuring scheme is introduced to implement the presented far-field potential evaluations in a binary tree framework as opposed to the existing quadtree and octree strategies of implementing fast multipole method. Using the presented Lagrangian grids, the electrostatic potential is recursively calculated via sweeping two passes: assembly and disassembly. In the assembly pass, adjacent charged bodies are combined together to form new clusters. Then, the potential field of each cluster due to its interaction with faraway resulting clusters is recursively calculated in the disassembly pass. The method is highly compatible with multibody dynamic schemes to model coarse-grained biopolymers. Since the proposed method takes advantage of constant physical and geometrical properties of rigid clusters, improvement in the overall computational cost is observed comparing to the tradition application of fast multipole method.

Schwarzschild black hole encircled by a rotating thin disc: Properties of perturbative solution

NASA Astrophysics Data System (ADS)

Kotlařík, P.; Semerák, O.; Čížek, P.

2018-04-01

Will [Astrophys. J. 191, 521 (1974), 10.1086/152992] solved the perturbation of a Schwarzschild black hole due to a slowly rotating light concentric thin ring, using Green's functions expressed as infinite-sum expansions in multipoles and in the small mass and rotational parameters. In a previous paper [P. Čížek and O. Semerák, Astrophys. J. Suppl. Ser. 232, 14 (2017), 10.3847/1538-4365/aa876b], we expressed the Green functions in closed form containing elliptic integrals, leaving just summation over the mass expansion. Such a form is more practical for numerical evaluation, but mainly for generalizing the problem to extended sources where the Green functions have to be integrated over the source. We exemplified the method by computing explicitly the first-order perturbation due to a slowly rotating thin disc lying between two finite radii. After finding basic parameters of the system—mass and angular momentum of the black hole and of the disc—we now add further properties, namely those which reveal how the disc gravity influences geometry of the black-hole horizon and those of circular equatorial geodesics (specifically, radii of the photon, marginally bound and marginally stable orbits). We also realize that, in the linear order, no ergosphere occurs and the central singularity remains pointlike, and check the implications of natural physical requirements (energy conditions and subluminal restriction on orbital speed) for the single-stream as well as counter-rotating double-stream interpretations of the disc.

Roles of NN-interaction components in shell-structure evolution

NASA Astrophysics Data System (ADS)

Umeya, Atsushi; Muto, Kazuo

2016-11-01

Since the importance of the monopole interaction was first emphasized in 1960s, roles of monopole strengths of two-body nucleon-nucleon interaction in shell structure have been discussed. Through the monopole strengths, we study the roles in shell-structure evolution, starting from explicit forms of the interaction. For the tensor component of the interaction, we show the derivation of the relation, (2j> + 1)Vjj> + (2j< + 1)Vjj< = 0, with a detailed manipulation. We show that one-body spin-orbit term appears in the multipole expansion of two-body spin-orbit interaction. Only the spin-orbit components can affect the spin-orbit energy splitting between spin-orbit partners, when the spin-orbit partner orbits are fully occupied.

Geometry-dependent atomic multipole models for the water molecule.

PubMed

Loboda, O; Millot, C

2017-10-28

Models of atomic electric multipoles for the water molecule have been optimized in order to reproduce the electric potential around the molecule computed by ab initio calculations at the coupled cluster level of theory with up to noniterative triple excitations in an augmented triple-zeta quality basis set. Different models of increasing complexity, from atomic charges up to models containing atomic charges, dipoles, and quadrupoles, have been obtained. The geometry dependence of these atomic multipole models has been investigated by changing bond lengths and HOH angle to generate 125 molecular structures (reduced to 75 symmetry-unique ones). For several models, the atomic multipole components have been fitted as a function of the geometry by a Taylor series of fourth order in monomer coordinate displacements.

Geometry-dependent atomic multipole models for the water molecule

NASA Astrophysics Data System (ADS)

Loboda, O.; Millot, C.

2017-10-01

Models of atomic electric multipoles for the water molecule have been optimized in order to reproduce the electric potential around the molecule computed by ab initio calculations at the coupled cluster level of theory with up to noniterative triple excitations in an augmented triple-zeta quality basis set. Different models of increasing complexity, from atomic charges up to models containing atomic charges, dipoles, and quadrupoles, have been obtained. The geometry dependence of these atomic multipole models has been investigated by changing bond lengths and HOH angle to generate 125 molecular structures (reduced to 75 symmetry-unique ones). For several models, the atomic multipole components have been fitted as a function of the geometry by a Taylor series of fourth order in monomer coordinate displacements.

15 cm mercury multipole thruster

NASA Technical Reports Server (NTRS)

Longhurst, G. R.; Wilbur, P. J.

1978-01-01

A 15 cm multipole ion thruster was adapted for use with mercury propellant. During the optimization process three separable functions of magnetic fields within the discharge chamber were identified: (1) they define the region where the bulk of ionization takes place, (2) they influence the magnitudes and gradients in plasma properties in this region, and (3) they control impedance between the cathode and main discharge plasmas in hollow cathode thrusters. The mechanisms for these functions are discussed. Data from SERT II and cusped magnetic field thrusters are compared with those measured in the multipole thruster. The performance of this thruster is shown to be similar to that of the other two thrusters. Means of achieving further improvement in the performance of the multipole thruster are suggested.

Testing Gravity and Cosmic Acceleration with Galaxy Clustering

NASA Astrophysics Data System (ADS)

Kazin, Eyal; Tinker, J.; Sanchez, A. G.; Blanton, M.

2012-01-01

The large-scale structure contains vast amounts of cosmological information that can help understand the accelerating nature of the Universe and test gravity on large scales. Ongoing and future sky surveys are designed to test these using various techniques applied on clustering measurements of galaxies. We present redshift distortion measurements of the Sloan Digital Sky Survey II Luminous Red Galaxy sample. We find that when combining the normalized quadrupole Q with the projected correlation function wp(rp) along with cluster counts (Rapetti et al. 2010), results are consistent with General Relativity. The advantage of combining Q and wp is the addition of the bias information, when using the Halo Occupation Distribution framework. We also present improvements to the standard technique of measuring Hubble expansion rates H(z) and angular diameter distances DA(z) when using the baryonic acoustic feature as a standard ruler. We introduce clustering wedges as an alternative basis to the multipole expansion and show that it yields similar constraints. This alternative basis serves as a useful technique to test for systematics, and ultimately improve measurements of the cosmic acceleration.

Collisionless Spectral Kinetic Simulation of Ideal Multipole Resonance Probe

NASA Astrophysics Data System (ADS)

Gong, Junbo; Wilczek, Sebastian; Szeremley, Daniel; Oberrath, Jens; Eremin, Denis; Dobrygin, Wladislaw; Schilling, Christian; Friedrichs, Michael; Brinkmann, Ralf Peter

2016-09-01

Active Plasma Resonance Spectroscopy denotes a class of industry-compatible plasma diagnostic methods which utilize the natural ability of plasmas to resonate on or near the electron plasma frequency ωpe. One particular realization of APRS with a high degree of geometric and electric symmetry is the Multipole Resonance Probe (MRP). The Ideal MRP(IMRP) is an even more symmetric idealization which is suited for theoretical investigations. In this work, a spectral kinetic scheme is presented to investigate the behavior of the IMRP in the low pressure regime. However, due to the velocity difference, electrons are treated as particles whereas ions are only considered as stationary background. In the scheme, the particle pusher integrates the equations of motion for the studied particles, the Poisson solver determines the electric field at each particle position. The proposed method overcomes the limitation of the cold plasma model and covers kinetic effects like collisionless damping.

Active Plasma Resonance Spectroscopy: Evaluation of a fluiddynamic-model of the planar multipole resonance probe using functional analytic methods

NASA Astrophysics Data System (ADS)

Friedrichs, Michael; Brinkmann, Ralf Peter; Oberrath, Jens

2016-09-01

Measuring plasma parameters, e.g. electron density and electron temperature, is an important procedure to verify the stability and behavior of a plasma process. For this purpose the multipole resonance probe (MRP) represents a satisfying solution to measure the electron density. However the influence of the probe on the plasma through its physical presence makes it unattractive for some processes in industrial application. A solution to combine the benefits of the spherical MRP with the ability to integrate the probe into the plasma reactor is introduced by the planar model of the MRP. By coupling the model of the cold plasma with the maxwell equations for electrostatics an analytical model for the admittance of the plasma is derivated, adjusted to cylindrical geometry and solved analytically for the planar MRP using functional analytic methods.

The Fast Multipole Method and Fourier Convolution for the Solution of Acoustic Scattering on Regular Volumetric Grids

PubMed Central

Hesford, Andrew J.; Waag, Robert C.

2010-01-01

The fast multipole method (FMM) is applied to the solution of large-scale, three-dimensional acoustic scattering problems involving inhomogeneous objects defined on a regular grid. The grid arrangement is especially well suited to applications in which the scattering geometry is not known a priori and is reconstructed on a regular grid using iterative inverse scattering algorithms or other imaging techniques. The regular structure of unknown scattering elements facilitates a dramatic reduction in the amount of storage and computation required for the FMM, both of which scale linearly with the number of scattering elements. In particular, the use of fast Fourier transforms to compute Green's function convolutions required for neighboring interactions lowers the often-significant cost of finest-level FMM computations and helps mitigate the dependence of FMM cost on finest-level box size. Numerical results demonstrate the efficiency of the composite method as the number of scattering elements in each finest-level box is increased. PMID:20835366

The fast multipole method and Fourier convolution for the solution of acoustic scattering on regular volumetric grids

NASA Astrophysics Data System (ADS)

Hesford, Andrew J.; Waag, Robert C.

2010-10-01

The fast multipole method (FMM) is applied to the solution of large-scale, three-dimensional acoustic scattering problems involving inhomogeneous objects defined on a regular grid. The grid arrangement is especially well suited to applications in which the scattering geometry is not known a priori and is reconstructed on a regular grid using iterative inverse scattering algorithms or other imaging techniques. The regular structure of unknown scattering elements facilitates a dramatic reduction in the amount of storage and computation required for the FMM, both of which scale linearly with the number of scattering elements. In particular, the use of fast Fourier transforms to compute Green's function convolutions required for neighboring interactions lowers the often-significant cost of finest-level FMM computations and helps mitigate the dependence of FMM cost on finest-level box size. Numerical results demonstrate the efficiency of the composite method as the number of scattering elements in each finest-level box is increased.

The Fast Multipole Method and Fourier Convolution for the Solution of Acoustic Scattering on Regular Volumetric Grids.

PubMed

Hesford, Andrew J; Waag, Robert C

2010-10-20

The fast multipole method (FMM) is applied to the solution of large-scale, three-dimensional acoustic scattering problems involving inhomogeneous objects defined on a regular grid. The grid arrangement is especially well suited to applications in which the scattering geometry is not known a priori and is reconstructed on a regular grid using iterative inverse scattering algorithms or other imaging techniques. The regular structure of unknown scattering elements facilitates a dramatic reduction in the amount of storage and computation required for the FMM, both of which scale linearly with the number of scattering elements. In particular, the use of fast Fourier transforms to compute Green's function convolutions required for neighboring interactions lowers the often-significant cost of finest-level FMM computations and helps mitigate the dependence of FMM cost on finest-level box size. Numerical results demonstrate the efficiency of the composite method as the number of scattering elements in each finest-level box is increased.

An accurate and efficient acoustic eigensolver based on a fast multipole BEM and a contour integral method

NASA Astrophysics Data System (ADS)

Zheng, Chang-Jun; Gao, Hai-Feng; Du, Lei; Chen, Hai-Bo; Zhang, Chuanzeng

2016-01-01

An accurate numerical solver is developed in this paper for eigenproblems governed by the Helmholtz equation and formulated through the boundary element method. A contour integral method is used to convert the nonlinear eigenproblem into an ordinary eigenproblem, so that eigenvalues can be extracted accurately by solving a set of standard boundary element systems of equations. In order to accelerate the solution procedure, the parameters affecting the accuracy and efficiency of the method are studied and two contour paths are compared. Moreover, a wideband fast multipole method is implemented with a block IDR (s) solver to reduce the overall solution cost of the boundary element systems of equations with multiple right-hand sides. The Burton-Miller formulation is employed to identify the fictitious eigenfrequencies of the interior acoustic problems with multiply connected domains. The actual effect of the Burton-Miller formulation on tackling the fictitious eigenfrequency problem is investigated and the optimal choice of the coupling parameter as α = i / k is confirmed through exterior sphere examples. Furthermore, the numerical eigenvalues obtained by the developed method are compared with the results obtained by the finite element method to show the accuracy and efficiency of the developed method.

Correlated isocurvature fluctuation in quintessence and suppressed cosmic microwave background anisotropies at low multipoles.

PubMed

Moroi, Takeo; Takahashi, Tomo

2004-03-05

We consider cosmic microwave background (CMB) anisotropy in models with quintessence, taking into account isocurvature fluctuation. It is shown that, if the primordial fluctuation of the quintessence has a correlation with the adiabatic density fluctuations, the CMB angular power spectrum C(l) at low multipoles can be suppressed without affecting C(l) at high multipoles. A possible scenario for generating a correlated mixture of the quintessence and adiabatic fluctuations is also discussed.

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→∞.

Electromagnetic multipole moments of the P_c^+(4380) pentaquark in light-cone QCD

NASA Astrophysics Data System (ADS)

Özdem, U.; Azizi, K.

2018-05-01

We calculate the electromagnetic multipole moments of the P_c^+(4380) pentaquark by modeling it as the diquark-diquark-antiquark and {\\bar{D}}^*Σ _c molecular state with quantum numbers J^P = 3/2^-. In particular, the magnetic dipole, electric quadrupole and magnetic octupole moments of this particle are extracted in the framework of light-cone QCD sum rule. The values of the electromagnetic multipole moments obtained via two pictures differ substantially from each other, which can be used to pin down the underlying structure of P_c^+(4380). The comparison of any future experimental data on the electromagnetic multipole moments of the P_c^+(4380) pentaquark with the results of the present work can shed light on the nature and inner quark organization of this state.

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: Inverse computation for cardiac sources using single current dipole and current multipole models

NASA Astrophysics Data System (ADS)

Wang, Qian; Ma, Ping; Lu, Hong; Tang, Xue-Zheng; Hua, Ning; Tang, Fa-Kuan

2009-12-01

Two cardiac functional models are constructed in this paper. One is a single current model and the other is a current multipole model. Parameters denoting the properties of these two models are calculated by a least-square fit to the measurements using a simulated annealing algorithm. The measured signals are detected at 36 observation nodes by a superconducting quantum interference device (SQUID). By studying the trends of position, orientation and magnitude of the single current dipole model and the current multipole model in the QRS complex during one time span and comparing the reconstructed magnetocardiography (MCG) of these two cardiac models, we find that the current multipole model is a more appropriate model to represent cardiac electrophysiological activity.

Application of Fast Multipole Methods to the NASA Fast Scattering Code

NASA Technical Reports Server (NTRS)

Dunn, Mark H.; Tinetti, Ana F.

2008-01-01

The NASA Fast Scattering Code (FSC) is a versatile noise prediction program designed to conduct aeroacoustic noise reduction studies. The equivalent source method is used to solve an exterior Helmholtz boundary value problem with an impedance type boundary condition. The solution process in FSC v2.0 requires direct manipulation of a large, dense system of linear equations, limiting the applicability of the code to small scales and/or moderate excitation frequencies. Recent advances in the use of Fast Multipole Methods (FMM) for solving scattering problems, coupled with sparse linear algebra techniques, suggest that a substantial reduction in computer resource utilization over conventional solution approaches can be obtained. Implementation of the single level FMM (SLFMM) and a variant of the Conjugate Gradient Method (CGM) into the FSC is discussed in this paper. The culmination of this effort, FSC v3.0, was used to generate solutions for three configurations of interest. Benchmarking against previously obtained simulations indicate that a twenty-fold reduction in computational memory and up to a four-fold reduction in computer time have been achieved on a single processor.

A minimally-resolved immersed boundary model for reaction-diffusion problems

NASA Astrophysics Data System (ADS)

Pal Singh Bhalla, Amneet; Griffith, Boyce E.; Patankar, Neelesh A.; Donev, Aleksandar

2013-12-01

We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blob model can provide an accurate representation at low to moderate packing densities of the reactive particles, at a cost not much larger than solving a Poisson equation in the same domain. Unlike multipole expansion methods, our method does not require analytically computed Green's functions, but rather, computes regularized discrete Green's functions on the fly by using a standard grid-based discretization of the Poisson equation. This allows for great flexibility in implementing different boundary conditions, coupling to fluid flow or thermal transport, and the inclusion of other effects such as temporal evolution and even nonlinearities. We develop multigrid-based preconditioners for solving the linear systems that arise when using implicit temporal discretizations or studying steady states. In the diffusion-limited case the resulting linear system is a saddle-point problem, the efficient solution of which remains a challenge for suspensions of many particles. We validate our method by comparing to published results on reaction-diffusion in ordered and disordered suspensions of reactive spheres.

Generic Long-Range Interactions Between Passive Bodies in an Active Fluid.

PubMed

Baek, Yongjoo; Solon, Alexandre P; Xu, Xinpeng; Nikola, Nikolai; Kafri, Yariv

2018-02-02

A single nonspherical body placed in an active fluid generates currents via breaking of time-reversal symmetry. We show that, when two or more passive bodies are placed in an active fluid, these currents lead to long-range interactions. Using a multipole expansion, we characterize their leading-order behaviors in terms of single-body properties and show that they decay as a power law with the distance between the bodies, are anisotropic, and do not obey an action-reaction principle. The interactions lead to rich dynamics of the bodies, illustrated by the spontaneous synchronized rotation of pinned nonchiral bodies and the formation of traveling bound pairs. The occurrence of these phenomena depends on tunable properties of the bodies, thus opening new possibilities for self-assembly mediated by active fluids.

Fast Particle Methods for Multiscale Phenomena Simulations

NASA Technical Reports Server (NTRS)

Koumoutsakos, P.; Wray, A.; Shariff, K.; Pohorille, Andrew

2000-01-01

We are developing particle methods oriented at improving computational modeling capabilities of multiscale physical phenomena in : (i) high Reynolds number unsteady vortical flows, (ii) particle laden and interfacial flows, (iii)molecular dynamics studies of nanoscale droplets and studies of the structure, functions, and evolution of the earliest living cell. The unifying computational approach involves particle methods implemented in parallel computer architectures. The inherent adaptivity, robustness and efficiency of particle methods makes them a multidisciplinary computational tool capable of bridging the gap of micro-scale and continuum flow simulations. Using efficient tree data structures, multipole expansion algorithms, and improved particle-grid interpolation, particle methods allow for simulations using millions of computational elements, making possible the resolution of a wide range of length and time scales of these important physical phenomena.The current challenges in these simulations are in : [i] the proper formulation of particle methods in the molecular and continuous level for the discretization of the governing equations [ii] the resolution of the wide range of time and length scales governing the phenomena under investigation. [iii] the minimization of numerical artifacts that may interfere with the physics of the systems under consideration. [iv] the parallelization of processes such as tree traversal and grid-particle interpolations We are conducting simulations using vortex methods, molecular dynamics and smooth particle hydrodynamics, exploiting their unifying concepts such as : the solution of the N-body problem in parallel computers, highly accurate particle-particle and grid-particle interpolations, parallel FFT's and the formulation of processes such as diffusion in the context of particle methods. This approach enables us to transcend among seemingly unrelated areas of research.

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

pureS2HAT: S 2HAT-based Pure E/B Harmonic Transforms

NASA Astrophysics Data System (ADS)

Grain, J.; Stompor, R.; Tristram, M.

2011-10-01

The pS2HAT routines allow efficient, parallel calculation of the so-called 'pure' polarized multipoles. The computed multipole coefficients are equal to the standard pseudo-multipoles calculated for the apodized sky maps of the Stokes parameters Q and U subsequently corrected by so-called counterterms. If the applied apodizations fullfill certain boundary conditions, these multipoles correspond to the pure multipoles. Pure multipoles of one type, i.e., either E or B, are ensured not to contain contributions from the other one, at least to within numerical artifacts. They can be therefore further used in the estimation of the sky power spectra via the pseudo power spectrum technique, which has to however correctly account for the applied apodization on the one hand, and the presence of the counterterms, on the other. In addition, the package contains the routines permitting calculation of the spin-weighted apodizations, given an input scalar, i.e., spin-0 window. The former are needed to compute the counterterms. It also provides routines for maps and window manipulations. The routines are written in C and based on the S2HAT library, which is used to perform all required spherical harmonic transforms as well as all inter-processor communication. They are therefore parallelized using MPI and follow the distributed-memory computational model. The data distribution patterns, pixelization choices, conventions etc are all as those assumed/allowed by the S2HAT library.

Pushing, pulling and electromagnetic radiation force cloaking by a pair of conducting cylindrical particles

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2018-02-01

The present analysis shows that two conducting cylindrical particles illuminated by an axially-polarized electric field of plane progressive waves at arbitrary incidence will attract, repel or become totally cloaked (i.e., invisible to the transfer of linear momentum carried by the incident waves), depending on their sizes, the interparticle distance as well as the angle of incidence of the incident field. Based on the rigorous multipole expansion method and the translational addition theorem of cylindrical wave functions, the electromagnetic (EM) radiation forces arising from multiple scattering effects between a pair of perfectly conducting cylindrical particles of circular cross-sections are derived and computed. An effective incident field on a particular particle is determined first, and used subsequently with its corresponding scattered field to derive the closed-form analytical expressions for the radiation force vector components. The mathematical expressions for the EM radiation force components (i.e. longitudinal and transverse) are exact, and have been formulated in partial-wave series expansions in cylindrical coordinates involving the angle of incidence, the interparticle distance and the expansion coefficients. Numerical examples illustrate the analysis for two perfectly conducting circular cylinders in a homogeneous nonmagnetic medium of wave propagation. The computations for the dimensionless radiation force functions are performed with particular emphasis on varying the angle of incidence, the interparticle distance, and the sizes of the particles. Depending on the interparticle distance and angle of incidence, the cylinders yield total neutrality (or invisibility); they experience no force and become unresponsive to the transfer of the EM linear momentum due to multiple scattering cancellation effects. Moreover, pushing or pulling EM forces between the two cylinders arise depending on the interparticle distance, the angle of incidence and their size parameters. This study provides a complete analytical method and computations for the longitudinal and transverse radiation force components in the multiple scattering of EM plane progressive waves with potential applications in particle manipulation, optically-engineered metamaterials with reconfigurable periodicities and cloaking devices to name a few examples.

Ab initio study of the electrostatic multipole nature of torsional potentials in CH3SSCH3, CH3SSH, and HOOH

NASA Technical Reports Server (NTRS)

Sokalski, W. A.; Lai, J.; Luo, N.; Sun, S.; Shibata, M.; Ornstein, R.; Rein, R.

1991-01-01

The origin of torsional potentials in H3CSSCH3, H3CSSH, and HOOH and the anisotropy of the local charge distribution has been analyzed in terms of atomic multipoles calculated from the ab initio LCAO-MO-SCF wave function in the 6-31G* basis set. The results indicate that for longer -S-S-bonds the major contribution to these torsional barriers are electrostatic interactions of the atomic multipoles located on two atoms forming the rotated bond. This finding demonstrates the important role of electrostatic 1-2 interatomic interactions, usually neglected in conformational studies. It also opens the possibility to derive directly from accurate ab initio wave functions a simple nonempirical torsional potential involving atomic multipoles of two bonded atoms defining the torsional angle. For shorter -O-O- bonds, use of more precise models and inclusion of 1-3 interactions seems to be necessary.

Tunable multipole resonances in plasmonic crystals made by four-beam holographic lithography

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

Luo, Y.; Li, X.; Zhang, X.

2016-02-01

Plasmonic nanostructures confine light to sub-wavelength scales, resulting in drastically enhanced light-matter interactions. Recent interest has focused on controlled symmetry breaking to create higher-order multipole plasmonic modes that store electromagnetic energy more efficiently than dipole modes. Here we demonstrate that four-beam holographic lithography enables fabrication of large-area plasmonic crystals with near-field coupled plasmons as well as deliberately broken symmetry to sustain multipole modes and Fano-resonances. Compared with the spectrally broad dipole modes we demonstrate an order of magnitude improved Q-factors (Q = 21) when the quadrupole mode is activated. We further demonstrate continuous tuning of the Fano-resonances using the polarization state ofmore » the incident light beam. The demonstrated technique opens possibilities to extend the rich physics of multipole plasmonic modes to wafer-scale applications that demand low-cost and high-throughput.« less

Analytic halo approach to the bispectrum of galaxies in redshift space

NASA Astrophysics Data System (ADS)

Yamamoto, Kazuhiro; Nan, Yue; Hikage, Chiaki

2017-02-01

We present an analytic formula for the galaxy bispectrum in redshift space on the basis of the halo approach description with the halo occupation distribution of central galaxies and satellite galaxies. This work is an extension of a previous work on the galaxy power spectrum, which illuminated the significant contribution of satellite galaxies to the higher multipole spectrum through the nonlinear redshift space distortions of their random motions. Behaviors of the multipoles of the bispectrum are compared with results of numerical simulations assuming a halo occupation distribution of the low-redshift (LOWZ) sample of the Sloan Digital Sky Survey (SDSS) III baryon oscillation spectroscopic survey (BOSS) survey. Also presented are analytic approximate formulas for the multipoles of the bispectrum, which is useful to understanding their characteristic properties. We demonstrate that the Fingers of God effect is quite important for the higher multipoles of the bispectrum in redshift space, depending on the halo occupation distribution parameters.

Visual Multipoles And The Assessment Of Visual Sensitivity To Displayed Images

NASA Astrophysics Data System (ADS)

Klein, Stanley A.

1989-08-01

The contrast sensitivity function (CSF) is widely used to specify the sensitivity of the visual system. Each point of the CSF specifies the amount of contrast needed to detect a sinusoidal grating of a given spatial frequency. This paper describes a set of five mathematically related visual patterns, called "multipoles," that should replace the CSF for measuring visual performance. The five patterns (ramp, edge, line, dipole and quadrupole) are localized in space rather than being spread out as sinusoidal gratings. The multipole sensitivity of the visual system provides an alternative characterization that complements the CSF in addition to offering several advantages. This paper provides an overview of the properties and uses of the multipole stimuli. This paper is largely a summary of several unpublished manuscripts with excerpts from them. Derivations and full references are omitted here. Please write me if you would like the full manuscripts.

Acoustic attraction, repulsion and radiation force cancellation on a pair of rigid particles with arbitrary cross-sections in 2D: Circular cylinders example

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2017-11-01

The acoustic radiation forces arising on a pair of sound impenetrable cylindrical particles of arbitrary cross-sections are derived. Plane progressive, standing or quasi-standing waves with an arbitrary incidence angle are considered. Multiple scattering effects are described using the multipole expansion formalism and the addition theorem of cylindrical wave functions. An effective incident acoustic field on a particular object is determined, and used with the scattered field to derive closed-form analytical expressions for the radiation force vector components. The mathematical expressions for the radiation force components are exact, and have been formulated in partial-wave series expansions in cylindrical coordinates involving the angle of incidence, the reflection coefficient forming the progressive or the (quasi)standing wave field, the addition theorem, and the expansion coefficients. Numerical examples illustrate the analysis for two rigid circular cross-sections immersed in a non-viscous fluid. Computations for the dimensionless radiation force functions are performed with emphasis on varying the angle of incidence, the interparticle distance, the sizes of the particles as well as the characteristics of the incident field. Depending on the interparticle distance and angle of incidence, one of the particles yields neutrality; it experiences no force and becomes unresponsive (i.e., ;invisible;) to the linear momentum transfer of the effective incident field due to multiple scattering cancellation effects. Moreover, attractive or repulsive forces between the two particles may arise depending on the interparticle distance, the angle of incidence and size parameters of the particles. This study provides a complete analytical method and computations for the axial and transverse radiation force components in multiple acoustic scattering encompassing the cases of plane progressive, standing or quasi-standing waves of arbitrary incidence by a pair of scatterers. Potential applications concern the prediction of the forces used in acoustically-engineered metamaterials with reconfigurable periodicities, cloaking devices, and liquid crystals to name a few examples.

Particle Tracking on the BNL Relativistic Heavy Ion Collider

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

Dell, G. F.

1986-08-07

Tracking studies including the effects of random multipole errors as well as the effects of random and systematic multipole errors have been made for RHIC. Initial results for operating at an off diagonal working point are discussed.

Comparison of temporal and spectral scattering methods using acoustically large breast models derived from magnetic resonance images.

PubMed

Hesford, Andrew J; Tillett, Jason C; Astheimer, Jeffrey P; Waag, Robert C

2014-08-01

Accurate and efficient modeling of ultrasound propagation through realistic tissue models is important to many aspects of clinical ultrasound imaging. Simplified problems with known solutions are often used to study and validate numerical methods. Greater confidence in a time-domain k-space method and a frequency-domain fast multipole method is established in this paper by analyzing results for realistic models of the human breast. Models of breast tissue were produced by segmenting magnetic resonance images of ex vivo specimens into seven distinct tissue types. After confirming with histologic analysis by pathologists that the model structures mimicked in vivo breast, the tissue types were mapped to variations in sound speed and acoustic absorption. Calculations of acoustic scattering by the resulting model were performed on massively parallel supercomputer clusters using parallel implementations of the k-space method and the fast multipole method. The efficient use of these resources was confirmed by parallel efficiency and scalability studies using large-scale, realistic tissue models. Comparisons between the temporal and spectral results were performed in representative planes by Fourier transforming the temporal results. An RMS field error less than 3% throughout the model volume confirms the accuracy of the methods for modeling ultrasound propagation through human breast.

Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Analytical gradients.

PubMed

Łazarski, Roman; Burow, Asbjörn Manfred; Grajciar, Lukáš; Sierka, Marek

2016-10-30

A full implementation of analytical energy gradients for molecular and periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. Its key component is a combination of density fitting (DF) approximation and continuous fast multipole method (CFMM) that allows for an efficient calculation of the Coulomb energy gradient. For exchange-correlation part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097) is extended to energy gradients. Computational efficiency and asymptotic O(N) scaling behavior of the implementation is demonstrated for various molecular and periodic model systems, with the largest unit cell of hematite containing 640 atoms and 19,072 basis functions. The overall computational effort of energy gradient is comparable to that of the Kohn-Sham matrix formation. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Magnetic measurements of the 12-pole trim magnets for the 200 MeV compact synchrotron XLS at the National Synchrotron Light Source

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

Krishnaswamy, J.; Kalsi, S.; Hsieh, H.

1991-01-01

Magnetic measurements performed on the 12-pole trim magnets is described including Hall probe measurements to verify symmetry of the field and, rotating coil measurements to map the multipoles. The rotating coil measurements were carried out using a HP Dynamic Signal Analyzer. Excited as a quadrupole the dominant error multipole is the 20th pole and excited as a sextrupole the dominant error multipole is the 18th pole. Reasonable agreement was found between the Hall probe measurements and the rotating coil measurements. 2 refs., 5 figs.

Bright-type and dark-type vector solitons of the (2 + 1)-dimensional spatially modulated quintic nonlinear Schrödinger equation in nonlinear optics and Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Wu, Hong-Yu; Jiang, Li-Hong

2018-03-01

We study a (2 + 1) -dimensional N -coupled quintic nonlinear Schrödinger equation with spatially modulated nonlinearity and transverse modulation in nonlinear optics and Bose-Einstein condensate, and obtain bright-type and dark-type vector multipole as well as vortex soliton solutions. When the modulation depth q is fixed as 0 and 1, we can construct vector multipole and vortex solitons, respectively. Based on these solutions, we investigate the form and phase characteristics of vector multipole and vortex solitons.

Newman-Penrose constants of the Kerr-Newman metric

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

Gong Xuefei; Shang Yu; Bai Shan

The Newman-Unti formalism of the Kerr-Newman metric near future null infinity is developed, with which the Newman-Penrose constants for both the gravitational and electromagnetic fields of the Kerr-Newman metric are computed and shown to be zero. The multipole structure near future null infinity in the sense of Janis-Newman of the Kerr-Newman metric is then further studied. It is found that up to the 2{sup 4}-pole, modulo a constant dependent upon the order of the pole, these multipole moments agree with those of Geroch-Hansen multipole moments defined at spatial infinity.

Heavy quarkonium suppression in a fireball

NASA Astrophysics Data System (ADS)

Brambilla, Nora; Escobedo, Miguel A.; Soto, Joan; Vairo, Antonio

2018-04-01

We perform a comprehensive study of the time evolution of heavy-quarkonium states in an expanding hot QCD medium by implementing effective field theory techniques in the framework of open quantum systems. The formalism incorporates quarkonium production and its subsequent evolution in the fireball including quarkonium dissociation and recombination. We consider a fireball with a local temperature that is much smaller than the inverse size of the quarkonium and much larger than its binding energy. The calculation is performed at an accuracy that is leading order in the heavy-quark density expansion and next-to-leading order in the multipole expansion. Within this accuracy, for a smooth variation of the temperature and large times, the evolution equation can be written as a Lindblad equation. We solve the Lindblad equation numerically both for a weakly coupled quark-gluon plasma and a strongly coupled medium. As an application, we compute the nuclear modification factor for the ϒ (1 S ) and ϒ (2 S ) states. We also consider the case of static quarks, which can be solved analytically. Our study fulfills three essential conditions: it conserves the total number of heavy quarks, it accounts for the non-Abelian nature of QCD, and it avoids classical approximations.

Petascale turbulence simulation using a highly parallel fast multipole method on GPUs

NASA Astrophysics Data System (ADS)

Yokota, Rio; Barba, L. A.; Narumi, Tetsu; Yasuoka, Kenji

2013-03-01

This paper reports large-scale direct numerical simulations of homogeneous-isotropic fluid turbulence, achieving sustained performance of 1.08 petaflop/s on GPU hardware using single precision. The simulations use a vortex particle method to solve the Navier-Stokes equations, with a highly parallel fast multipole method (FMM) as numerical engine, and match the current record in mesh size for this application, a cube of 40963 computational points solved with a spectral method. The standard numerical approach used in this field is the pseudo-spectral method, relying on the FFT algorithm as the numerical engine. The particle-based simulations presented in this paper quantitatively match the kinetic energy spectrum obtained with a pseudo-spectral method, using a trusted code. In terms of parallel performance, weak scaling results show the FMM-based vortex method achieving 74% parallel efficiency on 4096 processes (one GPU per MPI process, 3 GPUs per node of the TSUBAME-2.0 system). The FFT-based spectral method is able to achieve just 14% parallel efficiency on the same number of MPI processes (using only CPU cores), due to the all-to-all communication pattern of the FFT algorithm. The calculation time for one time step was 108 s for the vortex method and 154 s for the spectral method, under these conditions. Computing with 69 billion particles, this work exceeds by an order of magnitude the largest vortex-method calculations to date.

FleCSPH - a parallel and distributed SPH implementation based on the FleCSI framework

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

Junghans, Christoph; Loiseau, Julien

2017-06-20

FleCSPH is a multi-physics compact application that exercises FleCSI parallel data structures for tree-based particle methods. In particular, FleCSPH implements a smoothed-particle hydrodynamics (SPH) solver for the solution of Lagrangian problems in astrophysics and cosmology. FleCSPH includes support for gravitational forces using the fast multipole method (FMM).

Fast inverse scattering solutions using the distorted Born iterative method and the multilevel fast multipole algorithm

PubMed Central

Hesford, Andrew J.; Chew, Weng C.

2010-01-01

The distorted Born iterative method (DBIM) computes iterative solutions to nonlinear inverse scattering problems through successive linear approximations. By decomposing the scattered field into a superposition of scattering by an inhomogeneous background and by a material perturbation, large or high-contrast variations in medium properties can be imaged through iterations that are each subject to the distorted Born approximation. However, the need to repeatedly compute forward solutions still imposes a very heavy computational burden. To ameliorate this problem, the multilevel fast multipole algorithm (MLFMA) has been applied as a forward solver within the DBIM. The MLFMA computes forward solutions in linear time for volumetric scatterers. The typically regular distribution and shape of scattering elements in the inverse scattering problem allow the method to take advantage of data redundancy and reduce the computational demands of the normally expensive MLFMA setup. Additional benefits are gained by employing Kaczmarz-like iterations, where partial measurements are used to accelerate convergence. Numerical results demonstrate both the efficiency of the forward solver and the successful application of the inverse method to imaging problems with dimensions in the neighborhood of ten wavelengths. PMID:20707438

DEVELOPMENT OF A MODEL THAT CONTAINS BOTH MULTIPOLE MOMENTS AND GAUSSIANS FOR THE CALCULATION OF MOLECULAR ELECTROSTATIC POTENTIALS

EPA Science Inventory

The electrostatic interaction is a critical component of intermolecular interactions in biological processes. Rapid methods for the computation and characterization of the molecular electrostatic potential (MEP) that segment the molecular charge distribution and replace this cont...

Multi-scale and Multi-physics Numerical Methods for Modeling Transport in Mesoscopic Systems

DTIC Science & Technology

2014-10-13

function and wide band Fast multipole methods for Hankel waves. (2) a new linear scaling discontinuous Galerkin density functional theory, which provide a...inflow boundary condition for Wigner quantum transport equations. Also, a book titled "Computational Methods for Electromagnetic Phenomena...equationsin layered media with FMM for Bessel functions , Science China Mathematics, (12 2013): 2561. doi: TOTAL: 6 Number of Papers published in peer

Towards high-resolution laser ionization spectroscopy of the heaviest elements in supersonic gas jet expansion

PubMed Central

Ferrer, R.; Barzakh, A.; Bastin, B.; Beerwerth, R.; Block, M.; Creemers, P.; Grawe, H.; de Groote, R.; Delahaye, P.; Fléchard, X.; Franchoo, S.; Fritzsche, S.; Gaffney, L. P.; Ghys, L.; Gins, W.; Granados, C.; Heinke, R.; Hijazi, L.; Huyse, M.; Kron, T.; Kudryavtsev, Yu.; Laatiaoui, M.; Lecesne, N.; Loiselet, M.; Lutton, F.; Moore, I. D.; Martínez, Y.; Mogilevskiy, E.; Naubereit, P.; Piot, J.; Raeder, S.; Rothe, S.; Savajols, H.; Sels, S.; Sonnenschein, V.; Thomas, J-C; Traykov, E.; Van Beveren, C.; Van den Bergh, P.; Van Duppen, P.; Wendt, K.; Zadvornaya, A.

2017-01-01

Resonant laser ionization and spectroscopy are widely used techniques at radioactive ion beam facilities to produce pure beams of exotic nuclei and measure the shape, size, spin and electromagnetic multipole moments of these nuclei. However, in such measurements it is difficult to combine a high efficiency with a high spectral resolution. Here we demonstrate the on-line application of atomic laser ionization spectroscopy in a supersonic gas jet, a technique suited for high-precision studies of the ground- and isomeric-state properties of nuclei located at the extremes of stability. The technique is characterized in a measurement on actinium isotopes around the N=126 neutron shell closure. A significant improvement in the spectral resolution by more than one order of magnitude is achieved in these experiments without loss in efficiency. PMID:28224987

Inspiral, merger, and ringdown of unequal mass black hole binaries: A multipolar analysis

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

Berti, Emanuele; Cardoso, Vitor; Gonzalez, Jose A.

We study the inspiral, merger, and ringdown of unequal mass black hole binaries by analyzing a catalogue of numerical simulations for seven different values of the mass ratio (from q=M{sub 2}/M{sub 1}=1 to q=4). We compare numerical and post-Newtonian results by projecting the waveforms onto spin-weighted spherical harmonics, characterized by angular indices (l,m). We find that the post-Newtonian equations predict remarkably well the relation between the wave amplitude and the orbital frequency for each (l,m), and that the convergence of the post-Newtonian series to the numerical results is nonmonotonic. To leading order, the total energy emitted in the merger phasemore » scales like {eta}{sup 2} and the spin of the final black hole scales like {eta}, where {eta}=q/(1+q){sup 2} is the symmetric mass ratio. We study the multipolar distribution of the radiation, finding that odd-l multipoles are suppressed in the equal mass limit. Higher multipoles carry a larger fraction of the total energy as q increases. We introduce and compare three different definitions for the ringdown starting time. Applying linear-estimation methods (the so-called Prony methods) to the ringdown phase, we find resolution-dependent time variations in the fitted parameters of the final black hole. By cross correlating information from different multipoles, we show that ringdown fits can be used to obtain precise estimates of the mass and spin of the final black hole, which are in remarkable agreement with energy and angular momentum balance calculations.« less

LINEAR AND NONLINEAR CORRECTIONS IN THE RHIC INTERACTION REGIONS.

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

PILAT,F.; CAMERON,P.; PTITSYN,V.

