Higher-order force moments of active particles

NASA Astrophysics Data System (ADS)

Nasouri, Babak; Elfring, Gwynn J.

2018-04-01

Active particles moving through fluids generate disturbance flows due to their activity. For simplicity, the induced flow field is often modeled by the leading terms in a far-field approximation of the Stokes equations, whose coefficients are the force, torque, and stresslet (zeroth- and first-order force moments) of the active particle. This level of approximation is quite useful, but may also fail to predict more complex behaviors that are observed experimentally. In this study, to provide a better approximation, we evaluate the contribution of the second-order force moments to the flow field and, by reciprocal theorem, present explicit formulas for the stresslet dipole, rotlet dipole, and potential dipole for an arbitrarily shaped active particle. As examples of this method, we derive modified Faxén laws for active spherical particles and resolve higher-order moments for active rod-like particles.

Corrections to the thin wall approximation in general relativity

NASA Technical Reports Server (NTRS)

Garfinkle, David; Gregory, Ruth

1989-01-01

The question is considered whether the thin wall formalism of Israel applies to the gravitating domain walls of a lambda phi(exp 4) theory. The coupled Einstein-scalar equations that describe the thick gravitating wall are expanded in powers of the thickness of the wall. The solutions of the zeroth order equations reproduce the results of the usual Israel thin wall approximation for domain walls. The solutions of the first order equations provide corrections to the expressions for the stress-energy of the wall and to the Israel thin wall equations. The modified thin wall equations are then used to treat the motion of spherical and planar domain walls.

Stress stiffening and approximate equations in flexible multibody dynamics

NASA Technical Reports Server (NTRS)

Padilla, Carlos E.; Vonflotow, Andreas H.

1993-01-01

A useful model for open chains of flexible bodies undergoing large rigid body motions, but small elastic deformations, is one in which the equations of motion are linearized in the small elastic deformations and deformation rates. For slow rigid body motions, the correctly linearized, or consistent, set of equations can be compared to prematurely linearized, or inconsistent, equations and to 'oversimplified,' or ruthless, equations through the use of open loop dynamic simulations. It has been shown that the inconsistent model should never be used, while the ruthless model should be used whenever possible. The consistent and inconsistent models differ by stress stiffening terms. These are due to zeroth-order stresses effecting virtual work via nonlinear strain-displacement terms. In this paper we examine in detail the nature of these stress stiffening terms and conclude that they are significant only when the associated zeroth-order stresses approach 'buckling' stresses. Finally it is emphasized that when the stress stiffening terms are negligible the ruthlessly linearized equations should be used.

Marangoni bubble motion in zero gravity. [Lewis zero gravity drop tower

NASA Technical Reports Server (NTRS)

Thompson, R. L.; Dewitt, K. J.

1979-01-01

It was shown experimentally that the Marangoni phenomenon is a primary mechanism for the movement of a gas bubble in a nonisothermal liquid in a low gravity environment. A mathematical model consisting of the Navier-Stokes and thermal energy equations, together with the appropriate boundary conditions for both media, is presented. Parameter perturbation theory is used to solve this boundary value problem; the expansion parameter is the Marangoni number. The zeroth, first, and second order approximations for the velocity, temperature and pressure distributions in the liquid and in the bubble, and the deformation and terminal velocity of the bubble are determined. Experimental zero gravity data for a nitrogen bubble in ethylene glycol, ethanol, and silicone oil subjected to a linear temperature gradient were obtained using the NASA Lewis zero gravity drop tower. Comparison of the zeroth order analytical results for the bubble terminal velocity showed good agreement with the experimental measurements. The first and second order solutions for the bubble deformation and bubble terminal velocity are valid for liquids having Prandtl numbers on the order of one, but there is a lack of appropriate data to test the theory fully.

Theoretical L-shell Coster-Kronig energies 11 or equal to z or equal to 103

NASA Technical Reports Server (NTRS)

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

1976-01-01

Relativistic relaxed-orbital calculations of L-shell Coster-Kronig transition energies have been performed for all possible transitions in atoms with atomic numbers. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order approximation to the local approximation was thus included. Quantum-electrodynamic corrections were made. Each transition energy was computed as the difference between results of separate self-consistent-field calculations for the initial, singly ionized state and the final two-hole state. The following quantities are listed: total transition energy, 'electric' (Dirac-Hartree-Fock-Slater) contribution, magnetic and retardation contributions, and contributions due to vacuum polarization and self energy.

How calibration and reference spectra affect the accuracy of absolute soft X-ray solar irradiance measured by the SDO/EVE/ESP during high solar activity

NASA Astrophysics Data System (ADS)

Didkovsky, Leonid; Wieman, Seth; Woods, Thomas

2016-10-01

The Extreme ultraviolet Spectrophotometer (ESP), one of the channels of SDO's Extreme ultraviolet Variability Experiment (EVE), measures solar irradiance in several EUV and soft x-ray (SXR) bands isolated using thin-film filters and a transmission diffraction grating, and includes a quad-diode detector positioned at the grating zeroth-order to observe in a wavelength band from about 0.1 to 7.0 nm. The quad diode signal also includes some contribution from shorter wavelength in the grating's first-order and the ratio of zeroth-order to first-order signal depends on both source geometry, and spectral distribution. For example, radiometric calibration of the ESP zeroth-order at the NIST SURF BL-2 with a near-parallel beam provides a different zeroth-to-first-order ratio than modeled for solar observations. The relative influence of "uncalibrated" first-order irradiance during solar observations is a function of the solar spectral irradiance and the locations of large Active Regions or solar flares. We discuss how the "uncalibrated" first-order "solar" component and the use of variable solar reference spectra affect determination of absolute SXR irradiance which currently may be significantly overestimated during high solar activity.

Analysis of eccentric annular incompressible seals. II - Effects of eccentricity on rotordynamic coefficients

NASA Technical Reports Server (NTRS)

Nelson, C. C.; Nguyen, D. T.

1987-01-01

A new analysis procedure has been presented which solves for the flow variables of an annular pressure seal in which the rotor has a large static displacement (eccentricity) from the centered position. The present paper incorporates the solutions to investigate the effect of eccentricity on the rotordynamic coefficients. The analysis begins with a set of governing equations based on a turbulent bulk-flow model and Moody's friction factor equation. Perturbations of the flow variables yields a set of zeroth- and first-order equations. After integration of the zeroth-order equations, the resulting zeroth-order flow variables are used as input in the solution of the first-order equations. Further integration of the first order pressures yields the eccentric rotordynamic coefficients. The results from this procedure compare well with available experimental and theoretical data, with accuracy just as good or slightly better than the predictions based on a finite-element model.

Density-functional expansion methods: evaluation of LDA, GGA, and meta-GGA functionals and different integral approximations.

PubMed

Giese, Timothy J; York, Darrin M

2010-12-28

We extend the Kohn-Sham potential energy expansion (VE) to include variations of the kinetic energy density and use the VE formulation with a 6-31G* basis to perform a "Jacob's ladder" comparison of small molecule properties using density functionals classified as being either LDA, GGA, or meta-GGA. We show that the VE reproduces standard Kohn-Sham DFT results well if all integrals are performed without further approximation, and there is no substantial improvement in using meta-GGA functionals relative to GGA functionals. The advantages of using GGA versus LDA functionals becomes apparent when modeling hydrogen bonds. We furthermore examine the effect of using integral approximations to compute the zeroth-order energy and first-order matrix elements, and the results suggest that the origin of the short-range repulsive potential within self-consistent charge density-functional tight-binding methods mainly arises from the approximations made to the first-order matrix elements.

The discovery of [Ni(NHC)RCN]2 species and their role as cycloaddition catalysts for the formation of pyridines.

PubMed

Stolley, Ryan M; Duong, Hung A; Thomas, David R; Louie, Janis

2012-09-12

The reaction of Ni(COD)(2), IPr, and nitrile affords dimeric [Ni(IPr)RCN](2) in high yields. X-ray analysis revealed these species display simultaneous η(1)- and η(2)-nitrile binding modes. These dimers are catalytically competent in the formation of pyridines from the cycloaddition of diynes and nitriles. Kinetic analysis showed the reaction to be first order in [Ni(IPr)RCN](2), zeroth order in added IPr, zeroth order in nitrile, and zeroth order in diyne. Extensive stoichiometric competition studies were performed, and selective incorporation of the exogenous, not dimer bound, nitrile was observed. Post cycloaddition, the dimeric state was found to be largely preserved. Nitrile and ligand exchange experiments were performed and found to be inoperative in the catalytic cycle. These observations suggest a mechanism whereby the catalyst is activated by partial dimer-opening followed by binding of exogenous nitrile and subsequent oxidative heterocoupling.

Fringe Field Effects on Bending Magnets, Derived for TRANSPORT/TURTLE

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

Molloy, Riley; Blitz, Sam

2013-08-05

A realistic magnetic dipole has complex effects on a charged particle near the entrance and exit of the magnet, even with a constant and uniform magnetic field deep within the interior of the magnet. To satisfy Maxwell's equations, the field lines near either end of a realistic magnet are significantly more complicated, yielding non-trivial forces. The effects of this fringe field are calculated to first order, applying both the paraxial and thin lens approximations. We find that, in addition to zeroth order effects, the position of a particle directly impacts the forces in the horizontal and vertical directions.

Relativistic calculation of nuclear magnetic shielding using normalized elimination of the small component

NASA Astrophysics Data System (ADS)

Kudo, K.; Maeda, H.; Kawakubo, T.; Ootani, Y.; Funaki, M.; Fukui, H.

2006-06-01

The normalized elimination of the small component (NESC) theory, recently proposed by Filatov and Cremer [J. Chem. Phys. 122, 064104 (2005)], is extended to include magnetic interactions and applied to the calculation of the nuclear magnetic shielding in HX (X =F,Cl,Br,I) systems. The NESC calculations are performed at the levels of the zeroth-order regular approximation (ZORA) and the second-order regular approximation (SORA). The calculations show that the NESC-ZORA results are very close to the NESC-SORA results, except for the shielding of the I nucleus. Both the NESC-ZORA and NESC-SORA calculations yield very similar results to the previously reported values obtained using the relativistic infinite-order two-component coupled Hartree-Fock method. The difference between NESC-ZORA and NESC-SORA results is significant for the shieldings of iodine.

Mean dyadic Green's function for a two layer random medium

NASA Technical Reports Server (NTRS)

Zuniga, M. A.

1981-01-01

The mean dyadic Green's function for a two-layer random medium with arbitrary three-dimensional correlation functions has been obtained with the zeroth-order solution to the Dyson equation by applying the nonlinear approximation. The propagation of the coherent wave in the random medium is similar to that in an anisotropic medium with different propagation constants for the characteristic transverse electric and transverse magnetic polarizations. In the limit of a laminar structure, two propagation constants for each polarization are found to exist.

Controlling coherence using the internal structure of hard pi pulses.

PubMed

Dong, Yanqun; Ramos, R G; Li, Dale; Barrett, S E

2008-06-20

The tiny difference between hard pi pulses and their delta-function approximation can be exploited to control coherence. Variants on the magic echo that work despite a large spread in resonance offsets are demonstrated using the zeroth- and first-order average Hamiltonian terms, for 13C NMR in 60C. The 29Si NMR linewidth of silicon has been reduced by a factor of about 70,00 using this approach, which also has potential applications in magnetic resonance microscopy and imaging of solids.

Efficiency of unconstrained minimization techniques in nonlinear analysis

NASA Technical Reports Server (NTRS)

Kamat, M. P.; Knight, N. F., Jr.

1978-01-01

Unconstrained minimization algorithms have been critically evaluated for their effectiveness in solving structural problems involving geometric and material nonlinearities. The algorithms have been categorized as being zeroth, first, or second order depending upon the highest derivative of the function required by the algorithm. The sensitivity of these algorithms to the accuracy of derivatives clearly suggests using analytically derived gradients instead of finite difference approximations. The use of analytic gradients results in better control of the number of minimizations required for convergence to the exact solution.

The Physics of Ultracold Sr2 Molecules: Optical Production and Precision Measurement

DTIC Science & Technology

2013-01-01

causing stimulated emission. The wavelength of the feedback light is determined by the angle of the feedback mirror . The zeroth order is the output from...with representative mirror , diffraction grating and diode housing (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.14 Schematic of...of the feedback light is determined by the angle of the feedback mirror . The zeroth order is the output from the ECDL. . . . . . . . . . . . 23 2.15

The Effect of Concomitant Fields in Fast Spin Echo Acquisition on Asymmetric MRI Gradient Systems

PubMed Central

Tao, Shengzhen; Weavers, Paul T.; Trzasko, Joshua D.; Huston, John; Shu, Yunhong; Gray, Erin M.; Foo, Thomas K.F.; Bernstein, Matt A.

2017-01-01

Purpose To investigate the effect of the asymmetric gradient concomitant fields (CF) with zeroth and first-order spatial dependence on fast/turbo spin-echo acquisitions, and to demonstrate the effectiveness of their real-time compensation. Methods After briefly reviewing the CF produced by asymmetric gradients, the effects of the additional zeroth and first-order CFs on these systems are investigated using extended-phase graph simulations. Phantom and in vivo experiments are performed to corroborate the simulation. Experiments are performed before and after the real-time compensations using frequency tracking and gradient pre-emphasis to demonstrate their effectiveness in correcting the additional CFs. The interaction between the CFs and prescan-based correction to compensate for eddy currents is also investigated. Results It is demonstrated that, unlike the second-order CFs on conventional gradients, the additional zeroth/first-order CFs on asymmetric gradients cause substantial signal loss and dark banding in fast spin-echo acquisitions within a typical brain-scan field of view. They can confound the prescan correction for eddy currents and degrade image quality. Performing real-time compensation successfully eliminates the artifacts. Conclusions We demonstrate that the zeroth/first-order CFs specific to asymmetric gradients can cause substantial artifacts, including signal loss and dark bands for brain imaging. These effects can be corrected using real-time compensation. PMID:28643408

NEW DEVELOPMENTS ON INVERSE POLYGON MAPPING TO CALCULATE GRAVITATIONAL LENSING MAGNIFICATION MAPS: OPTIMIZED COMPUTATIONS

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

Mediavilla, E.; Lopez, P.; Mediavilla, T.

2011-11-01

We derive an exact solution (in the form of a series expansion) to compute gravitational lensing magnification maps. It is based on the backward gravitational lens mapping of a partition of the image plane in polygonal cells (inverse polygon mapping, IPM), not including critical points (except perhaps at the cell boundaries). The zeroth-order term of the series expansion leads to the method described by Mediavilla et al. The first-order term is used to study the error induced by the truncation of the series at zeroth order, explaining the high accuracy of the IPM even at this low order of approximation.more » Interpreting the Inverse Ray Shooting (IRS) method in terms of IPM, we explain the previously reported N {sup -3/4} dependence of the IRS error with the number of collected rays per pixel. Cells intersected by critical curves (critical cells) transform to non-simply connected regions with topological pathologies like auto-overlapping or non-preservation of the boundary under the transformation. To define a non-critical partition, we use a linear approximation of the critical curve to divide each critical cell into two non-critical subcells. The optimal choice of the cell size depends basically on the curvature of the critical curves. For typical applications in which the pixel of the magnification map is a small fraction of the Einstein radius, a one-to-one relationship between the cell and pixel sizes in the absence of lensing guarantees both the consistence of the method and a very high accuracy. This prescription is simple but very conservative. We show that substantially larger cells can be used to obtain magnification maps with huge savings in computation time.« less

The Discovery of [Ni(NHC)RCN]2 Species and their Role as Cycloaddition Catalysts for the Formation of Pyridines

PubMed Central

Stolley, Ryan M.; Duong, Hung A.; Thomas, David R.; Louie, Janis

2012-01-01

The reaction of Ni(COD)2, IPr, and nitrile affords dimeric [Ni(IPr)RCN]2 in high yields. X-ray analysis revealed these species display simultaneous η1- and η2-nitrile binding modes. These dimers are catalytically competent in the formation of pyridines from the cycloaddition of diynes and nitriles. Kinetic analysis showed the reaction to be first order in [Ni(IPr)RCN]2, zeroth order in added IPr, zeroth order in nitrile, and zeroth order in diyne. Extensive stoichiometric competition studies were performed, and selective incorporation of the exogenous, not dimer bound, nitrile was observed. Post cycloaddition, the dimeric state was found to be largely preserved. Nitrile and ligand exchange experiments were performed and found to be inoperative in the catalytic cycle. These observations suggest a mechanism whereby the catalyst is activated by partial dimer-opening followed by binding of exogenous nitrile and subsequent oxidative heterocoupling. PMID:22917161

Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport.

PubMed

Garzó, Vicente; Dufty, James W; Hrenya, Christine M

2007-09-01

A hydrodynamic description for an s -component mixture of inelastic, smooth hard disks (two dimensions) or spheres (three dimensions) is derived based on the revised Enskog theory for the single-particle velocity distribution functions. In this first part of the two-part series, the macroscopic balance equations for mass, momentum, and energy are derived. Constitutive equations are calculated from exact expressions for the fluxes by a Chapman-Enskog expansion carried out to first order in spatial gradients, thereby resulting in a Navier-Stokes order theory. Within this context of small gradients, the theory is applicable to a wide range of restitution coefficients and densities. The resulting integral-differential equations for the zeroth- and first-order approximations of the distribution functions are given in exact form. An approximate solution to these equations is required for practical purposes in order to cast the constitutive quantities as algebraic functions of the macroscopic variables; this task is described in the companion paper.

On optimizing the treatment of exchange perturbations.

NASA Technical Reports Server (NTRS)

Hirschfelder, J. O.; Chipman, D. M.

1972-01-01

Most theories of exchange perturbations would give the exact energy and wave function if carried out to an infinite order. However, the different methods give different values for the second-order energy, and different values for E(1), the expectation value of the Hamiltonian corresponding to the zeroth- plus first-order wave function. In the presented paper, it is shown that the zeroth- plus first-order wave function obtained by optimizing the basic equation which is used in most exchange perturbation treatments is the exact wave function for the perturbation system and E(1) is the exact energy.

Rotordynamic coefficients for labyrinth seals calculated by means of a finite difference technique

NASA Technical Reports Server (NTRS)

Nordmann, R.; Weiser, P.

1989-01-01

The compressible, turbulent, time dependent and three dimensional flow in a labyrinth seal can be described by the Navier-Stokes equations in conjunction with a turbulence model. Additionally, equations for mass and energy conservation and an equation of state are required. To solve these equations, a perturbation analysis is performed yielding zeroth order equations for centric shaft position and first order equations describing the flow field for small motions around the seal center. For numerical solution a finite difference method is applied to the zeroth and first order equations resulting in leakage and dynamic seal coefficients respectively.

Discontinuity-free edge-diffraction model for characterization of focused wave fields.

PubMed

Sedukhin, Andrey G

2010-03-01

A model of discontinuity-free edge diffraction is proposed that is valid in the framework of the scalar Debye approximation and describes the formation process and approximate structure of the stationary diffracted field of a monochromatic converging spherical wave of limited angular opening throughout the whole space about the focus. The field is represented semianalytically in terms of the sum of a direct quasi-spherical wave and two edge quasi-conical waves of the zeroth and first order. The angular spectrum amplitudes of all these waves have smooth continuous variations of the real and imaginary parts in polar angle and radius, the separable nonanalytic functions defining the polar-angle variations of the amplitudes being found by optimization techniques.

Noise is the new signal: Moving beyond zeroth-order geomorphology (Invited)

NASA Astrophysics Data System (ADS)

Jerolmack, D. J.

2010-12-01

The last several decades have witnessed a rapid growth in our understanding of landscape evolution, led by the development of geomorphic transport laws - time- and space-averaged equations relating mass flux to some physical process(es). In statistical mechanics this approach is called mean field theory (MFT), in which complex many-body interactions are replaced with an external field that represents the average effect of those interactions. Because MFT neglects all fluctuations around the mean, it has been described as a zeroth-order fluctuation model. The mean field approach to geomorphology has enabled the development of landscape evolution models, and led to a fundamental understanding of many landform patterns. Recent research, however, has highlighted two limitations of MFT: (1) The integral (averaging) time and space scales in geomorphic systems are sometimes poorly defined and often quite large, placing the mean field approximation on uncertain footing, and; (2) In systems exhibiting fractal behavior, an integral scale does not exist - e.g., properties like mass flux are scale-dependent. In both cases, fluctuations in sediment transport are non-negligible over the scales of interest. In this talk I will synthesize recent experimental and theoretical work that confronts these limitations. Discrete element models of fluid and grain interactions show promise for elucidating transport mechanics and pattern-forming instabilities, but require detailed knowledge of micro-scale processes and are computationally expensive. An alternative approach is to begin with a reasonable MFT, and then add higher-order terms that capture the statistical dynamics of fluctuations. In either case, moving beyond zeroth-order geomorphology requires a careful examination of the origins and structure of transport “noise”. I will attempt to show how studying the signal in noise can both reveal interesting new physics, and also help to formalize the applicability of geomorphic transport laws. Flooding on an experimental alluvial fan. Intensity is related to the cumulative amount of time flow has visited an area of the fan over the experiment. Dark areas represent an emergent channel network resulting from stochastic migration of river channels.

Failure of geometric electromagnetism in the adiabatic vector Kepler problem

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

Anglin, J.R.; Schmiedmayer, J.

2004-02-01

The magnetic moment of a particle orbiting a straight current-carrying wire may precess rapidly enough in the wire's magnetic field to justify an adiabatic approximation, eliminating the rapid time dependence of the magnetic moment and leaving only the particle position as a slow degree of freedom. To zeroth order in the adiabatic expansion, the orbits of the particle in the plane perpendicular to the wire are Keplerian ellipses. Higher-order postadiabatic corrections make the orbits precess, but recent analysis of this 'vector Kepler problem' has shown that the effective Hamiltonian incorporating a postadiabatic scalar potential ('geometric electromagnetism') fails to predict themore » precession correctly, while a heuristic alternative succeeds. In this paper we resolve the apparent failure of the postadiabatic approximation, by pointing out that the correct second-order analysis produces a third Hamiltonian, in which geometric electromagnetism is supplemented by a tensor potential. The heuristic Hamiltonian of Schmiedmayer and Scrinzi is then shown to be a canonical transformation of the correct adiabatic Hamiltonian, to second order. The transformation has the important advantage of removing a 1/r{sup 3} singularity which is an artifact of the adiabatic approximation.« less

Relativistic (SR-ZORA) quantum theory of atoms in molecules properties.

PubMed

Anderson, James S M; Rodríguez, Juan I; Ayers, Paul W; Götz, Andreas W

2017-01-15

The Quantum Theory of Atoms in Molecules (QTAIM) is used to elucidate the effects of relativity on chemical systems. To do this, molecules are studied using density-functional theory at both the nonrelativistic level and using the scalar relativistic zeroth-order regular approximation. Relativistic effects on the QTAIM properties and topology of the electron density can be significant for chemical systems with heavy atoms. It is important, therefore, to use the appropriate relativistic treatment of QTAIM (Anderson and Ayers, J. Phys. Chem. 2009, 115, 13001) when treating systems with heavy atoms. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Accuracy of the Generalized Self-Consistent Method in Modelling the Elastic Behaviour of Periodic Composites

NASA Technical Reports Server (NTRS)

Walker, Kevin P.; Freed, Alan D.; Jordan, Eric H.

1993-01-01

Local stress and strain fields in the unit cell of an infinite, two-dimensional, periodic fibrous lattice have been determined by an integral equation approach. The effect of the fibres is assimilated to an infinite two-dimensional array of fictitious body forces in the matrix constituent phase of the unit cell. By subtracting a volume averaged strain polarization term from the integral equation we effectively embed a finite number of unit cells in a homogenized medium in which the overall stress and strain correspond to the volume averaged stress and strain of the constrained unit cell. This paper demonstrates that the zeroth term in the governing integral equation expansion, which embeds one unit cell in the homogenized medium, corresponds to the generalized self-consistent approximation. By comparing the zeroth term approximation with higher order approximations to the integral equation summation, both the accuracy of the generalized self-consistent composite model and the rate of convergence of the integral summation can be assessed. Two example composites are studied. For a tungsten/copper elastic fibrous composite the generalized self-consistent model is shown to provide accurate, effective, elastic moduli and local field representations. The local elastic transverse stress field within the representative volume element of the generalized self-consistent method is shown to be in error by much larger amounts for a composite with periodically distributed voids, but homogenization leads to a cancelling of errors, and the effective transverse Young's modulus of the voided composite is shown to be in error by only 23% at a void volume fraction of 75%.

Stochastic multi-reference perturbation theory with application to the linearized coupled cluster method

NASA Astrophysics Data System (ADS)

Jeanmairet, Guillaume; Sharma, Sandeep; Alavi, Ali

2017-01-01

In this article we report a stochastic evaluation of the recently proposed multireference linearized coupled cluster theory [S. Sharma and A. Alavi, J. Chem. Phys. 143, 102815 (2015)]. In this method, both the zeroth-order and first-order wavefunctions are sampled stochastically by propagating simultaneously two populations of signed walkers. The sampling of the zeroth-order wavefunction follows a set of stochastic processes identical to the one used in the full configuration interaction quantum Monte Carlo (FCIQMC) method. To sample the first-order wavefunction, the usual FCIQMC algorithm is augmented with a source term that spawns walkers in the sampled first-order wavefunction from the zeroth-order wavefunction. The second-order energy is also computed stochastically but requires no additional overhead outside of the added cost of sampling the first-order wavefunction. This fully stochastic method opens up the possibility of simultaneously treating large active spaces to account for static correlation and recovering the dynamical correlation using perturbation theory. The method is used to study a few benchmark systems including the carbon dimer and aromatic molecules. We have computed the singlet-triplet gaps of benzene and m-xylylene. For m-xylylene, which has proved difficult for standard complete active space self consistent field theory with perturbative correction, we find the singlet-triplet gap to be in good agreement with the experimental values.

sdg Interacting boson hamiltonian in the seniority scheme

NASA Astrophysics Data System (ADS)

Yoshinaga, N.

1989-03-01

The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagonalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.

Atomic electron energies including relativistic effects and quantum electrodynamic corrections

NASA Technical Reports Server (NTRS)

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

1977-01-01

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

Second-order small disturbance theory for hypersonic flow over power-law bodies. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Townsend, J. C.

1974-01-01

A mathematical method for determining the flow field about power-law bodies in hypersonic flow conditions is developed. The second-order solutions, which reflect the effects of the second-order terms in the equations, are obtained by applying the method of small perturbations in terms of body slenderness parameter to the zeroth-order solutions. The method is applied by writing each flow variable as the sum of a zeroth-order and a perturbation function, each multiplied by the axial variable raised to a power. The similarity solutions are developed for infinite Mach number. All results obtained are for no flow through the body surface (as a boundary condition), but the derivation indicates that small amounts of blowing or suction through the wall can be accommodated.

Optimal symmetric flight studies

NASA Technical Reports Server (NTRS)

Weston, A. R.; Menon, P. K. A.; Bilimoria, K. D.; Cliff, E. M.; Kelley, H. J.

1985-01-01

Several topics in optimal symmetric flight of airbreathing vehicles are examined. In one study, an approximation scheme designed for onboard real-time energy management of climb-dash is developed and calculations for a high-performance aircraft presented. In another, a vehicle model intermediate in complexity between energy and point-mass models is explored and some quirks in optimal flight characteristics peculiar to the model uncovered. In yet another study, energy-modelling procedures are re-examined with a view to stretching the range of validity of zeroth-order approximation by special choice of state variables. In a final study, time-fuel tradeoffs in cruise-dash are examined for the consequences of nonconvexities appearing in the classical steady cruise-dash model. Two appendices provide retrospective looks at two early publications on energy modelling and related optimal control theory.

Exploration of zeroth-order wavefunctions and energies as a first step toward intramolecular symmetry-adapted perturbation theory

NASA Astrophysics Data System (ADS)

Gonthier, Jérôme F.; Corminboeuf, Clémence

2014-04-01

Non-covalent interactions occur between and within all molecules and have a profound impact on structural and electronic phenomena in chemistry, biology, and material science. Understanding the nature of inter- and intramolecular interactions is essential not only for establishing the relation between structure and properties, but also for facilitating the rational design of molecules with targeted properties. These objectives have motivated the development of theoretical schemes decomposing intermolecular interactions into physically meaningful terms. Among the various existing energy decomposition schemes, Symmetry-Adapted Perturbation Theory (SAPT) is one of the most successful as it naturally decomposes the interaction energy into physical and intuitive terms. Unfortunately, analogous approaches for intramolecular energies are theoretically highly challenging and virtually nonexistent. Here, we introduce a zeroth-order wavefunction and energy, which represent the first step toward the development of an intramolecular variant of the SAPT formalism. The proposed energy expression is based on the Chemical Hamiltonian Approach (CHA), which relies upon an asymmetric interpretation of the electronic integrals. The orbitals are optimized with a non-hermitian Fock matrix based on two variants: one using orbitals strictly localized on individual fragments and the other using canonical (delocalized) orbitals. The zeroth-order wavefunction and energy expression are validated on a series of prototypical systems. The computed intramolecular interaction energies demonstrate that our approach combining the CHA with strictly localized orbitals achieves reasonable interaction energies and basis set dependence in addition to producing intuitive energy trends. Our zeroth-order wavefunction is the primary step fundamental to the derivation of any perturbation theory correction, which has the potential to truly transform our understanding and quantification of non-bonded intramolecular interactions.

Exploration of zeroth-order wavefunctions and energies as a first step toward intramolecular symmetry-adapted perturbation theory

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

Gonthier, Jérôme F.; Corminboeuf, Clémence, E-mail: clemence.corminboeuf@epfl.ch

2014-04-21

Non-covalent interactions occur between and within all molecules and have a profound impact on structural and electronic phenomena in chemistry, biology, and material science. Understanding the nature of inter- and intramolecular interactions is essential not only for establishing the relation between structure and properties, but also for facilitating the rational design of molecules with targeted properties. These objectives have motivated the development of theoretical schemes decomposing intermolecular interactions into physically meaningful terms. Among the various existing energy decomposition schemes, Symmetry-Adapted Perturbation Theory (SAPT) is one of the most successful as it naturally decomposes the interaction energy into physical and intuitivemore » terms. Unfortunately, analogous approaches for intramolecular energies are theoretically highly challenging and virtually nonexistent. Here, we introduce a zeroth-order wavefunction and energy, which represent the first step toward the development of an intramolecular variant of the SAPT formalism. The proposed energy expression is based on the Chemical Hamiltonian Approach (CHA), which relies upon an asymmetric interpretation of the electronic integrals. The orbitals are optimized with a non-hermitian Fock matrix based on two variants: one using orbitals strictly localized on individual fragments and the other using canonical (delocalized) orbitals. The zeroth-order wavefunction and energy expression are validated on a series of prototypical systems. The computed intramolecular interaction energies demonstrate that our approach combining the CHA with strictly localized orbitals achieves reasonable interaction energies and basis set dependence in addition to producing intuitive energy trends. Our zeroth-order wavefunction is the primary step fundamental to the derivation of any perturbation theory correction, which has the potential to truly transform our understanding and quantification of non-bonded intramolecular interactions.« less

Is the choice of a standard zeroth-order hamiltonian in CASPT2 ansatz optimal in calculations of excitation energies in protonated and unprotonated schiff bases of retinal?

PubMed

Wolański, Łukasz; Grabarek, Dawid; Andruniów, Tadeusz

2018-04-10

To account for systematic error of CASPT2 method empirical modification of the zeroth-order Hamiltonian with Ionization Potential-Electron Affinity (IPEA) shift was introduced. The optimized IPEA value (0.25 a.u.), called standard IPEA (S-IPEA), was recommended but due to its unsatisfactory performance in multiple metallic and organic compounds it has been questioned lately as a general parameter working properly for all molecules under CASPT2 study. As we are interested in Schiff bases of retinal, an important question emerging from this conflict of choice, to use or not to use S-IPEA, is whether the introduction of the modified zeroth-order Hamiltonian into CASPT2 ansatz does really improve their energetics. To achieve this goal, we assessed an impact of the IPEA shift value, in a range of 0-0.35 a.u., on vertical excitation energies to low-lying singlet states of two protonated (RPSBs) and two unprotonated (RSBs) Schiff bases of retinal for which experimental data in gas phase are available. In addition, an effect of geometry, basis set, and active space on computed VEEs is also reported. We find, that for these systems, the choice of S-IPEA significantly overestimates both S 0 →S 1 and S 0 →S 2 energies and the best theoretical estimate, in reference to the experimental data, is provided with either unmodified zeroth-order Hamiltonian or small value of the IPEA shift in a range of 0.05-0.15 a.u., depending on active space and basis set size, equilibrium geometry, and character of the excited state. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.

Incident-beam effects in electron-stimulated Auger-electron diffraction

NASA Astrophysics Data System (ADS)

Gao, Y.; Cao, Jianming

1991-04-01

We have examined incident-beam effects in electron-stimulated Auger-electron diffraction (AED) on a cleaved GaAs(110) surface. The results indicate that incident-beam diffraction is significant in an AED experiment, and that the dissipative nature of the incident beam in contributing to the Auger process must be accounted for. We have developed a qualitative model that describes the trend of the polar-angle dependence of the Auger intensity for both the incident and exit beams. In calculating the diffraction features, we used a zeroth-order approximation to simulate the dissipation of the incident beam, which is found to adequately describe the experimental data.

Anomalous resonances of an optical microcavity with a hyperbolic metamaterial core

NASA Astrophysics Data System (ADS)

Travkin, Evgenij; Kiel, Thomas; Sadofev, Sergey; Busch, Kurt; Benson, Oliver; Kalusniak, Sascha

2018-05-01

We embed a hyperbolic metamaterial based on stacked layer pairs of epitaxially grown ZnO/ZnO:Ga in a monolithic optical microcavity, and we investigate the arising unique resonant effects experimentally and theoretically. Unlike traditional metals, the semiconductor-based approach allows us to utilize all three permittivity regions of the hyperbolic metamaterial in the near-infrared spectral range. This configuration gives rise to modes of identical orders appearing at different frequencies, a zeroth-order resonance in an all-positive permittivity region, and a continuum of high-order modes. In addition, an unusual lower cutoff frequency is introduced to the resonator mode spectrum. The observed effects expand the possibilities for customization of optical resonators; in particular, the zeroth-order and high-order modes hold strong potential for the realization of deeply subwavelength cavity sizes.

A comparative study of Laplacians and Schroedinger- Lichnerowicz-Weitzenboeck identities in Riemannian and antisymplectic geometry

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

Batalin, Igor A.; I.E. Tamm Theory Division, P.N. Lebedev Physics Institute, Russian Academy of Sciences, 53 Leninsky Prospect, Moscow 119991; Bering, Klaus

2009-07-15

We introduce an antisymplectic Dirac operator and antisymplectic gamma matrices. We explore similarities between, on one hand, the Schroedinger-Lichnerowicz formula for spinor bundles in Riemannian spin geometry, which contains a zeroth-order term proportional to the Levi-Civita scalar curvature, and, on the other hand, the nilpotent, Grassmann-odd, second-order {delta} operator in antisymplectic geometry, which, in general, has a zeroth-order term proportional to the odd scalar curvature of an arbitrary antisymplectic and torsion-free connection that is compatible with the measure density. Finally, we discuss the close relationship with the two-loop scalar curvature term in the quantum Hamiltonian for a particle in amore » curved Riemannian space.« less

A real-time approximate optimal guidance law for flight in a plane

NASA Technical Reports Server (NTRS)

Feeley, Timothy S.; Speyer, Jason L.

1990-01-01

A real-time guidance scheme is presented for the problem of maximizing the payload into orbit subject to the equations of motion of a rocket over a nonrotating spherical earth. The flight is constrained to a path in the equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of the problem can be separated into primary and perturbation effects by a small parameter, epsilon, which is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The neglected perturbation terms are included in the higher-order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only integrations which are quadratures. The quadratures can be performed rapidly with emerging computer capability, so that real-time approximate optimization can be used to construct the launch guidance law. The application of this technique to flight in three-dimensions is made apparent from the solution presented.

Connection between the regular approximation and the normalized elimination of the small component in relativistic quantum theory

NASA Astrophysics Data System (ADS)

Filatov, Michael; Cremer, Dieter

2005-02-01

The regular approximation to the normalized elimination of the small component (NESC) in the modified Dirac equation has been developed and presented in matrix form. The matrix form of the infinite-order regular approximation (IORA) expressions, obtained in [Filatov and Cremer, J. Chem. Phys. 118, 6741 (2003)] using the resolution of the identity, is the exact matrix representation and corresponds to the zeroth-order regular approximation to NESC (NESC-ZORA). Because IORA (=NESC-ZORA) is a variationally stable method, it was used as a suitable starting point for the development of the second-order regular approximation to NESC (NESC-SORA). As shown for hydrogenlike ions, NESC-SORA energies are closer to the exact Dirac energies than the energies from the fifth-order Douglas-Kroll approximation, which is much more computationally demanding than NESC-SORA. For the application of IORA (=NESC-ZORA) and NESC-SORA to many-electron systems, the number of the two-electron integrals that need to be evaluated (identical to the number of the two-electron integrals of a full Dirac-Hartree-Fock calculation) was drastically reduced by using the resolution of the identity technique. An approximation was derived, which requires only the two-electron integrals of a nonrelativistic calculation. The accuracy of this approach was demonstrated for heliumlike ions. The total energy based on the approximate integrals deviates from the energy calculated with the exact integrals by less than 5×10-9hartree units. NESC-ZORA and NESC-SORA can easily be implemented in any nonrelativistic quantum chemical program. Their application is comparable in cost with that of nonrelativistic methods. The methods can be run with density functional theory and any wave function method. NESC-SORA has the advantage that it does not imply a picture change.

An iwatsubo-based solution for labyrinth seals - comparison with experimental results

NASA Technical Reports Server (NTRS)

Childs, D. W.; Scharrer, J. K.

1984-01-01

The basic equations are derived for compressible flow in a labyrinth seal. The flow is assumed to be completely turbulent in the circumferential direction where the friction factor is determined by the Blasius relation. Linearized zeroth and first-order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth-order pressure distribution is found by satisfying the leakage equation while the circumferential velocity distribution is determined by satisfying the momentum equation. The first-order equations are solved by a separation of variables solution. Integration of the resultant pressure distribution along and around the seal defines the reaction force developed by the seal and the corresponding dynamic coefficients. The results of this analysis are compared to published test results.

Nuclear recoil effect on the binding energies in highly charged He-like ions

NASA Astrophysics Data System (ADS)

Malyshev, A. V.; Popov, R. V.; Shabaev, V. M.; Zubova, N. A.

2018-04-01

The most precise to-date evaluation of the nuclear recoil effect on the n = 1 and n = 2 energy levels of He-like ions is presented in the range Z = 12–100. The one-electron recoil contribution is calculated within the framework of the rigorous quantum electrodynamics approach to first order in the electron-to-nucleus mass ratio m/M and to all orders in the parameter αZ. The two-electron m/M recoil term is calculated employing the 1/Z perturbation theory. The recoil contribution of the zeroth order in 1/Z is evaluated to all orders in αZ, while the 1/Z term is calculated using the Breit approximation. The recoil corrections of the second and higher orders in 1/Z are taken into account within the nonrelativistic approach. The obtained results are compared with the previous evaluation of this effect (Artemyev et al 2005 Phys. Rev. A 71 062104).

B0 concomitant field compensation for MRI systems employing asymmetric transverse gradient coils.

PubMed

Weavers, Paul T; Tao, Shengzhen; Trzasko, Joshua D; Frigo, Louis M; Shu, Yunhong; Frick, Matthew A; Lee, Seung-Kyun; Foo, Thomas K-F; Bernstein, Matt A

2018-03-01

Imaging gradients result in the generation of concomitant fields, or Maxwell fields, which are of increasing importance at higher gradient amplitudes. These time-varying fields cause additional phase accumulation, which must be compensated for to avoid image artifacts. In the case of gradient systems employing symmetric design, the concomitant fields are well described with second-order spatial variation. Gradient systems employing asymmetric design additionally generate concomitant fields with global (zeroth-order or B 0 ) and linear (first-order) spatial dependence. This work demonstrates a general solution to eliminate the zeroth-order concomitant field by applying the correct B 0 frequency shift in real time to counteract the concomitant fields. Results are demonstrated for phase contrast, spiral, echo-planar imaging (EPI), and fast spin-echo imaging. A global phase offset is reduced in the phase-contrast exam, and blurring is virtually eliminated in spiral images. The bulk image shift in the phase-encode direction is compensated for in EPI, whereas signal loss, ghosting, and blurring are corrected in the fast-spin echo images. A user-transparent method to compensate the zeroth-order concomitant field term by center frequency shifting is proposed and implemented. This solution allows all the existing pulse sequences-both product and research-to be retained without any modifications. Magn Reson Med 79:1538-1544, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Optimal guidance law development for an advanced launch system

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Hodges, Dewey H.; Leung, Martin S.; Bless, Robert R.

1991-01-01

The proposed investigation on a Matched Asymptotic Expansion (MAE) method was carried out. It was concluded that the method of MAE is not applicable to launch vehicle ascent trajectory optimization due to a lack of a suitable stretched variable. More work was done on the earlier regular perturbation approach using a piecewise analytic zeroth order solution to generate a more accurate approximation. In the meantime, a singular perturbation approach using manifold theory is also under current investigation. Work on a general computational environment based on the use of MACSYMA and the weak Hamiltonian finite element method continued during this period. This methodology is capable of the solution of a large class of optimal control problems.

Thermohydrodynamic Analysis of Cryogenic Liquid Turbulent Flow Fluid Film Bearings

NASA Technical Reports Server (NTRS)

SanAndres, Luis

1996-01-01

Computational programs developed for the thermal analysis of tilting and flexure-pad hybrid bearings, and the unsteady flow and transient response of a point mass rotor supported on fluid film bearings are described. The motion of a cryogenic liquid on the thin film annular region of a fluid film bearing is described by a set of mass and momentum conservation, and energy transport equations for the turbulent bulk-flow velocities and pressure, and accompanied by thermophysical state equations for evaluation of the fluid material properties. Zeroth-order equations describe the fluid flow field for a journal static equilibrium position, while first-order (linear) equations govern the fluid flow for small amplitude-journal center translational motions. Solution to the zeroth-order flow field equations provides the bearing flow rate, load capacity, drag torque and temperature rise. Solution to the first-order equations determines the rotordynamic force coefficients due to journal radial motions.

Design and simulation of origami structures with smooth folds

PubMed Central

Peraza Hernandez, E. A.; Lagoudas, D. C.

2017-01-01

Origami has enabled new approaches to the fabrication and functionality of multiple structures. Current methods for origami design are restricted to the idealization of folds as creases of zeroth-order geometric continuity. Such an idealization is not proper for origami structures of non-negligible fold thickness or maximum curvature at the folds restricted by material limitations. For such structures, folds are not properly represented as creases but rather as bent regions of higher-order geometric continuity. Such fold regions of arbitrary order of continuity are termed as smooth folds. This paper presents a method for solving the following origami design problem: given a goal shape represented as a polygonal mesh (termed as the goal mesh), find the geometry of a single planar sheet, its pattern of smooth folds, and the history of folding motion allowing the sheet to approximate the goal mesh. The parametrization of the planar sheet and the constraints that allow for a valid pattern of smooth folds are presented. The method is tested against various goal meshes having diverse geometries. The results show that every determined sheet approximates its corresponding goal mesh in a known folded configuration having fold angles obtained from the geometry of the goal mesh. PMID:28484322

Design and simulation of origami structures with smooth folds.

PubMed

Peraza Hernandez, E A; Hartl, D J; Lagoudas, D C

2017-04-01

Origami has enabled new approaches to the fabrication and functionality of multiple structures. Current methods for origami design are restricted to the idealization of folds as creases of zeroth-order geometric continuity. Such an idealization is not proper for origami structures of non-negligible fold thickness or maximum curvature at the folds restricted by material limitations. For such structures, folds are not properly represented as creases but rather as bent regions of higher-order geometric continuity. Such fold regions of arbitrary order of continuity are termed as smooth folds . This paper presents a method for solving the following origami design problem: given a goal shape represented as a polygonal mesh (termed as the goal mesh ), find the geometry of a single planar sheet, its pattern of smooth folds, and the history of folding motion allowing the sheet to approximate the goal mesh. The parametrization of the planar sheet and the constraints that allow for a valid pattern of smooth folds are presented. The method is tested against various goal meshes having diverse geometries. The results show that every determined sheet approximates its corresponding goal mesh in a known folded configuration having fold angles obtained from the geometry of the goal mesh.

Charge renormalization at the large-D limit for N-electron atoms and weakly bound systems

NASA Astrophysics Data System (ADS)

Kais, S.; Bleil, R.

1995-05-01

We develop a systematic way to determine an effective nuclear charge ZRD such that the Hartree-Fock results will be significantly closer to the exact energies by utilizing the analytically known large-D limit energies. This method yields an expansion for the effective nuclear charge in powers of (1/D), which we have evaluated to the first order. This first order approximation to the desired effective nuclear charge has been applied to two-electron atoms with Z=2-20, and weakly bound systems such as H-. The errors for the two-electron atoms when compared with exact results were reduced from ˜0.2% for Z=2 to ˜0.002% for large Z. Although usual Hartree-Fock calculations for H- show this to be unstable, our results reduce the percent error of the Hartree-Fock energy from 7.6% to 1.86% and predicts the anion to be stable. For N-electron atoms (N=3-18, Z=3-28), using only the zeroth order approximation for the effective charge significantly reduces the error of Hartree-Fock calculations and recovers more than 80% of the correlation energy.

Analytic model of a multi-electron atom

NASA Astrophysics Data System (ADS)

Skoromnik, O. D.; Feranchuk, I. D.; Leonau, A. U.; Keitel, C. H.

2017-12-01

A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis completeness allows us to employ the secondary-quantized representation for the construction of regular perturbation theory, which includes in a natural way correlation effects, converges fast and enables an effective calculation of the subsequent corrections. The hydrogen-like basis set provides a possibility to perform all summations over intermediate states in closed form, including both the discrete and continuous spectra. This is achieved with the help of the decomposition of the multi-particle Green function in a convolution of single-electronic Coulomb Green functions. We demonstrate that our fully analytical zeroth-order approximation describes the whole spectrum of the system, provides accuracy, which is independent of the number of electrons and is important for applications where the Thomas-Fermi model is still utilized. In addition already in second-order perturbation theory our results become comparable with those via a multi-configuration Hartree-Fock approach.

Quantum transport in graphene in presence of strain-induced pseudo-Landau levels

NASA Astrophysics Data System (ADS)

Settnes, Mikkel; Leconte, Nicolas; Barrios-Vargas, Jose E.; Jauho, Antti-Pekka; Roche, Stephan

2016-09-01

We report on mesoscopic transport fingerprints in disordered graphene caused by strain-field induced pseudomagnetic Landau levels (pLLs). Efficient numerical real space calculations of the Kubo formula are performed for an ordered network of nanobubbles in graphene, creating pseudomagnetic fields up to several hundreds of Tesla, values inaccessible by real magnetic fields. Strain-induced pLLs yield enhanced scattering effects across the energy spectrum resulting in lower mean free path and enhanced localization effects. In the vicinity of the zeroth order pLL, we demonstrate an anomalous transport regime, where the mean free paths increases with disorder. We attribute this puzzling behavior to the low-energy sub-lattice polarization induced by the zeroth order pLL, which is unique to pseudomagnetic fields preserving time-reversal symmetry. These results, combined with the experimental feasibility of reversible deformation fields, open the way to tailor a metal-insulator transition driven by pseudomagnetic fields.

A Comparison of Experimental and Theoretical Results for Labyrinth Gas Seals. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Scharrer, Joseph Kirk

1987-01-01

The basic equations are derived for a two control volume model for compressible flow in a labyrinth seal. The flow is assumed to be completely turbulent and isoenergetic. The wall friction factors are determined using the Blasius formula. Jet flow theory is used for the calculation of the recirculation velocity in the cavity. Linearized zeroth and first order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth order pressure distribution is found by satisfying the leakage equation. The circumferential velocity distribution is determined by satisfying the momentum equations. The first order equations are solved by a separation of variable solution. Integration of the resultant pressure distribution along and around the seal defines the reaction force developed by the seal and the corresponding dynamic coefficients. The results of this analysis are compared to experimental test results.

Fokker-Planck electron diffusion caused by an obliquely propagating electromagnetic wave packet of narrow bandwidth

NASA Technical Reports Server (NTRS)

Hizanidis, Kyriakos

1989-01-01

The relativistic motion of electrons in an intense electromagnetic wave packet propagating obliquely to a uniform magnetic field is analytically studied on the basis of the Fokker-Planck-Kolmogorov (FPK) approach. The wavepacket consists of circularly polarized electron-cyclotron waves. The dynamical system in question is shown to be reducible to one with three degrees of freedom. Within the framework of the Hamiltonian analysis the nonlinear diffusion tensor is derived, and it is shown that this tensor can be separated into zeroth-, first-, and second-order parts with respect to the relative bandwidth. The zeroth-order part describes diffusive acceleration along lines of constant unperturbed Hamiltonian. The second-order part, which corresponds to the longest time scale, describes diffusion across those lines. A possible transport theory is outlined on the basis of this separation of the time scales.

Combinatorial Broadening Mechanism of O-H Stretching Bands in H-Bonded Molecular Clusters

NASA Astrophysics Data System (ADS)

Pitsevich, G. A.; Doroshenko, I. Yu.; Pogorelov, V. E.; Pettersson, L. G. M.; Sablinskas, V.; Sapeshko, V. V.; Balevicius, V.

2016-07-01

A new mechanism for combinatorial broadening of donor-OH stretching-vibration absorption bands in molecular clusters with H-bonds is proposed. It enables the experimentally observed increase of the O-H stretching-vibration bandwidth with increasing number of molecules in H-bonded clusters to be explained. Knowledge of the half-width of the OH stretching-vibration absorption band in the dimer and the number of H-bonds in the analyzed cluster is suffi cient in the zeroth-order approximation to estimate the O-H stretching-absorption bands in clusters containing several molecules. Good agreement between the calculated and published experimental half-widths of the OH stretching-vibration absorption bands in MeOH and PrOH clusters was obtained using this approach.

Quantum theory of atoms in molecules: results for the SR-ZORA Hamiltonian.

PubMed

Anderson, James S M; Ayers, Paul W

2011-11-17

The quantum theory of atoms in molecules (QTAIM) is generalized to include relativistic effects using the popular scalar-relativistic zeroth-order regular approximation (SR-ZORA). It is usually assumed that the definition of the atom as a volume bounded by a zero-flux surface of the electron density is closely linked to the form of the kinetic energy, so it is somewhat surprising that the atoms corresponding to the relativistic kinetic-energy operator in the SR-ZORA Hamiltonian are also bounded by zero-flux surfaces. The SR-ZORA Hamiltonian should be sufficient for qualitative descriptions of molecular electronic structure across the periodic table, which suggests that QTAIM-based analysis can be useful for molecules and solids containing heavy atoms.

Zeroth Law, Entropy, Equilibrium, and All That

ERIC Educational Resources Information Center

Canagaratna, Sebastian G.

2008-01-01

The place of the zeroth law in the teaching of thermodynamics is examined in the context of the recent discussion by Gislason and Craig of some problems involving the establishment of thermal equilibrium. The concept of thermal equilibrium is introduced through the zeroth law. The relation between the zeroth law and the second law in the…

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

NASA Technical Reports Server (NTRS)

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

1976-01-01

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

α '-corrected black holes in String Theory

NASA Astrophysics Data System (ADS)

Cano, Pablo A.; Meessen, Patrick; Ortín, Tomás; Ramírez, Pedro F.

2018-05-01

We consider the well-known solution of the Heterotic Superstring effective action to zeroth order in α ' that describes the intersection of a fundamental string with momentum and a solitonic 5-brane and which gives a 3-charge, static, extremal, supersymmetric black hole in 5 dimensions upon dimensional reduction on T5. We compute explicitly the first-order in α ' corrections to this solution, including SU(2) Yang-Mills fields which can be used to cancel some of these corrections and we study the main properties of this α '-corrected solution: supersymmetry, values of the near-horizon and asymptotic charges, behavior under α '-corrected T-duality, value of the entropy (using Wald formula directly in 10 dimensions), existence of small black holes etc. The value obtained for the entropy agrees, within the limits of approximation, with that obtained by microscopic methods. The α ' corrections coming from Wald's formula prove crucial for this result.

Scintillation analysis of truncated Bessel beams via numerical turbulence propagation simulation.

PubMed

Eyyuboğlu, Halil T; Voelz, David; Xiao, Xifeng

2013-11-20

Scintillation aspects of truncated Bessel beams propagated through atmospheric turbulence are investigated using a numerical wave optics random phase screen simulation method. On-axis, aperture averaged scintillation and scintillation relative to a classical Gaussian beam of equal source power and scintillation per unit received power are evaluated. It is found that in almost all circumstances studied, the zeroth-order Bessel beam will deliver the lowest scintillation. Low aperture averaged scintillation levels are also observed for the fourth-order Bessel beam truncated by a narrower source window. When assessed relative to the scintillation of a Gaussian beam of equal source power, Bessel beams generally have less scintillation, particularly at small receiver aperture sizes and small beam orders. Upon including in this relative performance measure the criteria of per unit received power, this advantageous position of Bessel beams mostly disappears, but zeroth- and first-order Bessel beams continue to offer some advantage for relatively smaller aperture sizes, larger source powers, larger source plane dimensions, and intermediate propagation lengths.

Transmission-line model to design matching stage for light coupling into two-dimensional photonic crystals.

PubMed

Miri, Mehdi; Khavasi, Amin; Mehrany, Khashayar; Rashidian, Bizhan

2010-01-15

The transmission-line analogy of the planar electromagnetic reflection problem is exploited to obtain a transmission-line model that can be used to design effective, robust, and wideband interference-based matching stages. The proposed model based on a new definition for a scalar impedance is obtained by using the reflection coefficient of the zeroth-order diffracted plane wave outside the photonic crystal. It is shown to be accurate for in-band applications, where the normalized frequency is low enough to ensure that the zeroth-order diffracted plane wave is the most important factor in determining the overall reflection. The frequency limitation of employing the proposed approach is explored, highly dispersive photonic crystals are considered, and wideband matching stages based on binomial impedance transformers are designed to work at the first two photonic bands.

All-temperature magnon theory of ferromagnetism

NASA Astrophysics Data System (ADS)

Datta, Sambhu N.; Panda, Anirban

2009-08-01

We present an all-temperature magnon formalism for ferromagnetic solids. To our knowledge, this is the first time that all-temperature spin statistics have been calculated. The general impression up to now is that the magnon formalism breaks down at the Curie point as it introduces a series expansion and unphysical states. Our treatment is based on an accurate quantum mechanical representation of the Holstein-Primakoff transformation. To achieve this end, we introduce the 'Kubo operator'. The treatment is valid for all 14 types of Bravais lattices, and not limited to simple cubic unit cells. In the present work, we carry out a zeroth-order treatment involving all possible spin states, and leaving out all unphysical states. In a subsequent paper we will show that the perturbed energy values are very different, but the magnetic properties undergo only small modifications from the zeroth-order results.

The super-NFW model: an analytic dynamical model for cold dark matter haloes and elliptical galaxies

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Evans, N. Wyn; Sanders, Jason L.

2018-05-01

An analytic galaxy model with ρ ˜ r-1 at small radii and ρ ˜ r-3.5 at large radii is presented. The asymptotic density fall-off is slower than the Hernquist model, but faster than the Navarro-Frenk-White (NFW) profile for dark matter haloes, and so in accord with recent evidence from cosmological simulations. The model provides the zeroth-order term in a biorthornomal basis function expansion, meaning that axisymmetric, triaxial, and lopsided distortions can easily be added (much like the Hernquist model itself which is the zeroth-order term of the Hernquist-Ostriker expansion). The properties of the spherical model, including analytic distribution functions which are either isotropic, radially anisotropic, or tangentially anisotropic, are discussed in some detail. The analogue of the mass-concentration relation for cosmological haloes is provided.

On optimizing the treatment of exchange perturbations

NASA Technical Reports Server (NTRS)

Hirschfelder, J. O.; Chipman, D. M.

1972-01-01

A method using the zeroth plus first order wave functions, obtained by optimizing the basic equation used in exchange perturbation treatments, is utilized in an attempt to determine the exact energy and wave function in the exchange process. Attempts to determine the first order perturbation solution by optimizing the sum of the first and second order energies were unsuccessful.

Morphing Continuum Theory: A First Order Approximation to the Balance Laws

NASA Astrophysics Data System (ADS)

Wonnell, Louis; Cheikh, Mohamad Ibrahim; Chen, James

2017-11-01

Morphing Continuum Theory is constructed under the framework of Rational Continuum Mechanics (RCM) for fluid flows with inner structure. This multiscale theory has been successfully emplyed to model turbulent flows. The framework of RCM ensures the mathematical rigor of MCT, but contains new material constants related to the inner structure. The physical meanings of these material constants have yet to be determined. Here, a linear deviation from the zeroth-order Boltzmann-Curtiss distribution function is derived. When applied to the Boltzmann-Curtiss equation, a first-order approximation of the MCT governing equations is obtained. The integral equations are then related to the appropriate material constants found in the heat flux, Cauchy stress, and moment stress terms in the governing equations. These new material properties associated with the inner structure of the fluid are compared with the corresponding integrals, and a clearer physical interpretation of these coefficients emerges. The physical meanings of these material properties is determined by analyzing previous results obtained from numerical simulations of MCT for compressible and incompressible flows. The implications for the physics underlying the MCT governing equations will also be discussed. This material is based upon work supported by the Air Force Office of Scientific Research under Award Number FA9550-17-1-0154.