2002-06-02

A method has been developed to measure operationally the linear and non-linear effects of the interaction region triplets, that gives access to the multipole content through the action kick, by applying closed orbit bumps and analysing tune and orbit shifts. This technique has been extensively tested and used during the RHIC operations in 2001. Measurements were taken at 3 different interaction regions and for different focusing at the interaction point. Non-linear effects up to the dodecapole have been measured as well as the effects of linear, sextupolar and octupolar corrections. An analysis package for the data processing has been developedmore » that through a precise fit of the experimental tune shift data (measured by a phase lock loop technique to better than 10{sup -5} resolution) determines the multipole content of an IR triplet.« less

Modeling Organochlorine Compounds and the σ-Hole Effect Using a Polarizable Multipole Force Field

PubMed Central

2015-01-01

The charge distribution of halogen atoms on organochlorine compounds can be highly anisotropic and even display a so-called σ-hole, which leads to strong halogen bonds with electron donors. In this paper, we have systematically investigated a series of chloromethanes with one to four chloro substituents using a polarizable multipole-based molecular mechanics model. The atomic multipoles accurately reproduced the ab initio electrostatic potential around chloromethanes, including CCl4, which has a prominent σ-hole on the Cl atom. The van der Waals parameters for Cl were fitted to the experimental density and heat of vaporization. The calculated hydration free energy, solvent reaction fields, and interaction energies of several homo- and heterodimer of chloromethanes are in good agreement with experimental and ab initio data. This study suggests that sophisticated electrostatic models, such as polarizable atomic multipoles, are needed for accurate description of electrostatics in organochlorine compounds and halogen bonds, although further improvement is necessary for better transferability. PMID:24484473

Pearson's random walk in the space of the CMB phases: Evidence for parity asymmetry

NASA Astrophysics Data System (ADS)

Hansen, M.; Frejsel, A. M.; Kim, J.; Naselsky, P.; Nesti, F.

2011-05-01

The temperature fluctuations of the cosmic microwave background (CMB) are supposed to be distributed randomly in both magnitude and phase, following to the simplest model of inflation. In this paper, we look at the odd and even multipoles of the spherical harmonic decomposition of the CMB, and the different characteristics of these, giving rise to a parity asymmetry. We compare the even and odd multipoles in the CMB power spectrum, and also the even and odd mean angles. We find for the multipoles of the power spectrum that there is power excess in odd multipoles, compared to even ones, meaning that we have a parity asymmetry. Further, for the phases, we present a random walk for the mean angles, and find a significant separation for even/odd mean angles, especially so for galactic coordinates. This is further tested and confirmed with a directional parity test, comparing the parity asymmetry in galactic and ecliptic coordinates.

Multipole gas thruster design. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Isaacson, G. C.

1977-01-01

The development of a low field strength multipole thruster operating on both argon and xenon is described. Experimental results were obtained with a 15-cm diameter multipole thruster and are presented for a wide range of discharge-chamber configurations. Minimum discharge losses were 300-350 eV/ion for argon and 200-250 eV/ion for xenon. Ion beam flatness parameters in the plane of the accelerator grid ranged from 0.85 to 0.93 for both propellants. Thruster performance is correlated for a range of ion chamber sizes and operating conditions as well as propellant type and accelerator system open area. A 30-cm diameter ion source designed and built using the procedure and theory presented here-in is shown capable of low discharge losses and flat ion-beam profiles without optimization. This indicates that by using the low field strength multipole design, as well as general performance correlation information provided herein, it should be possible to rapidly translate initial performance specifications into easily fabricated, high performance prototypes.

Influence of permittivity on gradient force exerted on Mie spheres.

PubMed

Chen, Jun; Li, Kaikai; Li, Xiao

2018-04-01

In optical trapping, whether a particle could be stably trapped into the focus region greatly depends on the strength of the gradient force. Individual theoretical study on gradient force exerted on a Mie particle is rare because the mathematical separation of the gradient force and the scattering force in the Mie regime is difficult. Based on the recent forces separation work by Du et al. [Sci. Rep.7, 18042 (2017)SRCEC32045-232210.1038/s41598-017-17874-1], we investigate the influence of permittivity (an important macroscopic physical quantity) on the gradient force exerted on a Mie particle by cooperating numerical calculation using fast Fourier transform and analytical analysis using multipole expansion. It is revealed that gradient forces exerted on small spheres are mainly determined by the electric dipole moment except for certain permittivity with which the real part of polarizability of the electric dipole approaches zero, and gradient forces exerted on larger spheres are complex because of the superposition of the multipole moments. The classification of permittivity corresponding to different varying tendencies of gradient forces exerted on small spheres or larger Mie particles are illustrated. Absorption of particles favors the trapping of small spheres by gradient force, while it is bad for the trapping of larger particles. Moreover, the absolute values of the maximal gradient forces exerted on larger Mie particles decline greatly versus the varied imaginary part of permittivity. This work provides elaborate investigation on the different varying tendencies of gradient forces versus permittivity, which favors more accurate and free optical trapping.

Seismic equivalents of volcanic jet scaling laws and multipoles in acoustics

NASA Astrophysics Data System (ADS)

Haney, Matthew M.; Matoza, Robin S.; Fee, David; Aldridge, David F.

2018-04-01

We establish analogies between equivalent source theory in seismology (moment-tensor and single-force sources) and acoustics (monopoles, dipoles and quadrupoles) in the context of volcanic eruption signals. Although infrasound (acoustic waves < 20 Hz) from volcanic eruptions may be more complex than a simple monopole, dipole or quadrupole assumption, these elementary acoustic sources are a logical place to begin exploring relations with seismic sources. By considering the radiated power of a harmonic force source at the surface of an elastic half-space, we show that a volcanic jet or plume modelled as a seismic force has similar scaling with respect to eruption parameters (e.g. exit velocity and vent area) as an acoustic dipole. We support this by demonstrating, from first principles, a fundamental relationship that ties together explosion, torque and force sources in seismology and highlights the underlying dipole nature of seismic forces. This forges a connection between the multipole expansion of equivalent sources in acoustics and the use of forces and moments as equivalent sources in seismology. We further show that volcanic infrasound monopole and quadrupole sources exhibit scalings similar to seismicity radiated by volume injection and moment sources, respectively. We describe a scaling theory for seismic tremor during volcanic eruptions that agrees with observations showing a linear relation between radiated power of tremor and eruption rate. Volcanic tremor over the first 17 hr of the 2016 eruption at Pavlof Volcano, Alaska, obeyed the linear relation. Subsequent tremor during the main phase of the eruption did not obey the linear relation and demonstrates that volcanic eruption tremor can exhibit other scalings even during the same eruption.

Emergent odd-parity multipoles and magnetoelectric effects on a diamond structure: Implication for the 5 d transition metal oxides A OsO4 (A =K ,Rb, and Cs)

NASA Astrophysics Data System (ADS)

Hayami, Satoru; Kusunose, Hiroaki; Motome, Yukitoshi

2018-01-01

We report our theoretical predictions on the linear magnetoelectric (ME) effects originating from odd-parity multipoles associated with spontaneous spin and orbital ordering on a diamond structure. We derive a two-orbital model for d electrons in eg orbitals by including the effective spin-orbit coupling which arises from the mixing between eg and t2 g orbitals. We show that the model acquires a net antisymmetric spin-orbit coupling once staggered spin and orbital orders occur spontaneously. The staggered orders are accompanied by odd-parity multipoles: magnetic monopole, quadrupoles, and toroidal dipoles. We classify the types of the odd-parity multipoles according to the symmetry of the spin and orbital orders. Furthermore, by computing the ME tensor using the linear response theory, we show that the staggered orders induce a variety of the linear ME responses. We elaborate all possible ME responses for each staggered order, which are useful to identify the order parameter and to detect the odd-parity multipoles by measuring the ME effects. We also elucidate the effect of lowering symmetry by a tetragonal distortion, which leads to richer ME responses. The implications of our results are discussed for the 5 d transition metal oxides, A OsO4 (A =K,Rb, and Cs) , in which the order parameters are not fully identified.

Understanding the many-body expansion for large systems. III. Critical role of four-body terms, counterpoise corrections, and cutoffs.

PubMed

Liu, Kuan-Yu; Herbert, John M

2017-10-28

Papers I and II in this series [R. M. Richard et al., J. Chem. Phys. 141, 014108 (2014); K. U. Lao et al., ibid. 144, 164105 (2016)] have attempted to shed light on precision and accuracy issues affecting the many-body expansion (MBE), which only manifest in larger systems and thus have received scant attention in the literature. Many-body counterpoise (CP) corrections are shown to accelerate convergence of the MBE, which otherwise suffers from a mismatch between how basis-set superposition error affects subsystem versus supersystem calculations. In water clusters ranging in size up to (H 2 O) 37 , four-body terms prove necessary to achieve accurate results for both total interaction energies and relative isomer energies, but the sheer number of tetramers makes the use of cutoff schemes essential. To predict relative energies of (H 2 O) 20 isomers, two approximations based on a lower level of theory are introduced and an ONIOM-type procedure is found to be very well converged with respect to the appropriate MBE benchmark, namely, a CP-corrected supersystem calculation at the same level of theory. Results using an energy-based cutoff scheme suggest that if reasonable approximations to the subsystem energies are available (based on classical multipoles, say), then the number of requisite subsystem calculations can be reduced even more dramatically than when distance-based thresholds are employed. The end result is several accurate four-body methods that do not require charge embedding, and which are stable in large basis sets such as aug-cc-pVTZ that have sometimes proven problematic for fragment-based quantum chemistry methods. Even with aggressive thresholding, however, the four-body approach at the self-consistent field level still requires roughly ten times more processors to outmatch the performance of the corresponding supersystem calculation, in test cases involving 1500-1800 basis functions.

Understanding the many-body expansion for large systems. III. Critical role of four-body terms, counterpoise corrections, and cutoffs

NASA Astrophysics Data System (ADS)

Liu, Kuan-Yu; Herbert, John M.

2017-10-01

Papers I and II in this series [R. M. Richard et al., J. Chem. Phys. 141, 014108 (2014); K. U. Lao et al., ibid. 144, 164105 (2016)] have attempted to shed light on precision and accuracy issues affecting the many-body expansion (MBE), which only manifest in larger systems and thus have received scant attention in the literature. Many-body counterpoise (CP) corrections are shown to accelerate convergence of the MBE, which otherwise suffers from a mismatch between how basis-set superposition error affects subsystem versus supersystem calculations. In water clusters ranging in size up to (H2O)37, four-body terms prove necessary to achieve accurate results for both total interaction energies and relative isomer energies, but the sheer number of tetramers makes the use of cutoff schemes essential. To predict relative energies of (H2O)20 isomers, two approximations based on a lower level of theory are introduced and an ONIOM-type procedure is found to be very well converged with respect to the appropriate MBE benchmark, namely, a CP-corrected supersystem calculation at the same level of theory. Results using an energy-based cutoff scheme suggest that if reasonable approximations to the subsystem energies are available (based on classical multipoles, say), then the number of requisite subsystem calculations can be reduced even more dramatically than when distance-based thresholds are employed. The end result is several accurate four-body methods that do not require charge embedding, and which are stable in large basis sets such as aug-cc-pVTZ that have sometimes proven problematic for fragment-based quantum chemistry methods. Even with aggressive thresholding, however, the four-body approach at the self-consistent field level still requires roughly ten times more processors to outmatch the performance of the corresponding supersystem calculation, in test cases involving 1500-1800 basis functions.

Multipole electrodynamic ion trap geometries for microparticle confinement under standard ambient temperature and pressure conditions

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

Mihalcea, Bogdan M., E-mail: bogdan.mihalcea@inflpr.ro; Vişan, Gina T.; Ganciu, Mihai

2016-03-21

Trapping of microparticles and aerosols is of great interest for physics and chemistry. We report microparticle trapping in case of multipole linear Paul trap geometries, operating under standard ambient temperature and pressure conditions. An 8- and 12-electrode linear trap geometries have been designed and tested with an aim to achieve trapping for larger number of particles and to study microparticle dynamical stability in electrodynamic fields. We report emergence of planar and volume ordered structures of microparticles, depending on the a.c. trapping frequency and particle specific charge ratio. The electric potential within the trap is mapped using the electrolytic tank method.more » Particle dynamics is simulated using a stochastic Langevin equation. We emphasize extended regions of stable trapping with respect to quadrupole traps, as well as good agreement between experiment and numerical simulations.« less

Combined fast multipole-QR compression technique for solving electrically small to large structures for broadband applications

NASA Technical Reports Server (NTRS)

Jandhyala, Vikram (Inventor); Chowdhury, Indranil (Inventor)

2011-01-01

An approach that efficiently solves for a desired parameter of a system or device that can include both electrically large fast multipole method (FMM) elements, and electrically small QR elements. The system or device is setup as an oct-tree structure that can include regions of both the FMM type and the QR type. An iterative solver is then used to determine a first matrix vector product for any electrically large elements, and a second matrix vector product for any electrically small elements that are included in the structure. These matrix vector products for the electrically large elements and the electrically small elements are combined, and a net delta for a combination of the matrix vector products is determined. The iteration continues until a net delta is obtained that is within predefined limits. The matrix vector products that were last obtained are used to solve for the desired parameter.

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

Meinke, Rainer

A method for manufacture of a conductor assembly. The assembly is of the type which, when conducting current, generates a magnetic field or in which, in the presence of a changing magnetic field, a voltage is induced. In an example embodiment one or more first coil rows are formed. The assembly has multiple coil rows about an axis with outer coil rows formed about inner coil rows. A determination is made of deviations from specifications associated with the formed one or more first coil rows. One or more deviations correspond to a magnitude of a multipole field component which departsmore » from a field specification. Based on the deviations, one or more wiring patterns are generated for one or more second coil rows to be formed about the one or more first coil rows. The one or more second coil rows are formed in the assembly. The magnitude of each multipole field component that departs from the field specification is offset.« less

A Very Fast and Angular Momentum Conserving Tree Code

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

Marcello, Dominic C., E-mail: dmarce504@gmail.com

There are many methods used to compute the classical gravitational field in astrophysical simulation codes. With the exception of the typically impractical method of direct computation, none ensure conservation of angular momentum to machine precision. Under uniform time-stepping, the Cartesian fast multipole method of Dehnen (also known as the very fast tree code) conserves linear momentum to machine precision. We show that it is possible to modify this method in a way that conserves both angular and linear momenta.

Improve the efficiency of the Cartesian tensor based fast multipole method for Coulomb interaction using the traces

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

Huang, He; Luo, Li -Shi; Li, Rui

To compute the non-oscillating mutual interaction for a systems with N points, the fast multipole method (FMM) has an efficiency that scales linearly with the number of points. Specifically, for Coulomb interaction, FMM can be constructed using either the spherical harmonic functions or the totally symmetric Cartesian tensors. In this paper, we will present that the effciency of the Cartesian tensor-based FMM for the Coulomb interaction can be significantly improved by implementing the traces of the Cartesian tensors in calculation to reduce the independent elements of the n-th rank totally symmetric Cartesian tensor from (n + 1)(n + 2)=2 tomore » 2n + 1. The computation complexity for the operations in FMM are analyzed and expressed as polynomials of the highest rank of the Cartesian tensors. For most operations, the complexity is reduced by one order. Numerical examples regarding the convergence and the effciency of the new algorithm are demonstrated. As a result, a reduction of computation time up to 50% has been observed for a moderate number of points and rank of tensors.« less

Improve the efficiency of the Cartesian tensor based fast multipole method for Coulomb interaction using the traces

DOE PAGES

Huang, He; Luo, Li -Shi; Li, Rui; ...

2018-05-17

To compute the non-oscillating mutual interaction for a systems with N points, the fast multipole method (FMM) has an efficiency that scales linearly with the number of points. Specifically, for Coulomb interaction, FMM can be constructed using either the spherical harmonic functions or the totally symmetric Cartesian tensors. In this paper, we will present that the effciency of the Cartesian tensor-based FMM for the Coulomb interaction can be significantly improved by implementing the traces of the Cartesian tensors in calculation to reduce the independent elements of the n-th rank totally symmetric Cartesian tensor from (n + 1)(n + 2)=2 tomore » 2n + 1. The computation complexity for the operations in FMM are analyzed and expressed as polynomials of the highest rank of the Cartesian tensors. For most operations, the complexity is reduced by one order. Numerical examples regarding the convergence and the effciency of the new algorithm are demonstrated. As a result, a reduction of computation time up to 50% has been observed for a moderate number of points and rank of tensors.« less

irGPU.proton.Net: Irregular strong charge interaction networks of protonatable groups in protein molecules--a GPU solver using the fast multipole method and statistical thermodynamics.

PubMed

Kantardjiev, Alexander A

2015-04-05

A cluster of strongly interacting ionization groups in protein molecules with irregular ionization behavior is suggestive for specific structure-function relationship. However, their computational treatment is unconventional (e.g., lack of convergence in naive self-consistent iterative algorithm). The stringent evaluation requires evaluation of Boltzmann averaged statistical mechanics sums and electrostatic energy estimation for each microstate. irGPU: Irregular strong interactions in proteins--a GPU solver is novel solution to a versatile problem in protein biophysics--atypical protonation behavior of coupled groups. The computational severity of the problem is alleviated by parallelization (via GPU kernels) which is applied for the electrostatic interaction evaluation (including explicit electrostatics via the fast multipole method) as well as statistical mechanics sums (partition function) estimation. Special attention is given to the ease of the service and encapsulation of theoretical details without sacrificing rigor of computational procedures. irGPU is not just a solution-in-principle but a promising practical application with potential to entice community into deeper understanding of principles governing biomolecule mechanisms. © 2015 Wiley Periodicals, Inc.

Identifying the Development in Phase and Amplitude of Dipole and Multipole Radiation

ERIC Educational Resources Information Center

Rice, E. M.; Bradshaw, D. S.; Saadi, K.; Andrews, D. L.

2012-01-01

The spatial variation in phase and the propagating wave-front of plane wave electromagnetic radiation are widely familiar text-book territory. In contrast, the developing amplitude and phase of radiation emitted by a dipole or multipole source generally receive less attention, despite the prevalence of these systems. There is additional complexity…

High-order multipole radiation from quantum Hall states in Dirac materials

NASA Astrophysics Data System (ADS)

Gullans, Michael J.; Taylor, Jacob M.; Imamoǧlu, Ataç; Ghaemi, Pouyan; Hafezi, Mohammad

2017-06-01

We investigate the optical response of strongly disordered quantum Hall states in two-dimensional Dirac materials and find qualitatively different effects in the radiation properties of the bulk versus the edge. We show that the far-field radiation from the edge is characterized by large multipole moments (>50 ) due to the efficient transfer of angular momentum from the electrons into the scattered light. The maximum multipole transition moment is a direct measure of the coherence length of the edge states. Accessing these multipole transitions would provide new tools for optical spectroscopy and control of quantum Hall edge states. On the other hand, the far-field radiation from the bulk appears as random dipole emission with spectral properties that vary with the local disorder potential. We determine the conditions under which this bulk radiation can be used to image the disorder landscape. Such optical measurements can probe submicron-length scales over large areas and provide complementary information to scanning probe techniques. Spatially resolving this bulk radiation would serve as a novel probe of the percolation transition near half filling.

The polarizability of diatomic helium. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Fortune, P. J.

1974-01-01

The calculation of the electric dipole polarizability tensor of the He 2 dimer is described, and the results are used in the computation of several dielectric and optical properties of helium gas, at both high (322 K) and low (4 K) temperatures. The properties considered are the second dielectric virial coefficient, the second Kerr virial coefficient, and the depolarization ratio of the integrated intensities for the Raman scattering experiments. The thesis consists of five parts: the polarizability and various properties are defined; the calculation of the polarizability in the long-range region in terms of a quantum mechanical multipole expansion is described; the calculation of the He2 polarizability in the overlap region via coupled Hartree-Fock perturbation theory is described; the calculation of the quantum pair distribution function for both the He-3 and He-4 isotopes at 4 K is discussed; and the calculated values of the properties of helium gas are given.

Dusty Plasmas in Planetary Magnetospheres Award

NASA Technical Reports Server (NTRS)

Horanyi, Mihaly

2005-01-01

This is my final report for the grant Dusty Plasmas in Planetary Magnetospheres. The funding from this grant supported our research on dusty plasmas to study: a) dust plasma interactions in general plasma environments, and b) dusty plasma processes in planetary magnetospheres (Earth, Jupiter and Saturn). We have developed a general purpose transport code in order to follow the spatial and temporal evolution of dust density distributions in magnetized plasma environments. The code allows the central body to be represented by a multipole expansion of its gravitational and magnetic fields. The density and the temperature of the possibly many-component plasma environment can be pre-defined as a function of coordinates and, if necessary, the time as well. The code simultaneously integrates the equations of motion with the equations describing the charging processes. The charging currents are dependent not only on the instantaneous plasma parameters but on the velocity, as well as on the previous charging history of the dust grains.

Effect of salt entropy on protein solubility and Hofmeister series

NASA Astrophysics Data System (ADS)

Dahal, Yuba; Schmit, Jeremy

We present a theory of salt effects on protein solubility that accounts for salting-in, salting-out, and the Hofmeister series. We represent protein charge by the first order multipole expansion to include attractive and repulsive electrostatic interactions in the model. Our model also includes non-electrostatic protein-ion interactions, and ion-solvent interactions via an effective solvated ion radius. We find that the finite size of the ions has significant effects on the translational entropy of the salt, which accounts for the changes in the protein solubility. At low salt the dominant effect comes from the entropic cost of confining ions within the aggregate. At high concentrations the salt drives a depletion attraction that favors aggregation. Our theory explains the reversal in the Hofmeister series observed in lysozyme cloud point measurements and semi-quantitatively describes the solubility of lysozyme and chymosin crystals.

A flat Universe from high-resolution maps of the cosmic microwave background radiation

PubMed

de Bernardis P; Ade; Bock; Bond; Borrill; Boscaleri; Coble; Crill; De Gasperis G; Farese; Ferreira; Ganga; Giacometti; Hivon; Hristov; Iacoangeli; Jaffe; Lange; Martinis; Masi; Mason; Mauskopf; Melchiorri; Miglio; Montroy; Netterfield

2000-04-27

The blackbody radiation left over from the Big Bang has been transformed by the expansion of the Universe into the nearly isotropic 2.73 K cosmic microwave background. Tiny inhomogeneities in the early Universe left their imprint on the microwave background in the form of small anisotropies in its temperature. These anisotropies contain information about basic cosmological parameters, particularly the total energy density and curvature of the Universe. Here we report the first images of resolved structure in the microwave background anisotropies over a significant part of the sky. Maps at four frequencies clearly distinguish the microwave background from foreground emission. We compute the angular power spectrum of the microwave background, and find a peak at Legendre multipole Ipeak = (197 +/- 6), with an amplitude delta T200 = (69 +/- 8) microK. This is consistent with that expected for cold dark matter models in a flat (euclidean) Universe, as favoured by standard inflationary models.

FDTD simulations of forces on particles during holographic assembly.

PubMed

Benito, David C; Simpson, Stephen H; Hanna, Simon

2008-03-03

We present finite-difference time-domain (FDTD) calculations of the forces and torques on dielectric particles of various shapes, held in one or many Gaussian optical traps, as part of a study of the physical limitations involved in the construction of micro- and nanostructures using a dynamic holographic assembler (DHA). We employ a full 3-dimensional FDTD implementation, which includes a complete treatment of optical anisotropy. The Gaussian beams are sourced using a multipole expansion of a fifth order Davis beam. Force and torques are calculated for pairs of silica spheres in adjacent traps, for silica cylinders trapped by multiple beams and for oblate silica spheroids and calcite spheres in both linearly and circularly polarized beams. Comparisons are drawn between the magnitudes of the optical forces and the Van der Waals forces acting on the systems. The paper also considers the limitations of the FDTD approach when applied to optical trapping.

Multipolar electrostatics based on the Kriging machine learning method: an application to serine.

PubMed

Yuan, Yongna; Mills, Matthew J L; Popelier, Paul L A

2014-04-01

A multipolar, polarizable electrostatic method for future use in a novel force field is described. Quantum Chemical Topology (QCT) is used to partition the electron density of a chemical system into atoms, then the machine learning method Kriging is used to build models that relate the multipole moments of the atoms to the positions of their surrounding nuclei. The pilot system serine is used to study both the influence of the level of theory and the set of data generator methods used. The latter consists of: (i) sampling of protein structures deposited in the Protein Data Bank (PDB), or (ii) normal mode distortion along either (a) Cartesian coordinates, or (b) redundant internal coordinates. Wavefunctions for the sampled geometries were obtained at the HF/6-31G(d,p), B3LYP/apc-1, and MP2/cc-pVDZ levels of theory, prior to calculation of the atomic multipole moments by volume integration. The average absolute error (over an independent test set of conformations) in the total atom-atom electrostatic interaction energy of serine, using Kriging models built with the three data generator methods is 11.3 kJ mol⁻¹ (PDB), 8.2 kJ mol⁻¹ (Cartesian distortion), and 10.1 kJ mol⁻¹ (redundant internal distortion) at the HF/6-31G(d,p) level. At the B3LYP/apc-1 level, the respective errors are 7.7 kJ mol⁻¹, 6.7 kJ mol⁻¹, and 4.9 kJ mol⁻¹, while at the MP2/cc-pVDZ level they are 6.5 kJ mol⁻¹, 5.3 kJ mol⁻¹, and 4.0 kJ mol⁻¹. The ranges of geometries generated by the redundant internal coordinate distortion and by extraction from the PDB are much wider than the range generated by Cartesian distortion. The atomic multipole moment and electrostatic interaction energy predictions for the B3LYP/apc-1 and MP2/cc-pVDZ levels are similar, and both are better than the corresponding predictions at the HF/6-31G(d,p) level.

A broadband fast multipole accelerated boundary element method for the three dimensional Helmholtz equation.

PubMed

Gumerov, Nail A; Duraiswami, Ramani

2009-01-01

The development of a fast multipole method (FMM) accelerated iterative solution of the boundary element method (BEM) for the Helmholtz equations in three dimensions is described. The FMM for the Helmholtz equation is significantly different for problems with low and high kD (where k is the wavenumber and D the domain size), and for large problems the method must be switched between levels of the hierarchy. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements), and these errors must be balanced against approximations introduced by the FMM and the convergence criterion for iterative solution. These different errors must all be chosen in a way that, on the one hand, excess work is not done and, on the other, that the error achieved by the overall computation is acceptable. Details of translation operators for low and high kD, choice of representations, and BEM quadrature schemes, all consistent with these approximations, are described. A novel preconditioner using a low accuracy FMM accelerated solver as a right preconditioner is also described. Results of the developed solvers for large boundary value problems with 0.0001 less, similarkD less, similar500 are presented and shown to perform close to theoretical expectations.

Multipole Vector Anomalies in the First-Year WMAP Data: A Cut-Sky Analysis

NASA Astrophysics Data System (ADS)

Bielewicz, P.; Eriksen, H. K.; Banday, A. J.; Górski, K. M.; Lilje, P. B.

2005-12-01

We apply the recently defined multipole vector framework to the frequency-specific first-year WMAP sky maps, estimating the low-l multipole coefficients from the high-latitude sky by means of a power equalization filter. While most previous analyses of this type have considered only heavily processed (and foreground-contaminated) full-sky maps, the present approach allows for greater control of residual foregrounds and therefore potentially also for cosmologically important conclusions. The low-l spherical harmonic coefficients and corresponding multipole vectors are tabulated for easy reference. Using this formalism, we reassess a set of earlier claims of both cosmological and noncosmological low-l correlations on the basis of multipole vectors. First, we show that the apparent l=3 and 8 correlation claimed by Copi and coworkers is present only in the heavily processed map produced by Tegmark and coworkers and must therefore be considered an artifact of that map. Second, the well-known quadrupole-octopole correlation is confirmed at the 99% significance level and shown to be robust with respect to frequency and sky cut. Previous claims are thus supported by our analysis. Finally, the low-l alignment with respect to the ecliptic claimed by Schwarz and coworkers is nominally confirmed in this analysis, but also shown to be very dependent on severe a posteriori choices. Indeed, we show that given the peculiar quadrupole-octopole arrangement, finding such a strong alignment with the ecliptic is not unusual.

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.

Determination of the topological shape of integral membrane protein light-harvesting complex LH2 from photosynthetic bacteria in the detergent solution by small-angle X-ray scattering.

PubMed

Hong, Xinguo; Weng, Yu-Xiang; Li, Ming

2004-02-01

The topological shape of the integral membrane protein light-harvesting complex LH2 from photosynthetic bacteria Rhodobacter spheroides 2.4.1 in detergent solution has been determined from synchrotron small-angle X-ray scattering data using direct curve-fitting by the ellipsoid, ab initio shape determination methods of simulated annealing algorithm and multipole expansion, respectively. The results indicate that the LH2 protein in aqueous solution is encapsulated by a monolayered detergent shell. The detergent-stabilized structure has the shape of an oblate plate, with a thickness of 40 A, a long axis of 110 A, and a short axis of 85 A. After correction for the detergent shell, the shape of the LH2 core is also an oblate plate with a height of 40 A, a long axis of 80 A, and a short axis of 55 A. In contrast to the cylindrical crystal structure with a height of 40 A and a diameter of 68 A, the molecular shape of the LH2 complex in detergent solution clearly deviates from the ringlike crystal structure, with an eccentricity found to be 0.59-consistent with the result of single molecular spectroscopy study of the isolated single LH2 molecules.

Determination of the Topological Shape of Integral Membrane Protein Light-Harvesting Complex LH2 from Photosynthetic Bacteria in the Detergent Solution by Small-Angle X-Ray Scattering

PubMed Central

Hong, Xinguo; Weng, Yu-Xiang; Li, Ming

2004-01-01

The topological shape of the integral membrane protein light-harvesting complex LH2 from photosynthetic bacteria Rhodobacter spheroides 2.4.1 in detergent solution has been determined from synchrotron small-angle X-ray scattering data using direct curve-fitting by the ellipsoid, ab initio shape determination methods of simulated annealing algorithm and multipole expansion, respectively. The results indicate that the LH2 protein in aqueous solution is encapsulated by a monolayered detergent shell. The detergent-stabilized structure has the shape of an oblate plate, with a thickness of 40 Å, a long axis of 110 Å, and a short axis of 85 Å . After correction for the detergent shell, the shape of the LH2 core is also an oblate plate with a height of 40 Å, a long axis of 80 Å, and a short axis of 55 Å. In contrast to the cylindrical crystal structure with a height of 40 Å and a diameter of 68 Å, the molecular shape of the LH2 complex in detergent solution clearly deviates from the ringlike crystal structure, with an eccentricity found to be 0.59—consistent with the result of single molecular spectroscopy study of the isolated single LH2 molecules. PMID:14747343

Energy Levels, Lifetimes, and Transition Rates for P-like Ions from Cr X to Zn XVI from Large-scale Relativistic Multiconfiguration Calculations

NASA Astrophysics Data System (ADS)

Wang, K.; Jönsson, P.; Gaigalas, G.; Radžiūtė, L.; Rynkun, P.; Del Zanna, G.; Chen, C. Y.

2018-04-01

The fully relativistic multiconfiguration Dirac–Hartree–Fock method is used to compute excitation energies and lifetimes for the 143 lowest states of the 3{s}23{p}3, 3s3p 4, 3{s}23{p}23d, 3s3p 33d, 3p 5, 3{s}23p3{d}2 configurations in P-like ions from Cr X to Zn XVI. Multipole (E1, M1, E2, M2) transition rates, line strengths, oscillator strengths, and branching fractions among these states are also given. Valence–valence and core–valence electron correlation effects are systematically accounted for using large basis function expansions. Computed excitation energies are compared with the NIST ASD and CHIANTI compiled values and previous calculations. The mean average absolute difference, removing obvious outliers, between computed and observed energies for the 41 lowest identified levels in Fe XII, is only 0.057%, implying that the computed energies are accurate enough to aid identification of new emission lines from the Sun and other astrophysical sources. The amount of energy and transition data of high accuracy are significantly increased for several P-like ions of astrophysics interest, where experimental data are still very scarce.

Earth's rotation in the framework of general relativity: rigid multipole moments

NASA Astrophysics Data System (ADS)

Klioner, S. A.; Soffel, M.; Xu, Ch.; Wu, X.

A set of equations describing the rotational motion of the Earth relative to the GCRS is formulated in the approximation of rigidly rotating multipoles. The external bodies are supposed to be mass monopoles. The derived set of formulas is supposed to form the theoretical basis for a practical post-Newtonian theory of Earth precession and nutation.

Electrostatic attraction between neutral microdroplets by ion fluctuations

NASA Astrophysics Data System (ADS)

Sheng, Yu-Jane; Tsao, Heng-Kwong

2004-06-01

The interaction between two aqueous droplets containing ions is investigated. The ion-fluctuation correlation gives rise to attraction between two neutral microdroplets, similar to the van der Waals interaction between neutral atoms. Electrostatic attraction consists of contributions from various induced multipole-multipole interactions, including dipole-dipole < P2z >2 r-6 , dipole-quadrupole < P2z > < Q 2zz > r-8 , dipole-octupole < P2z > < O 2zzz > r-10 , and quadrupole-quadrupole interactions < Q 2zz >2 r-10 . The mean-square multipole moments are determined analytically by linear response theory. The fluctuation-driven attraction is so strong at short distance that it may dominate over the Coulomb repulsion between like-charged droplets. These theoretical results are confirmed by Monte Carlo simulations.

Electrostatic attraction between neutral microdroplets by ion fluctuations.

PubMed

Sheng, Yu-Jane; Tsao, Heng-Kwong

2004-06-01

The interaction between two aqueous droplets containing ions is investigated. The ion-fluctuation correlation gives rise to attraction between two neutral microdroplets, similar to the van der Waals interaction between neutral atoms. Electrostatic attraction consists of contributions from various induced multipole-multipole interactions, including dipole-dipole < P(2)(z) >(2) r(-6), dipole-quadrupole < P(2)(z) > < Q (2)(zz ) > r(-8), dipole-octupole < P(2)(z) > < O (2)(zzz ) > r(-10), and quadrupole-quadrupole interactions < Q (2)(zz ) >(2) r(-10). The mean-square multipole moments are determined analytically by linear response theory. The fluctuation-driven attraction is so strong at short distance that it may dominate over the Coulomb repulsion between like-charged droplets. These theoretical results are confirmed by Monte Carlo simulations.

Combined cosmological tests of a bivalent tachyonic dark energy scalar field model

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

Keresztes, Zoltán; Gergely, László Á., E-mail: zkeresztes@titan.physx.u-szeged.hu, E-mail: gergely@physx.u-szeged.hu

A recently investigated tachyonic scalar field dark energy dominated universe exhibits a bivalent future: depending on initial parameters can run either into a de Sitter exponential expansion or into a traversable future soft singularity followed by a contraction phase. We also include in the model (i) a tiny amount of radiation, (ii) baryonic matter (Ω{sub b}h{sup 2} = 0.022161, where the Hubble constant is fixed as h = 0.706) and (iii) cold dark matter (CDM). Out of a variety of six types of evolutions arising in a more subtle classification, we identify two in which in the past the scalar field effectively degenerates intomore » a dust (its pressure drops to an insignificantly low negative value). These are the evolutions of type IIb converging to de Sitter and type III hitting the future soft singularity. We confront these background evolutions with various cosmological tests, including the supernova type Ia Union 2.1 data, baryon acoustic oscillation distance ratios, Hubble parameter-redshift relation and the cosmic microwave background (CMB) acoustic scale. We determine a subset of the evolutions of both types which at 1σ confidence level are consistent with all of these cosmological tests. At perturbative level we derive the CMB temperature power spectrum to find the best agreement with the Planck data for Ω{sub CDM} = 0.22. The fit is as good as for the ΛCDM model at high multipoles, but the power remains slightly overestimated at low multipoles, for both types of evolutions. The rest of the CDM is effectively generated by the tachyonic field, which in this sense acts as a combined dark energy and dark matter model.« less

Role of higher-multipole deformations in exotic {sup 14}C cluster radioactivity

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

Sawhney, Gudveen; Sharma, Manoj K.; Gupta, Raj K.

2011-06-15

We have studied nine cases of spontaneous emission of {sup 14}C clusters in the ground-state decays of the same number of parent nuclei from the trans-lead region, specifically from {sup 221}Fr to {sup 226}Th, using the preformed cluster model (PCM) of Gupta and collaborators, with choices of spherical, quadrupole deformation ({beta}{sub 2}) alone, and higher-multipole deformations ({beta}{sub 2}, {beta}{sub 3}, {beta}{sub 4}) with cold ''compact'' orientations {theta}{sup c} of decay products. The calculated {sup 14}C cluster decay half-life times are found to be in nice agreement with experimental data only for the case of higher-multipole deformations ({beta}{sub 2}-{beta}{sub 4}) andmore » {theta}{sup c} orientations of cold elongated configurations. In other words, compared to our earlier study of clusters heavier than {sup 14}C, where the inclusion of {beta}{sub 2} alone, with ''optimum'' orientations, was found to be enough to give the best comparison with data, here for {sup 14}C cluster decay the inclusion of higher-multipole deformations (up to hexadecapole), together with {theta}{sup c} orientations, is found to be essential on the basis of the PCM. Interestingly, whereas both the penetration probability and assault frequency work simply as scaling factors, the preformation probability is strongly influenced by the order of multipole deformations and orientations of nuclei. The possible role of Q value and angular-momentum effects are also considered in reference to {sup 14}C cluster radioactivity.« less

CMB EB and TB cross-spectrum estimation via pseudospectrum techniques

NASA Astrophysics Data System (ADS)

Grain, J.; Tristram, M.; Stompor, R.

2012-10-01

We discuss methods for estimating EB and TB spectra of the cosmic microwave background anisotropy maps covering limited sky area. Such odd-parity correlations are expected to vanish whenever parity is not broken. As this is indeed the case in the standard cosmologies, any evidence to the contrary would have a profound impact on our theories of the early Universe. Such correlations could also become a sensitive diagnostic of some particularly insidious instrumental systematics. In this work we introduce three different unbiased estimators based on the so-called standard and pure pseudo-spectrum techniques and later assess their performance by means of extensive Monte Carlo simulations performed for different experimental configurations. We find that a hybrid approach combining a pure estimate of B-mode multipoles with a standard one for E-mode (or T) multipoles, leads to the smallest error bars for both EB (or TB respectively) spectra as well as for the three other polarization-related angular power spectra (i.e., EE, BB, and TE). However, if both E and B multipoles are estimated using the pure technique, the loss of precision for the EB spectrum is not larger than ˜30%. Moreover, for the experimental configurations considered here, the statistical uncertainties-due to sampling variance and instrumental noise-of the pseudo-spectrum estimates is at most a factor ˜1.4 for TT, EE, and TE spectra and a factor ˜2 for BB, TB, and EB spectra, higher than the most optimistic Fisher estimate of the variance.

Predicting K0Λ photoproduction observables by using the multipole approach

NASA Astrophysics Data System (ADS)

Mart, T.; Rusli, A.

2017-12-01

We present an isobar model for kaon photoproduction on the proton γ p\\to K^+Λ that can nicely reproduce the available experimental data from threshold up to W=2.0 GeV. The background amplitude of the model is constructed from a covariant Feynman diagrammatic method, whereas the resonance one is formulated by using the multipole approach. All unknown parameters in both background and resonance amplitudes are extracted by adjusting the calculated observables to experimental data. With the help of SU(3) isospin symmetry and some information obtained from the Particle Data Group we estimate the cross section and polarization observables for the neutral kaon photoproduction on the neutron γ n\\to K^0Λ. The result indicates no sharp peak in the K^0Λ total cross section. The predicted differential cross section exhibits resonance structures only at cosθ=-1. To obtain sizable observables the present work recommends measurement of the K^0Λ cross section with W≳ 1.70 GeV, whereas for the recoiled Λ polarization measurement with W≈ 1.65-1.90 GeV would be advised, since the predictions of existing models show a large variance at this kinematics. The predicted electric and magnetic multipoles are found to be mostly different from those obtained in previous works. For W=1.75 and 1.95 GeV it is found that most of the single and double polarization observables demonstrate large asymmetries.

Negative refraction in metamaterials based on dielectric spherical particles

NASA Astrophysics Data System (ADS)

Huang, T. C.; Wang, B. X.; Zhao, C. Y.