Effect of collisions on photoelectron sheath in a gas

NASA Astrophysics Data System (ADS)

Sodha, Mahendra Singh; Mishra, S. K.

2016-02-01

This paper presents a study of the effect of the collision of electrons with atoms/molecules on the structure of a photoelectron sheath. Considering the half Fermi-Dirac distribution of photo-emitted electrons, an expression for the electron density in the sheath has been derived in terms of the electric potential and the structure of the sheath has been investigated by incorporating Poisson's equation in the analysis. The method of successive approximations has been used to solve Poisson's equation with the solution for the electric potential in the case of vacuum, obtained earlier [Sodha and Mishra, Phys. Plasmas 21, 093704 (2014)], being used as the zeroth order solution for the present analysis. The inclusion of collisions influences the photoelectron sheath structure significantly; a reduction in the sheath width with increasing collisions is obtained.

Force and moment rotordynamic coefficients for pump-impeller shroud surfaces

NASA Technical Reports Server (NTRS)

Childs, Dara W.

1987-01-01

Governing equations of motion are derived for a bulk-flow model of the leakage path between an impeller shroud and a pump housing. The governing equations consist of a path-momentum, a circumferential - momentum, and a continuity equation. The fluid annulus between the impeller shroud and pump housing is assumed to be circumferentially symmetric when the impeller is centered; i.e., the clearance can vary along the pump axis but does not vary in the circumferential direction. A perturbation expansion of the governing equations in the eccentricity ratio yields a set of zeroth and first-order governing equations. The zeroth-order equations define the leaking rate and the circumferential and path velocity distributions and pressure distributions for a centered impeller position. The first-order equations define the perturbations in the velocity and pressure distributions due to either a radial-displacement perturbation or a tilt perturbation of the impeller. Integration of the perturbed pressure and shear-stress distribution acting on the rotor yields the reaction forces and moments acting on the impeller face.

Potential Energy Surface of the Chromium Dimer Re-re-revisited with Multiconfigurational Perturbation Theory.

PubMed

Vancoillie, Steven; Malmqvist, Per Åke; Veryazov, Valera

2016-04-12

The chromium dimer has long been a benchmark molecule to evaluate the performance of different computational methods ranging from density functional theory to wave function methods. Among the latter, multiconfigurational perturbation theory was shown to be able to reproduce the potential energy surface of the chromium dimer accurately. However, for modest active space sizes, it was later shown that different definitions of the zeroth-order Hamiltonian have a large impact on the results. In this work, we revisit the system for the third time with multiconfigurational perturbation theory, now in order to increase the active space of the reference wave function. This reduces the impact of the choice of zeroth-order Hamiltonian and improves the shape of the potential energy surface significantly. We conclude by comparing our results of the dissocation energy and vibrational spectrum to those obtained from several highly accurate multiconfigurational methods and experiment. For a meaningful comparison, we used the extrapolation to the complete basis set for all methods involved.

Transient solute transport with sorption in Poiseuille flow

NASA Astrophysics Data System (ADS)

Hesse, M. A.; Zhang, L.; Wang, M.

2016-12-01

Sorption onto the wall has been observed to both increase [Lungu and Moffatt, 1982] and decrease the average solute transport velocity [Golay, 1958], relative to the mean flow velocity. Similarly, opposite conclusion have been reached for the effect of sorption on dispersion. In this work, we study transient solute transport in Poiseuille flow with sorptive boundary and initial transversely uniform distribution (linear release) to reconcile the two different views on solute transport (figure 1) with sorption. Two-dimensional simulations in figure 2 show that there is a transition from fast transport dominated by a fast-moving pulse in the middle of the channel at early times, to slow transport at late times once desorption from the walls becomes important. A set of series solutions for zeroth, first and second longitudinal moment have been derived and we show that the zeroth-order term in the solution corresponds to the slow transport in the late regime, while the first-order term corresponds to the fast transport in the early regime (figure 3). Based on the analytical solution, the time scales for early regime and late regimes of both the velocity and the dispersion coefficient have been determined for an equilibrium sorption model and a kinetic linear sorption model. Furthermore, we give approximated analytical solution when both adsorption and desorption are slow. References M.J.E. Golay. Theory of chromatography in open and coated tubular columns iwth round and rectangular cross-sections. In D.H.Desty, editor, Gas Chromatography, pages 36-53, New York, 1958. Academic Press Inc. E.M. Lungu and H.K. Moffatt. the effect of wall conductance on heat diffusion in duct flow. Journal of Engineering Mathematics, 1692 ;121-136, 1982.

A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn

2018-07-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in a closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.

A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn

2018-05-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. (2017a) expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.

A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn

2018-05-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. (2018b) expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.

Integrating aerodynamics and structures in the minimum weight design of a supersonic transport wing

NASA Technical Reports Server (NTRS)

Barthelemy, Jean-Francois M.; Wrenn, Gregory A.; Dovi, Augustine R.; Coen, Peter G.; Hall, Laura E.

1992-01-01

An approach is presented for determining the minimum weight design of aircraft wing models which takes into consideration aerodynamics-structure coupling when calculating both zeroth order information needed for analysis and first order information needed for optimization. When performing sensitivity analysis, coupling is accounted for by using a generalized sensitivity formulation. The results presented show that the aeroelastic effects are calculated properly and noticeably reduce constraint approximation errors. However, for the particular example selected, the error introduced by ignoring aeroelastic effects are not sufficient to significantly affect the convergence of the optimization process. Trade studies are reported that consider different structural materials, internal spar layouts, and panel buckling lengths. For the formulation, model and materials used in this study, an advanced aluminum material produced the lightest design while satisfying the problem constraints. Also, shorter panel buckling lengths resulted in lower weights by permitting smaller panel thicknesses and generally, by unloading the wing skins and loading the spar caps. Finally, straight spars required slightly lower wing weights than angled spars.

Charged plate in asymmetric electrolytes: One-loop renormalization of surface charge density and Debye length due to ionic correlations.

PubMed

Ding, Mingnan; Lu, Bing-Sui; Xing, Xiangjun

2016-10-01

Self-consistent field theory (SCFT) is used to study the mean potential near a charged plate inside a m:-n electrolyte. A perturbation series is developed in terms of g=4πκb, where band1/κ are Bjerrum length and bare Debye length, respectively. To the zeroth order, we obtain the nonlinear Poisson-Boltzmann theory. For asymmetric electrolytes (m≠n), the first order (one-loop) correction to mean potential contains a secular term, which indicates the breakdown of the regular perturbation method. Using a renormalizaton group transformation, we remove the secular term and obtain a globally well-behaved one-loop approximation with a renormalized Debye length and a renormalized surface charge density. Furthermore, we find that if the counterions are multivalent, the surface charge density is renormalized substantially downwards and may undergo a change of sign, if the bare surface charge density is sufficiently large. Our results agrees with large MC simulation even when the density of electrolytes is relatively high.

Theoretical contamination of cryogenic satellite telescopes

NASA Technical Reports Server (NTRS)

Murakami, M.

1978-01-01

The state of contaminant molecules, the deposition rate on key surfaces, and the heat transfer rate were estimated by the use of a zeroth-order approximation. Optical surfaces of infrared telescopes cooled to about 20 K should be considered to be covered with at least several deposition layers of condensible molecules without any contamination controls. The effectiveness of the purge gas method of contamination controls was discussed. This method attempts to drive condensible molecules from the telescope tube by impacts with a purge gas in the telescope tube. For this technique to be sufficiently effective, the pressure of the purge gas must be more than 2 x .000001 torr. The influence caused by interactions of the purged gas with the particulate contaminants was found to slightly increase the resident times of the particulate contaminants within the telescope field of view.

Cylinder and metal grating polarization beam splitter

NASA Astrophysics Data System (ADS)

Yang, Junbo; Xu, Suzhi

2017-08-01

We propose a novel and compact metal grating polarization beam splitter (PBS) based on its different reflected and transmitted orders. The metal grating exhibits a broadband high reflectivity and polarization dependence. The rigorous coupled wave analysis is used to calculate the reflectivity and the transmitting spectra and optimize the structure parameters to realize the broadband PBS. The finite-element method is used to calculate the field distribution. The characteristics of the broadband high reflectivity, transmitting and the polarization dependence are investigated including wavelength, period, refractive index and the radius of circle grating. When grating period d = 400 nm, incident wavelength λ = 441 nm, incident angle θ = 60° and radius of circle d/5, then the zeroth reflection order R0 = 0.35 and the transmission zeroth order T0 = 0.08 for TE polarization, however, T0 = 0.34 and R0 = 0.01 for TM mode. The simple fabrication method involves only single etch step and good compatibility with complementary metal oxide semiconductor technology. PBS designed here is particularly suited for optical communication and optical information processing.

Design of experiments for zeroth and first-order reaction rates.

PubMed

Amo-Salas, Mariano; Martín-Martín, Raúl; Rodríguez-Aragón, Licesio J

2014-09-01

This work presents optimum designs for reaction rates experiments. In these experiments, time at which observations are to be made and temperatures at which reactions are to be run need to be designed. Observations are performed along time under isothermal conditions. Each experiment needs a fixed temperature and so the reaction can be measured at the designed times. For these observations under isothermal conditions over the same reaction a correlation structure has been considered. D-optimum designs are the aim of our work for zeroth and first-order reaction rates. Temperatures for the isothermal experiments and observation times, to obtain the most accurate estimates of the unknown parameters, are provided in these designs. D-optimum designs for a single observation in each isothermal experiment or for several correlated observations have been obtained. Robustness of the optimum designs for ranges of the correlation parameter and comparisons of the information gathered by different designs are also shown. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Phase-shifting point diffraction interferometer grating designs

DOEpatents

Naulleau, Patrick; Goldberg, Kenneth Alan; Tejnil, Edita

2001-01-01

In a phase-shifting point diffraction interferometer, by sending the zeroth-order diffraction to the reference pinhole of the mask and the first-order diffraction to the test beam window of the mask, the test and reference beam intensities can be balanced and the fringe contrast improved. Additionally, using a duty cycle of the diffraction grating other than 50%, the fringe contrast can also be improved.

Estimates of the Modeling Error of the α -Models of Turbulence in Two and Three Space Dimensions

NASA Astrophysics Data System (ADS)

Dunca, Argus A.

2017-12-01

This report investigates the convergence rate of the weak solutions w^{α } of the Leray-α , modified Leray-α , Navier-Stokes-α and the zeroth ADM turbulence models to a weak solution u of the Navier-Stokes equations. It is assumed that this weak solution u of the NSE belongs to the space L^4(0, T; H^1) . It is shown that under this regularity condition the error u-w^{α } is O(α ) in the norms L^2(0, T; H^1) and L^{∞}(0, T; L^2) , thus improving related known results. It is also shown that the averaged error \\overline{u}-\\overline{w^{α }} is higher order, O(α ^{1.5}) , in the same norms, therefore the α -regularizations considered herein approximate better filtered flow structures than the exact (unfiltered) flow velocities.

Fields of an ultrashort tightly focused radially polarized laser pulse in a linear response plasma

NASA Astrophysics Data System (ADS)

Salamin, Yousef I.

2017-10-01

Analytical expressions for the fields of a radially polarized, ultrashort, and tightly focused laser pulse propagating in a linear-response plasma are derived and discussed. The fields are obtained from solving the inhomogeneous wave equations for the vector and scalar potentials, linked by the Lorenz gauge, in a plasma background. First, the scalar potential is eliminated using the gauge condition, then the vector potential is synthesized from Fourier components of an initial uniform distribution of wavenumbers, and the inverse Fourier transformation is carried out term-by-term in a truncated series (finite sum). The zeroth-order term in, for example, the axial electric field component is shown to model a pulse much better than its widely used paraxial approximation counterpart. Some of the propagation characteristics of the fields are discussed and all fields are shown to have manifested the expected limits for propagation in a vacuum.

Broadband mode conversion via gradient index metamaterials

PubMed Central

Wang, HaiXiao; Xu, YaDong; Genevet, Patrice; Jiang, Jian-Hua; Chen, HuanYang

2016-01-01

We propose a design for broadband waveguide mode conversion based on gradient index metamaterials (GIMs). Numerical simulations demonstrate that the zeroth order of transverse magnetic mode or the first order of transverse electric mode (TM0/TE1) can be converted into the first order of transverse magnetic mode or the second order of transverse electric mode (TM1/TE2) for a broadband of frequencies. As an application, an asymmetric propagation is achieved by integrating zero index metamaterials inside the GIM waveguide. PMID:27098456

Diagrammatic expansion for positive density-response spectra: Application to the electron gas

NASA Astrophysics Data System (ADS)

Uimonen, A.-M.; Stefanucci, G.; Pavlyukh, Y.; van Leeuwen, R.

2015-03-01

In a recent paper [Phys. Rev. B 90, 115134 (2014), 10.1103/PhysRevB.90.115134] we put forward a diagrammatic expansion for the self-energy which guarantees the positivity of the spectral function. In this work we extend the theory to the density-response function. We write the generic diagram for the density-response spectrum as the sum of "partitions." In a partition the original diagram is evaluated using time-ordered Green's functions on the left half of the diagram, antitime-ordered Green's functions on the right half of the diagram, and lesser or greater Green's function gluing the two halves. As there exists more than one way to cut a diagram in two halves, to every diagram corresponds more than one partition. We recognize that the most convenient diagrammatic objects for constructing a theory of positive spectra are the half-diagrams. Diagrammatic approximations obtained by summing the squares of half-diagrams do indeed correspond to a combination of partitions which, by construction, yield a positive spectrum. We develop the theory using bare Green's functions and subsequently extend it to dressed Green's functions. We further prove a connection between the positivity of the spectral function and the analytic properties of the polarizability. The general theory is illustrated with several examples and then applied to solve the long-standing problem of including vertex corrections without altering the positivity of the spectrum. In fact already the first-order vertex diagram, relevant to the study of gradient expansion, Friedel oscillations, etc., leads to spectra which are negative in certain frequency domain. We find that the simplest approximation to cure this deficiency is given by the sum of the zeroth-order bubble diagram, the first-order vertex diagram, and a partition of the second-order ladder diagram. We evaluate this approximation in the three-dimensional homogeneous electron gas and show the positivity of the spectrum for all frequencies and densities.

Addition by subtraction in coupled-cluster theory: a reconsideration of the CC and CI interface and the nCC hierarchy.

PubMed

Bartlett, Rodney J; Musiał, Monika

2006-11-28

The nCC hierarchy of coupled-cluster approximations, where n guarantees exactness for n electrons and all products of n electrons are derived and applied to several illustrative problems. The condition of exactness for n=2 defines nCCSD=2CC, with nCCSDT=3CC and nCCSDTQ=4CC being exact for three and four electrons. To achieve this, the minimum number of diagrams is evaluated, which is less than in the corresponding CC model. For all practical purposes, nCC is also the proper definition of a size-extensive CI. 2CC is also an orbitally invariant coupled electron pair approximation. The numerical results of nCC are close to those for the full CC variant, and in some cases are closer to the full CI reference result. As 2CC is exact for separated electron pairs, it is the natural zeroth-order approximation for the correlation problem in molecules with other effects introduced as these units start to interact. The nCC hierarchy of approximations has all the attractive features of CC including its size extensivity, orbital invariance, and orbital insensitivity, but in a conceptually appealing form suited to bond breaking, while being computationally less demanding. Excited states from the equation of motion (EOM-2CC) are also reported, which show results frequently approaching those of EOM-CCSDT.

Deep-etched sinusoidal polarizing beam splitter grating.

PubMed

Feng, Jijun; Zhou, Changhe; Cao, Hongchao; Lv, Peng

2010-04-01

A sinusoidal-shaped fused-silica grating as a highly efficient polarizing beam splitter (PBS) is investigated based on the simplified modal method. The grating structure depends mainly on the ratio of groove depth to grating period and the ratio of incident wavelength to grating period. These ratios can be used as a guideline for the grating design at different wavelengths. A sinusoidal-groove PBS grating is designed at a wavelength of 1310 nm under Littrow mounting, and the transmitted TM and TE polarized waves are mainly diffracted into the zeroth order and the -1st order, respectively. The grating profile is optimized by using rigorous coupled-wave analysis. The designed PBS grating is highly efficient (>95.98%) over the O-band wavelength range (1260-1360 nm) for both TE and TM polarizations. The sinusoidal grating can exhibit higher diffraction efficiency, larger extinction ratio, and less reflection loss than the rectangular-groove PBS grating. By applying wet etching technology on the rectangular grating, which was manufactured by holographic recording and inductively coupled plasma etching technology, the sinusoidal grating can be approximately fabricated. Experimental results are in agreement with theoretical values.

Longitudinal and bulk viscosities of Lennard-Jones fluids

NASA Astrophysics Data System (ADS)

Tankeshwar, K.; Pathak, K. N.; Ranganathan, S.

1996-12-01

Expressions for the longitudinal and bulk viscosities have been derived using Green Kubo formulae involving the time integral of the longitudinal and bulk stress autocorrelation functions. The time evolution of stress autocorrelation functions are determined using the Mori formalism and a memory function which is obtained from the Mori equation of motion. The memory function is of hyperbolic secant form and involves two parameters which are related to the microscopic sum rules of the respective autocorrelation function. We have derived expressions for the zeroth-, second-and fourth- order sum rules of the longitudinal and bulk stress autocorrelation functions. These involve static correlation functions up to four particles. The final expressions for these have been put in a form suitable for numerical calculations using low- order decoupling approximations. The numerical results have been obtained for the sum rules of longitudinal and bulk stress autocorrelation functions. These have been used to calculate the longitudinal and bulk viscosities and time evolution of the longitudinal stress autocorrelation function of the Lennard-Jones fluids over wide ranges of densities and temperatures. We have compared our results with the available computer simulation data and found reasonable agreement.

NATURAL GRADIENT EXPERIMENT ON SOLUTE TRANSPORT IN A SAND AQUIFER. 2. SPATIAL MOMENTS AND THE ADVECTION AND DISPERSION OF NONREACTIVE TRACERS

EPA Science Inventory

The three-dimensional movement of a tracer plume containing bromide and chloride is investigated using the data base from a large-scale natural gradient field experiment on groundwater solute transport. The analysis focuses on the zeroth-, first-, and second-order spatial moments...

Combustion Instability in Solid Propellant Rockets

DTIC Science & Technology

1989-03-21

adverse pressure gradients may arise. As suggested in Figure 5.1, the volume behind a submerged nozzle is especially likely to exhibit recircu- lation...ranges of interest. Therefore, the axial vortical velocity is governed to zeroth order in the mean flow Mach number by auz a2 2 U b+ Mbr -&r2 +O(Mb

Extreme depth-of-field intraocular lenses

NASA Astrophysics Data System (ADS)

Baker, Kenneth M.

1996-05-01

A new technology brings the full aperture single vision pseudophakic eye's effective hyperfocal distance within the half-meter range. A modulated index IOL containing a subsurface zeroth order coherent microlenticular mosaic defined by an index gradient adds a normalizing function to the vergences or parallactic angles of incoming light rays subtended from field object points and redirects them, in the case of near-field images, to that of far-field images. Along with a scalar reduction of the IOL's linear focal range, this results in an extreme depth of field with a narrow depth of focus and avoids the focal split-up, halo, and inherent reduction in contrast of multifocal IOLs. A high microlenticular spatial frequency, which, while still retaining an anisotropic medium, results in a nearly total zeroth order propagation throughout the visible spectrum. The curved lens surfaces still provide most of the refractive power of the IOL, and the unique holographic fabrication technology is especially suitable not only for IOLs but also for contact lenses, artificial corneas, and miniature lens elements for cameras and other optical devices.

High-resolution molybdenum K-edge X-ray absorption spectroscopy analyzed with time-dependent density functional theory.

PubMed

Lima, Frederico A; Bjornsson, Ragnar; Weyhermüller, Thomas; Chandrasekaran, Perumalreddy; Glatzel, Pieter; Neese, Frank; DeBeer, Serena

2013-12-28

X-ray absorption spectroscopy (XAS) is a widely used experimental technique capable of selectively probing the local structure around an absorbing atomic species in molecules and materials. When applied to heavy elements, however, the quantitative interpretation can be challenging due to the intrinsic spectral broadening arising from the decrease in the core-hole lifetime. In this work we have used high-energy resolution fluorescence detected XAS (HERFD-XAS) to investigate a series of molybdenum complexes. The sharper spectral features obtained by HERFD-XAS measurements enable a clear assignment of the features present in the pre-edge region. Time-dependent density functional theory (TDDFT) has been previously shown to predict K-pre-edge XAS spectra of first row transition metal compounds with a reasonable degree of accuracy. Here we extend this approach to molybdenum K-edge HERFD-XAS and present the necessary calibration. Modern pure and hybrid functionals are utilized and relativistic effects are accounted for using either the Zeroth Order Regular Approximation (ZORA) or the second order Douglas-Kroll-Hess (DKH2) scalar relativistic approximations. We have found that both the predicted energies and intensities are in excellent agreement with experiment, independent of the functional used. The model chosen to account for relativistic effects also has little impact on the calculated spectra. This study provides an important calibration set for future applications of molybdenum HERFD-XAS to complex catalytic systems.

The Influence of a Presence of a Heavy Atom on (13)C Shielding Constants in Organomercury Compounds and Halogen Derivatives.

PubMed

Wodyński, Artur; Gryff-Keller, Adam; Pecul, Magdalena

2013-04-09

(13)C nuclear magnetic resonance shielding constants have been calculated by means of density functional theory (DFT) for several organomercury compounds and halogen derivatives of aliphatic and aromatic compounds. Relativistic effects have been included through the four-component Dirac-Kohn-Sham (DKS) method, two-component Zeroth Order Regular Approximation (ZORA) DFT, and DFT with scalar effective core potentials (ECPs). The relative shieldings have been analyzed in terms of the position of carbon atoms with respect to the heavy atom and their hybridization. The results have been compared with the experimental values, some newly measured and some found in the literature. The main aim of the calculations has been to evaluate the magnitude of heavy atom effects on the (13)C shielding constants and to check what are the relative contributions of scalar relativistic effects and spin-orbit coupling. Another object has been to compare the DKS and ZORA results and to check how the approximate method of accounting for the heavy-atom-on-light-atom (HALA) relativistic effect by means of scalar effective core potentials on heavy atoms performs in comparison with the more rigorous two- and four-component treatment.

Relativistic effects on x-ray structure factors

NASA Astrophysics Data System (ADS)

Batke, Kilian; Eickerling, Georg

2016-04-01

Today, combined experimental and theoretical charge density studies based on quantum chemical calculations and x-ray diffraction experiments allow for the investigation of the topology of the electron density at subatomic resolution. When studying compounds containing transition metal elements, relativistic effects need to be adequately taken into account not only in quantum chemical calculations of the total electron density ρ ({r}), but also for the atomic scattering factors employed to extract ρ ({r}) from experimental x-ray diffraction data. In the present study, we investigate the magnitude of relativistic effects on x-ray structure factors and for this purpose {F}({{r}}*) have been calculated for the model systems M(C2H2) (M = Ni, Pd, Pt) from four-component molecular wave functions. Relativistic effects are then discussed by a comparison to structure factors obtained from a non-relativistic reference and different quasi-relativistic approximations. We show, that the overall effects of relativity on the structure factors on average amount to 0.81%, 1.51% and 2.78% for the three model systems under investigation, but that for individual reflections or reflection series the effects can be orders of magnitude larger. Employing the quasi-relativistic Douglas-Kroll-Hess second order or the zeroth order regular approximation Hamiltonian takes these effects into account to a large extend, reducing the differences between the (quasi-)relativistic and the non-relativistic result by one order of magnitude. In order to further determine the experimental significance of the results, the magnitude of the relativistic effects is compared to the changes of the model structure factor data when charge transfer and chemical bonding is taken into account by a multipolar expansion of {F}({{r}}*).

Kinematics, structural mechanics, and design of origami structures with smooth folds

NASA Astrophysics Data System (ADS)

Peraza Hernandez, Edwin Alexander

Origami provides novel approaches to the fabrication, assembly, and functionality of engineering structures in various fields such as aerospace, robotics, etc. With the increase in complexity of the geometry and materials for origami structures that provide engineering utility, computational models and design methods for such structures have become essential. Currently available models and design methods for origami structures are generally limited to the idealization of the folds as creases of zeroth-order geometric continuity. Such an idealization is not proper for origami structures having non-negligible thickness or maximum curvature at the folds restricted by material limitations. Thus, for general structures, creased folds of merely zeroth-order geometric continuity are not appropriate representations of structural response and a new approach is needed. The first contribution of this dissertation is a model for the kinematics of origami structures having realistic folds of non-zero surface area and exhibiting higher-order geometric continuity, here termed smooth folds. The geometry of the smooth folds and the constraints on their associated kinematic variables are presented. A numerical implementation of the model allowing for kinematic simulation of structures having arbitrary fold patterns is also described. Examples illustrating the capability of the model to capture realistic structural folding response are provided. Subsequently, a method for solving the origami design problem of determining the geometry of a single planar sheet and its pattern of smooth folds that morphs into a given three-dimensional goal shape, discretized as a polygonal mesh, is presented. The design parameterization of the planar sheet and the constraints that allow for a valid pattern of smooth folds and approximation of the goal shape in a known folded configuration are presented. Various testing examples considering goal shapes of diverse geometries are provided. Afterwards, a model for the structural mechanics of origami continuum bodies with smooth folds is presented. Such a model entails the integration of the presented kinematic model and existing plate theories in order to obtain a structural representation for folds having non-zero thickness and comprised of arbitrary materials. The model is validated against finite element analysis. The last contribution addresses the design and analysis of active material-based self-folding structures that morph via simultaneous folding towards a given three-dimensional goal shape starting from a planar configuration. Implementation examples including shape memory alloy (SMA)-based self-folding structures are provided.

Zeroth Law, Entropy, Equilibrium, and All That

NASA Astrophysics Data System (ADS)

Canagaratna, Sebastian G.

2008-05-01

The place of the zeroth law in the teaching of thermodynamics is examined in the context of the recent discussion by Gislason and Craig of some problems involving the establishment of thermal equilibrium. The concept of thermal equilibrium is introduced through the zeroth law. The relation between the zeroth law and the second law in the traditional approach to thermodynamics is discussed. It is shown that the traditional approach does not need to appeal to the second law to solve with rigor the type of problems discussed by Gislason and Craig: in problems not involving chemical reaction, the zeroth law and the condition for mechanical equilibrium, complemented by the first law and any necessary equations of state, are sufficient to determine the final state. We have to invoke the second law only if we wish to calculate the change of entropy. Since most students are exposed to a traditional approach to thermodynamics, the examples of Gislason and Craig are re-examined in terms of the traditional formulation. The maximization of the entropy in the final state can be verified in the traditional approach quite directly by the use of the fundamental equations of thermodynamics. This approach uses relatively simple mathematics in as general a setting as possible.

Rotordynamic coefficients for stepped labyrinth gas seals

NASA Technical Reports Server (NTRS)

Scharrer, Joseph K.

1989-01-01

The basic equations are derived for compressible flow in a stepped labyrinth gas seal. The flow is assumed to be completely turbulent in the circumferential direction where the friction factor is determined by the Blasius relation. Linearized zeroth and first-order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth-order pressure distribution is found by satisfying the leakage equation while the circumferential velocity distribution is determined by satisfying the momentum equations. The first order equations are solved by a separation of variables solution. Integration of the resultant pressure distribution along and around the seal defines the reaction force developed by the seal and the corresponding dynamic coefficients. The results of this analysis are presented in the form of a parametric study, since there are no known experimental data for the rotordynamic coefficients of stepped labyrinth gas seals. The parametric study investigates the relative rotordynamic stability of convergent, straight and divergent stepped labyrinth gas seals. The results show that, generally, the divergent seal is more stable, rotordynamically, than the straight or convergent seals. The results also show that the teeth-on-stator seals are not always more stable, rotordynamically, then the teeth-on-rotor seals as was shown by experiment by Childs and Scharrer (1986b) for a 15 tooth seal.

Asymptotic, multigroup flux reconstruction and consistent discontinuity factors

DOE PAGES

Trahan, Travis J.; Larsen, Edward W.

2015-05-12

Recent theoretical work has led to an asymptotically derived expression for reconstructing the neutron flux from lattice functions and multigroup diffusion solutions. The leading-order asymptotic term is the standard expression for flux reconstruction, i.e., it is the product of a shape function, obtained through a lattice calculation, and the multigroup diffusion solution. The first-order asymptotic correction term is significant only where the gradient of the diffusion solution is not small. Inclusion of this first-order correction term can significantly improve the accuracy of the reconstructed flux. One may define discontinuity factors (DFs) to make certain angular moments of the reconstructed fluxmore » continuous across interfaces between assemblies in 1-D. Indeed, the standard assembly discontinuity factors make the zeroth moment (scalar flux) of the reconstructed flux continuous. The inclusion of the correction term in the flux reconstruction provides an additional degree of freedom that can be used to make two angular moments of the reconstructed flux continuous across interfaces by using current DFs in addition to flux DFs. Thus, numerical results demonstrate that using flux and current DFs together can be more accurate than using only flux DFs, and that making the second angular moment continuous can be more accurate than making the zeroth moment continuous.« less

Multiple Quantum Coherences (MQ) NMR and Entanglement Dynamics in the Mixed-Three-Spin XXX Heisenberg Model with Single-Ion Anisotropy

NASA Astrophysics Data System (ADS)

Hamid, Arian Zad

2016-12-01

We analytically investigate Multiple Quantum (MQ) NMR dynamics in a mixed-three-spin (1/2,1,1/2) system with XXX Heisenberg model at the front of an external homogeneous magnetic field B. A single-ion anisotropy property ζ is considered for the spin-1. The intensities dependence of MQ NMR coherences on their orders (zeroth and second orders) for two pairs of spins (1,1/2) and (1/2,1/2) of the favorite tripartite system are obtained. It is also investigated dynamics of the pairwise quantum entanglement for the bipartite (sub)systems (1,1/2) and (1/2,1/2) permanently coupled by, respectively, coupling constants J}1 and J}2, by means of concurrence and fidelity. Then, some straightforward comparisons are done between these quantities and the intensities of MQ NMR coherences and ultimately some interesting results are reported. We also show that the time evolution of MQ coherences based on the reduced density matrix of the pair spins (1,1/2) is closely connected with the dynamics of the pairwise entanglement. Finally, we prove that one can introduce MQ coherence of the zeroth order corresponds to the pair spins (1,1/2) as an entanglement witness at some special time intervals.

A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods

NASA Astrophysics Data System (ADS)

Syrakos, Alexandros; Varchanis, Stylianos; Dimakopoulos, Yannis; Goulas, Apostolos; Tsamopoulos, John

2017-12-01

Finite volume methods (FVMs) constitute a popular class of methods for the numerical simulation of fluid flows. Among the various components of these methods, the discretisation of the gradient operator has received less attention despite its fundamental importance with regards to the accuracy of the FVM. The most popular gradient schemes are the divergence theorem (DT) (or Green-Gauss) scheme and the least-squares (LS) scheme. Both are widely believed to be second-order accurate, but the present study shows that in fact the common variant of the DT gradient is second-order accurate only on structured meshes whereas it is zeroth-order accurate on general unstructured meshes, and the LS gradient is second-order and first-order accurate, respectively. This is explained through a theoretical analysis and is confirmed by numerical tests. The schemes are then used within a FVM to solve a simple diffusion equation on unstructured grids generated by several methods; the results reveal that the zeroth-order accuracy of the DT gradient is inherited by the FVM as a whole, and the discretisation error does not decrease with grid refinement. On the other hand, use of the LS gradient leads to second-order accurate results, as does the use of alternative, consistent, DT gradient schemes, including a new iterative scheme that makes the common DT gradient consistent at almost no extra cost. The numerical tests are performed using both an in-house code and the popular public domain partial differential equation solver OpenFOAM.

Interrelating the breakage and composition of mined and drill core coal

NASA Astrophysics Data System (ADS)

Wilson, Terril Edward

Particle size distribution of coal is important if the coal is to be beneficiated, or if a coal sales contract includes particle size specifications. An exploration bore core sample of coal ought to be reduced from its original cylindrical form to a particle size distribution and particle composition that reflects, insofar as possible, a process stream of raw coal it represents. Often, coal cores are reduced with a laboratory crushing machine, the product of which does not match the raw coal size distribution. This study proceeds from work in coal bore core reduction by Australian investigators. In this study, as differentiated from the Australian work, drop-shatter impact breakage followed by dry batch tumbling in steel cylinder rotated about its transverse axis are employed to characterize the core material in terms of first-order and zeroth-order breakage rate constants, which are indices of the propensity of the coal to degrade during excavation and handling. Initial drop-shatter and dry tumbling calibrations were done with synthetic cores composed of controlled low-strength concrete incorporating fly ash (as a partial substitute for Portland cement) in order to reduce material variables and conserve difficult-to-obtain coal cores. Cores of three different coalbeds--Illinois No. 6, Upper Freeport, and Pocahontas No. 5 were subjected to drop-shatter and dry batch tumbling tests to determine breakage response. First-order breakage, characterized by a first-order breakage index for each coal, occurred in the drop-shatter tests. First- and zeroth-order breakage occurred in dry batch tumbling; disappearance of coarse particles and creation of fine particles occurred in a systematic way that could be represented mathematically. Certain of the coal cores available for testing were dry and friable. Comparison of coal preparation plant feed with a crushed bore core and a bore core prepared by drop-shatter and tumbling (all from the same Illinois No.6 coal mining property) indicated that the size distribution and size fraction composition of the drop-shattered/tumbled core more closely resembled the plant feed than the crushed core. An attempt to determine breakage parameters (to allow use of selection and breakage functions and population balance models in the description of bore core size reduction) was initiated. Rank determination of the three coal types was done, indicating that higher rank associates with higher breakage propensity. The two step procedure of drop-shatter and dry batch tumbling simulates the first-order (volume breakage) and zeroth-order (abrasion of particle surfaces) that occur in excavation and handling operations, and is appropriate for drill core reduction prior to laboratory analysis.

Lattice cluster theory of associating polymers. I. Solutions of linear telechelic polymer chains.

PubMed

Dudowicz, Jacek; Freed, Karl F

2012-02-14

The lattice cluster theory (LCT) for the thermodynamics of a wide array of polymer systems has been developed by using an analogy to Mayer's virial expansions for non-ideal gases. However, the high-temperature expansion inherent to the LCT has heretofore precluded its application to systems exhibiting strong, specific "sticky" interactions. The present paper describes a reformulation of the LCT necessary to treat systems with both weak and strong, "sticky" interactions. This initial study concerns solutions of linear telechelic chains (with stickers at the chain ends) as the self-assembling system. The main idea behind this extension of the LCT lies in the extraction of terms associated with the strong interactions from the cluster expansion. The generalized LCT for sticky systems reduces to the quasi-chemical theory of hydrogen bonding of Panyioutou and Sanchez when correlation corrections are neglected in the LCT. A diagrammatic representation is employed to facilitate the evaluation of the corrections to the zeroth-order approximation from short range correlations. © 2012 American Institute of Physics

The role of relativity in the optical response of gold within the time-dependent current-density-functional theory.

PubMed

Romaniello, P; de Boeij, P L

2005-04-22

We included relativistic effects in the formulation of the time-dependent current-density-functional theory for the calculation of linear response properties of metals [P. Romaniello and P. L. de Boeij, Phys. Rev. B (to be published)]. We treat the dominant scalar-relativistic effects using the zeroth-order regular approximation in the ground-state density-functional theory calculations, as well as in the time-dependent response calculations. The results for the dielectric function of gold calculated in the spectral range of 0-10 eV are compared with experimental data reported in literature and recent ellipsometric measurements. As well known, relativistic effects strongly influence the color of gold. We find that the onset of interband transitions is shifted from around 3.5 eV, obtained in a nonrelativistic calculation, to around 1.9 eV when relativity is included. With the inclusion of the scalar-relativistic effects there is an overall improvement of both real and imaginary parts of the dielectric function over the nonrelativistic ones. Nevertheless some important features in the absorption spectrum are not well reproduced, but can be explained in terms of spin-orbit coupling effects. The remaining deviations are attributed to the underestimation of the interband gap (5d-6sp band gap) in the local-density approximation and to the use of the adiabatic local-density approximation in the response calculation.

Optical diffraction by ordered 2D arrays of silica microspheres

NASA Astrophysics Data System (ADS)

Shcherbakov, A. A.; Shavdina, O.; Tishchenko, A. V.; Veillas, C.; Verrier, I.; Dellea, O.; Jourlin, Y.

2017-03-01

The article presents experimental and theoretical studies of angular dependent diffraction properties of 2D monolayer arrays of silica microspheres. High-quality large area defect-free monolayers of 1 μm diameter silica microspheres were deposited by the Langmuir-Blodgett technique under an accurate optical control. Measured angular dependencies of zeroth and one of the first order diffraction efficiencies produced by deposited samples were simulated by the rigorous Generalized Source Method taking into account particle size dispersion and lattice nonideality.

Shuttle rocket booster computational fluid dynamics

NASA Technical Reports Server (NTRS)

Chung, T. J.; Park, O. Y.

1988-01-01

Additional results and a revised and improved computer program listing from the shuttle rocket booster computational fluid dynamics formulations are presented. Numerical calculations for the flame zone of solid propellants are carried out using the Galerkin finite elements, with perturbations expanded to the zeroth, first, and second orders. The results indicate that amplification of oscillatory motions does indeed prevail in high frequency regions. For the second order system, the trend is similar to the first order system for low frequencies, but instabilities may appear at frequencies lower than those of the first order system. The most significant effect of the second order system is that the admittance is extremely oscillatory between moderately high frequency ranges.

Conservative treatment of boundary interfaces for overlaid grids and multi-level grid adaptations

NASA Technical Reports Server (NTRS)

Moon, Young J.; Liou, Meng-Sing

1989-01-01

Conservative algorithms for boundary interfaces of overlaid grids are presented. The basic method is zeroth order, and is extended to a higher order method using interpolation and subcell decomposition. The present method, strictly based on a conservative constraint, is tested with overlaid grids for various applications of unsteady and steady supersonic inviscid flows with strong shock waves. The algorithm is also applied to a multi-level grid adaptation in which the next level finer grid is overlaid on the coarse base grid with an arbitrary orientation.

Tunneling effects in electromagnetic wave scattering by nonspherical particles: A comparison of the Debye series and physical-geometric optics approximations

NASA Astrophysics Data System (ADS)

Bi, Lei; Yang, Ping

2016-07-01

The accuracy of the physical-geometric optics (PG-O) approximation is examined for the simulation of electromagnetic scattering by nonspherical dielectric particles. This study seeks a better understanding of the tunneling effect on the phase matrix by employing the invariant imbedding method to rigorously compute the zeroth-order Debye series, from which the tunneling efficiency and the phase matrix corresponding to the diffraction and external reflection are obtained. The tunneling efficiency is shown to be a factor quantifying the relative importance of the tunneling effect over the Fraunhofer diffraction near the forward scattering direction. Due to the tunneling effect, different geometries with the same projected cross section might have different diffraction patterns, which are traditionally assumed to be identical according to the Babinet principle. For particles with a fixed orientation, the PG-O approximation yields the external reflection pattern with reasonable accuracy, but ordinarily fails to predict the locations of peaks and minima in the diffraction pattern. The larger the tunneling efficiency, the worse the PG-O accuracy is at scattering angles less than 90°. If the particles are assumed to be randomly oriented, the PG-O approximation yields the phase matrix close to the rigorous counterpart, primarily due to error cancellations in the orientation-average process. Furthermore, the PG-O approximation based on an electric field volume-integral equation is shown to usually be much more accurate than the Kirchhoff surface integral equation at side-scattering angles, particularly when the modulus of the complex refractive index is close to unity. Finally, tunneling efficiencies are tabulated for representative faceted particles.

Navigation System Design and State Estimation for a Small Rigid Hull Inflatable Boat (RHIB)

DTIC Science & Technology

2014-09-01

addition of the Coriolis term as previously defined has no effect on pitch, only one measurement is compared against Condor’s true pitch angle values...33  B.  REFERENCE FRAME DEFINITIONS ......................................................33  1.  Earth Centered Inertial...the effect of higher order terms. Lastly, the zeroth weight of the scaled weight set can be modified to incorporate prior knowledge of the

Zeroth-order design report for the next linear collider. Volume 1

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

Raubenheimer, T.O.

1996-05-01

This Zeroth Order Design Report (ZDR) for the Next Linear Collider (NLC) has been completed as a feasibility study for a TeV-scale linear collider that incorporates a room-temperature accelerator powered by rf microwaves at 11.424 GHz--similar to that presently used in the SLC, but at four times the rf frequency. The purpose of this study is to examine the complete systems of such a collider, to understand how the parts fit together, and to make certain that every required piece has been included. The design presented here is not fully engineered in any sense, but to be assured that themore » NLC can be built, attention has been given to a number of critical components and issues that present special challenges. More engineering and development of a number of mechanical and electrical systems remain to be done, but the conclusion of this study is that indeed the NLC is technically feasible and can be expected to reach the performance levels required to perform research at the TeV energy scale. Volume one covers the following: the introduction; electron source; positron source; NLC damping rings; bunch compressors and prelinac; low-frequency linacs and compressors; main linacs; design and dynamics; and RF systems for main linacs.« less

Scattering and Emission from Inhomogeneous Vegetation Canopy and Alien Target by Using Three-Dimensional Vector Radiative Transfer (3D-VRT) Equation

NASA Astrophysics Data System (ADS)

Jin, Ya-Qiu; Liang, Zichang

2005-01-01

To solve 3D-VRT equation for the model of spatially inhomogeneous scatter media, the finite enclosure of the scatter media is geometrically divided, in both the vertical z and horizontal (x,y) directions, to form very thin multi-boxes. The zero-th order emission, first-order Mueller matrix of each thin box and an iterative approach of high-order radiative transfer are applied to deriving high-order scattering and emission of whole inhomogeneous scatter media. Numerical results of polarized brightness temperature at microwave frequency and under different radiometer's resolutions from inhomogeneous scatter model such as vegetation canopy and embedded alien target are simulated and discussed.

Revisiting HgCl 2: A solution- and solid-state 199Hg NMR and ZORA-DFT computational study

NASA Astrophysics Data System (ADS)

Taylor, R. E.; Carver, Colin T.; Larsen, Ross E.; Dmitrenko, Olga; Bai, Shi; Dybowski, C.

2009-07-01

The 199Hg chemical-shift tensor of solid HgCl 2 was determined from spectra of polycrystalline materials, using static and magic-angle spinning (MAS) techniques at multiple spinning frequencies and field strengths. The chemical-shift tensor of solid HgCl 2 is axially symmetric ( η = 0) within experimental error. The 199Hg chemical-shift anisotropy (CSA) of HgCl 2 in a frozen solution in dimethylsulfoxide (DMSO) is significantly smaller than that of the solid, implying that the local electronic structure in the solid is different from that of the material in solution. The experimental chemical-shift results (solution and solid state) are compared with those predicted by density functional theory (DFT) calculations using the zeroth-order regular approximation (ZORA) to account for relativistic effects. 199Hg spin-lattice relaxation of HgCl 2 dissolved in DMSO is dominated by a CSA mechanism, but a second contribution to relaxation arises from ligand exchange. Relaxation in the solid state is independent of temperature, suggesting relaxation by paramagnetic impurities or defects.

Halogen Bonding versus Hydrogen Bonding: A Molecular Orbital Perspective

PubMed Central

Wolters, Lando P; Bickelhaupt, F Matthias

2012-01-01

We have carried out extensive computational analyses of the structure and bonding mechanism in trihalides DX⋅⋅⋅A− and the analogous hydrogen-bonded complexes DH⋅⋅⋅A− (D, X, A=F, Cl, Br, I) using relativistic density functional theory (DFT) at zeroth-order regular approximation ZORA-BP86/TZ2P. One purpose was to obtain a set of consistent data from which reliable trends in structure and stability can be inferred over a large range of systems. The main objective was to achieve a detailed understanding of the nature of halogen bonds, how they resemble, and also how they differ from, the better understood hydrogen bonds. Thus, we present an accurate physical model of the halogen bond based on quantitative Kohn–Sham molecular orbital (MO) theory, energy decomposition analyses (EDA) and Voronoi deformation density (VDD) analyses of the charge distribution. It appears that the halogen bond in DX⋅⋅⋅A− arises not only from classical electrostatic attraction but also receives substantial stabilization from HOMO–LUMO interactions between the lone pair of A− and the σ* orbital of D–X. PMID:24551497

Modified Chapman-Enskog moment approach to diffusive phonon heat transport.

PubMed

Banach, Zbigniew; Larecki, Wieslaw

2008-12-01

A detailed treatment of the Chapman-Enskog method for a phonon gas is given within the framework of an infinite system of moment equations obtained from Callaway's model of the Boltzmann-Peierls equation. Introducing no limitations on the magnitudes of the individual components of the drift velocity or the heat flux, this method is used to derive various systems of hydrodynamic equations for the energy density and the drift velocity. For one-dimensional flow problems, assuming that normal processes dominate over resistive ones, it is found that the first three levels of the expansion (i.e., the zeroth-, first-, and second-order approximations) yield the equations of hydrodynamics which are linearly stable at all wavelengths. This result can be achieved either by examining the dispersion relations for linear plane waves or by constructing the explicit quadratic Lyapunov entropy functionals for the linear perturbation equations. The next order in the Chapman-Enskog expansion leads to equations which are unstable to some perturbations. Precisely speaking, the linearized equations of motion that describe the propagation of small disturbances in the flow have unstable plane-wave solutions in the short-wavelength limit of the dispersion relations. This poses no problem if the equations are used in their proper range of validity.

The Detection of Circumnuclear X-Ray Emission from the Seyfert Galaxy NGC 3516

NASA Technical Reports Server (NTRS)

George, I. M.; Turner, T. J.; Netzer, H.; Kraemer, S. B.; Ruiz, J.; Chelouche, D.; Crenshaw, D. M.; Yaqoob, T.; Nandra, K.; Mushotzky, R. F.;

Mechanistic Study of Nickel-Catalyzed Ynal Reductive Cyclizations Through Kinetic Analysis

PubMed Central

Baxter, Ryan D.; Montgomery, John

2011-01-01

The mechanism of nickel-catalyzed, silane-mediated reductive cyclization of ynals has been evaluated. The cyclizations are first-order in [Ni] and [ynal] and zeroth-order in [silane]. These results, in combination with the lack of rapid silane consumption upon reaction initiation are inconsistent with mechanisms involving reaction initiation by oxidative addition of Ni(0) to the silane. Silane consumption occurs only when both the alkyne and aldehyde and are present. Mechanisms involving rate-determining oxidative cyclization to a metallacycle followed by rapid reaction with the silane are consistent with the data obtained. PMID:21438642

CFD determination of flow perturbation boundary conditions for seal rotordynamic modeling

NASA Astrophysics Data System (ADS)

Venkatesan, Ganesh

2002-09-01

A new approach has been developed and utilized to determine the flow field perturbations (i.e. disturbance due to rotor eccentricity and/or motion) upstream of and within a non-contacting seal. The results are proposed for use with bulk-flow perturbation and CFD-perturbation seal rotordynamic models, as well as in fully 3-D CFD models, to specify approximate boundary conditions for the first-order variables at the computational domain inlet. The perturbation quantities were evaluated by subtracting the numerical flow field solutions corresponding to the concentric rotor position from that for an eccentric rotor position. The disturbance pressure quantities predicted from the numerical solutions were validated by comparing with previous pressure measurements. A parametric study was performed to understand the influence of upstream chamber height, seal clearance, shaft speed, whirl speed, zeroth-order streamwise and swirl velocities, and downstream pressure on the distribution of the first-order quantities in the upstream chamber, seal inlet and seal exit regions. Radially bulk-averaged first-order quantities were evaluated in the upstream chamber, as well as at the seal inlet and exit. The results were finally presented in the form of generalized dimensionless boundary condition correlations so that they can be applied to seal rotordynamic models over a wide range of operating conditions and geometries. To examine the effect of the proposed, approximate first-order boundary conditions on the solutions of the fully 3-D CFD rotordynamic models, the first-order boundary condition correlations for the upstream chamber were used to adjust the circumferential distribution of domain inlet values. The benefit of the boundary condition expressions was assessed for two previously measured test cases, one for a gas seal and the other for a liquid seal. For the gas seal case, a significant improvement in the prediction of the cross-coupled stiffness, when including the proposed first-order inlet boundary values, was found. In the case of liquid seals the tangential impedance values obtained with boundary condition adjustments showed a very slight improvement for a range of whirl speeds over those obtained without them. The radial impedance values obtained with the new adjustments showed a significant improvement over those obtained without them.

Simple and compact expressions for neutrino oscillation probabilities in matter

DOE PAGES

Minakata, Hisakazu; Parke, Stephen J.

2016-01-29

We reformulate perturbation theory for neutrino oscillations in matter with an expansion parameter related to the ratio of the solar to the atmospheric Δm 2 scales. Unlike previous works, use a renormalized basis in which certain first-order effects are taken into account in the zeroth-order Hamiltonian. Using this perturbation theory we derive extremely compact expressions for the neutrino oscillations probabilities in matter. We find, for example, that the ν e disappearance probability at this order is of a simple two flavor form with an appropriately identified mixing angle and Δm 2. Furthermore, despite exceptional simplicity in their forms they accommodatemore » all order effects θ 13 and the matter potential.« less

Scattering and emission from inhomogeneous vegetation canopy and alien target beneath by using three-dimensional vector radiative transfer (3D-VRT) equation

NASA Astrophysics Data System (ADS)

Jin, Ya-Qiu; Liang, Zichang

2005-05-01

To solve the 3D-VRT equation for the model of spatially inhomogeneous scatter media, the finite enclosure of the scatter media is geometrically divided, in both vertical z and transversal (x,y) directions, to form very thin multi-boxes. The zeroth order emission, first-order Mueller matrix of each thin box and an iterative approach of high-order radiative transfer are applied to derive high-order scattering and emission of whole inhomogeneous scatter media. Numerical results of polarized brightness temperature at microwave frequency and under different radiometer resolutions from inhomogeneous scatter model such as vegetation canopy and alien target beneath canopy are simulated and discussed.

Critical behavior and phase transition of dilaton black holes with nonlinear electrodynamics

NASA Astrophysics Data System (ADS)

Dayyani, Z.; Sheykhi, A.; Dehghani, M. H.; Hajkhalili, S.

2018-02-01

In this paper, we take into account the dilaton black hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics. First of all, we consider the cosmological constant and nonlinear parameter as thermodynamic quantities which can vary. We obtain thermodynamic quantities of the system such as pressure, temperature and Gibbs free energy in an extended phase space. We complete the analogy of the nonlinear dilaton black holes with the Van der Waals liquid-gas system. We work in the canonical ensemble and hence we treat the charge of the black hole as an external fixed parameter. Moreover, we calculate the critical values of temperature, volume and pressure and show that they depend on the dilaton coupling constant as well as on the nonlinear parameter. We also investigate the critical exponents and find that they are universal and independent of the dilaton and nonlinear parameters, which is an expected result. Finally, we explore the phase transition of nonlinear dilaton black holes by studying the Gibbs free energy of the system. We find that in the case of T>T_c, we have no phase transition. When T=T_c, the system admits a second-order phase transition, while for T=T_f

Wigner phase space distribution via classical adiabatic switching

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

Bose, Amartya; Makri, Nancy; Department of Physics, University of Illinois, 1110 W. Green Street, Urbana, Illinois 61801

2015-09-21

Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if themore » perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations.« less

Effect of the initial domain on the dispersion dynamics of a diffusing substance

NASA Astrophysics Data System (ADS)

Bestuzheva, A. N.; Smirnov, A. L.

2018-05-01

The formulation and analysis of ecological problems involves the mathematical modeling, when some assumptions concerning the nature of the processes are introduced. These assumptions must be justified. In the present paper the effect of the form of the initial domain occupied with a diffusing substance on the process of diffusion is studied. It's shown that the form of the initial domain plays unimportant role and it may be modeled as semi-sphere, for which the problem has analytical solution. That solution may serves as the zeroth approximation in modeling of actual ecological problem taking into account the relief of the bottom and the bottom currents.

Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds

NASA Astrophysics Data System (ADS)

Martínez-Torres, David; Miranda, Eva

2018-01-01

We prove that, for compact regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group, and we give some applications. In particular, we show that, for regular unimodular Poisson manifolds, top Poisson and foliated cohomology groups are isomorphic. Inspired by the symplectic setting, we define what a perfect Poisson manifold is. We use these Poisson homology computations to provide families of perfect Poisson manifolds.

Correlation functions from a unified variational principle: Trial Lie groups

NASA Astrophysics Data System (ADS)

Balian, R.; Vénéroni, M.

2015-11-01

Time-dependent expectation values and correlation functions for many-body quantum systems are evaluated by means of a unified variational principle. It optimizes a generating functional depending on sources associated with the observables of interest. It is built by imposing through Lagrange multipliers constraints that account for the initial state (at equilibrium or off equilibrium) and for the backward Heisenberg evolution of the observables. The trial objects are respectively akin to a density operator and to an operator involving the observables of interest and the sources. We work out here the case where trial spaces constitute Lie groups. This choice reduces the original degrees of freedom to those of the underlying Lie algebra, consisting of simple observables; the resulting objects are labeled by the indices of a basis of this algebra. Explicit results are obtained by expanding in powers of the sources. Zeroth and first orders provide thermodynamic quantities and expectation values in the form of mean-field approximations, with dynamical equations having a classical Lie-Poisson structure. At second order, the variational expression for two-time correlation functions separates-as does its exact counterpart-the approximate dynamics of the observables from the approximate correlations in the initial state. Two building blocks are involved: (i) a commutation matrix which stems from the structure constants of the Lie algebra; and (ii) the second-derivative matrix of a free-energy function. The diagonalization of both matrices, required for practical calculations, is worked out, in a way analogous to the standard RPA. The ensuing structure of the variational formulae is the same as for a system of non-interacting bosons (or of harmonic oscillators) plus, at non-zero temperature, classical Gaussian variables. This property is explained by mapping the original Lie algebra onto a simpler Lie algebra. The results, valid for any trial Lie group, fulfill consistency properties and encompass several special cases: linear responses, static and time-dependent fluctuations, zero- and high-temperature limits, static and dynamic stability of small deviations.

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

Balian, R., E-mail: roger.balian@cea.fr; Vénéroni, M.

Time-dependent expectation values and correlation functions for many-body quantum systems are evaluated by means of a unified variational principle. It optimizes a generating functional depending on sources associated with the observables of interest. It is built by imposing through Lagrange multipliers constraints that account for the initial state (at equilibrium or off equilibrium) and for the backward Heisenberg evolution of the observables. The trial objects are respectively akin to a density operator and to an operator involving the observables of interest and the sources. We work out here the case where trial spaces constitute Lie groups. This choice reduces themore » original degrees of freedom to those of the underlying Lie algebra, consisting of simple observables; the resulting objects are labeled by the indices of a basis of this algebra. Explicit results are obtained by expanding in powers of the sources. Zeroth and first orders provide thermodynamic quantities and expectation values in the form of mean-field approximations, with dynamical equations having a classical Lie–Poisson structure. At second order, the variational expression for two-time correlation functions separates–as does its exact counterpart–the approximate dynamics of the observables from the approximate correlations in the initial state. Two building blocks are involved: (i) a commutation matrix which stems from the structure constants of the Lie algebra; and (ii) the second-derivative matrix of a free-energy function. The diagonalization of both matrices, required for practical calculations, is worked out, in a way analogous to the standard RPA. The ensuing structure of the variational formulae is the same as for a system of non-interacting bosons (or of harmonic oscillators) plus, at non-zero temperature, classical Gaussian variables. This property is explained by mapping the original Lie algebra onto a simpler Lie algebra. The results, valid for any trial Lie group, fulfill consistency properties and encompass several special cases: linear responses, static and time-dependent fluctuations, zero- and high-temperature limits, static and dynamic stability of small deviations.« less

Simulation of light propagation in the thin-film waveguide lens

NASA Astrophysics Data System (ADS)

Malykh, M. D.; Divakov, D. V.; Sevastianov, L. A.; Sevastianov, A. L.

2018-04-01

In this paper we investigate the solution of the problem of modeling the propagation of electromagnetic radiation in three-dimensional integrated optical structures, such as waveguide lenses. When propagating through three-dimensional waveguide structures the waveguide modes can be hybridized, so the mathematical model of their propagation must take into account the connection of TE- and TM-mode components. Therefore, an adequate consideration of hybridization of the waveguide modes is possible only in vector formulation of the problem. An example of three-dimensional structure that hybridizes waveguide modes is the Luneburg waveguide lens, which also has focusing properties. If the waveguide lens has a radius of the order of several tens of wavelengths, its variable thickness at distances of the order of several wavelengths is almost constant. Assuming in this case that the electromagnetic field also varies slowly in the direction perpendicular to the direction of propagation, one can introduce a small parameter characterizing this slow varying and decompose the solution in powers of the small parameter. In this approach, in the zeroth approximation, scalar diffraction problems are obtained, the solution of which is less resource-consuming than the solution of vector problems. The calculated first-order corrections of smallness describe the connection of TE- and TM-modes, so the solutions obtained are weakly-hybridized modes. The formulation of problems and methods for their numerical solution in this paper are based on the authors' research on waveguide diffraction on a lens in a scalar formulation.

Competition Between Electromagnetic Modes in a Free-Electron Maser

DTIC Science & Technology

1994-02-28

electron perpendicular momentum familiar from gyrotron theory 111). The electron mass is me, initial electron velocity perpendicular and parallel to the...are Q Q2 of zeroth order (-1). Similarly, 48 Y tqfia IIOP --T-V I V s_*/ U- s sI J(93~+ I(*JQL4 8aq 5 Using matrix notation, we can write (i) = (C...disks were in turn electron beam welded to stainless steel flanges. While Kovar was needed to provide a good brazing interface, the mass of the material

Manipulating terahertz wave by a magnetically tunable liquid crystal phase grating.

PubMed

Lin, Chia-Jen; Li, Yu-Tai; Hsieh, Cho-Fan; Pan, Ru-Pin; Pan, Ci-Ling

2008-03-03

This investigation demonstrates the feasibility of a magnetically tunable liquid crystal phase grating for the terahertz wave. The phase grating can be used as a beam splitter. The ratio of the zeroth and first-order diffracted THz-beams (0.3 THz) polarized in a direction perpendicular to that of the grooves of the grating can be tuned from 4:1 to 1:2. When the THz wave is polarized in any other direction, this device can be operated as a polarizing beam splitter.

Numerical Computation of Flame Spread over a Thin Solid in Forced Concurrent Flow with Gas-phase Radiation

NASA Technical Reports Server (NTRS)

Jiang, Ching-Biau; T'ien, James S.

1994-01-01

Excerpts from a paper describing the numerical examination of concurrent-flow flame spread over a thin solid in purely forced flow with gas-phase radiation are presented. The computational model solves the two-dimensional, elliptic, steady, and laminar conservation equations for mass, momentum, energy, and chemical species. Gas-phase combustion is modeled via a one-step, second order finite rate Arrhenius reaction. Gas-phase radiation considering gray non-scattering medium is solved by a S-N discrete ordinates method. A simplified solid phase treatment assumes a zeroth order pyrolysis relation and includes radiative interaction between the surface and the gas phase.

The standard model on non-commutative space-time

NASA Astrophysics Data System (ADS)

Calmet, X.; Jurčo, B.; Schupp, P.; Wess, J.; Wohlgenannt, M.

2002-03-01

We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter θ^{μ ν}. No new particles are introduced; the structure group is SU(3)× SU(2)× U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in θ^{μν} we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered.

Neoclassical transport including collisional nonlinearity.

PubMed

Candy, J; Belli, E A

2011-06-10

In the standard δf theory of neoclassical transport, the zeroth-order (Maxwellian) solution is obtained analytically via the solution of a nonlinear equation. The first-order correction δf is subsequently computed as the solution of a linear, inhomogeneous equation that includes the linearized Fokker-Planck collision operator. This equation admits analytic solutions only in extreme asymptotic limits (banana, plateau, Pfirsch-Schlüter), and so must be solved numerically for realistic plasma parameters. Recently, numerical codes have appeared which attempt to compute the total distribution f more accurately than in the standard ordering by retaining some nonlinear terms related to finite-orbit width, while simultaneously reusing some form of the linearized collision operator. In this work we show that higher-order corrections to the distribution function may be unphysical if collisional nonlinearities are ignored.

Angular-spectrum representation of nondiffracting X waves

NASA Astrophysics Data System (ADS)

Fagerholm, Juha; Friberg, Ari T.; Huttunen, Juhani; Morgan, David P.; Salomaa, Martti M.

1996-10-01

We derive the nondiffracting X waves, first discussed within acoustics by Lu and Greenleaf [IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 19 (1992)], using the general mathematical formalism based on an angular spectrum of plane waves. This serves to provide a unified treatment of not only the fundamental zeroth-order X waves of Lu and Greenleaf, but also of the lesser-known higher-order derivative X waves, first discussed here in terms of a single, universal, angular spectrum. The characteristic crossed (letter-X-like) shape and the special properties of the X waves, as well as of their angular-spectrum representation, are discussed and illustrated in detail. Asymptotically, for increasing order, the appearance of the X waves is found to transform into a triangular wedgelike waveform.

Babinet’s principle for scalar complex objects in the far field

NASA Astrophysics Data System (ADS)

Rodriguez-Zurita, G.; Rickenstorff, C.; Pastrana-Sánchez, R.; Vázquez-Castillo, J. F.; Robledo-Sanchez, C.; Meneses-Fabian, C.; Toto-Arellano, N. I.

2014-10-01

Babinet’s principle is briefly reviewed, especially regarding the zeroth diffraction order of the far field diffraction pattern associated with a given aperture. The pattern is basically described by the squared modulus of the Fourier transform of its amplitude distribution (scalar case). In this paper, complementary objects are defined with respect to complex values and not only with respect to unity in order to include phase objects and phase modulation. It is shown that the difference in complementary patterns can be sometimes a bright spot at the zero order location as is widely known, but also, it can be a gray spot or even a dark one. Conditions of occurrence for each case are given as well as some numerical and experimental examples.

Formation of thermochemical laser-induced periodic surface structures on Ti films by a femtosecond IR Gaussian beam: regimes, limiting factors, and optical properties

NASA Astrophysics Data System (ADS)

Dostovalov, A. V.; Korolkov, V. P.; Babin, S. A.

2017-01-01

The formation of thermochemical laser-induced periodic surface structures (TLIPSS) on 400-nm Ti films deposited onto a glass substrate is investigated under irradiation by a femtosecond laser with a wavelength of 1026 nm, pulse duration of 232 fs, repetition rate of 200 kHz, and with different spot sizes of 4-21 μm. The optimal fluence for TLIPSS formation reduces monotonously with increasing the spot diameter in the range. It is found that the standard deviation of the TLIPSS period depends significantly on the beam size and reaches approximately 2% when the beam diameter is in the range of 10-21 μm. In addition to TLIPSS formation with the main period slightly smaller than the laser wavelength, an effect of TLIPSS spatial frequency doubling is detected. The optical properties of TLIPSS (reflection spectrum and diffraction efficiency at different incident angles and polarizations) are investigated and compared with theoretical ones to give a basis for the development of an optical inspecting method. The refractive index and absorption coefficient of oxidized ridges of the TLIPSS are theoretically estimated by simulation of the experimental reflection spectrum in the zeroth diffraction order.

The Relationship Between the Evolution of an Internal Structure and Drug Dissolution from Controlled-Release Matrix Tablets.

PubMed

Kulinowski, Piotr; Hudy, Wiktor; Mendyk, Aleksander; Juszczyk, Ewelina; Węglarz, Władysław P; Jachowicz, Renata; Dorożyński, Przemysław

2016-06-01

In the last decade, imaging has been introduced as a supplementary method to the dissolution tests, but a direct relationship of dissolution and imaging data has been almost completely overlooked. The purpose of this study was to assess the feasibility of relating magnetic resonance imaging (MRI) and dissolution data to elucidate dissolution profile features (i.e., kinetics, kinetics changes, and variability). Commercial, hydroxypropylmethyl cellulose-based quetiapine fumarate controlled-release matrix tablets were studied using the following two methods: (i) MRI inside the USP4 apparatus with subsequent machine learning-based image segmentation and (ii) dissolution testing with piecewise dissolution modeling. Obtained data were analyzed together using statistical data processing methods, including multiple linear regression. As a result, in this case, zeroth order release was found to be a consequence of internal structure evolution (interplay between region's areas-e.g., linear relationship between interface and core), which eventually resulted in core disappearance. Dry core disappearance had an impact on (i) changes in dissolution kinetics (from zeroth order to nonlinear) and (ii) an increase in variability of drug dissolution results. It can be concluded that it is feasible to parameterize changes in micro/meso morphology of hydrated, controlled release, swellable matrices using MRI to establish a causal relationship between the changes in morphology and drug dissolution. Presented results open new perspectives in practical application of combined MRI/dissolution to controlled-release drug products.

Zeroth-order design report for the next linear collider. Volume 2

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

Raubenheimer, T.O.

This Zeroth-Order Design Report (ZDR) for the Next Linear Collider (NLC) has been completed as a feasibility study for a TeV-scale linear collider that incorporates a room-temperature accelerator powered by rf microwaves at 11.424 GHz--similar to that presently used in the SLC, but at four times the rf frequency. The purpose of this study is to examine the complete systems of such a collider, to understand how the parts fit together, and to make certain that every required piece has been included. The ``design`` presented here is not fully engineered in any sense, but to be assured that the NLCmore » can be built, attention has been given to a number of critical components and issues that present special challenges. More engineering and development of a number of mechanical and electrical systems remain to be done, but the conclusion of this study is that indeed the NLC is technically feasible and can be expected to reach the performance levels required to perform research at the TeV energy scale. Volume II covers the following: collimation systems; IP switch and big bend; final focus; the interaction region; multiple bunch issues; control systems; instrumentation; machine protection systems; NLC reliability considerations; NLC conventional facilities. Also included are four appendices on the following topics: An RF power source upgrade to the NLC; a second interaction region for gamma-gamma, gamma-electron; ground motion: theory and measurement; and beam-based feedback: theory and implementation.« less

Degenerate R-S perturbation theory

NASA Technical Reports Server (NTRS)

Hirschfelder, J. O.; Certain, P. R.

1973-01-01

A concise, systematic procedure is given for determining the Rayleigh-Schrodinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n+1)st order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite order operators which are determined by the successive resolution of the space of the zeroth order functions.

Degenerate RS perturbation theory. [Rayleigh-Schroedinger energies and wave functions

NASA Technical Reports Server (NTRS)

Hirschfelder, J. O.; Certain, P. R.

1974-01-01

A concise, systematic procedure is given for determining the Rayleigh-Schroedinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n + 1)-th order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite-order operators which are determined by the successive resolution of the space of the zeroth-order functions.

Application of thermodynamics to silicate crystalline solutions

NASA Technical Reports Server (NTRS)

Saxena, S. K.

1972-01-01

A review of thermodynamic relations is presented, describing Guggenheim's regular solution models, the simple mixture, the zeroth approximation, and the quasi-chemical model. The possibilities of retrieving useful thermodynamic quantities from phase equilibrium studies are discussed. Such quantities include the activity-composition relations and the free energy of mixing in crystalline solutions. Theory and results of the study of partitioning of elements in coexisting minerals are briefly reviewed. A thermodynamic study of the intercrystalline and intracrystalline ion exchange relations gives useful information on the thermodynamic behavior of the crystalline solutions involved. Such information is necessary for the solution of most petrogenic problems and for geothermometry. Thermodynamic quantities for tungstates (CaWO4-SrWO4) are calculated.

A unified model of density limit in fusion plasmas

NASA Astrophysics Data System (ADS)

Zanca, P.; Sattin, F.; Escande, D. F.; Pucella, G.; Tudisco, O.

2017-05-01

In this work we identify by analytical and numerical means the conditions for the existence of a magnetic and thermal equilibrium of a cylindrical plasma, in the presence of Ohmic and/or additional power sources, heat conduction and radiation losses by light impurities. The boundary defining the solutions’ space having realistic temperature profile with small edge value takes mathematically the form of a density limit (DL). Compared to previous similar analyses the present work benefits from dealing with a more accurate set of equations. This refinement is elementary, but decisive, since it discloses a tenuous dependence of the DL on the thermal transport for configurations with an applied electric field. Thanks to this property, the DL scaling law is recovered almost identical for two largely different devices such as the ohmic tokamak and the reversed field pinch. In particular, they have in common a Greenwald scaling, linearly depending on the plasma current, quantitatively consistent with experimental results. In the tokamak case the DL dependence on any additional heating approximately follows a 0.5 power law, which is compatible with L-mode experiments. For a purely externally heated configuration, taken as a cylindrical approximation of the stellarator, the DL dependence on transport is found stronger. By adopting suitable transport models, DL takes on a Sudo-like form, in fair agreement with LHD experiments. Overall, the model provides a good zeroth-order quantitative description of the DL, applicable to widely different configurations.

Reaction kinetics and critical phenomena: iodination of acetone in isobutyric acid + water near the consolute point.

PubMed

Hu, Baichuan; Baird, James K

2010-01-14

The rate of iodination of acetone has been measured as a function of temperature in the binary solvent isobutyric acid (IBA) + water near the upper consolute point. The reaction mixture was prepared by the addition of acetone, iodine, and potassium iodide to IBA + water at its critical composition of 38.8 mass % IBA. The value of the critical temperature determined immediately after mixing was 25.43 degrees C. Aliquots were extracted from the mixture at regular intervals in order to follow the time course of the reaction. After dilution of the aliquot with water to quench the reaction, the concentration of triiodide ion was determined by the measurement of the optical density at a wavelength of 565 nm. These measurements showed that the kinetics were zeroth order. When at the end of 24 h the reaction had come to equilibrium, the critical temperature was determined again and found to be 24.83 degrees C. An Arrhenius plot of the temperature dependence of the observed rate constant, k(obs), was linear over the temperature range 27.00-38.00 degrees C, but between 25.43 and 27.00 degrees C, the values of k(obs) fell below the extrapolation of the Arrhenius line. This behavior is evidence in support of critical slowing down. Our experimental method and results are significant in three ways: (1) In contrast to in situ measurements of optical density, the determination of the optical density of diluted aliquots avoided any interference from critical opalescence. (2) The measured reaction rate exhibited critical slowing down. (3) The rate law was pseudo zeroth order both inside and outside the critical region, indicating that the reaction mechanism was unaffected by the presence of the critical point.

Asymmetric spin-wave dispersion in ferromagnetic nanotubes induced by surface curvature

NASA Astrophysics Data System (ADS)

Otálora, Jorge A.; Yan, Ming; Schultheiss, Helmut; Hertel, Riccardo; Kákay, Attila

2017-05-01

We present a detailed analytical derivation of the spin wave (SW) dispersion relation in magnetic nanotubes with magnetization along the azimuthal direction. The obtained formula can be used to calculate the dispersion relation for any longitudinal and azimuthal mode. The obtained dispersion is asymmetric for all azimuthal modes traveling along the axial direction. As reported in our recent publication [Phys. Rev. Lett. 117, 227203 (2016), 10.1103/PhysRevLett.117.227203], the asymmetry is a curvature-induced effect originating from the dipole-dipole interaction. Here, we discuss the asymmetry of the dispersion for azimuthal modes by analyzing the SW asymmetry Δ f (kz) =fn(kz) -fn(-kz) , where fn(kz) is the eigenfrequency of a magnon with a longitudinal and azimuthal wave vectors, kz and n , respectively; and the dependence of the maximum asymmetry with the nanotube radius R . The analytical results are in perfect agreement with micromagnetic simulations. Furthermore, we show that the dispersion relation simplifies to the thin-film dispersion relation with in-plane magnetization when analyzing the three limiting cases: (i) kz=0 , (ii) kz≫1 /R , and (iii) kz≪1 /R . In the first case, for the zeroth-order modes the thin-film Kittel formula is obtained. For modes with higher order the dispersion relation for the Backward-Volume geometry is recovered. In the second case, for the zeroth-order mode the exchange dominated dispersion relation for SW in Damon-Esbach configuration is obtained. For the case kz≪1 /R , we find that the dispersion relation can be reduced to a formula similar to the Kalinikos-Slavin [J. Phys. C: Sol. State Phys. 19, 7013 (1986), 10.1088/0022-3719/19/35/014] type.

Extension of the KLI approximation toward the exact optimized effective potential.

PubMed

Iafrate, G J; Krieger, J B

2013-03-07

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

Extension of the KLI approximation toward the exact optimized effective potential

NASA Astrophysics Data System (ADS)

Iafrate, G. J.; Krieger, J. B.

2013-03-01

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

Harmonic growth of spherical Rayleigh-Taylor instability in weakly nonlinear regime

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

Liu, Wanhai; LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190; Chen, Yulian

Harmonic growth in classical Rayleigh-Taylor instability (RTI) on a spherical interface is analytically investigated using the method of the parameter expansion up to the third order. Our results show that the amplitudes of the first four harmonics will recover those in planar RTI as the interface radius tends to infinity compared against the initial perturbation wavelength. The initial radius dramatically influences the harmonic development. The appearance of the second-order feedback to the initial unperturbed interface (i.e., the zeroth harmonic) makes the interface move towards the spherical center. For these four harmonics, the smaller the initial radius is, the faster theymore » grow.« less

The method for measuring the groove density of variable-line-space gratings with elimination of the eccentricity effect

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

Wang, Qingbo; Liu, Zhengkun, E-mail: zhkliu@ustc.edu.cn; Chen, Huoyao

2015-02-15

To eliminate the eccentricity effect, a new method for measuring the groove density of a variable-line-space grating was adapted. Based on grating equation, groove density is calculated by measuring the internal angles between zeroth-order and first-order diffracted light for two different wavelengths with the same angle of incidence. The measurement system mainly includes two laser sources, a phase plate, plane mirror, and charge coupled device. The measurement results of a variable-line-space grating demonstrate that the experiment data agree well with theoretical values, and the value of measurement error (ΔN/N) is less than 2.72 × 10{sup −4}.

Primordial SdS universe from a 5D vacuum: scalar field fluctuations on Schwarzschild and Hubble horizons

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

Aguilar, José Edgar Madriz; Bellini, Mauricio, E-mail: jemadriz@fisica.ugto.mx, E-mail: mbellini@mdp.edu.ar

2010-11-01

We study scalar field fluctuations of the inflaton field in an early inflationary universe on an effective 4D Schwarzschild-de Sitter (SdS) metric, which is obtained after make a planar coordinate transformation on a 5D Ricci-flat Schwarzschild-de Sitter (SdS) static metric. We obtain the important result that the spectrum of fluctuations at zeroth order is independent of the scalar field mass M on Schwarzschild scales, while on cosmological scales it exhibits a mass dependence. However, in the first-order expansion, the spectrum depends of the inflaton mass and the amplitude is linear with the Black-Hole (BH) mass m.

Nuclear polarization study: new frontiers for tests of QED in heavy highly charged ions.

PubMed

Volotka, Andrey V; Plunien, Günter

2014-07-11

A systematic investigation of the nuclear polarization effects in one- and few-electron heavy ions is presented. The nuclear polarization corrections in the zeroth and first orders in 1/Z are evaluated to the binding energies, the hyperfine splitting, and the bound-electron g factor. It is shown that the nuclear polarization contributions can be substantially canceled simultaneously with the rigid nuclear corrections. This allows for new prospects for probing the QED effects in a strong electromagnetic field and the determination of fundamental constants.

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

Amemiya, Kenta; Toyoshima, Akio; Kikuchi, Takashi

The design and commissioning of a new soft X-ray beamline, BL-16A, at the Photon Factory is presented. The beamline consists of a pre-focusing mirror, an entrance slit, a variable-included-angle varied-line-spacing plane grating monochromator, and a post-focusing system as usual, and provides circularly and linearly polarized soft X rays in the energy range 200-1500 eV with an APPLE-II type undulator. The commissioning procedure for the beamline optics is described in detail, especially the check of the focal position for the zero-th order and diffracted X rays.

A limiting analysis for edge effects in angle-ply laminates

NASA Technical Reports Server (NTRS)

Hsu, P. W.; Herakovich, C. T.

1976-01-01

A zeroth order solution for edge effects in angle ply composite laminates using perturbation techniques and a limiting free body approach was developed. The general method of solution for laminates is developed and then applied to the special case of a graphite/epoxy laminate. Interlaminar stress distributions are obtained as a function of the laminate thickness to width ratio h/b and compared to existing numerical results. The solution predicts stable, continuous stress distributions, determines finite maximum tensile interlaminar normal stress for two laminates, and provides mathematical evidence for singular interlaminar shear stresses.

SRB combustion dynamics analysis computer program (CDA-1)

NASA Technical Reports Server (NTRS)

Chung, T. J.; Park, O. Y.

1988-01-01

A two-dimensional numerical model is developed for the unsteady oscillatory combustion of the solid propellant flame zone. Variations of pressure with low and high frequency responses across the long flame, such as in the double-base propellants, are accommodated. The formulation is based on a premixed, laminar flame with a one-step overall chemical reaction and the Arrhenius law of decomposition for the gaseous phase with no condensed phase reaction. Numerical calculations are carried out using the Galerkin finite elements, with perturbations expanded to the zeroth, first, and second orders. The numerical results indicate that amplification of oscillatory motions does indeed prevail in high frequency regions. For the second order system, the trend is similar to the first order system for low frequencies, but instabilities may appear at frequencies lower than those of the first order system. The most significant effect of the second order system is that the admittance is extremely oscillatory between moderately high frequency ranges.

Optical pulling force on a magneto-dielectric Rayleigh sphere in Bessel tractor polarized beams

NASA Astrophysics Data System (ADS)

Mitri, F. G.; Li, R. X.; Yang, R. P.; Guo, L. X.; Ding, C. Y.

2016-11-01

The optical radiation force induced by Bessel (vortex) beams on a magneto-dielectric subwavelength sphere is investigated with particular emphasis on the beam polarization and order l (or topological charge). The analysis is focused on identifying the regions and some of the conditions to achieve retrograde motion of the sphere centered on the axis of wave propagation of the incident beam, or shifted off-axially. Exact non-paraxial analytical solutions are established, and computations for linear, circular, radial, azimuthal and mixed polarizations of the individual plane wave components forming the Bessel (vortex) beams by means of the angular spectrum decomposition method (ASDM) illustrate the theory with particular emphasis on the tractor (i.e. reversal) behavior of the force. This effect results in the pulling of the magneto-dielectric sphere against the forward linear momentum density flux associated with the incoming waves. Should some conditions related to the choice of the beam parameters as well as the permittivity and permeability of the sphere be met, the optical force vanishes and reverses sign. Moreover, the beam polarization is shown to affect differently the axial negative pulling force for either the zeroth- or the first-order Bessel beam. When the sphere is centered on the beam‧s axis, the axial force component is always negative for the zeroth-order Bessel beam except for the radial and azimuthal polarization configurations. Nonetheless, for the first-order Bessel beam, the axial force is negative for the radial polarization case only. Additional tractor beam effects arise when the sphere departs from the center of the beam. It is also demonstrated that the tractor beam effect arises from the force component originating from the cross-interaction between the electric and magnetic dipoles. Potential applications are in particle manipulation, optical levitation, tractor beam tweezers, and other emergent technologies using polarized Bessel beams on a small (Rayleigh) magneto-dielectric particle.

Examples of the Zeroth Theorem of the History of Science

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

Jackson, J.D.

2007-08-24

The zeroth theorem of the history of science, enunciated byE. P. Fischer, states that a discovery (rule,regularity, insight) namedafter someone (often) did not originate with that person. I present fiveexamples from physics: the Lorentz condition partial muAmu = 0 definingthe Lorentz gauge of the electromagnetic potentials; the Dirac deltafunction, delta(x); the Schumann resonances of the earth-ionospherecavity; the Weizsacker-Williams method of virtual quanta; the BMTequation of spin dynamics. I give illustrated thumbnail sketches of boththe true and reputed discoverers and quote from their "discovery"publications.

Analysis of forward scattering of an acoustical zeroth-order Bessel beam from rigid complicated (aspherical) structures

NASA Astrophysics Data System (ADS)

Li, Wei; Chai, Yingbin; Gong, Zhixiong; Marston, Philip L.

2017-10-01

The forward scattering from rigid spheroids and endcapped cylinders with finite length (even with a large aspect ratio) immersed in a non-viscous fluid under the illumination of an idealized zeroth-order acoustical Bessel beam (ABB) with arbitrary angles of incidence is calculated and analyzed in the implementation of the T-matrix method (TTM). Based on the present method, the incident coefficients of expansion for the incident ABB are derived and simplifying methods are proposed for the numerical accuracy and computational efficiency according to the geometrical symmetries. A home-made MATLAB software package is constructed accordingly, and then verified and validated for the ABB scattering from rigid aspherical obstacles. Several numerical examples are computed for the forward scattering from both rigid spheroids and finite cylinder, with particular emphasis on the aspect ratios, the half-cone angles of ABBs, the incident angles and the dimensionless frequencies. The rectangular patterns of target strength in the (β, θs) domain (where β is the half-cone angle of the ABB and θs is the scattered polar angle) and local/total forward scattering versus dimensionless frequency are exhibited, which could provide new insights into the physical mechanisms of Bessel beam scattering by rigid spheroids and finite cylinders. The ray diagrams in geometrical models for the scattering in the forward half-space and the optical cross-section theorem help to interpret the scattering mechanisms of ABBs. This research work may provide an alternative for the partial wave series solution under certain circumstances interacting with ABBs for complicated obstacles and benefit some related works in optics and electromagnetics.

Zero-field magnetic response functions in Landau levels

PubMed Central

Gao, Yang; Niu, Qian

2017-01-01

We present a fresh perspective on the Landau level quantization rule; that is, by successively including zero-field magnetic response functions at zero temperature, such as zero-field magnetization and susceptibility, the Onsager’s rule can be corrected order by order. Such a perspective is further reinterpreted as a quantization of the semiclassical electron density in solids. Our theory not only reproduces Onsager’s rule at zeroth order and the Berry phase and magnetic moment correction at first order but also explains the nature of higher-order corrections in a universal way. In applications, those higher-order corrections are expected to curve the linear relation between the level index and the inverse of the magnetic field, as already observed in experiments. Our theory then provides a way to extract the correct value of Berry phase as well as the magnetic susceptibility at zero temperature from Landau level fan diagrams in experiments. Moreover, it can be used theoretically to calculate Landau levels up to second-order accuracy for realistic models. PMID:28655849

Discrete ordinates solutions of nongray radiative transfer with diffusely reflecting walls

NASA Technical Reports Server (NTRS)

Menart, J. A.; Lee, Haeok S.; Kim, Tae-Kuk

1993-01-01

Nongray gas radiation in a plane parallel slab bounded by gray, diffusely reflecting walls is studied using the discrete ordinates method. The spectral equation of transfer is averaged over a narrow wavenumber interval preserving the spectral correlation effect. The governing equations are derived by considering the history of multiple reflections between two reflecting wails. A closure approximation is applied so that only a finite number of reflections have to be explicitly included. The closure solutions express the physics of the problem to a very high degree and show relatively little error. Numerical solutions are obtained by applying a statistical narrow-band model for gas properties and a discrete ordinates code. The net radiative wail heat fluxes and the radiative source distributions are obtained for different temperature profiles. A zeroth-degree formulation, where no wall reflection is handled explicitly, is sufficient to predict the radiative transfer accurately for most cases considered, when compared with increasingly accurate solutions based on explicitly tracing a larger number of wail reflections without any closure approximation applied.

Calculation of photoionization differential cross sections using complex Gauss-type orbitals.

PubMed

Matsuzaki, Rei; Yabushita, Satoshi

2017-09-05

Accurate theoretical calculation of photoelectron angular distributions for general molecules is becoming an important tool to image various chemical reactions in real time. We show in this article that not only photoionization total cross sections but also photoelectron angular distributions can be accurately calculated using complex Gauss-type orbital (cGTO) basis functions. Our method can be easily combined with existing quantum chemistry techniques including electron correlation effects, and applied to various molecules. The so-called two-potential formula is applied to represent the transition dipole moment from an initial bound state to a final continuum state in the molecular coordinate frame. The two required continuum functions, the zeroth-order final continuum state and the first-order wave function induced by the photon field, have been variationally obtained using the complex basis function method with a mixture of appropriate cGTOs and conventional real Gauss-type orbitals (GTOs) to represent the continuum orbitals as well as the remaining bound orbitals. The complex orbital exponents of the cGTOs are optimized by fitting to the outgoing Coulomb functions. The efficiency of the current method is demonstrated through the calculations of the asymmetry parameters and molecular-frame photoelectron angular distributions of H2+ and H2 . In the calculations of H2 , the static exchange and random phase approximations are employed, and the dependence of the results on the basis functions is discussed. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Orbit determination singularities in the Doppler tracking of a planetary orbiter

NASA Technical Reports Server (NTRS)

Wood, L. J.

1985-01-01

On a number of occasions, spacecraft launched by the U.S. have been placed into orbit about the moon, Venus, or Mars. It is pointed out that, in particular, in planetary orbiter missions two-way coherent Doppler data have provided the principal data type for orbit determination applications. The present investigation is concerned with the problem of orbit determination on the basis of Doppler tracking data in the case of a spacecraft in orbit about a natural body other than the earth or the sun. Attention is given to Doppler shift associated with a planetary orbiter, orbit determination using a zeroth-order model for the Doppler shift, and orbit determination using a first-order model for the Doppler shift.

Development of Thermodynamic Conceptual Evaluation

NASA Astrophysics Data System (ADS)

Talaeb, P.; Wattanakasiwich, P.

2010-07-01

This research aims to develop a test for assessing student understanding of fundamental principles in thermodynamics. Misconceptions found from previous physics education research were used to develop the test. Its topics include heat and temperature, the zeroth and the first law of thermodynamics, and the thermodynamics processes. The content validity was analyzed by three physics experts. Then the test was administered to freshmen, sophomores and juniors majored in physics in order to determine item difficulties and item discrimination of the test. A few items were eliminated from the test. Finally, the test will be administered to students taking Physics I course in order to evaluate the effectiveness of Interactive Lecture Demonstrations that will be used for the first time at Chiang Mai University.

Subwavelength structured surfaces and their applications

NASA Technical Reports Server (NTRS)

Raguin, Daniel H.; Morris, G. Michael

1993-01-01

The term subwavelength structured (SWS) surface describes any surface that contains a subwavelength-period grating or gratings. The grating may be of any type provided the period is sufficiently fine so that, unlike conventional gratings, no diffraction orders propagate other than the zeroth orders. Because of the fine periods involved, the fabrication of such surfaces for applications in the visible and infrared portions of the spectral regime have only recently been considered. With refinements in holographic procedures and the push of the semiconductor industry for submicron lithography, production of SWS surfaces is becoming increasingly viable. The topics covered include the following: analytic approaches to analyze SWS surfaces, 1D periodic stratification and effective medium theory, design of waveplates using form birefringence, and 2D binary antireflection structured surfaces.

Kinetic theory of two-temperature polyatomic plasmas

NASA Astrophysics Data System (ADS)

Orlac'h, Jean-Maxime; Giovangigli, Vincent; Novikova, Tatiana; Roca i Cabarrocas, Pere

2018-03-01

We investigate the kinetic theory of two-temperature plasmas for reactive polyatomic gas mixtures. The Knudsen number is taken proportional to the square root of the mass ratio between electrons and heavy-species, and thermal non-equilibrium between electrons and heavy species is allowed. The kinetic non-equilibrium framework also requires a weak coupling between electrons and internal energy modes of heavy species. The zeroth-order and first-order fluid equations are derived by using a generalized Chapman-Enskog method. Expressions for transport fluxes are obtained in terms of macroscopic variable gradients and the corresponding transport coefficients are expressed as bracket products of species perturbed distribution functions. The theory derived in this paper provides a consistent fluid model for non-thermal multicomponent plasmas.

Robust calibration of an optical-lattice depth based on a phase shift

NASA Astrophysics Data System (ADS)

Cabrera-Gutiérrez, C.; Michon, E.; Brunaud, V.; Kawalec, T.; Fortun, A.; Arnal, M.; Billy, J.; Guéry-Odelin, D.

2018-04-01

We report on a method to calibrate the depth of an optical lattice. It consists of triggering the intrasite dipole mode of the cloud by a sudden phase shift. The corresponding oscillatory motion is directly related to the interband frequencies on a large range of lattice depths. Remarkably, for a moderate displacement, a single frequency dominates the oscillation of the zeroth and first orders of the interference pattern observed after a sufficiently long time of flight. The method is robust against atom-atom interactions and the exact value of the extra weak external confinement superimposed to the optical lattice.

Newton's Zeroth Law: Learning from Listening to Our Students

NASA Astrophysics Data System (ADS)

Scherr, Rachel E.; Redish, Edward F.

2005-01-01

Modern instructional advice encourages us to not just tell our students what we want them to know, but to listen to them carefully. This helps us to find out "where they are" in order to better understand what tasks to offer them that might help them learn the physics most effectively. Sometimes, listening to students and trying to understand their intuitions not only helps them, it helps us—giving us new insights into the physics we are teaching. We had such an experience in the fall of 2003 in our algebra-based physics class at the University of Maryland.

Discovery of X-Ray Emission from the Crab Pulsar at Pulse Minimum

NASA Technical Reports Server (NTRS)

Tennant, Allyn F.; Becker, Werner; Juda, Michael X.; Elsner, Ronald F.; Kolodziejczak, Jeffery J.; Murray, Stephen S.; ODell, Stephen L.; Paerels, Frits; Swartz, Douglas A.; Shibazaki, Noriaki;

Discovery of X-Ray Emission from the Crab Pulsar at Pulse Minimum

NASA Technical Reports Server (NTRS)

Tennant, Allyn F.; Becker, Werner; Juda, Michael; Elsner, Ronald F.; Kolodziejczak, Jeffery J.; Murray, Stephen S.; ODell, Stephen L.; Paerels, Frits; Swartz, Douglas A.

2001-01-01

The Chandra X-Ray Observatory observed the Crab pulsar using the Low-Energy Transmission Grating with the High-Resolution Camera. Time-resolved zeroth-order images reveal that the pulsar emits X-rays at all pulse phases. Analysis of the flux at minimum - most likely non-thermal in origin - places an upper limit (T(sub infinity) < 2.1 MK) on the surface temperature of the underlying neutron star. In addition, analysis of the pulse profile establishes that the error in the Chandra-determined absolute time is quite small, -0.2 +/- 0.1 ms.

Edge effects in angle-ply composite laminates

NASA Technical Reports Server (NTRS)

Hsu, P. W.; Herakovich, C. T.

1977-01-01

This paper presents the results of a zeroth-order solution for edge effects in angle-ply composite laminates obtained using perturbation techniques and a limiting free body approach. The general solution for edge effects in laminates of arbitrary angle ply is applied to the special case of a (+ or - 45)s graphite/epoxy laminate. Interlaminar stress distributions are obtained as a function of the laminate thickness-to-width ratio and compared to finite difference results. The solution predicts stable, continuous stress distributions, determines finite maximum tensile interlaminar normal stress and provides mathematical evidence for singular interlaminar shear stresses in (+ or - 45) graphite/epoxy laminates.

Molecular orbital analysis of the inverse halogen dependence of nuclear magnetic shielding in LaX₃, X = F, Cl, Br, I.

PubMed

Moncho, Salvador; Autschbach, Jochen

2010-12-01

The NMR nuclear shielding tensors for the series LaX(3), with X = F, Cl, Br and I, have been computed using two-component relativistic density functional theory based on the zeroth-order regular approximation (ZORA). A detailed analysis of the inverse halogen dependence (IHD) of the La shielding was performed via decomposition of the shielding tensor elements into contributions from localized and delocalized molecular orbitals. Both spin-orbit and paramagnetic shielding terms are important, with the paramagnetic terms being dominant. Major contributions to the IHD can be attributed to the La-X bonding orbitals, as well as to trends associated with the La core and halogen lone pair orbitals, the latter being related to X-La π donation. An 'orbital rotation' model for the in-plane π acceptor f orbital of La helps to rationalize the significant magnitude of deshielding associated with the in-plane π donation. The IHD goes along with a large increase in the shielding tensor anisotropy as X becomes heavier, which can be associated with trends for the covalency of the La-X bonds, with a particularly effective transfer of spin-orbit coupling induced spin density from iodine to La in LaI(3). Copyright © 2010 John Wiley & Sons, Ltd.

S2p core level spectroscopy of short chain oligothiophenes

NASA Astrophysics Data System (ADS)

Baseggio, O.; Toffoli, D.; Stener, M.; Fronzoni, G.; de Simone, M.; Grazioli, C.; Coreno, M.; Guarnaccio, A.; Santagata, A.; D'Auria, M.

2017-12-01

The Near-Edge X-ray-Absorption Fine-Structure (NEXAFS) and X-ray Photoemission Spectroscopy (XPS) of short-chain oligothiophenes (thiophene, 2,2'-bithiophene, and 2,2':5',2″-terthiophene) in the gas phase have been measured in the sulfur L2,3-edge region. The assignment of the spectral features is based on the relativistic two-component zeroth-order regular approximation time dependent density functional theory approach. The calculations allow us to estimate both the contribution of the spin-orbit splitting and of the molecular-field splitting to the sulfur binding energies and give results in good agreement with the experimental measurements. The deconvolution of the calculated S2p NEXAFS spectra into the two manifolds of excited states converging to the LIII and LII edges facilitates the attribution of the spectral structures. The main S2p NEXAFS features are preserved along the series both as concerns the energy positions and the nature of the transitions. This behaviour suggests that the electronic and geometrical environment of the sulfur atom in the three oligomers is relatively unaffected by the increasing chain length. This trend is also observed in the XPS spectra. The relatively simple structure of S2p NEXAFS spectra along the series reflects the localized nature of the virtual states involved in the core excitation process.

Spin-orbit ZORA and four-component Dirac-Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers.

PubMed

Jankowska, Marzena; Kupka, Teobald; Stobiński, Leszek; Faber, Rasmus; Lacerda, Evanildo G; Sauer, Stephan P A

2016-02-05

Hartree-Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange-correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin-orbit zeroth-order regular approximation Hamiltonian in combination with the large Slater-type basis set QZ4P as well as with the four-component Dirac-Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization-consistent basis sets aug-pcSseg-4 for He, Ne and Ar, aug-pcSseg-3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero-point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed. © 2015 Wiley Periodicals, Inc.

Double vibrational collision-induced Raman scattering by SF{sub 6}-N{sub 2}: Beyond the point-polarizable molecule model

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

Verzhbitskiy, I. A.; Chrysos, M.; Kouzov, A. P.

2010-11-15

Collision-induced Raman bandshapes and zeroth-order spectral moments are calculated both for the depolarized spectrum and for the extremely weak isotropic spectrum of the SF{sub 6}({nu}{sub 1}) +N{sub 2}({nu}{sub 1}) double-Raman-scattering band. A critical comparison is made with experiments conducted recently by the authors [Phys. Rev. A 81, 012702 (2010); 81, 042705 (2010)]. The study of this transition, hitherto restricted to the model framework of two point-polarizable molecules, is now completed to incorporate effects beyond the point-molecule approximation. Whereas the extended model offers a few percent improvement in the depolarized spectrum, it reveals a huge 80% increase in the isotropic spectrummore » and its moment, owing essentially to the polarizability anisotropy of N{sub 2}. For both spectra, agreement between quantum-mechanical calculations and our experiments is found, provided that the best ab initio data for the (hyper)polarizability parameters are used. This refined study shows clearly the need to include all mechanisms and data to a high level of accuracy and allows one to decide between alternatives about difficult and controversial issues such as the intermolecular potential or the sensitive Hamaker force constants.« less

A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh

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

Bauer, Carl A., E-mail: carl.bauer@colorado.edu; Werner, Gregory R.; Cary, John R.

For embedded boundary electromagnetics using the Dey–Mittra (Dey and Mittra, 1997) [1] algorithm, a special grad–div matrix constructed in this work allows use of multigrid methods for efficient inversion of Maxwell’s curl–curl matrix. Efficient curl–curl inversions are demonstrated within a shift-and-invert Krylov-subspace eigensolver (open-sourced at ([ofortt]https://github.com/bauerca/maxwell[cfortt])) on the spherical cavity and the 9-cell TESLA superconducting accelerator cavity. The accuracy of the Dey–Mittra algorithm is also examined: frequencies converge with second-order error, and surface fields are found to converge with nearly second-order error. In agreement with previous work (Nieter et al., 2009) [2], neglecting some boundary-cut cell faces (as is requiredmore » in the time domain for numerical stability) reduces frequency convergence to first-order and surface-field convergence to zeroth-order (i.e. surface fields do not converge). Additionally and importantly, neglecting faces can reduce accuracy by an order of magnitude at low resolutions.« less

Refactorizing NRQCD short-distance coefficients in exclusive quarkonium production

NASA Astrophysics Data System (ADS)

Jia, Yu; Yang, Deshan

2009-06-01

In a typical exclusive quarkonium production process, when the center-of-mass energy, √{s}, is much greater than the heavy quark mass m, large kinematic logarithms of s/m will unavoidably arise at each order of perturbative expansion in the short-distance coefficients of the nonrelativistic QCD (NRQCD) factorization formalism, which may potentially harm the perturbative expansion. This symptom reflects that the hard regime in NRQCD factorization is too coarse and should be further factorized. We suggest that this regime can be further separated into "hard" and "collinear" degrees of freedom, so that the familiar light-cone approach can be employed to reproduce the NRQCD matching coefficients at the zeroth order of m/s and order by order in α. Taking two simple processes, exclusive η+γ production in ee annihilation and Higgs boson radiative decay into ϒ, as examples, we illustrate how the leading logarithms of s/m in the NRQCD matching coefficients are identified and summed to all orders in α with the aid of Brodsky-Lepage evolution equation.

Interactive 3-D registration of ultrasound and magnetic resonance images based on a magnetic position sensor.

PubMed

Pagoulatos, N; Edwards, W S; Haynor, D R; Kim, Y

1999-12-01

The use of stereotactic systems has been one of the main approaches for image-based guidance of the surgical tool within the brain. The main limitation of stereotactic systems is that they are based on preoperative images that might become outdated and invalid during the course of surgery. Ultrasound (US) is considered the most practical and cost-effective intraoperative imaging modality, but US images inherently have a low signal-to-noise ratio. Integrating intraoperative US with stereotactic systems has recently been attempted. In this paper, we present a new system for interactively registering two-dimensional US and three-dimensional magnetic resonance (MR) images. This registration is based on tracking the US probe with a dc magnetic position sensor. We have performed an extensive analysis of the errors of our system by using a custom-built phantom. The registration error between the MR and the position sensor space was found to have a mean value of 1.78 mm and a standard deviation of 0.18 mm. The registration error between US and MR space was dependent on the distance of the target point from the US probe face. For a 3.5-MHz phased one-dimensional array transducer and a depth of 6 cm, the mean value of the registration error was 2.00 mm and the standard deviation was 0.75 mm. The registered MR images were reconstructed using either zeroth-order or first-order interpolation. The ease of use and the interactive nature of our system (approximately 6.5 frames/s for 344 x 310 images and first-order interpolation on a Pentium II 450 MHz) demonstrates its potential to be used in the operating room.

Zeroth order Fabry-Perot resonance enabled ultra-thin perfect light absorber using percolation aluminum and silicon nanofilms

DOE PAGES

Mirshafieyan, Seyed Sadreddin; Luk, Ting S.; Guo, Junpeng

2016-03-04

Here, we demonstrated perfect light absorption in optical nanocavities made of ultra-thin percolation aluminum and silicon films deposited on an aluminum surface. The total layer thickness of the aluminum and silicon films is one order of magnitude less than perfect absorption wavelength in the visible spectral range. The ratio of silicon cavity layer thickness to perfect absorption wavelength decreases as wavelength decreases due to the increased phase delays at silicon-aluminum boundaries at shorter wavelengths. It is explained that perfect light absorption is due to critical coupling of incident wave to the fundamental Fabry-Perot resonance mode of the structure where themore » round trip phase delay is zero. Simulations were performed and the results agree well with the measurement results.« less

Excitation of higher radial modes of azimuthal surface waves in the electron cyclotron frequency range by rotating relativistic flow of electrons in cylindrical waveguides partially filled by plasmas

NASA Astrophysics Data System (ADS)

Girka, Igor O.; Pavlenko, Ivan V.; Thumm, Manfred

2018-05-01

Azimuthal surface waves are electromagnetic eigenwaves of cylindrical plasma-dielectric waveguides which propagate azimuthally nearby the plasma-dielectric interface across an axial external stationary magnetic field. Their eigenfrequency in particular can belong to the electron cyclotron frequency range. Excitation of azimuthal surface waves by rotating relativistic electron flows was studied in detail recently in the case of the zeroth radial mode for which the waves' radial phase change within the layer where the electrons gyrate is small. In this case, just the plasma parameters cause the main influence on the waves' dispersion properties. In the case of the first and higher radial modes, the wave eigenfrequency is higher and the wavelength is shorter than in the case of the zeroth radial mode. This gain being of interest for practical applications can be achieved without any change in the device design. The possibility of effective excitation of the higher order radial modes of azimuthal surface waves is demonstrated here. Getting shorter wavelengths of the excited waves in the case of higher radial modes is shown to be accompanied by decreasing growth rates of the waves. The results obtained here are of interest for developing new sources of electromagnetic radiation, in nano-physics and in medical physics.

Tunable rejection filters with ultra-wideband using zeroth shear mode plate wave resonators

NASA Astrophysics Data System (ADS)

Kadota, Michio; Sannomiya, Toshio; Tanaka, Shuji

2017-07-01

This paper reports wide band rejection filters and tunable rejection filters using ultra-wideband zeroth shear mode (SH0) plate wave resonators. The frequency range covers the digital TV band in Japan that runs from 470 to 710 MHz. This range has been chosen to meet the TV white space cognitive radio requirements of rejection filters. Wide rejection bands were obtained using several resonators with different frequencies. Tunable rejection filters were demonstrated using Si diodes connected to the band rejection filters. Wide tunable ranges as high as 31% were measured by applying a DC voltage to the Si diodes.

Charge density on thin straight wire, revisited

NASA Astrophysics Data System (ADS)

Jackson, J. D.

2000-09-01

The question of the equilibrium linear charge density on a charged straight conducting "wire" of finite length as its cross-sectional dimension becomes vanishingly small relative to the length is revisited in our didactic presentation. We first consider the wire as the limit of a prolate spheroidal conductor with semi-minor axis a and semi-major axis c when a/c<<1. We then treat an azimuthally symmetric straight conductor of length 2c and variable radius r(z) whose scale is defined by a parameter a. A procedure is developed to find the linear charge density λ(z) as an expansion in powers of 1/Λ, where Λ≡ln(4c2/a2), beginning with a uniform line charge density λ0. We show, for this rather general wire, that in the limit Λ>>1 the linear charge density becomes essentially uniform, but that the tiny nonuniformity (of order 1/Λ) is sufficient to produce a tangential electric field (of order Λ0) that cancels the zeroth-order field that naively seems to belie equilibrium. We specialize to a right circular cylinder and obtain the linear charge density explicitly, correct to order 1/Λ2 inclusive, and also the capacitance of a long isolated charged cylinder, a result anticipated in the published literature 37 years ago. The results for the cylinder are compared with published numerical computations. The second-order correction to the charge density is calculated numerically for a sampling of other shapes to show that the details of the distribution for finite 1/Λ vary with the shape, even though density becomes constant in the limit Λ→∞. We give a second method of finding the charge distribution on the cylinder, one that approximates the charge density by a finite polynomial in z2 and requires the solution of a coupled set of linear algebraic equations. Perhaps the most striking general observation is that the approach to uniformity as a/c→0 is extremely slow.

Efficient image projection by Fourier electroholography.

PubMed

Makowski, Michał; Ducin, Izabela; Kakarenko, Karol; Kolodziejczyk, Andrzej; Siemion, Agnieszka; Siemion, Andrzej; Suszek, Jaroslaw; Sypek, Maciej; Wojnowski, Dariusz

2011-08-15

An improved efficient projection of color images is presented. It uses a phase spatial light modulator with three iteratively optimized Fourier holograms displayed simultaneously--each for one primary color. This spatial division instead of time division provides stable images. A pixelated structure of the modulator and fluctuations of liquid crystal molecules cause a zeroth-order peak, eliminated by additional wavelength-dependent phase factors shifting it before the image plane, where it is blocked with a matched filter. Speckles are suppressed by time integration of variable speckle patterns generated by additional randomizations of an initial phase and minor changes of the signal. © 2011 Optical Society of America

Design of bent waveguide semiconductor lasers using nonlinear equivalent chirp

NASA Astrophysics Data System (ADS)

Li, Lianyan; Shi, Yuechun; Zhang, Yunshan; Chen, Xiangfei

2018-01-01

Reconstruction equivalent chirp (REC) technique is widely used in the design and fabrication of semiconductor laser arrays and tunable lasers with low cost and high wavelength accuracy. Bent waveguide is a promising method to suppress the zeroth order resonance, which is an intrinsic problem in REC technique. However, it may introduce basic grating chirp and deteriorate the single longitudinal mode (SLM) property of the laser. A nonlinear equivalent chirp pattern is proposed in this paper to compensate the grating chirp and improve the SLM property. It will benefit the realization of low-cost Distributed feedback (DFB) semiconductor laser arrays with accurate lasing wavelength.

Guidance law development for aeroassisted transfer vehicles using matched asymptotic expansions

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Melamed, Nahum

1993-01-01

This report addresses and clarifies a number of issues related to the Matched Asymptotic Expansion (MAE) analysis of skip trajectories, or any class of problems that give rise to inner layers that are not associated directly with satisfying boundary conditions. The procedure for matching inner and outer solutions, and using the composite solution to satisfy boundary conditions is developed and rigorously followed to obtain a set of algebraic equations for the problem of inclination change with minimum energy loss. A detailed evaluation of the zeroth order guidance algorithm for aeroassisted orbit transfer is performed. It is shown that by exploiting the structure of the MAE solution procedure, the original problem, which requires the solution of a set of 20 implicit algebraic equations, can be reduced to a problem of 6 implicit equations in 6 unknowns. A solution that is near optimal, requires a minimum of computation, and thus can be implemented in real time and on-board the vehicle, has been obtained. Guidance law implementation entails treating the current state as a new initial state and repetitively solving the zeroth order MAE problem to obtain the feedback controls. Finally, a general procedure is developed for constructing a MAE solution up to first order, of the Hamilton-Jacobi-Bellman equation based on the method of characteristics. The development is valid for a class of perturbation problems whose solution exhibits two-time-scale behavior. A regular expansion for problems of this type is shown to be inappropriate since it is not valid over a narrow range of the independent variable. That is, it is not uniformly valid. Of particular interest here is the manner in which matching and boundary conditions are enforced when the expansion is carried out to first order. Two cases are distinguished-one where the left boundary condition coincides with, or lies to the right of, the singular region, and another one where the left boundary condition lies to the left of the singular region. A simple example is used to illustrate the procedure where the obtained solution is uniformly valid to O(Epsilon(exp 2)). The potential application of this procedure to aeroassisted plane change is also described and partially evaluated.

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

Ghosh Deb, S.; Sinha, C.; Chattopadhyay, A.

The modification in the dynamics of the electron-impact ionization process of a Li{sup +} ion due to an intense linearly polarized monochromatic laser field (n{gamma}e,2e) is studied theoretically using coplanar geometry. Significant laser modifications are noted due to multiphoton effects both in the shape and magnitude of the triple-differential cross sections (TDCSs) with respect to the field-free (FF) situation. The net effect of the laser field is to suppress the FF cross sections in the zeroth-order approximation [Coulomb-Volkov (CV)] of the ejected electron wave function, while in the first order [modified Coulomb-Volkov (MCV)], the TDCSs are found to be enhancedmore » or suppressed depending on the kinematics of the process. The strong FF recoil dominance for the (e,2e) process of an ionic target at low incident energy is destroyed in the presence of the laser field. The FF binary-to-recoil ratio changes remarkably in the presence of the laser field, particularly at low incident energies. The difference between the multiphoton CV and the FF results indicates that for the ionic target, the Kroll-Watson sum rule does not hold well at the present energy range in contrast to the neutral atom (He) case. The TDCSs are found to be quite sensitive with respect to the initial phase of the laser field, particularly at higher incident energies. A significant qualitative difference is noted in the multiphoton ejected energy distribution (double-differential cross sections) between the CV and the MCV models. Variation of the TDCSs with respect to the laser phase is also studied.« less

Impact of pH on hydrogen oxidizing redox processes in aquifers due to gas intrusions

NASA Astrophysics Data System (ADS)

Metzgen, Adrian; Berta, Marton; Dethlefsen, Frank; Ebert, Markus; Dahmke, Andreas

2017-04-01

Hydrogen production from excess energy and its storage can help increasing the efficiency of solar and wind in the energy mix. Therefore, hydrogen needs large-scale intermediate storage independent of the intended later use as hydrogen gas or as reactant to produce methane in the Sabatier process. A possible storage solution is using the geological subsurface such as caverns built in salt deposits or aquifers that are not used for drinking water production. However, underground storage of hydrogen gas potentially leads to accidental gas leakages into near-surface potable aquifers triggering subsequent geochemical processes. These leakages pose potential risks that are currently not sufficiently understood. To close this gap in knowledge, a high-pressure laboratory column system was used to simulate a hydrogen gas intrusion into a shallow aquifer. Water and sediment were gained from a sandy Pleistocene aquifer near Neumünster, Germany. In the first stage of the experiment, 100% hydrogen gas was used to simulate dissolved hydrogen concentrations between 800 and 4000 µM by varying pH2 between 2 and 15 bars. pH values rose to between 7.9 and 10.4, partly due to stripping CO2 from the groundwater used during H2 gas addition. In a second stage, the pH was regulated in a range of 6.7 to 7.9 by using a gas mixture of 99% H2 and 1% CO2 at 5 bars of total gas pressure. Observed processes included hydrogen oxidation, sulfate reduction, acetogenesis, formate production, and methanogenesis, which were independent of the hydrogen concentration. Hydrogen oxidation and sulfate reduction showed zeroth order reaction rates and rate constants (106 to 412 µM/h and 12 to 33 µM/h, respectively) in the pH range between 8 and 10. At pH levels between 7 and 8, both reactions started out faster near the column's inflow but then seemed limited towards the columns outflow, suggesting the dependence of sulfate reduction on the pH-value. Acetogenesis dominated the pH range between 8 and 10 (first order rate constants between 0.029 and 0.036 1/h). Between pH 7 and 8, acetogenesis showed a linear trend (zeroth order rates between 3 and 5 µM/h) whereas formate production became the main process (zeroth order rates between 38 to 197 µM/h) together with methanogenesis as a minor process. The results indicated a strong dependency of the biogeochemical hydrogenotrophic redox reactions on the pH milieu. Thus, pH buffers such as dissolved or solid phase carbonates should be taken into account when predicting effects a hydrogen leakage may have on shallow aquifers. Additionally, parameters derived from the observed processes and their rates allow the design of a process based numerical model simulating a hydrogen intrusion into a shallow aquifer. Consequently the presented outcomes allow an exemplary quantification of the resulting geochemical effects. This study was carried out within the ANGUS+ project and was funded by the German Federal Ministry of Education and Research (BMBF) energy storage funding initiative.

Analytical formulas for short bunch wakes in a flat dechirper

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

Bane, Karl; Stupakov, Gennady; Zagorodnov, Igor

2016-08-04

We develop analytical models of the longitudinal and transverse wakes, on and off axis for a flat, corrugated beam pipe with realistic parameters, and then compare them with numerical calculations, and generally find good agreement. These analytical “first order” formulas approximate the droop at the origin of the longitudinal wake and of the slope of the transverse wakes; they represent an improvement in accuracy over earlier, “zeroth order” formulas. In example calculations for the RadiaBeam/LCLS dechirper using typical parameters, we find a 16% droop in the energy chirp at the bunch tail compared to simpler calculations. As a result, withmore » the beam moved to 200 μm from one jaw in one dechirper section, one can achieve a 3 MV transverse kick differential over a 30 μm length.« less

Adaptive slit beam shaping for direct laser written waveguides.

PubMed

Salter, P S; Jesacher, A; Spring, J B; Metcalf, B J; Thomas-Peter, N; Simmonds, R D; Langford, N K; Walmsley, I A; Booth, M J

2012-02-15

We demonstrate an improved method for fabricating optical waveguides in bulk materials by means of femtosecond laser writing. We use an LC spatial light modulator (SLM) to shape the beam focus by generating adaptive slit illumination in the pupil of the objective lens. A diffraction grating is applied in a strip across the SLM to simulate a slit, with the first diffracted order mapped onto the pupil plane of the objective lens while the zeroth order is blocked. This technique enables real-time control of the beam-shaping parameters during writing, facilitating the fabrication of more complicated structures than is possible using nonadaptive methods. Waveguides are demonstrated in fused silica with a coupling loss to single-mode fibers in the range of 0.2 to 0.5 dB and propagation loss <0.4 dB/cm.

Fate of sulfonamide antibiotics in contact with activated sludge--sorption and biodegradation.