2018-07-01

Negative refraction (NR) metamaterials are featured with unique physical properties and potential to realize full control of electromagnetic waves, which have attracted much attention since the last decade. However, few researches focus on the realization of three-dimensional dielectric NR metamaterials in optic frequency, and the current design methods need further development. In this paper, a three-dimensional all-dielectric NR metamaterial with two NR bands has been realized based on proper excitation of electric and magnetic multipoles. It is also predicted that the coupling of magnetic dipole and electric dipole can lead to the NR bands in near-infrared frequencies, and NR in the visible frequencies can be achieved by the coupling of magnetic quadrupole and electric dipole. Band structures and equal-frequency surfaces of proposed metamaterial arranged in the periodic cubic lattice are solved by adopting the plane wave expansion method, and then the results verify the existence of these two NR frequency bands in periodic metamaterials. In this way, the characteristic parameters such as transmission and absorption of light in two NR bands are also analyzed. In the meantime, the finite-deference time-domain method is used to intuitively display the phenomenon of NR and investigate the effects of disorder in particle arrangement. Besides, it is found that the proposed metamaterials have fine robustness to the disorder in particle arrangement, and these two NR bands can be tuned by adjusting volume fraction. In brief, this work provides means for preliminary designing, profound analysis and intuitively exhibition of NR metamaterials based on dielectric particles.

The electromagnetic multipole moments of the charged open-flavor {Z}_{\\bar{c}q} states

NASA Astrophysics Data System (ADS)

Azizi, K.; Özdem, U.

2018-05-01

The electromagnetic multipole moments of the open-flavor {Z}\\bar{cq} states are investigated by assuming a diquark–antidiquark picture for their internal structure and quantum numbers {J}{PC}={1}+- for their spin-parity. In particular, their magnetic and quadrupole moments are extracted in the framework of light-cone QCD sum rule by the help of the photon distribution amplitudes. The electromagnetic multipole moments of the open-flavor {Z}\\bar{cq} states are important dynamical observables, which encode valuable information on their underlying structure. The results obtained for the magnetic moments of different structures are considerably large and can be measured in future experiments. We obtain very small values for the quadrupole moments of {Z}\\bar{cq} states indicating a nonspherical charge distribution.

Rapid modelling of the redshift-space power spectrum multipoles for a masked density field

NASA Astrophysics Data System (ADS)

Wilson, M. J.; Peacock, J. A.; Taylor, A. N.; de la Torre, S.

2017-01-01

In this work, we reformulate the forward modelling of the redshift-space power spectrum multipole moments for a masked density field, as encountered in galaxy redshift surveys. Exploiting the symmetries of the redshift-space correlation function, we provide a masked-field generalization of the Hankel transform relation between the multipole moments in real and Fourier space. Using this result, we detail how a likelihood analysis requiring computation for a broad range of desired P(k) models may be executed 103-104 times faster than with other common approaches, together with significant gains in spectral resolution. We present a concrete application to the complex angular geometry of the VIMOS Public Extragalactic Redshift Survey PDR-1 release and discuss the validity of this technique for finite-angle surveys.

Transferability of electronic structure of four energetic materials by using single crystal and high resolution X-ray diffraction experiments

NASA Astrophysics Data System (ADS)

Chen, Yu-Sheng

The electronic structures of four energetic materials, trinitrodiazapentalene (C6H3N5O6, TNDAP), beta-1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (C4H8N8O8, beta-HMX), 1,3,3-trinitroazetidine (C3H4N4O6, TNAZ), and hexahydro-1,3,5-trinitro-1,3,5-s-triazine (C3H6N6O6, RDX), have been analyzed using Hansen-Coppens multipole refinements, using high resolution X-ray diffraction data collected at low temperature, as well as from theoretical calculated structure factors from the solid state phase using density functional theory (DFT), plus B3LYP level theory, and the 6-31G* basis set. However, when comparing both the deformation density and the electrostatic potentials from the theoretical results in TNDAP and TNAZ, they disagree with the experimental results. Therefore, those results have been deposited in appendices A4 and A6, for future reference. In HMX and RDX the theoretical results are in good agreement with experimental results. The physical properties derived from the electronic structure in these four energetic materials, such as multipole populations, the values of the electron density and its Laplacian of the electron density at the bond critical points, have also been calculated using "Atoms in Molecules" (AIM) theory both from the solid state phase calculation, and the experiment, as well as directly calculated from the free molecule in the gas phase. The electron density and the magnitude of its Laplacian from the gas phase are always larger than for the solid state phase calculation and the experiment. This may be due to the packing effect. The transferability of the experimental electronic structure of the NO 2 groups from HMX to TNDAP, TNAZ and RDX are also presented here. Even though the major populated multipoles are robust (small e.s.d.'s), these are few in number, compared with other lower populated multipoles for which the populations span a larger range. Since the deformation electron density distributions are reconstructed using linear combinations of the multipoles, it is necessary to give more degrees of freedom in the refinements. Therefore, those electron density distributions which have a wider range of the multipole populations should not be fixed in the refinements. Utilizing the same coordinate system setup in the multipole refinements of the functional groups, this system can be used as a starting point for solving the charge distribution of a larger system.

An O(N) and parallel approach to integral problems by a kernel-independent fast multipole method: Application to polarization and magnetization of interacting particles

NASA Astrophysics Data System (ADS)

Jiang, Xikai; Li, Jiyuan; Zhao, Xujun; Qin, Jian; Karpeev, Dmitry; Hernandez-Ortiz, Juan; de Pablo, Juan J.; Heinonen, Olle

2016-08-01

Large classes of materials systems in physics and engineering are governed by magnetic and electrostatic interactions. Continuum or mesoscale descriptions of such systems can be cast in terms of integral equations, whose direct computational evaluation requires O(N2) operations, where N is the number of unknowns. Such a scaling, which arises from the many-body nature of the relevant Green's function, has precluded wide-spread adoption of integral methods for solution of large-scale scientific and engineering problems. In this work, a parallel computational approach is presented that relies on using scalable open source libraries and utilizes a kernel-independent Fast Multipole Method (FMM) to evaluate the integrals in O(N) operations, with O(N) memory cost, thereby substantially improving the scalability and efficiency of computational integral methods. We demonstrate the accuracy, efficiency, and scalability of our approach in the context of two examples. In the first, we solve a boundary value problem for a ferroelectric/ferromagnetic volume in free space. In the second, we solve an electrostatic problem involving polarizable dielectric bodies in an unbounded dielectric medium. The results from these test cases show that our proposed parallel approach, which is built on a kernel-independent FMM, can enable highly efficient and accurate simulations and allow for considerable flexibility in a broad range of applications.

Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs

DTIC Science & Technology

2010-05-31

Todor , Karhúnen-Loève Approximation of Random Fields by General- ized Fast Multipole Methods, Journal of Computational Physics 217(2006), 100–122. [19...20] R. Todor , Robust eigenvalue computation for smoothing operators, SIAM J. Num. Anal. 44(2006), 865–878. 29 [21] R. Todor and Ch. Schwab, Convergence

Planning & Priority Setting for Basic Research

DTIC Science & Technology

2010-05-05

Integrated into numerous commercial codes in aerospace, automotive , semiconductor, and chemical industries Fast Multipole Methods (ONR 31) Applications... Use knowledge (even failures) to reduce risk in acquisition Provide the basis for future Navy and arine Corps syste s Ensure research...relevancy to Naval S&T strategy Transition pro ising Basic Research to applications Use kno ledge (even failures) to reduce risk in acquisition Maintain

Hartree-Fock limit values of multipole moments, polarizabilities, and hyperpolarizabilities for atoms and diatomic molecules

NASA Astrophysics Data System (ADS)

Kobus, Jacek

2015-02-01

Recently it has been demonstrated that the finite difference Hartree-Fock method can be used to deliver highly accurate values of electric multipole moments together with polarizabilities αz z,Az ,z z , and hyperpolarizabilities βz z z, γz z z,Bz z ,z z , for the ground states of various atomic and diatomic systems. Since these results can be regarded as de facto Hartree-Fock limit values their quality is of the utmost importance. This paper reexamines the use of the finite field method to calculate these electric properties, discusses its accuracy, and presents an updated list of the properties for the following atoms and diatomic molecules: H-, He, Li, Li+,Li2 +,Li-,Be2 + , Be, B+,C2 + , Ne, Mg2 +, Mg, Al+,Si2 + , Ar, K+,Ca2 +,Rb+,Sr2 +,Zr4 +,He2 , Be2,N2,F2,O2 , HeNe, LiH2 +, LiCl, LiBr, BH, CO, FH, NaCl, and KF. The potential energy curves and the dependence of the electric properties on the internuclear distance is also studied for He2,LiH+,Be2 , and HeNe systems.

Using the Multipole Resonance Probe to Stabilize the Electron Density During a Reactive Sputter Process

NASA Astrophysics Data System (ADS)

Oberberg, Moritz; Styrnoll, Tim; Ries, Stefan; Bienholz, Stefan; Awakowicz, Peter

2015-09-01

Reactive sputter processes are used for the deposition of hard, wear-resistant and non-corrosive ceramic layers such as aluminum oxide (Al2O3) . A well known problem is target poisoning at high reactive gas flows, which results from the reaction of the reactive gas with the metal target. Consequently, the sputter rate decreases and secondary electron emission increases. Both parameters show a non-linear hysteresis behavior as a function of the reactive gas flow and this leads to process instabilities. This work presents a new control method of Al2O3 deposition in a multiple frequency CCP (MFCCP) based on plasma parameters. Until today, process controls use parameters such as spectral line intensities of sputtered metal as an indicator for the sputter rate. A coupling between plasma and substrate is not considered. The control system in this work uses a new plasma diagnostic method: The multipole resonance probe (MRP) measures plasma parameters such as electron density by analyzing a typical resonance frequency of the system response. This concept combines target processes and plasma effects and directly controls the sputter source instead of the resulting target parameters.

Influence of kinetic effects on the resonance behavior of the Multipole Resonance Probe

NASA Astrophysics Data System (ADS)

Oberrath, Jens; Mussenbrock, Thomas; Brinkmann, Ralf Peter

2012-10-01

Active plasma resonance spectroscopy is a well known diagnostic method. Many concepts of this method are theoretically investigated and realized as a diagnostic tool. One of these tools is the multipole resonance probe (MRP) [1]. The application of such a probe in plasmas with pressures of only a few Pa raises the question whether kinetic effects have to be taken into account or not. To address this question a kinetic model is necessary. A general kinetic model for an electrostatic concept of active plasma resonance spectroscopy has already been presented by the authors [2]. This model can be used to describe the dynamical behavior of the MRP, which is interpretable as a special case of the general model. Neglecting electron-neutral collisions, this model can be solved analytically. Based on this solution we derive an approximated expression for the admittance of the system to investigate the influence of kinetic effects on the resonance behavior of the MRP. [4pt] [1] M. Lapke et al., Plasma Sources Sci. Technol. 20, 2011, 042001[0pt] [2] J. Oberrath et al., Proceedings of the 30th International Conference on Phenomena in Ionized Gases, 28th August - 2nd September, 2011

Construction and Performance of a Superconducting Multipole Wiggler

NASA Astrophysics Data System (ADS)

Hwang, C. S.; Wang, B.; Chen, J. Y.; Chang, C. H.; Chen, H. H.; Fan, T. C.; Lin, F. Y.; Huang, M. H.; Chang, C. C.; Hsu, S. N.; Hsiung, G. Y.; Hsu, K. T.; Chen, J.; Chien, Y. C.; Chen, J. R.; Chen, C. T.

2004-05-01

A 3.2 Tesla superconducting multipole wiggler was designed and fabricated as an X-ray source. The magnet assembly, which consists of 32 pairs of racetrack NbTi superconducting coils with a periodic length of 60 mm, provides 28 effective poles. A 1.4056 m long elliptical cold-bore stainless steel beam duct with taper flanges and a wall thickness of 1 mm, was developed and constructed to fit the ultra-high vacuum condition for electron beam. The magnetic field strength was measured in liquid helium using a cryogenic Hall probe, revealing a field behavior very close to behavior consistent with the designed values. A Hall generator and the stretch wire methods are used to determine the transfer function of the peak field, the first and second integrated field distributions, and the good field region of the magnet. The quench protection of the magnet, the control algorithm for automatic filling of liquid helium, and the boil off rate of liquid helium and liquid nitrogen will also be discussed.

STEM-EELS analysis of multipole surface plasmon modes in symmetry-broken AuAg nanowire dimers

NASA Astrophysics Data System (ADS)

Schubert, Ina; Sigle, Wilfried; van Aken, Peter A.; Trautmann, Christina; Toimil-Molares, Maria Eugenia

2015-03-01

Surface plasmon coupling in nanowires separated by small gaps generates high field enhancements at the position of the gap and is thus of great interest for sensing applications. It is known that the nanowire dimensions and in particular the symmetry of the structures has strong influence on the plasmonic properties of the dimer structure. Here, we report on multipole surface plasmon coupling in symmetry-broken AuAg nanowire dimers. Our dimers, consisting of two nanowires with different lengths and separated by gaps of only 10 to 30 nm, were synthesized by pulsed electrochemical deposition in ion track-etched polymer templates. Electron energy-loss spectroscopy in scanning transmission electron microscopy allows us to resolve up to nine multipole order surface plasmon modes of these dimers spectrally separated from each other. The spectra evidence plasmon coupling between resonances of different multipole order, resulting in the generation of additional plasmonic modes. Since such complex structures require elaborated synthesis techniques, dimer structures with complex composition, morphology and shape are created. We demonstrate that finite element simulations on pure Au dimers can predict the generated resonances in the fabricated structures. The excellent agreement of our experiment on AuAg dimers with finite integration simulations using CST microwave studio manifests great potential to design complex structures for sensing applications.

Quantum interference in laser spectroscopy of highly charged lithiumlike ions

NASA Astrophysics Data System (ADS)

Amaro, Pedro; Loureiro, Ulisses; Safari, Laleh; Fratini, Filippo; Indelicato, Paul; Stöhlker, Thomas; Santos, José Paulo

2018-02-01

We investigate the quantum interference induced shifts between energetically close states in highly charged ions, with the energy structure being observed by laser spectroscopy. In this work, we focus on hyperfine states of lithiumlike heavy-Z isotopes and quantify how much quantum interference changes the observed transition frequencies. The process of photon excitation and subsequent photon decay for the transition 2 s →2 p →2 s is implemented with fully relativistic and full-multipole frameworks, which are relevant for such relativistic atomic systems. We consider the isotopes 79+207Pb and 80+209Bi due to experimental interest, as well as other examples of isotopes with lower Z , namely 56+141Pr and 64+165Ho. We conclude that quantum interference can induce shifts up to 11% of the linewidth in the measurable resonances of the considered isotopes, if interference between resonances is neglected. The inclusion of relativity decreases the cross section by 35%, mainly due to the complete retardation form of the electric dipole multipole. However, the contribution of the next higher multipoles (e.g., magnetic quadrupole) to the cross section is negligible. This makes the contribution of relativity and higher-order multipoles to the quantum interference induced shifts a minor effect, even for heavy-Z elements.

Use of the ( e , e prime n ) reaction to study the giant multipole resonances in sup 116 Sn

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

Miskimen, R.A.; Ammons, E.A.; Arruda-Neto, J.D.T.

1991-04-01

The giant multipole resonances in {sup 116}Sn have been studied using the ({ital e},{ital e}{prime}{ital n}) reaction. Data were taken at effective momentum transfers of 0.37, 0.45, and 0.55 fm{sup {minus}1} and a multipole analysis of the data was performed. The inferred multipole strength functions identify the {ital E}2 and {ital E}0 resonances as distinct peaks at 12.2 and 17.9 MeV, respectively. The energy-weighted sum-rule strengths for the {ital E}2 and {ital E}0 resonances, obtained using a Lorentzian fit to the data, are 34{plus minus}13% and 93{plus minus}37%. When compared with results from alpha scattering and pion scattering the sum-rulemore » strengths exhibit approximate agreement, but the {ital E}0 strength identified in this measurement lies at higher excitation energy, consistent with the trend observed in heavier nuclei. The ({ital e},{ital e}{prime}{ital n}) data are compared with a continuum random phase approximation (RPA) calculation of the {ital E}2 and {ital E}0 strengths, and with an open-shell RPA calculation of the {ital E}2 strength. Both calculations disagree with the data in the region of the {ital E}2 resonance.« less

Resonance line polarization and the Hanle effect in optically thick media. I - Formulation for the two-level atom

NASA Astrophysics Data System (ADS)

Landi Degl'Innocenti, E.; Bommier, V.; Sahal-Brechot, S.

1990-08-01

A general formalism is presented to describe resonance line polarization for a two-level atom in an optically thick, three-dimensional medium embedded in an arbitrary varying magnetic field and irradiated by an arbitrary radiation field. The magnetic field is supposed sufficiently small to induce a Zeeman splitting much smaller than the typical line width. By neglecting atomic polarization in the lower level and stimulated emission, an integral equation is derived for the multipole moments of the density matrix of the upper level. This equation shows how the multipole moments at any assigned point of the medium are coupled to the multipole moments relative at a different point as a consequence of the propagation of polarized radiation between the two points. The equation also accounts for the effect of the magnetic field, described by a kernel locally connecting multipole moments of the same rank, and for the role of inelastic and elastic (or depolarizing) collisions. After having given its formal derivation for the general case, the integral equation is particularized to the one-dimensional and two-dimensional cases. For the one-dimensional case of a plane parallel atmosphere, neglecting both the magnetic field and depolarizing collisions, the equation here derived reduces to a previous one given by Rees (1978).

Implementation of a finite-amplitude method in a relativistic meson-exchange model

NASA Astrophysics Data System (ADS)

Sun, Xuwei; Lu, Dinghui

2017-08-01

The finite-amplitude method is a feasible numerical approach to large scale random phase approximation calculations. It avoids the storage and calculation of residual interaction elements as well as the diagonalization of the RPA matrix, which will be prohibitive when the configuration space is huge. In this work we finished the implementation of a finite-amplitude method in a relativistic meson exchange mean field model with axial symmetry. The direct variation approach makes our FAM scheme capable of being extended to the multipole excitation case.

Numerical realization of the variational method for generating self-trapped beams

NASA Astrophysics Data System (ADS)

Duque, Erick I.; Lopez-Aguayo, Servando; Malomed, Boris A.

2018-03-01

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schr\\"odinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.

Three-Dimensional Electromagnetic Scattering from Layered Media with Rough Interfaces for Subsurface Radar Remote Sensing

NASA Astrophysics Data System (ADS)

Duan, Xueyang

The objective of this dissertation is to develop forward scattering models for active microwave remote sensing of natural features represented by layered media with rough interfaces. In particular, soil profiles are considered, for which a model of electromagnetic scattering from multilayer rough surfaces with or without buried random media is constructed. Starting from a single rough surface, radar scattering is modeled using the stabilized extended boundary condition method (SEBCM). This method solves the long-standing instability issue of the classical EBCM, and gives three-dimensional full wave solutions over large ranges of surface roughnesses with higher computational efficiency than pure numerical solutions, e.g., method of moments (MoM). Based on this single surface solution, multilayer rough surface scattering is modeled using the scattering matrix approach and the model is used for a comprehensive sensitivity analysis of the total ground scattering as a function of layer separation, subsurface statistics, and sublayer dielectric properties. The buried inhomogeneities such as rocks and vegetation roots are considered for the first time in the forward scattering model. Radar scattering from buried random media is modeled by the aggregate transition matrix using either the recursive transition matrix approach for spherical or short-length cylindrical scatterers, or the generalized iterative extended boundary condition method we developed for long cylinders or root-like cylindrical clusters. These approaches take the field interactions among scatterers into account with high computational efficiency. The aggregate transition matrix is transformed to a scattering matrix for the full solution to the layered-medium problem. This step is based on the near-to-far field transformation of the numerical plane wave expansion of the spherical harmonics and the multipole expansion of plane waves. This transformation consolidates volume scattering from the buried random medium with the scattering from layered structure in general. Combined with scattering from multilayer rough surfaces, scattering contributions from subsurfaces and vegetation roots can be then simulated. Solutions of both the rough surface scattering and random media scattering are validated numerically, experimentally, or both. The experimental validations have been carried out using a laboratory-based transmit-receive system for scattering from random media and a new bistatic tower-mounted radar system for field-based surface scattering measurements.

Planck 2015 results: XI. CMB power spectra, likelihoods, and robustness of parameters

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

Aghanim, N.; Arnaud, M.; Ashdown, M.

This study presents the Planck 2015 likelihoods, statistical descriptions of the 2-point correlationfunctions of the cosmic microwave background (CMB) temperature and polarization fluctuations that account for relevant uncertainties, both instrumental and astrophysical in nature. They are based on the same hybrid approach used for the previous release, i.e., a pixel-based likelihood at low multipoles (ℓ< 30) and a Gaussian approximation to the distribution of cross-power spectra at higher multipoles. The main improvements are the use of more and better processed data and of Planck polarization information, along with more detailed models of foregrounds and instrumental uncertainties. The increased redundancy broughtmore » by more than doubling the amount of data analysed enables further consistency checks and enhanced immunity to systematic effects. It also improves the constraining power of Planck, in particular with regard to small-scale foreground properties. Progress in the modelling of foreground emission enables the retention of a larger fraction of the sky to determine the properties of the CMB, which also contributes to the enhanced precision of the spectra. Improvements in data processing and instrumental modelling further reduce uncertainties. Extensive tests establish the robustness and accuracy of the likelihood results, from temperature alone, from polarization alone, and from their combination. For temperature, we also perform a full likelihood analysis of realistic end-to-end simulations of the instrumental response to the sky, which were fed into the actual data processing pipeline; this does not reveal biases from residual low-level instrumental systematics. Even with the increase in precision and robustness, the ΛCDM cosmological model continues to offer a very good fit to the Planck data. The slope of the primordial scalar fluctuations, n s, is confirmed smaller than unity at more than 5σ from Planck alone. We further validate the robustness of the likelihood results against specific extensions to the baseline cosmology, which are particularly sensitive to data at high multipoles. For instance, the effective number of neutrino species remains compatible with the canonical value of 3.046. For this first detailed analysis of Planck polarization spectra, we concentrate at high multipoles on the E modes, leaving the analysis of the weaker B modes to future work. At low multipoles we use temperature maps at all Planck frequencies along with a subset of polarization data. These data take advantage of Planck’s wide frequency coverage to improve the separation of CMB and foreground emission. Within the baseline ΛCDM cosmology this requires τ = 0.078 ± 0.019 for the reionization optical depth, which is significantly lower than estimates without the use of high-frequency data for explicit monitoring of dust emission. At high multipoles we detect residual systematic errors in E polarization, typically at the μK 2 level; we therefore choose to retain temperature information alone for high multipoles as the recommended baseline, in particular for testing non-minimal models. Finally and nevertheless, the high-multipole polarization spectra from Planck are already good enough to enable a separate high-precision determination of the parameters of the ΛCDM model, showing consistency with those established independently from temperature information alone.« less

Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of parameters

NASA Astrophysics Data System (ADS)

Planck Collaboration; Aghanim, N.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A. J.; Barreiro, R. B.; Bartlett, J. G.; Bartolo, N.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bock, J. J.; Bonaldi, A.; Bonavera, L.; Bond, J. R.; Borrill, J.; Bouchet, F. R.; Boulanger, F.; Bucher, M.; Burigana, C.; Butler, R. C.; Calabrese, E.; Cardoso, J.-F.; Catalano, A.; Challinor, A.; Chiang, H. C.; Christensen, P. R.; Clements, D. L.; Colombo, L. P. L.; Combet, C.; Coulais, A.; Crill, B. P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R. D.; Davis, R. J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Désert, F.-X.; Di Valentino, E.; Dickinson, C.; Diego, J. M.; Dolag, K.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dunkley, J.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T. A.; Eriksen, H. K.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A. A.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Gauthier, C.; Gerbino, M.; Giard, M.; Gjerløw, E.; González-Nuevo, J.; Górski, K. M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J. E.; Hamann, J.; Hansen, F. K.; Harrison, D. L.; Helou, G.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S. R.; Hivon, E.; Holmes, W. A.; Hornstrup, A.; Huffenberger, K. M.; Hurier, G.; Jaffe, A. H.; Jones, W. C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kiiveri, K.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.-M.; Lasenby, A.; Lattanzi, M.; Lawrence, C. R.; Le Jeune, M.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Lewis, A.; Liguori, M.; Lilje, P. B.; Lilley, M.; Linden-Vørnle, M.; Lindholm, V.; López-Caniego, M.; Macías-Pérez, J. F.; Maffei, B.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Maris, M.; Martin, P. G.; Martínez-González, E.; Masi, S.; Matarrese, S.; Meinhold, P. R.; Melchiorri, A.; Migliaccio, M.; Millea, M.; Mitra, S.; Miville-Deschênes, M.-A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Mottet, S.; Munshi, D.; Murphy, J. A.; Narimani, A.; Naselsky, P.; Nati, F.; Natoli, P.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C. A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Partridge, B.; Pasian, F.; Patanchon, G.; Pearson, T. J.; Perdereau, O.; Perotto, L.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Ponthieu, N.; Pratt, G. W.; Prunet, S.; Puget, J.-L.; Rachen, J. P.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rossetti, M.; Roudier, G.; Rouillé d'Orfeuil, B.; Rubiño-Martín, J. A.; Rusholme, B.; Salvati, L.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Scott, D.; Serra, P.; Spencer, L. D.; Spinelli, M.; Stolyarov, V.; Stompor, R.; Sunyaev, R.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J. A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Trombetti, T.; Tucci, M.; Tuovinen, J.; Umana, G.; Valenziano, L.; Valiviita, J.; Van Tent, F.; Vielva, P.; Villa, F.; Wade, L. A.; Wandelt, B. D.; Wehus, I. K.; Yvon, D.; Zacchei, A.; Zonca, A.

2016-09-01

This paper presents the Planck 2015 likelihoods, statistical descriptions of the 2-point correlationfunctions of the cosmic microwave background (CMB) temperature and polarization fluctuations that account for relevant uncertainties, both instrumental and astrophysical in nature. They are based on the same hybrid approach used for the previous release, I.e., a pixel-based likelihood at low multipoles (ℓ< 30) and a Gaussian approximation to the distribution of cross-power spectra at higher multipoles. The main improvements are the use of more and better processed data and of Planck polarization information, along with more detailed models of foregrounds and instrumental uncertainties. The increased redundancy brought by more than doubling the amount of data analysed enables further consistency checks and enhanced immunity to systematic effects. It also improves the constraining power of Planck, in particular with regard to small-scale foreground properties. Progress in the modelling of foreground emission enables the retention of a larger fraction of the sky to determine the properties of the CMB, which also contributes to the enhanced precision of the spectra. Improvements in data processing and instrumental modelling further reduce uncertainties. Extensive tests establish the robustness and accuracy of the likelihood results, from temperature alone, from polarization alone, and from their combination. For temperature, we also perform a full likelihood analysis of realistic end-to-end simulations of the instrumental response to the sky, which were fed into the actual data processing pipeline; this does not reveal biases from residual low-level instrumental systematics. Even with the increase in precision and robustness, the ΛCDM cosmological model continues to offer a very good fit to the Planck data. The slope of the primordial scalar fluctuations, ns, is confirmed smaller than unity at more than 5σ from Planck alone. We further validate the robustness of the likelihood results against specific extensions to the baseline cosmology, which are particularly sensitive to data at high multipoles. For instance, the effective number of neutrino species remains compatible with the canonical value of 3.046. For this first detailed analysis of Planck polarization spectra, we concentrate at high multipoles on the E modes, leaving the analysis of the weaker B modes to future work. At low multipoles we use temperature maps at all Planck frequencies along with a subset of polarization data. These data take advantage of Planck's wide frequency coverage to improve the separation of CMB and foreground emission. Within the baseline ΛCDM cosmology this requires τ = 0.078 ± 0.019 for the reionization optical depth, which is significantly lower than estimates without the use of high-frequency data for explicit monitoring of dust emission. At high multipoles we detect residual systematic errors in E polarization, typically at the μK2 level; we therefore choose to retain temperature information alone for high multipoles as the recommended baseline, in particular for testing non-minimal models. Nevertheless, the high-multipole polarization spectra from Planck are already good enough to enable a separate high-precision determination of the parameters of the ΛCDM model, showing consistency with those established independently from temperature information alone.

Planck 2015 results: XI. CMB power spectra, likelihoods, and robustness of parameters

DOE PAGES

Aghanim, N.; Arnaud, M.; Ashdown, M.; ...

2016-09-20

This study presents the Planck 2015 likelihoods, statistical descriptions of the 2-point correlationfunctions of the cosmic microwave background (CMB) temperature and polarization fluctuations that account for relevant uncertainties, both instrumental and astrophysical in nature. They are based on the same hybrid approach used for the previous release, i.e., a pixel-based likelihood at low multipoles (ℓ< 30) and a Gaussian approximation to the distribution of cross-power spectra at higher multipoles. The main improvements are the use of more and better processed data and of Planck polarization information, along with more detailed models of foregrounds and instrumental uncertainties. The increased redundancy broughtmore » by more than doubling the amount of data analysed enables further consistency checks and enhanced immunity to systematic effects. It also improves the constraining power of Planck, in particular with regard to small-scale foreground properties. Progress in the modelling of foreground emission enables the retention of a larger fraction of the sky to determine the properties of the CMB, which also contributes to the enhanced precision of the spectra. Improvements in data processing and instrumental modelling further reduce uncertainties. Extensive tests establish the robustness and accuracy of the likelihood results, from temperature alone, from polarization alone, and from their combination. For temperature, we also perform a full likelihood analysis of realistic end-to-end simulations of the instrumental response to the sky, which were fed into the actual data processing pipeline; this does not reveal biases from residual low-level instrumental systematics. Even with the increase in precision and robustness, the ΛCDM cosmological model continues to offer a very good fit to the Planck data. The slope of the primordial scalar fluctuations, n s, is confirmed smaller than unity at more than 5σ from Planck alone. We further validate the robustness of the likelihood results against specific extensions to the baseline cosmology, which are particularly sensitive to data at high multipoles. For instance, the effective number of neutrino species remains compatible with the canonical value of 3.046. For this first detailed analysis of Planck polarization spectra, we concentrate at high multipoles on the E modes, leaving the analysis of the weaker B modes to future work. At low multipoles we use temperature maps at all Planck frequencies along with a subset of polarization data. These data take advantage of Planck’s wide frequency coverage to improve the separation of CMB and foreground emission. Within the baseline ΛCDM cosmology this requires τ = 0.078 ± 0.019 for the reionization optical depth, which is significantly lower than estimates without the use of high-frequency data for explicit monitoring of dust emission. At high multipoles we detect residual systematic errors in E polarization, typically at the μK 2 level; we therefore choose to retain temperature information alone for high multipoles as the recommended baseline, in particular for testing non-minimal models. Finally and nevertheless, the high-multipole polarization spectra from Planck are already good enough to enable a separate high-precision determination of the parameters of the ΛCDM model, showing consistency with those established independently from temperature information alone.« less

The zero-multipole summation method for estimating electrostatic interactions in molecular dynamics: analysis of the accuracy and application to liquid systems.

PubMed

Fukuda, Ikuo; Kamiya, Narutoshi; Nakamura, Haruki

2014-05-21

In the preceding paper [I. Fukuda, J. Chem. Phys. 139, 174107 (2013)], the zero-multipole (ZM) summation method was proposed for efficiently evaluating the electrostatic Coulombic interactions of a classical point charge system. The summation takes a simple pairwise form, but prevents the electrically non-neutral multipole states that may artificially be generated by a simple cutoff truncation, which often causes large energetic noises and significant artifacts. The purpose of this paper is to judge the ability of the ZM method by investigating the accuracy, parameter dependencies, and stability in applications to liquid systems. To conduct this, first, the energy-functional error was divided into three terms and each term was analyzed by a theoretical error-bound estimation. This estimation gave us a clear basis of the discussions on the numerical investigations. It also gave a new viewpoint between the excess energy error and the damping effect by the damping parameter. Second, with the aid of these analyses, the ZM method was evaluated based on molecular dynamics (MD) simulations of two fundamental liquid systems, a molten sodium-chlorine ion system and a pure water molecule system. In the ion system, the energy accuracy, compared with the Ewald summation, was better for a larger value of multipole moment l currently induced until l ≲ 3 on average. This accuracy improvement with increasing l is due to the enhancement of the excess-energy accuracy. However, this improvement is wholly effective in the total accuracy if the theoretical moment l is smaller than or equal to a system intrinsic moment L. The simulation results thus indicate L ∼ 3 in this system, and we observed less accuracy in l = 4. We demonstrated the origins of parameter dependencies appearing in the crossing behavior and the oscillations of the energy error curves. With raising the moment l we observed, smaller values of the damping parameter provided more accurate results and smoother behaviors with respect to cutoff length were obtained. These features can be explained, on the basis of the theoretical error analyses, such that the excess energy accuracy is improved with increasing l and that the total accuracy improvement within l ⩽ L is facilitated by a small damping parameter. Although the accuracy was fundamentally similar to the ion system, the bulk water system exhibited distinguishable quantitative behaviors. A smaller damping parameter was effective in all the practical cutoff distance, and this fact can be interpreted by the reduction of the excess subset. A lower moment was advantageous in the energy accuracy, where l = 1 was slightly superior to l = 2 in this system. However, the method with l = 2 (viz., the zero-quadrupole sum) gave accurate results for the radial distribution function. We confirmed the stability in the numerical integration for MD simulations employing the ZM scheme. This result is supported by the sufficient smoothness of the energy function. Along with the smoothness, the pairwise feature and the allowance of the atom-based cutoff mode on the energy formula lead to the exact zero total-force, ensuring the total-momentum conservations for typical MD equations of motion.

The zero-multipole summation method for estimating electrostatic interactions in molecular dynamics: Analysis of the accuracy and application to liquid systems

NASA Astrophysics Data System (ADS)

Fukuda, Ikuo; Kamiya, Narutoshi; Nakamura, Haruki

2014-05-01

In the preceding paper [I. Fukuda, J. Chem. Phys. 139, 174107 (2013)], the zero-multipole (ZM) summation method was proposed for efficiently evaluating the electrostatic Coulombic interactions of a classical point charge system. The summation takes a simple pairwise form, but prevents the electrically non-neutral multipole states that may artificially be generated by a simple cutoff truncation, which often causes large energetic noises and significant artifacts. The purpose of this paper is to judge the ability of the ZM method by investigating the accuracy, parameter dependencies, and stability in applications to liquid systems. To conduct this, first, the energy-functional error was divided into three terms and each term was analyzed by a theoretical error-bound estimation. This estimation gave us a clear basis of the discussions on the numerical investigations. It also gave a new viewpoint between the excess energy error and the damping effect by the damping parameter. Second, with the aid of these analyses, the ZM method was evaluated based on molecular dynamics (MD) simulations of two fundamental liquid systems, a molten sodium-chlorine ion system and a pure water molecule system. In the ion system, the energy accuracy, compared with the Ewald summation, was better for a larger value of multipole moment l currently induced until l ≲ 3 on average. This accuracy improvement with increasing l is due to the enhancement of the excess-energy accuracy. However, this improvement is wholly effective in the total accuracy if the theoretical moment l is smaller than or equal to a system intrinsic moment L. The simulation results thus indicate L ˜ 3 in this system, and we observed less accuracy in l = 4. We demonstrated the origins of parameter dependencies appearing in the crossing behavior and the oscillations of the energy error curves. With raising the moment l we observed, smaller values of the damping parameter provided more accurate results and smoother behaviors with respect to cutoff length were obtained. These features can be explained, on the basis of the theoretical error analyses, such that the excess energy accuracy is improved with increasing l and that the total accuracy improvement within l ⩽ L is facilitated by a small damping parameter. Although the accuracy was fundamentally similar to the ion system, the bulk water system exhibited distinguishable quantitative behaviors. A smaller damping parameter was effective in all the practical cutoff distance, and this fact can be interpreted by the reduction of the excess subset. A lower moment was advantageous in the energy accuracy, where l = 1 was slightly superior to l = 2 in this system. However, the method with l = 2 (viz., the zero-quadrupole sum) gave accurate results for the radial distribution function. We confirmed the stability in the numerical integration for MD simulations employing the ZM scheme. This result is supported by the sufficient smoothness of the energy function. Along with the smoothness, the pairwise feature and the allowance of the atom-based cutoff mode on the energy formula lead to the exact zero total-force, ensuring the total-momentum conservations for typical MD equations of motion.

Brittle fracture in viscoelastic materials as a pattern-formation process

NASA Astrophysics Data System (ADS)

Fleck, M.; Pilipenko, D.; Spatschek, R.; Brener, E. A.

2011-04-01

A continuum model of crack propagation in brittle viscoelastic materials is presented and discussed. Thereby, the phenomenon of fracture is understood as an elastically induced nonequilibrium interfacial pattern formation process. In this spirit, a full description of a propagating crack provides the determination of the entire time dependent shape of the crack surface, which is assumed to be extended over a finite and self-consistently selected length scale. The mechanism of crack propagation, that is, the motion of the crack surface, is then determined through linear nonequilibrium transport equations. Here we consider two different mechanisms, a first-order phase transformation and surface diffusion. We give scaling arguments showing that steady-state solutions with a self-consistently selected propagation velocity and crack shape can exist provided that elastodynamic or viscoelastic effects are taken into account, whereas static elasticity alone is not sufficient. In this respect, inertial effects as well as viscous damping are identified to be sufficient crack tip selection mechanisms. Exploring the arising description of brittle fracture numerically, we study steady-state crack propagation in the viscoelastic and inertia limit as well as in an intermediate regime, where both effects are important. The arising free boundary problems are solved by phase field methods and a sharp interface approach using a multipole expansion technique. Different types of loading, mode I, mode III fracture, as well as mixtures of them, are discussed.

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.

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

Benetti, Micol; Alcaniz, Jailson S.; Landau, Susana J., E-mail: micolbenetti@on.br, E-mail: slandau@df.uba.ar, E-mail: alcaniz@on.br

The hypothesis of the self-induced collapse of the inflaton wave function was proposed as responsible for the emergence of inhomogeneity and anisotropy at all scales. This proposal was studied within an almost de Sitter space-time approximation for the background, which led to a perfect scale-invariant power spectrum, and also for a quasi-de Sitter background, which allows to distinguish departures from the standard approach due to the inclusion of the collapse hypothesis. In this work we perform a Bayesian model comparison for two different choices of the self-induced collapse in a full quasi-de Sitter expansion scenario. In particular, we analyze themore » possibility of detecting the imprint of these collapse schemes at low multipoles of the anisotropy temperature power spectrum of the Cosmic Microwave Background (CMB) using the most recent data provided by the Planck Collaboration. Our results show that one of the two collapse schemes analyzed provides the same Bayesian evidence of the minimal standard cosmological model ΛCDM, while the other scenario is weakly disfavoured with respect to the standard cosmology.« less

High-order tail in Schwarzschild spacetime

NASA Astrophysics Data System (ADS)

Casals, Marc; Ottewill, Adrian

2015-12-01

We present an analysis of the behavior at late times of linear field perturbations of a Schwarzschild black hole spacetime. In particular, we give explicit analytic expressions for the field perturbations (for a specific ℓ-multipole) of general spin up to the first four orders at late times. These expressions are valid at arbitrary radius and include, apart from the well-known power-law tail decay at leading order (˜t-2 ℓ-3), a new logarithmic behavior at third leading order (˜t-2 ℓ-5ln t ). We obtain these late-time results by developing an analytical formalism initially formulated by Mano, Suzuki and Takasugi (MST) [Prog. Theor. Phys. 95, 1079 (1996); 96, 549 (1996)] formalism and by expanding the various MST Fourier-mode quantities for small frequency. While we give explicit expansions up to the first four leading orders (for small frequency for the Fourier modes, for late time for the field perturbation), we give a prescription for obtaining expressions to arbitrary order within a "perturbative regime."

Self-assembly of triangular particles via capillary interactions

NASA Astrophysics Data System (ADS)

Bedi, Deshpreet; Zhou, Shangnan; Ferrar, Joseph; Solomon, Michael; Mao, Xiaoming

Colloidal particles adsorbed to a fluid interface deform the interface around them, resulting in either attractive or repulsive forces mediated by the interface. In particular, particle shape and surface roughness can produce an undulating contact line, such that the particles will assume energetically-favorable relative orientations and inter-particle distances to minimize the excess interfacial surface area. By expediently selecting specific particle shapes and associated design parameters, capillary interactions can be utilized to promote self-assembly of these particles into extended regular open structures, such as the kagome lattice, which have novel mechanical properties. We present the results of numerical simulations of equilateral triangle microprisms at an interface, including individually and in pairs. We show how particle bowing can yield two distinct binding events and connect it to theory in terms of a capillary multipole expansion and also to experiment, as presented in an accompanying talk. We also discuss and suggest design principles that can be used to create desirable open structures.

Progress with the COGENT Edge Kinetic Code: Implementing the Fokker-Plank Collision Operator

DOE PAGES

Dorf, M. A.; Cohen, R. H.; Dorr, M.; ...

2014-06-20

Here, COGENT is a continuum gyrokinetic code for edge plasma simulations being developed by the Edge Simulation Laboratory collaboration. The code is distinguished by application of a fourth-order finite-volume (conservative) discretization, and mapped multiblock grid technology to handle the geometric complexity of the tokamak edge. The distribution function F is discretized in v∥ – μ (parallel velocity – magnetic moment) velocity coordinates, and the code presently solves an axisymmetric full-f gyro-kinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. COGENT capabilities are extended by implementing the fully nonlinear Fokker-Plank operator to model Coulomb collisions in magnetized edge plasmas.more » The corresponding Rosenbluth potentials are computed by making use of a finite-difference scheme and multipole-expansion boundary conditions. Details of the numerical algorithms and results of the initial verification studies are discussed. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)« less

The Galaxy Count Correlation Function in Redshift Space Revisited

NASA Astrophysics Data System (ADS)

Campagne, J.-E.; Plaszczynski, S.; Neveu, J.

2017-08-01

In the near future, cosmology will enter the wide and deep galaxy survey era, enabling high-precision studies of the large-scale structure of the universe in three dimensions. To test cosmological models and determine their parameters accurately, it is necessary to use data with exact theoretical expectations expressed in observational parameter space (angles and redshift). The data-driven, galaxy number count fluctuations on redshift shells can be used to build correlation functions ξ (θ ,{z}1,{z}2) on and between shells to probe the baryonic acoustic oscillations and distance-redshift distortions, as well as gravitational lensing and other relativistic effects. To obtain a numerical estimation of ξ (θ ,{z}1,{z}2) from a cosmological model, it is typical to use either a closed form derived from a tripolar spherical expansion or to compute the power spectrum {C}{\\ell }({z}1,{z}2) and perform a Legendre polynomial {P}{\\ell }(\\cos θ ) expansion. Here, we present a new derivation of a ξ (θ ,{z}1,{z}2) closed form using the spherical harmonic expansion and proceeding to an infinite sum over multipoles thanks to an addition theorem. We demonstrate that this new expression is perfectly compatible with the existing closed forms but is simpler to establish and manipulate. We provide formulas for the leading density and redshift-space contributions, but also show how Doppler-like and lensing terms can be easily included in this formalism. We have implemented and made publicly available software for computing those correlations efficiently, without any Limber approximation, and validated this software with the CLASSgal code. It is available at https://gitlab.in2p3.fr/campagne/AngPow.

An O( N) and parallel approach to integral problems by a kernel-independent fast multipole method: Application to polarization and magnetization of interacting particles

DOE PAGES

Jiang, Xikai; Li, Jiyuan; Zhao, Xujun; ...

2016-08-10

Large classes of materials systems in physics and engineering are governed by magnetic and electrostatic interactions. Continuum or mesoscale descriptions of such systems can be cast in terms of integral equations, whose direct computational evaluation requires O( N 2) operations, where N is the number of unknowns. Such a scaling, which arises from the many-body nature of the relevant Green's function, has precluded wide-spread adoption of integral methods for solution of large-scale scientific and engineering problems. In this work, a parallel computational approach is presented that relies on using scalable open source libraries and utilizes a kernel-independent Fast Multipole Methodmore » (FMM) to evaluate the integrals in O( N) operations, with O( N) memory cost, thereby substantially improving the scalability and efficiency of computational integral methods. We demonstrate the accuracy, efficiency, and scalability of our approach in the context of two examples. In the first, we solve a boundary value problem for a ferroelectric/ferromagnetic volume in free space. In the second, we solve an electrostatic problem involving polarizable dielectric bodies in an unbounded dielectric medium. Lastly, the results from these test cases show that our proposed parallel approach, which is built on a kernel-independent FMM, can enable highly efficient and accurate simulations and allow for considerable flexibility in a broad range of applications.« less

Ultrasonic superlensing jets and acoustic-fork sheets

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2017-05-01

Focusing acoustical (and optical) beams beyond the diffraction limit has remained a major challenge in imaging instruments and systems, until recent advances on ;hyper; or ;super; lensing and higher-resolution imaging techniques have shown the counterintuitive violation of this rule under certain circumstances. Nonetheless, the proposed technologies of super-resolution acoustical focusing beyond the diffraction barrier require complex tools such as artificially engineered metamaterials, and other hardware equipment that may not be easily synthesized or manufactured. The present contribution therefore suggests a simple and reliable method of using a sound-penetrable circular cylinder lens illuminated by a nonparaxial Gaussian acoustical sheet (i.e. finite beam in 2D) to produce non-evanescent ultrasonic superlensing jets (or bullets) and acoustical 'snail-fork' shaped wavefronts with limited diffraction. The generalized (near-field) scattering theory for acoustical sheets of arbitrary wavefronts and incidence is utilized to synthesize the incident beam based upon the angular spectrum decomposition method and the multipole expansion method in cylindrical wave functions to compute the scattered pressure around the cylinder with particular emphasis on its physical properties. The results show that depending on the beam and lens parameters, a tight focusing (with dimensions much smaller than the beam waist) can be achieved. Subwavelength resolution can be also achieved by selecting a lens material with a speed of sound exceeding that of the host fluid medium. The ultrasonic superlensing jets provide the impetus to develop improved subwavelength microscopy and acoustical image-slicing systems, cell lysis and surgery, and photoacoustic imaging to name a few examples. Moreover, an acoustical fork-sheet generation may open innovative avenues in reconfigurable on-chip micro/nanoparticle tweezers and surface acoustic waves devices.

NSLS-II BPM System Protection from Rogue Mode Coupling

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

Blednykh, A.; Bach, B.; Borrelli, A.

2011-03-28

Rogue mode RF shielding has been successfully designed and implemented into the production multipole vacuum chambers. In order to avoid systematic errors in the NSLS-II BPM system we introduced frequency shift of HOM's by using RF metal shielding located in the antechamber slot of each multipole vacuum chamber. To satisfy the pumping requirement the face of the shielding has been perforated with roughly 50 percent transparency. It stays clear of synchrotron radiation in each chamber.

The multipole resonance probe: characterization of a prototype

NASA Astrophysics Data System (ADS)

Lapke, Martin; Oberrath, Jens; Schulz, Christian; Storch, Robert; Styrnoll, Tim; Zietz, Christian; Awakowicz, Peter; Brinkmann, Ralf Peter; Musch, Thomas; Mussenbrock, Thomas; Rolfes, Ilona

2011-08-01

The multipole resonance probe (MRP) was recently proposed as an economical and industry compatible plasma diagnostic device (Lapke et al 2008 Appl. Phys. Lett. 93 051502). This communication reports the experimental characterization of a first MRP prototype in an inductively coupled argon/nitrogen plasma at 10 Pa. The behavior of the device follows the predictions of both an analytical model and a numerical simulation. The obtained electron densities are in excellent agreement with the results of Langmuir probe measurements.

Long term dynamics of the high luminosity Large Hadron Collider with crab cavities

NASA Astrophysics Data System (ADS)

Barranco García, J.; De Maria, R.; Grudiev, A.; Tomás García, R.; Appleby, R. B.; Brett, D. R.

2016-10-01

The High Luminosity upgrade of the Large Hadron Collider (HL-LHC) aims to achieve an integrated luminosity of 200 - 300 fb-1 per year, including the contribution from the upgrade of the injector chain. For the HL-LHC the larger crossing angle together with a smaller beta function at the collision point would result in more than 70% luminosity loss due to the incomplete geometric overlap of colliding bunches. To recover head-on collisions at the high-luminosity particle-physics detectors ATLAS and CMS and benefit from the very low β* provided by the Achromatic Telescopic Squeezing (ATS) optics, a local crab cavity scheme provides transverse kicks to the proton bunches. The tight space constraints at the location of these cavities leads to designs which are axially non-symmetric, giving rise to high order multipoles components of the main deflecting mode and, since these kicks are harmonic in time, we expand them in a series of multipoles in a similar fashion as is done for static field magnets. In this work we calculate, for the first time, the higher order multipoles and their impact on beam dynamics for three different crab cavity prototypes. Different approaches to calculate the multipoles are presented. Furthermore, we perform the first calculation of their impact on the long term stability of the machine using the concept of dynamic aperture.

POWER ASYMMETRY IN COSMIC MICROWAVE BACKGROUND FLUCTUATIONS FROM FULL SKY TO SUB-DEGREE SCALES: IS THE UNIVERSE ISOTROPIC?

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

Hansen, F. K.; Eriksen, H. K.; Lilje, P. B.

We repeat and extend the analysis of Eriksen et al. and Hansen et al., testing the isotropy of the cosmic microwave background fluctuations. We find that the hemispherical power asymmetry previously reported for the largest scales l = 2-40 extends to much smaller scales. In fact, for the full multipole range l = 2-600, significantly more power is found in the hemisphere centered at (theta = 107{sup 0} +- 10{sup 0}, phi = 226{sup 0} +- 10{sup 0}) in galactic co-latitude and longitude than in the opposite hemisphere, consistent with the previously detected direction of asymmetry for l = 2-40.more » We adopt a model selection test where the direction and amplitude of asymmetry, as well as the multipole range, are free parameters. A model with an asymmetric distribution of power for l = 2-600 is found to be preferred over the isotropic model at the 0.4% significance level, taking into account the additional parameters required to describe it. A similar direction of asymmetry is found independently in all six subranges of 100 multipoles between l = 2-600. None of our 9800 isotropic simulated maps show a similarly consistent direction of asymmetry over such a large multipole range. No known systematic effects or foregrounds are found to be able to explain the asymmetry.« less

Scattering of Airy elastic sheets by a cylindrical cavity in a solid.

PubMed

Mitri, F G

2017-11-01

The prediction of the elastic scattering by voids (and cracks) in materials is an important process in structural health monitoring, phononic crystals, metamaterials and non-destructive evaluation/imaging to name a few examples. Earlier analytical theories and numerical computations considered the elastic scattering by voids in plane waves of infinite extent. However, current research suggesting the use of (limited-diffracting, accelerating and self-healing) Airy acoustical-sheet beams for non-destructive evaluation or imaging applications in elastic solids requires the development of an improved analytical formalism to predict the scattering efficiency used as a priori information in quantitative material characterization. Based on the definition of the time-averaged scattered power flow density, an analytical expression for the scattering efficiency of a cylindrical empty cavity (i.e., void) encased in an elastic medium is derived for compressional and normally-polarized shear-wave Airy beams. The multipole expansion method using cylindrical wave functions is utilized. Numerical computations for the scattering energy efficiency factors for compressional and shear waves illustrate the analysis with particular emphasis on the Airy beam parameters and the non-dimensional frequency, for various elastic materials surrounding the cavity. The ratio of the compressional to the shear wave speed stimulates the generation of elastic resonances, which are manifested as a series of peaks in the scattering efficiency plots. The present analysis provides an improved method for the computations of the scattering energy efficiency factors using compressional and shear-wave Airy beams in elastic materials as opposed to plane waves of infinite extent. Copyright © 2017 Elsevier B.V. All rights reserved.

Theory of Dielectric Breakdown in Randomly Inhomogeneous Materials

NASA Astrophysics Data System (ADS)

Gyure, Mark Franklin

1990-01-01

Two models of dielectric breakdown in disordered metal-insulator composites have been developed in an attempt to explain in detail the greatly reduced breakdown electric field observed in these materials. The first model is a two dimensional model in which the composite is treated as a random array of conducting cylinders embedded in an otherwise uniform dielectric background. The two dimensional samples are generated by the Monte Carlo method and a discretized version of the integral form of Laplace's equation is solved to determine the electric field in each sample. Breakdown is modeled as a quasi-static process by which one breakdown at a time occurs at the point of maximum electric field in the system. A cascade of these local breakdowns leads to complete dielectric failure of the system after which the breakdown field can be determined. A second model is developed that is similar to the first in terms of breakdown dynamics, but uses coupled multipole expansions of the electrostatic potential centered at each particle to obtain a more computationally accurate and faster solution to the problem of determining the electric field at an arbitrary point in a random medium. This new algorithm allows extension of the model to three dimensions and treats conducting spherical inclusions as well as cylinders. Successful implementation of this algorithm relies on the use of analytical forms for off-centered expansions of cylindrical and spherical harmonics. Scaling arguments similar to those used in theories of phase transitions are developed for the breakdown field and these arguments are discussed in context with other theories that have been developed to explain the break-down behavior of random resistor and fuse networks. Finally, one of the scaling arguments is used to predict the breakdown field for some samples of solid fuel rocket propellant tested at the China Lake Naval Weapons Center and is found to compare quite well with the experimentally measured breakdown fields.

The experimental charge-density approach in the evaluation of intermolecular interactions. Application of a new module of the XD programming package to several solids including a pentapeptide.

PubMed

Abramov, Y A; Volkov, A; Wu, G; Coppens, P

2000-11-01

A new module interfaced to the XD programming package has been used in the evaluation of intermolecular interactions and lattice energies of the crystals of p-nitroaniline, L-asparagine monohydrate and the pentapeptide Boc-Gln-D-Iva-Hyp-Ala-Phol (Boc = butoxycarbonyl, Iva = isovaline = ethylalanine, Phol = phenylalaninol). The electrostatic interactions are evaluated with the atom-centered distributed multipoles from KRMM (kappa'-restricted multipole model) refinements, using the Buckingham expression for non-overlapping charge densities. Results for p-nitroaniline are compared with Hartree-Fock (HF), density functional (DFT) and Moller-Plesset (MP2) supermolecular calculations and with HF and DFT periodic calculations. The HF and DFT methods fail to predict the stability of the p-nitroaniline crystal but the results of the experimental charge-density approach (ECDA) are in good agreement with both MP2 interaction energies and the experimental lattice energy. ECDA results for L-asparagine monohydrate compare well with those from DFT supermolecular and periodic HF calculations. The disorder of the terminal group in the pentapeptide, which persists at the experimental temperature of 20 K, corresponds to an energy difference of only 0.35 kJ mol(-1), which is too small to be reproduced with current methods.

A Comparison of Cosmological Parameters Determined from CMB Temperature Power Spectra from the South Pole Telescope and the Planck Satellite

DOE PAGES

Aylor, K.; Hou, Z.; Knox, L.; ...

2017-11-20

The Planck cosmic microwave background temperature data are best fit with a ΛCDM model that mildly contradicts constraints from other cosmological probes. The South Pole Telescope (SPT) 2540more » $${\\deg }^{2}$$ SPT-SZ survey offers measurements on sub-degree angular scales (multipoles $$650\\leqslant {\\ell }\\leqslant 2500$$) with sufficient precision to use as an independent check of the Planck data. Here we build on the recent joint analysis of the SPT-SZ and Planck data in Hou et al. by comparing ΛCDM parameter estimates using the temperature power spectrum from both data sets in the SPT-SZ survey region. We also restrict the multipole range used in parameter fitting to focus on modes measured well by both SPT and Planck, thereby greatly reducing sample variance as a driver of parameter differences and creating a stringent test for systematic errors. We find no evidence of systematic errors from these tests. When we expand the maximum multipole of SPT data used, we see low-significance shifts in the angular scale of the sound horizon and the physical baryon and cold dark matter densities, with a resulting trend to higher Hubble constant. When we compare SPT and Planck data on the SPT-SZ sky patch to Planck full-sky data but keep the multipole range restricted, we find differences in the parameters n s and $${A}_{s}{e}^{-2\\tau }$$. We perform further checks, investigating instrumental effects and modeling assumptions, and we find no evidence that the effects investigated are responsible for any of the parameter shifts. Taken together, these tests reveal no evidence for systematic errors in SPT or Planck data in the overlapping sky coverage and multipole range and at most weak evidence for a breakdown of ΛCDM or systematic errors influencing either the Planck data outside the SPT-SZ survey area or the SPT data at $${\\ell }\\gt 2000$$.« less

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

Aylor, K.; Hou, Z.; Knox, L.

The Planck cosmic microwave background temperature data are best fit with a ΛCDM model that mildly contradicts constraints from other cosmological probes. The South Pole Telescope (SPT) 2540more » $${\\deg }^{2}$$ SPT-SZ survey offers measurements on sub-degree angular scales (multipoles $$650\\leqslant {\\ell }\\leqslant 2500$$) with sufficient precision to use as an independent check of the Planck data. Here we build on the recent joint analysis of the SPT-SZ and Planck data in Hou et al. by comparing ΛCDM parameter estimates using the temperature power spectrum from both data sets in the SPT-SZ survey region. We also restrict the multipole range used in parameter fitting to focus on modes measured well by both SPT and Planck, thereby greatly reducing sample variance as a driver of parameter differences and creating a stringent test for systematic errors. We find no evidence of systematic errors from these tests. When we expand the maximum multipole of SPT data used, we see low-significance shifts in the angular scale of the sound horizon and the physical baryon and cold dark matter densities, with a resulting trend to higher Hubble constant. When we compare SPT and Planck data on the SPT-SZ sky patch to Planck full-sky data but keep the multipole range restricted, we find differences in the parameters n s and $${A}_{s}{e}^{-2\\tau }$$. We perform further checks, investigating instrumental effects and modeling assumptions, and we find no evidence that the effects investigated are responsible for any of the parameter shifts. Taken together, these tests reveal no evidence for systematic errors in SPT or Planck data in the overlapping sky coverage and multipole range and at most weak evidence for a breakdown of ΛCDM or systematic errors influencing either the Planck data outside the SPT-SZ survey area or the SPT data at $${\\ell }\\gt 2000$$.« less

A Comparison of Cosmological Parameters Determined from CMB Temperature Power Spectra from the South Pole Telescope and the Planck Satellite

NASA Astrophysics Data System (ADS)

Aylor, K.; Hou, Z.; Knox, L.; Story, K. T.; Benson, B. A.; Bleem, L. E.; Carlstrom, J. E.; Chang, C. L.; Cho, H.-M.; Chown, R.; Crawford, T. M.; Crites, A. T.; de Haan, T.; Dobbs, M. A.; Everett, W. B.; George, E. M.; Halverson, N. W.; Harrington, N. L.; Holder, G. P.; Holzapfel, W. L.; Hrubes, J. D.; Keisler, R.; Lee, A. T.; Leitch, E. M.; Luong-Van, D.; Marrone, D. P.; McMahon, J. J.; Meyer, S. S.; Millea, M.; Mocanu, L. M.; Mohr, J. J.; Natoli, T.; Omori, Y.; Padin, S.; Pryke, C.; Reichardt, C. L.; Ruhl, J. E.; Sayre, J. T.; Schaffer, K. K.; Shirokoff, E.; Staniszewski, Z.; Stark, A. A.; Vanderlinde, K.; Vieira, J. D.; Williamson, R.

2017-11-01

The Planck cosmic microwave background temperature data are best fit with a ΛCDM model that mildly contradicts constraints from other cosmological probes. The South Pole Telescope (SPT) 2540 {\\deg }2 SPT-SZ survey offers measurements on sub-degree angular scales (multipoles 650≤slant {\\ell }≤slant 2500) with sufficient precision to use as an independent check of the Planck data. Here we build on the recent joint analysis of the SPT-SZ and Planck data in Hou et al. by comparing ΛCDM parameter estimates using the temperature power spectrum from both data sets in the SPT-SZ survey region. We also restrict the multipole range used in parameter fitting to focus on modes measured well by both SPT and Planck, thereby greatly reducing sample variance as a driver of parameter differences and creating a stringent test for systematic errors. We find no evidence of systematic errors from these tests. When we expand the maximum multipole of SPT data used, we see low-significance shifts in the angular scale of the sound horizon and the physical baryon and cold dark matter densities, with a resulting trend to higher Hubble constant. When we compare SPT and Planck data on the SPT-SZ sky patch to Planck full-sky data but keep the multipole range restricted, we find differences in the parameters n s and {A}s{e}-2τ . We perform further checks, investigating instrumental effects and modeling assumptions, and we find no evidence that the effects investigated are responsible for any of the parameter shifts. Taken together, these tests reveal no evidence for systematic errors in SPT or Planck data in the overlapping sky coverage and multipole range and at most weak evidence for a breakdown of ΛCDM or systematic errors influencing either the Planck data outside the SPT-SZ survey area or the SPT data at {\\ell }> 2000.

Efficient Kriging via Fast Matrix-Vector Products

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess; Raykar, Vikas C.; Duraiswami, Ramani; Mount, David M.

2008-01-01

Interpolating scattered data points is a problem of wide ranging interest. Ordinary kriging is an optimal scattered data estimator, widely used in geosciences and remote sensing. A generalized version of this technique, called cokriging, can be used for image fusion of remotely sensed data. However, it is computationally very expensive for large data sets. We demonstrate the time efficiency and accuracy of approximating ordinary kriging through the use of fast matrixvector products combined with iterative methods. We used methods based on the fast Multipole methods and nearest neighbor searching techniques for implementations of the fast matrix-vector products.

A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems

NASA Astrophysics Data System (ADS)

Dölz, Jürgen; Harbrecht, Helmut; Kurz, Stefan; Schöps, Sebastian; Wolf, Felix

2018-03-01

We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract the problems arising due to the dense matrices produced by boundary element methods. By solving Laplace and Helmholtz problems via a single layer approach we show, through a series of numerical examples suitable for easy comparison with other numerical schemes, that one can indeed achieve extremely high rates of convergence of the pointwise potential through the utilisation of higher order B-spline-based ansatz functions.

Computation of scattering matrix elements of large and complex shaped absorbing particles with multilevel fast multipole algorithm

NASA Astrophysics Data System (ADS)

Wu, Yueqian; Yang, Minglin; Sheng, Xinqing; Ren, Kuan Fang

2015-05-01

Light scattering properties of absorbing particles, such as the mineral dusts, attract a wide attention due to its importance in geophysical and environment researches. Due to the absorbing effect, light scattering properties of particles with absorption differ from those without absorption. Simple shaped absorbing particles such as spheres and spheroids have been well studied with different methods but little work on large complex shaped particles has been reported. In this paper, the surface Integral Equation (SIE) with Multilevel Fast Multipole Algorithm (MLFMA) is applied to study scattering properties of large non-spherical absorbing particles. SIEs are carefully discretized with piecewise linear basis functions on triangle patches to model whole surface of the particle, hence computation resource needs increase much more slowly with the particle size parameter than the volume discretized methods. To improve further its capability, MLFMA is well parallelized with Message Passing Interface (MPI) on distributed memory computer platform. Without loss of generality, we choose the computation of scattering matrix elements of absorbing dust particles as an example. The comparison of the scattering matrix elements computed by our method and the discrete dipole approximation method (DDA) for an ellipsoid dust particle shows that the precision of our method is very good. The scattering matrix elements of large ellipsoid dusts with different aspect ratios and size parameters are computed. To show the capability of the presented algorithm for complex shaped particles, scattering by asymmetry Chebyshev particle with size parameter larger than 600 of complex refractive index m = 1.555 + 0.004 i and different orientations are studied.

Neutronics Assessments for a RIA Fragmentation Line Beam Dump Concept

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

Boles, J L; Reyes, S; Ahle, L E

Heavy ion and radiation transport calculations are in progress for conceptual beam dump designs for the fragmentation line of the proposed Rare Isotope Accelerator (RIA). Using the computer code PHITS, a preliminary design of a motor-driven rotating wheel beam dump and adjacent downstream multipole has been modeled. Selected results of these calculations are given, including neutron and proton flux in the wheel, absorbed dose and displacements per atom in the hub materials, and heating from prompt radiation and from decay heat in the multipole.

Experimental test of an online ion-optics optimizer

NASA Astrophysics Data System (ADS)

Amthor, A. M.; Schillaci, Z. M.; Morrissey, D. J.; Portillo, M.; Schwarz, S.; Steiner, M.; Sumithrarachchi, Ch.

2018-07-01

A technique has been developed and tested to automatically adjust multiple electrostatic or magnetic multipoles on an ion optical beam line - according to a defined optimization algorithm - until an optimal tune is found. This approach simplifies the process of determining high-performance optical tunes, satisfying a given set of optical properties, for an ion optical system. The optimization approach is based on the particle swarm method and is entirely model independent, thus the success of the optimization does not depend on the accuracy of an extant ion optical model of the system to be optimized. Initial test runs of a first order optimization of a low-energy (<60 keV) all-electrostatic beamline at the NSCL show reliable convergence of nine quadrupole degrees of freedom to well-performing tunes within a reasonable number of trial solutions, roughly 500, with full beam optimization run times of roughly two hours. Improved tunes were found both for quasi-local optimizations and for quasi-global optimizations, indicating a good ability of the optimizer to find a solution with or without a well defined set of initial multipole settings.

Physical nature of ethidium and proflavine interactions with nucleic acid bases in the intercalation plane.

PubMed

Langner, Karol M; Kedzierski, Pawel; Sokalski, W Andrzej; Leszczynski, Jerzy

2006-05-18

On the basis of the crystallographic structures of three nucleic acid intercalation complexes involving ethidium and proflavine, we have analyzed the interaction energies between intercalator chromophores and their four nearest bases, using a hybrid variation-perturbation method at the second-order Møller-Plesset theory level (MP2) with a 6-31G(d,p) basis set. A total MP2 interaction energy minimum precisely reproduces the crystallographic position of the ethidium chromophore in the intercalation plane between UA/AU bases. The electrostatic component constitutes the same fraction of the total energy for all three studied structures. The multipole electrostatic interaction energy, calculated from cumulative atomic multipole moments (CAMMs), was found to converge only after including components above the fifth order. CAMM interaction surfaces, calculated on grids in the intercalation planes of these structures, reasonably reproduce the alignment of intercalators in crystal structures; they exhibit additional minima in the direction of the DNA grooves, however, which also need to be examined at higher theory levels if no crystallographic data are given.

KiDS-450 + 2dFLenS: Cosmological parameter constraints from weak gravitational lensing tomography and overlapping redshift-space galaxy clustering

NASA Astrophysics Data System (ADS)

Joudaki, Shahab; Blake, Chris; Johnson, Andrew; Amon, Alexandra; Asgari, Marika; Choi, Ami; Erben, Thomas; Glazebrook, Karl; Harnois-Déraps, Joachim; Heymans, Catherine; Hildebrandt, Hendrik; Hoekstra, Henk; Klaes, Dominik; Kuijken, Konrad; Lidman, Chris; Mead, Alexander; Miller, Lance; Parkinson, David; Poole, Gregory B.; Schneider, Peter; Viola, Massimo; Wolf, Christian

2018-03-01

We perform a combined analysis of cosmic shear tomography, galaxy-galaxy lensing tomography, and redshift-space multipole power spectra (monopole and quadrupole) using 450 deg2 of imaging data by the Kilo Degree Survey (KiDS-450) overlapping with two spectroscopic surveys: the 2-degree Field Lensing Survey (2dFLenS) and the Baryon Oscillation Spectroscopic Survey (BOSS). We restrict the galaxy-galaxy lensing and multipole power spectrum measurements to the overlapping regions with KiDS, and self-consistently compute the full covariance between the different observables using a large suite of N-body simulations. We methodically analyse different combinations of the observables, finding that the galaxy-galaxy lensing measurements are particularly useful in improving the constraint on the intrinsic alignment amplitude, while the multipole power spectra are useful in tightening the constraints along the lensing degeneracy direction. The fully combined constraint on S_8 ≡ σ _8 √{Ω _m/0.3}=0.742± 0.035, which is an improvement by 20 per cent compared to KiDS alone, corresponds to a 2.6σ discordance with Planck, and is not significantly affected by fitting to a more conservative set of scales. Given the tightening of the parameter space, we are unable to resolve the discordance with an extended cosmology that is simultaneously favoured in a model selection sense, including the sum of neutrino masses, curvature, evolving dark energy and modified gravity. The complementarity of our observables allows for constraints on modified gravity degrees of freedom that are not simultaneously bounded with either probe alone, and up to a factor of three improvement in the S8 constraint in the extended cosmology compared to KiDS alone.

Elongation cutoff technique armed with quantum fast multipole method for linear scaling.

PubMed

Korchowiec, Jacek; Lewandowski, Jakub; Makowski, Marcin; Gu, Feng Long; Aoki, Yuriko

2009-11-30

A linear-scaling implementation of the elongation cutoff technique (ELG/C) that speeds up Hartree-Fock (HF) self-consistent field calculations is presented. The cutoff method avoids the known bottleneck of the conventional HF scheme, that is, diagonalization, because it operates within the low dimension subspace of the whole atomic orbital space. The efficiency of ELG/C is illustrated for two model systems. The obtained results indicate that the ELG/C is a very efficient sparse matrix algebra scheme. Copyright 2009 Wiley Periodicals, Inc.

Numerical realization of the variational method for generating self-trapped beams.

PubMed

Duque, Erick I; Lopez-Aguayo, Servando; Malomed, Boris A

2018-03-19

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schrödinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.

Polarizable atomic multipole-based force field for DOPC and POPE membrane lipids

NASA Astrophysics Data System (ADS)

Chu, Huiying; Peng, Xiangda; Li, Yan; Zhang, Yuebin; Min, Hanyi; Li, Guohui

2018-04-01

A polarizable atomic multipole-based force field for the membrane bilayer models 1,2-dioleoyl-phosphocholine (DOPC) and 1-palmitoyl-2-oleoyl-phosphatidylethanolamine (POPE) has been developed. The force field adopts the same framework as the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) model, in which the charge distribution of each atom is represented by the permanent atomic monopole, dipole and quadrupole moments. Many-body polarization including the inter- and intra-molecular polarization is modelled in a consistent manner with distributed atomic polarizabilities. The van der Waals parameters were first transferred from existing AMOEBA parameters for small organic molecules and then optimised by fitting to ab initio intermolecular interaction energies between models and a water molecule. Molecular dynamics simulations of the two aqueous DOPC and POPE membrane bilayer systems, consisting of 72 model molecules, were then carried out to validate the force field parameters. Membrane width, area per lipid, volume per lipid, deuterium order parameters, electron density profile, etc. were consistent with experimental values.

The evens and odds of CMB anomalies

NASA Astrophysics Data System (ADS)

Gruppuso, A.; Kitazawa, N.; Lattanzi, M.; Mandolesi, N.; Natoli, P.; Sagnotti, A.

2018-06-01

The lack of power of large-angle CMB anisotropies is known to increase its statistical significance at higher Galactic latitudes, where a string-inspired pre-inflationary scale Δ can also be detected. Considering the Planck 2015 data, and relying largely on a Bayesian approach, we show that the effect is mostly driven by the even - ℓ harmonic multipoles with ℓ ≲ 20, which appear sizably suppressed in a way that is robust with respect to Galactic masking, along with the corresponding detections of Δ. On the other hand, the first odd - ℓ multipoles are only suppressed at high Galactic latitudes. We investigate this behavior in different sky masks, constraining Δ through even and odd multipoles, and we elaborate on possible implications. We include low- ℓ polarization data which, despite being noise-limited, help in attaining confidence levels of about 3 σ in the detection of Δ. We also show by direct forecasts that a future all-sky E-mode cosmic-variance-limited polarization survey may push the constraining power for Δ beyond 5 σ.

Multipole mixing ratios and substate populations in Rn-219

NASA Astrophysics Data System (ADS)

Jones, G. D.

2016-08-01

Historical alpha-gamma angular correlation data for the decay of 223Ra into excited states of 219Rn have been analysed, using the correct spins of the states involved, for the first time. The analyses produced multipole mixing ratios (E2/M1) of δ (144)=-0.11\\+/- 0.03, δ (154)=0, δ (158)=-0.205\\+/- 0.018 and δ (269)=-0.149\\+/- 0.004 where the nominal transition energies, in keV, are given in brackets. These values are consistent with published values obtained from internal conversion electron spectroscopy. It is also found that δ (324)=0 and δ (338)=-0.235\\+/- 0.030 (where both values differ from current tabulations) and that the sign of the multipole mixing ratio for the 122 keV transition is negative. The 158, 269 and 338 keV states are found to be aligned with high population of M=+/- 3/2 substates and the 127 keV state is believed to have undergone spin relaxation.

The Anisotropy of the Microwave Background to l = 3500: Deep Field Observations with the Cosmic Background Imager

NASA Technical Reports Server (NTRS)

Mason, B. S.; Pearson, T. J.; Readhead, A. C. S.; Shepherd, M. C.; Sievers, J.; Udomprasert, P. S.; Cartwright, J. K.; Farmer, A. J.; Padin, S.; Myers, S. T.;

Experimental study of the formation of field-reversed configurations employing high-order multipole fields

NASA Astrophysics Data System (ADS)

Slough, J. T.; Hoffman, A. L.

1990-04-01

A high-order multipole ``barrier'' field was applied at the vacuum tube wall in the TRX experiment [Phys. Fluids B 1, 840 (1989)] during both the preionization and field reversal phases of field-reversed configuration (FRC) formation. Use of this field during field reversal resulted in a significant reduction of impurities as well as increased flux trapping. With a large enough Bθ at the wall, sheath detachment from the wall became apparent, and flux loss through the sheath became negligible (<10%). At larger wall Bθ (>1.5 kG), destructive rotational spin-up occurred, driven by Hall current forces. When the multipole barrier field was also applied during either axial discharge or ringing theta current preionization, a very symmetric and uniform breakdown of the fill gas was achieved. In particular, using ringing theta preionization, complete ionization of the fill gas was accomplished with purely inductive fields of remarkably low magnitude, where Ez≤3 V/cm, and Eθ≤20 V/cm. Due to the improved ionization symmetry, about 65% to 75% of the lift-off flux (flux remaining after field reversal) could be retained through the remaining formation processes into an equilibrium FRC. Using the multipole field during both preionization and formation, it was possible to form FRC's with good confinement with greater than 3 mWb of trapped flux at 15 mTorr D2 or H2 in a 10 cm radius device. Values of s in excess of 4 could be achieved in this manner.

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (IV) HFODD (v2.08i): a new version of the program

NASA Astrophysics Data System (ADS)

Dobaczewski, J.; Olbratowski, P.

2004-04-01

We describe the new version (v2.08i) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. The new version contains an interface to the LAPACK subroutine ZHPEVX. Program summaryTitle of the program:HFODD (v2.08i) Catalogue number: ADTO Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTO Reference in CPC for earlier version of program: J. Dobaczewski and J. Dudek, Comput. Phys. Commun. 131 (2000) 164 (v1.75r) Catalogue number of previous version: ADML Licensing provisions: none Does the new version supersede the previous one: yes Computers on which the program has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems: UNIX, LINUX, Windows-2000 Programming language used: FORTRAN-77 and FORTRAN-90 Memory required to execute with typical data: 10 Mwords No. of bits in a word: The code is written in single-precision for the use on a 64-bit processor. The compiler option -r8 or +autodblpad (or equivalent) has to be used to promote all real and complex single-precision floating-point items to double precision when the code is used on a 32-bit machine. Has the code been vectorised?: Yes No. of bytes in distributed program, including test data, etc.: 265352 No. of lines in distributed program: 52656 Distribution format: tar gzip file Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic (n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree-Fock-Bogolyubov method. Method of solution: The program uses the Cartesian harmonic oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constraints are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in: J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 102 (1997) 166. Summary of revisions:Two insignificant errors have been corrected. Breaking of all the three plane-reflection symmetries has been implemented. Breaking of all the three time-reversal×plane-reflection symmetries has been implemented. Conservation of parity with simultaneously broken simplex has been implemented. Tilted-axis cranking has been implemented. Cranking with isovector angular frequency has been implemented. Quadratic constraint on tilted angular momentum has been added. Constraint on the vector product of angular frequency and angular momentum has been added. Calculation of surface multipole moments has been added. Constraints on surface multipole moments have been added. Calculation of magnetic moments has been added. Calculation of multipole and surface multipole moments in the center-of-mass reference frame has been added. Calculation of multipole, surface multipole, and magnetic moments in the principal-axes (intrinsic) reference frame has been added. Calculation of angular momenta in the center-of-mass and principal-axes reference frames has been added. New single-particle observables for a diabatic blocking have been added. Solution of the Hartree-Fock-Bogolyubov equations has been implemented. Non-standard spin-orbit energy density has been implemented. Non-standard center-of-mass corrections have been implemented. Definition of the time-odd terms through the Landau parameters has been implemented. Definition of Skyrme forces taken from the literature now includes the force parameters as well as the value of the nucleon mass and the treatment of tensor, spin-orbit, and center-of-mass terms specific to the given force. Interface to the LAPACK subroutine ZHPEVX has been implemented. Computer memory management has been improved by implementing the memory-allocation features available within FORTRAN-90. Restrictions on the complexity of the problem: The main restriction is the CPU time required for calculations of heavy deformed nuclei and for a given precision required. Pairing correlations are only included for even-even nuclei and conserved simplex symmetry. Typical running time: One Hartree-Fock iteration for the superdeformed, rotating, parity conserving state of 15266Dy 86 takes about six seconds on the AMD-Athlon 1600+ processor. Starting from the Woods-Saxon wave functions, about fifty iterations are required to obtain the energy converged within the precision of about 0.1 keV. In case when every value of the angular velocity is converged separately, the complete superdeformed band with precisely determined dynamical moments J(2) can be obtained within forty minutes of CPU on the AMD-Athlon 1600+ processor. This time can be often reduced by a factor of three when a self-consistent solution for a given rotational frequency is used as a starting point for a neighboring rotational frequency. Unusual features of the program: The user must have an access to the NAGLIB subroutine F02AXE, or to the LAPACK subroutines ZHPEV or ZHPEVX, which diagonalize complex hermitian matrices, or provide another subroutine which can perform such a task. The LAPACK subroutines ZHPEV and ZHPEVX can be obtained from the Netlib Repository at University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/cgi-bin/netlibfiles.pl?filename=/lapack/complex16/zhpev.f and http://netlib2.cs.utk.edu/cgi-bin/netlibfiles.pl?filename=/lapack/complex16/zhpevx.f respectively.

Stress fields and energy of disclination-type defects in zones of localized elastic distortions

NASA Astrophysics Data System (ADS)

Sukhanov, Ivan I.; Tyumentsev, Alexander N.; Ditenberg, Ivan A.

2016-11-01

This paper studies theoretically the elastically deformed state and analyzes deformation mechanisms in nanocrystals in the zones of localized elastic distortions and related disclination-type defects, such as dipole, quadrupole and multipole of partial disclinations. Significant differences in the energies of quadrupole and multipole configurations in comparison with nanodipole are revealed. The mechanism of deformation localization in the field of elastic distortions is proposed, which is a quasi-periodic sequence of formation and relaxation of various disclination ensembles with a periodic change in the energy of the defect.

Multipole Plasmon Resonances in Gold Nanorods

PubMed Central

Payne, Emma Kathryn; Shuford, Kevin L.; Park, Sungho; Schatz, George C.

2011-01-01

The optical properties of gold rods electrochemically deposited in anodic aluminum oxide templates have been investigated. Homogeneous suspensions of rods with average diameter of 85 nm and varying lengths of 96, 186, 321, 465, 495, 578, 641, 735, and 1175 nm were fabricated. The purity and dimensions of these rod nanostructures allowed us to observe higher order multipole resonances for the first time in a colloidal suspension. The experimental optical spectra agree with discrete dipole approximation calculations that have been modeled from the dimensions of the gold nanorods. PMID:16471797

BOOK REVIEW: Multipole Theory in Electromagnetism: Classical, Quantum and Symmetry Aspects, with Applications

NASA Astrophysics Data System (ADS)

Sihvola, Ari

2005-03-01

`Good reasons must, of force, give place to better', observes Brutus to Cassius, according to William Shakespeare in Julius Caesar. Roger Raab and Owen de Lange seem to agree, as they cite this sentence in the concluding chapter of their new book on the importance of exact multipole analysis in macroscopic electromagnetics. Very true and essential to remember in our daily research work. The two scientists from the University of Natal in Pietermaritzburg, South Africa (presently University of KwaZulu-Natal) have been working for a very long time on the accurate description of electric and magnetic response of matter and have published much of their findings in various physics journals. The present book gives us a clear and coherent exposition of many of these results. The important message of Raab and de Lange is that in the macroscopic description of matter, a correct balance between the various orders of electric and magnetic multipole terms has to be respected. If the inclusion of magnetic dipole terms is not complemented with electric quadrupoles, there is a risk of losing the translational invariance of certain important quantities. This means that the values of these quantities depend on the choice of the origin! `It canÂ't be Nature, for it is not sense' is another of the apt literary citations in the book. Often monographs written by researchers look like they have been produced using a cut-and-paste technique; earlier published articles are included in the same book but, unfortunately, too little additional effort is expended into moulding the totality into a unified story. This is not the case with Raab and de Lange. The structure and the text flow of the book serve perfectly its important message. After the obligatory introduction of material response to electromagnetic fields, constitutive relations, basic quantum theory and spacetime properties, a chapter follows with transmission and scattering effects where everything seems to work well with the `old' multipole theory. But then the focus is shifted to observables associated with the reflection of waves from a surface. And there the classical analysis fails. This gives the motivation for the following chapters where the transformed multipole theory is represented. As expected, the correct multipole balance restores the physicality of the results in the reflection problem. One of the healthy reminders for an electrical engineer-scientist reading the book is the fact that E and B are the primary electric and magnetic fields. The other two field quantities, D and H, are the response fields (which, by the way, are also shown to be origin-dependent and poorly\\endcolumn defined in the framework of classical multipole theory). In defence, however, for these poor latter quantities one can mention the many advantages of the engineering-type constitutive relations where D and B are expressed as responses to E and H. An example is the beautiful symmetry and complete analogy between the electric and magnetic quantities (voltage becomes current and vice versa in the duality transformation) which helps us write down solutions to electromagnetic problems from other known cases. From a pragmatic point of view we would also favour the use of quantities like Poynting vector and energy density (which require the H field). Another discussion-provoking question to the authors of the book might be whether their new multipole balance could be broken in the analysis of artificial materials. New nanotechnological discoveries and devices make it look like engineers can do anything. Perhaps in the design of complex media and metamaterials, a hot topic in todayÂ's materials science, such macroscopic responses can be tailored where a certain high-order multipole contribution dominates over other, more basic ones. Multiple Theory in Electromagnetism is suitable for a broad spectrum of readers: solid-state physicists, molecular chemists, theoretical and experimental optics scientists, radiophysics experts, electromagnetists and other electrical engineers, students and working scientists alike. This is a wonderful book. It certainly should appeal to them all.