PubMed

Yang, Sheng-Fu; Lin, Cheng-Fang; Wu, Chien-Ju; Ng, Kok-Kwang; Lin, Angela Yu-Chen; Hong, Pui-Kwan Andy

2012-03-15

The sorption and biodegradation of three sulfonamide antibiotics, namely sulfamethoxazole (SMX), sulfadimethoxine (SDM), and sulfamonomethoxine (SMM), in an activated sludge system were investigated. Experiments were carried out by contacting 100 μg/L of each sulfonamide compound individually with 2.56 g/L of MLSS at 25±0.5 °C, pH 7.0, and dissolved oxygen of 3.0±0.1 mg/L in a batch reactor over different periods of 2 d and 14 d. All sulfonamides were removed completely over 11-13 d. Sorptive equilibrium was established well within the first few hours, followed by a lag period of 1-3 days before biodegradation was to deplete the antibiotic compounds linearly in the ensuing 10 days. Apparent zeroth-order rate constants were obtained by regression analysis of measured aqueous concentration vs. time profiles to a kinetic model accounting for sorption and biodegradation; they were 8.1, 7.9, and 7.7 μg/L/d for SDM, SMX, and SMM, respectively, at activated sludge concentration of 2.56 g/L. The measured kinetics implied that with typical hydraulic retention time (e.g. 6 h) provided by WWTP the removal of sulfonamide compounds from the wastewater during the activated sludge process would approximate 2 μg/L. Copyright © 2011 Elsevier Ltd. All rights reserved.

Effect of Spin Multiplicity in O2 Adsorption and Dissociation on Small Bimetallic AuAg Clusters.

PubMed

García-Cruz, Raúl; Poulain, Enrique; Hernández-Pérez, Isaías; Reyes-Nava, Juan A; González-Torres, Julio C; Rubio-Ponce, A; Olvera-Neria, Oscar

2017-08-17

To dispose of atomic oxygen, it is necessary the O 2 activation; however, an energy barrier must be overcome to break the O-O bond. This work presents theoretical calculations of the O 2 adsorption and dissociation on small pure Au n and Ag m and bimetallic Au n Ag m (n + m ≤ 6) clusters using the density functional theory (DFT) and the zeroth-order regular approximation (ZORA) to explicitly include scalar relativistic effects. The most stable Au n Ag m clusters contain a higher concentration of Au with Ag atoms located in the center of the cluster. The O 2 adsorption energy on pure and bimetallic clusters and the ensuing geometries depend on the spin multiplicity of the system. For a doublet multiplicity, O 2 is adsorbed in a bridge configuration, whereas for a triplet only one O-metal bond is formed. The charge transfer from metal toward O 2 occupies the σ* O-O antibonding natural bond orbital, which weakens the oxygen bond. The Au 3 ( 2 A) cluster presents the lowest activation energy to dissociate O 2 , whereas the opposite applies to the AuAg ( 3 A) system. In the O 2 activation, bimetallic clusters are not as active as pure Au n clusters due to the charge donated by Ag atoms being shared between O 2 and Au atoms.

Tetraphenylporphyrin electronic properties: a combined theoretical and experimental study of thin films deposited by SuMBD.

PubMed

Nardi, Marco; Verucchi, Roberto; Corradi, Claudio; Pola, Marco; Casarin, Maurizio; Vittadini, Andrea; Iannotta, Salvatore

2010-01-28

Porphyrins and their metal complexes are particularly well suitable for applications in photoelectronics, sensing, energy production, because of their chemical, electronic and optical properties. The understanding of the electronic properties of the pristine molecule is of great relevance for the study and application of the wide class of these compounds. This is notably important for the recently achieved in-vacuo synthesis of organo-metallic thin films directly from the pure free base organic-inorganic precursors in the vapor phase, and its interpretation by means of surface electron spectroscopies. We report on a combined experimental and theoretical study of the physical/chemical properties of tetraphenylporphyrin, H(2)TPP, deposited on the SiO(2)/Si(100) native oxide surface by supersonic molecular beam deposition (SuMBD). Valence states and 1s core level emissions of carbon and nitrogen have been investigated with surface photoelectron spectroscopies by using synchrotron radiation light. The interpretation of the spectra has been guided by density functional numerical experiments on the gas-phase molecule. Non-relativistic calculations were carried out for the valence states, whereas a two component relativistic approach in the zeroth-order regular approximation was used to investigate the core levels. The good agreement between theoretical and experimental analysis results in a comprehensive overview of the chemical properties of the H(2)TPP molecule, highly improving reliability in the interpretation of experimental photoemission spectra.

Two dimensional J-matrix approach to quantum scattering

NASA Astrophysics Data System (ADS)

Olumegbon, Ismail Adewale

We present an extension of the J-matrix method of scattering to two dimensions in cylindrical coordinates. In the J-matrix approach we select a zeroth order Hamiltonian, H0, which is exactly solvable in the sense that we select a square integrable basis set that enable us to have an infinite tridiagonal representation for H0. Expanding the wavefunction in this basis makes the wave equation equivalent to a three-term recursion relation for the expansion coefficients. Consequently, finding solutions of the recursion relation is equivalent to solving the original H0 problem (i.e., determining the expansion coefficients of the system's wavefunction). The part of the original potential interaction which cannot be brought to an exact tridiagonal form is cut in an NxN basis space and its matrix elements are computed numerically using Gauss quadrature approach. Hence, this approach embodies powerful tools in the analysis of solutions of the wave equation by exploiting the intimate connection and interplay between tridiagonal matrices and the theory of orthogonal polynomials. In such analysis, one is at liberty to employ a wide range of well established methods and numerical techniques associated with these settings such as quadrature approximation and continued fractions. To demonstrate the utility, usefulness, and accuracy of the extended method we use it to obtain the bound states for an illustrative short range potential problem.

Two dimensional J-matrix approach to quantum scattering

NASA Astrophysics Data System (ADS)

Olumegbon, Ismail Adewale

2013-01-01

We present an extension of the J-matrix method of scattering to two dimensions in cylindrical coordinates. In the J-matrix approach we select a zeroth order Hamiltonian, H0, which is exactly solvable in the sense that we select a square integrable basis set that enable us to have an infinite tridiagonal representation for H0. Expanding the wavefunction in this basis makes the wave equation equivalent to a three-term recursion relation for the expansion coefficients. Consequently, finding solutions of the recursion relation is equivalent to solving the original H0 problem (i.e., determining the expansion coefficients of the system's wavefunction). The part of the original potential interaction which cannot be brought to an exact tridiagonal form is cut in an NxN basis space and its matrix elements are computed numerically using Gauss quadrature approach. Hence, this approach embodies powerful tools in the analysis of solutions of the wave equation by exploiting the intimate connection and interplay between tridiagonal matrices and the theory of orthogonal polynomials. In such analysis, one is at liberty to employ a wide range of well established methods and numerical techniques associated with these settings such as quadrature approximation and continued fractions. To demonstrate the utility, usefulness, and accuracy of the extended method we use it to obtain the bound states for an illustrative short range potential problem.

Off-shell hydrodynamics from holography

DOE PAGES

Crossley, Michael; Glorioso, Paolo; Liu, Hong; ...

2016-02-18

In this article, we outline a program for obtaining an action principle for dissipative fluid dynamics by considering the holographic Wilsonian renormalization group applied to systems with a gravity dual. As a first step, in this paper we restrict to systems with a non-dissipative horizon. By integrating out gapped degrees of freedom in the bulk gravitational system between an asymptotic boundary and a horizon, we are led to a formulation of hydrodynamics where the dynamical variables are not standard velocity and temperature fields, but the relative embedding of the boundary and horizon hypersurfaces. At zeroth order, this action reduces tomore » that proposed by Dubovsky et al. as an off-shell formulation of ideal fluid dynamics.« less

Nonlinear radiative heat flux and heat source/sink on entropy generation minimization rate

NASA Astrophysics Data System (ADS)

Hayat, T.; Khan, M. Waleed Ahmed; Khan, M. Ijaz; Alsaedi, A.

2018-06-01

Entropy generation minimization in nonlinear radiative mixed convective flow towards a variable thicked surface is addressed. Entropy generation for momentum and temperature is carried out. The source for this flow analysis is stretching velocity of sheet. Transformations are used to reduce system of partial differential equations into ordinary ones. Total entropy generation rate is determined. Series solutions for the zeroth and mth order deformation systems are computed. Domain of convergence for obtained solutions is identified. Velocity, temperature and concentration fields are plotted and interpreted. Entropy equation is studied through nonlinear mixed convection and radiative heat flux. Velocity and temperature gradients are discussed through graphs. Meaningful results are concluded in the final remarks.

Single-shot high aspect ratio bulk nanostructuring of fused silica using chirp-controlled ultrafast laser Bessel beams

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

Bhuyan, M. K.; Velpula, P. K.; Colombier, J. P.

2014-01-13

We report single-shot, high aspect ratio nanovoid fabrication in bulk fused silica using zeroth order chirp-controlled ultrafast laser Bessel beams. We identify a unique laser pulse length and energy dependence of the physical characteristics of machined structures over which nanovoids of diameter in the range 200–400 nm and aspect ratios exceeding 1000 can be fabricated. A mechanism based on the axial energy deposition of nonlinear ultrashort Bessel beams and subsequent material densification or rarefaction in fused silica is proposed, intricating the non-diffractive nature with the diffusing character of laser-generated free carriers. Fluid flow through nanochannel is also demonstrated.

Polarization analysis of diamond subwavelength gratings acting as space-variant birefringent elements

NASA Astrophysics Data System (ADS)

Piron, P.; Vargas Catalan, E.; Karlsson, M.

2018-02-01

Subwavelength gratings are gratings with a period smaller than the incident wavelength. They only allow the zeroth order of diffraction, they possess form birefringence and they can be modeled as birefringent plates. In this paper, we present the first results of an experimental method designed to measure their polarization properties. The method consists in measuring the variation of the light transmitted through two linear polarizers with the subwavelength component between them for several orientations of the polarizers. In this paper, the basic principles of the method are introduced and the experimental setup is presented. Several types of components are numerically studied and the optical measurements of one component are presented.

Characterization and correction of eddy-current artifacts in unipolar and bipolar diffusion sequences using magnetic field monitoring.

PubMed

Chan, Rachel W; von Deuster, Constantin; Giese, Daniel; Stoeck, Christian T; Harmer, Jack; Aitken, Andrew P; Atkinson, David; Kozerke, Sebastian

2014-07-01

Diffusion tensor imaging (DTI) of moving organs is gaining increasing attention but robust performance requires sequence modifications and dedicated correction methods to account for system imperfections. In this study, eddy currents in the "unipolar" Stejskal-Tanner and the velocity-compensated "bipolar" spin-echo diffusion sequences were investigated and corrected for using a magnetic field monitoring approach in combination with higher-order image reconstruction. From the field-camera measurements, increased levels of second-order eddy currents were quantified in the unipolar sequence relative to the bipolar diffusion sequence while zeroth and linear orders were found to be similar between both sequences. Second-order image reconstruction based on field-monitoring data resulted in reduced spatial misalignment artifacts and residual displacements of less than 0.43 mm and 0.29 mm (in the unipolar and bipolar sequences, respectively) after second-order eddy-current correction. Results demonstrate the need for second-order correction in unipolar encoding schemes but also show that bipolar sequences benefit from second-order reconstruction to correct for incomplete intrinsic cancellation of eddy-currents. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Off-axis digital holographic microscopy with LED illumination based on polarization filtering.

PubMed

Guo, Rongli; Yao, Baoli; Gao, Peng; Min, Junwei; Zhou, Meiling; Han, Jun; Yu, Xun; Yu, Xianghua; Lei, Ming; Yan, Shaohui; Yang, Yanlong; Dan, Dan; Ye, Tong

2013-12-01

A reflection mode digital holographic microscope with light emitting diode (LED) illumination and off-axis interferometry is proposed. The setup is comprised of a Linnik interferometer and a grating-based 4f imaging unit. Both object and reference waves travel coaxially and are split into multiple diffraction orders in the Fourier plane by the grating. The zeroth and first orders are filtered by a polarizing array to select orthogonally polarized object waves and reference waves. Subsequently, the object and reference waves are combined again in the output plane of the 4f system, and then the hologram with uniform contrast over the entire field of view can be acquired with the aid of a polarizer. The one-shot nature in the off-axis configuration enables an interferometric recording time on a millisecond scale. The validity of the proposed setup is illustrated by imaging nanostructured substrates, and the experimental results demonstrate that the phase noise is reduced drastically by an order of 68% when compared to a He-Ne laser-based result.

Entanglement entropy between virtual and real excitations in quantum electrodynamics

NASA Astrophysics Data System (ADS)

Ardenghi, Juan Sebastián

2018-05-01

The aim of this work is to introduce the entanglement entropy of real and virtual excitations of fermion and photon fields. By rewriting the generating functional of quantum electrodynamics theory as an inner product between quantum operators, it is possible to obtain quantum density operators representing the propagation of real and virtual particles. These operators are partial traces, where the degrees of freedom traced out are unobserved excitations. Then the von Neumann definition of entropy can be applied to these quantum operators and in particular, for the partial traces taken over by the internal or external degrees of freedom. A universal behavior is obtained for the entanglement entropy for different quantum fields at zeroth order in the coupling constant. In order to obtain numerical results at different orders in the perturbation expansion, the Bloch-Nordsieck model is considered, where it is shown that for some particular values of the electric charge, the von Neumann entropy increases or decreases with respect to the noninteracting case.

A Unified Model for Predicting the Open Hole Tensile and Compressive Strengths of Composite Laminates for Aerospace Applications

NASA Technical Reports Server (NTRS)

Davidson, Paul; Pineda, Evan J.; Heinrich, Christian; Waas, Anthony M.

2013-01-01

The open hole tensile and compressive strengths are important design parameters in qualifying fiber reinforced laminates for a wide variety of structural applications in the aerospace industry. In this paper, we present a unified model that can be used for predicting both these strengths (tensile and compressive) using the same set of coupon level, material property data. As a prelude to the unified computational model that follows, simplified approaches, referred to as "zeroth order", "first order", etc. with increasing levels of fidelity are first presented. The results and methods presented are practical and validated against experimental data. They serve as an introductory step in establishing a virtual building block, bottom-up approach to designing future airframe structures with composite materials. The results are useful for aerospace design engineers, particularly those that deal with airframe design.

Novel 2D CRLH TL and Its ZOR and FOR Applied on Dual-Band Omnidirectional Radiation Antenna

NASA Astrophysics Data System (ADS)

Li, Tian-Peng; Wang, Guang-Ming; Duan, Feifei; Zhou, Cheng; Tan, Rui-Lian

2015-11-01

A new type of two-dimensional (2D) composite right/left-handed transmission lines (CRLH TL) which is composed of four one-dimensional (1D) CRLH TL is proposed in this letter. Each 1D CRLH TL consists of three metallic vias added for shunt inductance and an etched patch slot for series capacitance. Based on this structure, an antenna operating on zeroth-order resonance (ZOR) and first-order resonance (FOR) is designed and fabricated. By taking advantage of coaxially center feed and symmetric structure, a well omnidirectional radiation in XoY plane both in ZOR and FOR and a homogeneously suppressed cross-polarization is obtained. Also, the antenna has a gain value of 2.06 dB in ZOR f1 = 3.52 GHz and 2.94 dB in FOR f2 = 5.25 GHz, respectively.

Discovery of Spatial and Spectral Structure in the X-Ray Emission from the Crab Nebula

NASA Technical Reports Server (NTRS)

Weisskopf, M.; Hester, J. J.; Tennant, A. F.; Elsner, R. F.; Schulz, N. S.; Marshall, H. L.; Karovska, M.; Nichols, J. S.; Swartz, D. A.; Kolodziejczak, J. J.

2000-01-01

The Chandra X-ray Observatory observed the Crab Nebula and Pulsar During orbital calibration. Zeroth-order images with the High-Energy Transmission Grating (HETG) read-out by the Advanced CCD Imaging Spectrometer spectroscopy array (ACIS-S) show a striking richness of X-ray structure, at a resolution comparable to that of the best ground-based visible-light observations. The HETG-ACIS-S images reveal, for the first time, an X-ray knots along the inner ring and (perhaps) along the inward extension of the X-ray jet. Although complicated by instrumental effects and the brightness of the Crab Nebula, the spectrometric analysis shows systematic variations of the X-ray spectrum throughout the Nebula.

Revisiting Adiabatic Switching for Initial Conditions in Quasi-Classical Trajectory Calculations: Application to CH4.

PubMed

Qu, Chen; Bowman, Joel M

2016-07-14

Semiclassical quantization of vibrational energies, using adiabatic switching (AS), is applied to CH4 using a recent ab initio potential energy surface, for which exact quantum calculations of vibrational energies are available. Details of the present calculations, which employ a harmonic normal-mode zeroth-order Hamiltonian, emphasize the importance of transforming to the Eckart frame during the propagation of the adiabatically switched Hamiltonian. The AS energies for the zero-point, and fundamental excitations of two modes are in good agreement with the quantum ones. The use of AS in the context of quasi-classical trajectory calculations is revisited, following previous work reported in 1995, which did not recommend the procedure. We come to a different conclusion here.

Singlet-triplet splittings from the virial theorem and single-particle excitation energies

NASA Astrophysics Data System (ADS)

Becke, Axel D.

2018-01-01

The zeroth-order (uncorrelated) singlet-triplet energy difference in single-particle excited configurations is 2Kif, where Kif is the Coulomb self-energy of the product of the transition orbitals. Here we present a non-empirical, virial-theorem argument that the correlated singlet-triplet energy difference should be half of this, namely, Kif. This incredibly simple result gives vertical HOMO-LUMO excitation energies in small-molecule benchmarks as good as the popular TD-B3LYP time-dependent approach to excited states. For linear acenes and nonlinear polycyclic aromatic hydrocarbons, the performance is significantly better than TD-B3LYP. In addition to the virial theorem, the derivation borrows intuitive pair-density concepts from density-functional theory.

Linearity of the Faraday-rotation-type ac magnetic-field sensor with a ferrimagnetic or ferromagnetic rotator film

NASA Astrophysics Data System (ADS)

Mori, Hiroshi; Asahara, Yousuke

1996-03-01

We analyze the linearity and modulation depth of ac magnetic-field sensors or current sensors, using a ferrimagnetic or ferromagnetic film as the Faraday rotator and employing the detection of only the zeroth-order optical diffraction component from the rotator. It is theoretically shown that for this class of sensor the condition of a constant modulation depth and that of a constant ratio error give an identical series of curves for the relationship between Faraday rotation angle greater than or equals V and polarizer/analyzer relative angle Phi . We give some numerical examples to demonstrate the usefulness of the result with reference to a rare-earth iron garnet film as the rotator.

Transverse circular-polarized Bessel beam generation by inward cylindrical aperture distribution.

PubMed

Pavone, S C; Ettorre, M; Casaletti, M; Albani, M

2016-05-16

In this paper the focusing capability of a radiating aperture implementing an inward cylindrical traveling wave tangential electric field distribution directed along a fixed polarization unit vector is investigated. In particular, it is shown that such an aperture distribution generates a non-diffractive Bessel beam whose transverse component (with respect to the normal of the radiating aperture) of the electric field takes the form of a zero-th order Bessel function. As a practical implementation of the theoretical analysis, a circular-polarized Bessel beam launcher, made by a radial parallel plate waveguide loaded with several slot pairs, arranged on a spiral pattern, is designed and optimized. The proposed launcher performance agrees with the theoretical model and exhibits an excellent polarization purity.

Double-quantum homonuclear rotary resonance: Efficient dipolar recovery in magic-angle spinning nuclear magnetic resonance

NASA Astrophysics Data System (ADS)

Nielsen, N. C.; Bildsøe, H.; Jakobsen, H. J.; Levitt, M. H.

1994-08-01

We describe an efficient method for the recovery of homonuclear dipole-dipole interactions in magic-angle spinning NMR. Double-quantum homonuclear rotary resonance (2Q-HORROR) is established by fulfilling the condition ωr=2ω1, where ωr is the sample rotation frequency and ω1 is the nutation frequency around an applied resonant radio frequency (rf) field. This resonance can be used for double-quantum filtering and measurement of homonuclear dipolar interactions in the presence of magic-angle spinning. The spin dynamics depend only weakly on crystallite orientation allowing good performance for powder samples. Chemical shift effects are suppressed to zeroth order. The method is demonstrated for singly and doubly 13C labeled L-alanine.

DFT benchmark study for the oxidative addition of CH 4 to Pd. Performance of various density functionals

NASA Astrophysics Data System (ADS)

de Jong, G. Theodoor; Geerke, Daan P.; Diefenbach, Axel; Matthias Bickelhaupt, F.

2005-06-01

We have evaluated the performance of 24 popular density functionals for describing the potential energy surface (PES) of the archetypal oxidative addition reaction of the methane C-H bond to the palladium atom by comparing the results with our recent ab initio [CCSD(T)] benchmark study of this reaction. The density functionals examined cover the local density approximation (LDA), the generalized gradient approximation (GGA), meta-GGAs as well as hybrid density functional theory. Relativistic effects are accounted for through the zeroth-order regular approximation (ZORA). The basis-set dependence of the density-functional-theory (DFT) results is assessed for the Becke-Lee-Yang-Parr (BLYP) functional using a hierarchical series of Slater-type orbital (STO) basis sets ranging from unpolarized double-ζ (DZ) to quadruply polarized quadruple-ζ quality (QZ4P). Stationary points on the reaction surface have been optimized using various GGA functionals, all of which yield geometries that differ only marginally. Counterpoise-corrected relative energies of stationary points are converged to within a few tenths of a kcal/mol if one uses the doubly polarized triple-ζ (TZ2P) basis set and the basis-set superposition error (BSSE) drops to 0.0 kcal/mol for our largest basis set (QZ4P). Best overall agreement with the ab initio benchmark PES is achieved by functionals of the GGA, meta-GGA, and hybrid-DFT type, with mean absolute errors of 1.3-1.4 kcal/mol and errors in activation energies ranging from +0.8 to -1.4 kcal/mol. Interestingly, the well-known BLYP functional compares very reasonably with an only slightly larger mean absolute error of 2.5 kcal/mol and an underestimation by -1.9 kcal/mol of the overall barrier (i.e., the difference in energy between the TS and the separate reactants). For comparison, with B3LYP we arrive at a mean absolute error of 3.8 kcal/mol and an overestimation of the overall barrier by 4.5 kcal/mol.

Generalizing the ADM computation to quantum field theory

NASA Astrophysics Data System (ADS)

Mora, P. J.; Tsamis, N. C.; Woodard, R. P.

2012-01-01

The absence of recognizable, low energy quantum gravitational effects requires that some asymptotic series expansion be wonderfully accurate, but the correct expansion might involve logarithms or fractional powers of Newton’s constant. That would explain why conventional perturbation theory shows uncontrollable ultraviolet divergences. We explore this possibility in the context of the mass of a charged, gravitating scalar. The classical limit of this system was solved exactly in 1960 by Arnowitt, Deser and Misner, and their solution does exhibit nonanalytic dependence on Newton’s constant. We derive an exact functional integral representation for the mass of the quantum field theoretic system, and then develop an alternate expansion for it based on a correct implementation of the method of stationary phase. The new expansion entails adding an infinite class of new diagrams to each order and subtracting them from higher orders. The zeroth-order term of the new expansion has the physical interpretation of a first quantized Klein-Gordon scalar which forms a bound state in the gravitational and electromagnetic potentials sourced by its own probability current. We show that such bound states exist and we obtain numerical results for their masses.

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

Imazono, Takashi, E-mail: imazono.takashi@jaea.go.jp; Koike, Masato; Nagano, Tetsuya

Efficiently detecting the B-K emission band around 6.76 nm from a trace concentration of boron in steel compounds has motivated a theoretical exploration of means of increasing the diffraction efficiency of a laminar grating with carbon overcoating. To experimentally evaluate this enhancement, a Ni grating was coated with a high-density carbon film, i.e., diamond-like carbon (DLC). The first order diffraction efficiencies of the Ni gratings coated with and without DLC were measured to be 25.8 % and 16.9 %, respectively, at a wavelength of 6.76 nm and an angle of incidence of 87.07°. The ratio of diffraction efficiency obtained experimentallymore » vs. that calculated by numerical simulation is 0.87 for the DLC-coated Ni grating. The diffraction efficiency of a Ni grating coated with a low-density carbon film, amorphous carbon (a-C), was also slightly improved to be 19.6 %. Furthermore, a distinct minimum of the zeroth order lights of the two carbon-coated Ni gratings were observed at around 6.76 nm, which is coincident with the maximum of the first order light.« less

Nuclear magnetic resonance shielding constants and chemical shifts in linear 199Hg compounds: a comparison of three relativistic computational methods.

PubMed

Arcisauskaite, Vaida; Melo, Juan I; Hemmingsen, Lars; Sauer, Stephan P A

2011-07-28

We investigate the importance of relativistic effects on NMR shielding constants and chemical shifts of linear HgL(2) (L = Cl, Br, I, CH(3)) compounds using three different relativistic methods: the fully relativistic four-component approach and the two-component approximations, linear response elimination of small component (LR-ESC) and zeroth-order regular approximation (ZORA). LR-ESC reproduces successfully the four-component results for the C shielding constant in Hg(CH(3))(2) within 6 ppm, but fails to reproduce the Hg shielding constants and chemical shifts. The latter is mainly due to an underestimation of the change in spin-orbit contribution. Even though ZORA underestimates the absolute Hg NMR shielding constants by ∼2100 ppm, the differences between Hg chemical shift values obtained using ZORA and the four-component approach without spin-density contribution to the exchange-correlation (XC) kernel are less than 60 ppm for all compounds using three different functionals, BP86, B3LYP, and PBE0. However, larger deviations (up to 366 ppm) occur for Hg chemical shifts in HgBr(2) and HgI(2) when ZORA results are compared with four-component calculations with non-collinear spin-density contribution to the XC kernel. For the ZORA calculations it is necessary to use large basis sets (QZ4P) and the TZ2P basis set may give errors of ∼500 ppm for the Hg chemical shifts, despite deceivingly good agreement with experimental data. A Gaussian nucleus model for the Coulomb potential reduces the Hg shielding constants by ∼100-500 ppm and the Hg chemical shifts by 1-143 ppm compared to the point nucleus model depending on the atomic number Z of the coordinating atom and the level of theory. The effect on the shielding constants of the lighter nuclei (C, Cl, Br, I) is, however, negligible. © 2011 American Institute of Physics

Block correlated second order perturbation theory with a generalized valence bond reference function.

PubMed

Xu, Enhua; Li, Shuhua

2013-11-07

The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a "multi-orbital" block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Mo̸ller-Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods.

Pretreatment of whole blood using hydrogen peroxide and UV irradiation. Design of the advanced oxidation process.

PubMed

Bragg, Stefanie A; Armstrong, Kristie C; Xue, Zi-Ling

2012-08-15

A new process to pretreat blood samples has been developed. This process combines the Advanced Oxidation Process (AOP) treatment (using H(2)O(2) and UV irradiation) with acid deactivation of the enzyme catalase in blood. A four-cell reactor has been designed and built in house. The effect of pH on the AOP process has been investigated. The kinetics of the pretreatment process shows that at high C(H(2)O(2),t=0), the reaction is zeroth order with respect to C(H(2)O(2)) and first order with respect to C(blood). The rate limiting process is photon flux from the UV lamp. Degradation of whole blood has been compared with that of pure hemoglobin samples. The AOP pretreatment of the blood samples has led to the subsequent determination of chromium and zinc concentrations in the samples using electrochemical methods. Copyright © 2012 Elsevier B.V. All rights reserved.

Kinetics modelling of color deterioration during thermal processing of tomato paste with the use of response surface methodology

NASA Astrophysics Data System (ADS)

Ganje, Mohammad; Jafari, Seid Mahdi; Farzaneh, Vahid; Malekjani, Narges

2018-06-01

To study the kinetics of color degradation, the tomato paste was designed to be processed at three different temperatures including 60, 70 and 80 °C for 25, 50, 75 and 100 min. a/b ratio, total color difference, saturation index and hue angle were calculated with the use of three main color parameters including L (lightness), a (redness-greenness) and b (yellowness-blueness) values. Kinetics of color degradation was developed by Arrhenius equation and the alterations were modelled with the use of response surface methodology (RSM). It was detected that all of the studied responses followed a first order reaction kinetics with an exception in TCD parameter (zeroth order). TCD and a/b respectively with the highest and lowest activation energy presented the highest sensitivity to the temperature alterations. The maximum and minimum rates of alterations were observed by TCD and b parameters, respectively. It was obviously determined that all of the studied parameters (responses) were affected by the selected independent parameters.

Ultra-broadband and efficient surface plasmon polariton launching through metallic nanoslits of subwavelength period

PubMed Central

Li, Guangyuan; Zhang, Jiasen

2014-01-01

Ultra-broadband, efficient and unidirectional surface plasmon polariton (SPP) launching is of great concern in plasmonic devices and circuits. To address this challenge, a novel method adopting deep-subwavelength slits of subwavelength period (λSPP/4 ~ λSPP/3) in a thick metal film and under backside illumination is proposed. A new band pattern featuring broadband and wide angular characteristics, which is due to the coupling of the zeroth-order SPP resonance at the superstrate–metal interface and the first-order SPP resonance at the metal–substrate interface, is observed for the first time in the dispersion diagram. Unidirectional SPP launching efficiency of ~50%, ultra-broad bandwidth of up to 780 nm, covering the entire optical fiber communication bands, and relatively wide angular range of 7° are achieved. This remarkable efficient, ultra-broadband and wide angular performance is demonstrated by carefully designed experiments in the near infrared regime, showing good agreement with numerical results. PMID:25081812

Ultra-broadband and efficient surface plasmon polariton launching through metallic nanoslits of subwavelength period.

PubMed

Li, Guangyuan; Zhang, Jiasen

2014-08-01

Ultra-broadband, efficient and unidirectional surface plasmon polariton (SPP) launching is of great concern in plasmonic devices and circuits. To address this challenge, a novel method adopting deep-subwavelength slits of subwavelength period (λSPP/4 ~ λSPP/3) in a thick metal film and under backside illumination is proposed. A new band pattern featuring broadband and wide angular characteristics, which is due to the coupling of the zeroth-order SPP resonance at the superstrate-metal interface and the first-order SPP resonance at the metal-substrate interface, is observed for the first time in the dispersion diagram. Unidirectional SPP launching efficiency of ~50%, ultra-broad bandwidth of up to 780 nm, covering the entire optical fiber communication bands, and relatively wide angular range of 7° are achieved. This remarkable efficient, ultra-broadband and wide angular performance is demonstrated by carefully designed experiments in the near infrared regime, showing good agreement with numerical results.

On the mechanism of action of gated molecular baskets: The synchronicity of the revolving motion of gates and in/out trafficking of guests

PubMed Central

Hermann, Keith; Rieth, Stephen; Taha, Hashem A; Wang, Bao-Yu; Hadad, Christopher M

2012-01-01

Summary We used dynamic 1H NMR spectroscopic methods to examine the kinetics and thermodynamics of CH3CCl3 (2) entering and leaving the gated molecular basket 1. We found that the encapsulation is first-order in basket 1 and guest 2, while the decomplexation is zeroth-order in the guest. Importantly, the interchange mechanism in which a molecule of CH3CCl3 directly displaces the entrapped CH3CCl3 was not observed. Furthermore, the examination of the additivity of free energies characterizing the encapsulation process led to us to deduce that the revolving motion of the gates and in/out trafficking of guests is synchronized, yet still a function of the affinity of the guest for occupying the basket: Specifically, the greater the affinity of the guest for occupying the basket, the less effective the gates are in “sweeping” the guest as the gates undergo their revolving motion. PMID:22423275

Floating phase in the one-dimensional transverse axial next-nearest-neighbor Ising model.

PubMed

Chandra, Anjan Kumar; Dasgupta, Subinay

2007-02-01

To study the ground state of an axial next-nearest-neighbor Ising chain under transverse field as a function of frustration parameter kappa and field strength Gamma, we present here two different perturbative analyses. In one, we consider the (known) ground state at kappa=0.5 and Gamma=0 as the unperturbed state and treat an increase of the field from 0 to Gamma coupled with an increase of kappa from 0.5 to 0.5+rGamma/J as perturbation. The first-order perturbation correction to eigenvalue can be calculated exactly and we could conclude that there are only two phase-transition lines emanating from the point kappa=0.5, Gamma=0. In the second perturbation scheme, we consider the number of domains of length 1 as the perturbation and obtain the zeroth-order eigenfunction for the perturbed ground state. From the longitudinal spin-spin correlation, we conclude that floating phase exists for small values of transverse field over the entire region intermediate between the ferromagnetic phase and antiphase.

Scattering of a longitudinal Bessel beam by a sphere embedded in an isotropic elastic solid.

PubMed

Leão-Neto, J P; Lopes, J H; Silva, G T

2017-11-01

The scattering of a longitudinal Bessel beam of arbitrary order by a sphere embedded in an isotropic solid matrix is theoretically analyzed. The spherical inclusion can be made of a viscoelastic, elastic, or fluid-filled isotropic material. In the analysis, the absorbing, scattering, and extinction efficiency factors are obtained, e.g., the corresponding power per characteristic beam intensity per sphere's cross-section area. Furthermore, the extended optical theorem, which expresses the extinction efficiency in terms of an integral of the longitudinal scattering function is derived. Several features of zeroth- and first-order Bessel beams scattering in solids are illustrated considering a polymer adhesive (cured) sphere embedded in a stainless steel matrix. For instance, omnidirectional scattering can be achieved by choosing specific values of the half-cone angle of the Bessel beam, which is the beam's geometrical parameter. Additionally, it is demonstrated that mode suppression leads to lower absorption inside the inclusion when compared to plane wave scattering results.

Zeroth-order phase-contrast technique.

PubMed

Pizolato, José Carlos; Cirino, Giuseppe Antonio; Gonçalves, Cristhiane; Neto, Luiz Gonçalves

2007-11-01

What we believe to be a new phase-contrast technique is proposed to recover intensity distributions from phase distributions modulated by spatial light modulators (SLMs) and binary diffractive optical elements (DOEs). The phase distribution is directly transformed into intensity distributions using a 4f optical correlator and an iris centered in the frequency plane as a spatial filter. No phase-changing plates or phase dielectric dots are used as a filter. This method allows the use of twisted nematic liquid-crystal televisions (LCTVs) operating in the real-time phase-mostly regime mode between 0 and p to generate high-intensity multiple beams for optical trap applications. It is also possible to use these LCTVs as input SLMs for optical correlators to obtain high-intensity Fourier transform distributions of input amplitude objects.

A comparison of the coupled cluster and internally contracted averaged coupled-pair functional levels of theory for the calculation of the MCH2(+) binding energies for M = Sc to Cu

NASA Technical Reports Server (NTRS)

Bauschlicher, Charles W., Jr.; Partridge, Harry; Scuseria, Gustavo E.

1992-01-01

The correlation contribution to the M-C binding energy for the MCH2(+) systems can exceed 100 kcal/mol. At the self-consistent field (SCF) level, these systems can be more than 50 kcal/mol above the fragment energies. In spite of the poor zeroth-order reference, the coupled cluster single and double excitation method with a perturbational estimate of triple excitations, CCSD(T), method is shown to provide an accurate description of these systems. The maximum difference between the CCSD(T) and internally contracted averaged coupled-pair functional binding energies is 1.5 kcal/mol for CrCH2(+), with the remaining systems agreeing to within 1.0 kcal/mol.

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

Chen, Xiuguo; Ma, Zhichao; Xu, Zhimou

Mueller matrix ellipsometry (MME) is applied to detect foot-like asymmetry encountered in nanoimprint lithography (NIL) processes. We present both theoretical and experimental results which show that MME has good sensitivity to both the magnitude and direction of asymmetric profiles. The physics behind the use of MME for asymmetry detection is the breaking of electromagnetic reciprocity theorem for the zeroth-order diffraction of asymmetric gratings. We demonstrate that accurate characterization of asymmetric nanoimprinted gratings can be achieved by performing MME measurements in a conical mounting with the plane of incidence parallel to grating lines and meanwhile incorporating depolarization effects into the opticalmore » model. The comparison of MME-extracted asymmetric profile with the measurement by cross-sectional scanning electron microscopy also reveals the strong potential of this technique for in-line monitoring NIL processes, where symmetric structures are desired.« less

Ion-Acoustic Wave-Particle Energy Flow Rates

NASA Astrophysics Data System (ADS)

Berumen, Jorge; Chu, Feng; Hood, Ryan; Mattingly, Sean; Skiff, Fred

2017-10-01

We present an experimental characterization of the energy flow rates for ion acoustic waves. The experiment is performed in a cylindrical, magnetized, singly-ionized Argon, inductively-coupled gas discharge plasma that is weakly collisional with typical conditions: n 109cm-3 Te 9 eV and B 660 kG. A 4 ring antenna with diameter similar to the plasma diameter is used for launching the waves. A survey of the zeroth and first order ion velocity distribution functions (IVDF) is done using Laser-Induced Fluorescence (LIF) as the main diagnostics method. Using these IVDFs along with Vlasov's equation the different energy rates are measured for different values of ion velocity and separation from the antenna. We would like to acknowledge DOE DE-FG02-99ER54543 for their financial support throughout this research.

Aberration measurement of projection optics in lithographic tools based on two-beam interference theory.

PubMed

Ma, Mingying; Wang, Xiangzhao; Wang, Fan

2006-11-10

The degradation of image quality caused by aberrations of projection optics in lithographic tools is a serious problem in optical lithography. We propose what we believe to be a novel technique for measuring aberrations of projection optics based on two-beam interference theory. By utilizing the partial coherent imaging theory, a novel model that accurately characterizes the relative image displacement of a fine grating pattern to a large pattern induced by aberrations is derived. Both even and odd aberrations are extracted independently from the relative image displacements of the printed patterns by two-beam interference imaging of the zeroth and positive first orders. The simulation results show that by using this technique we can measure the aberrations present in the lithographic tool with higher accuracy.

Fabrication and Testing of Binary-Phase Fourier Gratings for Nonuniform Array Generation

NASA Technical Reports Server (NTRS)

Keys, Andrew S.; Crow, Robert W.; Ashley, Paul R.; Nelson, Tom R., Jr.; Parker, Jack H.; Beecher, Elizabeth A.

2004-01-01

This effort describes the fabrication and testing of binary-phase Fourier gratings designed to generate an incoherent array of output source points with nonuniform user-defined intensities, symmetric about the zeroth order. Like Dammann fanout gratings, these binary-phase Fourier gratings employ only two phase levels to generate a defined output array. Unlike Dammann fanout gratings, these gratings generate an array of nonuniform, user-defined intensities when projected into the far-field regime. The paper describes the process of design, fabrication, and testing for two different version of the binary-phase grating; one designed for a 12 micron wavelength, referred to as the Long-Wavelength Infrared (LWIR) grating, and one designed for a 5 micron wavelength, referred to as the Mid-Wavelength Infrared Grating (MWIR).

Trans-dimensional joint inversion of seabed scattering and reflection data.

PubMed

Steininger, Gavin; Dettmer, Jan; Dosso, Stan E; Holland, Charles W

2013-03-01

This paper examines joint inversion of acoustic scattering and reflection data to resolve seabed interface roughness parameters (spectral strength, exponent, and cutoff) and geoacoustic profiles. Trans-dimensional (trans-D) Bayesian sampling is applied with both the number of sediment layers and the order (zeroth or first) of auto-regressive parameters in the error model treated as unknowns. A prior distribution that allows fluid sediment layers over an elastic basement in a trans-D inversion is derived and implemented. Three cases are considered: Scattering-only inversion, joint scattering and reflection inversion, and joint inversion with the trans-D auto-regressive error model. Including reflection data improves the resolution of scattering and geoacoustic parameters. The trans-D auto-regressive model further improves scattering resolution and correctly differentiates between strongly and weakly correlated residual errors.

Surface spin-electron acoustic waves in magnetically ordered metals

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

Andreev, Pavel A., E-mail: andreevpa@physics.msu.ru; Kuz'menkov, L. S., E-mail: lsk@phys.msu.ru

2016-05-09

Degenerate plasmas with motionless ions show existence of three surface waves: the Langmuir wave, the electromagnetic wave, and the zeroth sound. Applying the separated spin evolution quantum hydrodynamics to half-space plasma, we demonstrate the existence of the surface spin-electron acoustic wave (SSEAW). We study dispersion of the SSEAW. We show that there is hybridization between the surface Langmuir wave and the SSEAW at rather small spin polarization. In the hybridization area, the dispersion branches are located close to each other. In this area, there is a strong interaction between these waves leading to the energy exchange. Consequently, generating the Langmuirmore » waves with the frequencies close to hybridization area we can generate the SSEAWs. Thus, we report a method of creation of the spin-electron acoustic waves.« less

STANDING SHOCK INSTABILITY IN ADVECTION-DOMINATED ACCRETION FLOWS

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

Le, Truong; Wood, Kent S.; Wolff, Michael T.

2016-03-10

Depending on the values of the energy and angular momentum per unit mass in the gas supplied at large radii, inviscid advection-dominated accretion flows can display velocity profiles with either preshock deceleration or preshock acceleration. Nakayama has shown that these two types of flow configurations are expected to have different stability properties. By employing the Chevalier and Imamura linearization method and the Nakayama instability boundary conditions, we discover that there are regions of parameter space where disks/shocks with outflows can be stable or unstable. In regions of instability, we find that preshock deceleration is always unstable to the zeroth mode withmore » zero frequency of oscillation, but is always stable to the fundamental mode and overtones. Furthermore, we also find that preshock acceleration is always unstable to the zeroth mode and that the fundamental mode and overtones become increasingly less stable as the shock location moves away from the horizon when the disk half-height expands above ∼12 gravitational radii at the shock radius. In regions of stability, we demonstrate the zeroth mode to be stable for the velocity profiles that exhibit preshock acceleration and deceleration. Moreover, for models that are linearly unstable, our model suggests the possible existence of quasi-periodic oscillations (QPOs) with ratios 2:3 and 3:5. These ratios are believed to occur in stellar and supermassive black hole candidates, for example, in GRS 1915+105 and Sgr A*, respectively. We expect that similar QPO ratios also exist in regions of stable shocks.« less

The analysis of harmonic generation coefficients in the ablative Rayleigh-Taylor instability

NASA Astrophysics Data System (ADS)

Lu, Yan; Fan, Zhengfeng; Lu, Xinpei; Ye, Wenhua; Zou, Changlin; Zhang, Ziyun; Zhang, Wen

2017-10-01

In this research, we use the numerical simulation method to investigate the generation coefficients of the first three harmonics and the zeroth harmonic in the Ablative Rayleigh-Taylor Instability. It is shown that the interface shifts to the low temperature side during the ablation process. In consideration of the third-order perturbation theory, the first three harmonic amplitudes of the weakly nonlinear regime are calculated and then the harmonic generation coefficients are obtained by curve fitting. The simulation results show that the harmonic generation coefficients changed with time and wavelength. Using the higher-order perturbation theory, we find that more and more harmonics are generated in the later weakly nonlinear stage, which is caused by the negative feedback of the later higher harmonics. Furthermore, extending the third-order theory to the fifth-order theory, we find that the second and the third harmonics coefficients linearly depend on the wavelength, while the feedback coefficients are almost constant. Further analysis also shows that when the fifth-order theory is considered, the normalized effective amplitudes of second and third harmonics can reach about 25%-40%, which are only 15%-25% in the frame of the previous third-order theory. Therefore, the third order perturbation theory is needed to be modified by the higher-order theory when ηL reaches about 20% of the perturbation wavelength.

Chemical and morphological characterization of III-V strained layered heterostructures

NASA Astrophysics Data System (ADS)

Gray, Allen Lindsay

This dissertation describes investigations into the chemical and morphological characterization of III-V strained layered heterostructures by high-resolution x-ray diffraction. The purpose of this work is two-fold. The first was to use high-resolution x-ray diffraction coupled with transmission electron microscopy to characterize structurally a quaternary AlGaAsSb/InGaAsSb multiple quantum well heterostructure laser device. A method for uniquely determining the chemical composition of the strain quaternary quantum well, information previously thought to be unattainable using high resolution x-ray diffraction is thoroughly described. The misconception that high-resolution x-ray diffraction can separately find the well and barrier thickness of a multi-quantum well from the pendellosung fringe spacing is corrected, and thus the need for transmission electron microscopy is motivated. Computer simulations show that the key in finding the well composition is the intensity of the -3rd order satellite peaks in the diffraction pattern. The second part of this work addresses the evolution of strain relief in metastable multi-period InGaAs/GaAs multi-layered structures by high-resolution x-ray reciprocal space maps. Results are accompanied by transmission electron and differential contrast microscopy. The evolution of strain relief is tracked from a coherent "pseudomorphic" growth to a dislocated state as a function of period number by examining the x-ray diffuse scatter emanating from the average composition (zeroth-order) of the multi-layer. Relaxation is determined from the relative positions of the substrate with respect to the zeroth-order peak. For the low period number, the diffuse scatter from the multi-layer structure region arises from periodic, coherent crystallites. For the intermediate period number, the displacement fields around the multi-layer structure region transition to random coherent crystallites. At the higher period number, displacement fields of overlapping dislocations from relaxation of the random crystallites cause the initial stages of relaxation of the multi-layer structure. At the highest period number studied, relaxation of the multi-layer structure becomes bi-modal characterized by overlapping dislocations caused by mosaic block relaxation and periodically spaced misfit dislocations formed by 60°-type dislocations. The relaxation of the multi-layer structure has an exponential dependence on the diffuse scatter length-scale, which is shown to be a sensitive measure of the onset of relaxation.

Comments on X. Yin, A. Wen, Y. Chen, and T. Wang, `Studies in an optical millimeter-wave generation scheme via two parallel dual-parallel Mach-Zehnder modulators', Journal of Modern Optics, 58(8), 2011, pp. 665-673

NASA Astrophysics Data System (ADS)

Hasan, Mehedi; Maldonado-Basilio, Ramón; Hall, Trevor J.

2015-04-01

Yin et al. have described an innovative filter-less optical millimeter-wave generation scheme for octotupling of a 10 GHz RF oscillator, or sedecimtupling of a 5 GHz RF oscillator using two parallel dual-parallel Mach-Zehnder modulators (DP-MZMs). The great merit of their design is the suppression of all harmonics except those of order ? (octotupling) or all harmonics except those of order ? (sedecimtupling), where ? is an integer. A demerit of their scheme is the requirement to set a precise RF signal modulation index in order to suppress the zeroth order optical carrier. The purpose of this comment is to show that, in the case of the octotupling function, all harmonics may be suppressed except those of order ?, where ? is an odd integer, by the simple addition of an optical ? phase shift between the two DP-MZMs and an adjustment of the RF drive phases. Since the carrier is suppressed in the modified architecture, the octotupling circuit is thereby released of the strict requirement to set the drive level to a precise value without any significant increase in circuit complexity.

Wavelet-promoted sparsity for non-invasive reconstruction of electrical activity of the heart.

PubMed

Cluitmans, Matthijs; Karel, Joël; Bonizzi, Pietro; Volders, Paul; Westra, Ronald; Peeters, Ralf

2018-05-12

We investigated a novel sparsity-based regularization method in the wavelet domain of the inverse problem of electrocardiography that aims at preserving the spatiotemporal characteristics of heart-surface potentials. In three normal, anesthetized dogs, electrodes were implanted around the epicardium and body-surface electrodes were attached to the torso. Potential recordings were obtained simultaneously on the body surface and on the epicardium. A CT scan was used to digitize a homogeneous geometry which consisted of the body-surface electrodes and the epicardial surface. A novel multitask elastic-net-based method was introduced to regularize the ill-posed inverse problem. The method simultaneously pursues a sparse wavelet representation in time-frequency and exploits correlations in space. Performance was assessed in terms of quality of reconstructed epicardial potentials, estimated activation and recovery time, and estimated locations of pacing, and compared with performance of Tikhonov zeroth-order regularization. Results in the wavelet domain obtained higher sparsity than those in the time domain. Epicardial potentials were non-invasively reconstructed with higher accuracy than with Tikhonov zeroth-order regularization (p < 0.05), and recovery times were improved (p < 0.05). No significant improvement was found in terms of activation times and localization of origin of pacing. Next to improved estimation of recovery isochrones, which is important when assessing substrate for cardiac arrhythmias, this novel technique opens potentially powerful opportunities for clinical application, by allowing to choose wavelet bases that are optimized for specific clinical questions. Graphical Abstract The inverse problem of electrocardiography is to reconstruct heart-surface potentials from recorded bodysurface electrocardiograms (ECGs) and a torso-heart geometry. However, it is ill-posed and solving it requires additional constraints for regularization. We introduce a regularization method that simultaneously pursues a sparse wavelet representation in time-frequency and exploits correlations in space. Our approach reconstructs epicardial (heart-surface) potentials with higher accuracy than common methods. It also improves the reconstruction of recovery isochrones, which is important when assessing substrate for cardiac arrhythmias. This novel technique opens potentially powerful opportunities for clinical application, by allowing to choose wavelet bases that are optimized for specific clinical questions.

Geographical representation of radial orbit perturbations due to ocean tides: Implications for satellite altimetry

NASA Technical Reports Server (NTRS)

Bettadpur, Srinivas V.; Eanes, Richard J.

1994-01-01

In analogy to the geographical representation of the zeroth-order radial orbit perturbations due to the static geopotential, similar relationships have been derived for radial orbit perturbations due to the ocean tides. At each location these perturbations are seen to be coherent with the tide height variations. The study of this singularity is of obvious importance to the estimation of ocean tides from satellite altimeter data. We derive analytical expressions for the sensitivity of altimeter derived ocean tide models to the ocean tide force model induced errors in the orbits of the altimeter satellite. In particular, we focus on characterizing and quantifying the nonresonant tidal orbit perturbations, which cannot be adjusted into the empirical accelerations or radial perturbation adjustments commonly used during orbit determination and in altimeter data processing. As an illustration of the utility of this technique, we study the differences between a TOPEX/POSEIDON-derived ocean tide model and the Cartwright and Ray 1991 Geosat model. This analysis shows that nearly 60% of the variance of this difference for M(sub 2) can be explained by the Geosat radial orbit eror due to the omission of coefficients from the GEM-T2 background ocean tide model. For O(sub 1), K(sub 1), S(sub 2), and K(sub 2) the orbital effects account for approximately 10 to 40% of the variances of these differences. The utility of this technique to assessment of the ocean tide induced errors in the TOPEX/POSEIDON-derived tide models is also discussed.

Discovery of Spatial and Spectral Structure in the X-Ray Emission from the Crab Nebula

NASA Technical Reports Server (NTRS)

Weisskopf, Martin C.; Hester, J. Jeff; Tennant, Allyn F.; Elsner, Ronald F.; Schulz, Norbert S.; Marshall, Herman L.; Karovska, Margarita; Nichols, Joy S.; Swartz, Douglas A.; Kolodziejczak, Jeffery J.

2000-01-01

The Chandra X-Ray Observatory observed the Crab Nebula and pulsar during orbital calibration. Zeroth-order images with the High-Energy Transmission Grating (HETG) readout by the Advanced Charge Coupled Devices (CCD) Imaging Spectrometer spectroscopy array (ACIS-S) show a striking richness of X-ray structure at a resolution comparable to that of the best ground-based visible-light observations. The HETG-ACIS-S images reveal, for the first time, an X-ray inner ring within the X-ray torus, the suggestion of a hollow-tube structure for the torus, and X-ray knots along the inner ring and (perhaps) along the inward extension of the X-ray jet. Although complicated by instrumental effects and the brightness of the Crab Nebula, the spectrometric analysis shows systematic variations of the X-ray spectrum throughout the nebula.

Discovery of Spatial and Spectral Structure in the X-Ray Emission from the Crab Nebula.

PubMed

Weisskopf; Hester; Tennant; Elsner; Schulz; Marshall; Karovska; Nichols; Swartz; Kolodziejczak; O'Dell

2000-06-20

The Chandra X-Ray Observatory observed the Crab Nebula and pulsar during orbital calibration. Zeroth-order images with the High-Energy Transmission Grating (HETG) readout by the Advanced CCD Imaging Spectrometer spectroscopy array (ACIS-S) show a striking richness of X-ray structure at a resolution comparable to that of the best ground-based visible-light observations. The HETG-ACIS-S images reveal, for the first time, an X-ray inner ring within the X-ray torus, the suggestion of a hollow-tube structure for the torus, and X-ray knots along the inner ring and (perhaps) along the inward extension of the X-ray jet. Although complicated by instrumental effects and the brightness of the Crab Nebula, the spectrometric analysis shows systematic variations of the X-ray spectrum throughout the nebula.

A Relationship Between the 2-body Energy of Kaxiras Pandey and Pearson Takai Halicioglu Tiller Potential Functions

NASA Astrophysics Data System (ADS)

Lim, Teik-Cheng

2004-01-01

A parametric relationship between the Pearson Takai Halicioglu Tiller (PTHT) and the Kaxiras Pandey (KP) empirical potential energy functions is developed for the case of 2-body interaction. The need for such relationship arises when preferred parametric data and adopted software correspond to different potential functions. The analytical relationship was obtained by equating the potential functions' derivatives at zeroth, first and second order with respect to the interatomic distance at the equilibrium bond length, followed by comparison of coefficients in the repulsive and attractive terms. Plots of non-dimensional 2-body energy versus the nondimensional interatomic distance verified the analytical relationships developed herein. The discrepancy revealed in theoretical plots suggests that the 2-body PTHT and KP potentials are more suitable for curve-fitting "softer" and "harder" bonds respectively.

Relativistic effects on the NMR parameters of Si, Ge, Sn, and Pb alkynyl compounds: Scalar versus spin-orbit effects

NASA Astrophysics Data System (ADS)

Demissie, Taye B.

2017-11-01

The NMR chemical shifts and indirect spin-spin coupling constants of 12 molecules containing 29Si, 73Ge, 119Sn, and 207Pb [X(CCMe)4, Me2X(CCMe)2, and Me3XCCH] are presented. The results are obtained from non-relativistic as well as two- and four-component relativistic density functional theory (DFT) calculations. The scalar and spin-orbit relativistic contributions as well as the total relativistic corrections are determined. The main relativistic effect in these molecules is not due to spin-orbit coupling but rather to the scalar relativistic contraction of the s-shells. The correlation between the calculated and experimental indirect spin-spin coupling constants showed that the four-component relativistic density functional theory (DFT) approach using the Perdew's hybrid scheme exchange-correlation functional (PBE0; using the Perdew-Burke-Ernzerhof exchange and correlation functionals) gives results in good agreement with experimental values. The indirect spin-spin coupling constants calculated using the spin-orbit zeroth order regular approximation together with the hybrid PBE0 functional and the specially designed J-coupling (JCPL) basis sets are in good agreement with the results obtained from the four-component relativistic calculations. For the coupling constants involving the heavy atoms, the relativistic corrections are of the same order of magnitude compared to the non-relativistically calculated results. Based on the comparisons of the calculated results with available experimental values, the best results for all the chemical shifts and non-existing indirect spin-spin coupling constants for all the molecules are reported, hoping that these accurate results will be used to benchmark future DFT calculations. The present study also demonstrates that the four-component relativistic DFT method has reached a level of maturity that makes it a convenient and accurate tool to calculate indirect spin-spin coupling constants of "large" molecular systems involving heavy atoms.

Filtrations on Springer fiber cohomology and Kostka polynomials

NASA Astrophysics Data System (ADS)

Bellamy, Gwyn; Schedler, Travis

2018-03-01

We prove a conjecture which expresses the bigraded Poisson-de Rham homology of the nilpotent cone of a semisimple Lie algebra in terms of the generalized (one-variable) Kostka polynomials, via a formula suggested by Lusztig. This allows us to construct a canonical family of filtrations on the flag variety cohomology, and hence on irreducible representations of the Weyl group, whose Hilbert series are given by the generalized Kostka polynomials. We deduce consequences for the cohomology of all Springer fibers. In particular, this computes the grading on the zeroth Poisson homology of all classical finite W-algebras, as well as the filtration on the zeroth Hochschild homology of all quantum finite W-algebras, and we generalize to all homology degrees. As a consequence, we deduce a conjecture of Proudfoot on symplectic duality, relating in type A the Poisson homology of Slodowy slices to the intersection cohomology of nilpotent orbit closures. In the last section, we give an analogue of our main theorem in the setting of mirabolic D-modules.

Steady Secondary Flows Generated by Periodic Compression and Expansion of an Ideal Gas in a Pulse Tube

NASA Technical Reports Server (NTRS)

Lee, Jeffrey M.

1999-01-01

This study establishes a consistent set of differential equations for use in describing the steady secondary flows generated by periodic compression and expansion of an ideal gas in pulse tubes. Also considered is heat transfer between the gas and the tube wall of finite thickness. A small-amplitude series expansion solution in the inverse Strouhal number is proposed for the two-dimensional axisymmetric mass, momentum and energy equations. The anelastic approach applies when shock and acoustic energies are small compared with the energy needed to compress and expand the gas. An analytic solution to the ordered series is obtained in the strong temperature limit where the zeroth-order temperature is constant. The solution shows steady velocities increase linearly for small Valensi number and can be of order I for large Valensi number. A conversion of steady work flow to heat flow occurs whenever temperature, velocity or phase angle gradients are present. Steady enthalpy flow is reduced by heat transfer and is scaled by the Prandtl times Valensi numbers. Particle velocities from a smoke-wire experiment were compared with predictions for the basic and orifice pulse tube configurations. The theory accurately predicted the observed steady streaming.

A perturbative correction for electron-inertia in magnetized sheath structures

NASA Astrophysics Data System (ADS)

Gohain, Munmi; Karmakar, Pralay K.