Measuring the 2D baryon acoustic oscillation signal of galaxies in WiggleZ: cosmological constraints

PubMed Central

Hinton, Samuel R.; Kazin, Eyal; Davis, Tamara M.; Blake, Chris; Brough, Sarah; Colless, Matthew; Couch, Warrick J.; Drinkwater, Michael J.; Glazebrook, Karl; Jurek, Russell J.; Parkinson, David; Pimbblet, Kevin A.; Poole, Gregory B.; Pracy, Michael; Woods, David

2016-01-01

We present results from the 2D anisotropic baryon acoustic oscillation (BAO) signal present in the final data set from the WiggleZ Dark Energy Survey. We analyse the WiggleZ data in two ways: first using the full shape of the 2D correlation function and secondly focusing only on the position of the BAO peak in the reconstructed data set. When fitting for the full shape of the 2D correlation function we use a multipole expansion to compare with theory. When we use the reconstructed data we marginalize over the shape and just measure the position of the BAO peak, analysing the data in wedges separating the signal along the line of sight from that parallel to the line of sight. We verify our method with mock data and find the results to be free of bias or systematic offsets. We also redo the pre-reconstruction angle-averaged (1D) WiggleZ BAO analysis with an improved covariance and present an updated result. The final results are presented in the form of Ωc h2, H(z), and DA(z) for three redshift bins with effective redshifts z = 0.44, 0.60, and 0.73. Within these bins and methodologies, we recover constraints between 5 and 22 per cent error. Our cosmological constraints are consistent with flat ΛCDM cosmology and agree with results from the Baryon Oscillation Spectroscopic Survey. PMID:28066154

Comparing Neutron Star Kicks to Supernova Remnant Asymmetries

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

Holland-Ashford, Tyler; Lopez, Laura A.; Auchettl, Katie

2017-07-20

Supernova explosions are inherently asymmetric and can accelerate new-born neutron stars (NSs) to hundreds of km s{sup −1}. Two prevailing theories to explain NS kicks are ejecta asymmetries (e.g., conservation of momentum between NS and ejecta) and anisotropic neutrino emission. Observations of supernova remnants (SNRs) can give us insights into the mechanism that generates these NS kicks. In this paper, we investigate the relationship between NS kick velocities and the X-ray morphologies of 18 SNRs observed with the Chandra X-ray Observatory and the Röntgen Satellite ( ROSAT ). We measure SNR asymmetries using the power-ratio method (a multipole expansion technique),more » focusing on the dipole, quadrupole, and octupole power ratios. Our results show no correlation between the magnitude of the power ratios and NS kick velocities, but we find that for Cas A and G292.0+1.8, whose emission traces the ejecta distribution, their NSs are preferentially moving opposite to the bulk of the X-ray emission. In addition, we find a similar result for PKS 1209–51, CTB 109, and Puppis A; however, their emission is dominated by circumstellar/interstellar material, so their asymmetries may not reflect their ejecta distributions. Our results are consistent with the theory that NS kicks are a consequence of ejecta asymmetries as opposed to anisotropic neutrino emission. In the future, additional observations to measure NS proper motions within ejecta-dominated SNRs are necessary to robustly constrain the NS kick mechanism.« less

Measuring the 2D baryon acoustic oscillation signal of galaxies in WiggleZ: cosmological constraints.

PubMed

Hinton, Samuel R; Kazin, Eyal; Davis, Tamara M; Blake, Chris; Brough, Sarah; Colless, Matthew; Couch, Warrick J; Drinkwater, Michael J; Glazebrook, Karl; Jurek, Russell J; Parkinson, David; Pimbblet, Kevin A; Poole, Gregory B; Pracy, Michael; Woods, David

2017-02-01

We present results from the 2D anisotropic baryon acoustic oscillation (BAO) signal present in the final data set from the WiggleZ Dark Energy Survey. We analyse the WiggleZ data in two ways: first using the full shape of the 2D correlation function and secondly focusing only on the position of the BAO peak in the reconstructed data set. When fitting for the full shape of the 2D correlation function we use a multipole expansion to compare with theory. When we use the reconstructed data we marginalize over the shape and just measure the position of the BAO peak, analysing the data in wedges separating the signal along the line of sight from that parallel to the line of sight. We verify our method with mock data and find the results to be free of bias or systematic offsets. We also redo the pre-reconstruction angle-averaged (1D) WiggleZ BAO analysis with an improved covariance and present an updated result. The final results are presented in the form of Ω c   h 2 , H ( z ), and D A ( z ) for three redshift bins with effective redshifts z = 0.44, 0.60, and 0.73. Within these bins and methodologies, we recover constraints between 5 and 22 per cent error. Our cosmological constraints are consistent with flat ΛCDM cosmology and agree with results from the Baryon Oscillation Spectroscopic Survey.

Measuring the 2D baryon acoustic oscillation signal of galaxies in WiggleZ: cosmological constraints

NASA Astrophysics Data System (ADS)

Hinton, Samuel R.; Kazin, Eyal; Davis, Tamara M.; Blake, Chris; Brough, Sarah; Colless, Matthew; Couch, Warrick J.; Drinkwater, Michael J.; Glazebrook, Karl; Jurek, Russell J.; Parkinson, David; Pimbblet, Kevin A.; Poole, Gregory B.; Pracy, Michael; Woods, David

2017-02-01

We present results from the 2D anisotropic baryon acoustic oscillation (BAO) signal present in the final data set from the WiggleZ Dark Energy Survey. We analyse the WiggleZ data in two ways: first using the full shape of the 2D correlation function and secondly focusing only on the position of the BAO peak in the reconstructed data set. When fitting for the full shape of the 2D correlation function we use a multipole expansion to compare with theory. When we use the reconstructed data we marginalize over the shape and just measure the position of the BAO peak, analysing the data in wedges separating the signal along the line of sight from that parallel to the line of sight. We verify our method with mock data and find the results to be free of bias or systematic offsets. We also redo the pre-reconstruction angle-averaged (1D) WiggleZ BAO analysis with an improved covariance and present an updated result. The final results are presented in the form of Ωc h2, H(z), and DA(z) for three redshift bins with effective redshifts z = 0.44, 0.60, and 0.73. Within these bins and methodologies, we recover constraints between 5 and 22 per cent error. Our cosmological constraints are consistent with flat ΛCDM cosmology and agree with results from the Baryon Oscillation Spectroscopic Survey.

Probing the E2 properties of the scissors mode with real photons

NASA Astrophysics Data System (ADS)

Beck, Tobias; Pietralla, Norbert; Beller, Jacob; Derya, Vera; Löher, Bastian; Savran, Deniz; Tornow, Werner; Werner, Volker; Zilges, Andreas

2018-05-01

The E2/M1 multipole mixing ratio δ1→2 of the 1+ sc → 2+ 1 γ-ray transition of 156Gd and 164Dy has been measured using the linearly polarized photon beams of the HIγS facility. The employed method of photonscattering experiments in combination with polarized, quasi-monochromatic beams and a dedicated detector setup is highly sensitive to the electric quadrupole-decay properties of the scissors mode.

TINKTEP: A fully self-consistent, mutually polarizable QM/MM approach based on the AMOEBA force field

NASA Astrophysics Data System (ADS)

Dziedzic, Jacek; Mao, Yuezhi; Shao, Yihan; Ponder, Jay; Head-Gordon, Teresa; Head-Gordon, Martin; Skylaris, Chris-Kriton

2016-09-01

We present a novel quantum mechanical/molecular mechanics (QM/MM) approach in which a quantum subsystem is coupled to a classical subsystem described by the AMOEBA polarizable force field. Our approach permits mutual polarization between the QM and MM subsystems, effected through multipolar electrostatics. Self-consistency is achieved for both the QM and MM subsystems through a total energy minimization scheme. We provide an expression for the Hamiltonian of the coupled QM/MM system, which we minimize using gradient methods. The QM subsystem is described by the onetep linear-scaling DFT approach, which makes use of strictly localized orbitals expressed in a set of periodic sinc basis functions equivalent to plane waves. The MM subsystem is described by the multipolar, polarizable force field AMOEBA, as implemented in tinker. Distributed multipole analysis is used to obtain, on the fly, a classical representation of the QM subsystem in terms of atom-centered multipoles. This auxiliary representation is used for all polarization interactions between QM and MM, allowing us to treat them on the same footing as in AMOEBA. We validate our method in tests of solute-solvent interaction energies, for neutral and charged molecules, demonstrating the simultaneous optimization of the quantum and classical degrees of freedom. Encouragingly, we find that the inclusion of explicit polarization in the MM part of QM/MM improves the agreement with fully QM calculations.

An implicit boundary integral method for computing electric potential of macromolecules in solvent

NASA Astrophysics Data System (ADS)

Zhong, Yimin; Ren, Kui; Tsai, Richard

2018-04-01

A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equation that arises in mathematical models for the electrostatics of molecules in solvent. The proposed method uses an implicit boundary integral formulation to derive a linear system defined on Cartesian nodes in a narrowband surrounding the closed surface that separates the molecule and the solvent. The needed implicit surface is constructed from the given atomic description of the molecules, by a sequence of standard level set algorithms. A fast multipole method is applied to accelerate the solution of the linear system. A few numerical studies involving some standard test cases are presented and compared to other existing results.

Optical tractor Bessel polarized beams

NASA Astrophysics Data System (ADS)

Mitri, F. G.; Li, R. X.; Guo, L. X.; Ding, C. Y.

2017-01-01

Axial and transverse radiation force cross-sections of optical tractor Bessel polarized beams are theoretically investigated for a dielectric sphere with particular emphasis on the beam topological charge (or order), half-cone angle and polarization. The angular spectrum decomposition method (ASDM) is used to derive the non-paraxial electromagnetic (EM) field components of the Bessel beams. The multipole expansion method using vector spherical harmonics is utilized and appropriate beam-shape coefficients are derived in order to compute the radiation force cross-sections. The analysis has no limitation to a particular range of frequencies such that the Rayleigh, Mie or geometrical optics regimes can all be considered effectively using the present rigorous formalism. The focus of this investigation is to identify some of the tractor beam conditions so as to achieve retrograde motion of a dielectric sphere located arbitrarily in space. Numerical computations for the axial and transverse radiation force cross-sections are presented for linear, right-circular, radial, azimuthal and mixed polarizations of the individual plane waves forming the Bessel beams of zeroth- and first-order (with positive or negative helicity), respectively. As the sphere shifts off the beam's axis, the axial pulling (tractor) force is weakened. Moreover, the transverse radiation force cross-section field changes with the sphere's size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beam's axis are found, depending on the choice of ka and the half-cone angle α0. These results are particularly important in the development of emergent technologies for the photophoretic assembly of optically-engineered (meta)materials with designed properties using optical tractor (vortex) beams, particle manipulation, levitation and positioning, and other applications.

Effects of elastic bed on hydrodynamic forces for a submerged sphere in an ocean of finite depth

NASA Astrophysics Data System (ADS)

Mohapatra, Smrutiranjan

2017-08-01

In this paper, we consider a hydroelastic model to examine the radiation of waves by a submerged sphere for both heave and sway motions in a single-layer fluid flowing over an infinitely extended elastic bottom surface in an ocean of finite depth. The elastic bottom is modeled as a thin elastic plate and is based on the Euler-Bernoulli beam equation. The effect of the presence of surface tension at the free-surface is neglected. In such situation, there exist two modes of time-harmonic waves: the one with a lower wavenumber (surface mode) propagates along the free-surface and the other with higher wavenumber (flexural mode) propagates along the elastic bottom surface. Based on the small amplitude wave theory and by using the multipole expansion method, we find the particular solution for the problem of wave radiation by a submerged sphere of finite depth. Furthermore, this method eliminates the need to use large and cumbersome numerical packages for the solution of such problem and leads to an infinite system of linear algebraic equations which are easily solved numerically by any standard technique. The added-mass and damping coefficients for both heave and sway motions are derived and plotted for different submersion depths of the sphere and flexural rigidity of the elastic bottom surface. It is observed that, whenever the sphere nearer to the elastic bed, the added-mass move toward to a constant value of 1, which is approximately twice of the value of added-mass of a moving sphere in a single-layer fluid flowing over a rigid and flat bottom surface.

Gravitational radiation from compact binary systems: Gravitational waveforms and energy loss to second post-Newtonian order

NASA Astrophysics Data System (ADS)

Will, Clifford M.; Wiseman, Alan G.

1996-10-01

We derive the gravitational waveform and gravitational-wave energy flux generated by a binary star system of compact objects (neutron stars or black holes), accurate through second post-Newtonian order (O[(v/c)4]=O[(Gm/rc2)2]) beyond the lowest-order quadrupole approximation. We cast the Einstein equations into the form of a flat-spacetime wave equation together with a harmonic gauge condition, and solve it formally as a retarded integral over the past null cone of the chosen field point. The part of this integral that involves the matter sources and the near-zone gravitational field is evaluated in terms of multipole moments using standard techniques; the remainder of the retarded integral, extending over the radiation zone, is evaluated in a novel way. The result is a manifestly convergent and finite procedure for calculating gravitational radiation to arbitrary orders in a post-Newtonian expansion. Through second post-Newtonian order, the radiation is also shown to propagate toward the observer along true null rays of the asymptotically Schwarzschild spacetime, despite having been derived using flat-spacetime wave equations. The method cures defects that plagued previous ``brute-force'' slow-motion approaches to the generation of gravitational radiation, and yields results that agree perfectly with those recently obtained by a mixed post-Minkowskian post-Newtonian method. We display explicit formulas for the gravitational waveform and the energy flux for two-body systems, both in arbitrary orbits and in circular orbits. In an appendix, we extend the formalism to bodies with finite spatial extent, and derive the spin corrections to the waveform and energy loss.

The Spectrum of the Universe.

PubMed

Hill, Ryley; Masui, Kiyoshi W; Scott, Douglas

2018-05-01

Cosmic background (CB) radiation, encompassing the sum of emission from all sources outside our own Milky Way galaxy across the entire electromagnetic spectrum, is a fundamental phenomenon in observational cosmology. Many experiments have been conceived to measure it (or its constituents) since the extragalactic Universe was first discovered; in addition to estimating the bulk (cosmic monopole) spectrum, directional variations have also been detected over a wide range of wavelengths. Here we gather the most recent of these measurements and discuss the current status of our understanding of the CB from radio to γ-ray energies. Using available data in the literature, we piece together the sky-averaged intensity spectrum and discuss the emission processes responsible for what is observed. We examine the effect of perturbations to the continuum spectrum from atomic and molecular line processes and comment on the detectability of these signals. We also discuss how one could, in principle, obtain a complete census of the CB by measuring the full spectrum of each spherical harmonic expansion coefficient. This set of spectra of multipole moments effectively encodes the entire statistical history of nuclear, atomic, and molecular processes in the Universe.

Integral representation of channel flow with interacting particles

NASA Astrophysics Data System (ADS)

Fouxon, Itzhak; Ge, Zhouyang; Brandt, Luca; Leshansky, Alexander

2017-12-01

We construct a boundary integral representation for the low-Reynolds-number flow in a channel in the presence of freely suspended particles (or droplets) of arbitrary size and shape. We demonstrate that lubrication theory holds away from the particles at horizontal distances exceeding the channel height and derive a multipole expansion of the flow which is dipolar to the leading approximation. We show that the dipole moment of an arbitrary particle is a weighted integral of the stress and the flow at the particle surface, which can be determined numerically. We introduce the equation of motion that describes hydrodynamic interactions between arbitrary, possibly different, distant particles, with interactions determined by the product of the mobility matrix and the dipole moment. Further, the problem of three identical interacting spheres initially aligned in the streamwise direction is considered and the experimentally observed "pair exchange" phenomenon is derived analytically and confirmed numerically. For nonaligned particles, we demonstrate the formation of a configuration with one particle separating from a stable pair. Our results suggest that in a dilute initially homogenous particulate suspension flowing in a channel the particles will eventually separate into singlets and pairs.

The Zeldovich approximation and wide-angle redshift-space distortions

NASA Astrophysics Data System (ADS)

Castorina, Emanuele; White, Martin

2018-06-01

The contribution of line-of-sight peculiar velocities to the observed redshift of objects breaks the translational symmetry of the underlying theory, modifying the predicted 2-point functions. These `wide angle effects' have mostly been studied using linear perturbation theory in the context of the multipoles of the correlation function and power spectrum . In this work we present the first calculation of wide angle terms in the Zeldovich approximation, which is known to be more accurate than linear theory on scales probed by the next generation of galaxy surveys. We present the exact result for dark matter and perturbatively biased tracers as well as the small angle expansion of the configuration- and Fourier-space two-point functions and the connection to the multi-frequency angular power spectrum. We compare different definitions of the line-of-sight direction and discuss how to translate between them. We show that wide angle terms can reach tens of percent of the total signal in a measurement at low redshift in some approximations, and that a generic feature of wide angle effects is to slightly shift the Baryon Acoustic Oscillation scale.

The Spectrum of the Universe

NASA Astrophysics Data System (ADS)

Hill, Ryley; Masui, Kiyoshi W.; Scott, Douglas

2018-05-01

The cosmic background (CB) radiation, encompassing the sum of emission from all sources outside our own Milky Way galaxy across the entire electromagnetic spectrum, is a fundamental phenomenon in observational cosmology. Many experiments have been conceived to measure it (or its constituents) since the extragalactic Universe was first discovered; in addition to estimating the bulk (cosmic monopole) spectrum, directional variations have also been detected over a wide range of wavelengths. Here we gather the most recent of these measurements and discuss the current status of our understanding of the CB from radio to $\\gamma$-ray energies. Using available data in the literature we piece together the sky-averaged intensity spectrum, and discuss the emission processes responsible for what is observed. We examine the effect of perturbations to the continuum spectrum from atomic and molecular line processes and comment on the detectability of these signals. We also discuss how one could in principle obtain a complete census of the CB by measuring the full spectrum of each spherical harmonic expansion coefficient. This set of spectra of multipole moments effectively encodes the entire statistical history of nuclear, atomic and molecular processes in the Universe.

Modeling the characteristics of wheel/rail rolling noise

NASA Astrophysics Data System (ADS)

Lui, Wai Keung; Li, Kai Ming; Frommer, Glenn H.

2005-04-01

To study the sound radiation characteristics of a passing train, four sets of noise measurements for different train operational conditions have been conducted at three different sites, including ballast tracks at grade and railway on a concrete viaduct. The time histories computed by the horizontal radiation models were compared with the measured noise profiles. The measured sound exposure levels are used to deduce the vertical directivity pattern for different railway systems. It is found that the vertical directivity of different railway systems shows a rather similar pattern. The vertical directivity of train noise is shown to increase up to about 30× before reducing to a minimum at 90×. A multipole expansion model is proposed to account for the vertical radiation directivity of the train noise. An empirical formula, which has been derived, compares well with the experimental data. The empirical model is found to be applicable to different train/rail systems at train speeds ranging up to 120 km/h in this study. [Work supported by MTR Corporation Ltd., Innovation Technology Commission of the HKSAR Government and The Hong Kong Polytechnic University.

Multi-excitonic (N=1,2 and 3) quantum dots in magnetic field: Analytical mapping of correlations (exchange) by multipole expansion

NASA Astrophysics Data System (ADS)

Singh, Sunny; Kaur, Harsimran; Sharma, Shivalika; Aggarwal, Priyanka; Hazra, Ram Kuntal

2017-04-01

The understanding of the physics of exciton, bi-exciton, tri-exciton and the subsequent insight into controlling the properties of mesoscopic systems holds the key to various exotic optical, electrical and magnetic phenomena like superconductivity, Mott insulation, Quantum Hall effect etc. Many of exciton properties are similar to atomic hydrogen that attracts researchers to explore electronic structure of exciton in quantum dots, but nontriviality arises due to coulombic interactions among electrons and holes. We propose an exact integral of coulomb (exchange) correlation in terms of finitely summed Lauricella functions to examine 3-D exciton of harmonic dots confined in zero and non-zero arbitrary magnetic field. The highlight of our work is the use of exact variational solution for coloumbic interaction between the hole and the electron and evaluation of the cross terms arising out of the coupling among centre-of-mass and relative coordinates. We also have extended the size of the system to generalized N-body problem with N=3,4 for tri-exciton (e-e-h/e-h-h)

Efficient calculation of the energy of a molecule in an arbitrary electric field

NASA Astrophysics Data System (ADS)

Pulay, Peter; Janowski, Tomasz

In thermodynamic (e.g., Monte Carlo) simulations with electronic embedding, the energy of the active site or solute must be calculated for millions of configurations of the environment (solvent or protein matrix) to obtain reliable statistics. This precludes the use of accurate but expensive ab initio and density functional techniques. Except for the immediate neighbors, the effect of the environment is electrostatic. We show that the energy of a molecule in the irregular field of the environment can be determined very efficiently by expanding the electric potential in known functions, and precalculating the first and second order response of the molecule to the components of the potential. These generalized multipole moments and polarizabilities allow the calculation of the energy of the system without further ab initio calculations. Several expansion functions were explored: polynomials, distributed inverse powers, and sine functions. The latter provide the numerically most stable fit but require new types of integrals. Distributed inverse powers can be simulated using dummy atoms, and energies calculated this way provide a very good approximation to the actual energies in the field of the environment.

The Gaia–WISE Extragalactic Astrometric Catalog

NASA Astrophysics Data System (ADS)

Paine, Jennie; Darling, Jeremy; Truebenbach, Alexandra

2018-06-01

The Gaia mission has detected a large number of active galactic nuclei (AGNs) and galaxies, but these objects must be identified among the thousandfold more numerous stars. Extant astrometric AGN catalogs do not have the uniform sky coverage required to detect and characterize the all-sky, low-multipole proper motion signals produced by the barycenter motion, gravitational waves, and cosmological effects. To remedy this, we present an all-sky sample of 567,721 AGNs in Gaia Data Release 1, selected using WISE two-color criteria. The catalog has fairly uniform sky coverage beyond the Galactic plane, with a mean density of 12.8 AGNs per square degree. The objects have magnitudes ranging from G = 8.8 down to Gaia’s magnitude limit, G = 20.7. The catalog is approximately 50% complete but suffers from low stellar contamination, roughly 0.2%. We predict that the end-of-mission Gaia proper motions for this catalog will enable detection of the secular aberration drift to high significance (23σ) and will place an upper limit on the anisotropy of the Hubble expansion of about 2%.

Magnetic ground state of Sr 2 IrO 4 and implications for second-harmonic generation

DOE PAGES

Di Matteo, S.; Norman, M. R.

2016-08-24

The currently accepted magnetic ground state of Sr 2IrO 4 (the -++- state) preserves inversion symmetry. This is at odds, though, with recent experiments that indicate a magnetoelectric ground state, leading to the speculation that orbital currents or more exotic magnetic multipoles might exist in this material. In this paper, we analyze various magnetic configurations and demonstrate that two of them, the magnetoelectric -+-+ state and the nonmagnetoelectric ++++ state, can explain these recent second-harmonic generation (SHG) experiments, obviating the need to invoke orbital currents. The SHG-probed magnetic order parameter has the symmetry of a parity-breaking multipole in the -+-+more » state and of a parity-preserving multipole in the ++++ state. We speculate that either might have been created by the laser pump used in the experiments. An alternative is that the observed magnetic SHG signal is a surface effect. Finally, we suggest experiments that could be performed to test these various possibilities and also address the important issue of the suppression of the RXS intensity at the L 2 edge.« less

Magnetic ground state of Sr 2 IrO 4 and implications for second-harmonic generation

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

Di Matteo, S.; Norman, M. R.

The currently accepted magnetic ground state of Sr 2IrO 4 (the -++- state) preserves inversion symmetry. This is at odds, though, with recent experiments that indicate a magnetoelectric ground state, leading to the speculation that orbital currents or more exotic magnetic multipoles might exist in this material. In this paper, we analyze various magnetic configurations and demonstrate that two of them, the magnetoelectric -+-+ state and the nonmagnetoelectric ++++ state, can explain these recent second-harmonic generation (SHG) experiments, obviating the need to invoke orbital currents. The SHG-probed magnetic order parameter has the symmetry of a parity-breaking multipole in the -+-+more » state and of a parity-preserving multipole in the ++++ state. We speculate that either might have been created by the laser pump used in the experiments. An alternative is that the observed magnetic SHG signal is a surface effect. Finally, we suggest experiments that could be performed to test these various possibilities and also address the important issue of the suppression of the RXS intensity at the L 2 edge.« less

Multipole and field uniformity tailoring of a 750 MHz rf dipole

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

Delayen, Jean R.; Castillo, Alejandro

2014-12-01

In recent years great interest has been shown in developing rf structures for beam separation, correction of geometrical degradation on luminosity, and diagnostic applications in both lepton and hadron machines. The rf dipole being a very promising one among all of them. The rf dipole has been tested and proven to have attractive properties that include high shunt impedance, low and balance surface fields, absence of lower order modes and far-spaced higher order modes that simplify their damping scheme. As well as to be a compact and versatile design in a considerable range of frequencies, its fairly simple geometry dependencymore » is suitable both for fabrication and surface treatment. The rf dipole geometry can also be optimized for lowering multipacting risk and multipole tailoring to meet machine specific field uniformity tolerances. In the present work a survey of field uniformities, and multipole contents for a set of 750 MHz rf dipole designs is presented as both a qualitative and quantitative analysis of the inherent flexibility of the structure and its limitations.« less

A Simple Force-Motion Relation for Migrating Cells Revealed by Multipole Analysis of Traction Stress

PubMed Central

Tanimoto, Hirokazu; Sano, Masaki

2014-01-01

For biophysical understanding of cell motility, the relationship between mechanical force and cell migration must be uncovered, but it remains elusive. Since cells migrate at small scale in dissipative circumstances, the inertia force is negligible and all forces should cancel out. This implies that one must quantify the spatial pattern of the force instead of just the summation to elucidate the force-motion relation. Here, we introduced multipole analysis to quantify the traction stress dynamics of migrating cells. We measured the traction stress of Dictyostelium discoideum cells and investigated the lowest two moments, the force dipole and quadrupole moments, which reflect rotational and front-rear asymmetries of the stress field. We derived a simple force-motion relation in which cells migrate along the force dipole axis with a direction determined by the force quadrupole. Furthermore, as a complementary approach, we also investigated fine structures in the stress field that show front-rear asymmetric kinetics consistent with the multipole analysis. The tight force-motion relation enables us to predict cell migration only from the traction stress patterns. PMID:24411233

Protein simulation using coarse-grained two-bead multipole force field with polarizable water models.

PubMed

Li, Min; Zhang, John Z H

2017-02-14

A recently developed two-bead multipole force field (TMFF) is employed in coarse-grained (CG) molecular dynamics (MD) simulation of proteins in combination with polarizable CG water models, the Martini polarizable water model, and modified big multipole water model. Significant improvement in simulated structures and dynamics of proteins is observed in terms of both the root-mean-square deviations (RMSDs) of the structures and residue root-mean-square fluctuations (RMSFs) from the native ones in the present simulation compared with the simulation result with Martini's non-polarizable water model. Our result shows that TMFF simulation using CG water models gives much stable secondary structures of proteins without the need for adding extra interaction potentials to constrain the secondary structures. Our result also shows that by increasing the MD time step from 2 fs to 6 fs, the RMSD and RMSF results are still in excellent agreement with those from all-atom simulations. The current study demonstrated clearly that the application of TMFF together with a polarizable CG water model significantly improves the accuracy and efficiency for CG simulation of proteins.

Protein simulation using coarse-grained two-bead multipole force field with polarizable water models

NASA Astrophysics Data System (ADS)

Li, Min; Zhang, John Z. H.

2017-02-01

A recently developed two-bead multipole force field (TMFF) is employed in coarse-grained (CG) molecular dynamics (MD) simulation of proteins in combination with polarizable CG water models, the Martini polarizable water model, and modified big multipole water model. Significant improvement in simulated structures and dynamics of proteins is observed in terms of both the root-mean-square deviations (RMSDs) of the structures and residue root-mean-square fluctuations (RMSFs) from the native ones in the present simulation compared with the simulation result with Martini's non-polarizable water model. Our result shows that TMFF simulation using CG water models gives much stable secondary structures of proteins without the need for adding extra interaction potentials to constrain the secondary structures. Our result also shows that by increasing the MD time step from 2 fs to 6 fs, the RMSD and RMSF results are still in excellent agreement with those from all-atom simulations. The current study demonstrated clearly that the application of TMFF together with a polarizable CG water model significantly improves the accuracy and efficiency for CG simulation of proteins.

Optical response of hybrid semiconductor quantum dot-metal nanoparticle system: Beyond the dipole approximation

NASA Astrophysics Data System (ADS)

Mohammadzadeh, Atefeh; Miri, MirFaez

2018-01-01

We study the response of a semiconductor quantum dot-metal nanoparticle system to an external field E 0 cos ( ω t ) . The borders between Fano, double peaks, weak transition, strong transition, and bistability regions of the phase diagram move considerably as one regards the multipole effects. The exciton-induced transparency is an artifact of the dipole approximation. The absorption of the nanoparticle, the population inversion of the quantum dot, the upper and lower limits of intensity where bistability occurs, the characteristic time to reach the steady state, and other features of the hybrid system change due to the multipole effects. The phase diagrams corresponding to the fields parallel and perpendicular to the axis of system are quite distinguishable. Thus, both the intensity and the polarization of the incident field can be used to control the system. In particular, the incident polarization can be used to switch on and switch off the bistable behavior. For applications such as miniaturized bistable devices and nanosensors sensitive to variations of the dielectric constant of the surrounding medium, multipole effects must be considered.

Classification of "multipole" superconductivity in multiorbital systems and its implications

NASA Astrophysics Data System (ADS)

Nomoto, T.; Hattori, K.; Ikeda, H.

2016-11-01

Motivated by a growing interest in multiorbital superconductors with spin-orbit interactions, we perform the group-theoretical classification of various unconventional superconductivity emerging in symmorphic O , D4, and D6 space groups. The generalized Cooper pairs, which we here call "multipole" superconductivity, possess spin-orbital coupled (multipole) degrees of freedom, instead of the conventional spin singlet/triplet in single-orbital systems. From the classification, we obtain the following key consequences, which have never been focused in the long history of research in this field: (1) A superconducting gap function with Γ9⊗Γ9 in D6 possesses nontrivial momentum dependence different from the usual spin-1/2 classification. (2) Unconventional gap structure can be realized in the BCS approximation of purely local (onsite) interactions irrespective of attraction/repulsion. It implies the emergence of an electron-phonon (e-ph) driven unconventional superconductivity. (3) Reflecting symmetry of orbital basis functions there appear not symmetry protected but inevitable line nodes/gap minima, and thus, anisotropic s -wave superconductivity can be naturally explained even in the absence of competing fluctuations.

Nuclear longitudinal form factors for axially deformed charge distributions expanded by nonorthogonal basis functions

NASA Astrophysics Data System (ADS)

Liu, Jian; Zhang, Jinjuan; Xu, Chang; Ren, Zhongzhou

2017-05-01

In this paper, the nuclear longitudinal form factors are systematically studied from the intrinsic charge multipoles. For axially deformed nuclei, two different types of density profiles are used to describe their charge distributions. For the same charge distributions expanded with different basis functions, the corresponding longitudinal form factors are derived and compared with each other. Results show the multipoles Cλ of longitudinal form factors are independent of the basis functions of charge distributions. Further numerical calculations of longitudinal form factors of 12C indicates that the C 0 multipole reflects the contributions of spherical components of all nonorthogonal basis functions. For deformed nuclei, their charge RMS radii can also be determined accurately by the C 0 measurement. The studies in this paper examine the model-independent properties of electron scattering, which are useful for interpreting electron scattering experiments on exotic deformed nuclei. Supported by National Natural Science Foundation of China (11505292, 11175085, 11575082, 11235001, 11275138, and 11447226), by Shandong Provincial Natural Science Foundation, China (BS2014SF007), Fundamental Research Funds for Central Universities (15CX02072A).

Impedance loading and radiation of finite aperture multipole sources in fluid filled boreholes

NASA Astrophysics Data System (ADS)

Geerits, Tim W.; Kranz, Burkhard

2017-04-01

In the exploration of oil and gas finite aperture multipole borehole acoustic sources are commonly used to excite borehole modes in a fluid-filled borehole surrounded by a (poro-) elastic formation. Due to the mutual interaction of the constituent sources and their immediate proximity to the formation it has been unclear how and to what extent these effects influence radiator performance. We present a theory, based on the equivalent surface source formulation for fluid-solid systems that incorporates these 'loading' effects and allows for swift computation of the multipole source dimensionless impedance, the associated radiator motion and the resulting radiated wave field in borehole fluid and formation. Dimensionless impedance results are verified through a comparison with finite element modeling results in the cases of a logging while drilling tool submersed in an unbounded fluid and a logging while drilling tool submersed in a fluid filled borehole surrounded by a fast and a slow formation. In all these cases we consider a monopole, dipole and quadrupole excitation, as these cases are relevant to many borehole acoustic applications. Overall, we obtain a very good agreement.

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.

Continuum description of ionic and dielectric shielding for molecular-dynamics simulations of proteins in solution

NASA Astrophysics Data System (ADS)

Egwolf, Bernhard; Tavan, Paul

2004-01-01

We extend our continuum description of solvent dielectrics in molecular-dynamics (MD) simulations [B. Egwolf and P. Tavan, J. Chem. Phys. 118, 2039 (2003)], which has provided an efficient and accurate solution of the Poisson equation, to ionic solvents as described by the linearized Poisson-Boltzmann (LPB) equation. We start with the formulation of a general theory for the electrostatics of an arbitrarily shaped molecular system, which consists of partially charged atoms and is embedded in a LPB continuum. This theory represents the reaction field induced by the continuum in terms of charge and dipole densities localized within the molecular system. Because these densities cannot be calculated analytically for systems of arbitrary shape, we introduce an atom-based discretization and a set of carefully designed approximations. This allows us to represent the densities by charges and dipoles located at the atoms. Coupled systems of linear equations determine these multipoles and can be rapidly solved by iteration during a MD simulation. The multipoles yield the reaction field forces and energies. Finally, we scrutinize the quality of our approach by comparisons with an analytical solution restricted to perfectly spherical systems and with results of a finite difference method.

Low pressure characteristics of the multipole resonance probe

NASA Astrophysics Data System (ADS)

Brinkmann, Ralf Peter; Oberrath, Jens

2014-10-01

The term ``Active plasma resonance spectroscopy'' (APRS) denotes a class of related techniques which utilize, for diagnostic purposes, the natural ability of plasmas to resonate on or near the electron plasma frequency ωpe. The basic idea dates back to the early days of discharge physics but has recently found renewed interest as an approach to industry-compatible plasma diagnostics: A radio frequent signal (in the GHz range) is coupled into the plasma via an antenna or probe, the spectral response is recorded (with the same or another antenna or probe), and a mathematical model is used to determine plasma parameters like the electron density or the electron temperature. When the method is applied to low pressure plasmas (of a few Pa and lower), kinetic effects must be accounted for in the mathematical model. This contribution studies a particular realization of the APRS scheme, the geometrically and electrically symmetric Multipole Resonance Probe (MRP). It is shown that the resonances of the MRP exhibit a residual damping in the limit p --> 0 which cannot be explained by Ohmic dissipation but only by kinetic effects. Supported by the German Federal Ministry of Education and Research (BMBF) in the framework of the PluTO project.

Multipole ordering and collective excitations in the excitonic phase of Pr0.5Ca0.5CoO3

NASA Astrophysics Data System (ADS)

Yamaguchi, Tomoki; Sugimoto, Koudai; Ohta, Yukinori

2018-05-01

As an extension of our previous paper (Yamaguchi et al., 2017) [24], we study the carrier doping dependence of the excitonic condensation in Pr0.5Ca0.5CoO3 using the random-phase and mean-field approximations for the realistic five-orbital Hubbard model. We show that the spin-triplet excitonic phase with a magnetic multipole ordering is stable against the doping of carriers in a considerable range around Co3+ (or 3d6). We discuss experimental relevance of our results.

Application of ion thruster technology to a 30-cm multipole sputtering ion source

NASA Technical Reports Server (NTRS)

Robinson, R. S.; Kaufman, H. R.

1976-01-01

A 30-cm electron-bombardment ion source has been designed and fabricated for micromachining and sputtering applications. This source has a multipole magnetic field that employs permanent magnets between permeable pole pieces. An average ion current density of 1 ma/sq cm with 500-eV argon ions was selected as a design operating condition. The ion beam at this operating condition was uniform and well collimated, with an average variation of + or -5 percent over the center 20 cm of the beam at a distance up to 30 cm from the ion source.

Ion flow experiments in a multipole discharge chamber

NASA Technical Reports Server (NTRS)

Kaufman, H. R.; Robinson, R. S.; Frisa, L. E.

1982-01-01

It has been customary to assume that ions flow nearly equally in all directions from the ion production region within an electron-bombardment discharge chamber. Ion flow measurements in a multipole discharge chamber have shown that this assumption is not true. In general, the electron current through a magnetic field can alter the electron density, and hence the ion density, in such a way that ions tend to be directed away from the region bounded by the magnetic field. When this mechanism is understood, it becomes evident that many past discharge chamber designs have operated with a preferentially directed flow of ions.

Penning ionization widths by Fano-algebraic diagrammatic construction method

NASA Astrophysics Data System (ADS)

Yun, Renjie; Narevicius, Edvardas; Averbukh, Vitali

2018-03-01

We present an ab initio theory and computational method for Penning ionization widths. Our method is based on the Fano theory of resonances, algebraic diagrammatic construction (ADC) scheme for many-electron systems, and Stieltjes imaging procedure. It includes an extension of the Fano-ADC scheme [V. Averbukh and L. S. Cederbaum, J. Chem. Phys. 123, 204107 (2005)] to triplet excited states. Penning ionization widths of various He*-H2 states are calculated as a function of the distance R between He* and H2. We analyze the asymptotic (large-R) dependences of the Penning widths in the region where the well-established electron transfer mechanism of the decay is suppressed by the multipole- and/or spin-forbidden energy transfer. The R-12 and R-8 power laws are derived for the asymptotes of the Penning widths of the singlet and triplet excited states of He*(1s2s1,3S), respectively. We show that the electron transfer mechanism dominates Penning ionization of He*(1s2s 3S)-H2 up until the He*-H2 separation is large enough for the radiative decay of He* to become the dominant channel. The same mechanism also dominates the ionization of He*(1s2s 1S)-H2 when R < 5 Å. We estimate that the regime of energy transfer in the He*-H2 Penning ionization cannot be reached by approaching zero collisional temperature. However, the multipole-forbidden energy transfer mechanism can become important for Penning ionization in doped helium droplets.

Improved Diffuse Foreground Subtraction with the ILC Method: CMB Map and Angular Power Spectrum Using Planck and WMAP Observations

NASA Astrophysics Data System (ADS)

Sudevan, Vipin; Aluri, Pavan K.; Yadav, Sarvesh Kumar; Saha, Rajib; Souradeep, Tarun

2017-06-01

We report an improved technique for diffuse foreground minimization from Cosmic Microwave Background (CMB) maps using a new multiphase iterative harmonic space internal-linear-combination (HILC) approach. Our method nullifies a foreground leakage that was present in the old and usual iterative HILC method. In phase 1 of the multiphase technique, we obtain an initial cleaned map using the single iteration HILC approach over the desired portion of the sky. In phase 2, we obtain a final CMB map using the iterative HILC approach; however, now, to nullify the leakage, during each iteration, some of the regions of the sky that are not being cleaned in the current iteration are replaced by the corresponding cleaned portions of the phase 1 map. We bring all input frequency maps to a common and maximum possible beam and pixel resolution at the beginning of the analysis, which significantly reduces data redundancy, memory usage, and computational cost, and avoids, during the HILC weight calculation, the deconvolution of partial sky harmonic coefficients by the azimuthally symmetric beam and pixel window functions, which in a strict mathematical sense, are not well defined. Using WMAP 9 year and Planck 2015 frequency maps, we obtain foreground-cleaned CMB maps and a CMB angular power spectrum for the multipole range 2≤slant {\\ell }≤slant 2500. Our power spectrum matches the published Planck results with some differences at different multipole ranges. We validate our method by performing Monte Carlo simulations. Finally, we show that the weights for HILC foreground minimization have the intrinsic characteristic that they also tend to produce a statistically isotropic CMB map.

Variations of solar, interplanetary, and geomagnetic parameters with solar magnetic multipole fields during Solar Cycles 21-24

NASA Astrophysics Data System (ADS)

Kim, Bogyeong; Lee, Jeongwoo; Yi, Yu; Oh, Suyeon

2015-01-01

In this study we compare the temporal variations of the solar, interplanetary, and geomagnetic (SIG) parameters with that of open solar magnetic flux from 1976 to 2012 (from Solar Cycle 21 to the early phase of Cycle 24) for a purpose of identifying their possible relationships. By the open flux, we mean the average magnetic field over the source surface (2.5 solar radii) times the source area as defined by the potential field source surface (PFSS) model of the Wilcox Solar Observatory (WSO). In our result, most SIG parameters except the solar wind dynamic pressure show rather poor correlations with the open solar magnetic field. Good correlations are recovered when the contributions from individual multipole components are counted separately. As expected, solar activity indices such as sunspot number, total solar irradiance, 10.7 cm radio flux, and solar flare occurrence are highly correlated with the flux of magnetic quadrupole component. The dynamic pressure of solar wind is strongly correlated with the dipole flux, which is in anti-phase with Solar Cycle (SC). The geomagnetic activity represented by the Ap index is correlated with higher order multipole components, which show relatively a slow time variation with SC. We also found that the unusually low geomagnetic activity during SC 23 is accompanied by the weak open solar fields compared with those in other SCs. It is argued that such dependences of the SIG parameters on the individual multipole components of the open solar magnetic flux may clarify why some SIG parameters vary in phase with SC and others show seemingly delayed responses to SC variation.

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

A fast multipole method combined with a reaction field for long-range electrostatics in molecular dynamics simulations: The effects of truncation on the properties of water

NASA Astrophysics Data System (ADS)

Mathias, Gerald; Egwolf, Bernhard; Nonella, Marco; Tavan, Paul

2003-06-01

We present a combination of the structure adapted multipole method with a reaction field (RF) correction for the efficient evaluation of electrostatic interactions in molecular dynamics simulations under periodic boundary conditions. The algorithm switches from an explicit electrostatics evaluation to a continuum description at the maximal distance that is consistent with the minimum image convention, and, thus, avoids the use of a periodic electrostatic potential. A physically motivated switching function enables charge clusters interacting with a given charge to smoothly move into the solvent continuum by passing through the spherical dielectric boundary surrounding this charge. This transition is complete as soon as the cluster has reached the so-called truncation radius Rc. The algorithm is used to examine the dependence of thermodynamic properties and correlation functions on Rc in the three point transferable intermolecular potential water model. Our test simulations on pure liquid water used either the RF correction or a straight cutoff and values of Rc ranging from 14 Å to 40 Å. In the RF setting, the thermodynamic properties and the correlation functions show convergence for Rc increasing towards 40 Å. In the straight cutoff case no such convergence is found. Here, in particular, the dipole-dipole correlation functions become completely artificial. The RF description of the long-range electrostatics is verified by comparison with the results of a particle-mesh Ewald simulation at identical conditions.

The FEM-R-Matrix Approach: Use of Mixed Finite Element and Gaussian Basis Sets for Electron Molecule Collisions

NASA Technical Reports Server (NTRS)

Thuemmel, Helmar T.; Huo, Winifred M.; Langhoff, Stephen R. (Technical Monitor)

1995-01-01

For the calculation of electron molecule collision cross sections R-matrix methods automatically take advantage of the division of configuration space into an inner region (I) bounded by radius tau b, where the scattered electron is within the molecular charge cloud and the system is described by an correlated Configuration Interaction (CI) treatment in close analogy to bound state calculations, and an outer region (II) where the scattered electron moves in the long-range multipole potential of the target and efficient analytic methods can be used for solving the asymptotic Schroedinger equation plus boundary conditions.

Tunable properties of light propagation in photonic liquid crystal fibers

NASA Astrophysics Data System (ADS)

Szaniawska, K.; Nasilowski, T.; Woliński, T. R.; Thienpont, H.

2006-12-01

Tunable properties of light propagation in photonic crystal fibers filled with liquid crystals, called photonic liquid crystal fibers (PLCFs) are presented. The propagation properties of PLCFs strongly depend on contrast between refractive indices of the solid core (pure silica glass) and liquid crystals (LCs) filing the holes of the fiber. Due to relatively strong thermo-optical effect, we can change the refractive index of the LC by changing its temperature. Numerical analysis of light propagation in PLCF, based on two simulation methods, such as finite difference (FD) and multipole method (MM) is presented. The numerical results obtained are in good agreement with our earlier experimental results presented elsewhere [1].

Solutions of large-scale electromagnetics problems involving dielectric objects with the parallel multilevel fast multipole algorithm.

PubMed

Ergül, Özgür

2011-11-01

Fast and accurate solutions of large-scale electromagnetics problems involving homogeneous dielectric objects are considered. Problems are formulated with the electric and magnetic current combined-field integral equation and discretized with the Rao-Wilton-Glisson functions. Solutions are performed iteratively by using the multilevel fast multipole algorithm (MLFMA). For the solution of large-scale problems discretized with millions of unknowns, MLFMA is parallelized on distributed-memory architectures using a rigorous technique, namely, the hierarchical partitioning strategy. Efficiency and accuracy of the developed implementation are demonstrated on very large problems involving as many as 100 million unknowns.

Multipolar electromagnetic fields around neutron stars: general-relativistic vacuum solutions

NASA Astrophysics Data System (ADS)

Pétri, J.

2017-12-01

Magnetic fields inside and around neutron stars are at the heart of pulsar magnetospheric activity. Strong magnetic fields are responsible for quantum effects, an essential ingredient to produce leptonic pairs and the subsequent broad-band radiation. The variety of electromagnetic field topologies could lead to the observed diversity of neutron star classes. Thus, it is important to include multipolar components to a presumably dominant dipolar magnetic field. Exact analytical solutions for these multipoles in Newtonian gravity have been computed in recent literature. However, flat space-time is not adequate to describe physics in the immediate surroundings of neutron stars. We generalize the multipole expressions to the strong gravity regime by using a slowly rotating metric approximation such as the one expected around neutron stars. Approximate formulae for the electromagnetic field including frame dragging are computed from which we estimate the Poynting flux and the braking index. Corrections to leading order in compactness and spin parameter are presented. As far as spin-down luminosity is concerned, it is shown that frame dragging remains irrelevant. For high-order multipoles starting from the quadrupole, the electric part can radiate more efficiently than the magnetic part. Both analytical and numerical tools are employed.

A simple force-motion relation for migrating cells revealed by multipole analysis of traction stress.

PubMed

Tanimoto, Hirokazu; Sano, Masaki

2014-01-07

For biophysical understanding of cell motility, the relationship between mechanical force and cell migration must be uncovered, but it remains elusive. Since cells migrate at small scale in dissipative circumstances, the inertia force is negligible and all forces should cancel out. This implies that one must quantify the spatial pattern of the force instead of just the summation to elucidate the force-motion relation. Here, we introduced multipole analysis to quantify the traction stress dynamics of migrating cells. We measured the traction stress of Dictyostelium discoideum cells and investigated the lowest two moments, the force dipole and quadrupole moments, which reflect rotational and front-rear asymmetries of the stress field. We derived a simple force-motion relation in which cells migrate along the force dipole axis with a direction determined by the force quadrupole. Furthermore, as a complementary approach, we also investigated fine structures in the stress field that show front-rear asymmetric kinetics consistent with the multipole analysis. The tight force-motion relation enables us to predict cell migration only from the traction stress patterns. Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Negative running of the spectral index, hemispherical asymmetry and the consistency of Planck with large r

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

McDonald, John, E-mail: j.mcdonald@lancaster.ac.uk

Planck favours a negative running of the spectral index, with the likelihood being dominated by low multipoles l ∼< 50 and no preference for running at higher l. A negative spectral index is also necessary for the 2- Planck upper bound on the tensor-to-scalar ratio r to be consistent with values significantly larger than 0.1. Planck has also observed a hemispherical asymmetry of the CMB power spectrum, again mostly at low multipoles. Here we consider whether the physics responsible for the hemispherical asymmetry could also account for the negative running of the spectral index and the consistency of Planck with a largemore » value of r. A negative running of the spectral index can be generated if the hemispherical asymmetry is due to a scale- and space-dependent modulation which suppresses the CMB power spectrum at low multipoles. We show that the observed hemispherical asymmetry at low l can be generated while satisfying constraints on the asymmetry at higher l and generating a negative spectral index of the right magnitude to account for the Planck observation and to allow Planck to be consistent with a large value of r.« less

Efficient minimization of multipole electrostatic potentials in torsion space

PubMed Central

Bodmer, Nicholas K.

2018-01-01

The development of models of macromolecular electrostatics capable of delivering improved fidelity to quantum mechanical calculations is an active field of research in computational chemistry. Most molecular force field development takes place in the context of models with full Cartesian coordinate degrees of freedom. Nevertheless, a number of macromolecular modeling programs use a reduced set of conformational variables limited to rotatable bonds. Efficient algorithms for minimizing the energies of macromolecular systems with torsional degrees of freedom have been developed with the assumption that all atom-atom interaction potentials are isotropic. We describe novel modifications to address the anisotropy of higher order multipole terms while retaining the efficiency of these approaches. In addition, we present a treatment for obtaining derivatives of atom-centered tensors with respect to torsional degrees of freedom. We apply these results to enable minimization of the Amoeba multipole electrostatics potential in a system with torsional degrees of freedom, and validate the correctness of the gradients by comparison to finite difference approximations. In the interest of enabling a complete model of electrostatics with implicit treatment of solvent-mediated effects, we also derive expressions for the derivative of solvent accessible surface area with respect to torsional degrees of freedom. PMID:29641557

Determining pseudoscalar meson photoproduction amplitudes from complete experiments

NASA Astrophysics Data System (ADS)

Sandorfi, A. M.; Hoblit, S.; Kamano, H.; Lee, T.-S. H.

2011-05-01

A new generation of complete experiments is focused on a high precision extraction of pseudoscalar meson photoproduction amplitudes. Here, we review the development of the most general analytic form of the cross section, dependent upon the three polarization vectors of the beam, target and recoil baryon, including all single-, double- and triple-polarization terms involving 16 spin-dependent observables. We examine the different conventions that have been used by different authors, and we present expressions that allow the direct numerical calculation of any pseudoscalar meson photoproduction observables with arbitrary spin projections from the Chew-Goldberger-Low-Nambu amplitudes. We use this numerical tool to clarify apparent sign differences that exist in the literature, in particular with the definitions of six double-polarization observables. We also present analytic expressions that determine the recoil baryon polarization, together with examples of their potential use with quasi-4π detectors to deduce observables. As an illustration of the use of the consistent machinery presented in this review, we carry out a multipole analysis of the γp → K+Λ reaction and examine the impact of recently published polarization measurements. When combining data from different experiments, we utilize the Fierz identities to fit a consistent set of scales. In fitting multipoles, we use a combined Monte Carlo sampling of the amplitude space, with gradient minimization, and find a shallow χ2 valley pitted with a very large number of local minima. This results in broad bands of multipole solutions that are experimentally indistinguishable. While these bands have been noticeably narrowed by the inclusion of new polarization measurements, many of the multipoles remain very poorly determined, even in sign, despite the inclusion of data on eight different observables. We have compared multipoles from recent PWA codes with our model-independent solution bands and found that such comparisons provide useful consistency tests which clarify model interpretations. The potential accuracy of amplitudes that could be extracted from measurements of all 16 polarization observables has been studied with mock data using the statistical variations that are expected from ongoing experiments. We conclude that, while a mathematical solution to the problem of determining an amplitude free of ambiguities may require eight observables, as has been pointed out in the literature, experiments with realistically achievable uncertainties will require a significantly larger number.

Collisional disruptions of rotating targets

NASA Astrophysics Data System (ADS)

Ševeček, Pavel; Broz, Miroslav

2017-10-01

Collisions are key processes in the evolution of the Main Asteroid Belt and impact events - i.e. target fragmentation and gravitational reaccumulation - are commonly studied by numerical simulations, namely by SPH and N-body methods. In our work, we extend the previous studies by assuming rotating targets and we study the dependence of resulting size-distributions on the pre-impact rotation of the target. To obtain stable initial conditions, it is also necessary to include the self-gravity already in the fragmentation phase which was previously neglected.To tackle this problem, we developed an SPH code, accelerated by SSE/AVX instruction sets and parallelized. The code solves the standard set of hydrodynamic equations, using the Tillotson equation of state, von Mises criterion for plastic yielding and scalar Grady-Kipp model for fragmentation. We further modified the velocity gradient by a correction tensor (Schäfer et al. 2007) to ensure a first-order conservation of the total angular momentum. As the intact target is a spherical body, its gravity can be approximated by a potential of a homogeneous sphere, making it easy to set up initial conditions. This is however infeasible for later stages of the disruption; to this point, we included the Barnes-Hut algorithm to compute the gravitational accelerations, using a multipole expansion of distant particles up to hexadecapole order.We tested the code carefully, comparing the results to our previous computations obtained with the SPH5 code (Benz and Asphaug 1994). Finally, we ran a set of simulations and we discuss the difference between the synthetic families created by rotating and static targets.

Towards a formalism for mapping the spacetimes of massive compact objects: Bumpy black holes and their orbits

NASA Astrophysics Data System (ADS)

Collins, Nathan A.; Hughes, Scott A.

2004-06-01

Astronomical observations have established that extremely compact, massive objects are common in the Universe. It is generally accepted that these objects are, in all likelihood, black holes. As observational technology has improved, it has become possible to test this hypothesis in ever greater detail. In particular, it is or will be possible to measure the properties of orbits deep in the strong field of a black hole candidate (using x-ray timing or future gravitational-wave measurements) and to test whether they have the characteristics of black hole orbits in general relativity. Past work has shown that, in principle, such measurements can be used to map the spacetime of a massive compact object, testing in particular whether the object’s multipolar structure satisfies the rather strict constraints imposed by the black hole hypothesis. Performing such a test in practice requires that we be able to compare against objects with the “wrong” multipole structure. In this paper, we present tools for constructing the spacetimes of bumpy black holes: objects that are almost black holes, but that have some multipoles with the wrong value. In this first analysis, we focus on objects with no angular momentum. Generalization to bumpy Kerr black holes should be straightforward, albeit labor intensive. Our construction has two particularly desirable properties. First, the spacetimes which we present are good deep into the strong field of the object—we do not use a “large r” expansion (except to make contact with weak field intuition). Second, our spacetimes reduce to the exact black hole spacetimes of general relativity in a natural way, by dialing the “bumpiness” of the black hole to zero. We propose that bumpy black holes can be used as the foundation for a null experiment: if black hole candidates are indeed the black holes of general relativity, their bumpiness should be zero. By comparing the properties of orbits in a bumpy spacetime with those measured from an astrophysical source, observations should be able to test this hypothesis, stringently testing whether they are in fact the black holes of general relativity.

Earthquake models using rate and state friction and fast multipoles

NASA Astrophysics Data System (ADS)

Tullis, T.

2003-04-01

The most realistic current earthquake models employ laboratory-derived non-linear constitutive laws. These are the rate and state friction laws having both a non-linear viscous or direct effect and an evolution effect in which frictional resistance depends on time of stationary contact and has a memory of past slip velocity that fades with slip. The frictional resistance depends on the log of the slip velocity as well as the log of stationary hold time, and the fading memory involves an approximately exponential decay with slip. Due to the nonlinearly of these laws, analytical earthquake models are not attainable and numerical models are needed. The situation is even more difficult if true dynamic models are sought that deal with inertial forces and slip velocities on the order of 1 m/s as are observed during dynamic earthquake slip. Additional difficulties that exist if the dynamic slip phase of earthquakes is modeled arise from two sources. First, many physical processes might operate during dynamic slip, but they are only poorly understood, the relative importance of the processes is unknown, and the processes are even more nonlinear than those described by the current rate and state laws. Constitutive laws describing such behaviors are still being developed. Second, treatment of inertial forces and the influence that dynamic stresses from elastic waves may have on slip on the fault requires keeping track of the history of slip on remote parts of the fault as far into the past as it takes waves to travel from there. This places even more stringent requirements on computer time. Challenges for numerical modeling of complete earthquake cycles are that both time steps and mesh sizes must be small. Time steps must be milliseconds during dynamic slip, and yet models must represent earthquake cycles 100 years or more in length; methods using adaptive step sizes are essential. Element dimensions need to be on the order of meters, both to approximate continuum behavior adequately and to model microseismicity as well as large earthquakes. In order to model significant sized earthquakes this requires millions of elements. Modeling methods like the boundary element method that involve Green's functions normally require computation times that increase with the number N of elements squared, so using large N becomes impossible. We have adapted the Fast Multipole method to this problem in which the influence of sufficiently remote elements are grouped together and the elements are indexed such that the computations more efficient when run on parallel computers. Compute time varies with N log N rather than N squared. Computer programs are available that use this approach (http://www.servogrid.org/slide/GEM/PARK). Whether the multipole approach can be adapted to dynamic modeling is unclear.

Harmonic Kicker RF Cavity for the Jefferson Lab Electron-Ion Collider EM Simulation, Modification, and Measurements

NASA Astrophysics Data System (ADS)

Overstreet, Sarah; Wang, Haipeng

2017-09-01

An important step in the conceptual design for the future Jefferson Lab Electron-Ion Collider (JLEIC) is the development of supporting technologies for the Energy Recovery Linac (ERL) Electron Cooling Facility. The Harmonic Radiofrequency (RF) kicker cavity is one such device that is responsible for switching electron bunches in and out of the Circulator Cooling Ring (CCR) from and to the ERL, which is a critical part of the ion cooling process. Last year, a half scale prototype of the JLEIC harmonic RF kicker model was designed with resonant frequencies to support the summation of 5 odd harmonics (95.26 MHz, 285.78 MHz, 476.30 MHz, 666.82 MHz, and 857.35 MHz); however, the asymmetry of the kicker cavity gives rise to multipole components of the electric field at the electron-beam axis of the cavity. Previous attempts to symmetrize the electric field of this asymmetrical RF cavity have been unsuccessful. The aim of this study is to modify the existing prototype for a uniform electric field across the beam pathway so that the electron bunches will experience nearly zero beam current loading. In addition to this, we have driven the unmodified cavity with the harmonic sum and used the wire stretching method for an analysis of the multipole electric field components.

Characterization of low-pressure microwave and radio frequency discharges in oxygen applying optical emission spectroscopy and multipole resonance probe

NASA Astrophysics Data System (ADS)

Steves, Simon; Styrnoll, Tim; Mitschker, Felix; Bienholz, Stefan; Nikita, Bibinov; Awakowicz, Peter

2013-11-01

Optical emission spectroscopy (OES) and multipole resonance probe (MRP) are adopted to characterize low-pressure microwave (MW) and radio frequency (RF) discharges in oxygen. In this context, both discharges are usually applied for the deposition of permeation barrier SiOx films on plastic foils or the inner surface of plastic bottles. For technological reasons the MW excitation is modulated and a continuous wave (cw) RF bias is used. The RF voltage produces a stationary low-density plasma, whereas the high-density MW discharge is pulsed. For the optimization of deposition process and the quality of the deposited barrier films, plasma conditions are characterized using OES and MRP. To simplify the comparison of applied diagnostics, both MW and RF discharges are studied separately in cw mode. The OES and MRP diagnostic methods complement each other and provide reliable information about electron density and electron temperature. In the MW case, electron density amounts to ne = (1.25 ± 0.26) × 1017 m-3, and kTe to 1.93 ± 0.20 eV, in the RF case ne = (6.8 ± 1.8)×1015 m-3 and kTe = 2.6 ± 0.35 eV. The corresponding gas temperatures are 760±40 K and 440±20 K.

Electromagnetic Launch Vehicle Fairing and Acoustic Blanket Model of Received Power Using FEKO

NASA Technical Reports Server (NTRS)

Trout, Dawn H.; Stanley, James E.; Wahid, Parveen F.

2011-01-01

Evaluating the impact of radio frequency transmission in vehicle fairings is important to sensitive spacecraft. This paper employees the Multilevel Fast Multipole Method (MLFMM) feature of a commercial electromagnetic tool to model the fairing electromagnetic environment in the presence of an internal transmitter. This work is an extension of the perfect electric conductor model that was used to represent the bare aluminum internal fairing cavity. This fairing model includes typical acoustic blanketing commonly used in vehicle fairings. Representative material models within FEKO were successfully used to simulate the test case.

The polarization observables T, P, and H and their impact on γp → pπ0 multipoles

NASA Astrophysics Data System (ADS)

Hartmann, J.; Dutz, H.; Anisovich, A. V.; Bayadilov, D.; Beck, R.; Becker, M.; Beloglazov, Y.; Berlin, A.; Bichow, M.; Böse, S.; Brinkmann, K.-Th.; Crede, V.; Dieterle, M.; Eberhardt, H.; Elsner, D.; Fornet-Ponse, K.; Friedrich, St.; Frommberger, F.; Funke, Ch.; Gottschall, M.; Gridnev, A.; Grüner, M.; Goertz, St.; Gutz, E.; Hammann, Ch.; Hannappel, J.; Hannen, V.; Herick, J.; Hillert, W.; Hoffmeister, Ph.; Honisch, Ch.; Jahn, O.; Jude, T.; Käser, A.; Kaiser, D.; Kalinowsky, H.; Kalischewski, F.; Klassen, P.; Keshelashvili, I.; Klein, F.; Klempt, E.; Koop, K.; Krusche, B.; Kube, M.; Lang, M.; Lopatin, I.; Makonyi, K.; Messi, F.; Metag, V.; Meyer, W.; Müller, J.; Nanova, M.; Nikonov, V.; Novinski, D.; Novotny, R.; Piontek, D.; Reeve, S.; Rosenbaum, Ch.; Roth, B.; Reicherz, G.; Rostomyan, T.; Runkel, St.; Sarantsev, A.; Schmidt, Ch.; Schmieden, H.; Schmitz, R.; Seifen, T.; Sokhoyan, V.; Thämer, Ph.; Thiel, A.; Thoma, U.; Urban, M.; van Pee, H.; Walther, D.; Wendel, Ch.; Wiedner, U.; Wilson, A.; Winnebeck, A.; Witthauer, L.

2015-09-01

Data on the polarization observables T, P, and H for the reaction γp → pπ0 are reported. Compared to earlier data from other experiments, our data are more precise and extend the covered range in energy and angle substantially. The results were extracted from azimuthal asymmetries measured using a transversely polarized target and linearly polarized photons. The data were taken at the Bonn electron stretcher accelerator ELSA with the CBELSA/TAPS detector. Within the Bonn-Gatchina partial wave analysis, the new polarization data lead to a significant narrowing of the error band for the multipoles for neutral-pion photoproduction.

On the existence of black holes in distorted Schwarzschild spacetime using marginally trapped surfaces

NASA Astrophysics Data System (ADS)

Pilkington, Terry

The classical definition of a black hole in terms of an event horizon relies on global properties of the spacetime. Realistic black holes have matter distributions surrounding them, which negates the asymptotic flatness needed for an event horizon. Using the (quasi-)local concept of marginally trapped surfaces, we investigate the Schwarzschild spacetime distorted by an axisymmetric matter distribution. We determine that it is possible to locate a future outer trapping horizon for a given foliation within certain value ranges of multipole moments. Furthermore, we show that there are no marginally trapped surfaces for arbitrary values of the multipole moment magnitudes. KEYWORDS: SCHWARZSCHILD; BLACK HOLE; DISTORTED SPACETIME; MARGINALLY TRAPPED SURFACE; FUTURE OUTER TRAPPING HORIZON

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.

Experimental investigations of argon and xenon ion sources

NASA Technical Reports Server (NTRS)

Kaufman, H. R.

1975-01-01

The multipole thruster was used to investigate the use of argon and xenon propellants as possible alternatives to the electric thruster propellants of mercury and cesium. The multipole approach was used because of its general high performance level. The design employed, using flat and cylindrical rolled sections of sheet metal, was selected for ease of fabrication, design, assembly, and modification. All testing was conducted in a vacuum facility and the pumping was accomplished by a 0.8 m diffusion pump together with liquid nitrogen cooled liner. Minimum discharge losses were in the 200-250 ev. ion range for both argon and xenon. Flatness parameters were typically in the 0.70-0.75 range.

General quadrupolar statistical anisotropy: Planck limits

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

Ramazanov, S.; Rubtsov, G.; Thorsrud, M.

2017-03-01

Several early Universe scenarios predict a direction-dependent spectrum of primordial curvature perturbations. This translates into the violation of the statistical isotropy of cosmic microwave background radiation. Previous searches for statistical anisotropy mainly focussed on a quadrupolar direction-dependence characterised by a single multipole vector and an overall amplitude g {sub *}. Generically, however, the quadrupole has a more complicated geometry described by two multipole vectors and g {sub *}. This is the subject of the present work. In particular, we limit the amplitude g {sub *} for different shapes of the quadrupole by making use of Planck 2015 maps. We alsomore » constrain certain inflationary scenarios which predict this kind of more general quadrupolar statistical anisotropy.« less

Possible connection between the location of the cutoff in the cosmic microwave background spectrum and the equation of state of dark energy.

PubMed

Enqvist, Kari; Sloth, Martin S

2004-11-26

We investigate a possible connection between the suppression of the power at low multipoles in the cosmic microwave background (CMB) spectrum and the late time acceleration. We show that, assuming a cosmic IR/UV duality between the UV cutoff and a global infrared cutoff given by the size of the future event horizon, the equation of state of the dark energy can be related to the apparent cutoff in the CMB spectrum. The present limits on the equation of state of dark energy are shown to imply an IR cutoff in the CMB multipole interval of 9>l>8.5.

Anapoles in Free-Standing III-V Nanodisks Enhancing Second-Harmonic Generation.

PubMed

Timofeeva, Maria; Lang, Lukas; Timpu, Flavia; Renaut, Claude; Bouravleuv, Alexei; Shtrom, Igor; Cirlin, George; Grange, Rachel

2018-06-13

Nonradiating electromagnetic configurations in nanostructures open new horizons for applications due to two essential features: a lack of energy losses and invisibility to the propagating electromagnetic field. Such radiationless configurations form a basis for new types of nanophotonic devices, in which a strong electromagnetic field confinement can be achieved together with lossless interactions between nearby components. In our work, we present a new design of free-standing disk nanoantennas with nonradiating current distributions for the optical near-infrared range. We show a novel approach to creating nanoantennas by slicing III-V nanowires into standing disks using focused ion-beam milling. We experimentally demonstrate the suppression of the far-field radiation and the associated strong enhancement of the second-harmonic generation from the disk nanoantennas. With a theoretical analysis of the electromagnetic field distribution using multipole expansions in both spherical and Cartesian coordinates, we confirm that the demonstrated nonradiating configurations are anapoles. We expect that the presented procedure of designing and producing disk nanoantennas from nanowires becomes one of the standard approaches to fabricating controlled chains of standing nanodisks with different designs and configurations. These chains can be essential building blocks for new types of lasers and sensors with low power consumption.

Vortices for K-shell ionization of carbon by electron impact

NASA Astrophysics Data System (ADS)

Ward, S. J.; Macek, J. H.

2014-05-01

Using the Coulomb-Born approximation, we obtained a deep minimum in the TDCS for K-shell ionization of carbon by electron impact. The minimum is due to a vortex in the velocity field. We considered the electron to be ejected in the scattering plane, which we took to be the xz -plane. The minimum was obtained for the kinematics of an incident energy Ei = 1801 . 2 eV , scattering angle θf =4° , energy of ejected electron Ek = 5 . 5 eV , and angle of the ejected electron θk =239° . We analyzed the importance of various multipole components in an expansion of the Coulomb-Born T-matrix. We also considered the electron ejected out of the scattering plane for Ei = 1801 . 2 eV and θf =4° and located the positions of vortices for small but nonzero values of ky, the y - component of the momentum of the ejected electron. We constructed the vortex line for the kinematics of Ei = 1801 . 2 eV and θf =4° . S. J. W. and J. H. M. acknowledge support from NSF under grant no. PHYS- 0968638 and from D.O.E. under grant number DE-FG02-02ER15283, respectively.

On the Inversion for Mass (Re)Distribution from Global (Time-Variable) Gravity Field

NASA Technical Reports Server (NTRS)

Chao, Benjamin F.

2004-01-01

The well-known non-uniqueness of the gravitational inverse problem states the following: The external gravity field, even if completely and exactly known, cannot Uniquely determine the density distribution of the body that produces the gravity field. This is an intrinsic property of a field that obeys the Laplace equation, as already treated in mathematical as well as geophysical literature. In this paper we provide conceptual insight by examining the problem in terms of spherical harmonic expansion of the global gravity field. By comparing the multipoles and the moments of the density function, we show that in 3-S the degree of knowledge deficiency in trying to inversely recover the density distribution from external gravity field is (n+l)(n+2)/2 - (2n+l) = n(n-1)/2 for each harmonic degree n. On the other hand, on a 2-D spherical shell we show via a simple relationship that the inverse solution of the surface density distribution is unique. The latter applies quite readily in the inversion of time-variable gravity signals (such as those observed by the GRACE space mission) where the sources over a wide range of the scales largely come from the Earth's Surface.

Design, simulation and testing of a novel radial multi-pole multi-layer magnetorheological brake

NASA Astrophysics Data System (ADS)

Wu, Jie; Li, Hua; Jiang, Xuezheng; Yao, Jin

2018-02-01

This paper deals with design, simulation and experimental testing of a novel radial multi-pole multi-layer magnetorheological (MR) brake. This MR brake has an innovative structural design with superposition principle of two magnetic fields generated by the inner coils and the outer coils. The MR brake has several media layers of magnetorheological (MR) fluid located between the inner coils and the outer coils, and it can provide higher torque and higher torque density than conventional single-disk or multi-disk or multi-pole single-layer MR brakes can. In this paper, a brief introduction to the structure of the proposed MR brake was given first. Then, theoretical analysis of the magnetic circuit and the braking torque was conducted. In addition, a 3D electromagnetic model of the MR brake was developed to simulate and examine the magnetic flux intensity and corresponding braking torque. A prototype of the brake was fabricated and several tests were carried out to validate its torque capacity. The results show that the proposed MR brake can produce a maximum braking torque of 133 N m and achieve a high torque density of 25.0 kN m-2, a high torque range of 42 and a high torque-to-power ratio of 0.95 N m W-1.

Anatomy of the binary black hole recoil: A multipolar analysis

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

Schnittman, Jeremy D.; Buonanno, Alessandra; Meter, James R. van

2008-02-15

We present a multipolar analysis of the gravitational recoil computed in recent numerical simulations of binary black hole coalescence, for both unequal masses and nonzero, nonprecessing spins. We show that multipole moments up to and including l=4 are sufficient to accurately reproduce the final recoil velocity (within {approx_equal}2%) and that only a few dominant modes contribute significantly to it (within {approx_equal}5%). We describe how the relative amplitudes, and more importantly, the relative phases, of these few modes control the way in which the recoil builds up throughout the inspiral, merger, and ringdown phases. We also find that the numerical resultsmore » can be reproduced by an 'effective Newtonian' formula for the multipole moments obtained by replacing the radial separation in the Newtonian formulas with an effective radius computed from the numerical data. Beyond the merger, the numerical results are reproduced by a superposition of three Kerr quasinormal modes. Analytic formulas, obtained by expressing the multipole moments in terms of the fundamental quasinormal modes of a Kerr black hole, are able to explain the onset and amount of 'antikick' for each of the simulations. Lastly, we apply this multipolar analysis to help explain the remarkable difference between the amplitudes of planar and nonplanar kicks for equal-mass spinning black holes.« less

Anatomy of the Binary Black Hole Recoil: A Multipolar Analysis

NASA Technical Reports Server (NTRS)

Schnittman, Jeremy; Buonanno, Alessandra; vanMeter, James R.; Baker, John G.; Boggs, William D.; Centrella, Joan; Kelly, Bernard J.; McWilliams, Sean T.

2007-01-01

We present a multipolar analysis of the recoil velocity computed in recent numerical simulations of binary black hole coalescence, for both unequal masses and non-zero, non-precessing spins. We show that multipole moments up to and including 1 = 4 are sufficient to accurately reproduce the final recoil velocity (= 98%) and that only a few dominant modes contribute significantly to it (2 95%). We describe how the relative amplitude, and more importantly, the relative phase, of these few modes control the way in which the recoil builds up throughout the inspiral, merger, and ring-down phases. We also find that the numerical results can be reproduced, to a high level of accuracy, by an effective Newtonian formula for the multipole moments obtained by replacing in the Newtonian formula the radial separation with an effective radius computed from the numerical data. Beyond the merger, the numerical results are reproduced by a superposition of three Kerr quasi-normal modes. Analytic formulae, obtained by expressing the multipole moments in terms of the fundamental QNMs of a Kerr BH, are able to explain the onset and amount of '.anti-kick" for each of the simulations. Lastly, we apply this multipolar analysis to understand the remarkable difference between the amplitudes of planar and non-planar kicks for equal-mass spinning black holes.

Rectangular beam (5 X 40 cm multipole ion source). M.S. Thesis - Nov. 1979; [applications to electron bombardment in materials processing

NASA Technical Reports Server (NTRS)

Haynes, C. M.

1980-01-01

A 5 x 40 cm rectangular-beam ion source was designed and fabricated. A multipole field configuration was used to facilitate design of the modular rectangular chamber, while a three-grid ion optics system was used for increased ion current densities. For the multipole chamber, a magnetic integral of 0.000056 Tesla-m was used to contain the primary electrons. This integral value was reduced from the initial design value, with the reduction found necessary for discharge stability. The final value of magnetic integral resulted in discharge losses at typical operating conditions which ranged from 600 to 1000 eV/ion, in good agreement with the design value of 800 eV/ion. The beam current density at the ion optics was limited to about 3.2 mA/sq cm at 500 eV and to about 3.5 mA/sq cm at 1000 ev. The effects of nonuniform ion current, dimension tolerance, and grid thermal warping were considered. The use of multiple rectangular-beam ion sources to process wider areas than would be possible with a single source (approx. 40 cm) was also studied. Beam profiles were surveyed at a variety of operating conditions and the results of various amounts of beam overlap calculated.

Vector matter waves in two-component Bose-Einstein condensates with spatially modulated nonlinearities

NASA Astrophysics Data System (ADS)

Xu, Si-Liu; He, Jun-Rong; Xue, Li; Belić, Milivoj R.

2018-02-01

We demonstrate three-dimensional (3D) vector solitary waves in the coupled (3 + 1)-D nonlinear Gross-Pitaevskii equations with variable nonlinearity coefficients. The analysis is carried out in spherical coordinates, providing novel localized solutions that depend on three modal numbers, l, m, and n. Using the similarity transformation (ST) method in 3D, vector solitary waves are built with the help of a combination of harmonic and trapping potentials, including multipole solutions and necklace rings. In general, the solutions found are stable for low values of the modal numbers; for values larger than 2, the solutions are found to be unstable. Variable nonlinearity allows the utilization of soliton management methods.

Neutrino and dark radiation properties in light of recent CMB observations

NASA Astrophysics Data System (ADS)

Archidiacono, Maria; Giusarma, Elena; Melchiorri, Alessandro; Mena, Olga

2013-05-01

Recent cosmic microwave background measurements at high multipoles from the South Pole Telescope and from the Atacama Cosmology Telescope seem to disagree in their conclusions for the neutrino and dark radiation properties. In this paper we set new bounds on the dark radiation and neutrino properties in different cosmological scenarios combining the ACT and SPT data with the nine-year data release of the Wilkinson Microwave Anisotropy Probe (WMAP-9), baryon acoustic oscillation data, Hubble Telescope measurements of the Hubble constant, and supernovae Ia luminosity distance data. In the standard three massive neutrino case, the two high multipole probes give similar results if baryon acoustic oscillation data are removed from the analyses and Hubble Telescope measurements are also exploited. A similar result is obtained within a standard cosmology with Neff massless neutrinos, although in this case the agreement between these two measurements is also improved when considering simultaneously baryon acoustic oscillation data and Hubble Space Telescope measurements. In the Neff massive neutrino case the two high multipole probes give very different results regardless of the external data sets used in the combined analyses. When considering extended cosmological scenarios with a dark energy equation of state or with a running of the scalar spectral index, the evidence for neutrino masses found for the South Pole Telescope in the three neutrino scenario disappears for all the data combinations explored here. Again, adding Hubble Telescope data seems to improve the agreement between the two high multipole cosmic microwave background measurements considered here. In the case in which a dark radiation background with unknown clustering properties is also considered, SPT data seem to exclude the standard value for the dark radiation viscosity cvis2=1/3 at the 2σ C.L., finding evidence for massive neutrinos only when combining SPT data with baryon acoustic oscillation measurements.

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

Aylor, K.; Hou, Z.; Knox, L.

The Planck cosmic microwave background temperature data are best fit with a Lambda CDM model that mildly contradicts constraints from other cosmological probes. The South Pole Telescope (SPT) 2540 deg(2) SPT-SZ survey offers measurements on sub-degree angular scales (multipoles 650 <= l <= 2500) with sufficient precision to use as an independent check of the Planck data. Here we build on the recent joint analysis of the SPT-SZ and Planck data in Hou et al. by comparing Lambda CDM parameter estimates using the temperature power spectrum from both data sets in the SPT-SZ survey region. We also restrict the multipolemore » range used in parameter fitting to focus on modes measured well by both SPT and Planck, thereby greatly reducing sample variance as a driver of parameter differences and creating a stringent test for systematic errors. We find no evidence of systematic errors from these tests. When we expand the maximum multipole of SPT data used, we see low-significance shifts in the angular scale of the sound horizon and the physical baryon and cold dark matter densities, with a resulting trend to higher Hubble constant. When we compare SPT and Planck data on the SPT-SZ sky patch to Planck full-sky data but keep the multipole range restricted, we find differences in the parameters n(s) and A(s)e(-2 tau). We perform further checks, investigating instrumental effects and modeling assumptions, and we find no evidence that the effects investigated are responsible for any of the parameter shifts. Taken together, these tests reveal no evidence for systematic errors in SPT or Planck data in the overlapping sky coverage and multipole range and at most weak evidence for a breakdown of Lambda CDM or systematic errors influencing either the Planck data outside the SPT-SZ survey area or the SPT data at l > 2000.« less

High-Resolution Crystal Structures of Protein Helices Reconciled with Three-Centered Hydrogen Bonds and Multipole Electrostatics

PubMed Central

Kuster, Daniel J.; Liu, Chengyu; Fang, Zheng; Ponder, Jay W.; Marshall, Garland R.

2015-01-01

Theoretical and experimental evidence for non-linear hydrogen bonds in protein helices is ubiquitous. In particular, amide three-centered hydrogen bonds are common features of helices in high-resolution crystal structures of proteins. These high-resolution structures (1.0 to 1.5 Å nominal crystallographic resolution) position backbone atoms without significant bias from modeling constraints and identify Φ = -62°, ψ = -43 as the consensus backbone torsional angles of protein helices. These torsional angles preserve the atomic positions of α-β carbons of the classic Pauling α-helix while allowing the amide carbonyls to form bifurcated hydrogen bonds as first suggested by Némethy et al. in 1967. Molecular dynamics simulations of a capped 12-residue oligoalanine in water with AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications), a second-generation force field that includes multipole electrostatics and polarizability, reproduces the experimentally observed high-resolution helical conformation and correctly reorients the amide-bond carbonyls into bifurcated hydrogen bonds. This simple modification of backbone torsional angles reconciles experimental and theoretical views to provide a unified view of amide three-centered hydrogen bonds as crucial components of protein helices. The reason why they have been overlooked by structural biologists depends on the small crankshaft-like changes in orientation of the amide bond that allows maintenance of the overall helical parameters (helix pitch (p) and residues per turn (n)). The Pauling 3.613 α-helix fits the high-resolution experimental data with the minor exception of the amide-carbonyl electron density, but the previously associated backbone torsional angles (Φ, Ψ) needed slight modification to be reconciled with three-atom centered H-bonds and multipole electrostatics. Thus, a new standard helix, the 3.613/10-, Némethy- or N-helix, is proposed. Due to the use of constraints from monopole force fields and assumed secondary structures used in low-resolution refinement of electron density of proteins, such structures in the PDB often show linear hydrogen bonding. PMID:25894612

High-resolution crystal structures of protein helices reconciled with three-centered hydrogen bonds and multipole electrostatics.