2016-10-01

We propose a hydrodynamic model to study the equilibrium properties of planar plasma sheaths in two-component quasi-neutral magnetized plasmas. It includes weak but finite electron-inertia incorporated via a regular perturbation of the electronic fluid dynamics only relative to a new smallness parameter, δ, assessing the weak inertial-to-electromagnetic strengths. The zeroth-order perturbation around δ leads to the usual Boltzmann distribution law, which describes inertialess thermalized electrons. The forthwith next higher-order yields the modified Boltzmann law describing the putative lowest-order electron-inertial correction, which is applied meticulously to derive the local Bohm criterion for sheath formation. It is found to be influenced jointly by electron-inertial corrective effects, magnetic field and field orientation relative to the bulk plasma flow. We establish that the mutualistic action of electron-inertia amid gyro-kinetic effects slightly enhances the ion-flow Mach threshold value (typically, M i0 ⩾ 1.140), against the normal value of unity, confrontationally towards the sheath entrance. A numerical illustrative scheme is methodically constructed to see the parametric dependence of the new sheath properties on diverse problem arguments. The merits and demerits are highlighted in the light of the existing results conjointly with clear indication to future ameliorations.

Two-dimensional potential double layers and discrete auroras

NASA Technical Reports Server (NTRS)

Kan, J. R.; Lee, L. C.; Akasofu, S.-I.

1979-01-01

This paper is concerned with the formation of the acceleration region for electrons which produce the visible auroral arc and with the formation of the inverted V precipitation region. The former is embedded in the latter, and both are associated with field-aligned current sheets carried by plasma sheet electrons. It is shown that an electron current sheet driven from the plasma sheet into the ionosphere leads to the formation of a two-dimensional potential double layer. For a current sheet of a thickness less than the proton gyrodiameter solutions are obtained in which the field-aligned potential drop is distributed over a length much greater than the Debye length. For a current sheet of a thickness much greater than the proton gyrodiameter solutions are obtained in which the potential drop is confined to a distance on the order of the Debye length. The electric field in the two-dimensional double-layer model is the zeroth-order field inherent to the current sheet configuration, in contrast to those models in which the electric field is attributed to the first-order field due to current instabilities or turbulences. The maximum potential in the two-dimensional double-layer models is on the order of the thermal energy of plasma sheet protons, which ranges from 1 to 10 keV.

Symmetries of the Space of Linear Symplectic Connections

NASA Astrophysics Data System (ADS)

Fox, Daniel J. F.

2017-01-01

There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic manifold. The associated equivariant moment map is a formal sum of the Cahen-Gutt moment map, the Ricci tensor, and a translational term. The critical points of a functional constructed from it interpolate between the equations for preferred symplectic connections and the equations for critical symplectic connections. The commutative algebra of formal sums of symmetric tensors on a symplectic manifold carries a pair of compatible Poisson structures, one induced from the canonical Poisson bracket on the space of functions on the cotangent bundle polynomial in the fibers, and the other induced from the algebraic fiberwise Schouten bracket on the symmetric algebra of each fiber of the cotangent bundle. These structures are shown to be compatible, and the required Lie algebras are constructed as central extensions of their! linear combinations restricted to formal sums of symmetric tensors whose first order term is a multiple of the differential of its zeroth order term.

Density and pressure variability in the mesosphere and thermosphere

NASA Technical Reports Server (NTRS)

Davis, T. M.

1986-01-01

In an effort to isolate the essential physics of the mesosphere and the thermosphere, a steady one-dimensional density and pressure model has been developed in support of related NASA activities, i.e., projects such as the AOTV and the Space Station. The model incorporates a zeroth order basic state including both the three-dimensional wind field and its associated shear structure, etc. A first order wave field is also incorporated in period bands ranging from about one second to one day. Both basic state and perturbation quantities satsify the combined constraints of mass, linear momentum and energy conservation on the midlatitude beta plane. A numerical (iterative) technique is used to solve for the vertical wind which is coupled to the density and pressure fields. The temperature structure from 1 to 1000 km and the lower boundary conditions are specified using the U.S. Standard Atmosphere 1976. Vertical winds are initialized at the top of the Planetary Boundary Layer using Ekman pumping values over flat terrain. The model also allows for the generation of waves during the geostrophic adjustment process and incorporates wave nonlinearity effects.

The origin of and conditions for clustering in fluids with competing interactions

NASA Astrophysics Data System (ADS)

Jadrich, Ryan; Bollinger, Jonathan; Truskett, Thomas

2015-03-01

Fluids with competing short-range attractions and long-range repulsions exhibit a rich phase behavior characterized by intermediate range order (IRO), as quantified via the static structure factor. This phase behavior includes cluster formation depending upon density-controlled packing effects and the magnitude and range of the attractive and repulsive interactions. Such model systems mimic (to zeroth order) screened, charge-stabilized, aqueous colloidal dispersions of, e.g., proteins. We employ molecular dynamics simulations and integral equation theory to elucidate a more fundamental microscopic explanation for IRO-driven clustering. A simple criterion is identified that indicates when dynamic, amorphous clustering emerges in a polydisperse system, namely when the Ornstein-Zernike thermal correlation length in the system exceeds the repulsive potential tail range. Remarkably, this criterion also appears tightly correlated to crystalline cluster formation in a monodisperse system. Our new gauge is compared to another phenomenological condition for clustering which is when the IRO peak magnitude exceeds ~ 2.7. Ramifications of crystalline versus amorphous clustering are discussed and potential ways of using our new measure in experiment are put forward.

Renormalization of the weak hadronic current in the nuclear medium

NASA Astrophysics Data System (ADS)

Siiskonen, T.; Hjorth-Jensen, M.; Suhonen, J.

2001-05-01

The renormalization of the weak charge-changing hadronic current as a function of the reaction energy release is studied at the nucleonic level. We have calculated the average quenching factors for each type of current (vector, axial vector, and induced pseudoscalar). The obtained quenching in the axial vector part is, at zero momentum transfer, 19% for the 1s0d shell and 23% in the 1p0f shell. We have extended the calculations also to heavier systems such as 56Ni and 100Sn, where we obtain stronger quenchings, 44% and 59%, respectively. Gamow-Teller-type transitions are discussed, along with the higher-order matrix elements. The quenching factors are constant up to roughly 60 MeV momentum transfer. Therefore the use of energy-independent quenching factors in beta decay is justified. We also found that going beyond the zeroth and first order operators (in inverse nucleon mass) does not give any substantial contribution. The extracted renormalization to the ratio CP/CA at q=100 MeV is -3.5%, -7.1%, -28.6%, and +8.7% for mass 16, 40, 56, and 100, respectively.

A density matrix-based method for the linear-scaling calculation of dynamic second- and third-order properties at the Hartree-Fock and Kohn-Sham density functional theory levels.

PubMed

Kussmann, Jörg; Ochsenfeld, Christian

2007-11-28

A density matrix-based time-dependent self-consistent field (D-TDSCF) method for the calculation of dynamic polarizabilities and first hyperpolarizabilities using the Hartree-Fock and Kohn-Sham density functional theory approaches is presented. The D-TDSCF method allows us to reduce the asymptotic scaling behavior of the computational effort from cubic to linear for systems with a nonvanishing band gap. The linear scaling is achieved by combining a density matrix-based reformulation of the TDSCF equations with linear-scaling schemes for the formation of Fock- or Kohn-Sham-type matrices. In our reformulation only potentially linear-scaling matrices enter the formulation and efficient sparse algebra routines can be employed. Furthermore, the corresponding formulas for the first hyperpolarizabilities are given in terms of zeroth- and first-order one-particle reduced density matrices according to Wigner's (2n+1) rule. The scaling behavior of our method is illustrated for first exemplary calculations with systems of up to 1011 atoms and 8899 basis functions.

On the zeroth-order hamiltonian for CASPT2 calculations of spin crossover compounds.

PubMed

Vela, Sergi; Fumanal, Maria; Ribas-Ariño, Jordi; Robert, Vincent

2016-04-15

Complete active space self-consistent field theory (CASSCF) calculations and subsequent second-order perturbation theory treatment (CASPT2) are discussed in the evaluation of the spin-states energy difference (ΔH(elec)) of a series of seven spin crossover (SCO) compounds. The reference values have been extracted from a combination of experimental measurements and DFT + U calculations, as discussed in a recent article (Vela et al., Phys Chem Chem Phys 2015, 17, 16306). It is definitely proven that the critical IPEA parameter used in CASPT2 calculations of ΔH(elec), a key parameter in the design of SCO compounds, should be modified with respect to its default value of 0.25 a.u. and increased up to 0.50 a.u. The satisfactory agreement observed previously in the literature might result from an error cancellation originated in the default IPEA, which overestimates the stability of the HS state, and the erroneous atomic orbital basis set contraction of carbon atoms, which stabilizes the LS states. © 2015 Wiley Periodicals, Inc.

Asymptotic derivation of nonlocal plate models from three-dimensional stress gradient elasticity

NASA Astrophysics Data System (ADS)

Hache, F.; Challamel, N.; Elishakoff, I.

2018-01-01

This paper deals with the asymptotic derivation of thin and thick nonlocal plate models at different orders from three-dimensional stress gradient elasticity, through the power series expansions of the displacements in the thickness ratio of the plate. Three nonlocal asymptotic approaches are considered: a partial nonlocality following the thickness of the plate, a partial nonlocality following the two directions of the plates and a full nonlocality (following all the directions). The three asymptotic approaches lead at the zeroth order to a nonlocal Kirchhoff-Love plate model, but differ in the expression of the length scale. The nonlocal asymptotic models coincide at this order with the stress gradient Kirchhoff-Love plate model, only when the nonlocality is following the two directions of the plate and expressed through a nabla operator. This asymptotic model also yields the nonlocal truncated Uflyand-Mindlin plate model at the second order. However, the two other asymptotic models lead to equations that differ from the current existing nonlocal engineering models (stress gradient engineering plate models). The natural frequencies for an all-edges simply supported plate are obtained for each model. It shows that the models provide similar results for low orders of frequencies or small thickness ratio or nonlocal lengths. Moreover, only the asymptotic model with a partial nonlocality following the two directions of the plates is consistent with a stress gradient plate model, whatever the geometry of the plate.

On the spin separation of algebraic two-component relativistic Hamiltonians: Molecular properties

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

Li, Zhendong; Xiao, Yunlong; Liu, Wenjian, E-mail: liuwjbdf@gmail.com

2014-08-07

The idea for separating the algebraic exact two-component (X2C) relativistic Hamiltonians into spin-free (sf) and spin-dependent terms [Z. Li, Y. Xiao, and W. Liu, J. Chem. Phys. 137, 154114 (2012)] is extended to both electric and magnetic molecular properties. Taking the spin-free terms (which are correct to infinite order in α ≈ 1/137) as zeroth order, the spin-dependent terms can be treated to any desired order via analytic derivative technique. This is further facilitated by unified Sylvester equations for the response of the decoupling and renormalization matrices to single or multiple perturbations. For practical purposes, explicit expressions of order α{supmore » 2} in spin are also given for electric and magnetic properties, as well as two-electron spin-orbit couplings. At this order, the response of the decoupling and renormalization matrices is not required, such that the expressions are very compact and completely parallel to those based on the Breit-Pauli (BP) Hamiltonian. However, the former employ sf-X2C wave functions, whereas the latter can only use nonrelativistic wave functions. As the sf-X2C terms can readily be interfaced with any nonrelativistic program, the implementation of the O(α{sup 2}) spin-orbit corrections to sf-X2C properties requires only marginal revisions of the routines for evaluating the BP type of corrections.« less

On the spin separation of algebraic two-component relativistic Hamiltonians: Molecular properties

NASA Astrophysics Data System (ADS)

Li, Zhendong; Xiao, Yunlong; Liu, Wenjian

2014-08-01

The idea for separating the algebraic exact two-component (X2C) relativistic Hamiltonians into spin-free (sf) and spin-dependent terms [Z. Li, Y. Xiao, and W. Liu, J. Chem. Phys. 137, 154114 (2012)] is extended to both electric and magnetic molecular properties. Taking the spin-free terms (which are correct to infinite order in α ≈ 1/137) as zeroth order, the spin-dependent terms can be treated to any desired order via analytic derivative technique. This is further facilitated by unified Sylvester equations for the response of the decoupling and renormalization matrices to single or multiple perturbations. For practical purposes, explicit expressions of order α2 in spin are also given for electric and magnetic properties, as well as two-electron spin-orbit couplings. At this order, the response of the decoupling and renormalization matrices is not required, such that the expressions are very compact and completely parallel to those based on the Breit-Pauli (BP) Hamiltonian. However, the former employ sf-X2C wave functions, whereas the latter can only use nonrelativistic wave functions. As the sf-X2C terms can readily be interfaced with any nonrelativistic program, the implementation of the O(α ^2) spin-orbit corrections to sf-X2C properties requires only marginal revisions of the routines for evaluating the BP type of corrections.

Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: theory and application to the study of chromium dimer.

PubMed

Kurashige, Yuki; Yanai, Takeshi

2011-09-07

We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian. © 2011 American Institute of Physics

Complex Sequencing Rules of Birdsong Can be Explained by Simple Hidden Markov Processes

PubMed Central

Katahira, Kentaro; Suzuki, Kenta; Okanoya, Kazuo; Okada, Masato

2011-01-01

Complex sequencing rules observed in birdsongs provide an opportunity to investigate the neural mechanism for generating complex sequential behaviors. To relate the findings from studying birdsongs to other sequential behaviors such as human speech and musical performance, it is crucial to characterize the statistical properties of the sequencing rules in birdsongs. However, the properties of the sequencing rules in birdsongs have not yet been fully addressed. In this study, we investigate the statistical properties of the complex birdsong of the Bengalese finch (Lonchura striata var. domestica). Based on manual-annotated syllable labeles, we first show that there are significant higher-order context dependencies in Bengalese finch songs, that is, which syllable appears next depends on more than one previous syllable. We then analyze acoustic features of the song and show that higher-order context dependencies can be explained using first-order hidden state transition dynamics with redundant hidden states. This model corresponds to hidden Markov models (HMMs), well known statistical models with a large range of application for time series modeling. The song annotation with these models with first-order hidden state dynamics agreed well with manual annotation, the score was comparable to that of a second-order HMM, and surpassed the zeroth-order model (the Gaussian mixture model; GMM), which does not use context information. Our results imply that the hierarchical representation with hidden state dynamics may underlie the neural implementation for generating complex behavioral sequences with higher-order dependencies. PMID:21915345

Generic weak isolated horizons

NASA Astrophysics Data System (ADS)

Chatterjee, Ayan; Ghosh, Amit

2006-12-01

Weak isolated horizon boundary conditions have been relaxed supposedly to their weakest form so that both zeroth and first laws of black hole mechanics hold. This makes the formulation more amenable for applications in both analytic and numerical relativities. It also unifies the phase spaces of non-extremal and extremal black holes.

Electron acceleration by an obliquely propagating electromagnetic wave in the regime of validity of the Fokker-Planck-Kolmogorov approach

NASA Technical Reports Server (NTRS)

Hizanidis, Kyriakos; Vlahos, L.; Polymilis, C.

1989-01-01

The relativistic motion of an ensemble of electrons in an intense monochromatic electromagnetic wave propagating obliquely in a uniform external magnetic field is studied. The problem is formulated from the viewpoint of Hamiltonian theory and the Fokker-Planck-Kolmogorov approach analyzed by Hizanidis (1989), leading to a one-dimensional diffusive acceleration along paths of constant zeroth-order generalized Hamiltonian. For values of the wave amplitude and the propagating angle inside the analytically predicted stochastic region, the numerical results suggest that the diffusion probes proceeds in stages. In the first stage, the electrons are accelerated to relatively high energies by sampling the first few overlapping resonances one by one. During that stage, the ensemble-average square deviation of the variable involved scales quadratically with time. During the second stage, they scale linearly with time. For much longer times, deviation from linear scaling slowly sets in.

Astronomical reach of fundamental physics.

PubMed

Burrows, Adam S; Ostriker, Jeremiah P

2014-02-18

Using basic physical arguments, we derive by dimensional and physical analysis the characteristic masses and sizes of important objects in the universe in terms of just a few fundamental constants. This exercise illustrates the unifying power of physics and the profound connections between the small and the large in the cosmos we inhabit. We focus on the minimum and maximum masses of normal stars, the corresponding quantities for neutron stars, the maximum mass of a rocky planet, the maximum mass of a white dwarf, and the mass of a typical galaxy. To zeroth order, we show that all these masses can be expressed in terms of either the Planck mass or the Chandrasekar mass, in combination with various dimensionless quantities. With these examples, we expose the deep interrelationships imposed by nature between disparate realms of the universe and the amazing consequences of the unifying character of physical law.

Determining partial differential cross sections for low-energy electron photodetachment involving conical intersections using the solution of a Lippmann-Schwinger equation constructed with standard electronic structure techniques.

PubMed

Han, Seungsuk; Yarkony, David R

2011-05-07

A method for obtaining partial differential cross sections for low energy electron photodetachment in which the electronic states of the residual molecule are strongly coupled by conical intersections is reported. The method is based on the iterative solution to a Lippmann-Schwinger equation, using a zeroth order Hamiltonian consisting of the bound nonadiabatically coupled residual molecule and a free electron. The solution to the Lippmann-Schwinger equation involves only standard electronic structure techniques and a standard three-dimensional free particle Green's function quadrature for which fast techniques exist. The transition dipole moment for electron photodetachment, is a sum of matrix elements each involving one nonorthogonal orbital obtained from the solution to the Lippmann-Schwinger equation. An expression for the electron photodetachment transition dipole matrix element in terms of Dyson orbitals, which does not make the usual orthogonality assumptions, is derived.

Monitoring of chlorsulfuron in biological fluids and water samples by molecular fluorescence using rhodamine B as fluorophore.

PubMed

Alesso, Magdalena; Escudero, Luis A; Talio, María Carolina; Fernández, Liliana P

2016-11-01

A new simple methodology is proposed for chlorsufuron (CS) traces quantification based upon enhancement of rhodamine B (RhB) fluorescent signal. Experimental variables that influence fluorimetric sensitivity have been studied and optimized. The zeroth order regression calibration was linear from 0.866 to 35.800µgL(-1) CS, with a correlation coefficient of 0.99. At optimal experimental conditions, a limit of detection of 0.259µgL(-1) and a limit of quantification of 0.866µgL(-1) were obtained. The method showed good sensitivity and adequate selectivity and was applied to the determination of trace amounts of CS in plasma, serum and water samples with satisfactory results analyzed by ANOVA test. The proposed methodology represents an alternative to traditional chromatographic techniques for CS monitoring in complex samples, using an accessible instrument in control laboratories. Copyright © 2016 Elsevier B.V. All rights reserved.

Polarizing beam splitter of deep-etched triangular-groove fused-silica gratings.

PubMed

Zheng, Jiangjun; Zhou, Changhe; Feng, Jijun; Wang, Bo

2008-07-15

We investigated the use of a deep-etched fused-silica grating with triangular-shaped grooves as a highly efficient polarizing beam splitter (PBS). A triangular-groove PBS grating is designed at a wavelength of 1550 nm to be used in optical communication. When it is illuminated in Littrow mounting, the transmitted TE- and TM-polarized waves are mainly diffracted in the minus-first and zeroth orders, respectively. The design condition is based on the average differences of the grating mode indices, which is verified by using rigorous coupled-wave analysis. The designed PBS grating is highly efficient over the C+L band range for both TE and TM polarizations (>97.68%). It is shown that such a triangular-groove PBS grating can exhibit a higher diffraction efficiency, a larger extinction ratio, and less reflection loss than the binary-phase fused-silica PBS grating.

Intramolecular symmetry-adapted perturbation theory with a single-determinant wavefunction

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

Pastorczak, Ewa; Prlj, Antonio; Corminboeuf, Clémence, E-mail: clemence.corminboeuf@epfl.ch

2015-12-14

We introduce an intramolecular energy decomposition scheme for analyzing non-covalent interactions within molecules in the spirit of symmetry-adapted perturbation theory (SAPT). The proposed intra-SAPT approach is based upon the Chemical Hamiltonian of Mayer [Int. J. Quantum Chem. 23(2), 341–363 (1983)] and the recently introduced zeroth-order wavefunction [J. F. Gonthier and C. Corminboeuf, J. Chem. Phys. 140(15), 154107 (2014)]. The scheme decomposes the interaction energy between weakly bound fragments located within the same molecule into physically meaningful components, i.e., electrostatic-exchange, induction, and dispersion. Here, we discuss the key steps of the approach and demonstrate that a single-determinant wavefunction can already delivermore » a detailed and insightful description of a wide range of intramolecular non-covalent phenomena such as hydrogen bonds, dihydrogen contacts, and π − π stacking interactions. Intra-SAPT is also used to shed the light on competing intra- and intermolecular interactions.« less

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

Wang, Weizhou, E-mail: wzw@lynu.edu.cn, E-mail: ybw@gzu.edu.cn; Zhang, Yu; Sun, Tao

High-level coupled cluster singles, doubles, and perturbative triples [CCSD(T)] computations with up to the aug-cc-pVQZ basis set (1924 basis functions) and various extrapolations toward the complete basis set (CBS) limit are presented for the sandwich, T-shaped, and parallel-displaced benzene⋯naphthalene complex. Using the CCSD(T)/CBS interaction energies as a benchmark, the performance of some newly developed wave function and density functional theory methods has been evaluated. The best performing methods were found to be the dispersion-corrected PBE0 functional (PBE0-D3) and spin-component scaled zeroth-order symmetry-adapted perturbation theory (SCS-SAPT0). The success of SCS-SAPT0 is very encouraging because it provides one method for energy componentmore » analysis of π-stacked complexes with 200 atoms or more. Most newly developed methods do, however, overestimate the interaction energies. The results of energy component analysis show that interaction energies are overestimated mainly due to the overestimation of dispersion energy.« less

Astronomical reach of fundamental physics

PubMed Central

Burrows, Adam S.; Ostriker, Jeremiah P.

2014-01-01

Using basic physical arguments, we derive by dimensional and physical analysis the characteristic masses and sizes of important objects in the universe in terms of just a few fundamental constants. This exercise illustrates the unifying power of physics and the profound connections between the small and the large in the cosmos we inhabit. We focus on the minimum and maximum masses of normal stars, the corresponding quantities for neutron stars, the maximum mass of a rocky planet, the maximum mass of a white dwarf, and the mass of a typical galaxy. To zeroth order, we show that all these masses can be expressed in terms of either the Planck mass or the Chandrasekar mass, in combination with various dimensionless quantities. With these examples, we expose the deep interrelationships imposed by nature between disparate realms of the universe and the amazing consequences of the unifying character of physical law. PMID:24477692

Normal incidence infrared modulator based on single quantum well intersubband transitions

NASA Astrophysics Data System (ADS)

Vandermeiren, W.; Stiens, J.; Shkerdin, G.; De Tandt, C.; Vounckx, R.

2014-01-01

An infrared modulator of which the working principle is based on evanescent wave generation and intersubband transitions in a single AlGaAs/GaAs quantum well is presented here. CO2 laser light at normal incidence is coupled to an evanescent wave by means of a sub-wavelength diffraction grating. Modulation of the zeroth order reflective mode is achieved by applying an electric field across the quantum well. The model for deriving the complex refractive index of the quantum well region is presented and used for numerical diffraction efficiency simulations as a function of the groove height and period. Two specimens with different groove heights were fabricated. Experiments are conducted at a wavelength of 10.6 µm. At this wavelength a relatively strong absolute modulation depth of about 20% could be observed. The experimental results are in good agreement with our model and diffraction efficiency calculations.

Facile synthesis of ZnFe2O4 photocatalysts for decolourization of organic dyes under solar irradiation

PubMed Central

Behera, Arjun; Kandi, Debasmita; Majhi, Sanjit Manohar

2018-01-01

ZnFe2O4 was fabricated by a simple solution-combustion method. The structural, optical and electronic properties are investigated by XRD, TEM, FESEM, UV–vis DRS, PL, FTIR and photocurrent measurements. The photocatalytic activity of the prepared material is studied with regard to the degradation of rhodamine B (Rh B) and Congo red under solar irradiation. The kinetic study showed that the material exhibits zeroth and first order reaction kinetics for the degradation of Rh B and Congo red, respectively. The photocatalytic behaviour of ZnFe2O4 was systematically studied as a function of the activation temperature. ZnFe2O4 prepared at 500 °C showed the highest activity in degrading Rh B and Congo red. The highest activity of ZnFe2O4-500 °C correlates well with the lowest PL intensity, highest photocurrent and lowest particle size. PMID:29515956

A generalized weight-based particle-in-cell simulation scheme

NASA Astrophysics Data System (ADS)

Lee, W. W.; Jenkins, T. G.; Ethier, S.

2011-03-01

A generalized weight-based particle simulation scheme suitable for simulating magnetized plasmas, where the zeroth-order inhomogeneity is important, is presented. The scheme is an extension of the perturbative simulation schemes developed earlier for particle-in-cell (PIC) simulations. The new scheme is designed to simulate both the perturbed distribution ( δf) and the full distribution (full- F) within the same code. The development is based on the concept of multiscale expansion, which separates the scale lengths of the background inhomogeneity from those associated with the perturbed distributions. The potential advantage for such an arrangement is to minimize the particle noise by using δf in the linear stage of the simulation, while retaining the flexibility of a full- F capability in the fully nonlinear stage of the development when signals associated with plasma turbulence are at a much higher level than those from the intrinsic particle noise.

Relations for lipid bilayers. Connection of electron density profiles to other structural quantities.

PubMed Central

Nagle, J F; Wiener, M C

1989-01-01

Three relations are derived that connect low angle diffraction/scattering results obtained from lipid bilayers to other structural quantities of interest. The first relates the area along the surface of the bilayer, the measured specific volume, and the zeroth order structure factor, F(0). The second relates the size of the trough in the center of the electron density profile, the volume of the terminal methyl groups, and the volume of the methylene groups in the fatty acid chains. The third relates the size of the headgroup electron density peak, the volume of the headgroup, and the volumes of water and hydrocarbon in the headgroup region. These relations, which are easily modified for neutron diffraction, are useful for obtaining structural quantities from electron density profiles obtained by fitting model profiles to measured low angle x-ray intensities. PMID:2713444

Active galactic nuclei. II - The acceleration of relativistic particles in a cluster of accreting black holes

NASA Technical Reports Server (NTRS)

Pacholczyk, A. G.; Stepinski, T. F.

1988-01-01

An accreting cluster of black holes in an active galactic nucleus is a natural site for a system of shock structures with a hierarchy of sizes, corresponding to the distribution of masses in the cluster. Accreted gas containing some magnetic fields and supersonically falling onto the core forms shocks on the outside of each hole and these shocks are capable of accelerating relativistic particles. The energies reached in a single shock are size rather than acceleration time limited and are proportional to the mass of the hole with a proportionality constant being a function of the position of the hole within a cluster and the model of the cluster and the shock formation. These energies are adequate to explain the observed properties of synchrotron and inverse-Compton radiation from these objects. The resulting energy spectrum of particles in the cluster in 'zeroth' approximation has the form of a doubly broken power law with indices of two and three on both extremes of the energy domain respectively, bridged by an index of about 2.5.

The ASTRA Spectrophotometer: Design and Overview

NASA Astrophysics Data System (ADS)

Adelman, S. J.; Gulliver, A. F.; Smalley, B.; Pazder, J. S.; Younger, P. F.; Boyd, L. J.; Epand, D.; Younger, T.

2007-04-01

The ASTRA Cassegrain Spectrophotometer and its automated 0.5-m f/16 telescope will soon be working together at the Fairborn Observatory near Nogales, Arizona. Scientific observations are expected to begin in 2007. We provide an overview of this project and review the design of the system. A separate paper in these Proceedings presents details of the data reduction and flux calibrations. The Nogales site averages 150 photometric nights per year. ASTRA should observe stars whose declinations are in the range +80° to -35°. In an hour the system should obtain S/N = 200 observations of stars as faint as 9.5 mag after correction for instrumental errors. Vega will require about 25 seconds for observation and CCD readout. Usually the telescope will find its next target in less than a minute. A small CCD camera finds and centers the target and a second then guides on the zeroth order spectrum. The spectrophotometer uses both a grating and a cross-dispersing prism to produce spectra from both the first and the second orders simultaneously. The square 30 arc second sky fields for each order do not overlap. The resolution is 7 Å in second and 14 Å in first order. The wavelength range is approximately λλ3300-9000. We are initially using about 10 minutes/hour to observe Vega and secondary standard candidates. Our scientific CCD is electronically cooled to -50° C with a water recirculation system heat sink. The same 4° C recycling water system provides thermal stabilization of the instrument. Our flat fielding system uses a second 0.5-m telescope to produce a collimated beam from a 100 μm pinhole illuminated by a quartz halogen lamp. When the two telescopes point at one another this ``artificial star" is focused by the ASTRA telescope which is then rocked to expose the image from the top to the bottom of the entrance aperture. A LINUX HP server at The Citadel will have databases of ASTRA observations. Each observing request has its own priority and observing window, ASTRA can observe standard stars at a regular rate throughout the night, any accessible target at a given time, and variable stars. ASTRA will produce considerable high quality data.

Redox properties of biscyclopentadienyl uranium(V) imido-halide complexes: a relativistic DFT study.

PubMed

Elkechai, Aziz; Kias, Farida; Talbi, Fazia; Boucekkine, Abdou

2014-06-01

Calculations of ionization energies (IE) and electron affinities (EA) of a series of biscyclopentadienyl imido-halide uranium(V) complexes Cp*2U(=N-2,6-(i)Pr2-C6H3)(X) with X =  F, Cl, Br, and I, related to the U(IV)/U(V) and U(V)/U(VI) redox systems, were carried out, for the first time, using density functional theory (DFT) in the framework of the relativistic zeroth order regular approximation (ZORA) coupled with the conductor-like screening model (COSMO) solvation approach. A very good linear correlation (R(2) =  0.993) was obtained, between calculated ionization energies at the ZORA/BP86/TZP level, and the experimental half-wave oxidation potentials E1/2. A similar linear correlation between the computed electron affinities and the electrochemical reduction U(IV)/U(III) potentials (R(2) =  0.996) is obtained. The importance of solvent effects and of spin-orbit coupling is definitively confirmed. The molecular orbital analysis underlines the crucial role played by the 5f orbitals of the central metal whereas the Nalewajski-Mrozek (N-M) bond indices explain well the bond distances variations following the redox processes. The IE variation of the complexes, i.e., IE(F) < IE(Cl) < IE(Br) < IE(I) is also well rationalized considering the frontier MO diagrams of these species. Finally, this work confirms the relevance of the Hirshfeld charges analysis which bring to light an excellent linear correlation (R(2) =  0.999) between the variations of the uranium charges and E1/2 in the reduction process of the U(V) species.

NMR shielding calculations across the periodic table: diamagnetic uranium compounds. 2. Ligand and metal NMR.

PubMed

Schreckenbach, Georg

2002-12-16

In this and a previous article (J. Phys. Chem. A 2000, 104, 8244), the range of application for relativistic density functional theory (DFT) is extended to the calculation of nuclear magnetic resonance (NMR) shieldings and chemical shifts in diamagnetic actinide compounds. Two relativistic DFT methods are used, ZORA ("zeroth-order regular approximation") and the quasirelativistic (QR) method. In the given second paper, NMR shieldings and chemical shifts are calculated and discussed for a wide range of compounds. The molecules studied comprise uranyl complexes, [UO(2)L(n)](+/-)(q); UF(6); inorganic UF(6) derivatives, UF(6-n)Cl(n), n = 0-6; and organometallic UF(6) derivatives, UF(6-n)(OCH(3))(n), n = 0-5. Uranyl complexes include [UO(2)F(4)](2-), [UO(2)Cl(4)](2-), [UO(2)(OH)(4)](2-), [UO(2)(CO(3))(3)](4-), and [UO(2)(H(2)O)(5)](2+). For the ligand NMR, moderate (e.g., (19)F NMR chemical shifts in UF(6-n)Cl(n)) to excellent agreement [e.g., (19)F chemical shift tensor in UF(6) or (1)H NMR in UF(6-n)(OCH(3))(n)] has been found between theory and experiment. The methods have been used to calculate the experimentally unknown (235)U NMR chemical shifts. A large chemical shift range of at least 21,000 ppm has been predicted for the (235)U nucleus. ZORA spin-orbit appears to be the most accurate method for predicting actinide metal chemical shifts. Trends in the (235)U NMR chemical shifts of UF(6-n)L(n) molecules are analyzed and explained in terms of the calculated electronic structure. It is argued that the energy separation and interaction between occupied and virtual orbitals with f-character are the determining factors.

Destructive quantum interference in electron transport: A reconciliation of the molecular orbital and the atomic orbital perspective

NASA Astrophysics Data System (ADS)

Zhao, Xin; Geskin, Victor; Stadler, Robert

2017-03-01

Destructive quantum interference (DQI) in single molecule electronics is a purely quantum mechanical effect and is entirely defined by the inherent properties of the molecule in the junction such as its structure and symmetry. This definition of DQI by molecular properties alone suggests its relation to other more general concepts in chemistry as well as the possibility of deriving simple models for its understanding and molecular device design. Recently, two such models have gained a wide spread attention, where one was a graphical scheme based on visually inspecting the connectivity of the carbon sites in conjugated π systems in an atomic orbital (AO) basis and the other one puts the emphasis on the amplitudes and signs of the frontier molecular orbitals (MOs). There have been discussions on the range of applicability for these schemes, but ultimately conclusions from topological molecular Hamiltonians should not depend on whether they are drawn from an AO or a MO representation, as long as all the orbitals are taken into account. In this article, we clarify the relation between both models in terms of the zeroth order Green's function and compare their predictions for a variety of systems. From this comparison, we conclude that for a correct description of DQI from a MO perspective, it is necessary to include the contributions from all MOs rather than just those from the frontier orbitals. The cases where DQI effects can be successfully predicted within a frontier orbital approximation we show them to be limited to alternant even-membered hydrocarbons, as a direct consequence of the Coulson-Rushbrooke pairing theorem in quantum chemistry.

Gutzwiller wave-function solution for Anderson lattice model: Emerging universal regimes of heavy quasiparticle states

NASA Astrophysics Data System (ADS)

Wysokiński, Marcin M.; Kaczmarczyk, Jan; Spałek, Jozef

2015-09-01

The recently proposed diagrammatic expansion (DE) technique for the full Gutzwiller wave function (GWF) is applied to the Anderson lattice model. This approach allows for a systematic evaluation of the expectation values with full Gutzwiller wave function in finite-dimensional systems. It introduces results extending in an essential manner those obtained by means of the standard Gutzwiller approximation (GA), which is variationally exact only in infinite dimensions. Within the DE-GWF approach we discuss the principal paramagnetic properties and their relevance to heavy-fermion systems. We demonstrate the formation of an effective, narrow f band originating from atomic f -electron states and subsequently interpret this behavior as a direct itineracy of f electrons; it represents a combined effect of both the hybridization and the correlations induced by the Coulomb repulsive interaction. Such a feature is absent on the level of GA, which is equivalent to the zeroth order of our expansion. Formation of the hybridization- and electron-concentration-dependent narrow f band rationalizes the common assumption of such dispersion of f levels in the phenomenological modeling of the band structure of CeCoIn5. Moreover, it is shown that the emerging f -electron direct itineracy leads in a natural manner to three physically distinct regimes within a single model that are frequently discussed for 4 f - or 5 f -electron compounds as separate model situations. We identify these regimes as (i) the mixed-valence regime, (ii) Kondo/almost-Kondo insulating regime, and (iii) the Kondo-lattice limit when the f -electron occupancy is very close to the f -state half filling, →1 . The nonstandard features of the emerging correlated quantum liquid state are stressed.

Investigating Trojan Asteroids at the L4/L5 Sun-Earth Lagrange Points

NASA Technical Reports Server (NTRS)

John, K. K.; Graham, L. D.; Abell, P. A.

2015-01-01

Investigations of Earth's Trojan asteroids will have benefits for science, exploration, and resource utilization. By sending a small spacecraft to the Sun-Earth L4 or L5 Lagrange points to investigate near-Earth objects, Earth's Trojan population can be better understood. This could lead to future missions for larger precursor spacecraft as well as human missions. The presence of objects in the Sun-Earth L4 and L5 Lagrange points has long been suspected, and in 2010 NASA's Wide-field Infrared Survey Explorer (WISE) detected a 300 m object. To investigate these Earth Trojan asteroid objects, it is both essential and feasible to send spacecraft to these regions. By exploring a wide field area, a small spacecraft equipped with an IR camera could hunt for Trojan asteroids and other Earth co-orbiting objects at the L4 or L5 Lagrange points in the near-term. By surveying the region, a zeroth-order approximation of the number of objects could be obtained with some rough constraints on their diameters, which may lead to the identification of potential candidates for further study. This would serve as a precursor for additional future robotic and human exploration targets. Depending on the inclination of these potential objects, they could be used as proving areas for future missions in the sense that the delta-V's to get to these targets are relatively low as compared to other rendezvous missions. They can serve as platforms for extended operations in deep space while interacting with a natural object in microgravity. Theoretically, such low inclination Earth Trojan asteroids exist. By sending a spacecraft to L4 or L5, these likely and potentially accessible targets could be identified.

Deterministic time-reversible thermostats: chaos, ergodicity, and the zeroth law of thermodynamics

NASA Astrophysics Data System (ADS)

Patra, Puneet Kumar; Sprott, Julien Clinton; Hoover, William Graham; Griswold Hoover, Carol

2015-09-01

The relative stability and ergodicity of deterministic time-reversible thermostats, both singly and in coupled pairs, are assessed through their Lyapunov spectra. Five types of thermostat are coupled to one another through a single Hooke's-law harmonic spring. The resulting dynamics shows that three specific thermostat types, Hoover-Holian, Ju-Bulgac, and Martyna-Klein-Tuckerman, have very similar Lyapunov spectra in their equilibrium four-dimensional phase spaces and when coupled in equilibrium or nonequilibrium pairs. All three of these oscillator-based thermostats are shown to be ergodic, with smooth analytic Gaussian distributions in their extended phase spaces (coordinate, momentum, and two control variables). Evidently these three ergodic and time-reversible thermostat types are particularly useful as statistical-mechanical thermometers and thermostats. Each of them generates Gibbs' universal canonical distribution internally as well as for systems to which they are coupled. Thus they obey the zeroth law of thermodynamics, as a good heat bath should. They also provide dissipative heat flow with relatively small nonlinearity when two or more such temperature baths interact and provide useful deterministic replacements for the stochastic Langevin equation.

Transformation of body force localized near the surface of a half-space into equivalent surface stresses.

PubMed

Rouge, Clémence; Lhémery, Alain; Ségur, Damien

2013-10-01

An electromagnetic acoustic transducer (EMAT) or a laser used to generate elastic waves in a component is often described as a source of body force confined in a layer close to the surface. On the other hand, models for elastic wave radiation more efficiently handle sources described as distributions of surface stresses. Equivalent surface stresses can be obtained by integrating the body force with respect to depth. They are assumed to generate the same field as the one that would be generated by the body force. Such an integration scheme can be applied to Lorentz force for conventional EMAT configuration. When applied to magnetostrictive force generated by an EMAT in a ferromagnetic material, the same scheme fails, predicting a null stress. Transforming body force into equivalent surface stresses therefore, requires taking into account higher order terms of the force moments, the zeroth order being the simple force integration over the depth. In this paper, such a transformation is derived up to the second order, assuming that body forces are localized at depths shorter than the ultrasonic wavelength. Two formulations are obtained, each having some advantages depending on the application sought. They apply regardless of the nature of the force considered.

Investigation of micromixing by acoustically oscillated sharp-edges

PubMed Central

Nama, Nitesh; Huang, Po-Hsun; Huang, Tony Jun; Costanzo, Francesco

2016-01-01

Recently, acoustically oscillated sharp-edges have been utilized to achieve rapid and homogeneous mixing in microchannels. Here, we present a numerical model to investigate acoustic mixing inside a sharp-edge-based micromixer in the presence of a background flow. We extend our previously reported numerical model to include the mixing phenomena by using perturbation analysis and the Generalized Lagrangian Mean (GLM) theory in conjunction with the convection-diffusion equation. We divide the flow variables into zeroth-order, first-order, and second-order variables. This results in three sets of equations representing the background flow, acoustic response, and the time-averaged streaming flow, respectively. These equations are then solved successively to obtain the mean Lagrangian velocity which is combined with the convection-diffusion equation to predict the concentration profile. We validate our numerical model via a comparison of the numerical results with the experimentally obtained values of the mixing index for different flow rates. Further, we employ our model to study the effect of the applied input power and the background flow on the mixing performance of the sharp-edge-based micromixer. We also suggest potential design changes to the previously reported sharp-edge-based micromixer to improve its performance. Finally, we investigate the generation of a tunable concentration gradient by a linear arrangement of the sharp-edge structures inside the microchannel. PMID:27158292

Investigation of micromixing by acoustically oscillated sharp-edges.

PubMed

Nama, Nitesh; Huang, Po-Hsun; Huang, Tony Jun; Costanzo, Francesco

2016-03-01

Recently, acoustically oscillated sharp-edges have been utilized to achieve rapid and homogeneous mixing in microchannels. Here, we present a numerical model to investigate acoustic mixing inside a sharp-edge-based micromixer in the presence of a background flow. We extend our previously reported numerical model to include the mixing phenomena by using perturbation analysis and the Generalized Lagrangian Mean (GLM) theory in conjunction with the convection-diffusion equation. We divide the flow variables into zeroth-order, first-order, and second-order variables. This results in three sets of equations representing the background flow, acoustic response, and the time-averaged streaming flow, respectively. These equations are then solved successively to obtain the mean Lagrangian velocity which is combined with the convection-diffusion equation to predict the concentration profile. We validate our numerical model via a comparison of the numerical results with the experimentally obtained values of the mixing index for different flow rates. Further, we employ our model to study the effect of the applied input power and the background flow on the mixing performance of the sharp-edge-based micromixer. We also suggest potential design changes to the previously reported sharp-edge-based micromixer to improve its performance. Finally, we investigate the generation of a tunable concentration gradient by a linear arrangement of the sharp-edge structures inside the microchannel.

Phase sensitive diffraction sensor for high sensitivity refractive index measurement

NASA Astrophysics Data System (ADS)

Kumawat, Nityanand; Varma, Manoj; Kumar, Sunil

2018-02-01

In this study a diffraction based sensor has been developed for bio molecular sensing applications and performing assays in real time. A diffraction grating fabricated on a glass substrate produced diffraction patterns both in transmission and reflection when illuminated by a laser diode. We used zeroth order I(0,0) as reference and first order I(0,1) as signal channel and conducted ratiometric measurements that reduced noise by more than 50 times. The ratiometric approach resulted in a very simple instrumentation with very high sensitivity. In the past, we have shown refractive index measurements both for bulk and surface adsorption using the diffractive self-referencing approach. In the current work we extend the same concept to higher diffraction orders. We have considered order I(0,1) and I(1,1) and performed ratiometric measurements I(0,1)/I(1,1) to eliminate the common mode fluctuations. Since orders I(0,1) and I(1,1) behaved opposite to each other, the resulting ratio signal amplitude increased more than twice compared to our previous results. As a proof of concept we used different salt concentrations in DI water. Increased signal amplitude and improved fluid injection system resulted in more than 4 times improvement in detection limit, giving limit of detection 1.3×10-7 refractive index unit (RIU) compared to our previous results. The improved refractive index sensitivity will help significantly for high sensitivity label free bio sensing application in a very cost-effective and simple experimental set-up.

Order-parameter model for unstable multilane traffic flow

NASA Astrophysics Data System (ADS)

Lubashevsky, Ihor A.; Mahnke, Reinhard

2000-11-01

We discuss a phenomenological approach to the description of unstable vehicle motion on multilane highways that explains in a simple way the observed sequence of the ``free flow <--> synchronized mode <--> jam'' phase transitions as well as the hysteresis in these transitions. We introduce a variable called an order parameter that accounts for possible correlations in the vehicle motion at different lanes. So, it is principally due to the ``many-body'' effects in the car interaction in contrast to such variables as the mean car density and velocity being actually the zeroth and first moments of the ``one-particle'' distribution function. Therefore, we regard the order parameter as an additional independent state variable of traffic flow. We assume that these correlations are due to a small group of ``fast'' drivers and by taking into account the general properties of the driver behavior we formulate a governing equation for the order parameter. In this context we analyze the instability of homogeneous traffic flow that manifested itself in the above-mentioned phase transitions and gave rise to the hysteresis in both of them. Besides, the jam is characterized by the vehicle flows at different lanes which are independent of one another. We specify a certain simplified model in order to study the general features of the car cluster self-formation under the ``free flow <--> synchronized motion'' phase transition. In particular, we show that the main local parameters of the developed cluster are determined by the state characteristics of vehicle motion only.

Towards understanding the kinetic behaviour and limitations in photo-induced copper(i) catalyzed azide-alkyne cycloaddition (CuAAC) reactions.

PubMed

El-Zaatari, Bassil M; Shete, Abhishek U; Adzima, Brian J; Kloxin, Christopher J

2016-09-14

The kinetic behaviour of the photo-induced copper(i) catalyzed azide-alkyne cycloaddition (CuAAC) reaction was studied in detail using real-time Fourier transform infrared (FTIR) spectroscopy on both a solvent-based monofunctional and a neat polymer network forming system. The results in the solvent-based system showed near first-order kinetics on copper and photoinitiator concentrations up to a threshold value in which the kinetics switch to zeroth-order. This kinetic shift shows that the photo-CuAAC reaction is not susceptible from side reactions such as copper disproportionation, copper(i) reduction, and radical termination at the early stages of the reaction. The overall reaction rate and conversion is highly dependent on the initial concentrations of photoinitiator and copper(ii) as well as their relative ratios. The conversion was decreased when an excess of photoinitiator was utilized compared to its threshold value. Interestingly, the reaction showed an induction period at relatively low intensities. The induction period is decreased by increasing light intensity and photoinitiator concentration. The reaction trends and limitations were further observed in a solventless polymer network forming system, exhibiting a similar copper and photoinitiator threshold behaviour.

Towards understanding the kinetic behaviour and limitations in photo-induced copper(I) catalyzed azide-alkyne cycloaddition (CuAAC) reactions

PubMed Central

El-Zaatari, Bassil M.; Shete, Abhishek U.; Adzima, Brian J.; Kloxin, Christopher J.

2016-01-01

The kinetic behaviour of the photo-induced copper(I) catalyzed azide—alkyne cycloaddition (CuAAC) reaction was studied in detail using real-time Fourier Transform Infrared Spectroscopy (FTIR) on both a solvent-based monofunctional and a neat polymer network forming system. The results in the solvent-based system showed near first-order kinetics on copper and photoinitiator concentrations up to a threshold value in which the kinetics switch to zeroth-order. This kinetic shift shows that the photo-CuAAC reaction is not suseptible from side reactions such as copper disproportionation, copper(I) reduction, and radical termination at the early stages of the reaction. The overall reaction rate and conversion is highly dependent on the initial concentrations of photoinitiator and copper(II), as well as their relative ratios. The conversion was decreased when an excess of photoinitiator was utilized compared to its threshold value. Interestingly, the reaction showed an induction period at relatively low intensities. The induction period is decreased by increasing light intensity, and photoinitiator concentration. The reaction trends and limitations were further observed in a solventless polymer network forming system, exhibiting a similar copper and photoinitiator threshold behaviour. PMID:27711587

Tilting Styx and Nix but not Uranus with a Spin-Precession-Mean-motion resonance

NASA Astrophysics Data System (ADS)

Quillen, Alice C.; Chen, Yuan-Yuan; Noyelles, Benoît; Loane, Santiago

2018-02-01

A Hamiltonian model is constructed for the spin axis of a planet perturbed by a nearby planet with both planets in orbit about a star. We expand the planet-planet gravitational potential perturbation to first order in orbital inclinations and eccentricities, finding terms describing spin resonances involving the spin precession rate and the two planetary mean motions. Convergent planetary migration allows the spinning planet to be captured into spin resonance. With initial obliquity near zero, the spin resonance can lift the planet's obliquity to near 90° or 180° depending upon whether the spin resonance is first or zeroth order in inclination. Past capture of Uranus into such a spin resonance could give an alternative non-collisional scenario accounting for Uranus's high obliquity. However, we find that the time spent in spin resonance must be so long that this scenario cannot be responsible for Uranus's high obliquity. Our model can be used to study spin resonance in satellite systems. Our Hamiltonian model explains how Styx and Nix can be tilted to high obliquity via outward migration of Charon, a phenomenon previously seen in numerical simulations.

Extended depth of focus intraocular lens: Chromatic performance

PubMed Central

Millán, Maria S.; Vega, Fidel

2017-01-01

We describe a first-and-second-diffractive-order intraocular lens ((1st,2nd)DIOL) within the class of hybrid refractive-diffractive designs for intraocular lenses (IOLs) and analyse its properties of focus extension and compensation of longitudinal chromatic aberration (LCA), particularly for lenses with low addition. Power, energy efficiency and their wavelength dependence are extended from monofocal IOL and conventional bifocal zeroth-and-first-diffractive-order IOL ((0th,1st)DIOL) to (1st,2nd)DIOL of low addition. Compensation of LCA is experimentally assessed in optical bench through the through-focus energy efficiency of three Tecnis IOLs with red, green and blue illuminations: ZA9003 (monofocal), ZKB00 (bifocal (0th,1st)DIOL with + 2.75 D add) and Symfony ZXR00. We prove Tecnis Symfony ZXR00 IOL can be considered an example of (1st,2nd)DIOL design of low addition, with LCA compensation in both the distance and intermediate foci, whereas the bifocal (0th,1st)DIOL does not compensate in the distance focus. However, the energy efficiency of (1st,2nd)DIOL for wavelengths other than the design wavelength is markedly more asymmetric. PMID:28966865

Wavelength-Agile External-Cavity Diode Laser for DWDM

NASA Technical Reports Server (NTRS)

Pilgrim, Jeffrey S.; Bomse, David S.

2006-01-01

A prototype external-cavity diode laser (ECDL) has been developed for communication systems utilizing dense wavelength- division multiplexing (DWDM). This ECDL is an updated version of the ECDL reported in Wavelength-Agile External- Cavity Diode Laser (LEW-17090), NASA Tech Briefs, Vol. 25, No. 11 (November 2001), page 14a. To recapitulate: The wavelength-agile ECDL combines the stability of an external-cavity laser with the wavelength agility of a diode laser. Wavelength is modulated by modulating the injection current of the diode-laser gain element. The external cavity is a Littman-Metcalf resonator, in which the zeroth-order output from a diffraction grating is used as the laser output and the first-order-diffracted light is retro-reflected by a cavity feedback mirror, which establishes one end of the resonator. The other end of the resonator is the output surface of a Fabry-Perot resonator that constitutes the diode-laser gain element. Wavelength is selected by choosing the angle of the diffracted return beam, as determined by position of the feedback mirror. The present wavelength-agile ECDL is distinguished by design details that enable coverage of all 60 channels, separated by 100-GHz frequency intervals, that are specified in DWDM standards.

Trace of the Twisted Heisenberg Category

NASA Astrophysics Data System (ADS)

Oğuz, Can Ozan; Reeks, Michael

2017-12-01

We show that the trace decategorification, or zeroth Hochschild homology, of the twisted Heisenberg category defined by Cautis and Sussan is isomorphic to a quotient of {W^-}, a subalgebra of W_{1+∞} defined by Kac, Wang, and Yan. Our result is a twisted analogue of that by Cautis, Lauda, Licata, and Sussan relating W_{1+∞} and the trace decategorification of the Heisenberg category.

A Mo-95 and C-13 Solid-state NMR and Relativistic DFT Investigation of Mesitylenetricarbonylmolybdenum(0) -a Typical Transition Metal Piano-stool Complex

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

Bryce, David L.; Wasylishen, Roderick E.

2002-06-21

The chemical shift (CS) and electric field gradient (EFG) tensors in the piano-stool compound mesitylenetricarbonylmolybdenum(0), 1, have been investigated via {sup 95}Mo and {sup 13}C solid-state magic-angle spinning (MAS) NMR as well as relativistic zeroth-order regular approximation density functional theory (ZORA-DFT) calculations. Molybdenum-95 (I = 5/2) MAS NMR spectra acquired at 18.8 T are dominated by the anisotropic chemical shift interaction ({Omega} = 775 {+-} 30 ppm) rather than the 2nd-order quadrupolar interaction (C{sub Q} = -0.96 {+-} 0.15 MHz), an unusual situation for a quadrupolar nucleus. ZORA-DFT calculations of the {sup 95}Mo EFG and CS tensors are in agreementmore » with the experimental data. Mixing of appropriate occupied and virtual d-orbital dominated MOs in the region of the HOMO-LUMO gap are shown to be responsible for the large chemical shift anisotropy. The small, but non-negligible, {sup 95}Mo quadrupolar interaction is discussed in terms of the geometry about Mo. Carbon-13 CPMAS spectra acquired at 4.7 T demonstrate the crystallographic and magnetic nonequivalence of the twelve {sup 13}C nuclei in 1, despite the chemical equivalence of some of these nuclei in isotropic solutions. The principal components of the carbon CS tensors are determined via a Herzfeld-Berger analysis, and indicate that motion of the mesitylene ring is slow compared to a rate which would influence the carbon CS tensors (i.e. tens of {micro}s). ZORA-DFT calculations reproduce the experimental carbon CS tensors accurately. Oxygen-17 EFG and CS tensors for 1 are also calculated and discussed in terms of existing experimental data for related molybdenum carbonyl compounds. This work provides an example of the information available from combined multi-field solid-state multinuclear magnetic resonance and computational investigations of transition metal compounds, in particular the direct study of quadrupolar transition metal nuclei with relatively small magnetic moments.« less

Density functional studies on the exchange interaction of a dinuclear Gd(iii)-Cu(ii) complex: method assessment, magnetic coupling mechanism and magneto-structural correlations.

PubMed

Rajaraman, Gopalan; Totti, Federico; Bencini, Alessandro; Caneschi, Andrea; Sessoli, Roberta; Gatteschi, Dante

2009-05-07

Density functional calculations have been performed on a [Gd(iii)Cu(ii)] complex [L(1)CuGd(O(2)CCF(3))(3)(C(2)H(5)OH)(2)] () (where L(1) is N,N'-bis(3-ethoxy-salicylidene)-1,2-diamino-2-methylpropanato) with an aim of assessing a suitable functional within the DFT formalism to understand the mechanism of magnetic coupling and also to develop magneto-structural correlations. Encouraging results have been obtained in our studies where the application of B3LYP on the crystal structure of yields a ferromagnetic J value of -5.8 cm(-1) which is in excellent agreement with the experimental value of -4.42 cm(-1) (H = JS(Gd).S(Cu)). After testing varieties of functional for the method assessment we recommend the use of B3LYP with a combination of an effective core potential basis set. For all electron basis sets the relativistic effects should be incorporated either via the Douglas-Kroll-Hess (DKH) or zeroth-order regular approximation (ZORA) methods. A breakdown approach has been adopted where the calculations on several model complexes of have been performed. Their wave functions have been analysed thereafter (MO and NBO analysis) in order to gain some insight into the coupling mechanism. The results suggest, unambiguously, that the empty Gd(iii) 5d orbitals have a prominent role on the magnetic coupling. These 5d orbitals gain partial occupancy via Cu(ii) charge transfer as well as from the Gd(iii) 4f orbitals. A competing 4f-3d interaction associated with the symmetry of the complex has also been observed. The general mechanism hence incorporates both contributions and sets forth rather a prevailing mechanism for the 3d-4f coupling. The magneto-structural correlations reveal that there is no unique parameter which the J values are strongly correlated with, but an exponential relation to the J value found for the O-Cu-O-Gd dihedral angle parameter is the most credible correlation.

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

Zhang Yu; Liu Jinliang; Fan Xuliang

In this paper, the electromagnetic dispersion theory and the classic telegraph equations were combined to calculate the important parameters of the helical Blumlein pulse forming line (BPFL) of accelerator based on tape helix. In the work band of the BPFL at several hundred ns range, electromagnetic dispersion characteristics were almost determined by the zeroth harmonic. In order to testify the dispersion theory of BPFL in this paper, filling dielectrics, such as de-ionized water, transformer oil, and air were employed in the helical BPFL, respectively. Parameters such as capacitance, inductance, characteristic impedance, and pulse duration of the BPFL were calculated. Effectsmore » of dispersion on these parameters were analyzed. Circuit simulation and electromagnetic simulation were carried out to prove these parameters of BPFL filled with these three kinds of dielectrics, respectively. The accelerator system was set up, and experimental results also corresponded to the theoretical calculations. The average theoretical errors of impedances and pulse durations were 3.5% and 3.4%, respectively, which proved the electromagnetic dispersion analyses in this paper.« less

Thermodynamics, stability and Hawking-Page transition of Kerr black holes from Rényi statistics

NASA Astrophysics Data System (ADS)

Czinner, Viktor G.; Iguchi, Hideo

2017-12-01

Thermodynamics of rotating black holes described by the Rényi formula as equilibrium and zeroth law compatible entropy function is investigated. We show that similarly to the standard Boltzmann approach, isolated Kerr black holes are stable with respect to axisymmetric perturbations in the Rényi model. On the other hand, when the black holes are surrounded by a bath of thermal radiation, slowly rotating black holes can also be in stable equilibrium with the heat bath at a fixed temperature, in contrast to the Boltzmann description. For the question of possible phase transitions in the system, we show that a Hawking-Page transition and a first order small black hole/large black hole transition occur, analogous to the picture of rotating black holes in AdS space. These results confirm the similarity between the Rényi-asymptotically flat and Boltzmann-AdS approaches to black hole thermodynamics in the rotating case as well. We derive the relations between the thermodynamic parameters based on this correspondence.