PubMed

Kuster, Daniel J; Liu, Chengyu; Fang, Zheng; Ponder, Jay W; Marshall, Garland R

2015-01-01

Theoretical and experimental evidence for non-linear hydrogen bonds in protein helices is ubiquitous. In particular, amide three-centered hydrogen bonds are common features of helices in high-resolution crystal structures of proteins. These high-resolution structures (1.0 to 1.5 Å nominal crystallographic resolution) position backbone atoms without significant bias from modeling constraints and identify Φ = -62°, ψ = -43 as the consensus backbone torsional angles of protein helices. These torsional angles preserve the atomic positions of α-β carbons of the classic Pauling α-helix while allowing the amide carbonyls to form bifurcated hydrogen bonds as first suggested by Némethy et al. in 1967. Molecular dynamics simulations of a capped 12-residue oligoalanine in water with AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications), a second-generation force field that includes multipole electrostatics and polarizability, reproduces the experimentally observed high-resolution helical conformation and correctly reorients the amide-bond carbonyls into bifurcated hydrogen bonds. This simple modification of backbone torsional angles reconciles experimental and theoretical views to provide a unified view of amide three-centered hydrogen bonds as crucial components of protein helices. The reason why they have been overlooked by structural biologists depends on the small crankshaft-like changes in orientation of the amide bond that allows maintenance of the overall helical parameters (helix pitch (p) and residues per turn (n)). The Pauling 3.6(13) α-helix fits the high-resolution experimental data with the minor exception of the amide-carbonyl electron density, but the previously associated backbone torsional angles (Φ, Ψ) needed slight modification to be reconciled with three-atom centered H-bonds and multipole electrostatics. Thus, a new standard helix, the 3.6(13/10)-, Némethy- or N-helix, is proposed. Due to the use of constraints from monopole force fields and assumed secondary structures used in low-resolution refinement of electron density of proteins, such structures in the PDB often show linear hydrogen bonding.

Fast Multipole Methods for Three-Dimensional N-body Problems

NASA Technical Reports Server (NTRS)

Koumoutsakos, P.

1995-01-01

We are developing computational tools for the simulations of three-dimensional flows past bodies undergoing arbitrary motions. High resolution viscous vortex methods have been developed that allow for extended simulations of two-dimensional configurations such as vortex generators. Our objective is to extend this methodology to three dimensions and develop a robust computational scheme for the simulation of such flows. A fundamental issue in the use of vortex methods is the ability of employing efficiently large numbers of computational elements to resolve the large range of scales that exist in complex flows. The traditional cost of the method scales as Omicron (N(sup 2)) as the N computational elements/particles induce velocities at each other, making the method unacceptable for simulations involving more than a few tens of thousands of particles. In the last decade fast methods have been developed that have operation counts of Omicron (N log N) or Omicron (N) (referred to as BH and GR respectively) depending on the details of the algorithm. These methods are based on the observation that the effect of a cluster of particles at a certain distance may be approximated by a finite series expansion. In order to exploit this observation we need to decompose the element population spatially into clusters of particles and build a hierarchy of clusters (a tree data structure) - smaller neighboring clusters combine to form a cluster of the next size up in the hierarchy and so on. This hierarchy of clusters allows one to determine efficiently when the approximation is valid. This algorithm is an N-body solver that appears in many fields of engineering and science. Some examples of its diverse use are in astrophysics, molecular dynamics, micro-magnetics, boundary element simulations of electromagnetic problems, and computer animation. More recently these N-body solvers have been implemented and applied in simulations involving vortex methods. Koumoutsakos and Leonard (1995) implemented the GR scheme in two dimensions for vector computer architectures allowing for simulations of bluff body flows using millions of particles. Winckelmans presented three-dimensional, viscous simulations of interacting vortex rings, using vortons and an implementation of a BH scheme for parallel computer architectures. Bhatt presented a vortex filament method to perform inviscid vortex ring interactions, with an alternative implementation of a BH scheme for a Connection Machine parallel computer architecture.

Hyper-Rayleigh scattering in centrosymmetric systems

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

Williams, Mathew D.; Ford, Jack S.; Andrews, David L., E-mail: david.andrews@physics.org

Hyper-Rayleigh scattering (HRS) is an incoherent mechanism for optical second harmonic generation. The frequency-doubled light that emerges from this mechanism is not emitted in a laser-like manner, in the forward direction; it is scattered in all directions. The underlying theory for this effect involves terms that are quadratic in the incident field and involves an even-order optical susceptibility (for a molecule, its associated hyperpolarizability). In consequence, HRS is often regarded as formally forbidden in centrosymmetric media. However, for the fundamental three-photon interaction, theory based on the standard electric dipole approximation, representable as E1{sup 3}, does not account for all experimentalmore » observations. The relevant results emerge upon extending the theory to include E1{sup 2}M1 and E1{sup 2}E2 contributions, incorporating one magnetic dipolar or electric quadrupolar interaction, respectively, to a consistent level of multipolar expansion. Both additional interactions require the deployment of higher orders in the multipole expansion, with the E1{sup 2}E2 interaction analogous in rank and parity to a four-wave susceptibility. To elicit the correct form of response from fluid or disordered media invites a tensor representation which does not oversimplify the molecular components, yet which can produce results to facilitate the interpretation of experimental observations. The detailed derivation in this work leads to results which are summarized for the following: perpendicular detection of polarization components both parallel and perpendicular to the pump radiation, leading to distinct polarization ratio results, as well as a reversal ratio for forward scattered circular polarizations. The results provide a route to handling data with direct physical interpretation, to enable the more sophisticated design of molecules with sought nonlinear optical properties.« less

Hyper-Rayleigh scattering in centrosymmetric systems

NASA Astrophysics Data System (ADS)

Williams, Mathew D.; Ford, Jack S.; Andrews, David L.

2015-09-01

Hyper-Rayleigh scattering (HRS) is an incoherent mechanism for optical second harmonic generation. The frequency-doubled light that emerges from this mechanism is not emitted in a laser-like manner, in the forward direction; it is scattered in all directions. The underlying theory for this effect involves terms that are quadratic in the incident field and involves an even-order optical susceptibility (for a molecule, its associated hyperpolarizability). In consequence, HRS is often regarded as formally forbidden in centrosymmetric media. However, for the fundamental three-photon interaction, theory based on the standard electric dipole approximation, representable as E13, does not account for all experimental observations. The relevant results emerge upon extending the theory to include E12M1 and E12E2 contributions, incorporating one magnetic dipolar or electric quadrupolar interaction, respectively, to a consistent level of multipolar expansion. Both additional interactions require the deployment of higher orders in the multipole expansion, with the E12E2 interaction analogous in rank and parity to a four-wave susceptibility. To elicit the correct form of response from fluid or disordered media invites a tensor representation which does not oversimplify the molecular components, yet which can produce results to facilitate the interpretation of experimental observations. The detailed derivation in this work leads to results which are summarized for the following: perpendicular detection of polarization components both parallel and perpendicular to the pump radiation, leading to distinct polarization ratio results, as well as a reversal ratio for forward scattered circular polarizations. The results provide a route to handling data with direct physical interpretation, to enable the more sophisticated design of molecules with sought nonlinear optical properties.

Non-linear non-local molecular electrodynamics with nano-optical fields.

PubMed

Chernyak, Vladimir Y; Saurabh, Prasoon; Mukamel, Shaul

2015-10-28

The interaction of optical fields sculpted on the nano-scale with matter may not be described by the dipole approximation since the fields may vary appreciably across the molecular length scale. Rather than incrementally adding higher multipoles, it is advantageous and more physically transparent to describe the optical process using non-local response functions that intrinsically include all multipoles. We present a semi-classical approach for calculating non-local response functions based on the minimal coupling Hamiltonian. The first, second, and third order response functions are expressed in terms of correlation functions of the charge and the current densities. This approach is based on the gauge invariant current rather than the polarization, and on the vector potential rather than the electric and magnetic fields.

Planar Multipol-Resonance-Probe: A Spectral Kinetic Approach

NASA Astrophysics Data System (ADS)

Friedrichs, Michael; Gong, Junbo; Brinkmann, Ralf Peter; Oberrath, Jens; Wilczek, Sebastian

2016-09-01

Measuring plasma parameters, e.g. electron density and electron temperature, is an important procedure to verify the stability and behavior of a plasma process. For this purpose the multipole resonance probe (MRP) represents a satisfying solution to measure the electron density. However the influence of the probe on the plasma through its physical presence makes it unattractive for some processes in industrial application. A solution to combine the benefits of the spherical MRP with the ability to integrate the probe into the plasma reactor is introduced by the planar model of the MRP (pMRP). Introducing the spectral kinetic formalism leads to a reduced simulation-circle compared to particle-in-cell simulations. The model of the pMRP is implemented and first simulation results are presented.

Can cosmic shear shed light on low cosmic microwave background multipoles?

PubMed

Kesden, Michael; Kamionkowski, Marc; Cooray, Asantha

2003-11-28

The lowest multipole moments of the cosmic microwave background (CMB) are smaller than expected for a scale-invariant power spectrum. One possible explanation is a cutoff in the primordial power spectrum below a comoving scale of k(c) approximately equal to 5.0 x 10(-4) Mpc(-1). Such a cutoff would increase significantly the cross correlation between the large-angle CMB and cosmic-shear patterns. The cross correlation may be detectable at >2sigma which, combined with the low CMB moments, may tilt the balance between a 2sigma result and a firm detection of a large-scale power-spectrum cutoff. The cutoff also increases the large-angle cross correlation between the CMB and the low-redshift tracers of the mass distribution.

Low-energy nuclear spectroscopy in a microscopic multiphonon approach

NASA Astrophysics Data System (ADS)

Lo Iudice, N.; Ponomarev, V. Yu; Stoyanov, Ch; Sushkov, A. V.; Voronov, V. V.

2012-04-01

The low-lying spectra of heavy nuclei are investigated within the quasiparticle-phonon model. This microscopic approach goes beyond the quasiparticle random-phase approximation by treating a Hamiltonian of separable form in a microscopic multiphonon basis. It is therefore able to describe the anharmonic features of collective modes as well as the multiphonon states, whose experimental evidence is continuously growing. The method can be put in close correspondence with the proton-neutron interacting boson model. By associating the microscopic isoscalar and isovector quadrupole phonons with proton-neutron symmetric and mixed-symmetry quadrupole bosons, respectively, the microscopic states can be classified, just as in the algebraic model, according to their phonon content and their symmetry. In addition, these states disclose the nuclear properties which are to be ascribed to genuine shell effects, not included in the algebraic approach. Due to its flexibility, the method can be implemented numerically for systematic studies of spectroscopic properties throughout entire regions of vibrational nuclei. The spectra and multipole transition strengths so computed are in overall good agreement with the experimental data. By exploiting the correspondence of the method with the interacting boson model, it is possible to embed the microscopic states into this algebraic frame and, therefore, face the study of nuclei far from shell closures, not directly accessible to merely microscopic approaches. Here, it is shown how this task is accomplished through systematic investigations of magnetic dipole and, especially, electric dipole modes along paths moving from the vibrational to the transitional regions. The method is very well suited to the study of well-deformed nuclei. It provides reliable descriptions of low-lying magnetic as well as electric multipole modes of nuclei throughout the rare-earth and actinide regions. Attention is focused here on the low-lying 0+ states produced in large abundance in recent experiments. The analysis shows that the quasiparticle-phonon model accounts for the occurrence of so many 0+ levels and discloses their nature.

Kinetic Description of the Impedance Probe

NASA Astrophysics Data System (ADS)

Oberrath, Jens; Lapke, Martin; Mussenbrock, Thomas; Brinkmann, Ralf

2011-10-01

Active plasma resonance spectroscopy is a well known diagnostic method. Many concepts of this method are theoretically investigated and realized as a diagnostic tool, one of which is the impedance probe (IP). The application of such a probe in plasmas with pressures of a few Pa raises the question whether kinetic effects have to be taken into account or not. To address this question a kinetic model is necessary. A general kinetic model for an electrostatic concept of active plasma spectroscopy was presented by R.P. Brinkmann and can be used to describe the multipole resonance probe (MRP). In principle the IP is interpretable as a special case of the MRP in lower order. Thus, we are able to describe the IP by the kinetic model of the MRP. Based on this model we derive a solution to investigate the influence of kinetic effects to the resonance behavior of the IP. Active plasma resonance spectroscopy is a well known diagnostic method. Many concepts of this method are theoretically investigated and realized as a diagnostic tool, one of which is the impedance probe (IP). The application of such a probe in plasmas with pressures of a few Pa raises the question whether kinetic effects have to be taken into account or not. To address this question a kinetic model is necessary. A general kinetic model for an electrostatic concept of active plasma spectroscopy was presented by R.P. Brinkmann and can be used to describe the multipole resonance probe (MRP). In principle the IP is interpretable as a special case of the MRP in lower order. Thus, we are able to describe the IP by the kinetic model of the MRP. Based on this model we derive a solution to investigate the influence of kinetic effects to the resonance behavior of the IP. The authors acknowledge the support by the Deutsche Forschungsgemeinschaft (DFG) via the Ruhr University Research School and the Federal Ministry of Education and Research in frame of the PluTO project.

Review of Maxillary Expansion Appliance Activation Methods: Engineering and Clinical Perspectives

PubMed Central

Romanyk, D. L.; Lagravere, M. O.; Toogood, R. W.; Major, P. W.; Carey, J. P.

2010-01-01

Objective. Review the reported activation methods of maxillary expansion devices for midpalatal suture separation from an engineering perspective and suggest areas of improvement. Materials and Methods. A literature search of Scopus and PubMed was used to determine current expansion methods. A U.S. and Canadian patent database search was also conducted using patent classification and keywords. Any paper presenting a new method of expansion was included. Results. Expansion methods in use, or patented, can be classified as either a screw- or spring-type, magnetic, or shape memory alloy expansion appliance. Conclusions. Each activation method presented unique advantages and disadvantages from both clinical and engineering perspectives. Areas for improvement still remain and are identified in the paper. PMID:20948570

On the gravitational field of static and stationary axial symmetric bodies with multi-polar structure

NASA Astrophysics Data System (ADS)

Letelier, Patricio S.

1999-04-01

We give a physical interpretation to the multi-polar Erez-Rozen-Quevedo solution of the Einstein equations in terms of bars. We find that each multi-pole corresponds to the Newtonian potential of a bar with linear density proportional to a Legendre polynomial. We use this fact to find an integral representation of the 0264-9381/16/4/010/img1 function. These integral representations are used in the context of the inverse scattering method to find solutions associated with one or more rotating bodies each with their own multi-polar structure.

Comparison of the convolution quadrature method and enhanced inverse FFT with application in elastodynamic boundary element method

NASA Astrophysics Data System (ADS)

Schanz, Martin; Ye, Wenjing; Xiao, Jinyou

2016-04-01

Transient problems can often be solved with transformation methods, where the inverse transformation is usually performed numerically. Here, the discrete Fourier transform in combination with the exponential window method is compared with the convolution quadrature method formulated as inverse transformation. Both are inverse Laplace transforms, which are formally identical but use different complex frequencies. A numerical study is performed, first with simple convolution integrals and, second, with a boundary element method (BEM) for elastodynamics. Essentially, when combined with the BEM, the discrete Fourier transform needs less frequency calculations, but finer mesh compared to the convolution quadrature method to obtain the same level of accuracy. If further fast methods like the fast multipole method are used to accelerate the boundary element method the convolution quadrature method is better, because the iterative solver needs much less iterations to converge. This is caused by the larger real part of the complex frequencies necessary for the calculation, which improves the conditions of system matrix.

An inventory of bispectrum estimators for redshift space distortions

NASA Astrophysics Data System (ADS)

Regan, Donough

2017-12-01

In order to best improve constraints on cosmological parameters and on models of modified gravity using current and future galaxy surveys it is necessary maximally exploit the available data. As redshift-space distortions mean statistical translation invariance is broken for galaxy observations, this will require measurement of the monopole, quadrupole and hexadecapole of not just the galaxy power spectrum, but also the galaxy bispectrum. A recent (2015) paper by Scoccimarro demonstrated how the standard bispectrum estimator may be expressed in terms of Fast Fourier Transforms (FFTs) to afford an extremely efficient algorithm, allowing the bispectrum multipoles on all scales and triangle shapes to be measured in comparable time to those of the power spectrum. In this paper we present a suite of alternative proxies to measure the three-point correlation multipoles. In particular, we describe a modal (or plane wave) decomposition to capture the information in each multipole in a series of basis coefficients, and also describe three compressed estimators formed using the skew-spectrum, the line correlation function and the integrated bispectrum, respectively. As well as each of the estimators offering a different measurement channel, and thereby a robustness check, it is expected that some (especially the modal estimator) will offer a vast data compression, and so a much reduced covariance matrix. This compression may be vital to reduce the computational load involved in extracting the available three-point information.

Static electric and magnetic multipole susceptibilities for Dirac one-electron atoms in the ground state

NASA Astrophysics Data System (ADS)

Szmytkowski, Radosław; Łukasik, Grzegorz

2016-09-01

We present tabulated data for several families of static electric and magnetic multipole susceptibilities for hydrogenic atoms with nuclear charge numbers from the range 1 ⩽ Z ⩽ 137. Atomic nuclei are assumed to be point-like and spinless. The susceptibilities considered include the multipole electric polarizabilities α E L → E L and magnetizabilities (magnetic susceptibilities) χ M L → M L with 1 ⩽ L ⩽ 4 (i.e., the dipole, quadrupole, octupole and hexadecapole ones), the electric-to-magnetic cross-susceptibilities α E L → M(L - 1) with 2 ⩽ L ⩽ 5 and α E L → M(L + 1) with 1 ⩽ L ⩽ 4, the magnetic-to-electric cross-susceptibilities χ M L → E(L - 1) with 2 ⩽ L ⩽ 5 and χ M L → E(L + 1) with 1 ⩽ L ⩽ 4 (it holds that χ M L → E(L ∓ 1) =α E(L ∓ 1) → M L), and the electric-to-toroidal-magnetic cross-susceptibilities α E L → T L with 1 ⩽ L ⩽ 4. Numerical values are computed from general exact analytical formulas, derived by us elsewhere within the framework of the Dirac relativistic quantum mechanics, and involving generalized hypergeometric functions 3F2 of the unit argument.

Detection of cosmic microwave background structure in a second field with the Cosmic Anisotropy Telescope

NASA Astrophysics Data System (ADS)

Baker, Joanne C.; Grainge, Keith; Hobson, M. P.; Jones, Michael E.; Kneissl, R.; Lasenby, A. N.; O'Sullivan, C. M. M.; Pooley, Guy; Rocha, G.; Saunders, Richard; Scott, P. F.; Waldram, E. M.

1999-10-01

We describe observations at frequencies near 15GHz of the second 2x2deg^2 field imaged with the Cambridge Cosmic Anisotropy Telescope (CAT). After the removal of discrete radio sources, structure is detected in the images on characteristic scales of about half a degree, corresponding to spherical harmonic multipoles in the range l~330-680. A Bayesian analysis confirms that the signal arises predominantly from the cosmic microwave background (CMB) radiation for multipoles in the lower half of this range; the average broad-band power in a bin with centroid l=422 (θ~51arcmin) is estimated to be ΔTT 2.1-0.5+0.4 x10-5. For multipoles centred on l=615 (θ~35arcmin), we find contamination from Galactic emission is significant, and constrain the CMB contribution to the measured power in this bin to be ΔTT<2.0x10^-5 (1σ upper limit). These new results are consistent with the first detection made by CAT in a completely different area of sky. Together with data from other experiments, this new CAT detection adds weight to earlier evidence from CAT for a downturn in the CMB power spectrum on scales smaller than 1deg. Improved limits on the values of H0 and Ω are determined using the new CAT data.

The impact of new polarization data from Bonn, Mainz and Jefferson Laboratory on γ p → π N multipoles

NASA Astrophysics Data System (ADS)

Anisovich, A. V.; Beck, R.; Döring, M.; Gottschall, M.; Hartmann, J.; Kashevarov, V.; Klempt, E.; Meißner, Ulf-G.; Nikonov, V.; Ostrick, M.; Rönchen, D.; Sarantsev, A.; Strakovsky, I.; Thiel, A.; Tiator, L.; Thoma, U.; Workman, R.; Wunderlich, Y.

2016-09-01

New data on pion-photoproduction off the proton have been included in the partial-wave analyses Bonn-Gatchina and SAID and in the dynamical coupled-channel approach Jülich-Bonn. All reproduce the recent new data well: the double-polarization data for E, G, H, P and T in γ p→ π0p from ELSA, the beam asymmetry Σ for γ p→ π0p and π+n from Jefferson Laboratory, and the precise new differential cross section and beam asymmetry data Σ for γ p→ π0p from MAMI. The new fit results for the multipoles are compared with predictions not taking into account the new data. The mutual agreement is improved considerably but still far from being perfect.

N* resonances from KΛ amplitudes in sliced bins in energy

NASA Astrophysics Data System (ADS)

Anisovich, A. V.; Burkert, V.; Hadžimehmedović, M.; Ireland, D. G.; Klempt, E.; Nikonov, V. A.; Omerović, R.; Sarantsev, A. V.; Stahov, J.; Švarc, A.; Thoma, U.

2017-12-01

The two reactions γ p→ K+Λ and π- p→ K0Λ are analyzed to determine the leading photoproduction multipoles and the pion-induced partial wave amplitudes in slices of the invariant mass. The multipoles and the partial-wave amplitudes are simultaneously fitted in a multichannel Laurent+Pietarinen model (L+P model), which determines the poles in the complex energy plane on the second Riemann sheet close to the physical axes. The results from the L+P fit are compared with the results of an energy-dependent fit based on the Bonn-Gatchina (BnGa) approach. The study confirms the existence of several poles due to nucleon resonances in the region at about 1.9 GeV with quantum numbers JP = 1/2+, 3/2+, 1/2-, 3/2-, 5/2-.

Cs 62 DJ Rydberg-atom macrodimers formed by long-range multipole interaction

NASA Astrophysics Data System (ADS)

Han, Xiaoxuan; Bai, Suying; Jiao, Yuechun; Hao, Liping; Xue, Yongmei; Zhao, Jianming; Jia, Suotang; Raithel, Georg

2018-03-01

Long-range macrodimers formed by D -state cesium Rydberg atoms are studied in experiments and calculations. Cesium [62DJ]2 Rydberg-atom macrodimers, bonded via long-range multipole interaction, are prepared by two-color photoassociation in a cesium atom trap. The first color (pulse A) resonantly excites seed Rydberg atoms, while the second (pulse B, detuned by the molecular binding energy) resonantly excites the Rydberg-atom macrodimers below the [62DJ]2 asymptotes. The molecules are measured by extraction of autoionization products and Rydberg-atom electric-field ionization, and ion detection. Molecular spectra are compared with calculations of adiabatic molecular potentials. From the dependence of the molecular signal on the detection delay time, the lifetime of the molecules is estimated to be 3 -6 μ s .

Oxidation of gallium arsenide in a plasma multipole device. Study of the MOS structures obtained

NASA Technical Reports Server (NTRS)

Gourrier, S.; Mircea, A.; Simondet, F.

1980-01-01

The oxygen plasma oxidation of GaAs was studied in order to obtain extremely high frequency responses with MOS devices. In the multipole system a homogeneous oxygen plasma of high density can easily be obtained in a large volume. This system is thus convenient for the study of plasma oxidation of GaAs. The electrical properties of the MOS diodes obtained in this way are controlled by interface states, located mostly in the upper half of the band gap where densities in the 10 to the 13th power/(sq cm) (eV) range can be estimated. Despite these interface states the possibility of fabricating MOSFET transistors working mostly in the depletion mode for a higher frequency cut-off still exists.

Final-state QED multipole radiation in antenna parton showers

NASA Astrophysics Data System (ADS)

Kleiss, Ronald; Verheyen, Rob

2017-11-01

We present a formalism for a fully coherent QED parton shower. The complete multipole structure of photonic radiation is incorporated in a single branching kernel. The regular on-shell 2 → 3 kinematic picture is kept intact by dividing the radiative phase space into sectors, allowing for a definition of the ordering variable that is similar to QCD antenna showers. A modified version of the Sudakov veto algorithm is discussed that increases performance at the cost of the introduction of weighted events. Due to the absence of a soft singularity, the formalism for photon splitting is very similar to the QCD analogon of gluon splitting. However, since no color structure is available to guide the selection of a spectator, a weighted selection procedure from all available spectators is introduced.

Symmetry breaking in linear multipole traps

NASA Astrophysics Data System (ADS)

Pedregosa-Gutierrez, J.; Champenois, C.; Kamsap, M. R.; Hagel, G.; Houssin, M.; Knoop, M.

2018-03-01

Radiofrequency multipole traps have been used for some decades in cold collision experiments and are gaining interest for precision spectroscopy due to their low micromotion contribution and the predicted unusual cold-ion structures. However, the experimental realisation is not yet fully controlled, and open questions in the operation of these devices remain. We present experimental observations of symmetry breaking of the trapping potential in a macroscopic octupole trap with laser-cooled ions. Numerical simulations have been performed in order to explain the appearance of additional local potential minima and be able to control them in a next step. We characterise these additional potential minima, in particular with respect to their position, their potential depth and their probability of population as a function of the radial and angular displacement of the trapping rods.

Prospects for Ultra-Stable Timekeeping with Sealed Vacuum Operation in Multi-Pole Linear Ion Trap Standards

NASA Technical Reports Server (NTRS)

Burt, Eric A.; Tjoelker, R. L.

2007-01-01

A recent long-term comparison between the compensated multi-pole Linear Ion Trap Standard (LITS) and the laser-cooled primary standards via GPS carrier phase time transfer showed a deviation of less than 2.7x10(exp -17)/day. A subsequent evaluation of potential drift contributors in the LITS showed that the leading candidates are fluctuations in background gases and the neon buffer gas. The current vacuum system employs a "flow-through" turbomolecular pump and a diaphragm fore pump. Here we consider the viability of a "sealed" vacuum system pumped by a non-evaporable getter for long-term ultra-stable clock operation. Initial tests suggests that both further stability improvement and longer mean-time-between-maintenance can be achieved using this approach

Optical Radiation from Integer Quantum Hall States in Dirac Materials

NASA Astrophysics Data System (ADS)

Gullans, Michael; Taylor, Jacob; Ghaemi, Pouyan; Hafezi, Mohammad

Quantum Hall systems exhibit topologically protected edge states, which can have a macroscopic spatial extent. Such edge states provide a unique opportunity to study a quantum emitter whose size far exceeds the wavelength of emitted light. To better understand this limit, we theoretically characterize the optical radiation from integer quantum Hall states in two-dimensional Dirac materials. We show that the scattered light from the bulk reflects the spatial profile of the wavefunctions, enabling spatial imaging of the disorder landscape. We find that the radiation from the edge states are characterized by the presence of large multipole moments in the far-field. This multipole radiation arises from the transfer of angular momentum from the electrons into the scattered light, enabling the generation of coherent light with high orbital angular momentum.

Generalization of the optical theorem for an arbitrary multipole in the presence of a transparent half-space

NASA Astrophysics Data System (ADS)

Eremin, Yu. A.; Sveshnikov, A. G.

2017-07-01

The optical theorem is generalized to the case of excitation of a local inhomogeneity introduced in a transparent substrate by a multipole of arbitrary order. It is shown that, to calculate the generalized extinction cross section, it is sufficient to calculate the derivatives of the scattered field at a single point by adding a constant and a definite integral. Apart from general scientific interest, the proposed generalization makes it possible to calculate the absorption cross section by subtracting the scattering cross section from the extinction cross section. The latter fact is important, because the scattered field in the far zone contains no Sommerfeld integrals. In addition, the proposed generalization allows one to test computer modules for the case where a lossless inhomogeneity is considered.

Effects of nonadditive interactions on ion solvation at the water/vapor interface: a molecular dynamics study.

PubMed

Yagasaki, Takuma; Saito, Shinji; Ohmine, Iwao

2010-12-09

The solvation of halide ions at the water/vapor interface is investigated by using molecular dynamics simulations with nonpolarizable molecular mechanical (MM), polarizable MM, and quantum mechanical (QM)/MM methods. The free energy profile of the ion solvation is decomposed into the energy and the entropic contributions along the ion displacement from inside to the surface of water. It is found that the surface affinity of the ion, relative to the bulk value, is determined by a subtle balance between the energetic destabilization and the entropic stabilization with the ion displacement. The amount of energetic destabilization is found to be reduced when nonadditive interactions are included, as in the polarizable MM and QM/MM models. The structure of water around the ion at the interface is also largely modified when the higher order effects are considered. For example, the induced dipole effect enhances the solvation structure around the ion at the interface significantly and thus reduces the amount of entropic stabilization at the interface, relative to in the bulk. It is found that this induced dipole effect causes the slowing in the ion-water hydrogen bond dynamics at the interface. On the other hand, the higher order induced multipole effects in the QM/MM method suppress both the excessive enhancement of the solvation structure and the slowing of the ion-water hydrogen bond dynamics at the interface. The present study demonstrates that not only the induced dipole moment but also the higher order induced multipole moments, which are neglected in standard empirical models, are essential for the correct description of the ion solvation at the water/vapor interface.

Computational study of scattering of a zero-order Bessel beam by large nonspherical homogeneous particles with the multilevel fast multipole algorithm

NASA Astrophysics Data System (ADS)

Yang, Minglin; Wu, Yueqian; Sheng, Xinqing; Ren, Kuan Fang

2017-12-01

Computation of scattering of shaped beams by large nonspherical particles is a challenge in both optics and electromagnetics domains since it concerns many research fields. In this paper, we report our new progress in the numerical computation of the scattering diagrams. Our algorithm permits to calculate the scattering of a particle of size as large as 110 wavelengths or 700 in size parameter. The particle can be transparent or absorbing of arbitrary shape, smooth or with a sharp surface, such as the Chebyshev particles or ice crystals. To illustrate the capacity of the algorithm, a zero order Bessel beam is taken as the incident beam, and the scattering of ellipsoidal particles and Chebyshev particles are taken as examples. Some special phenomena have been revealed and examined. The scattering problem is formulated with the combined tangential formulation and solved iteratively with the aid of the multilevel fast multipole algorithm, which is well parallelized with the message passing interface on the distributed memory computer platform using the hybrid partitioning strategy. The numerical predictions are compared with the results of the rigorous method for a spherical particle to validate the accuracy of the approach. The scattering diagrams of large ellipsoidal particles with various parameters are examined. The effect of aspect ratios, as well as half-cone angle of the incident zero-order Bessel beam and the off-axis distance on scattered intensity, is studied. Scattering by asymmetry Chebyshev particle with size parameter larger than 700 is also given to show the capability of the method for computing scattering by arbitrary shaped particles.

SevenOperators, a Mathematica script for harmonic oscillator nuclear matrix elements arising in semileptonic electroweak interactions

NASA Astrophysics Data System (ADS)

Haxton, Wick; Lunardini, Cecilia

2008-09-01

Semi-leptonic electroweak interactions in nuclei—such as β decay, μ capture, charged- and neutral-current neutrino reactions, and electron scattering—are described by a set of multipole operators carrying definite parity and angular momentum, obtained by projection from the underlying nuclear charge and three-current operators. If these nuclear operators are approximated by their one-body forms and expanded in the nucleon velocity through order |p→|/M, where p→ and M are the nucleon momentum and mass, a set of seven multipole operators is obtained. Nuclear structure calculations are often performed in a basis of Slater determinants formed from harmonic oscillator orbitals, a choice that allows translational invariance to be preserved. Harmonic-oscillator single-particle matrix elements of the multipole operators can be evaluated analytically and expressed in terms of finite polynomials in q, where q is the magnitude of the three-momentum transfer. While results for such matrix elements are available in tabular form, with certain restriction on quantum numbers, the task of determining the analytic form of a response function can still be quite tedious, requiring the folding of the tabulated matrix elements with the nuclear density matrix, and subsequent algebra to evaluate products of operators. Here we provide a Mathematica script for generating these matrix elements, which will allow users to carry out all such calculations by symbolic manipulation. This will eliminate the errors that may accompany hand calculations and speed the calculation of electroweak nuclear cross sections and rates. We illustrate the use of the new script by calculating the cross sections for charged- and neutral-current neutrino scattering in 12C. Program summaryProgram title: SevenOperators Catalogue identifier: AEAY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAY_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.: 2227 No. of bytes in distributed program, including test data, etc.: 19 382 Distribution format: tar.gz Programming language: Mathematica Computer: Any computer running Mathematica; tested on Mac OS X PowerPC (32-bit) running Mathematica 6.0.0 Operating system: Any running Mathematica RAM: Memory requirements determined by Mathematica; 512 MB or greater RAM and hard drive space of at least 3.0 GB recommended Classification: 17.16, 17.19 Nature of problem: Algebraic evaluation of harmonic oscillator nuclear matrix elements for the one-body multipole operators governing semi-leptonic weak interactions, such as charged- or neutral-current neutrino scattering off nuclei. Solution method: Mathematica evaluation of associated angular momentum algebra and spherical Bessel function radial integrals. Running time: Depends on the complexity of the one-body density matrix employed, but times of a few seconds are typical.

Speed-up of the volumetric method of moments for the approximate RCS of large arbitrary-shaped dielectric targets

NASA Astrophysics Data System (ADS)

Moreno, Javier; Somolinos, Álvaro; Romero, Gustavo; González, Iván; Cátedra, Felipe

2017-08-01

A method for the rigorous computation of the electromagnetic scattering of large dielectric volumes is presented. One goal is to simplify the analysis of large dielectric targets with translational symmetries taken advantage of their Toeplitz symmetry. Then, the matrix-fill stage of the Method of Moments is efficiently obtained because the number of coupling terms to compute is reduced. The Multilevel Fast Multipole Method is applied to solve the problem. Structured meshes are obtained efficiently to approximate the dielectric volumes. The regular mesh grid is achieved by using parallelepipeds whose centres have been identified as internal to the target. The ray casting algorithm is used to classify the parallelepiped centres. It may become a bottleneck when too many points are evaluated in volumes defined by parametric surfaces, so a hierarchical algorithm is proposed to minimize the number of evaluations. Measurements and analytical results are included for validation purposes.

A polyvalent harmonic coil testing method for small-aperture magnets

NASA Astrophysics Data System (ADS)

Arpaia, Pasquale; Buzio, Marco; Golluccio, Giancarlo; Walckiers, Louis

2012-08-01

A method to characterize permanent and fast-pulsed iron-dominated magnets with small apertures is presented. The harmonic coil measurement technique is enhanced specifically for small-aperture magnets by (1) in situ calibration, for facing search-coil production inaccuracy, (2) rotating the magnet around its axis, for correcting systematic effects, and (3) measuring magnetic fluxes by stationary coils at different angular positions for measuring fast pulsed magnets. This method allows a quadrupole magnet for particle accelerators to be characterized completely, by assessing multipole field components, magnetic axis position, and field direction. In this paper, initially the metrological problems arising from testing small-aperture magnets are highlighted. Then, the basic ideas of the proposed method and the architecture of the corresponding measurement system are illustrated. Finally, experimental validation results are shown for small-aperture permanent and fast-ramped quadrupole magnets for the new linear accelerator Linac4 at CERN (European Organization for Nuclear Research).

Scattering properties of electromagnetic waves from metal object in the lower terahertz region

NASA Astrophysics Data System (ADS)

Chen, Gang; Dang, H. X.; Hu, T. Y.; Su, Xiang; Lv, R. C.; Li, Hao; Tan, X. M.; Cui, T. J.

2018-01-01

An efficient hybrid algorithm is proposed to analyze the electromagnetic scattering properties of metal objects in the lower terahertz (THz) frequency. The metal object can be viewed as perfectly electrical conducting object with a slightly rough surface in the lower THz region. Hence the THz scattered field from metal object can be divided into coherent and incoherent parts. The physical optics and truncated-wedge incremental-length diffraction coefficients methods are combined to compute the coherent part; while the small perturbation method is used for the incoherent part. With the MonteCarlo method, the radar cross section of the rough metal surface is computed by the multilevel fast multipole algorithm and the proposed hybrid algorithm, respectively. The numerical results show that the proposed algorithm has good accuracy to simulate the scattering properties rapidly in the lower THz region.

Consistent force field modeling of matrix isolated molecules. V. Minimum energy path potential to the conformer conversion of 1,2-difluoroethane: Ar 364, ab initio calculation of electric multipole moments and electric polarization contribution to the conversion barrier

NASA Astrophysics Data System (ADS)

Gunde, R.; Ha, T.-K.; Günthard, H. H.

1990-08-01

In this paper results of consistent force field modeling (CFF) of the potential function to conversion of the gauche (g) to the trans (t) conformer of 1,2-difluoroethane (DFE) isolated in an argon matrix will be reported. Starting point are locally stable configurations gDFE:Ar 364 (defect GH1) and tDFE:Ar 364 (TH1) obtained in previous work from CFF modeling of a cube shaped Ar 364 fragment containing one DFE molecule in its center. Using the dihedral angle of DFE as an independent parameter the minimum energy path of the conversion process gDFE:Ar 364→tDFE:Ar 364 will be determined by CFF energy minimization. Determination of the minimum energy path is found to require large numbers of energy minimization steps and to lead to a rather complicated motion of the molecule with respect to the crystal fragment. Surprisingly the molecule-matrix interactions lead to a reduction of the g-t barrier by ≈500 cal/mol and to a stabilization of the trans species by ≈500 cal/mol. This finding is a consequence of a delicate interplay of matrix-molecule and matrix-matrix interactions. Calculation of the electric polarization energy (induced dipole-first-order polarization approximation) is based on extended ab initio calculations of dipole and quadrupole moments and a bond polarizability estimate of the first-order polarizability of DFE as a function of the internal rotation angle, on Fourier expansion of multipole components and use of symmetry for reduction of the order of the linear system defining the (self-consistent) induced dipole moments of all Ar atoms. Electric polarization is found to alter the potential function of the conversion process in a profound way: the g-t barrier and the t-g energy difference are increased to ≈3000 cal/mol and to ≈1500 cal/mol respectively (≈2500 and ≈530 cal/mol respectively for free DFE). Further applications of the technique developed in this work to related problems of matrix isolated molecules, e.g., vibrational matrix shifts will be discussed.

Research progress on expansive soil cracks under changing environment.

PubMed

Shi, Bei-xiao; Zheng, Cheng-feng; Wu, Jin-kun

2014-01-01

Engineering problems shunned previously rise to the surface gradually with the activities of reforming the natural world in depth, the problem of expansive soil crack under the changing environment becoming a control factor of expansive soil slope stability. The problem of expansive soil crack has gradually become a research hotspot, elaborates the occurrence and development of cracks from the basic properties of expansive soil, and points out the role of controlling the crack of expansive soil strength. We summarize the existing research methods and results of expansive soil crack characteristics. Improving crack measurement and calculation method and researching the crack depth measurement, statistical analysis method, crack depth and surface feature relationship will be the future direction.

A new approach for modeling gravitational radiation from the inspiral of two neutron stars

NASA Astrophysics Data System (ADS)

Luke, Stephen A.

In this dissertation, a new method of applying the ADM formalism of general relativity to model the gravitational radiation emitted from the realistic inspiral of a neutron star binary is described. A description of the conformally flat condition (CFC) is summarized, and the ADM equations are solved by use of the CFC approach for a neutron star binary. The advantages and limitations of this approach are discussed, and the need for a more accurate improvement to this approach is described. To address this need, a linearized perturbation of the CFC spatial three metric is then introduced. The general relativistic hydrodynamic equations are then allowed to evolve against this basis under the assumption that the first-order corrections to the hydrodynamic variables are negligible compared to their CFC values. As a first approximation, the linear corrections to the conformal factor, lapse function, and shift vector are also assumed to be small compared to the extrinsic curvature and the three metric. A boundary matching method is then introduced as a way of computing the gravitational radiation of this relativistic system without use of the multipole expansion as employed by earlier applications of the CFC approach. It is assumed that at a location far from the source, the three metric is accurately described by a linear correction to Minkowski spacetime. The two polarizations of gravitational radiation can then be computed at that point in terms of the linearized correction to the metric. The evolution equations obtained from the linearized perturbative correction to the CFC approach and the method for recovery of the gravity wave signal are then tested by use of a three-dimensional numerical simulation. This code is used to compute the gravity wave signal emitted a pair of equal mass neutron stars in quasi-stable circular orbits at a point early in their inspiral phase. From this simple numerical analysis, the correct general trend of gravitational radiation is recovered. Comparisons with (5/2) post-Newtonian solutions show a similar gravitational waveform, although inaccuracies are still found to exist from this computation. Finally, several areas for improvement and potential future applications of this technique are discussed.