Elemental compositions of two extrasolar rocky planetesimals

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

Xu, S.; Jura, M.; Klein, B.

2014-03-10

We report Keck/HIRES and Hubble Space Telescope/COS spectroscopic studies of extrasolar rocky planetesimals accreted onto two hydrogen atmosphere white dwarfs, G29-38 and GD 133. In G29-38, eight elements are detected, including C, O, Mg, Si, Ca, Ti, Cr, and Fe while in GD 133, O, Si, Ca, and marginally Mg are seen. These two extrasolar planetesimals show a pattern of refractory enhancement and volatile depletion. For G29-38, the observed composition can be best interpreted as a blend of a chondritic object with some refractory-rich material, a result from post-nebular processing. Water is very depleted in the parent body accreted ontomore » G29-38, based on the derived oxygen abundance. The inferred total mass accretion rate in GD 133 is the lowest of all known dusty white dwarfs, possibly due to non-steady state accretion. We continue to find that a variety of extrasolar planetesimals all resemble to zeroth order the elemental composition of bulk Earth.« less

A path-independent integral for the characterization of solute concentration and flux at biofilm detachments

USGS Publications Warehouse

Moran, B.; Kulkarni, S.S.; Reeves, H.W.

2007-01-01

A path-independent (conservation) integral is developed for the characterization of solute concentration and flux in a biofilm in the vicinity of a detachment or other flux limiting boundary condition. Steady state conditions of solute diffusion are considered and biofilm kinetics are described by an uptake term which can be expressed in terms of a potential (Michaelis-Menten kinetics). An asymptotic solution for solute concentration at the tip of the detachment is obtained and shown to be analogous to that of antiplane crack problems in linear elasticity. It is shown that the amplitude of the asymptotic solution can be calculated by evaluating a path-independent integral. The special case of a semi-infinite detachment in an infinite strip is considered and the amplitude of the asymptotic field is related to the boundary conditions and problem parameters in closed form for zeroth and first order kinetics and numerically for Michaelis-Menten kinetics. ?? Springer Science+Business Media, Inc. 2007.

A combined reconstruction-classification method for diffuse optical tomography.

PubMed

Hiltunen, P; Prince, S J D; Arridge, S

2009-11-07

We present a combined classification and reconstruction algorithm for diffuse optical tomography (DOT). DOT is a nonlinear ill-posed inverse problem. Therefore, some regularization is needed. We present a mixture of Gaussians prior, which regularizes the DOT reconstruction step. During each iteration, the parameters of a mixture model are estimated. These associate each reconstructed pixel with one of several classes based on the current estimate of the optical parameters. This classification is exploited to form a new prior distribution to regularize the reconstruction step and update the optical parameters. The algorithm can be described as an iteration between an optimization scheme with zeroth-order variable mean and variance Tikhonov regularization and an expectation-maximization scheme for estimation of the model parameters. We describe the algorithm in a general Bayesian framework. Results from simulated test cases and phantom measurements show that the algorithm enhances the contrast of the reconstructed images with good spatial accuracy. The probabilistic classifications of each image contain only a few misclassified pixels.

Noncovalent π⋅⋅⋅π interaction between graphene and aromatic molecule: Structure, energy, and nature

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

Wang, Weizhou, E-mail: wzw@lynu.edu.cn, E-mail: ybw@gzu.edu.cn; Zhang, Yu; Wang, Yi-Bo, E-mail: wzw@lynu.edu.cn, E-mail: ybw@gzu.edu.cn

2014-03-07

Noncovalent π⋅⋅⋅π interactions between graphene and aromatic molecules have been studied by using density functional theory with empirical dispersion correction (ωB97X-D) combined with zeroth-order symmetry adapted perturbation theory (SAPT0). Excellent agreement of the interaction energies computed by means of ωB97X-D and spin component scaled (SCS) SAPT0 methods, respectively, shows great promise for the two methods in the study of the adsorption of aromatic molecules on graphene. The other important finding in this study is that, according to SCS-SAPT0 analyses, π⋅⋅⋅π interactions between graphene and aromatic molecules are largely dependent on both dispersion and electrostatic type interactions. It is also noticedmore » that π⋅⋅⋅π interactions become stronger and more dispersive (less electrostatic) upon substitution of the very electronegative fluorine atoms onto the aromatic molecules.« less

FLiT: a field line trace code for magnetic confinement devices

NASA Astrophysics Data System (ADS)

Innocente, P.; Lorenzini, R.; Terranova, D.; Zanca, P.

2017-04-01

This paper presents a field line tracing code (FLiT) developed to study particle and energy transport as well as other phenomena related to magnetic topology in reversed-field pinch (RFP) and tokamak experiments. The code computes magnetic field lines in toroidal geometry using curvilinear coordinates (r, ϑ, ϕ) and calculates the intersections of these field lines with specified planes. The code also computes the magnetic and thermal diffusivity due to stochastic magnetic field in the collisionless limit. Compared to Hamiltonian codes, there are no constraints on the magnetic field functional formulation, which allows the integration of whichever magnetic field is required. The code uses the magnetic field computed by solving the zeroth-order axisymmetric equilibrium and the Newcomb equation for the first-order helical perturbation matching the edge magnetic field measurements in toroidal geometry. Two algorithms are developed to integrate the field lines: one is a dedicated implementation of a first-order semi-implicit volume-preserving integration method, and the other is based on the Adams-Moulton predictor-corrector method. As expected, the volume-preserving algorithm is accurate in conserving divergence, but slow because the low integration order requires small amplitude steps. The second algorithm proves to be quite fast and it is able to integrate the field lines in many partially and fully stochastic configurations accurately. The code has already been used to study the core and edge magnetic topology of the RFX-mod device in both the reversed-field pinch and tokamak magnetic configurations.

A Jeziorski-Monkhorst fully uncontracted multi-reference perturbative treatment. I. Principles, second-order versions, and tests on ground state potential energy curves

NASA Astrophysics Data System (ADS)

Giner, Emmanuel; Angeli, Celestino; Garniron, Yann; Scemama, Anthony; Malrieu, Jean-Paul

2017-06-01

The present paper introduces a new multi-reference perturbation approach developed at second order, based on a Jeziorski-Mokhorst expansion using individual Slater determinants as perturbers. Thanks to this choice of perturbers, an effective Hamiltonian may be built, allowing for the dressing of the Hamiltonian matrix within the reference space, assumed here to be a CAS-CI. Such a formulation accounts then for the coupling between the static and dynamic correlation effects. With our new definition of zeroth-order energies, these two approaches are strictly size-extensive provided that local orbitals are used, as numerically illustrated here and formally demonstrated in the Appendix. Also, the present formalism allows for the factorization of all double excitation operators, just as in internally contracted approaches, strongly reducing the computational cost of these two approaches with respect to other determinant-based perturbation theories. The accuracy of these methods has been investigated on ground-state potential curves up to full dissociation limits for a set of six molecules involving single, double, and triple bond breaking together with an excited state calculation. The spectroscopic constants obtained with the present methods are found to be in very good agreement with the full configuration interaction results. As the present formalism does not use any parameter or numerically unstable operation, the curves obtained with the two methods are smooth all along the dissociation path.

Biodegradation and kinetics of organic compounds and heavy metals in an artificial wetland system (AWS) by using water hyacinths as a biological filter.

PubMed

Rodríguez-Espinosa, P F; Mendoza-Pérez, J A; Tabla-Hernandez, J; Martínez-Tavera, E; Monroy-Mendieta, M M

2018-01-02

The objective of the present study was to investigate the ability of water hyacinth (Eichhornia crassipes) to absorb organic compounds (potassium hydrogen phthalate, sodium tartrate, malathion, 2,4-dichlorophenoxy acetic acid (2,4-D), and piroxicam). For the aforementioned purpose, an artificial wetland system (AWS) was constructed and filled with water hyacinth collected from the Valsequillo Reservoir, Puebla, Mexico. Potassium hydrogen phthalate and sodium tartrate were measured in terms of chemical oxygen demand (COD) and biological oxygen demand (BOD). The present study indicated that the water hyacinths absorbed nearly 1.8-16.6 g of COD kg -1 dm (dry mass of water hyacinth), while the absorbance efficiency of BOD was observed to be 45.8%. The results also indicated that the maximum absorbance efficiency of malathion, 2,4-D, and piroxicam was observed to be 67.6%, 58.3%, and 99.1%, respectively. The kinetics of organic compounds fitted different orders as malathion followed a zeroth-order reaction, while 2,4-D and piroxicam followed the first-order reactions. Preliminary assessment of absorption of heavy metals by the water hyacinth in the AWS was observed to be (all values in mg g -1 ) 7 (Ni), 13.4 (Cd), 16.3 (Pb), and 17.5 (Zn) of dry biomass, thus proving its feasibility to depurate wastewater.

Laser induced photoluminescence spectroscopy of cometary radicals

NASA Technical Reports Server (NTRS)

Jackson, W. M.; Cody, R. J.; Sabety-Dzvonik, M.

1976-01-01

Flash photolysis together with laser excitation of the product fragments was used in laboratory studies of cometary radicals. The LIPS method has been applied to the CN radical to determine: (1) Radiative lifetimes of individual rotational levels in the zeroth vibrational level of the B state; (2) energy partitioning during photodissociation of C2N2; and (3) vibrational and rotational excitation during formation of CN radicals in the photodissociation of dicyanoacetylene.

DFT calculations in the assignment of solid-state NMR and crystal structure elucidation of a lanthanum(iii) complex with dithiocarbamate and phenanthroline.

PubMed

Gowda, Vasantha; Laitinen, Risto S; Telkki, Ville-Veikko; Larsson, Anna-Carin; Antzutkin, Oleg N; Lantto, Perttu

2016-12-06

The molecular, crystal, and electronic structures as well as spectroscopic properties of a mononuclear heteroleptic lanthanum(iii) complex with diethyldithiocarbamate and 1,10-phenanthroline ligands (3 : 1) were studied by solid-state 13 C and 15 N cross-polarisation (CP) magic-angle-spinning (MAS) NMR, X-ray diffraction (XRD), and first principles density functional theory (DFT) calculations. A substantially different powder XRD pattern and 13 C and 15 N CP-MAS NMR spectra indicated that the title compound is not isostructural to the previously reported analogous rare earth complexes with the space group P2 1 /n. Both 13 C and 15 N CP-MAS NMR revealed the presence of six structurally different dithiocarbamate groups in the asymmetric unit cell, implying a non-centrosymmetric packing arrangement of molecules. This was supported by single-crystal X-ray crystallography showing that the title compound crystallised in the triclinic space group P1[combining macron]. In addition, the crystal structure also revealed that one of the dithiocarbamate ligands has a conformational disorder. NMR chemical shift calculations employing the periodic gauge including projector augmented wave (GIPAW) approach supported the assignment of the experimental 13 C and 15 N NMR spectra. However, the best correspondences were obtained with the structure where the atomic positions in the X-ray unit cell were optimised at the DFT level. The roles of the scalar and spin-orbit relativistic effects on NMR shielding were investigated using the zeroth-order regular approximation (ZORA) method with the outcome that already the scalar relativistic level qualitatively reproduces the experimental chemical shifts. The electronic properties of the complex were evaluated based on the results of the natural bond orbital (NBO) and topology of the electron density analyses. Overall, we apply a multidisciplinary approach acquiring comprehensive information about the solid-state structure and the metal-ligand bonding of the heteroleptic lanthanum complex.

Oligomeric complexes of some heteroaromatic ligands and aromatic diamines with rhodium and molybdenum tetracarboxylates: 13C and 15N CPMAS NMR and density functional theory studies.

PubMed

Leniak, Arkadiusz; Kamieński, Bohdan; Jaźwiński, Jarosław

2015-05-01

Seven new oligomeric complexes of 4,4'-bipyridine; 3,3'-bipyridine; benzene-1,4-diamine; benzene-1,3-diamine; benzene-1,2-diamine; and benzidine with rhodium tetraacetate, as well as 4,4'-bipyridine with molybdenum tetraacetate, have been obtained and investigated by elemental analysis and solid-state nuclear magnetic resonance spectroscopy, (13)C and (15)N CPMAS NMR. The known complexes of pyrazine with rhodium tetrabenzoate, benzoquinone with rhodium tetrapivalate, 4,4'-bipyridine with molybdenum tetrakistrifluoroacetate and the 1 : 1 complex of 2,2'-bipyridine with rhodium tetraacetate exhibiting axial-equatorial ligation mode have been obtained as well for comparison purposes. Elemental analysis revealed 1 : 1 complex stoichiometry of all complexes. The (15)N CPMAS NMR spectra of all new complexes consist of one narrow signal, indicating regular uniform structures. Benzidine forms a heterogeneous material, probably containing linear oligomers and products of further reactions. The complexes were characterized by the parameter complexation shift Δδ (Δδ = δcomplex  - δligand). This parameter ranged from around -40 to -90 ppm in the case of heteroaromatic ligands, from around -12 to -22 ppm for diamines and from -16 to -31 ppm for the complexes of molybdenum tetracarboxylates with 4,4'-bipyridine. The experimental results have been supported by a density functional theory computation of (15)N NMR chemical shifts and complexation shifts at the non-relativistic Becke, three-parameter, Perdew-Wang 91/[6-311++G(2d,p), Stuttgart] and GGA-PBE/QZ4P levels of theory and at the relativistic scalar and spin-orbit zeroth order regular approximation/GGA-PBE/QZ4P level of theory. Nucleus-independent chemical shifts have been calculated for the selected compounds. Copyright © 2015 John Wiley & Sons, Ltd.

Common Envelope Light Curves. I. Grid-code Module Calibration

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

Galaviz, Pablo; Marco, Orsola De; Staff, Jan E.

The common envelope (CE) binary interaction occurs when a star transfers mass onto a companion that cannot fully accrete it. The interaction can lead to a merger of the two objects or to a close binary. The CE interaction is the gateway of all evolved compact binaries, all stellar mergers, and likely many of the stellar transients witnessed to date. CE simulations are needed to understand this interaction and to interpret stars and binaries thought to be the byproduct of this stage. At this time, simulations are unable to reproduce the few observational data available and several ideas have been putmore » forward to address their shortcomings. The need for more definitive simulation validation is pressing and is already being fulfilled by observations from time-domain surveys. In this article, we present an initial method and its implementation for post-processing grid-based CE simulations to produce the light curve so as to compare simulations with upcoming observations. Here we implemented a zeroth order method to calculate the light emitted from CE hydrodynamic simulations carried out with the 3D hydrodynamic code Enzo used in unigrid mode. The code implements an approach for the computation of luminosity in both optically thick and optically thin regimes and is tested using the first 135 days of the CE simulation of Passy et al., where a 0.8  M {sub ⊙} red giant branch star interacts with a 0.6  M {sub ⊙} companion. This code is used to highlight two large obstacles that need to be overcome before realistic light curves can be calculated. We explain the nature of these problems and the attempted solutions and approximations in full detail to enable the next step to be identified and implemented. We also discuss our simulation in relation to recent data of transients identified as CE interactions.« less

One-electron versus electron-electron interaction contributions to the spin-spin coupling mechanism in nuclear magnetic resonance spectroscopy: Analysis of basic electronic effects

NASA Astrophysics Data System (ADS)

Gräfenstein, Jürgen; Cremer, Dieter

2004-12-01

For the first time, the nuclear magnetic resonance (NMR) spin-spin coupling mechanism is decomposed into one-electron and electron-electron interaction contributions to demonstrate that spin-information transport between different orbitals is not exclusively an electron-exchange phenomenon. This is done using coupled perturbed density-functional theory in conjunction with the recently developed J-OC-PSP [=J-OC-OC-PSP: Decomposition of J into orbital contributions using orbital currents and partial spin polarization)] method. One-orbital contributions comprise Ramsey response and self-exchange effects and the two-orbital contributions describe first-order delocalization and steric exchange. The two-orbital effects can be characterized as external orbital, echo, and spin transport contributions. A relationship of these electronic effects to zeroth-order orbital theory is demonstrated and their sign and magnitude predicted using simple models and graphical representations of first order orbitals. In the case of methane the two NMR spin-spin coupling constants result from totally different Fermi contact coupling mechanisms. 1J(C,H) is the result of the Ramsey response and the self-exchange of the bond orbital diminished by external first-order delocalization external one-orbital effects whereas 2J(H,H) spin-spin coupling is almost exclusively mitigated by a two-orbital steric exchange effect. From this analysis, a series of prediction can be made how geometrical deformations, electron lone pairs, and substituent effects lead to a change in the values of 1J(C,H) and 2J(H,H), respectively, for hydrocarbons.

Application of the method of temporal moments to interpret solute transport with sorption and degradation

NASA Astrophysics Data System (ADS)

Pang, Liping; Goltz, Mark; Close, Murray

2003-01-01

In this note, we applied the temporal moment solutions of [Das and Kluitenberg, 1996. Soil Sci. Am. J. 60, 1724] for one-dimensional advective-dispersive solute transport with linear equilibrium sorption and first-order degradation for time pulse sources to analyse soil column experimental data. Unlike most other moment solutions, these solutions consider the interplay of degradation and sorption. This permits estimation of a first-order degradation rate constant using the zeroth moment of column breakthrough data, as well as estimation of the retardation factor or sorption distribution coefficient of a degrading solute using the first moment. The method of temporal moment (MOM) formulae was applied to analyse breakthrough data from a laboratory column study of atrazine, hexazinone and rhodamine WT transport in volcanic pumice sand, as well as experimental data from the literature. Transport and degradation parameters obtained using the MOM were compared to parameters obtained by fitting breakthrough data from an advective-dispersive transport model with equilibrium sorption and first-order degradation, using the nonlinear least-square curve-fitting program CXTFIT. The results derived from using the literature data were also compared with estimates reported in the literature using different equilibrium models. The good agreement suggests that the MOM could provide an additional useful means of parameter estimation for transport involving equilibrium sorption and first-order degradation. We found that the MOM fitted breakthrough curves with tailing better than curve fitting. However, the MOM analysis requires complete breakthrough curves and relatively frequent data collection to ensure the accuracy of the moments obtained from the breakthrough data.

Designing optimal nanofocusing with a gradient hyperlens

NASA Astrophysics Data System (ADS)

Shen, Lian; Prokopeva, Ludmila J.; Chen, Hongsheng; Kildishev, Alexander V.

2017-11-01

We report the design of a high-throughput gradient hyperbolic lenslet built with real-life materials and capable of focusing a beam into a deep sub-wavelength spot of λ/23. This efficient design is achieved through high-order transformation optics and circular effective-medium theory (CEMT), which are used to engineer the radially varying anisotropic artificial material based on the thin alternating cylindrical metal and dielectric layers. The radial gradient of the effective anisotropic optical constants allows for matching the impedances at the input and output interfaces, drastically improving the throughput of the lenslet. However, it is the use of the zeroth-order CEMT that enables the practical realization of a gradient hyperlens with realistic materials. To illustrate the importance of using the CEMT versus the conventional planar effective-medium theory (PEMT) for cylindrical anisotropic systems, such as our hyperlens, both the CEMT and PEMT are adopted to design gradient hyperlenses with the same materials and order of elemental layers. The CEMT- and PEMT-based designs show similar performance if the number of metal-dielectric binary layers is sufficiently large (9+ pairs) and if the layers are sufficiently thin. However, for the manufacturable lenses with realistic numbers of layers (e.g. five pairs) and thicknesses, the performance of the CEMT design continues to be practical, whereas the PEMT-based design stops working altogether. The accurate design of transformation optics-based layered cylindrical devices enabled by CEMT allow for a new class of robustly manufacturable nanophotonic systems, even with relatively thick layers of real-life materials.

On the inscription of period and half-period surface relief gratings in azobenzene-functionalized polymers.

PubMed

Sobolewska, Anna; Miniewicz, Andrzej

2008-04-17

Laser-light-induced surface relief grating inscription was carried out in the newly synthesized azobenzene-functionalized poly(amide-imide)s having the same main- and side-chain structures but different substituents in the azobenzene groups. The gratings were inscribed employing the two-wave mixing technique with linearly polarized laser beams. Three different polarization configurations were used: s-s, p-p, and s-p. The relatively deep surface relief gratings of period Lambda were formed for the case of s-s and p-p polarizations, whereas the s-p inscription resulted in the half-period grating (Lambda/2) with the weak surface modulation. The origin of the formation of Lambda/2 structure for s-p configuration results from the interference between zeroth- and first-order beams scattered on the polarization refractive index grating and having the same polarization. On the basis of this idea, we presented the simple kinetic model predicting and modeling the half-period grating formation with its temporal evolution. The proposed model is consistent with the experimental findings.

Computation of Temperature-Dependent Legendre Moments of a Double-Differential Elastic Cross Section

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

Arbanas, Goran; Dunn, Michael E; Larson, Nancy M

2011-01-01

A general expression for temperature-dependent Legendre moments of a double-differential elastic scattering cross section was derived by Ouisloumen and Sanchez [Nucl. Sci. Eng. 107, 189-200 (1991)]. Attempts to compute this expression are hindered by the three-fold nested integral, limiting their practical application to just the zeroth Legendre moment of an isotropic scattering. It is shown that the two innermost integrals could be evaluated analytically to all orders of Legendre moments, and for anisotropic scattering, by a recursive application of the integration by parts method. For this method to work, the anisotropic angular distribution in the center of mass is expressedmore » as an expansion in Legendre polynomials. The first several Legendre moments of elastic scattering of neutrons on U-238 are computed at T=1000 K at incoming energy 6.5 eV for isotropic scattering in the center of mass frame. Legendre moments of the anisotropic angular distribution given via Blatt-Biedenharn coefficients are computed at ~1 keV. The results are in agreement with those computed by the Monte Carlo method.« less

Numerical analysis of mixing by sharp-edge-based acoustofluidic micromixer

NASA Astrophysics Data System (ADS)

Nama, Nitesh; Huang, Po-Hsun; Jun Huang, Tony; Costanzo, Francesco

2015-11-01

Recently, acoustically oscillated sharp-edges have been employed to realize rapid and homogeneous mixing at microscales (Huang, Lab on a Chip, 13, 2013). Here, we present a numerical model, qualitatively validated by experimental results, to analyze the acoustic mixing inside a sharp-edge-based micromixer. We extend our previous numerical model (Nama, Lab on a Chip, 14, 2014) to combine the Generalized Lagrangian Mean (GLM) theory with the convection-diffusion equation, while also allowing for the presence of a background flow as observed in a typical sharp-edge-based micromixer. We employ a perturbation approach to divide the flow variables into zeroth-, first- and second-order fields which are successively solved to obtain the Lagrangian mean velocity. The Langrangian mean velocity and the background flow velocity are further employed with the convection-diffusion equation to obtain the concentration profile. We characterize the effects of various operational and geometrical parameters to suggest potential design changes for improving the mixing performance of the sharp-edge-based micromixer. Lastly, we investigate the possibility of generation of a spatio-temporally controllable concentration gradient by placing sharp-edge structures inside the microchannel.

A Compact Via-free Composite Right/Left Handed Low-pass Filter with Improved Selectivity

NASA Astrophysics Data System (ADS)

Kumar, Ashish; Choudhary, Dilip Kumar; Chaudhary, Raghvendra Kumar

2017-07-01

In this paper, a compact via-free low pass filter is designed based on composite right/left handed (CRLH) concept. The structure uses open ended concept. Rectangular slots are etched on signal transmission line (TL) to suppress the spurious band without altering the performance and size of filter. The filter is designed for low pass frequency band with cut-off frequency of 3.5 GHz. The proposed metamaterial structure has several prominent advantages in term of selectivity up to 34 dB/GHz and compactness with average insertion loss less than 0.4 dB. It has multiple applications in wireless communication (such as GSM900, global navigation satellite system (1.559-1.610 GHz), GSM1800, WLAN/WiFi (2.4-2.49 GHz) and WiMAX (2.5-2.69 GHz)). The design parameters have been measured and compared with the simulated results and found excellent agreement. The electrical size of proposed filter is 0.14λ0× 0.11λ0 (where λ0 is free space wavelength at zeroth order resonance (ZOR) frequency 2.7 GHz).

IMAGE: A Design Integration Framework Applied to the High Speed Civil Transport

NASA Technical Reports Server (NTRS)

Hale, Mark A.; Craig, James I.

1993-01-01

Effective design of the High Speed Civil Transport requires the systematic application of design resources throughout a product's life-cycle. Information obtained from the use of these resources is used for the decision-making processes of Concurrent Engineering. Integrated computing environments facilitate the acquisition, organization, and use of required information. State-of-the-art computing technologies provide the basis for the Intelligent Multi-disciplinary Aircraft Generation Environment (IMAGE) described in this paper. IMAGE builds upon existing agent technologies by adding a new component called a model. With the addition of a model, the agent can provide accountable resource utilization in the presence of increasing design fidelity. The development of a zeroth-order agent is used to illustrate agent fundamentals. Using a CATIA(TM)-based agent from previous work, a High Speed Civil Transport visualization system linking CATIA, FLOPS, and ASTROS will be shown. These examples illustrate the important role of the agent technologies used to implement IMAGE, and together they demonstrate that IMAGE can provide an integrated computing environment for the design of the High Speed Civil Transport.

On the nonlinear variation of dc conductivity with dielectric relaxation time

NASA Astrophysics Data System (ADS)

Johari, G. P.; Andersson, Ove

2006-09-01

The long-known observations that dc conductivity σdc of an ultraviscous liquid varies nonlinearly with the dielectric relaxation time τ, and the slope of the logσdc against logτ plot deviates from -1 are currently seen as two of the violations of the Debye-Stokes-Einstein equation. Here we provide a formalism using a zeroth order Bjerrum description for ion association to show that in addition to its variation with temperature T and pressure P, impurity ion population varies with a liquid's equilibrium dielectric permittivity. Inclusion of this electrostatic effect modifies the Debye-Stokes-Einstein equation to log(σdcτ )=constant+logα, where α is the T and P-dependent degree of ionic dissociation of an electrolytic impurity. Variation of a liquid's shear modulus with T and P would add to the nonlinearity of σdc-τ relation, as would a nonequivalence of the shear and dielectric relaxation times, proton transfer along the hydrogen bonds, or occurrence of another chemical process. This is illustrated by using the data for ultraviscous acetaminophen-aspirin liquid.

Stochastic theory of nonequilibrium steady states and its applications. Part I

NASA Astrophysics Data System (ADS)

Zhang, Xue-Juan; Qian, Hong; Qian, Min

2012-01-01

The concepts of equilibrium and nonequilibrium steady states are introduced in the present review as mathematical concepts associated with stationary Markov processes. For both discrete stochastic systems with master equations and continuous diffusion processes with Fokker-Planck equations, the nonequilibrium steady state (NESS) is characterized in terms of several key notions which are originated from nonequilibrium physics: time irreversibility, breakdown of detailed balance, free energy dissipation, and positive entropy production rate. After presenting this NESS theory in pedagogically accessible mathematical terms that require only a minimal amount of prerequisites in nonlinear differential equations and the theory of probability, it is applied, in Part I, to two widely studied problems: the stochastic resonance (also known as coherent resonance) and molecular motors (also known as Brownian ratchet). Although both areas have advanced rapidly on their own with a vast amount of literature, the theory of NESS provides them with a unifying mathematical foundation. Part II of this review contains applications of the NESS theory to processes from cellular biochemistry, ranging from enzyme catalyzed reactions, kinetic proofreading, to zeroth-order ultrasensitivity.

Seabed roughness parameters from joint backscatter and reflection inversion at the Malta Plateau.

PubMed

Steininger, Gavin; Holland, Charles W; Dosso, Stan E; Dettmer, Jan

2013-09-01

This paper presents estimates of seabed roughness and geoacoustic parameters and uncertainties on the Malta Plateau, Mediterranean Sea, by joint Bayesian inversion of mono-static backscatter and spherical wave reflection-coefficient data. The data are modeled using homogeneous fluid sediment layers overlying an elastic basement. The scattering model assumes a randomly rough water-sediment interface with a von Karman roughness power spectrum. Scattering and reflection data are inverted simultaneously using a population of interacting Markov chains to sample roughness and geoacoustic parameters as well as residual error parameters. Trans-dimensional sampling is applied to treat the number of sediment layers and the order (zeroth or first) of an autoregressive error model (to represent potential residual correlation) as unknowns. Results are considered in terms of marginal posterior probability profiles and distributions, which quantify the effective data information content to resolve scattering/geoacoustic structure. Results indicate well-defined scattering (roughness) parameters in good agreement with existing measurements, and a multi-layer sediment profile over a high-speed (elastic) basement, consistent with independent knowledge of sand layers over limestone.

Polyad breaking phenomenon associated with a local-to-normal mode transition and suitability to estimate force constants

NASA Astrophysics Data System (ADS)

Bermúdez-Montaña, M.; Lemus, R.; Castaños, O.

2017-12-01

In a system of two interacting harmonic oscillators a local-to-normal mode transition is manifested as a polyad breaking phenomenon. This phenomenon is associated with the suitability to estimate zeroth-order force constants in the framework of a local mode description. This transition is also exhibited in two interacting Morse oscillators. To study this case, an appropriate parameterisation going from a molecule with local mode behaviour (H2O) to a molecule presenting a normal mode behaviour (CO2) is introduced. Concepts from quantum mechanics like fidelity, entropy and probability density, as well from nonlinear classical mechanics like Poincaré sections are used to detect the transition region. It is found that fidelity and entropy are sensitive complementary properties to detect the local-to-normal transition. Poincaré sections allow the local-to-normal transition to be detected through the appearance of chaos as a consequence of the polyad breaking phenomenon. In addition, two kinds of avoided energy crossings are identified in accordance with the different regions of the spectrum.

Gravitational potential energy of the earth: A spherical harmonic approach

NASA Technical Reports Server (NTRS)

Rubincam, D. P.

1977-01-01

A spherical harmonic equation for the gravitational potential energy of the earth is derived for an arbitrary density distribution by conceptually bringing in mass-elements from infinity and building up the earth shell upon spherical shell. The zeroth degree term in the spherical harmonic equation agrees with the usual expression for the energy of a radial density distribution. The second degree terms give a maximum nonhydrostatic energy in the mantle and crust of -2.77 x 10 to the twenty-ninth power ergs, an order of magnitude. If the earth is assumed to be a homogeneous viscous oblate spheroid relaxing to an equilibrium shape, then a lower limit to the mantle viscosity of 1.3 x 10 to the twentieth power poises is found by assuming the total geothermal flux is due to viscous dissipation. If the nonequilibrium figure is dynamically maintained by the earth acting as a heat engine at one per cent efficiency, then the viscosity is ten to the twenty second power poises, a number preferred by some as the viscosity of the mantle.

Confining and repulsive potentials from effective non-Abelian gauge fields in graphene bilayers

NASA Astrophysics Data System (ADS)

González, J.

2016-10-01

We investigate the effect of shear and strain in graphene bilayers, under conditions where the distortion of the lattice gives rise to a smooth one-dimensional modulation in the stacking sequence of the bilayer. We show that strain and shear produce characteristic Moiré patterns which can have the same visual appearance on a large scale, but representing graphene bilayers with quite different electronic properties. The different features in the low-energy electronic bands can be ascribed to the effect of a fictitious non-Abelian gauge field mimicking the smooth modulation of the stacking order. Strained and sheared bilayers show a complementary behavior, which can be understood from the fact that the non-Abelian gauge field acts as a repulsive interaction in the former, expelling the electron density away from the stacking domain walls, while behaving as a confining interaction leading to localization of the electronic states in the sheared bilayers. In this latter case, the presence of the effective gauge field explains the development of almost flat low-energy bands, resembling the form of the zeroth Landau level characteristic of a Dirac fermion field. The estimate of the gauge field strength in those systems gives a magnitude of the order of several tens of tesla, implying a robust phenomenology that should be susceptible of being observed in suitably distorted bilayer samples.

Dispersion characteristics of the flexural wave assessed using low frequency (50-150kHz) point-contact transducers: A feasibility study on bone-mimicking phantoms.

PubMed

Kassou, Koussila; Remram, Youcef; Laugier, Pascal; Minonzio, Jean-Gabriel

2017-11-01

Guided waves-based techniques are currently under development for quantitative cortical bone assessment. However, the signal interpretation is challenging due to multiple mode overlapping. To overcome this limitation, dry point-contact transducers have been used at low frequencies for a selective excitation of the zeroth order anti-symmetric Lamb A0 mode, a mode whose dispersion characteristics can be used to infer the thickness of the waveguide. In this paper, our purpose was to extend the technique by combining a dry point-contact transducers approach to the SVD-enhanced 2-D Fourier transform in order to measure the dispersion characteristics of the flexural mode. The robustness of our approach is assessed on bone-mimicking phantoms covered or not with soft tissue-mimicking layer. Experiments were also performed on a bovine bone. Dispersion characteristics of measured modes were extracted using a SVD-based signal processing technique. The thickness was obtained by fitting a free plate model to experimental data. The results show that, in all studied cases, the estimated thickness values are in good agreement with the actual thickness values. From the results, we speculate that in vivo cortical thickness assessment by measuring the flexural wave using point-contact transducers is feasible. However, this assumption has to be confirmed by further in vivo studies. Copyright © 2017 Elsevier B.V. All rights reserved.

Isotopic effects in vibrational relaxation dynamics of H on a Si(100) surface

NASA Astrophysics Data System (ADS)

Bouakline, F.; Lorenz, U.; Melani, G.; Paramonov, G. K.; Saalfrank, P.

2017-10-01

In a recent paper [U. Lorenz and P. Saalfrank, Chem. Phys. 482, 69 (2017)], we proposed a robust scheme to set up a system-bath model Hamiltonian, describing the coupling of adsorbate vibrations (system) to surface phonons (bath), from first principles. The method is based on an embedded cluster approach, using orthogonal coordinates for system and bath modes, and an anharmonic phononic expansion of the system-bath interaction up to second order. In this contribution, we use this model Hamiltonian to calculate vibrational relaxation rates of H-Si and D-Si bending modes, coupled to a fully H(D)-covered Si(100)-( 2 × 1 ) surface, at zero temperature. The D-Si bending mode has an anharmonic frequency lying inside the bath frequency spectrum, whereas the H-Si bending mode frequency is outside the bath Debye band. Therefore, in the present calculations, we only take into account one-phonon system-bath couplings for the D-Si system and both one- and two-phonon interaction terms in the case of H-Si. The computation of vibrational lifetimes is performed with two different approaches, namely, Fermi's golden rule, and a generalized Bixon-Jortner model built in a restricted vibrational space of the adsorbate-surface zeroth-order Hamiltonian. For D-Si, the Bixon-Jortner Hamiltonian can be solved by exact diagonalization, serving as a benchmark, whereas for H-Si, an iterative scheme based on the recursive residue generation method is applied, with excellent convergence properties. We found that the lifetimes obtained with perturbation theory, albeit having almost the same order of magnitude—a few hundred fs for D-Si and a couple of ps for H-Si—, are strongly dependent on the discretized numerical representation of the bath spectral density. On the other hand, the Bixon-Jortner model is free of such numerical deficiencies, therefore providing better estimates of vibrational relaxation rates, at a very low computational cost. The results obtained with this model clearly show a net exponential decay of the time-dependent survival probability for the H-Si initial vibrational state, allowing an easy extraction of the bending mode "lifetime." This is in contrast with the D-Si system, whose survival probability exhibits a non-monotonic decay, making it difficult to define such a lifetime. This different behavior of the vibrational decay is rationalized in terms of the power spectrum of the adsorbate-surface system. In the case of D-Si, it consists of several, non-uniformly distributed peaks around the bending mode frequency, whereas the H-Si spectrum exhibits a single Lorentzian lineshape, whose width corresponds to the calculated lifetime. The present work gives some insight into mechanisms of vibration-phonon coupling at surfaces. It also serves as a benchmark for multidimensional system-bath quantum dynamics, for comparison with approximate schemes such as reduced, open-system density matrix theory (where the bath is traced out and a Liouville-von Neumann equation is solved) or approximate wavefunction methods to solve the combined system-bath Schrödinger equation.

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

Abanin, D. A.; Department of Physics, Princeton University, Princeton, New Jersey 08544; Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106

Quantum Hall states that result from interaction induced lifting of the eightfold degeneracy of the zeroth Landau level in bilayer graphene are considered. We show that at even filling factors electric charge is injected into the system in the form of charge 2e Skyrmions. This is a rare example of binding of charges in a system with purely repulsive interactions. We calculate the Skyrmion energy and size as a function of the effective Zeeman interaction and discuss the signatures of the charge 2e Skyrmions in the scanning probe experiments.

What Force and Metrics for What End - Characterizing the Future Leadership and Force

DTIC Science & Technology

2006-06-01

interest of humanity as a whole, and may overrule all other laws whenever it seems necessary for the ultimate good. Source – Asimov , Isaac. “I, Robot...Robotics + the Zeroth Law’ ( Asimov , 2006 Command and Control Research and Technology Symposium ‘The Sate of the Art and the State of the Practice’ ASD...outcomes. Here the author returns to the introduction of the example derived from Asimov (1940, 1970) and Brin (1999) ‘four laws of robotics

Inferring regional vertical crustal velocities from averaged relative sea level trends: A proof of concept

NASA Astrophysics Data System (ADS)

Bâki Iz, H.; Shum, C. K.; Zhang, C.; Kuo, C. Y.

2017-11-01

We report the design of a high-throughput gradient hyperbolic lenslet built with real-life materials and capable of focusing a beam into a deep sub-wavelength spot of λ/23. This efficient design is achieved through high-order transformation optics and circular effective-medium theory (CEMT), which are used to engineer the radially varying anisotropic artificial material based on the thin alternating cylindrical metal and dielectric layers. The radial gradient of the effective anisotropic optical constants allows for matching the impedances at the input and output interfaces, drastically improving the throughput of the lenslet. However, it is the use of the zeroth-order CEMT that enables the practical realization of a gradient hyperlens with realistic materials. To illustrate the importance of using the CEMT versus the conventional planar effective-medium theory (PEMT) for cylindrical anisotropic systems, such as our hyperlens, both the CEMT and PEMT are adopted to design gradient hyperlenses with the same materials and order of elemental layers. The CEMT- and PEMT-based designs show similar performance if the number of metal-dielectric binary layers is sufficiently large (9+ pairs) and if the layers are sufficiently thin. However, for the manufacturable lenses with realistic numbers of layers (e.g. five pairs) and thicknesses, the performance of the CEMT design continues to be practical, whereas the PEMT-based design stops working altogether. The accurate design of transformation optics-based layered cylindrical devices enabled by CEMT allow for a new class of robustly manufacturable nanophotonic systems, even with relatively thick layers of real-life materials.

Modeling self-consistent multi-class dynamic traffic flow

NASA Astrophysics Data System (ADS)

Cho, Hsun-Jung; Lo, Shih-Ching

2002-09-01

In this study, we present a systematic self-consistent multiclass multilane traffic model derived from the vehicular Boltzmann equation and the traffic dispersion model. The multilane domain is considered as a two-dimensional space and the interaction among vehicles in the domain is described by a dispersion model. The reason we consider a multilane domain as a two-dimensional space is that the driving behavior of road users may not be restricted by lanes, especially motorcyclists. The dispersion model, which is a nonlinear Poisson equation, is derived from the car-following theory and the equilibrium assumption. Under the concept that all kinds of users share the finite section, the density is distributed on a road by the dispersion model. In addition, the dynamic evolution of the traffic flow is determined by the systematic gas-kinetic model derived from the Boltzmann equation. Multiplying Boltzmann equation by the zeroth, first- and second-order moment functions, integrating both side of the equation and using chain rules, we can derive continuity, motion and variance equation, respectively. However, the second-order moment function, which is the square of the individual velocity, is employed by previous researches does not have physical meaning in traffic flow. Although the second-order expansion results in the velocity variance equation, additional terms may be generated. The velocity variance equation we propose is derived from multiplying Boltzmann equation by the individual velocity variance. It modifies the previous model and presents a new gas-kinetic traffic flow model. By coupling the gas-kinetic model and the dispersion model, a self-consistent system is presented.

ROTATING ACCRETION FLOWS: FROM INFINITY TO THE BLACK HOLE

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

Li, Jason; Ostriker, Jeremiah; Sunyaev, Rashid, E-mail: jgli@astro.princeton.edu

2013-04-20

Accretion onto a supermassive black hole of a rotating inflow is a particularly difficult problem to study because of the wide range of length scales involved. There have been broadly utilized analytic and numerical treatments of the global properties of accretion flows, but detailed numerical simulations are required to address certain critical aspects. We use the ZEUS code to run hydrodynamical simulations of rotating, axisymmetric accretion flows with Bremsstrahlung cooling, considering solutions for which the centrifugal balance radius significantly exceeds the Schwarzschild radius, with and without viscous angular momentum transport. Infalling gas is followed from well beyond the Bondi radiusmore » down to the vicinity of the black hole. We produce a continuum of solutions with respect to the single parameter M-dot{sub B}/ M-dot{sub Edd}, and there is a sharp transition between two general classes of solutions at an Eddington ratio of M-dot{sub B}/M-dot{sub Edd}{approx}few Multiplication-Sign 10{sup -2}. Our high inflow solutions are very similar to the standard Shakura and Sunyaev results. But our low inflow results are to zeroth order the stationary Papaloizou and Pringle solution, which has no accretion. To next order in the small, assumed viscosity they show circulation, with disk and conical wind outflows almost balancing inflow. These solutions are characterized by hot, vertically extended disks, and net accretion proceeds at an extremely low rate, only of order {alpha} times the inflow rate. Our simulations have converged with respect to spatial resolution and temporal duration, and they do not depend strongly on our choice of boundary conditions.« less

An analytical equation of state for describing isotropic-nematic phase equilibria of Lennard-Jones chain fluids with variable degree of molecular flexibility

NASA Astrophysics Data System (ADS)

van Westen, Thijs; Oyarzún, Bernardo; Vlugt, Thijs J. H.; Gross, Joachim

2015-06-01

We develop an equation of state (EoS) for describing isotropic-nematic (IN) phase equilibria of Lennard-Jones (LJ) chain fluids. The EoS is developed by applying a second order Barker-Henderson perturbation theory to a reference fluid of hard chain molecules. The chain molecules consist of tangentially bonded spherical segments and are allowed to be fully flexible, partially flexible (rod-coil), or rigid linear. The hard-chain reference contribution to the EoS is obtained from a Vega-Lago rescaled Onsager theory. For the description of the (attractive) dispersion interactions between molecules, we adopt a segment-segment approach. We show that the perturbation contribution for describing these interactions can be divided into an "isotropic" part, which depends only implicitly on orientational ordering of molecules (through density), and an "anisotropic" part, for which an explicit dependence on orientational ordering is included (through an expansion in the nematic order parameter). The perturbation theory is used to study the effect of chain length, molecular flexibility, and attractive interactions on IN phase equilibria of pure LJ chain fluids. Theoretical results for the IN phase equilibrium of rigid linear LJ 10-mers are compared to results obtained from Monte Carlo simulations in the isobaric-isothermal (NPT) ensemble, and an expanded formulation of the Gibbs-ensemble. Our results show that the anisotropic contribution to the dispersion attractions is irrelevant for LJ chain fluids. Using the isotropic (density-dependent) contribution only (i.e., using a zeroth order expansion of the attractive Helmholtz energy contribution in the nematic order parameter), excellent agreement between theory and simulations is observed. These results suggest that an EoS contribution for describing the attractive part of the dispersion interactions in real LCs can be obtained from conventional theoretical approaches designed for isotropic fluids, such as a Perturbed-Chain Statistical Associating Fluid Theory approach.

Form finding in elastic gridshells.

PubMed

Baek, Changyeob; Sageman-Furnas, Andrew O; Jawed, Mohammad K; Reis, Pedro M

2018-01-02

Elastic gridshells comprise an initially planar network of elastic rods that are actuated into a shell-like structure by loading their extremities. The resulting actuated form derives from the elastic buckling of the rods subjected to inextensibility. We study elastic gridshells with a focus on the rational design of the final shapes. Our precision desktop experiments exhibit complex geometries, even from seemingly simple initial configurations and actuation processes. The numerical simulations capture this nonintuitive behavior with excellent quantitative agreement, allowing for an exploration of parameter space that reveals multistable states. We then turn to the theory of smooth Chebyshev nets to address the inverse design of hemispherical elastic gridshells. The results suggest that rod inextensibility, not elastic response, dictates the zeroth-order shape of an actuated elastic gridshell. As it turns out, this is the shape of a common household strainer. Therefore, the geometry of Chebyshev nets can be further used to understand elastic gridshells. In particular, we introduce a way to quantify the intrinsic shape of the empty, but enclosed regions, which we then use to rationalize the nonlocal deformation of elastic gridshells to point loading. This justifies the observed difficulty in form finding. Nevertheless, we close with an exploration of concatenating multiple elastic gridshell building blocks.

The problem of hole localization in inner-shell states of N2 and CO2 revisited with complete active space self-consistent field approach.

PubMed

Rocha, Alexandre B; de Moura, Carlos E V

2011-12-14

Potential energy curves for inner-shell states of nitrogen and carbon dioxide molecules are calculated by inner-shell complete active space self-consistent field (CASSCF) method, which is a protocol, recently proposed, to obtain specifically converged inner-shell states at multiconfigurational level. This is possible since the collapse of the wave function to a low-lying state is avoided by a sequence of constrained optimization in the orbital mixing step. The problem of localization of K-shell states is revisited by calculating their energies at CASSCF level based on both localized and delocalized orbitals. The localized basis presents the best results at this level of calculation. Transition energies are also calculated by perturbation theory, by taking the above mentioned MCSCF function as zeroth order wave function. Values for transition energy are in fairly good agreement with experimental ones. Bond dissociation energies for N(2) are considerably high, which means that these states are strongly bound. Potential curves along ground state normal modes of CO(2) indicate the occurrence of Renner-Teller effect in inner-shell states. © 2011 American Institute of Physics

Driving forces: Slab subduction and mantle convection

NASA Technical Reports Server (NTRS)

Hager, Bradford H.

1988-01-01

Mantle convection is the mechanism ultimately responsible for most geological activity at Earth's surface. To zeroth order, the lithosphere is the cold outer thermal boundary layer of the convecting mantle. Subduction of cold dense lithosphere provides tha major source of negative buoyancy driving mantle convection and, hence, surface tectonics. There are, however, importnat differences between plate tectonics and the more familiar convecting systems observed in the laboratory. Most important, the temperature dependence of the effective viscosity of mantle rocks makes the thermal boundary layer mechanically strong, leading to nearly rigid plates. This strength stabilizes the cold boundary layer against small amplitude perturbations and allows it to store substantial gravitational potential energy. Paradoxically, through going faults at subduction zones make the lithosphere there locally weak, allowing rapid convergence, unlike what is observed in laboratory experiments using fluids with temperature dependent viscosities. This bimodal strength distribution of the lithosphere distinguishes plate tectonics from simple convection experiments. In addition, Earth has a buoyant, relatively weak layer (the crust) occupying the upper part of the thermal boundary layer. Phase changes lead to extra sources of heat and bouyancy. These phenomena lead to observed richness of behavior of the plate tectonic style of mantle convection.

the Ĝ infrared search for extraterrestrial civilizations with large energy supplies. II. Framework, strategy, and first result

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

Wright, J. T.; Griffith, R. L.; Sigurdsson, S.

We describe the framework and strategy of the Ĝ infrared search for extraterrestrial civilizations with large energy supplies, which will use the wide-field infrared surveys of WISE and Spitzer to search for these civilizations' waste heat. We develop a formalism for translating mid-infrared photometry into quantitative upper limits on extraterrestrial energy supplies. We discuss the likely sources of false positives, how dust can and will contaminate our search, and prospects for distinguishing dust from alien waste heat. We argue that galaxy-spanning civilizations may be easier to distinguish from natural sources than circumstellar civilizations (i.e., Dyson spheres), although GAIA will significantlymore » improve our capability to identify the latter. We present a zeroth order null result of our search based on the WISE all-sky catalog: we show, for the first time, that Kardashev Type III civilizations (as Kardashev originally defined them) are very rare in the local universe. More sophisticated searches can extend our methodology to smaller waste heat luminosities, and potentially entirely rule out (or detect) both Kardashev Type III civilizations and new physics that allows for unlimited 'free' energy generation.« less

Form finding in elastic gridshells

NASA Astrophysics Data System (ADS)

Baek, Changyeob; Sageman-Furnas, Andrew O.; Jawed, Mohammad K.; Reis, Pedro M.

2018-01-01

Elastic gridshells comprise an initially planar network of elastic rods that are actuated into a shell-like structure by loading their extremities. The resulting actuated form derives from the elastic buckling of the rods subjected to inextensibility. We study elastic gridshells with a focus on the rational design of the final shapes. Our precision desktop experiments exhibit complex geometries, even from seemingly simple initial configurations and actuation processes. The numerical simulations capture this nonintuitive behavior with excellent quantitative agreement, allowing for an exploration of parameter space that reveals multistable states. We then turn to the theory of smooth Chebyshev nets to address the inverse design of hemispherical elastic gridshells. The results suggest that rod inextensibility, not elastic response, dictates the zeroth-order shape of an actuated elastic gridshell. As it turns out, this is the shape of a common household strainer. Therefore, the geometry of Chebyshev nets can be further used to understand elastic gridshells. In particular, we introduce a way to quantify the intrinsic shape of the empty, but enclosed regions, which we then use to rationalize the nonlocal deformation of elastic gridshells to point loading. This justifies the observed difficulty in form finding. Nevertheless, we close with an exploration of concatenating multiple elastic gridshell building blocks.

Binary-Phase Fourier Gratings for Nonuniform Array Generation

NASA Technical Reports Server (NTRS)

Keys, Andrew S.; Crow, Robert W.; Ashley, Paul R.

2003-01-01

We describe a design method for a binary-phase Fourier grating that generates an array of spots with nonuniform, user-defined intensities symmetric about the zeroth order. Like the Dammann fanout grating approach, the binary-phase Fourier grating uses only two phase levels in its grating surface profile to generate the final spot array. Unlike the Dammann fanout grating approach, this method allows for the generation of nonuniform, user-defined intensities within the final fanout pattern. Restrictions governing the specification and realization of the array's individual spot intensities are discussed. Design methods used to realize the grating employ both simulated annealing and nonlinear optimization approaches to locate optimal solutions to the grating design problem. The end-use application driving this development operates in the near- to mid-infrared spectrum - allowing for higher resolution in grating specification and fabrication with respect to wavelength than may be available in visible spectrum applications. Fabrication of a grating generating a user-defined nine spot pattern is accomplished in GaAs for the near-infrared. Characterization of the grating is provided through the measurement of individual spot intensities, array uniformity, and overall efficiency. Final measurements are compared to calculated values with a discussion of the results.

Diffusion of Sticky Nanoparticles in a Polymer Melt: Crossover from Suppressed to Enhanced Transport

DOE PAGES

Carroll, Bobby; Bocharova, Vera; Carrillo, Jan-Michael Y.; ...

2018-03-09

The self-diffusion of a single large particle in a fluid is usually described by the classic Stokes–Einstein (SE) hydrodynamic relation. However, there are many fluids where the SE prediction for nanoparticles diffusion fails. These systems include diffusion of nanoparticles in porous media, in entangled and unentangled polymer melts and solutions, and protein diffusion in biological environments. A fundamental understanding of the microscopic parameters that govern nanoparticle diffusion is relevant to a wide range of applications. Here in this work, we present experimental measurements of the tracer diffusion coefficient of small and large nanoparticles that experience strong attractions with unentangled andmore » entangled polymer melt matrices. For the small nanoparticle system, a crossover from suppressed to enhanced diffusion is observed with increasing polymer molecular weight. We interpret these observations based on our theoretical and simulation insights of the preceding article (paper 1) as a result of a crossover from an effective hydrodynamic core–shell to a nonhydrodynamic vehicle mechanism of transport, with the latter strongly dependent on polymer–nanoparticle desorption time. In conclusion, a general zeroth-order qualitative picture for small sticky nanoparticle diffusion in polymer melts is proposed.« less

Diffusion of Sticky Nanoparticles in a Polymer Melt: Crossover from Suppressed to Enhanced Transport

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

Carroll, Bobby; Bocharova, Vera; Carrillo, Jan-Michael Y.

The self-diffusion of a single large particle in a fluid is usually described by the classic Stokes–Einstein (SE) hydrodynamic relation. However, there are many fluids where the SE prediction for nanoparticles diffusion fails. These systems include diffusion of nanoparticles in porous media, in entangled and unentangled polymer melts and solutions, and protein diffusion in biological environments. A fundamental understanding of the microscopic parameters that govern nanoparticle diffusion is relevant to a wide range of applications. Here in this work, we present experimental measurements of the tracer diffusion coefficient of small and large nanoparticles that experience strong attractions with unentangled andmore » entangled polymer melt matrices. For the small nanoparticle system, a crossover from suppressed to enhanced diffusion is observed with increasing polymer molecular weight. We interpret these observations based on our theoretical and simulation insights of the preceding article (paper 1) as a result of a crossover from an effective hydrodynamic core–shell to a nonhydrodynamic vehicle mechanism of transport, with the latter strongly dependent on polymer–nanoparticle desorption time. In conclusion, a general zeroth-order qualitative picture for small sticky nanoparticle diffusion in polymer melts is proposed.« less

Detection of free nickel monocarbonyl, NiCO: rotational spectrum and structure.

PubMed

Yamazaki, Emi; Okabayashi, Toshiaki; Tanimoto, Mitsutoshi

2004-02-04

Unsaturated transition metal carbonyls are important in processes such as organometallic synthesis, homogeneous catalysis, and photochemical decomposition of organometallics. In particular, a metal monocarbonyl offers a zeroth-order model for interpreting the chemisorption of a CO molecule on a metal surface in catalytic activation processes. Quite large numbers of theoretical papers have appeared which predict spectroscopic and structural properties of transition metal carbonyls. The nickel monocarbonyl NiCO has been one of the metal carbonyls most extensively studied by the theoretical calculations. At least 50 theoretical studies have been published on this simplest transition metal carbonyl up to the present time. However, experimental evidence of NiCO is much more sparse than theoretical predictions, and the actual structure of NiCO has never been determined by any experimental methods. This Communication reports the first preparation of free nickel monocarbonyl and observation of its rotational transitions. The NiCO molecule was generated by the sputtering reaction of a Ni cathode in the presence of CO. The accurate bond lengths of Ni-C and C-O were experimentally determined from isotopic data and were compared with the theoretical predictions for the first time.

A statistical study of gyro-averaging effects in a reduced model of drift-wave transport

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

Fonseca, Julio; Del-Castillo-Negrete, Diego B.; Sokolov, Igor M.

2016-08-25

Here, a statistical study of finite Larmor radius (FLR) effects on transport driven by electrostatic driftwaves is presented. The study is based on a reduced discrete Hamiltonian dynamical system known as the gyro-averaged standard map (GSM). In this system, FLR effects are incorporated through the gyro-averaging of a simplified weak-turbulence model of electrostatic fluctuations. Formally, the GSM is a modified version of the standard map in which the perturbation amplitude, K 0, becomes K 0J 0(more » $$\\hat{p}$$), where J 0 is the zeroth-order Bessel function and $$\\hat{p}$$ s the Larmor radius. Assuming a Maxwellian probability density function (pdf) for $$\\hat{p}$$ , we compute analytically and numerically the pdf and the cumulative distribution function of the effective drift-wave perturba- tion amplitude K 0J 0($$\\hat{p}$$). Using these results, we compute the probability of loss of confinement (i.e., global chaos), P c provides an upper bound for the escape rate, and that P t rovides a good estimate of the particle trapping rate. Lastly. the analytical results are compared with direct numerical Monte-Carlo simulations of particle transport.« less

The Ĝ Infrared Search for Extraterrestrial Civilizations with Large Energy Supplies. II. Framework, Strategy, and First Result

NASA Astrophysics Data System (ADS)

Wright, J. T.; Griffith, R. L.; Sigurdsson, S.; Povich, M. S.; Mullan, B.

2014-09-01

We describe the framework and strategy of the Ĝ infrared search for extraterrestrial civilizations with large energy supplies, which will use the wide-field infrared surveys of WISE and Spitzer to search for these civilizations' waste heat. We develop a formalism for translating mid-infrared photometry into quantitative upper limits on extraterrestrial energy supplies. We discuss the likely sources of false positives, how dust can and will contaminate our search, and prospects for distinguishing dust from alien waste heat. We argue that galaxy-spanning civilizations may be easier to distinguish from natural sources than circumstellar civilizations (i.e., Dyson spheres), although GAIA will significantly improve our capability to identify the latter. We present a zeroth order null result of our search based on the WISE all-sky catalog: we show, for the first time, that Kardashev Type III civilizations (as Kardashev originally defined them) are very rare in the local universe. More sophisticated searches can extend our methodology to smaller waste heat luminosities, and potentially entirely rule out (or detect) both Kardashev Type III civilizations and new physics that allows for unlimited "free" energy generation.