The impact of new polarization data from Bonn, Mainz and Jefferson Laboratory on $$\\gamma p \\rightarrow \\pi N$$ multipoles

DOE PAGES

Anisovich, A. V.; Beck, R.; Döring, M.; ...

2016-09-16

New data on pion-photoproduction off the proton have been included in the partial wave analyses Bonn-Gatchina and SAID and in the dynamical coupled-channel approach Julich-Bonn. All reproduce the recent new data well: the double polarization data for E, G, H, P and T inmore » $$\\gamma p \\to \\pi^0 p$$ from ELSA, the beam asymmetry $$\\Sigma$$ for $$\\gamma p \\to \\pi^0 p$$ and $$\\pi^+ n$$ from Jefferson Laboratory, and the precise new differential cross section and beam asymmetry data $$\\Sigma$$ for $$\\gamma p \\to \\pi^0 p$$ from MAMI. The new fit results for the multipoles are compared with predictions not taking into account the new data. Lastly, the mutual agreement is improved considerably but still far from being perfect.« less

The impact of new polarization data from Bonn, Mainz and Jefferson Laboratory on $$\\gamma p \\rightarrow \\pi N$$ multipoles

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

Anisovich, A. V.; Beck, R.; Döring, M.

New data on pion-photoproduction off the proton have been included in the partial wave analyses Bonn-Gatchina and SAID and in the dynamical coupled-channel approach Julich-Bonn. All reproduce the recent new data well: the double polarization data for E, G, H, P and T inmore » $$\\gamma p \\to \\pi^0 p$$ from ELSA, the beam asymmetry $$\\Sigma$$ for $$\\gamma p \\to \\pi^0 p$$ and $$\\pi^+ n$$ from Jefferson Laboratory, and the precise new differential cross section and beam asymmetry data $$\\Sigma$$ for $$\\gamma p \\to \\pi^0 p$$ from MAMI. The new fit results for the multipoles are compared with predictions not taking into account the new data. Lastly, the mutual agreement is improved considerably but still far from being perfect.« less

Effects on the CMB from compactification before inflation

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

Kontou, Eleni-Alexandra; Blanco-Pillado, Jose J.; Hertzberg, Mark P.

2017-04-01

Many theories beyond the Standard Model include extra dimensions, though these have yet to be directly observed. In this work we consider the possibility of a compactification mechanism which both allows extra dimensions and is compatible with current observations. This compactification is predicted to leave a signature on the CMB by altering the amplitude of the low l multipoles, dependent on the amount of inflation. Recently discovered CMB anomalies at low multipoles may be evidence for this. In our model we assume the spacetime is the product of a four-dimensional spacetime and flat extra dimensions. Before the compactification, both themore » four-dimensional spacetime and the extra dimensions can either be expanding or contracting independently. Taking into account physical constraints, we explore the observational consequences and the plausibility of these different models.« less

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

Ghosh, Shamik; Kothari, Rahul; Jain, Pankaj

We propose a dipole modulation model for the Cosmic Microwave Background Radiation (CMBR) polarization field. We show that the model leads to correlations between l and l+1 multipoles, exactly as in the case of temperature. We obtain results for the case of TE, EE and BB correlations. An anisotropic or inhomogeneous model of primordial power spectrum which leads to such correlations in temperature field also predicts similar correlations in CMBR polarization. We analyze the CMBR temperature and polarization data in order to extract the signal of these correlation between l and l+1 multipoles. Our results for the case of temperaturemore » using the latest PLANCK data agree with those obtained by an earlier analysis. A detailed study of the correlation in the polarization data is not possible at present. Hence we restrict ourselves to a preliminary investigation in this case.« less

Threshold π 0 Photoproduction on Transverse Polarised Protons at MAMI

DOE PAGES

Schumann, S.

2015-09-14

Polarisation-dependent differential cross sections σ T associated with the target asymmetry T have been measured for the reaction γ p -→ p π 0 with transverse target polarisation from π 0 threshold up to photon energies of 190 MeV. Additionally, the data were obtained using a frozen-spin butanol target with the Crystal Ball / TAPS detector set-up and the Glasgow photon tagging system at the Mainz Microtron MAMI. Our results for σ T have been used in combination with our previous measurements of the unpolarised cross section σ 0 and the beam asymmetry Σ for a model-independent determination of Smore » and P wave multipoles in the π 0 threshold region, which includes for the first time a direct determination of the imaginary part of the E 0+ multipole.« less

Power Spectrum Analysis of Polarized Emission from the Canadian Galactic Plane Survey

NASA Astrophysics Data System (ADS)

Stutz, R. A.; Rosolowsky, E. W.; Kothes, R.; Landecker, T. L.

2014-05-01

Angular power spectra are calculated and presented for the entirety of the Canadian Galactic Plane Survey polarization data set at 1.4 GHz covering an area of 1060 deg2. The data analyzed are a combination of data from the 100 m Effelsberg Telescope, the 26 m Telescope at the Dominion Radio Astrophysical Observatory, and the Synthesis Telescope at the Dominion Radio Astrophysical Observatory, allowing all scales to be sampled down to arcminute resolution. The resulting power spectra cover multipoles from l ≈ 60 to l ≈ 104 and display both a power-law component at low multipoles and a flattening at high multipoles from point sources. We fit the power spectrum with a model that accounts for these components and instrumental effects. The resulting power-law indices are found to have a mode of 2.3, similar to previous results. However, there are significant regional variations in the index, defying attempts to characterize the emission with a single value. The power-law index is found to increase away from the Galactic plane. A transition from small-scale to large-scale structure is evident at b = 9°, associated with the disk-halo transition in a 15° region around l = 108°. Localized variations in the index are found toward H II regions and supernova remnants, but the interpretation of these variations is inconclusive. The power in the polarized emission is anticorrelated with bright thermal emission (traced by Hα emission) indicating that the thermal emission depolarizes background synchrotron emission.

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

Chiral NNLOsat descriptions of nuclear multipole resonances within the random-phase approximation

NASA Astrophysics Data System (ADS)

Wu, Q.; Hu, B. S.; Xu, F. R.; Ma, Y. Z.; Dai, S. J.; Sun, Z. H.; Jansen, G. R.

2018-05-01

We study nuclear multipole resonances in the framework of the random-phase approximation by using the chiral potential NNLOsat. This potential includes two- and three-body terms that have been simultaneously optimized to low-energy nucleon-nucleon scattering data and selected nuclear structure data. Our main focuses have been the isoscalar monopole, isovector dipole, and isoscalar quadrupole resonances of the closed-shell nuclei, 4He, O 16 ,22 ,24 , and Ca,4840. These resonance modes have been widely observed in experiment. In addition, we use a renormalized chiral potential Vlow-k, based on the N3LO two-body potential by Entem and Machleidt [Phys. Rev. C 68, 041001 (2011), 10.1103/PhysRevC.68.041001]. This introduces a dependency on the cutoff parameter used in the normalization procedure as reported in previous works by other groups. While NNLOsat can reasonably reproduce observed multipole resonances, it is not possible to find a single cutoff parameter for the Vlow-k potential that simultaneously describes the different types of resonance modes. The sensitivity to the cutoff parameter can be explained by missing induced three-body forces in the calculations. Our results for neutron-rich O,2422 show a mixing nature of isoscalar and isovector resonances in the dipole channel at low energies. We predict that 22O and 24O have low-energy isoscalar quadrupole resonances at energies lower than 5 MeV.

Analysis and Implementation of Particle-to-Particle (P2P) Graphics Processor Unit (GPU) Kernel for Black-Box Adaptive Fast Multipole Method

DTIC Science & Technology

2015-06-01

5110P and 16 dx360M4 nodes each with one NVIDIA Kepler K20M/K40M GPU. Each node contained dual Intel Xeon E5-2670 (Sandy Bridge) central processing...kernel and as such does not employ multiple processors. This work makes use of a single processing core and a single NVIDIA Kepler K40 GK110...bandwidth (2 × 16 slot), 7.877 GFloat/s; Kepler K40 peak, 4,290 × 1 billion floating-point operations (GFLOPs), and 288 GB/s Kepler K40 memory

Efficient Kriging Algorithms

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess

2011-01-01

More efficient versions of an interpolation method, called kriging, have been introduced in order to reduce its traditionally high computational cost. Written in C++, these approaches were tested on both synthetic and real data. Kriging is a best unbiased linear estimator and suitable for interpolation of scattered data points. Kriging has long been used in the geostatistic and mining communities, but is now being researched for use in the image fusion of remotely sensed data. This allows a combination of data from various locations to be used to fill in any missing data from any single location. To arrive at the faster algorithms, sparse SYMMLQ iterative solver, covariance tapering, Fast Multipole Methods (FMM), and nearest neighbor searching techniques were used. These implementations were used when the coefficient matrix in the linear system is symmetric, but not necessarily positive-definite.

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

Fedorovich, S V; Protsenko, I E

We report the results of numerical modelling of emission of a two-level atom near a metal nanoparticle under resonant interaction of light with plasmon modes of the particle. Calculations have been performed for different polarisations of light by a dipole approximation method and a complex multipole method. Depending on the distance between a particle and an atom, the contribution of the nonradiative process of electron tunnelling from a two-level atom into a particle, which is calculated using the quasi-classical approximation, has been taken into account and assessed. We have studied spherical gold and silver particles of different diameters (10 –more » 100 nm). The rates of electron tunnelling and of spontaneous decay of the excited atomic state are found. The results can be used to develop nanoscale plasmonic emitters, lasers and photodetectors. (nanooptics)« less

Ultra High Mass Range Mass Spectrometer System

DOEpatents

Reilly, Peter T. A. [Knoxville, TN

2005-12-06

Applicant's present invention comprises mass spectrometer systems that operate in a mass range from 1 to 10.sup.16 DA. The mass spectrometer system comprising an inlet system comprising an aerodynamic lens system, a reverse jet being a gas flux generated in an annulus moving in a reverse direction and a multipole ion guide; a digital ion trap; and a thermal vaporization/ionization detector system. Applicant's present invention further comprises a quadrupole mass spectrometer system comprising an inlet system having a quadrupole mass filter and a thermal vaporization/ionization detector system. Applicant's present invention further comprises an inlet system for use with a mass spectrometer system, a method for slowing energetic particles using an inlet system. Applicant's present invention also comprises a detector device and a method for detecting high mass charged particles.

Relativistic many-body calculation of energies, multipole transition rates, and lifetimes in tungsten ions

NASA Astrophysics Data System (ADS)

Safronova, U. I.; Safronova, M. S.; Nakamura, N.

2017-04-01

Atomic properties of Cd-like W26 +, In-like W25 +, and Sn-like W24 + ions are evaluated by using a relativistic CI+all -order approach that combines configuration-interaction and the coupled-cluster methods. The energies, transition rates, and lifetimes of low-lying levels are calculated and compared with available theoretical and experimental values. The magnetic-dipole transition rates are calculated to determine the branching ratios and lifetimes for the 4 f3 states in W25 + and for the 4 f4 states in W24 + ions. Excellent agreement of the CI+all -order values provided a benchmark test of this method for the 4 fn configurations validating the recommended values of tungsten ion properties calculated in this work.

Directional Dependence of Hydrogen Bonds: a Density-based Energy Decomposition Analysis and Its Implications on Force Field Development

PubMed Central

Lu, Zhenyu; Zhou, Nengjie; Wu, Qin; Zhang, Yingkai

2011-01-01

One well-known shortcoming of widely-used biomolecular force fields is the description of the directional dependence of hydrogen bonding (HB). Here we aim to better understand the origin of this difficulty and thus provide some guidance for further force field development. Our theoretical approaches center on a novel density-based energy decomposition analysis (DEDA) method [J. Chem. Phys., 131, 164112 (2009)], in which the frozen density energy is variationally determined through constrained search. This unique and most significant feature of DEDA enables us to find that the frozen density interaction term is the key factor in determining the HB orientation, while the sum of polarization and charge-transfer components shows very little HB directional dependence. This new insight suggests that the difficulty for current non-polarizable force fields to describe the HB directional dependence is not due to the lack of explicit polarization or charge-transfer terms. Using the DEDA results as reference, we further demonstrate that the main failure coming from the atomic point charge model can be overcome largely by introducing extra charge sites or higher order multipole moments. Among all the electrostatic models explored, the smeared charge distributed multipole model (up to quadrupole), which also takes account of charge penetration effects, gives the best agreement with the corresponding DEDA results. Meanwhile, our results indicate that the van der Waals interaction term needs to be further improved to better model directional hydrogen bonding. PMID:22267958

Conformational analysis of a polyconjugated protein-binding ligand by joint quantum chemistry and polarizable molecular mechanics. Addressing the issues of anisotropy, conjugation, polarization, and multipole transferability.

PubMed

Goldwaser, Elodie; de Courcy, Benoit; Demange, Luc; Garbay, Christiane; Raynaud, Françoise; Hadj-Slimane, Reda; Piquemal, Jean-Philip; Gresh, Nohad

2014-11-01

We investigate the conformational properties of a potent inhibitor of neuropilin-1, a protein involved in cancer processes and macular degeneration. This inhibitor consists of four aromatic/conjugated fragments: a benzimidazole, a methylbenzene, a carboxythiourea, and a benzene-linker dioxane, and these fragments are all linked together by conjugated bonds. The calculations use the SIBFA polarizable molecular mechanics procedure. Prior to docking simulations, it is essential to ensure that variations in the ligand conformational energy upon rotations around its six main-chain torsional bonds are correctly represented (as compared to high-level ab initio quantum chemistry, QC). This is done in two successive calibration stages and one validation stage. In the latter, the minima identified following independent stepwise variations of each of the six main-chain torsion angles are used as starting points for energy minimization of all the torsion angles simultaneously. Single-point QC calculations of the minimized structures are then done to compare their relative energies ΔE conf to the SIBFA ones. We compare three different methods of deriving the multipoles and polarizabilities of the central, most critical moiety of the inhibitor: carboxythiourea (CTU). The representation that gives the best agreement with QC is the one that includes the effects of the mutual polarization energy E pol between the amide and thioamide moieties. This again highlights the critical role of this contribution. The implications and perspectives of these findings are discussed.

A double expansion method for the frequency response of finite-length beams with periodic parameters

NASA Astrophysics Data System (ADS)

Ying, Z. G.; Ni, Y. Q.

2017-03-01

A double expansion method for the frequency response of finite-length beams with periodic distribution parameters is proposed. The vibration response of the beam with spatial periodic parameters under harmonic excitations is studied. The frequency response of the periodic beam is the function of parametric period and then can be expressed by the series with the product of periodic and non-periodic functions. The procedure of the double expansion method includes the following two main steps: first, the frequency response function and periodic parameters are expanded by using identical periodic functions based on the extension of the Floquet-Bloch theorem, and the period-parametric differential equation for the frequency response is converted into a series of linear differential equations with constant coefficients; second, the solutions to the linear differential equations are expanded by using modal functions which satisfy the boundary conditions, and the linear differential equations are converted into algebraic equations according to the Galerkin method. The expansion coefficients are obtained by solving the algebraic equations and then the frequency response function is finally determined. The proposed double expansion method can uncouple the effects of the periodic expansion and modal expansion so that the expansion terms are determined respectively. The modal number considered in the second expansion can be reduced remarkably in comparison with the direct expansion method. The proposed double expansion method can be extended and applied to the other structures with periodic distribution parameters for dynamics analysis. Numerical results on the frequency response of the finite-length periodic beam with various parametric wave numbers and wave amplitude ratios are given to illustrate the effective application of the proposed method and the new frequency response characteristics, including the parameter-excited modal resonance, doubling-peak frequency response and remarkable reduction of the maximum frequency response for certain parametric wave number and wave amplitude. The results have the potential application to structural vibration control.

Non-Invasive Method of Determining Absolute Intracranial Pressure

NASA Technical Reports Server (NTRS)

Yost, William T. (Inventor); Cantrell, John H., Jr. (Inventor); Hargens, Alan E. (Inventor)

2004-01-01

A method is presented for determining absolute intracranial pressure (ICP) in a patient. Skull expansion is monitored while changes in ICP are induced. The patient's blood pressure is measured when skull expansion is approximately zero. The measured blood pressure is indicative of a reference ICP value. Subsequently, the method causes a known change in ICP and measured the change in skull expansion associated therewith. The absolute ICP is a function of the reference ICP value, the known change in ICP and its associated change in skull expansion; and a measured change in skull expansion.

Multipole Vortex Blobs (MVB): Symplectic Geometry and Dynamics.

PubMed

Holm, Darryl D; Jacobs, Henry O

2017-01-01

Vortex blob methods are typically characterized by a regularization length scale, below which the dynamics are trivial for isolated blobs. In this article, we observe that the dynamics need not be trivial if one is willing to consider distributional derivatives of Dirac delta functionals as valid vorticity distributions. More specifically, a new singular vortex theory is presented for regularized Euler fluid equations of ideal incompressible flow in the plane. We determine the conditions under which such regularized Euler fluid equations may admit vorticity singularities which are stronger than delta functions, e.g., derivatives of delta functions. We also describe the symplectic geometry associated with these augmented vortex structures, and we characterize the dynamics as Hamiltonian. Applications to the design of numerical methods similar to vortex blob methods are also discussed. Such findings illuminate the rich dynamics which occur below the regularization length scale and enlighten our perspective on the potential for regularized fluid models to capture multiscale phenomena.

SU-E-J-221: A Novel Expansion Method for MRI Based Target Delineation in Prostate Radiotherapy

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

Ruiz, B; East Carolina University, Greenville, NC; Feng, Y

Purpose: To compare a novel bladder/rectum carveout expansion method on MRI delineated prostate to standard CT and expansion based methods for maintaining prostate coverage while providing superior bladder and rectal sparing. Methods: Ten prostate cases were planned to include four trials: MRI vs CT delineated prostate/proximal seminal vesicles, and each image modality compared to both standard expansions (8mm 3D expansion and 5mm posterior, i.e. ∼8mm) and carveout method expansions (5mm 3D expansion, 4mm posterior for GTV-CTV excluding expansion into bladder/rectum followed by additional 5mm 3D expansion to PTV, i.e. ∼1cm). All trials were planned to total dose 7920 cGy viamore » IMRT. Evaluation and comparison was made using the following criteria: QUANTEC constraints for bladder/rectum including analysis of low dose regions, changes in PTV volume, total control points, and maximum hot spot. Results: ∼8mm MRI expansion consistently produced the most optimal plan with lowest total control points and best bladder/rectum sparing. However, this scheme had the smallest prostate (average 22.9% reduction) and subsequent PTV volume, consistent with prior literature. ∼1cm MRI had an average PTV volume comparable to ∼8mm CT at 3.79% difference. Bladder QUANTEC constraints were on average less for the ∼1cm MRI as compared to the ∼8mm CT and observed as statistically significant with 2.64% reduction in V65. Rectal constraints appeared to follow the same trend. Case-by-case analysis showed variation in rectal V30 with MRI delineated prostate being most favorable regardless of expansion type. ∼1cm MRI and ∼8mm CT had comparable plan quality. Conclusion: MRI delineated prostate with standard expansions had the smallest PTV leading to margins that may be too tight. Bladder/rectum carveout expansion method on MRI delineated prostate was found to be superior to standard CT based methods in terms of bladder and rectal sparing while maintaining prostate coverage. Continued investigation is warranted for further validation.« less

Does query expansion limit our learning? A comparison of social-based expansion to content-based expansion for medical queries on the internet.

PubMed

Pentoney, Christopher; Harwell, Jeff; Leroy, Gondy

2014-01-01

Searching for medical information online is a common activity. While it has been shown that forming good queries is difficult, Google's query suggestion tool, a type of query expansion, aims to facilitate query formation. However, it is unknown how this expansion, which is based on what others searched for, affects the information gathering of the online community. To measure the impact of social-based query expansion, this study compared it with content-based expansion, i.e., what is really in the text. We used 138,906 medical queries from the AOL User Session Collection and expanded them using Google's Autocomplete method (social-based) and the content of the Google Web Corpus (content-based). We evaluated the specificity and ambiguity of the expansion terms for trigram queries. We also looked at the impact on the actual results using domain diversity and expansion edit distance. Results showed that the social-based method provided more precise expansion terms as well as terms that were less ambiguous. Expanded queries do not differ significantly in diversity when expanded using the social-based method (6.72 different domains returned in the first ten results, on average) vs. content-based method (6.73 different domains, on average).

Error and Complexity Analysis for a Collocation-Grid-Projection Plus Precorrected-FFT Algorithm for Solving Potential Integral Equations with LaPlace or Helmholtz Kernels

NASA Technical Reports Server (NTRS)

Phillips, J. R.

1996-01-01

In this paper we derive error bounds for a collocation-grid-projection scheme tuned for use in multilevel methods for solving boundary-element discretizations of potential integral equations. The grid-projection scheme is then combined with a precorrected FFT style multilevel method for solving potential integral equations with 1/r and e(sup ikr)/r kernels. A complexity analysis of this combined method is given to show that for homogeneous problems, the method is order n natural log n nearly independent of the kernel. In addition, it is shown analytically and experimentally that for an inhomogeneity generated by a very finely discretized surface, the combined method slows to order n(sup 4/3). Finally, examples are given to show that the collocation-based grid-projection plus precorrected-FFT scheme is competitive with fast-multipole algorithms when considering realistic problems and 1/r kernels, but can be used over a range of spatial frequencies with only a small performance penalty.

Diffraction of seismic waves from 3-D canyons and alluvial basins modeled using the Fast Multipole-accelerated BEM

NASA Astrophysics Data System (ADS)

Chaillat, S.; Bonnet, M.; Semblat, J.

2007-12-01

Seismic wave propagation and amplification in complex media is a major issue in the field of seismology. To compute seismic wave propagation in complex geological structures such as in alluvial basins, various numerical methods have been proposed. The main advantage of the Boundary Element Method (BEM) is that only the domain boundaries (and possibly interfaces) are discretized, leading to a reduction of the number of degrees of freedom. The main drawback of the standard BEM is that the governing matrix is full and non- symmetric, which gives rise to high computational and memory costs. In other areas where the BEM is used (electromagnetism, acoustics), considerable speedup of solution time and decrease of memory requirements have been achieved through the development, over the last decade, of the Fast Multipole Method (FMM). The goal of the FMM is to speed up the matrix-vector product computation needed at each iteration of the GMRES iterative solver. Moreover, the governing matrix is never explicitly formed, which leads to a storage requirement well below the memory necessary for holding the complete matrix. The FMM-accelerated BEM therefore achieves substantial savings in both CPU time and memory. In this work, the FMM is extended to the 3-D frequency-domain elastodynamics and applied to the computation of seismic wave propagation in 3-D. The efficiency of the present FMM-BEM is demonstrated on seismology- oriented examples. First, the diffraction of a plane wave or a point source by a 3-D canyon is studied. The influence of the size of the meshed part of the free surface is studied, and computations are performed for non- dimensional frequencies higher than those considered in other studies (thanks to the use of the FM-BEM), with which comparisons are made whenever possible. The method is also applied to analyze the diffraction of a plane wave or a point source by a 3-D alluvial basin. A parametrical study is performed on the effect of the shape of the basin and the interaction of the wavefield with the basin edges is analyzed.

Interpreting angular momentum transfer between electromagnetic multipoles using vector spherical harmonics.

PubMed

Grinter, Roger; Jones, Garth A

2018-02-01

The transfer of angular momentum between a quadrupole emitter and a dipole acceptor is investigated theoretically. Vector spherical harmonics are used to describe the angular part of the field of the mediating photon. Analytical results are presented for predicting angular momentum transfer between the emitter and absorber within a quantum electrodynamical framework. We interpret the allowability of such a process, which appears to violate conservation of angular momentum, in terms of the breakdown of the isotropy of space at the point of photon absorption (detection). That is, collapse of the wavefunction results in loss of all angular momentum information. This is consistent with Noether's Theorem and demystifies some common misconceptions about the nature of the photon. The results have implications for interpreting the detection of photons from multipole sources and offers insight into limits on information that can be extracted from quantum measurements in photonic systems.

First measurement of the polarization observable E in the p → (γ → ,π+) n reaction up to 2.25 GeV

NASA Astrophysics Data System (ADS)

Strauch, S.; Briscoe, W. J.; Döring, M.; Klempt, E.; Nikonov, V. A.; Pasyuk, E.; Rönchen, D.; Sarantsev, A. V.; Strakovsky, I.; Workman, R.; Adhikari, K. P.; Adikaram, D.; Anderson, M. D.; Anefalos Pereira, S.; Anisovich, A. V.; Badui, R. A.; Ball, J.; Batourine, V.; Battaglieri, M.; Bedlinskiy, I.; Benmouna, N.; Biselli, A. S.; Brock, J.; Brooks, W. K.; Burkert, V. D.; Cao, T.; Carlin, C.; Carman, D. S.; Celentano, A.; Chandavar, S.; Charles, G.; Colaneri, L.; Cole, P. L.; Compton, N.; Contalbrigo, M.; Cortes, O.; Crede, V.; Dashyan, N.; D'Angelo, A.; De Vita, R.; De Sanctis, E.; Deur, A.; Djalali, C.; Dugger, M.; Dupre, R.; Egiyan, H.; El Alaoui, A.; El Fassi, L.; Elouadrhiri, L.; Eugenio, P.; Fedotov, G.; Fegan, S.; Filippi, A.; Fleming, J. A.; Forest, T. A.; Fradi, A.; Gevorgyan, N.; Ghandilyan, Y.; Giovanetti, K. L.; Girod, F. X.; Glazier, D. I.; Gohn, W.; Golovatch, E.; Gothe, R. W.; Griffioen, K. A.; Guidal, M.; Guo, L.; Hafidi, K.; Hakobyan, H.; Hanretty, C.; Harrison, N.; Hattawy, M.; Hicks, K.; Ho, D.; Holtrop, M.; Hughes, S. M.; Ilieva, Y.; Ireland, D. G.; Ishkhanov, B. S.; Isupov, E. L.; Jenkins, D.; Jiang, H.; Jo, H. S.; Joo, K.; Joosten, S.; Keith, C. D.; Keller, D.; Khachatryan, G.; Khandaker, M.; Kim, A.; Kim, W.; Klein, A.; Klein, F. J.; Kubarovsky, V.; Kuhn, S. E.; Lenisa, P.; Livingston, K.; Lu, H. Y.; MacGregor, I. J. D.; Markov, N.; McKinnon, B.; Meekins, D. G.; Meyer, C. A.; Mokeev, V.; Montgomery, R. A.; Moody, C. I.; Moutarde, H.; Movsisyan, A.; Munevar, E.; Munoz Camacho, C.; Nadel-Turonski, P.; Net, L. A.; Niccolai, S.; Niculescu, G.; Niculescu, I.; O'Rielly, G.; Osipenko, M.; Ostrovidov, A. I.; Park, K.; Peng, P.; Phelps, W.; Phillips, J. J.; Pisano, S.; Pogorelko, O.; Pozdniakov, S.; Price, J. W.; Procureur, S.; Prok, Y.; Protopopescu, D.; Puckett, A. J. R.; Raue, B. A.; Ripani, M.; Ritchie, B. G.; Rizzo, A.; Rosner, G.; Roy, P.; Sabatié, F.; Salgado, C.; Schott, D.; Schumacher, R. A.; Seder, E.; Seely, M. L.; Senderovich, I.; Sharabian, Y. G.; Simonyan, A.; Skorodumina, Iu.; Smith, G. D.; Sober, D. I.; Sokhan, D.; Sparveris, N.; Stoler, P.; Stepanyan, S.; Sytnik, V.; Taiuti, M.; Tian, Ye; Trivedi, A.; Tucker, R.; Ungaro, M.; Voskanyan, H.; Voutier, E.; Walford, N. K.; Watts, D. P.; Wei, X.; Wood, M. H.; Zachariou, N.; Zana, L.; Zhang, J.; Zhao, Z. W.; Zonta, I.

2015-11-01

First results from the longitudinally polarized frozen-spin target (FROST) program are reported. The double-polarization observable E, for the reaction γ → p → →π+ n, has been measured using a circularly polarized tagged-photon beam, with energies from 0.35 to 2.37 GeV. The final-state pions were detected with the CEBAF Large Acceptance Spectrometer in Hall B at the Thomas Jefferson National Accelerator Facility. These polarization data agree fairly well with previous partial-wave analyses at low photon energies. Over much of the covered energy range, however, significant deviations are observed, particularly in the high-energy region where high-L multipoles contribute. The data have been included in new multipole analyses resulting in updated nucleon resonance parameters. We report updated fits from the Bonn-Gatchina, Jülich-Bonn, and SAID groups.

General-relativistic celestial mechanics. 4: Theory of satellite motion

NASA Astrophysics Data System (ADS)

Damour, T.; Soffel, M.; Xu, C.

1993-09-01

The basic equations needed for developing a complete relativistic theory of artificial Earth satellites are explicitly written down. These equations are given both in a local, geocentric frame and in the global, barycentric one. They are derived within our recently introduced general-relativistic celestial mechanics framework. Our approach is more satisfactory than previous ones, especially with regard to its consistency, completeness, and flexibility. In particular, the problem of representing the relativistic gravitational effects associated with the quadrupole and higher multipole moments of the moving Earth, which caused difficulties in several other approaches, is easily dealth with in our approach, thanks to the use of previously developed tools: definition of relativistic multipole moments and transformation theory between reference frames. With this last paper in a series, we hope to indicate the way of using our formalism in specific problems in applied celestial mechanics and astrometry.

N* resonances from K $$\\Lambda$$ Λ amplitudes in sliced bins in energy

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

Anisovich, A. V.; Burkert, V.; Hadžimehmedović, M.

The two reactionsmore » $$\\gamma p\\to K^+\\Lambda$$ and $$\\pi^-p\\to K^0\\Lambda$$ are analyzed to determine the leading photoproduction multipoles and the pion-induced partial wave amplitudes in slices of the invariant mass. The multipoles and the partial-wave amplitudes are simultaneously fitted in a multichannel Laurent+Pietarinen model (L+P model), which determines the poles in the complex energy plane on the second Riemann sheet close to the physical axes. The results from the L+P fit are compared with the results of an energy-dependent fit based on the Bonn-Gatchina (BnGa) approach. The study confirms the existence of several poles due to nucleon resonances in the region at about 1.9\\,GeV with quantum numbers $J^P = 1/2^+$, $3/2^+, 1/2^-, 3/2^-, 5/2^-$.« less

Atomic spectroscopy with twisted photons: Separation of M 1 -E 2 mixed multipoles

NASA Astrophysics Data System (ADS)

Afanasev, Andrei; Carlson, Carl E.; Solyanik, Maria

2018-02-01

We analyze atomic photoexcitation into the discrete states by twisted photons, or photons carrying extra orbital angular momentum along their direction of propagation. From the angular momentum and parity considerations, we are able to relate twisted-photon photoexcitation amplitudes to their plane-wave analogs, independently of the details of the atomic wave functions. We analyze the photoabsorption cross sections of mixed-multipolarity E 2 -M 1 transitions in ionized atoms and found fundamental differences coming from the photon topology. Our theoretical analysis demonstrates that it is possible to extract the relative transition rates of different multipolar contributions by measuring the photoexcitation rate as a function of the atom's position (or impact parameter) with respect to the optical vortex center. The proposed technique for separation of multipoles can be implemented if the target's atom position is resolved with subwavelength accuracy; for example, with Paul traps. Numerical examples are presented for Boron-like highly charged ions.

Strong dipole and higher multi-pole Mie resonance modes with all-dielectric nanoring metasurfaces structure

NASA Astrophysics Data System (ADS)

Zhu, Huihui; Jing, Xufeng; Zhou, Pengwei

2018-01-01

Strong electric and magnetic dipole in infrared region and higher order multi-pole resonance at visible wavelengths are observed in all-dielectric nanoring metasurfaces. We discuss some of the parameters that influence the optical response of the dielectric nanoring. Adjustment of nanoring radius (inner radius and outer radius) and height can change the absorption intensity and the resonance peaks. Dipole, quadrupole, six-pole and ten-pole resonance modes can be found in the silicon nanoring at resonance wavelength. The transmission spectrum of nanoring with high Q-factor and contrast is achieved with appropriate parameters. Further the nanoring is used to application of sensing in which the sensitivity reaches 228 nm/RIU. This research is an important step to understand resonance in silicon nanoring and paves way for designing some optic devices such as sensor, nanoantennas, and photovoltaics.

Multipole Superconductivity in Nonsymmorphic Sr_{2}IrO_{4}.

PubMed

Sumita, Shuntaro; Nomoto, Takuya; Yanase, Youichi

2017-07-14

Discoveries of marked similarities to high-T_{c} cuprate superconductors point to the realization of superconductivity in the doped J_{eff}=1/2 Mott insulator Sr_{2}IrO_{4}. Contrary to the mother compound of cuprate superconductors, several stacking patterns of in-plane canted antiferromagnetic moments have been reported, which are distinguished by the ferromagnetic components as -++-, ++++, and -+-+. In this paper, we clarify unconventional features of the superconductivity coexisting with -++- and -+-+ structures. Combining the group theoretical analysis and numerical calculations for an effective J_{eff}=1/2 model, we show unusual superconducting gap structures in the -++- state protected by nonsymmorphic magnetic space group symmetry. Furthermore, our calculation shows that the Fulde-Ferrell-Larkin-Ovchinnikov superconductivity is inevitably stabilized in the -+-+ state since the odd-parity magnetic -+-+ order makes the band structure asymmetric by cooperating with spin-orbit coupling. These unusual superconducting properties are signatures of magnetic multipole order in nonsymmorphic crystal.

Near-threshold neutral pion electroproduction at high momentum transfers and generalized form factors

NASA Astrophysics Data System (ADS)

Khetarpal, P.; Stoler, P.; Aznauryan, I. G.; Kubarovsky, V.; Adhikari, K. P.; Adikaram, D.; Aghasyan, M.; Amaryan, M. J.; Anderson, M. D.; Anefalos Pereira, S.; Anghinolfi, M.; Avakian, H.; Baghdasaryan, H.; Ball, J.; Baltzell, N. A.; Battaglieri, M.; Batourine, V.; Bedlinskiy, I.; Biselli, A. S.; Bono, J.; Boiarinov, S.; Briscoe, W. J.; Brooks, W. K.; Burkert, V. D.; Carman, D. S.; Celentano, A.; Charles, G.; Cole, P. L.; Contalbrigo, M.; Crede, V.; D'Angelo, A.; Dashyan, N.; De Vita, R.; De Sanctis, E.; Deur, A.; Djalali, C.; Doughty, D.; Dugger, M.; Dupre, R.; Egiyan, H.; El Alaoui, A.; El Fassi, L.; Eugenio, P.; Fedotov, G.; Fegan, S.; Fersch, R.; Fleming, J. A.; Fradi, A.; Gabrielyan, M. Y.; Garçon, M.; Gevorgyan, N.; Gilfoyle, G. P.; Giovanetti, K. L.; Girod, F. X.; Goetz, J. T.; Gohn, W.; Golovatch, E.; Gothe, R. W.; Griffioen, K. A.; Guegan, B.; Guidal, M.; Guo, L.; Hafidi, K.; Hakobyan, H.; Hanretty, C.; Harrison, N.; Hicks, K.; Ho, D.; Holtrop, M.; Hyde, C. E.; Ilieva, Y.; Ireland, D. G.; Ishkhanov, B. S.; Isupov, E. L.; Jo, H. S.; Joo, K.; Keller, D.; Khandaker, M.; Kim, A.; Kim, W.; Klein, F. J.; Koirala, S.; Kubarovsky, A.; Kuleshov, S. V.; Kvaltine, N. D.; Lewis, S.; Livingston, K.; Lu, H. Y.; MacGregor, I. J. D.; Mao, Y.; Martinez, D.; Mayer, M.; McKinnon, B.; Meyer, C. A.; Mineeva, T.; Mirazita, M.; Mokeev, V.; Montgomery, R. A.; Moutarde, H.; Munevar, E.; Munoz Camacho, C.; Nadel-Turonski, P.; Nasseripour, R.; Niccolai, S.; Niculescu, G.; Niculescu, I.; Osipenko, M.; Ostrovidov, A. I.; Pappalardo, L. L.; Paremuzyan, R.; Park, K.; Park, S.; Pasyuk, E.; Phelps, E.; Phillips, J. J.; Pisano, S.; Pogorelko, O.; Pozdniakov, S.; Price, J. W.; Procureur, S.; Protopopescu, D.; Puckett, A. J. R.; Raue, B. A.; Ricco, G.; Rimal, D.; Ripani, M.; Rosner, G.; Rossi, P.; Sabatié, F.; Saini, M. S.; Salgado, C.; Saylor, N. A.; Schott, D.; Schumacher, R. A.; Seder, E.; Seraydaryan, H.; Sharabian, Y. G.; Smith, G. D.; Sober, D. I.; Sokhan, D.; Stepanyan, S. S.; Stepanyan, S.; Strakovsky, I. I.; Strauch, S.; Taiuti, M.; Tang, W.; Taylor, C. E.; Tkachenko, S.; Ungaro, M.; Vernarsky, B.; Voskanyan, H.; Voutier, E.; Walford, N. K.; Weinstein, L. B.; Weygand, D. P.; Wood, M. H.; Zachariou, N.; Zhang, J.; Zhao, Z. W.; Zonta, I.

2013-04-01

We report the measurement of near-threshold neutral pion electroproduction cross sections and the extraction of the associated structure functions on the proton in the kinematic range Q2 from 2 to 4.5 GeV2 and W from 1.08 to 1.16 GeV. These measurements allow us to access the dominant pion-nucleon s-wave multipoles E0+ and S0+ in the near-threshold region. In the light-cone sum-rule framework (LCSR), these multipoles are related to the generalized form factors G1π0p(Q2) and G2π0p(Q2). The data are compared to these generalized form factors and the results for G1π0p(Q2) are found to be in good agreement with the LCSR predictions, but the level of agreement with G2π0p(Q2) is poor.

Multipole Superconductivity in Nonsymmorphic Sr2IrO4

NASA Astrophysics Data System (ADS)

Sumita, Shuntaro; Nomoto, Takuya; Yanase, Youichi

2017-07-01

Discoveries of marked similarities to high-Tc cuprate superconductors point to the realization of superconductivity in the doped Jeff=1 /2 Mott insulator Sr2IrO4. Contrary to the mother compound of cuprate superconductors, several stacking patterns of in-plane canted antiferromagnetic moments have been reported, which are distinguished by the ferromagnetic components as -++-, ++++, and -+-+ . In this paper, we clarify unconventional features of the superconductivity coexisting with -++- and -+-+ structures. Combining the group theoretical analysis and numerical calculations for an effective Jeff=1 /2 model, we show unusual superconducting gap structures in the -++- state protected by nonsymmorphic magnetic space group symmetry. Furthermore, our calculation shows that the Fulde-Ferrell-Larkin-Ovchinnikov superconductivity is inevitably stabilized in the -+-+ state since the odd-parity magnetic -+-+ order makes the band structure asymmetric by cooperating with spin-orbit coupling. These unusual superconducting properties are signatures of magnetic multipole order in nonsymmorphic crystal.

Forbidden atomic transitions driven by an intensity-modulated laser trap.

PubMed

Moore, Kaitlin R; Anderson, Sarah E; Raithel, Georg

2015-01-20

Spectroscopy is an essential tool in understanding and manipulating quantum systems, such as atoms and molecules. The model describing spectroscopy includes the multipole-field interaction, which leads to established spectroscopic selection rules, and an interaction that is quadratic in the field, which is not often employed. However, spectroscopy using the quadratic (ponderomotive) interaction promises two significant advantages over spectroscopy using the multipole-field interaction: flexible transition rules and vastly improved spatial addressability of the quantum system. Here we demonstrate ponderomotive spectroscopy by using optical-lattice-trapped Rydberg atoms, pulsating the lattice light and driving a microwave atomic transition that would otherwise be forbidden by established spectroscopic selection rules. This ability to measure frequencies of previously inaccessible transitions makes possible improved determinations of atomic characteristics and constants underlying physics. The spatial resolution of ponderomotive spectroscopy is orders of magnitude better than the transition frequency would suggest, promising single-site addressability in dense particle arrays for quantum computing applications.