Extended magnetohydrodynamic simulations of field reversed configuration formation and sustainment with rotating magnetic field current drive

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

Milroy, R. D.; Kim, C. C.; Sovinec, C. R.

Three-dimensional simulations of field reversed configuration (FRC) formation and sustainment with rotating magnetic field (RMF) current drive have been performed with the NIMROD code [C. R. Sovinec et al., J. Comput. Phys. 195, 355 (2004)]. The Hall term is a zeroth order effect with strong coupling between Fourier components, and recent enhancements to the NIMROD preconditioner allow much larger time steps than was previously possible. Boundary conditions to capture the effects of a finite length RMF antenna have been added, and simulations of FRC formation from a uniform background plasma have been performed with parameters relevant to the translation, confinement,more » and sustainment-upgrade experiment at the University of Washington [H. Y. Guo, A. L. Hoffman, and R. D. Milroy, Phys. Plasmas 14, 112502 (2007)]. The effects of both even-parity and odd-parity antennas have been investigated, and there is no evidence of a disruptive instability for either antenna type. It has been found that RMF effects extend considerably beyond the ends of the antenna, and that a large n=0 B{sub t}heta can develop in the open-field line region, producing a back torque opposing the RMF.« less

Test-particle simulations in increasingly strong turbulence

NASA Technical Reports Server (NTRS)

Pontius, D. H., Jr.; Gray, P. C.; Matthaeus, W. H.

1995-01-01

Quasi-linear theory supposes that the energy in resonant fluctuations is small compared to that in the mean magnetic field. This is evident in the fact that the zeroth-order particle trajectories are helices about a mean field B(sub o) that is spatially uniform over many correlation lengths. However, in the solar wind it is often the case that the fluctuating part of the field is comparable in magnitude to the mean part. It is generally expected that quasi-linear theory remains viable for particles that are in resonance with a region of the fluctuation spectrum having only small energy density, but even so, care must be taken when comparing simulations to theoretical predictions. We have performed a series of test-particle simulations to explore the evolution of ion distributions in turbulent situations with varying levels of magnetic fluctuations. As delta-B/B(sub o) is increased the distinctions among absolute pitch angle (defined relative to B(sub o)), local pitch angle (defined relative to B(x)), and magnetic moment become important, some of them exhibiting periodic sloshing unrelated to the nonadiabatic processes of interest. Comparing and contrasting the various runs illustrates the phenomena that must be considered when the premise underlying quasi-linear theory are relaxed.

Construction of all N=4 conformal supergravities.

PubMed

Butter, Daniel; Ciceri, Franz; de Wit, Bernard; Sahoo, Bindusar

2017-02-24

All N=4 conformal supergravities in four space-time dimensions are constructed. These are the only N=4 supergravity theories whose actions are invariant under off-shell supersymmetry. They are encoded in terms of a holomorphic function that is homogeneous of zeroth degree in scalar fields that parametrize an SU(1,1)/U(1) coset space. When this function equals a constant the Lagrangian is invariant under continuous SU(1,1) transformations. The construction of these higher-derivative invariants also opens the door to various applications for nonconformal theories.

Effect of water depth on wind-wave frequency spectrum I. Spectral form

NASA Astrophysics Data System (ADS)

Wen, Sheng-Chang; Guan, Chang-Long; Sun, Shi-Cai; Wu, Ke-Jian; Zhang, Da-Cuo

1996-06-01

Wen et al's method developed to obtain wind-wave frequency spectrum in deep water was used to derive the spectrum in finite depth water. The spectrum S(ω) (ω being angular frequency) when normalized with the zeroth moment m 0 and peak frequency {ie97-1}, contains in addition to the peakness factor {ie97-2} a depth parameter η=(2π m o)1/2/ d ( d being water depth), so the spectrum behavior can be studied for different wave growth stages and water depths.

The physical and compositional properties of dust: what do we really know?

NASA Astrophysics Data System (ADS)

Jones, A.

Many things in current interstellar dust studies are taken as well understood givens by much of the community. For example, it is widely held that interstellar dust is made up of only three components, i.e., “astronomical silicates”, graphite and polycyclic aromatic hydrocarbons, and that our understanding of these is now complete and sufficient enough to interpret astronomical observations of dust in galaxies. To zeroth order this is a reasonable approximation. However, while these “three pillars” of dust modelling have been useful in advancing our understanding over the last few decades, it is now apparent that they are insufficient to explain the observed evolution of the dust properties from one region to another. Thus, it is time to abandon the “three pillars” approach and to seek more physically-realistic interstellar dust analogues. The analysis of the pre-solar grains extracted from meteorites, interplanetary dust particles and from the Stardust mission, and the interpretation of x-ray scattering and absorption observations, supports the view that our current view of the interstellar dust composition(s) is indeed too naïve. The aim of this review is to point out where our current views are rather secure and, perhaps more importantly, where they are far from secure and we must re-think our ideas. To this aim ten aspects of interstellar dust will be scrutinised and re-evaluated in terms of their validity within the current observational, experimental, modelling and theoretical constraints. It is concluded from this analysis that we really do need to re-assess many of the fundamental assumptions relating to what we think we really do ‘know’ about interstellar dust. In particular, it is clear that unravelling the nature dust evolution in the interstellar medium is perhaps the key to significantly advancing our current understanding of interstellar dust. For example, the dust in the diffuse interstellar medium, molecular clouds, photo-dissociation regions and HII regions is not exactly the same but exhibits important evolution within and between these different regions. An understanding of these evolutionary and regional variations exhibited by dust is now critical.

Multinuclear Solid-State Magnetic Resonance as a Sensitive Probe of Structural Changes upon the Occurrence of Halogen Bonding in Co-crystals.

PubMed

Widdifield, Cory M; Cavallo, Gabriella; Facey, Glenn A; Pilati, Tullio; Lin, Jingxiang; Metrangolo, Pierangelo; Resnati, Giuseppe; Bryce, David L

2013-09-02

Although the understanding of intermolecular interactions, such as hydrogen bonding, is relatively well-developed, many additional weak interactions work both in tandem and competitively to stabilize a given crystal structure. Due to a wide array of potential applications, a substantial effort has been invested in understanding the halogen bond. Here, we explore the utility of multinuclear ((13)C, (14/15)N, (19)F, and (127)I) solid-state magnetic resonance experiments in characterizing the electronic and structural changes which take place upon the formation of five halogen-bonded co-crystalline product materials. Single-crystal X-ray diffraction (XRD) structures of three novel co-crystals which exhibit a 1:1 stoichiometry between decamethonium diiodide (i.e., [(CH3)3N(+)(CH2)10N(+)(CH3)3][2 I(-)]) and different para-dihalogen-substituted benzene moieties (i.e., p-C6X2Y4, X=Br, I; Y=H, F) are presented. (13)C and (15)N NMR experiments carried out on these and related systems validate sample purity, but also serve as indirect probes of the formation of a halogen bond in the co-crystal complexes in the solid state. Long-range changes in the electronic environment, which manifest through changes in the electric field gradient (EFG) tensor, are quantitatively measured using (14)N NMR spectroscopy, with a systematic decrease in the (14)N quadrupolar coupling constant (CQ) observed upon halogen bond formation. Attempts at (127)I solid-state NMR spectroscopy experiments are presented and variable-temperature (19)F NMR experiments are used to distinguish between dynamic and static disorder in selected product materials, which could not be conclusively established using solely XRD. Quantum chemical calculations using the gauge-including projector augmented-wave (GIPAW) or relativistic zeroth-order regular approximation (ZORA) density functional theory (DFT) approaches complement the experimental NMR measurements and provide theoretical corroboration for the changes in NMR parameters observed upon the formation of a halogen bond. Copyright © 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim.

Resolution-of-identity stochastic time-dependent configuration interaction for dissipative electron dynamics in strong fields.

PubMed

Klinkusch, Stefan; Tremblay, Jean Christophe

2016-05-14

In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electron ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN.

Resolution-of-identity stochastic time-dependent configuration interaction for dissipative electron dynamics in strong fields

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

Klinkusch, Stefan; Tremblay, Jean Christophe

In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electronmore » ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN.« less

Lunar orbiting microwave beam power system

NASA Technical Reports Server (NTRS)

Fay, Edgar H.; Cull, Ronald C.

1990-01-01

A microwave beam power system using lunar orbiting solar powered satellite(s) and surface rectenna(s) was investigated as a possible energy source for the Moon's surface. The concept has the potential of reduced system mass by placing the power source in orbit. This can greatly reduce and/or eliminate the 14 day energy storage requirement of a lunar surface solar system. Also propellants required to de-orbit to the surface are greatly reduced. To determine the practicality of the concept and the most important factors, a zero-th order feasibility analysis was performed. Three different operational scenarios employing state of the art technology and forecasts for two different sets of advanced technologies were investigated. To reduce the complexity of the problem, satellite(s) were assumed in circular equatorial orbits around the Moon, supplying continuous power to a single equatorial base through a fixed horizontal rectenna on the surface. State of the art technology yielded specific masses greater than 2500 kg/kw, well above projections for surface systems. Using advanced technologies the specific masses are on the order of 100 kg/kw which is within the range of projections for surface nuclear (20 kg/kw) and solar systems (500 kg/kw). Further studies examining optimization of the scenarios, other technologies such as lasers transmitters and nuclear sources, and operational issues such as logistics, maintenance and support are being carried out to support the Space Exploration Initiative (SEI) to the Moon and Mars.

A finite-element-based perturbation model for the rotordynamic analysis of shrouded pump impellers: Part 2: User's guide

NASA Technical Reports Server (NTRS)

Baskharone, Erian A.

1993-01-01

This report describes the computational steps involved in executing a finite-element-based perturbation model for computing the rotor dynamic coefficients of a shrouded pump impeller or a simple seal. These arise from the fluid/rotor interaction in the clearance gap. In addition to the sample cases, the computational procedure also applies to a separate category of problems referred to as the 'seal-like' category. The problem, in this case, concerns a shrouded impeller, with the exception that the secondary, or leakage, passage is totally isolated from the primary-flow passage. The difference between this and the pump problem is that the former is analytically of the simple 'seal-like' configuration, with two (inlet and exit) flow-permeable stations, while the latter constitutes a double-entry / double-discharge flow problem. In all cases, the problem is that of a rotor clearance gap. The problem here is that of a rotor excitation in the form of a cylindrical whirl around the housing centerline for a smooth annular seal. In its centered operation mode, the rotor is assumed to give rise to an axisymmetric flow field in the clearance gap. As a result, problems involving longitudinal or helical grooves, in the rotor or housing surfaces, go beyond the code capabilities. Discarding, for the moment, the pre- and post-processing phases, the bulk of the computational procedure consists of two main steps. The first is aimed at producing the axisymmetric 'zeroth-order' flow solution in the given flow domain. Detailed description of this problem, including the flow-governing equations, turbulence closure, boundary conditions, and the finite-element formulation, was covered by Baskharone and Hensel. The second main step is where the perturbation model is implemented, with the input being the centered-rotor 'zeroth-order' flow solution and a prescribed whirl frequency ratio (whirl frequency divided by the impeller speed). The computational domain, in the latter case, is treated as three dimensional, with the number of computational planes in the circumferential direction being specified a priori. The reader is reminded that the deformations in the finite elements are all infinitesimally small because the rotor eccentricity itself is a virtual displacement. This explains why we have generically termed the perturbation model the 'virtually' deformable finite-element category. The primary outcome of implementing the perturbation model is the tangential and radial components, F(sub theta)(sup *) and F(sub r)(sup *) of the fluid-exerted force on the rotor surface due to the whirling motion. Repetitive execution of the perturbation model subprogram over a sufficient range of whirl frequency ratios, and subsequent interpolation of these fluid forces, using the least-square method, finally enable the user to compute the impeller rotor dynamic coefficients of the fluid/rotor interaction. These are the direct and cross-coupled stiffness, damping, and inertia effects of the fluid/rotor interaction.

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

Broda, Jill Terese

The neutron flux across the nuclear reactor core is of interest to reactor designers and others. The diffusion equation, an integro-differential equation in space and energy, is commonly used to determine the flux level. However, the solution of a simplified version of this equation when automated is very time consuming. Since the flux level changes with time, in general, this calculation must be made repeatedly. Therefore solution techniques that speed the calculation while maintaining accuracy are desirable. One factor that contributes to the solution time is the spatial flux shape approximation used. It is common practice to use the samemore » order flux shape approximation in each energy group even though this method may not be the most efficient. The one-dimensional, two-energy group diffusion equation was solved, for the node average flux and core k-effective, using two sets of spatial shape approximations for each of three reactor types. A fourth-order approximation in both energy groups forms the first set of approximations used. The second set used combines a second-order approximation with a fourth-order approximation in energy group two. Comparison of the results from the two approximation sets show that the use of a different order spatial flux shape approximation results in considerable loss in accuracy for the pressurized water reactor modeled. However, the loss in accuracy is small for the heavy water and graphite reactors modeled. The use of different order approximations in each energy group produces mixed results. Further investigation into the accuracy and computing time is required before any quantitative advantage of the use of the second-order approximation in energy group one and the fourth-order approximation in energy group two can be determined.« less

EIGENVECTOR-BASED CENTRALITY MEASURES FOR TEMPORAL NETWORKS*

PubMed Central

TAYLOR, DANE; MYERS, SEAN A.; CLAUSET, AARON; PORTER, MASON A.; MUCHA, PETER J.

2017-01-01

Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvector-based centrality. We consider a temporal network with N nodes as a sequence of T layers that describe the network during different time windows, and we couple centrality matrices for the layers into a supra-centrality matrix of size NT × NT whose dominant eigenvector gives the centrality of each node i at each time t. We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node i and the time layer t. We also introduce the concepts of marginal and conditional centralities, which facilitate the study of centrality trajectories over time. We find that the strength of coupling between layers is important for determining multiscale properties of centrality, such as localization phenomena and the time scale of centrality changes. In the strong-coupling regime, we derive expressions for time-averaged centralities, which are given by the zeroth-order terms of a singular perturbation expansion. We also study first-order terms to obtain first-order-mover scores, which concisely describe the magnitude of nodes’ centrality changes over time. As examples, we apply our method to three empirical temporal networks: the United States Ph.D. exchange in mathematics, costarring relationships among top-billed actors during the Golden Age of Hollywood, and citations of decisions from the United States Supreme Court. PMID:29046619

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.

Compton Scattering by Static and Moving Media. Part 1; The Transfer Equation and its Moments

NASA Technical Reports Server (NTRS)

Psaltis, Dimitrios; Lamb, Frederick K.

1997-01-01

Compton scattering of photons by nonrelativistic particles is thought to play an important role in forming the radiation spectrum of many astrophysical systems. Here we derive the time-dependent photon kinetic equation that describes spontaneous and induced Compton scattering, as well as absorption and emission by static and moving media, the corresponding radiative transfer equation, and their zeroth and first angular moments, both in the system frame and in the frame comoving with the medium. We show that it is necessary to use the correct relativistic differential scattering cross section in order to obtain a photon kinetic equation that is correct to first order in Epsilon/m(sub e), T(sub e)/m(sub e), and V, where Epsilon is the photon energy, T(sub e) and m(sub e) are the electron temperature and rest mass, and V is the electron bulk velocity in units of the speed of light. We also demonstrate that the terms in the radiative transfer equation that are second order in V should usually be retained, because if the radiation energy density is sufficiently large, compared to the radiation flux, the effects of bulk Comptonization described by the terms that are second order in V can be as important as the effects described by the terms that are first order in V, even when V is small. The system- and fluid-frame equations that we derive are correct to first order in Epsilon/m(sub e). Our system-frame equations, which are correct to second order in V, may be used when V is not too large. Our fluid-frame equations, which are exact in V, may be used when V approaches 1. Both sets of equations are valid for systems of arbitrary optical depth and can therefore be used in both the free-streaming and diffusion regimes. We demonstrate that Comptonization by the electron bulk motion occurs whether or not the radiation field is isotropic or the bulk flow converges and that it is more important than thermal Comptonization if V(sup 2) is greater than 3T(sub e)/m(sub e).

Fourier decomposition of polymer orientation in large-amplitude oscillatory shear flow

DOE PAGES

Giacomin, A. J.; Gilbert, P. H.; Schmalzer, A. M.

2015-03-19

In our previous work, we explored the dynamics of a dilute suspension of rigid dumbbells as a model for polymeric liquids in large-amplitude oscillatory shear flow, a flow experiment that has gained a significant following in recent years. We chose rigid dumbbells since these are the simplest molecular model to give higher harmonics in the components of the stress response. We derived the expression for the dumbbell orientation distribution, and then we used this function to calculate the shear stress response, and normal stress difference responses in large-amplitude oscillatory shear flow. In this paper, we deepen our understanding of themore » polymer motion underlying large-amplitude oscillatory shear flow by decomposing the orientation distribution function into its first five Fourier components (the zeroth, first, second, third, and fourth harmonics). We use three-dimensional images to explore each harmonic of the polymer motion. Our analysis includes the three most important cases: (i) nonlinear steady shear flow (where the Deborah number λω is zero and the Weissenberg number λγ 0 is above unity), (ii) nonlinear viscoelasticity (where both λω and λγ 0 exceed unity), and (iii) linear viscoelasticity (where λω exceeds unity and where λγ 0 approaches zero). We learn that the polymer orientation distribution is spherical in the linear viscoelastic regime, and otherwise tilted and peanut-shaped. We find that the peanut-shaping is mainly caused by the zeroth harmonic, and the tilting, by the second. The first, third, and fourth harmonics of the orientation distribution make only slight contributions to the overall polymer motion.« less

Thermodynamic laws in isolated systems.

PubMed

Hilbert, Stefan; Hänggi, Peter; Dunkel, Jörn

2014-12-01

The recent experimental realization of exotic matter states in isolated quantum systems and the ensuing controversy about the existence of negative absolute temperatures demand a careful analysis of the conceptual foundations underlying microcanonical thermostatistics. Here we provide a detailed comparison of the most commonly considered microcanonical entropy definitions, focusing specifically on whether they satisfy or violate the zeroth, first, and second laws of thermodynamics. Our analysis shows that, for a broad class of systems that includes all standard classical Hamiltonian systems, only the Gibbs volume entropy fulfills all three laws simultaneously. To avoid ambiguities, the discussion is restricted to exact results and analytically tractable examples.

Classical and Quantum Thermal Physics

NASA Astrophysics Data System (ADS)

Prasad, R.

2016-11-01

List of figures; List of tables; Preface; Acknowledgement; Dedication; 1. The kinetic theory of gases; 2. Ideal to real gas, viscosity, conductivity and diffusion; 3. Thermodynamics: definitions and Zeroth law; 4. First Law of Thermodynamics and some of its applications; 5. Second Law of Thermodynamics and some of its applications; 6. TdS equations and their applications; 7. Thermodynamic functions, potentials, Maxwell equations, the Third Law and equilibrium; 8. Some applications of thermodynamics to problems of physics and engineering; 9. Application of thermodynamics to chemical reactions; 10. Quantum thermodynamics; 11. Some applications of quantum thermodynamics; 12. Introduction to the thermodynamics of irreversible processes; Index.

The second laws of quantum thermodynamics.

PubMed

Brandão, Fernando; Horodecki, Michał; Ng, Nelly; Oppenheim, Jonathan; Wehner, Stephanie

2015-03-17

The second law of thermodynamics places constraints on state transformations. It applies to systems composed of many particles, however, we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are approximately cyclic, the second law for microscopic systems takes on a different form compared to the macroscopic scale, imposing not just one constraint on state transformations, but an entire family of constraints. We find a family of free energies which generalize the traditional one, and show that they can never increase. The ordinary second law relates to one of these, with the remainder imposing additional constraints on thermodynamic transitions. We find three regimes which determine which family of second laws govern state transitions, depending on how cyclic the process is. In one regime one can cause an apparent violation of the usual second law, through a process of embezzling work from a large system which remains arbitrarily close to its original state. These second laws are relevant for small systems, and also apply to individual macroscopic systems interacting via long-range interactions. By making precise the definition of thermal operations, the laws of thermodynamics are unified in this framework, with the first law defining the class of operations, the zeroth law emerging as an equivalence relation between thermal states, and the remaining laws being monotonicity of our generalized free energies.

The second laws of quantum thermodynamics

PubMed Central

Brandão, Fernando; Horodecki, Michał; Ng, Nelly; Oppenheim, Jonathan; Wehner, Stephanie

2015-01-01

The second law of thermodynamics places constraints on state transformations. It applies to systems composed of many particles, however, we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are approximately cyclic, the second law for microscopic systems takes on a different form compared to the macroscopic scale, imposing not just one constraint on state transformations, but an entire family of constraints. We find a family of free energies which generalize the traditional one, and show that they can never increase. The ordinary second law relates to one of these, with the remainder imposing additional constraints on thermodynamic transitions. We find three regimes which determine which family of second laws govern state transitions, depending on how cyclic the process is. In one regime one can cause an apparent violation of the usual second law, through a process of embezzling work from a large system which remains arbitrarily close to its original state. These second laws are relevant for small systems, and also apply to individual macroscopic systems interacting via long-range interactions. By making precise the definition of thermal operations, the laws of thermodynamics are unified in this framework, with the first law defining the class of operations, the zeroth law emerging as an equivalence relation between thermal states, and the remaining laws being monotonicity of our generalized free energies. PMID:25675476

Construction and accuracy of partial differential equation approximations to the chemical master equation.

PubMed

Grima, Ramon

2011-11-01

The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion.

Prospects for Dating the South Pole-Aitken Basin through Impact-Melt Rock Samples

NASA Technical Reports Server (NTRS)

Cohen, B. A.; Coker, R. F.; Petro, N. E.

2016-01-01

Much of the present debate about the ages of the nearside basins arises because of the difficulty in understanding the relationship of recovered samples to their parent basin. The Apollo breccias are from basin ejecta formations, which are ballistically-emplaced distal deposits that have mixed provenances. The Nectaris, Imbrium, and Serenitatis basins all have mare-basalt fill obscuring their original melt sheets, so geochemical ties are indirect. Though the geological processes acting to vertically and laterally mix materials into regolith are the same as at the Apollo sites, the SPA interior is a fundamentally different geologic setting than the Apollo sites. The South Pole-Aitken basin was likely filled by a large impact melt sheet, possibly differentiated into cumulate horizons. It is on this distinctive melt sheet that the regolith has formed, somewhat diluting but not erasing the prominent geochemical signature seen from orbital assets. By analogy to the Apollo 16 site, a zeroth-order expectation is that bulk samples taken from regolith within SPA will contain abundant samples gardened from the SPA melt sheet. However, questions persist as to whether the SPA melt sheet has been so extensively contaminated with foreign ejecta that a simple robotic scoop sample of such regolith would be unlikely to yield the age of the basin.

Comments on baseline correction of digital strong-motion data: Examples from the 1999 Hector Mine, California, earthquake

USGS Publications Warehouse

Boore, D.M.; Stephens, C.D.; Joyner, W.B.

2002-01-01

Residual displacements for large earthquakes can sometimes be determined from recordings on modern digital instruments, but baseline offsets of unknown origin make it difficult in many cases to do so. To recover the residual displacement, we suggest tailoring a correction scheme by studying the character of the velocity obtained by integration of zeroth-order-corrected acceleration and then seeing if the residual displacements are stable when the various parameters in the particular correction scheme are varied. For many seismological and engineering purposes, however, the residual displacement are of lesser importance than ground motions at periods less than about 20 sec. These ground motions are often recoverable with simple baseline correction and low-cut filtering. In this largely empirical study, we illustrate the consequences of various correction schemes, drawing primarily from digital recordings of the 1999 Hector Mine, California, earthquake. We show that with simple processing the displacement waveforms for this event are very similar for stations separated by as much as 20 km. We also show that a strong pulse on the transverse component was radiated from the Hector Mine earthquake and propagated with little distortion to distances exceeding 170 km; this pulse leads to large response spectral amplitudes around 10 sec.

Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid.

PubMed

Mitri, Farid G

2015-10-01

Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure (θ = π) in the near field and the backscattering form function in the far field for both prolate and oblate spheroids are presented and discussed, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle of the Bessel beam, and the dimensionless frequency. The plots display periodic oscillations (versus the dimensionless frequency) because of the interference of specularly reflected waves in the backscattering direction with circumferential Franz' waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3-D directivity patterns illustrate the near- and far-field axisymmetric scattering. Investigations in underwater acoustics, particle levitation, scattering, and the detection of submerged elongated objects and other related applications utilizing Bessel waves would benefit from the results of the present study.

The multi-reference retaining the excitation degree perturbation theory: A size-consistent, unitary invariant, and rapidly convergent wavefunction based ab initio approach

NASA Astrophysics Data System (ADS)

Fink, Reinhold F.

2009-02-01

The retaining the excitation degree (RE) partitioning [R.F. Fink, Chem. Phys. Lett. 428 (2006) 461(20 September)] is reformulated and applied to multi-reference cases with complete active space (CAS) reference wave functions. The generalised van Vleck perturbation theory is employed to set up the perturbation equations. It is demonstrated that this leads to a consistent and well defined theory which fulfils all important criteria of a generally applicable ab initio method: The theory is proven numerically and analytically to be size-consistent and invariant with respect to unitary orbital transformations within the inactive, active and virtual orbital spaces. In contrast to most previously proposed multi-reference perturbation theories the necessary condition for a proper perturbation theory to fulfil the zeroth order perturbation equation is exactly satisfied with the RE partitioning itself without additional projectors on configurational spaces. The theory is applied to several excited states of the benchmark systems CH2 , SiH2 , and NH2 , as well as to the lowest states of the carbon, nitrogen and oxygen atoms. In all cases comparisons are made with full configuration interaction results. The multi-reference (MR)-RE method is shown to provide very rapidly converging perturbation series. Energy differences between states of similar configurations converge even faster.

Engineering the on-axis intensity of Bessel beam by a feedback tuning loop

NASA Astrophysics Data System (ADS)

Li, Runze; Yu, Xianghua; Yang, Yanlong; Peng, Tong; Yao, Baoli; Zhang, Chunmin; Ye, Tong

2018-02-01

The Bessel beam belongs to a typical class of non-diffractive optical fields that are characterized by their invariant focal profiles along the propagation direction. However, ideal Bessel beams only rigorously exist in theory; Bessel beams generated in the lab are quasi-Bessel beams with finite focal extensions and varying intensity profiles along the propagation axis. The ability to engineer the on-axis intensity profile to the desired shape is essential for many applications. Here we demonstrate an iterative optimization-based approach to engineering the on-axis intensity of Bessel beams. The genetic algorithm is used to demonstrate this approach. Starting with a traditional axicon phase mask, in the design process, the computed on-axis beam profile is fed into a feedback tuning loop of an iterative optimization process, which searches for an optimal radial phase distribution that can generate a generalized Bessel beam with the desired onaxis intensity profile. The experimental implementation involves a fine-tuning process that adjusts the originally targeted profile so that the optimization process can optimize the phase mask to yield an improved on-axis profile. Our proposed method has been demonstrated in engineering several zeroth-order Bessel beams with customized on-axis profiles. High accuracy and high energy throughput merit its use in many applications.

Burgers Vector Analysis of Vertical Dislocations in Ge Crystals by Large-Angle Convergent Beam Electron Diffraction.

PubMed

Groiss, Heiko; Glaser, Martin; Marzegalli, Anna; Isa, Fabio; Isella, Giovanni; Miglio, Leo; Schäffler, Friedrich

2015-06-01

By transmission electron microscopy with extended Burgers vector analyses, we demonstrate the edge and screw character of vertical dislocations (VDs) in novel SiGe heterostructures. The investigated pillar-shaped Ge epilayers on prepatterned Si(001) substrates are an attempt to avoid the high defect densities of lattice mismatched heteroepitaxy. The Ge pillars are almost completely strain-relaxed and essentially defect-free, except for the rather unexpected VDs. We investigated both pillar-shaped and unstructured Ge epilayers grown either by molecular beam epitaxy or by chemical vapor deposition to derive a general picture of the underlying dislocation mechanisms. For the Burgers vector analysis we used a combination of dark field imaging and large-angle convergent beam electron diffraction (LACBED). With LACBED simulations we identify ideally suited zeroth and second order Laue zone Bragg lines for an unambiguous determination of the three-dimensional Burgers vectors. By analyzing dislocation reactions we confirm the origin of the observed types of VDs, which can be efficiently distinguished by LACBED. The screw type VDs are formed by a reaction of perfect 60° dislocations, whereas the edge types are sessile dislocations that can be formed by cross-slips and climbing processes. The understanding of these origins allows us to suggest strategies to avoid VDs.

Using the Chebychev expansion in quantum transport calculations

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

Popescu, Bogdan; Rahman, Hasan; Kleinekathöfer, Ulrich, E-mail: u.kleinekathoefer@jacobs-university.de

2015-04-21

Irradiation by laser pulses and a fluctuating surrounding liquid environment can, for example, lead to time-dependent effects in the transport through molecular junctions. From the theoretical point of view, time-dependent theories of quantum transport are still challenging. In one of these existing transport theories, the energy-dependent coupling between molecule and leads is decomposed into Lorentzian functions. This trick has successfully been combined with quantum master approaches, hierarchical formalisms, and non-equilibrium Green’s functions. The drawback of this approach is, however, its serious limitation to certain forms of the molecule-lead coupling and to higher temperatures. Tian and Chen [J. Chem. Phys. 137,more » 204114 (2012)] recently employed a Chebychev expansion to circumvent some of these latter problems. Here, we report on a similar approach also based on the Chebychev expansion but leading to a different set of coupled differential equations using the fact that a derivative of a zeroth-order Bessel function can again be given in terms of Bessel functions. Test calculations show the excellent numerical accuracy and stability of the presented formalism. The time span for which this Chebychev expansion scheme is valid without any restrictions on the form of the spectral density or temperature can be determined a priori.« less

Improved Resolution Optical Time Stretch Imaging Based on High Efficiency In-Fiber Diffraction.

PubMed

Wang, Guoqing; Yan, Zhijun; Yang, Lei; Zhang, Lin; Wang, Chao

2018-01-12

Most overlooked challenges in ultrafast optical time stretch imaging (OTSI) are sacrificed spatial resolution and higher optical loss. These challenges are originated from optical diffraction devices used in OTSI, which encode image into spectra of ultrashort optical pulses. Conventional free-space diffraction gratings, as widely used in existing OTSI systems, suffer from several inherent drawbacks: limited diffraction efficiency in a non-Littrow configuration due to inherent zeroth-order reflection, high coupling loss between free-space gratings and optical fibers, bulky footprint, and more importantly, sacrificed imaging resolution due to non-full-aperture illumination for individual wavelengths. Here we report resolution-improved and diffraction-efficient OTSI using in-fiber diffraction for the first time to our knowledge. The key to overcome the existing challenges is a 45° tilted fiber grating (TFG), which serves as a compact in-fiber diffraction device offering improved diffraction efficiency (up to 97%), inherent compatibility with optical fibers, and improved imaging resolution owning to almost full-aperture illumination for all illumination wavelengths. 50 million frames per second imaging of fast moving object at 46 m/s with improved imaging resolution has been demonstrated. This conceptually new in-fiber diffraction design opens the way towards cost-effective, compact and high-resolution OTSI systems for image-based high-throughput detection and measurement.

Performance of a double tilted-Rowland-spectrometer on Arcus

NASA Astrophysics Data System (ADS)

Günther, Hans M.; Cheimets, P. N.; Heilmann, R. K.; Smith, R. K.

2017-08-01

Spectroscopy of soft X-rays is an extremely powerful tool to understand the physics of the hot plasma in the universe but in many cases, such as kinematic properties of stellar emission lines or weak absorption features, we have reached the limits of current instrumentation. Critical-angle transmission (CAT) gratings blaze the dispersed spectra into high orders and also offer a high throughput. We present detailed ray-traces for the Arcus mission, which promises an effective area > 0.5 m2 and resolving power > 2500 in the soft X-rays. The mirror consists of Athena-like silicon pore optics (SPOs) arranged in four petals. Each petal spans an azimuth of about 30 degrees and thus offers a point-spread function that is significantly narrower in one dimension than a full mirror would provide. The four channels are split into two pairs, where each pair has its own optical axis. For each pair, CAT gratings are arranged on a tilted Rowland torus and the two separate tori are positioned to overlap in such a way that the dispersed spectra from both pairs can be imaged onto a common set of CCD detectors, while at the same time keeping the requirement of the spectroscopic focus. Our ray-traces show that a set of 16 CCDs is sufficient to cover both zeroths orders and over 90% of the dispersed signal. We study the impact of misalignment, finite size of components, and spacecraft jitter on the spectral resolution and effective area and prove that the design achieves R > 4000 even in the presence of these non-ideal effects.

Inverse analysis and regularisation in conditional source-term estimation modelling

NASA Astrophysics Data System (ADS)

Labahn, Jeffrey W.; Devaud, Cecile B.; Sipkens, Timothy A.; Daun, Kyle J.

2014-05-01

Conditional Source-term Estimation (CSE) obtains the conditional species mass fractions by inverting a Fredholm integral equation of the first kind. In the present work, a Bayesian framework is used to compare two different regularisation methods: zeroth-order temporal Tikhonov regulatisation and first-order spatial Tikhonov regularisation. The objectives of the current study are: (i) to elucidate the ill-posedness of the inverse problem; (ii) to understand the origin of the perturbations in the data and quantify their magnitude; (iii) to quantify the uncertainty in the solution using different priors; and (iv) to determine the regularisation method best suited to this problem. A singular value decomposition shows that the current inverse problem is ill-posed. Perturbations to the data may be caused by the use of a discrete mixture fraction grid for calculating the mixture fraction PDF. The magnitude of the perturbations is estimated using a box filter and the uncertainty in the solution is determined based on the width of the credible intervals. The width of the credible intervals is significantly reduced with the inclusion of a smoothing prior and the recovered solution is in better agreement with the exact solution. The credible intervals for temporal and spatial smoothing are shown to be similar. Credible intervals for temporal smoothing depend on the solution from the previous time step and a smooth solution is not guaranteed. For spatial smoothing, the credible intervals are not dependent upon a previous solution and better predict characteristics for higher mixture fraction values. These characteristics make spatial smoothing a promising alternative method for recovering a solution from the CSE inversion process.

Modeling of the Earth's gravity field using the New Global Earth Model (NEWGEM)

NASA Technical Reports Server (NTRS)

Kim, Yeong E.; Braswell, W. Danny

1989-01-01

Traditionally, the global gravity field was described by representations based on the spherical harmonics (SH) expansion of the geopotential. The SH expansion coefficients were determined by fitting the Earth's gravity data as measured by many different methods including the use of artificial satellites. As gravity data have accumulated with increasingly better accuracies, more of the higher order SH expansion coefficients were determined. The SH representation is useful for describing the gravity field exterior to the Earth but is theoretically invalid on the Earth's surface and in the Earth's interior. A new global Earth model (NEWGEM) (KIM, 1987 and 1988a) was recently proposed to provide a unified description of the Earth's gravity field inside, on, and outside the Earth's surface using the Earth's mass density profile as deduced from seismic studies, elevation and bathymetric information, and local and global gravity data. Using NEWGEM, it is possible to determine the constraints on the mass distribution of the Earth imposed by gravity, topography, and seismic data. NEWGEM is useful in investigating a variety of geophysical phenomena. It is currently being utilized to develop a geophysical interpretation of Kaula's rule. The zeroth order NEWGEM is being used to numerically integrate spherical harmonic expansion coefficients and simultaneously determine the contribution of each layer in the model to a given coefficient. The numerically determined SH expansion coefficients are also being used to test the validity of SH expansions at the surface of the Earth by comparing the resulting SH expansion gravity model with exact calculations of the gravity at the Earth's surface.

First and second order approximations to stage numbers in multicomponent enrichment cascades

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

Scopatz, A.

2013-07-01

This paper describes closed form, Taylor series approximations to the number product stages in a multicomponent enrichment cascade. Such closed form approximations are required when a symbolic, rather than a numeric, algorithm is used to compute the optimal cascade state. Both first and second order approximations were implemented. The first order solution was found to be grossly incorrect, having the wrong functional form over the entire domain. On the other hand, the second order solution shows excellent agreement with the 'true' solution over the domain of interest. An implementation of the symbolic, second order solver is available in the freemore » and open source PyNE library. (authors)« less

Finite-dimensional approximation for optimal fixed-order compensation of distributed parameter systems

NASA Technical Reports Server (NTRS)

Bernstein, Dennis S.; Rosen, I. G.

1988-01-01

In controlling distributed parameter systems it is often desirable to obtain low-order, finite-dimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. This approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for one-dimensional, single-input/single-output, parabolic (heat/diffusion) and hereditary systems using spline-based, Ritz-Galerkin, finite element approximation. Numerical studies indicate convergence of the feedback gains with less than 2 percent performance degradation over full-order LQG controllers for the parabolic system and 10 percent degradation for the hereditary system.

Valley-chiral quantum Hall state in graphene superlattice structure

NASA Astrophysics Data System (ADS)

Tian, H. Y.; Tao, W. W.; Wang, J.; Cui, Y. H.; Xu, N.; Huang, B. B.; Luo, G. X.; Hao, Y. H.

2016-05-01

We theoretically investigate the quantum Hall effect in a graphene superlattice (GS) system, in which the two valleys of graphene are coupled together. In the presence of a perpendicular magnetic field, an ordinary quantum Hall effect is found with the sequence σxy=ν e^2/h(ν=0,+/-1,+/-2,\\cdots) . At the zeroth Hall platform, a valley-chiral Hall state stemming from the single K or K' valley is found and it is localized only on one sample boundary contributing to the longitudinal conductance but not to the Hall conductivity. Our findings may shed light on the graphene-based valleytronics applications.

Unconventional fractional quantum Hall effect in monolayer and bilayer graphene

PubMed Central

Jacak, Janusz; Jacak, Lucjan

2016-01-01

The commensurability condition is applied to determine the hierarchy of fractional fillings of Landau levels in monolayer and in bilayer graphene. The filling rates for fractional quantum Hall effect (FQHE) in graphene are found in the first three Landau levels in one-to-one agreement with the experimental data. The presence of even denominator filling fractions in the hierarchy for FQHE in bilayer graphene is explained. Experimentally observed hierarchy of FQHE in the first and second Landau levels in monolayer graphene and in the zeroth Landau level in bilayer graphene is beyond the conventional composite fermion interpretation but fits to the presented nonlocal topology commensurability condition. PMID:27877866

A comparison of zero-order, first-order, and monod biotransformation models

USGS Publications Warehouse

Bekins, B.A.; Warren, E.; Godsy, E.M.

1998-01-01

Under some conditions, a first-order kinetic model is a poor representation of biodegradation in contaminated aquifers. Although it is well known that the assumption of first-order kinetics is valid only when substrate concentration, S, is much less than the half-saturation constant, K(s), this assumption is often made without verification of this condition. We present a formal error analysis showing that the relative error in the first-order approximation is S/K(S) and in the zero-order approximation the error is K(s)/S. We then examine the problems that arise when the first-order approximation is used outside the range for which it is valid. A series of numerical simulations comparing results of first- and zero-order rate approximations to Monod kinetics for a real data set illustrates that if concentrations observed in the field are higher than K(s), it may better to model degradation using a zero-order rate expression. Compared with Monod kinetics, extrapolation of a first-order rate to lower concentrations under-predicts the biotransformation potential, while extrapolation to higher concentrations may grossly over-predict the transformation rate. A summary of solubilities and Monod parameters for aerobic benzene, toluene, and xylene (BTX) degradation shows that the a priori assumption of first-order degradation kinetics at sites contaminated with these compounds is not valid. In particular, out of six published values of KS for toluene, only one is greater than 2 mg/L, indicating that when toluene is present in concentrations greater than about a part per million, the assumption of first-order kinetics may be invalid. Finally, we apply an existing analytical solution for steady-state one-dimensional advective transport with Monod degradation kinetics to a field data set.A formal error analysis is presented showing that the relative error in the first-order approximation is S/KS and in the zero-order approximation the error is KS/S where S is the substrate concentration and KS is the half-saturation constant. The problems that arise when the first-order approximation is used outside the range for which it is valid are examined. A series of numerical simulations comparing results of first- and zero-order rate approximations to Monod kinetics for a real data set illustrates that if concentrations observed in the field are higher than KS, it may be better to model degradation using a zero-order rate expression.

Solid-state (185/187)Re NMR and GIPAW DFT study of perrhenates and Re2(CO)10: chemical shift anisotropy, NMR crystallography, and a metal-metal bond.

PubMed

Widdifield, Cory M; Perras, Frédéric A; Bryce, David L

2015-04-21

Advances in solid-state nuclear magnetic resonance (SSNMR) methods, such as dynamic nuclear polarization (DNP), intricate pulse sequences, and increased applied magnetic fields, allow for the study of systems which even very recently would be impractical. However, SSNMR methods using certain quadrupolar probe nuclei (i.e., I > 1/2), such as (185/187)Re remain far from fully developed due to the exceedingly strong interaction between the quadrupole moment of these nuclei and local electric field gradients (EFGs). We present a detailed high-field (B0 = 21.1 T) experimental SSNMR study on several perrhenates (KReO4, AgReO4, Ca(ReO4)2·2H2O), as well as ReO3 and Re2(CO)10. We propose solid ReO3 as a new rhenium SSNMR chemical shift standard due to its reproducible and sharp (185/187)Re NMR resonances. We show that for KReO4, previously poorly understood high-order quadrupole-induced effects (HOQIE) on the satellite transitions can be used to measure the EFG tensor asymmetry (i.e., ηQ) to nearly an order-of-magnitude greater precision than competing SSNMR and nuclear quadrupole resonance (NQR) approaches. Samples of AgReO4 and Ca(ReO4)2·2H2O enable us to comment on the effects of counter-ions and hydration upon Re(vii) chemical shifts. Calcium-43 and (185/187)Re NMR tensor parameters allow us to conclude that two proposed crystal structures for Ca(ReO4)2·2H2O, which would be considered as distinct, are in fact the same structure. Study of Re2(CO)10 provides insights into the effects of Re-Re bonding on the rhenium NMR tensor parameters and rhenium oxidation state on the Re chemical shift value. As overtone NQR experiments allowed us to precisely measure the (185/187)Re EFG tensor of Re2(CO)10, we were able to measure rhenium chemical shift anisotropy (CSA) for the first time in a powdered sample. Experimental observations are supported by gauge-including projector augmented-wave (GIPAW) density functional theory (DFT) calculations, with NMR tensor calculations also provided for NH4ReO4, NaReO4 and RbReO4. These calculations are able to reproduce many of the experimental trends in rhenium δiso values and EFG tensor magnitudes. Using KReO4 as a prototypical perrhenate-containing system, we establish a correlation between the tetrahedral shear strain parameter (|ψ|) and the nuclear electric quadrupolar coupling constant (CQ), which enables the refinement of the structure of ND4ReO4. Shortcomings in traditional DFT approaches, even when including relativistic effects via the zeroth-order regular approximation (ZORA), for calculating rhenium NMR tensor parameters are identified for Re2(CO)10.

An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order

PubMed Central

Almeida, Ricardo

2013-01-01

We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve differential equations, and problems of the calculus of variations that depend on fractional derivatives of Marchaud type. PMID:24319382

Second-order singular pertubative theory for gravitational lenses

NASA Astrophysics Data System (ADS)

Alard, C.

2018-03-01

The extension of the singular perturbative approach to the second order is presented in this paper. The general expansion to the second order is derived. The second-order expansion is considered as a small correction to the first-order expansion. Using this approach, it is demonstrated that in practice the second-order expansion is reducible to a first order expansion via a re-definition of the first-order pertubative fields. Even if in usual applications the second-order correction is small the reducibility of the second-order expansion to the first-order expansion indicates a potential degeneracy issue. In general, this degeneracy is hard to break. A useful and simple second-order approximation is the thin source approximation, which offers a direct estimation of the correction. The practical application of the corrections derived in this paper is illustrated by using an elliptical NFW lens model. The second-order pertubative expansion provides a noticeable improvement, even for the simplest case of thin source approximation. To conclude, it is clear that for accurate modelization of gravitational lenses using the perturbative method the second-order perturbative expansion should be considered. In particular, an evaluation of the degeneracy due to the second-order term should be performed, for which the thin source approximation is particularly useful.

Structural Reliability Analysis and Optimization: Use of Approximations

NASA Technical Reports Server (NTRS)

Grandhi, Ramana V.; Wang, Liping

1999-01-01

This report is intended for the demonstration of function approximation concepts and their applicability in reliability analysis and design. Particularly, approximations in the calculation of the safety index, failure probability and structural optimization (modification of design variables) are developed. With this scope in mind, extensive details on probability theory are avoided. Definitions relevant to the stated objectives have been taken from standard text books. The idea of function approximations is to minimize the repetitive use of computationally intensive calculations by replacing them with simpler closed-form equations, which could be nonlinear. Typically, the approximations provide good accuracy around the points where they are constructed, and they need to be periodically updated to extend their utility. There are approximations in calculating the failure probability of a limit state function. The first one, which is most commonly discussed, is how the limit state is approximated at the design point. Most of the time this could be a first-order Taylor series expansion, also known as the First Order Reliability Method (FORM), or a second-order Taylor series expansion (paraboloid), also known as the Second Order Reliability Method (SORM). From the computational procedure point of view, this step comes after the design point identification; however, the order of approximation for the probability of failure calculation is discussed first, and it is denoted by either FORM or SORM. The other approximation of interest is how the design point, or the most probable failure point (MPP), is identified. For iteratively finding this point, again the limit state is approximated. The accuracy and efficiency of the approximations make the search process quite practical for analysis intensive approaches such as the finite element methods; therefore, the crux of this research is to develop excellent approximations for MPP identification and also different approximations including the higher-order reliability methods (HORM) for representing the failure surface. This report is divided into several parts to emphasize different segments of the structural reliability analysis and design. Broadly, it consists of mathematical foundations, methods and applications. Chapter I discusses the fundamental definitions of the probability theory, which are mostly available in standard text books. Probability density function descriptions relevant to this work are addressed. In Chapter 2, the concept and utility of function approximation are discussed for a general application in engineering analysis. Various forms of function representations and the latest developments in nonlinear adaptive approximations are presented with comparison studies. Research work accomplished in reliability analysis is presented in Chapter 3. First, the definition of safety index and most probable point of failure are introduced. Efficient ways of computing the safety index with a fewer number of iterations is emphasized. In chapter 4, the probability of failure prediction is presented using first-order, second-order and higher-order methods. System reliability methods are discussed in chapter 5. Chapter 6 presents optimization techniques for the modification and redistribution of structural sizes for improving the structural reliability. The report also contains several appendices on probability parameters.

Combination of the pair density approximation and the Takahashi–Imada approximation for path integral Monte Carlo simulations

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

Zillich, Robert E., E-mail: robert.zillich@jku.at

2015-11-15

We construct an accurate imaginary time propagator for path integral Monte Carlo simulations for heterogeneous systems consisting of a mixture of atoms and molecules. We combine the pair density approximation, which is highly accurate but feasible only for the isotropic interactions between atoms, with the Takahashi–Imada approximation for general interactions. We present finite temperature simulations results for energy and structure of molecules–helium clusters X{sup 4}He{sub 20} (X=HCCH and LiH) which show a marked improvement over the Trotter approximation which has a 2nd-order time step bias. We show that the 4th-order corrections of the Takahashi–Imada approximation can also be applied perturbativelymore » to a 2nd-order simulation.« less

An approximation technique for predicting the transient response of a second order nonlinear equation

NASA Technical Reports Server (NTRS)

Laurenson, R. M.; Baumgarten, J. R.

1975-01-01

An approximation technique has been developed for determining the transient response of a nonlinear dynamic system. The nonlinearities in the system which has been considered appear in the system's dissipation function. This function was expressed as a second order polynomial in the system's velocity. The developed approximation is an extension of the classic Kryloff-Bogoliuboff technique. Two examples of the developed approximation are presented for comparative purposes with other approximation methods.

Coupled orbit-attitude dynamics and relative state estimation of spacecraft near small Solar System bodies

NASA Astrophysics Data System (ADS)

Misra, Gaurav; Izadi, Maziar; Sanyal, Amit; Scheeres, Daniel

2016-04-01

The effects of dynamical coupling between the rotational (attitude) and translational (orbital) motion of spacecraft near small Solar System bodies is investigated. This coupling arises due to the weak gravity of these bodies, as well as solar radiation pressure. The traditional approach assumes a point-mass spacecraft model to describe the translational motion of the spacecraft, while the attitude motion is considered to be completely decoupled from the translational motion. The model used here to describe the rigid-body spacecraft dynamics includes the non-uniform rotating gravity field of the small body up to second degree and order along with the attitude dependent terms, solar tide, and solar radiation pressure. This model shows that the second degree and order gravity terms due to the small body affect the dynamics of the spacecraft to the same extent as the orbit-attitude coupling due to the primary gravity (zeroth order) term. Variational integrators are used to simulate the dynamics of both the rigid spacecraft and the point mass. The small bodies considered here are modeled after Near-Earth Objects (NEO) 101955 Bennu, and 25143 Itokawa, and are assumed to be triaxial ellipsoids with uniform density. Differences in the numerically obtained trajectories of a rigid spacecraft and a point mass are then compared, to illustrate the impact of the orbit-attitude coupling on spacecraft dynamics in proximity of small bodies. Possible implications on the performance of model-based spacecraft control and on the station-keeping budget, if the orbit-attitude coupling is not accounted for in the model of the dynamics, are also discussed. An almost globally asymptotically stable motion estimation scheme based solely on visual/optical feedback that estimates the relative motion of the asteroid with respect to the spacecraft is also obtained. This estimation scheme does not require a model of the dynamics of the asteroid, which makes it perfectly suited for asteroids whose properties are not well known.

Molecular and Silica-Supported Molybdenum Alkyne Metathesis Catalysts: Influence of Electronics and Dynamics on Activity Revealed by Kinetics, Solid-State NMR, and Chemical Shift Analysis.

PubMed

Estes, Deven P; Gordon, Christopher P; Fedorov, Alexey; Liao, Wei-Chih; Ehrhorn, Henrike; Bittner, Celine; Zier, Manuel Luca; Bockfeld, Dirk; Chan, Ka Wing; Eisenstein, Odile; Raynaud, Christophe; Tamm, Matthias; Copéret, Christophe

2017-12-06

Molybdenum-based molecular alkylidyne complexes of the type [MesC≡Mo{OC(CH 3 ) 3-x (CF 3 ) x } 3 ] (MoF 0 , x = 0; MoF 3 , x = 1; MoF 6 , x = 2; MoF 9 , x = 3; Mes = 2,4,6-trimethylphenyl) and their silica-supported analogues are prepared and characterized at the molecular level, in particular by solid-state NMR, and their alkyne metathesis catalytic activity is evaluated. The 13 C NMR chemical shift of the alkylidyne carbon increases with increasing number of fluorine atoms on the alkoxide ligands for both molecular and supported catalysts but with more shielded values for the supported complexes. The activity of these catalysts increases in the order MoF 0 < MoF 3 < MoF 6 before sharply decreasing for MoF 9 , with a similar effect for the supported systems (MoF 0 ≈ MoF 9 < MoF 6 < MoF 3 ). This is consistent with the different kinetic behavior (zeroth order in alkyne for MoF 9 derivatives instead of first order for the others) and the isolation of stable metallacyclobutadiene intermediates of MoF 9 for both molecular and supported species. Detailed solid-state NMR analysis of molecular and silica-supported metal alkylidyne catalysts coupled with DFT/ZORA calculations rationalize the NMR spectroscopic signatures and discernible activity trends at the frontier orbital level: (1) increasing the number of fluorine atoms lowers the energy of the π*(M≡C) orbital, explaining the more deshielded chemical shift values; it also leads to an increased electrophilicity and higher reactivity for catalysts up to MoF 6 , prior to a sharp decrease in reactivity for MoF 9 due to the formation of stable metallacyclobutadiene intermediates; (2) the silica-supported catalysts are less active than their molecular analogues because they are less electrophilic and dynamic, as revealed by their 13 C NMR chemical shift tensors.

Inferring gene regression networks with model trees

PubMed Central

2010-01-01

Background Novel strategies are required in order to handle the huge amount of data produced by microarray technologies. To infer gene regulatory networks, the first step is to find direct regulatory relationships between genes building the so-called gene co-expression networks. They are typically generated using correlation statistics as pairwise similarity measures. Correlation-based methods are very useful in order to determine whether two genes have a strong global similarity but do not detect local similarities. Results We propose model trees as a method to identify gene interaction networks. While correlation-based methods analyze each pair of genes, in our approach we generate a single regression tree for each gene from the remaining genes. Finally, a graph from all the relationships among output and input genes is built taking into account whether the pair of genes is statistically significant. For this reason we apply a statistical procedure to control the false discovery rate. The performance of our approach, named REGNET, is experimentally tested on two well-known data sets: Saccharomyces Cerevisiae and E.coli data set. First, the biological coherence of the results are tested. Second the E.coli transcriptional network (in the Regulon database) is used as control to compare the results to that of a correlation-based method. This experiment shows that REGNET performs more accurately at detecting true gene associations than the Pearson and Spearman zeroth and first-order correlation-based methods. Conclusions REGNET generates gene association networks from gene expression data, and differs from correlation-based methods in that the relationship between one gene and others is calculated simultaneously. Model trees are very useful techniques to estimate the numerical values for the target genes by linear regression functions. They are very often more precise than linear regression models because they can add just different linear regressions to separate areas of the search space favoring to infer localized similarities over a more global similarity. Furthermore, experimental results show the good performance of REGNET. PMID:20950452

Polarization and propagation characteristics of switchable first-order azimuthally asymmetric beam generated in dual-mode fiber.

PubMed

Khan, Saba N; Chatterjee, Sudip K; Chaudhuri, Partha Roy

2015-02-20

We report here the controlled generation of a linearly polarized first-order azimuthally asymmetric beam (F-AAB) in a dual-mode fiber (DMF) by appropriate superposition of selectively excited zeroth-order vector modes that are doughnut-shaped azimuthally symmetric beams (D-ASBs). We first demonstrate continually switching polarization mode structures having an identical two-lobe intensity profile (i.e., intra-F-AAB conversion). Then, under a distinct launching state, we generate mode structures progressively toggling between the doughnut-shaped profile and two-lobe pattern having dissimilar polarization orientations (i.e., F-AAB to D-ASB conversion). Interestingly, a decentralized elliptical Gaussian beam possessing homogenous spatial polarization is obtained by enhancing the contribution of the fundamental mode (HE₁₁/LP₀₁) in selectively excited F-AAB. A smoothly varying azimuth of the input beam in this situation resulted in redistribution of transverse energy procuring a unique and exciting unconventional two-grain T-polarized beam having mutually orthogonal state of polarization (SOP). All of the above three were achieved under a given set of launching conditions (tilt/offset) of a Gaussian mode (TEM₀₀) devised with changing SOP of the input beam. A strong modulation in the output beam characteristics was also observed with the variation in propagation distance (for a fixed input SOP) owing to the large difference in propagation constants of the participating modes (LP₀₁ and one of the F-AABs). Finally, this particular study led to a design for a low-cost highly sensitive strain measuring device based on tracking the centroid movement of the output intensity pattern. Each of our experimentally observed intensity/polarization distributions is theoretically mapped on a one-to-one basis considering a linear superposition of appropriately excited LP basis modes of the waveguide toward a complete understanding of the polarization and mode propagation in the dual-mode structure.

The column density distribution of hard X-ray radio galaxies

NASA Astrophysics Data System (ADS)

Panessa, F.; Bassani, L.; Landi, R.; Bazzano, A.; Dallacasa, D.; La Franca, F.; Malizia, A.; Venturi, T.; Ubertini, P.

2016-09-01

In order to investigate the role of absorption in active galactic nuclei (AGN) with jets, we have studied the column density distribution of a hard X-ray selected sample of radio galaxies, derived from the INTEGRAL/Imager on Board the Integral Satellite (IBIS) and Swift/The Burst Alert Telescope (BAT) AGN catalogues (˜7-10 per cent of the total AGN population). The 64 radio galaxies have a typical FR II radio morphology and are characterized by high 20-100 keV luminosities (from 1042 to 1046 erg s-1) and high Eddington ratios (log LBol/LEdd typically larger than ˜0.01). The observed fraction of absorbed AGN (NH > 1022 cm-2) is around 40 per cent among the total sample, and ˜75 per cent among type 2 AGN. The majority of obscured AGN are narrow-line objects, while unobscured AGN are broad-line objects, obeying to the zeroth-order predictions of unified models. A significant anti-correlation between the radio core dominance parameter and the X-ray column density is found. The observed fraction of Compton thick AGN is ˜2-3 per cent, in comparison with the 5-7 per cent found in radio-quiet hard X-ray selected AGN. We have estimated the absorption and Compton thick fractions in a hard X-ray sample containing both radio galaxies and non-radio galaxies and therefore affected by the same selection biases. No statistical significant difference was found in the absorption properties of radio galaxies and non-radio galaxies sample. In particular, the Compton thick objects are likely missing in both samples and the fraction of obscured radio galaxies appears to decrease with luminosity as observed in hard X-ray non-radio galaxies.

Effect of a relative phase of waves constituting the initial perturbation and the wave interference on the dynamics of strong-shock-driven Richtmyer-Meshkov flows

NASA Astrophysics Data System (ADS)

Pandian, Arun; Stellingwerf, Robert F.; Abarzhi, Snezhana I.

2017-07-01

While it is a common wisdom that initial conditions influence the evolution of the Richtmyer-Meshkov instability (RMI), the research in this area is focused primarily on the effects of the wavelength and amplitude of the interface perturbation. The information has hitherto largely ignored the influences on RMI dynamics of the relative phase of waves constituting a multiwave initial perturbation and the interference of the perturbation waves. In this work we systematically study the influence of the relative phase and the interference of waves constituting a multiwave initial perturbation on a strong-shock-driven Richtmyer-Meshkov unstable interface separating ideal fluids with contrast densities. We apply group theory analysis and smoothed particle hydrodynamics numerical simulations. For verification and validation of the simulations, qualitative and quantitative comparisons are performed with rigorous zeroth-order, linear, and nonlinear theories as well as with gas dynamics experiments achieving good agreement. For a sample case of a two-wave (two-mode) initial perturbation we select the first-wave amplitude enabling the maximum initial growth rate of the RMI and we vary the second-wave amplitude from 1% to 100% of the first-wave amplitude. We also vary the relative phase of the first and second waves and consider the in-phase, the antiphase and the random-phase cases. We find that the relative phase and the interference of waves are important factors of RMI dynamics influencing qualitatively and quantitatively the symmetry, morphology, and growth rate of the Richtmyer-Meshkov unstable interface, as well as the order and disorder in strong-shock-driven RMI.

Localization and elasticity in entangled polymer liquids as a mesoscopic glass transition

NASA Astrophysics Data System (ADS)

Schweizer, Kenneth

2010-03-01

The reptation-tube model is widely viewed as the correct zeroth order model for entangled linear polymer dynamics under quiescent conditions. Its key ansatz is the existence of a mesoscopic dynamical length scale that prohibits transverse chain motion beyond a tube diameter of order 3-10 nm. However, the theory is phenomenological and lacks a microscopic foundation, and many fundamental questions remain unanswered. These include: (i) where does the confining tube field come from and can it be derived from statistical mechanics? (ii) what is the microscopic origin of the magnitude, and power law scaling with concentration and packing length, of the plateau shear modulus? (iii) is the tube diameter time-dependent? (iv) does the confinement field contribute to elasticity ? (v) do entanglement constraints have a finite strength? Building on our new force-level theories for the dynamical crossover and activated barrier hopping in glassy colloidal suspensions and polymer melts, a first principles self-consistent theory has been developed for entangled polymers. Its basic physical elements, and initial results that address the questions posed above, will be presented. The key idea is that beyond a critical degree of polymerization, the chain connectivity and excluded volume induced intermolecular correlation hole drives temporary localization on an intermediate length scale resulting in a mesoscopic ``ideal kinetic glass transition.'' Large scale isotropic motion is effectively quenched due to the emergence of chain length dependent entropic barriers. However, the barrier height is not infinite, resulting in softening of harmonic localization at large displacements, temporal increase of the confining length scale, and a finite strength of entanglement constraints which can be destroyed by applied stress.

Homogenization of the Brush Problem with a Source Term in L 1

NASA Astrophysics Data System (ADS)

Gaudiello, Antonio; Guibé, Olivier; Murat, François

2017-07-01

We consider a domain which has the form of a brush in 3 D or the form of a comb in 2 D, i.e. an open set which is composed of cylindrical vertical teeth distributed over a fixed basis. All the teeth have a similar fixed height; their cross sections can vary from one tooth to another and are not supposed to be smooth; moreover the teeth can be adjacent, i.e. they can share parts of their boundaries. The diameter of every tooth is supposed to be less than or equal to ɛ, and the asymptotic volume fraction of the teeth (as ɛ tends to zero) is supposed to be bounded from below away from zero, but no periodicity is assumed on the distribution of the teeth. In this domain we study the asymptotic behavior (as ɛ tends to zero) of the solution of a second order elliptic equation with a zeroth order term which is bounded from below away from zero, when the homogeneous Neumann boundary condition is satisfied on the whole of the boundary. First, we revisit the problem where the source term belongs to L 2. This is a classical problem, but our homogenization result takes place in a geometry which is more general that the ones which have been considered before. Moreover we prove a corrector result which is new. Then, we study the case where the source term belongs to L 1. Working in the framework of renormalized solutions and introducing a definition of renormalized solutions for degenerate elliptic equations where only the vertical derivative is involved (such a definition is new), we identify the limit problem and prove a corrector result.

High-Resolution X-Ray Spectroscopy of the Seyfert 2 Galaxy Circinus with Chandra

NASA Technical Reports Server (NTRS)

Sambruna, Rita M.; Netzer, Hagai; Kaspi, Shai; Brandt, W. N.; Chartas, G.; Garmire, G. P.; Nousek, John A.; Weaver, K. A.

2000-01-01

Results from a 60 ks Chandra High Energy Transmission Grating Spectrometer (HETGS) observation of the nearby Seyfert 2 Circinus are presented. The spectrum shows a wealth of emission lines at both soft and hard X-rays, including lines of Ne, Mg, Si, S, Ar, Ca, and Fe, and a prominent Fe K(alpha) line at 6.4 keV. We identify several of the He-like components and measure several of the Lyman lines of the N-like ions. The lines' profiles are unresolved at the limited signal-to-noise ratio of the data. Our analysis of the zeroth-order image in a companion paper constrains the size of the emission region to be 20-60 pc, suggesting that emission within this volume is almost entirely due to the reprocessing of the obscured central source. Here we show that a model containing two distinct components can reproduce almost all the observed properties of this gas. The ionized component can explain the observed intensities of the ionized species, assuming twice-solar composition and an N is proportional r(exp -1.5) density distribution. The neutral component is highly concentrated, well within the 0.8" point source, and is responsible for almost all of the observed K(alpha) (6.4 keV) emission. Circinus seems to be different than Mkn 3 in terms of its gas distribution.

Finding a Hadamard matrix by simulated annealing of spin vectors

NASA Astrophysics Data System (ADS)

Bayu Suksmono, Andriyan

2017-05-01

Reformulation of a combinatorial problem into optimization of a statistical-mechanics system enables finding a better solution using heuristics derived from a physical process, such as by the simulated annealing (SA). In this paper, we present a Hadamard matrix (H-matrix) searching method based on the SA on an Ising model. By equivalence, an H-matrix can be converted into a seminormalized Hadamard (SH) matrix, whose first column is unit vector and the rest ones are vectors with equal number of -1 and +1 called SH-vectors. We define SH spin vectors as representation of the SH vectors, which play a similar role as the spins on Ising model. The topology of the lattice is generalized into a graph, whose edges represent orthogonality relationship among the SH spin vectors. Starting from a randomly generated quasi H-matrix Q, which is a matrix similar to the SH-matrix without imposing orthogonality, we perform the SA. The transitions of Q are conducted by random exchange of {+, -} spin-pair within the SH-spin vectors that follow the Metropolis update rule. Upon transition toward zeroth energy, the Q-matrix is evolved following a Markov chain toward an orthogonal matrix, at which the H-matrix is said to be found. We demonstrate the capability of the proposed method to find some low-order H-matrices, including the ones that cannot trivially be constructed by the Sylvester method.

Numerical investigation and electro-acoustic modeling of measurement methods for the in-duct acoustical source parameters.

PubMed

Jang, Seung-Ho; Ih, Jeong-Guon

2003-02-01

It is known that the direct method yields different results from the indirect (or load) method in measuring the in-duct acoustic source parameters of fluid machines. The load method usually comes up with a negative source resistance, although a fairly accurate prediction of radiated noise can be obtained from any method. This study is focused on the effect of the time-varying nature of fluid machines on the output results of two typical measurement methods. For this purpose, a simplified fluid machine consisting of a reservoir, a valve, and an exhaust pipe is considered as representing a typical periodic, time-varying system and the measurement situations are simulated by using the method of characteristics. The equivalent circuits for such simulations are also analyzed by considering the system as having a linear time-varying source. It is found that the results from the load method are quite sensitive to the change of cylinder pressure or valve profile, in contrast to those from the direct method. In the load method, the source admittance turns out to be predominantly dependent on the valve admittance at the calculation frequency as well as the valve and load admittances at other frequencies. In the direct method, however, the source resistance is always positive and the source admittance depends mainly upon the zeroth order of valve admittance.

Approach for Input Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

NASA Technical Reports Server (NTRS)

Putko, Michele M.; Taylor, Arthur C., III; Newman, Perry A.; Green, Lawrence L.

2002-01-01

An implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for quasi 3-D Euler CFD code is presented. Given uncertainties in statistically independent, random, normally distributed input variables, first- and second-order statistical moment procedures are performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, these moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Modeling the global positioning system signal propagation through the ionosphere

NASA Technical Reports Server (NTRS)

Bassiri, S.; Hajj, G. A.

1992-01-01

Based on realistic modeling of the electron density of the ionosphere and using a dipole moment approximation for the Earth's magnetic field, one is able to estimate the effect of the ionosphere on the Global Positioning System (GPS) signal for a ground user. The lowest order effect, which is on the order of 0.1-100 m of group delay, is subtracted out by forming a linear combination of the dual frequencies of the GPS signal. One is left with second- and third-order effects that are estimated typically to be approximately 0-2 cm and approximately 0-2 mm at zenith, respectively, depending on the geographical location, the time of day, the time of year, the solar cycle, and the relative geometry of the magnetic field and the line of sight. Given the total electron content along a line of sight, the authors derive an approximation to the second-order term which is accurate to approximately 90 percent within the magnetic dipole moment model; this approximation can be used to reduce the second-order term to the millimeter level, thus potentially improving precise positioning in space and on the ground. The induced group delay, or phase advance, due to second- and third-order effects is examined for two ground receivers located at equatorial and mid-latitude regions tracking several GPS satellites.

Axial acoustic radiation force on rigid oblate and prolate spheroids in Bessel vortex beams of progressive, standing and quasi-standing waves.

PubMed

Mitri, F G

2017-02-01

The analysis using the partial-wave series expansion (PWSE) method in spherical coordinates is extended to evaluate the acoustic radiation force experienced by rigid oblate and prolate spheroids centered on the axis of wave propagation of high-order Bessel vortex beams composed of progressive, standing and quasi-standing waves, respectively. A coupled system of linear equations is derived after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid, and solved numerically by matrix inversion after performing a single numerical integration procedure. The system of linear equations depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated but converging PWSEs in the least-squares sense. Numerical results for the radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface, are computed with particular emphasis on the amplitude ratio describing the transition from the progressive to the pure standing waves cases, the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle and order of the Bessel vortex beam, as well as the dimensionless size parameter. A generalized expression for the radiation force function is derived for cases encompassing the progressive, standing and quasi-standing waves of Bessel vortex beams. This expression can be reduced to other types of beams/waves such as the zeroth-order Bessel non-vortex beam or the infinite plane wave case by appropriate selection of the beam parameters. The results for progressive waves reveal a tractor beam behavior, characterized by the emergence of an attractive pulling force acting in opposite direction of wave propagation. Moreover, the transition to the quasi-standing and pure standing wave cases shows the acoustical tweezers behavior in dual-beam Bessel vortex beams. Applications in acoustic levitation, particle manipulation and acousto-fluidics would benefit from the results of the present investigation. Copyright © 2016 Elsevier B.V. All rights reserved.

An analytical technique for approximating unsteady aerodynamics in the time domain

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1980-01-01

An analytical technique is presented for approximating unsteady aerodynamic forces in the time domain. The order of elements of a matrix Pade approximation was postulated, and the resulting polynomial coefficients were determined through a combination of least squares estimates for the numerator coefficients and a constrained gradient search for the denominator coefficients which insures stable approximating functions. The number of differential equations required to represent the aerodynamic forces to a given accuracy tends to be smaller than that employed in certain existing techniques where the denominator coefficients are chosen a priori. Results are shown for an aeroelastic, cantilevered, semispan wing which indicate a good fit to the aerodynamic forces for oscillatory motion can be achieved with a matrix Pade approximation having fourth order numerator and second order denominator polynomials.

The use of fractional orders in the determination of birefringence of highly dispersive materials by the channelled spectrum method

NASA Astrophysics Data System (ADS)

Nagarajan, K.; Shashidharan Nair, C. K.

2007-07-01

The channelled spectrum employing polarized light interference is a very convenient method for the study of dispersion of birefringence. However, while using this method, the absolute order of the polarized light interference fringes cannot be determined easily. Approximate methods are therefore used to estimate the order. One of the approximations is that the dispersion of birefringence across neighbouring integer order fringes is negligible. In this paper, we show how this approximation can cause errors. A modification is reported whereby the error in the determination of absolute fringe order can be reduced using fractional orders instead of integer orders. The theoretical background for this method supported with computer simulation is presented. An experimental arrangement implementing these modifications is described. This method uses a Constant Deviation Spectrometer (CDS) and a Soleil Babinet Compensator (SBC).

Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

NASA Technical Reports Server (NTRS)

Buchert, T.; Melott, A. L.; Weiss, A. G.

1993-01-01

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.

Pseudospectral collocation methods for fourth order differential equations

NASA Technical Reports Server (NTRS)

Malek, Alaeddin; Phillips, Timothy N.

1994-01-01

Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.

Symmetric Positive 4th Order Tensors & Their Estimation from Diffusion Weighted MRI⋆

PubMed Central

Barmpoutis, Angelos; Jian, Bing; Vemuri, Baba C.; Shepherd, Timothy M.

2009-01-01

In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing a 2nd order tensor has been commonly used to approximate the diffusivity function at each lattice point of the DW-MRI data. It is now well known that this 2nd-order approximation fails to approximate complex local tissue structures, such as fibers crossings. In this paper we employ a 4th order symmetric positive semi-definite (PSD) tensor approximation to represent the diffusivity function and present a novel technique to estimate these tensors from the DW-MRI data guaranteeing the PSD property. There have been several published articles in literature on higher order tensor approximations of the diffusivity function but none of them guarantee the positive semi-definite constraint, which is a fundamental constraint since negative values of the diffusivity coefficients are not meaningful. In our methods, we parameterize the 4th order tensors as a sum of squares of quadratic forms by using the so called Gram matrix method from linear algebra and its relation to the Hilbert’s theorem on ternary quartics. This parametric representation is then used in a nonlinear-least squares formulation to estimate the PSD tensors of order 4 from the data. We define a metric for the higher-order tensors and employ it for regularization across the lattice. Finally, performance of this model is depicted on synthetic data as well as real DW-MRI from an isolated rat hippocampus. PMID:17633709

Influence of natural organic matter on fate and transport of silver nanoparticles in saturated porous media: laboratory experiments and modeling

NASA Astrophysics Data System (ADS)

Kanel, Sushil R.; Flory, Jason; Meyerhoefer, Allie; Fraley, Jessica L.; Sizemore, Ioana E.; Goltz, Mark N.

2015-03-01

Understanding the fate and transport of silver nanoparticles (AgNPs) is of importance due to their widespread use and potential harmful effects on humans and the environment. The present study investigates the fate and transport of widely used Creighton AgNPs in saturated porous media. Previous investigations of AgNP transport in the presence of natural organic matter (NOM) report contradictory results regarding how the presence of NOM affected the stability and mobility of AgNPs. In this work, a nonreactive tracer, AgNPs and a mixture of AgNPs and NOM were injected into a background solution (0.01 mM of NaNO3) flowing through laboratory columns packed with water-saturated glass beads to obtain concentration versus time breakthrough curves. Transport of AgNPs in the presence of NOM was simulated with a model that accounted for both reversible and irreversible attachment. Based upon an analysis of the AgNP breakthrough curves, it was found that addition of NOM at concentrations ranging from 1 to 40 mg L-1 resulted in significant decreases in both the zeroth and first moments of the breakthrough curves. These observations may be attributed to NOM promoting AgNP aggregation and irreversible attachment. Raman and surface-enhanced Raman scattering analysis of NOM-AgNP mixtures revealed that a possible interaction of NOM with AgNP occurred through the carboxylic moieties (-COO-) located in the immediate vicinity of the metallic surface. At higher concentrations of NOM, both the zeroth and first moments of the breakthrough curves increased. Based on modeling and the literature, we hypothesize that as the NOM concentration increases, it begins to coat both the AgNPs and the glass beads, leading to a situation where AgNP transport may be described in the same way that transport of a sorbing hydrophobic compound partitioning to an immobile organic phase is typically described, assuming reversible, rate-limited sorption.

Uniformly high-order accurate non-oscillatory schemes, 1

NASA Technical Reports Server (NTRS)

Harten, A.; Osher, S.

1985-01-01

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws was begun. These schemes share many desirable properties with total variation diminishing schemes (TVD), but TVD schemes have at most first order accuracy, in the sense of truncation error, at extreme of the solution. A uniformly second order approximation was constucted, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Antiferromagnetic order and the structural order-disorder transition in the Cd6Ho quasicrystal approximant

NASA Astrophysics Data System (ADS)

Kreyssig, Andreas; Beutier, Guillaume; Hiroto, Takanobu; Kim, Min Gyu; Tucker, Gregory S.; de Boissieu, Marc; Tamura, Ryuji; Goldman, Alan I.

2013-09-01

It has generally been accepted that the orientational ordering of the Cd4 tetrahedron within the Cd6 R quasicrystal approximants is kinetically inhibited for R = Ho, Er, Tm and Lu by steric constraints. Our high-resolution X-ray scattering measurements of the Cd6Ho quasicrystal approximant, however, reveal an abrupt (first-order) transition to a monoclinic structure below T S = 178 K for samples that have 'aged' at room temperature for approximately one year, reopening this question. Using X-ray resonant magnetic scattering at the Ho L 3-edge we have elucidated the nature of the antiferromagnetic ordering below T N = 8.5 K in Cd6Ho. The magnetic Bragg peaks are found at the charge forbidden H + K + L = 2n + 1 positions, referenced to the high-temperature body-centred cubic structure. In general terms, this corresponds to antiferromagnetic arrangements of the Ho moments on adjacent clusters in the unit cell as previously found for Cd6Tb.

Approach for Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

NASA Technical Reports Server (NTRS)

Putko, Michele M.; Newman, Perry A.; Taylor, Arthur C., III; Green, Lawrence L.

2001-01-01

This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1-D Euler CFD (computational fluid dynamics) code. Given uncertainties in statistically independent, random, normally distributed input variables, a first- and second-order statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Cosmological collapse and the improved Zel'dovich approximation.

NASA Astrophysics Data System (ADS)

Salopek, D. S.; Stewart, J. M.; Croudace, K. M.; Parry, J.

Using a general relativistic formulation, the authors show how to compute the higher order terms in the Zel'dovich approximation which describes cosmological collapse. They evolve the 3-metric in a spatial gradient expansion. Their method is an advance over earlier work because it is local at each order. Using the improved Zel'dovich approximation, they compute the epoch of collapse.

Basement-involved faults and deep structures in the West Philippine Basin: constrains from gravity field

NASA Astrophysics Data System (ADS)

Wang, Gang; Jiang, Suhua; Li, Sanzhong; Zhang, Huixuan; Lei, Jianping; Gao, Song; Zhao, Feiyu

2017-06-01

To reveal the basement-involved faults and deep structures of the West Philippine Basin (WPB), the gravitational responses caused by these faults are observed and analyzed based on the latest spherical gravity model: WGM2012 Model. By mapping the free-air and Bouguer gravity anomalies, several main faults and some other linear structures are located and observed in the WPB. Then, by conducting a 2D discrete multi-scale wavelet decomposition, the Bouguer anomalies are decomposed into the first- to eighth-order detail and approximation fields (the first- to eighth-order Details and Approximations). The first- to third-order Details reflect detailed and localized geological information of the crust at different depths, and of which the higher-order reflects gravity field of the deeper depth. The first- to fourth-order Approximations represent the regional gravity fields at different depths of the crust, respectively. The fourth-order Approximation represents the regional gravity fluctuation caused by the density inhomogeneity of Moho interface. Therefore, taking the fourth-order Approximation as input, and adopting Parker-Oldenburg interactive inversion, We calculated the depth of Moho interface in the WPB. Results show that the Moho interface depth in the WPB ranges approximately from 8 to 12 km, indicating that there is typical oceanic crust in the basin. In the Urdaneta Plateau and the Benham Rise, the Moho interface depths are about 14 and 16 km, respectively, which provides a piece of evidence to support that the Banham Rise could be a transitional crust caused by a large igneous province. The second-order vertical derivative and the horizontal derivatives in direction 0° and 90° are computed based on the data of the third-order Detail, and most of the basement-involved faults and structures in the WPB, such as the Central Basin Fault Zone, the Gagua Ridge, the Luzon-Okinawa Fault Zone, and the Mindanao Fault Zone are interpreted by the gravity derivatives.

Atmospheric Turbulence Modeling for Aerospace Vehicles: Fractional Order Fit

NASA Technical Reports Server (NTRS)

Kopasakis, George (Inventor)

2015-01-01

An improved model for simulating atmospheric disturbances is disclosed. A scale Kolmogorov spectral may be scaled to convert the Kolmogorov spectral into a finite energy von Karman spectral and a fractional order pole-zero transfer function (TF) may be derived from the von Karman spectral. Fractional order atmospheric turbulence may be approximated with an integer order pole-zero TF fit, and the approximation may be stored in memory.

Higher-order harmonics of general limited diffraction Bessel beams

NASA Astrophysics Data System (ADS)

Ding, De-Sheng; Huang, Jin-Huang

2016-12-01

In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m-th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. Project supported by the National Natural Science Foundation of China (Grant Nos. 11074038 and 11374051).

Open-Closed Homotopy Algebras and Strong Homotopy Leibniz Pairs Through Koszul Operad Theory

NASA Astrophysics Data System (ADS)

Hoefel, Eduardo; Livernet, Muriel

2012-08-01

Open-closed homotopy algebras (OCHA) and strong homotopy Leibniz pairs (SHLP) were introduced by Kajiura and Stasheff in 2004. In an appendix to their paper, Markl observed that an SHLP is equivalent to an algebra over the minimal model of a certain operad, without showing that the operad is Koszul. In the present paper, we show that both OCHA and SHLP are algebras over the minimal model of the zeroth homology of two versions of the Swiss-cheese operad and prove that these two operads are Koszul. As an application, we show that the OCHA operad is non-formal as a 2-colored operad but is formal as an algebra in the category of 2-collections.

M.S.L.A.P. Modular Spectral Line Analysis Program documentation

NASA Technical Reports Server (NTRS)

Joseph, Charles L.; Jenkins, Edward B.

1991-01-01

MSLAP is a software for analyzing spectra, providing the basic structure to identify spectral features, to make quantitative measurements of this features, and to store the measurements for convenient access. MSLAP can be used to measure not only the zeroth moment (equivalent width) of a profile, but also the first and second moments. Optical depths and the corresponding column densities across the profile can be measured as well for sufficiently high resolution data. The software was developed for an interactive, graphical analysis where the computer carries most of the computational and data organizational burden and the investigator is responsible only for all judgement decisions. It employs sophisticated statistical techniques for determining the best polynomial fit to the continuum and for calculating the uncertainties.

Interpretation of electron diffraction patterns from amorphous and fullerene-like carbon allotropes.

PubMed

Czigány, Zsolt; Hultman, Lars

2010-06-01

The short range order in amorphous and fullerene-like carbon compounds has been characterized by selected area electron diffraction (SAED) patterns and compared with simulations of model nanoclusters. Broad rings in SAED pattern from fullerene-like CN(x) at approximately 1.2, approximately 2, and approximately 3.5A indicate short-range order similar to that in graphite, but peak shifts indicate sheet curvature in agreement with high-resolution transmission electron microscopy images. Fullerene-like CP(x) exhibits rings at approximately 1.6 and 2.6A, which can be explained if it consists of fragments with short-range order and high curvature similar to that of C(20). Copyright 2010 Elsevier B.V. All rights reserved.

The equilibrium-diffusion limit for radiation hydrodynamics

DOE PAGES

Ferguson, J. M.; Morel, J. E.; Lowrie, R.

2017-07-27

The equilibrium-diffusion approximation (EDA) is used to describe certain radiation-hydrodynamic (RH) environments. When this is done the RH equations reduce to a simplified set of equations. The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibrium-diffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both first-order accurate with transport corrections occurring at second order. Having established the EDA’s first-order accuracy we then analyze the grey nonequilibrium-diffusion approximation and the grey Eddington approximation and show that they both preserve this first-order accuracy.more » Further, these approximations preserve the EDA’s first-order accuracy when made in either the comoving-frame (CMF) or the lab-frame (LF). And while analyzing the Eddington approximation, we found that the CMF and LF radiation-source equations are equivalent when neglecting O(β 2) terms and compared in the LF. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this first-order accuracy will not retain the correct equilibrium-diffusion solutions. As a practical example, we show that nonequilibrium-diffusion radiative-shock solutions devolve to equilibrium-diffusion solutions when the asymptotic parameter is small.« less

Fourth-order numerical solutions of diffusion equation by using SOR method with Crank-Nicolson approach

NASA Astrophysics Data System (ADS)

Muhiddin, F. A.; Sulaiman, J.

2017-09-01

The aim of this paper is to investigate the effectiveness of the Successive Over-Relaxation (SOR) iterative method by using the fourth-order Crank-Nicolson (CN) discretization scheme to derive a five-point Crank-Nicolson approximation equation in order to solve diffusion equation. From this approximation equation, clearly, it can be shown that corresponding system of five-point approximation equations can be generated and then solved iteratively. In order to access the performance results of the proposed iterative method with the fourth-order CN scheme, another point iterative method which is Gauss-Seidel (GS), also presented as a reference method. Finally the numerical results obtained from the use of the fourth-order CN discretization scheme, it can be pointed out that the SOR iterative method is superior in terms of number of iterations, execution time, and maximum absolute error.

Higher and lowest order mixed finite element approximation of subsurface flow problems with solutions of low regularity

NASA Astrophysics Data System (ADS)

Bause, Markus

2008-02-01

In this work we study mixed finite element approximations of Richards' equation for simulating variably saturated subsurface flow and simultaneous reactive solute transport. Whereas higher order schemes have proved their ability to approximate reliably reactive solute transport (cf., e.g. [Bause M, Knabner P. Numerical simulation of contaminant biodegradation by higher order methods and adaptive time stepping. Comput Visual Sci 7;2004:61-78]), the Raviart- Thomas mixed finite element method ( RT0) with a first order accurate flux approximation is popular for computing the underlying water flow field (cf. [Bause M, Knabner P. Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods. Adv Water Resour 27;2004:565-581, Farthing MW, Kees CE, Miller CT. Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow. Adv Water Resour 26;2003:373-394, Starke G. Least-squares mixed finite element solution of variably saturated subsurface flow problems. SIAM J Sci Comput 21;2000:1869-1885, Younes A, Mosé R, Ackerer P, Chavent G. A new formulation of the mixed finite element method for solving elliptic and parabolic PDE with triangular elements. J Comp Phys 149;1999:148-167, Woodward CS, Dawson CN. Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media. SIAM J Numer Anal 37;2000:701-724]). This combination might be non-optimal. Higher order techniques could increase the accuracy of the flow field calculation and thereby improve the prediction of the solute transport. Here, we analyse the application of the Brezzi- Douglas- Marini element ( BDM1) with a second order accurate flux approximation to elliptic, parabolic and degenerate problems whose solutions lack the regularity that is assumed in optimal order error analyses. For the flow field calculation a superiority of the BDM1 approach to the RT0 one is observed, which however is less significant for the accompanying solute transport.

Efficient High-Order Accurate Methods using Unstructured Grids for Hydrodynamics and Acoustics

DTIC Science & Technology

2007-08-31

Leer. On upstream differencing and godunov-type schemes for hyperbolic conservation laws. SIAM Review, 25(1):35-61, 1983. [46] F . Eleuterio Toro ...early stage [4-61. The basic idea can be surmised from simple approximation theory. If a continuous function f is to be approximated over a set of...a2f 4h4 a4ff(x+eh) = f (x)+-- + _ •-+• e +0 +... (1) where 0 < e < 1 for approximations inside the interval of width h. For a second-order approximation

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

Comparison of dynamical approximation schemes for nonlinear gravitaional clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.

1994-01-01

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the lognormal approximation, the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by smoothing the initial conditions with various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was cross-correlation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(sub G(exp 2)), where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present. This in turn provides a natural explanation for the presence of sheets and filaments in the observed galaxy distribution. Use of the approximation scheme can permit extremely rapid generation of large numbers of realizations of model universes with good accuracy down to galaxy group mass scales.

Second-order numerical solution of time-dependent, first-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Shah, Patricia L.; Hardin, Jay

1995-01-01

A finite difference scheme is developed to find an approximate solution of two similar hyperbolic equations, namely a first-order plane wave and spherical wave problem. Finite difference approximations are made for both the space and time derivatives. The result is a conditionally stable equation yielding an exact solution when the Courant number is set to one.

Breakdown of the single-exchange approximation in third-order symmetry-adapted perturbation theory.

PubMed

Lao, Ka Un; Herbert, John M

2012-03-22

We report third-order symmetry-adapted perturbation theory (SAPT) calculations for several dimers whose intermolecular interactions are dominated by induction. We demonstrate that the single-exchange approximation (SEA) employed to derive the third-order exchange-induction correction (E(exch-ind)((30))) fails to quench the attractive nature of the third-order induction (E(ind)((30))), leading to one-dimensional potential curves that become attractive rather than repulsive at short intermolecular separations. A scaling equation for (E(exch-ind)((30))), based on an exact formula for the first-order exchange correction, is introduced to approximate exchange effects beyond the SEA, and qualitatively correct potential energy curves that include third-order induction are thereby obtained. For induction-dominated systems, our results indicate that a "hybrid" SAPT approach, in which a dimer Hartree-Fock calculation is performed in order to obtain a correction for higher-order induction, is necessary not only to obtain quantitative binding energies but also to obtain qualitatively correct potential energy surfaces. These results underscore the need to develop higher-order exchange-induction formulas that go beyond the SEA. © 2012 American Chemical Society

Bulk-Flow Analysis of Hybrid Thrust Bearings for Advanced Cryogenic Turbopumps

NASA Technical Reports Server (NTRS)

SanAndres, Luis

1998-01-01

A bulk-flow analysis and computer program for prediction of the static load performance and dynamic force coefficients of angled injection, orifice-compensated hydrostatic/hydrodynamic thrust bearings have been completed. The product of the research is an efficient computational tool for the design of high-speed thrust bearings for cryogenic fluid turbopumps. The study addresses the needs of a growing technology that requires of reliable fluid film bearings to provide the maximum operating life with optimum controllable rotordynamic characteristics at the lowest cost. The motion of a cryogenic fluid on the thin film lands of a thrust bearing is governed by a set of bulk-flow mass and momentum conservation and energy transport equations. Mass flow conservation and a simple model for momentum transport within the hydrostatic bearing recesses are also accounted for. The bulk-flow model includes flow turbulence with fluid inertia advection, Coriolis and centrifugal acceleration effects on the bearing recesses and film lands. The cryogenic fluid properties are obtained from realistic thermophysical equations of state. Turbulent bulk-flow shear parameters are based on Hirs' model with Moody's friction factor equations allowing a simple simulation for machined bearing surface roughness. A perturbation analysis leads to zeroth-order nonlinear equations governing the fluid flow for the thrust bearing operating at a static equilibrium position, and first-order linear equations describing the perturbed fluid flow for small amplitude shaft motions in the axial direction. Numerical solution to the zeroth-order flow field equations renders the bearing flow rate, thrust load, drag torque and power dissipation. Solution to the first-order equations determines the axial stiffness, damping and inertia force coefficients. The computational method uses well established algorithms and generic subprograms available from prior developments. The Fortran9O computer program hydrothrust runs on a Windows 95/NT personal computer. The program, help files and examples are licensed by Texas A&M University Technology License Office. The study of the static and dynamic performance of two hydrostatic/hydrodynamic bearings demonstrates the importance of centrifugal and advection fluid inertia effects for operation at high rotational speeds. The first example considers a conceptual hydrostatic thrust bearing for an advanced liquid hydrogen turbopump operating at 170,000 rpm. The large axial stiffness and damping coefficients of the bearing should provide accurate control and axial positioning of the turbopump and also allow for unshrouded impellers, therefore increasing the overall pump efficiency. The second bearing uses a refrigerant R134a, and its application in oil-free air conditioning compressors is of great technological importance and commercial value. The computed predictions reveal that the LH2 bearing load capacity and flow rate increase with the recess pressure (i.e. increasing orifice diameters). The bearing axial stiffness has a maximum for a recess pressure rati of approx. 0.55. while the axial damping coefficient decreases as the recess pressure ratio increases. The computer results from three flow models are compared. These models are a) inertialess, b) fluid inertia at recess edges only, and c) full fluid inertia at both recess edges and film lands. The full inertia model shows the lowest flow rates, axial load capacity and stiffness coefficient but on the other hand renders the largest damping coefficients and inertia coefficients. The most important findings are related to the reduction of the outflow through the inner radius and the appearance of subambient pressures. The performance of the refrigerant hybrid thrust bearing is evaluated at two operating speeds and pressure drops. The computed results are presented in dimensionless form to evidence consistent trends in the bearing performance characteristics. As the applied axial load increases, the bearing film thickness and flow rate decrease while the recess pressure increases. The axial stiffness coefficient shows a maximum for a certain intermediate load while the damping coefficient steadily increases. The computed results evidence the paramount of centrifugal fluid inertia at low recess pressures (i.e. low loads), and where there is actually an inflow through the bearing inner diameter, accompanied by subambient pressures just downstream of the bearing recess edge. These results are solely due to centrifugal fluid inertia and advection transport effects. Recommendations include the extension of the computer program to handle flexure pivot tilting pad hybrid bearings and the ability to calculate moment coefficients for shaft angular misalignments.

Electroencephalography in ellipsoidal geometry with fourth-order harmonics.

PubMed

Alcocer-Sosa, M; Gutierrez, D

2016-08-01

We present a solution to the electroencephalographs (EEG) forward problem of computing the scalp electric potentials for the case when the head's geometry is modeled using a four-shell ellipsoidal geometry and the brain sources with an equivalent current dipole (ECD). The proposed solution includes terms up to the fourth-order ellipsoidal harmonics and we compare this new approximation against those that only considered up to second- and third-order harmonics. Our comparisons use as reference a solution in which a tessellated volume approximates the head and the forward problem is solved through the boundary element method (BEM). We also assess the solution to the inverse problem of estimating the magnitude of an ECD through different harmonic approximations. Our results show that the fourth-order solution provides a better estimate of the ECD in comparison to lesser order ones.

The 4th order GISS model of the global atmosphere

NASA Technical Reports Server (NTRS)

Kalnay-Rivas, E.; Bayliss, A.; Storch, J.

1977-01-01

The new GISS 4th order model of the global atmosphere is described. It is based on 4th order quadratically conservative differences with the periodic application of a 16th order filter on the sea level pressure and potential temperature equations, a combination which is approximately enstrophy conserving. Several short range forecasts indicate a significant improvement over 2nd order forecasts with the same resolution (approximately 400 km). However the 4th order forecasts are somewhat inferior to 2nd order forecasts with double resolution. This is probably due to the presence of short waves in the range between 1000 km and 2000 km, which are computed more accurately by the 2nd order high resolution model. An operation count of the schemes indicates that with similar code optimization, the 4th order model will require approximately the same amount of computer time as the 2nd order model with the same resolution. It is estimated that the 4th order model with a grid size of 200 km provides enough accuracy to make horizontal truncation errors negligible over a period of a week for all synoptic scales (waves longer than 1000 km).

Raman scattering of IrTe2

NASA Astrophysics Data System (ADS)

Lee, Alexander; Thorsmolle, Verner; Artyukhin, Sergey; Yang, Jun; Cheong, Sang-Wook; Blumberg, Girsh

2014-03-01

IrTe2 presents a layered compound with a triangular lattice. It is known to exhibit a first order structural phase transition at approximately 260 K which is of a first order, corresponding to a formation of a superstructure with a period of five unit cells. Using polarized Raman spectroscopy we have studied the temperature dependence of 14 observed Raman allowed phononic modes. These phonons couple strongly to this transition and one additional first order transition at approximately 170 K. In the high-temperature phase only 3 modes are observed, while below approximately 280 K all 14 modes become visible. Below approximately 170 K only 11 modes are observed. Our results shed light on the possible mechanism driving the transitions. ACL, VKT and GB acknowledge support by NSF DMR-1104884.

Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator

NASA Astrophysics Data System (ADS)

Wu, Baisheng; Liu, Weijia; Lim, C. W.

2017-07-01

A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps, a predictor and a corrector step. In each step, the harmonic balance method is used in an appropriate manner to obtain a set of linear algebraic equations. With only one simple second-order Newton iteration step, a short, explicit, and highly accurate analytical approximate solution can be derived. The approximate solutions are valid for all amplitudes of the pseudo-oscillator. Furthermore, the method incorporates second-order Taylor expansion in a natural way, and it is of significant faster convergence rate.

Bayesian approach for three-dimensional aquifer characterization at the Hanford 300 Area

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

Murakami, Haruko; Chen, X.; Hahn, Melanie S.

2010-10-21

This study presents a stochastic, three-dimensional characterization of a heterogeneous hydraulic conductivity field within DOE's Hanford 300 Area site, Washington, by assimilating large-scale, constant-rate injection test data with small-scale, three-dimensional electromagnetic borehole flowmeter (EBF) measurement data. We first inverted the injection test data to estimate the transmissivity field, using zeroth-order temporal moments of pressure buildup curves. We applied a newly developed Bayesian geostatistical inversion framework, the method of anchored distributions (MAD), to obtain a joint posterior distribution of geostatistical parameters and local log-transmissivities at multiple locations. The unique aspects of MAD that make it suitable for this purpose are itsmore » ability to integrate multi-scale, multi-type data within a Bayesian framework and to compute a nonparametric posterior distribution. After we combined the distribution of transmissivities with depth-discrete relative-conductivity profile from EBF data, we inferred the three-dimensional geostatistical parameters of the log-conductivity field, using the Bayesian model-based geostatistics. Such consistent use of the Bayesian approach throughout the procedure enabled us to systematically incorporate data uncertainty into the final posterior distribution. The method was tested in a synthetic study and validated using the actual data that was not part of the estimation. Results showed broader and skewed posterior distributions of geostatistical parameters except for the mean, which suggests the importance of inferring the entire distribution to quantify the parameter uncertainty.« less

Ultracold fermions in a one-dimensional bipartite optical lattice: Metal-insulator transitions driven by shaking

NASA Astrophysics Data System (ADS)

Di Liberto, M.; Malpetti, D.; Japaridze, G. I.; Morais Smith, C.

2014-08-01

We theoretically investigate the behavior of a system of fermionic atoms loaded in a bipartite one-dimensional optical lattice that is under the action of an external time-periodic driving force. By using Floquet theory, an effective model is derived. The bare hopping coefficients are renormalized by zeroth-order Bessel functions of the first kind with different arguments for the nearest-neighbor and next-nearest-neighbor hopping. The insulating behavior characterizing the system at half filling in the absence of driving is dynamically suppressed, and for particular values of the driving parameter the system becomes either a standard metal or an unconventional metal with four Fermi points. The existence of the four-Fermi-point metal relies on the fact that, as a consequence of the shaking procedure, the next-nearest-neighbor hopping coefficients become significant compared to the nearest-neighbor ones. We use the bosonization technique to investigate the effect of on-site Hubbard interactions on the four-Fermi-point metal-insulator phase transition. Attractive interactions are expected to enlarge the regime of parameters where the unconventional metallic phase arises, whereas repulsive interactions reduce it. This metallic phase is known to be a Luther-Emery liquid (spin-gapped metal) for both repulsive and attractive interactions, contrary to the usual Hubbard model, which exhibits a Mott-insulator phase for repulsive interactions. Ultracold fermions in driven one-dimensional bipartite optical lattices provide an interesting platform for the realization of this long-studied four-Fermi-point unconventional metal.

Second order nonlinear QED processes in ultra-strong laser fields

NASA Astrophysics Data System (ADS)

Mackenroth, Felix

2017-10-01

In the interaction of ultra-intense laser fields with matter the ever increasing peak laser intensities render nonlinear QED effects ever more important. For long, ultra-intense laser pulses scattering large systems, like a macroscopic plasma, the interaction time can be longer than the scattering time, leading to multiple scatterings. These are usually approximated as incoherent cascades of single-vertex processes. Under certain conditions, however, this common cascade approximation may be insufficient, as it disregards several effects such as coherent processes, quantum interferences or pulse shape effects. Quantifying deviations of the full amplitude of multiple scatterings from the commonly employed cascade approximations is a formidable, yet unaccomplished task. In this talk we are going to discuss how to compute second order nonlinear QED amplitudes and relate them to the conventional cascade approximation. We present examples for typical second order processes and benchmark the full result against common approximations. We demonstrate that the approximation of multiple nonlinear QED scatterings as a cascade of single interactions has certain limitations and discuss these limits in light of upcoming experimental tests.

Minimal-Approximation-Based Distributed Consensus Tracking of a Class of Uncertain Nonlinear Multiagent Systems With Unknown Control Directions.

PubMed

Choi, Yun Ho; Yoo, Sung Jin

2017-03-28

A minimal-approximation-based distributed adaptive consensus tracking approach is presented for strict-feedback multiagent systems with unknown heterogeneous nonlinearities and control directions under a directed network. Existing approximation-based consensus results for uncertain nonlinear multiagent systems in lower-triangular form have used multiple function approximators in each local controller to approximate unmatched nonlinearities of each follower. Thus, as the follower's order increases, the number of the approximators used in its local controller increases. However, the proposed approach employs only one function approximator to construct the local controller of each follower regardless of the order of the follower. The recursive design methodology using a new error transformation is derived for the proposed minimal-approximation-based design. Furthermore, a bounding lemma on parameters of Nussbaum functions is presented to handle the unknown control direction problem in the minimal-approximation-based distributed consensus tracking framework and the stability of the overall closed-loop system is rigorously analyzed in the Lyapunov sense.

Absolute phase estimation: adaptive local denoising and global unwrapping.

PubMed

Bioucas-Dias, Jose; Katkovnik, Vladimir; Astola, Jaakko; Egiazarian, Karen

2008-10-10

The paper attacks absolute phase estimation with a two-step approach: the first step applies an adaptive local denoising scheme to the modulo-2 pi noisy phase; the second step applies a robust phase unwrapping algorithm to the denoised modulo-2 pi phase obtained in the first step. The adaptive local modulo-2 pi phase denoising is a new algorithm based on local polynomial approximations. The zero-order and the first-order approximations of the phase are calculated in sliding windows of varying size. The zero-order approximation is used for pointwise adaptive window size selection, whereas the first-order approximation is used to filter the phase in the obtained windows. For phase unwrapping, we apply the recently introduced robust (in the sense of discontinuity preserving) PUMA unwrapping algorithm [IEEE Trans. Image Process.16, 698 (2007)] to the denoised wrapped phase. Simulations give evidence that the proposed algorithm yields state-of-the-art performance, enabling strong noise attenuation while preserving image details. (c) 2008 Optical Society of America

Orbitally invariant internally contracted multireference unitary coupled cluster theory and its perturbative approximation: theory and test calculations of second order approximation.

PubMed

Chen, Zhenhua; Hoffmann, Mark R

2012-07-07

A unitary wave operator, exp (G), G(+) = -G, is considered to transform a multiconfigurational reference wave function Φ to the potentially exact, within basis set limit, wave function Ψ = exp (G)Φ. To obtain a useful approximation, the Hausdorff expansion of the similarity transformed effective Hamiltonian, exp (-G)Hexp (G), is truncated at second order and the excitation manifold is limited; an additional separate perturbation approximation can also be made. In the perturbation approximation, which we refer to as multireference unitary second-order perturbation theory (MRUPT2), the Hamiltonian operator in the highest order commutator is approximated by a Mo̸ller-Plesset-type one-body zero-order Hamiltonian. If a complete active space self-consistent field wave function is used as reference, then the energy is invariant under orbital rotations within the inactive, active, and virtual orbital subspaces for both the second-order unitary coupled cluster method and its perturbative approximation. Furthermore, the redundancies of the excitation operators are addressed in a novel way, which is potentially more efficient compared to the usual full diagonalization of the metric of the excited configurations. Despite the loss of rigorous size-extensivity possibly due to the use of a variational approach rather than a projective one in the solution of the amplitudes, test calculations show that the size-extensivity errors are very small. Compared to other internally contracted multireference perturbation theories, MRUPT2 only needs reduced density matrices up to three-body even with a non-complete active space reference wave function when two-body excitations within the active orbital subspace are involved in the wave operator, exp (G). Both the coupled cluster and perturbation theory variants are amenable to large, incomplete model spaces. Applications to some widely studied model systems that can be problematic because of geometry dependent quasidegeneracy, H4, P4, and BeH(2), are performed in order to test the new methods on problems where full configuration interaction results are available.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

Path integrals with higher order actions: Application to realistic chemical systems

NASA Astrophysics Data System (ADS)

Lindoy, Lachlan P.; Huang, Gavin S.; Jordan, Meredith J. T.

2018-02-01

Quantum thermodynamic parameters can be determined using path integral Monte Carlo (PIMC) simulations. These simulations, however, become computationally demanding as the quantum nature of the system increases, although their efficiency can be improved by using higher order approximations to the thermal density matrix, specifically the action. Here we compare the standard, primitive approximation to the action (PA) and three higher order approximations, the Takahashi-Imada action (TIA), the Suzuki-Chin action (SCA) and the Chin action (CA). The resulting PIMC methods are applied to two realistic potential energy surfaces, for H2O and HCN-HNC, both of which are spectroscopically accurate and contain three-body interactions. We further numerically optimise, for each potential, the SCA parameter and the two free parameters in the CA, obtaining more significant improvements in efficiency than seen previously in the literature. For both H2O and HCN-HNC, accounting for all required potential and force evaluations, the optimised CA formalism is approximately twice as efficient as the TIA formalism and approximately an order of magnitude more efficient than the PA. The optimised SCA formalism shows similar efficiency gains to the CA for HCN-HNC but has similar efficiency to the TIA for H2O at low temperature. In H2O and HCN-HNC systems, the optimal value of the a1 CA parameter is approximately 1/3 , corresponding to an equal weighting of all force terms in the thermal density matrix, and similar to previous studies, the optimal α parameter in the SCA was ˜0.31. Importantly, poor choice of parameter significantly degrades the performance of the SCA and CA methods. In particular, for the CA, setting a1 = 0 is not efficient: the reduction in convergence efficiency is not offset by the lower number of force evaluations. We also find that the harmonic approximation to the CA parameters, whilst providing a fourth order approximation to the action, is not optimal for these realistic potentials: numerical optimisation leads to better approximate cancellation of the fifth order terms, with deviation between the harmonic and numerically optimised parameters more marked in the more quantum H2O system. This suggests that numerically optimising the CA or SCA parameters, which can be done at high temperature, will be important in fully realising the efficiency gains of these formalisms for realistic potentials.

A Second-Order Phase Transition as a Limit of the First-Order Phase Transitions —Coherent Anomalies and Critical Phenomena in the Potts Models—

NASA Astrophysics Data System (ADS)

Katori, Makoto

1988-12-01

A new scheme of the coherent-anomaly method (CAM) is proposed to study critical phenomena in the models for which a mean-field description gives spurious first-order phase transition. A canonical series of mean-field-type approximations are constructed so that the spurious discontinuity should vanish asymptotically as the approximate critical temperature approachs the true value. The true value of the critical exponents β and γ are related to the coherent-anomaly exponents defined among the classical approximations. The formulation is demonstrated in the two-dimensional q-state Potts models for q{=}3 and 4. The result shows that the present method enables us to estimate the critical exponents with high accuracy by using the date of the cluster-mean-field approximations.

ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide

NASA Technical Reports Server (NTRS)

Fleury, C.; Schmit, L. A., Jr.

1980-01-01

A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included.

Fabrication of Ordered Blue Nanostructure by Anodization of an Aluminum Plate

NASA Astrophysics Data System (ADS)

Kurashima, Yuichi; Yokota, Yoshihiko; Miyamoto, Iwao; Itatani, Taro

2007-03-01

Colors in organisms are created by chemical interactions of molecular pigments and by optical interactions of incident light with biological nanostructures. The latter classes are called structural colors and form an important component of the phenotypes of many animals and even some plants. In this paper, we report on the fabrication of an ordered blue nanostructure by the anodization of an Al plate. In the fabrication of such an ordered nanostructure by the anodization of an Al plate, ordered nanostructures with a pitch and an alumina thickness of approximately 100 nm were produced on the Al plate. The ordered nanostructures on the Al plate showed no colors. However, an ordered nanostructure deposited with a Pt thin film with a thickness of approximately 10 nm showed a blue reflection with a peak reflectivity of approximately 370 nm. We conclude that this blue nanostructure on the Al plate is caused by an interference between the Al surface and the Pt surface.

Topographical scattering of gravity waves

NASA Astrophysics Data System (ADS)

Miles, J. W.; Chamberlain, P. G.

1998-04-01

A systematic hierarchy of partial differential equations for linear gravity waves in water of variable depth is developed through the expansion of the average Lagrangian in powers of [mid R:][nabla del, Hamilton operator][mid R:] (h=depth, [nabla del, Hamilton operator]h=slope). The first and second members of this hierarchy, the Helmholtz and conventional mild-slope equations, are second order. The third member is fourth order but may be approximated by Chamberlain & Porter's (1995) ‘modified mild-slope’ equation, which is second order and comprises terms in [nabla del, Hamilton operator]2h and ([nabla del, Hamilton operator]h)2 that are absent from the mild-slope equation. Approximate solutions of the mild-slope and modified mild-slope equations for topographical scattering are determined through an iterative sequence, starting from a geometrical-optics approximation (which neglects reflection), then a quasi-geometrical-optics approximation, and on to higher-order results. The resulting reflection coefficient for a ramp of uniform slope is compared with the results of numerical integrations of each of the mild-slope equation (Booij 1983), the modified mild-slope equation (Porter & Staziker 1995), and the full linear equations (Booij 1983). Also considered is a sequence of sinusoidal sandbars, for which Bragg resonance may yield rather strong reflection and for which the modified mild-slope approximation is in close agreement with Mei's (1985) asymptotic approximation.

APPROXIMATING SYMMETRIC POSITIVE SEMIDEFINITE TENSORS OF EVEN ORDER*

PubMed Central

BARMPOUTIS, ANGELOS; JEFFREY, HO; VEMURI, BABA C.

2012-01-01

Tensors of various orders can be used for modeling physical quantities such as strain and diffusion as well as curvature and other quantities of geometric origin. Depending on the physical properties of the modeled quantity, the estimated tensors are often required to satisfy the positivity constraint, which can be satisfied only with tensors of even order. Although the space P02m of 2mth-order symmetric positive semi-definite tensors is known to be a convex cone, enforcing positivity constraint directly on P02m is usually not straightforward computationally because there is no known analytic description of P02m for m > 1. In this paper, we propose a novel approach for enforcing the positivity constraint on even-order tensors by approximating the cone P02m for the cases 0 < m < 3, and presenting an explicit characterization of the approximation Σ2m ⊂ Ω2m for m ≥ 1, using the subset Ω2m⊂P02m of semi-definite tensors that can be written as a sum of squares of tensors of order m. Furthermore, we show that this approximation leads to a non-negative linear least-squares (NNLS) optimization problem with the complexity that equals the number of generators in Σ2m. Finally, we experimentally validate the proposed approach and we present an application for computing 2mth-order diffusion tensors from Diffusion Weighted Magnetic Resonance Images. PMID:23285313

The wave equation in Friedmann-Robertson-Walker space-times and asymptotics of the intensity and distance relationship of a localised source

NASA Astrophysics Data System (ADS)

Starko, Darij; Craig, Walter

2018-04-01

Variations in redshift measurements of Type 1a supernovae and intensity observations from large sky surveys are an indicator of a component of acceleration in the rate of expansion of space-time. A key factor in the measurements is the intensity-distance relation for Maxwell's equations in Friedmann-Robertson-Walker (FRW) space-times. In view of future measurements of the decay of other fields on astronomical time and spatial scales, we determine the asymptotic behavior of the intensity-distance relationship for the solution of the wave equation in space-times with an FRW metric. This builds on previous work done on initial value problems for the wave equation in FRW space-time [Abbasi, B. and Craig, W., Proc. R. Soc. London, Ser. A 470, 20140361 (2014)]. In this paper, we focus on the precise intensity decay rates of the special cases for curvature k = 0 and k = -1, as well as giving a general derivation of the wave solution for -∞ < k < 0. We choose a Cauchy surface {(t, x) : t = t0 > 0} where t0 represents the time of an initial emission source, relative to the Big Bang singularity at t = 0. The initial data [g(x), h(x)] are assumed to be compactly supported; supp(g, h) ⊆ BR(0) and terms in the expression for the fundamental solution for the wave equation with the slowest decay rate are retained. The intensities calculated for coordinate time {t : t > 0} contain correction terms proportional to the ratio of t0 and the time differences ρ = t - t0. For the case of general curvature k, these expressions for the intensity reduce by scaling to the same form as for k = -1, from which we deduce the general formula. We note that for typical astronomical events such as Type 1a supernovae, the first order correction term for all curvatures -∞ < k < 0 is on the order of 10-4 smaller than the zeroth order term. These correction terms are small but may be significant in applications to alternative observations of cosmological space-time expansion rates.

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

Zhang, Zuocheng; Wei, Wei; Yang, Fangyuan

In this paper, we report quantum oscillation studies on the Bi 2Te 3-xS x topological insulator single crystals in pulsed magnetic fields up to 91 T. For the x = 0.4 sample with the lowest bulk carrier density, the surface and bulk quantum oscillations can be disentangled by combined Shubnikov–de Haas and de Hass–van Alphen oscillations, as well as quantum oscillations in nanometer-thick peeled crystals. At high magnetic fields beyond the bulk quantum limit, our results suggest that the zeroth Landau level of topological surface states is shifted due to the Zeeman effect. The g factor of the topological surfacemore » states is estimated to be between 1.8 and 4.5. Lastly, these observations shed new light on the quantum transport phenomena of topological insulators in ultrahigh magnetic fields.« less

OPTOELECTRONICS, FIBER OPTICS, AND OTHER ASPECTS OF QUANTUM ELECTRONICS: Influence of the Rayleigh backscattering on the mode composition of radiation in multimode graded-index waveguides with a quadratic refractive-index profile

NASA Astrophysics Data System (ADS)

Esayan, G. L.; Krivoshlykov, S. G.

1989-08-01

A method of coherent states is used to describe the process of Rayleigh scattering in a multimode graded-index waveguide with a quadratic refractive-index profile. Explicit expressions are obtained for the coefficients representing excitation of Gaussian-Hermite backscattering modes in two cases of practical importance: excitation of a waveguide by an extended noncoherent light source and selective excitation of different modes at the entry to a waveguide. An analysis is also made of the coefficients of coupling between forward and backward modes. Explicit expressions for the coefficients representing capture of backscattered radiation by a waveguide are obtained for two special cases of excitation (extended light source and zeroth mode).

Periodic response of nonlinear systems

NASA Technical Reports Server (NTRS)

Nataraj, C.; Nelson, H. D.

1988-01-01

A procedure is developed to determine approximate periodic solutions of autonomous and non-autonomous systems. The trignometric collocation method (TCM) is formalized to allow for the analysis of relatively small order systems directly in physical coordinates. The TCM is extended to large order systems by utilizing modal analysis in a component mode synthesis strategy. The procedure was coded and verified by several check cases. Numerical results for two small order mechanical systems and one large order rotor dynamic system are presented. The method allows for the possibility of approximating periodic responses for large order forced and self-excited nonlinear systems.

Convergence of the strong-potential-Born approximation in Z/sub less-than//Z/sub greater-than/

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

McGuire, J.H.; Sil, N.C.

1986-01-01

Convergence of the strong-potential Born (SPB) approximation as a function of the charges of the projectile and target is studied numerically. Time-reversal invariance (or detailed balance) is satisfied at sufficiently high velocities even when the charges are asymmetric. This demonstarates that the SPB approximation converges to the correct result even when the charge of the ''weak'' potential, which is kept to first order, is larger than the charge of the ''strong'' potential, which is retained to all orders. Consequently, the SPB approximation is valid for systems of arbitrary charge symmetry (including symmetric systems) at sufficiently high velocities.

Spline function approximation techniques for image geometric distortion representation. [for registration of multitemporal remote sensor imagery

NASA Technical Reports Server (NTRS)

Anuta, P. E.

1975-01-01

Least squares approximation techniques were developed for use in computer aided correction of spatial image distortions for registration of multitemporal remote sensor imagery. Polynomials were first used to define image distortion over the entire two dimensional image space. Spline functions were then investigated to determine if the combination of lower order polynomials could approximate a higher order distortion with less computational difficulty. Algorithms for generating approximating functions were developed and applied to the description of image distortion in aircraft multispectral scanner imagery. Other applications of the techniques were suggested for earth resources data processing areas other than geometric distortion representation.

Conservative and bounded volume-of-fluid advection on unstructured grids

NASA Astrophysics Data System (ADS)

Ivey, Christopher B.; Moin, Parviz

2017-12-01

This paper presents a novel Eulerian-Lagrangian piecewise-linear interface calculation (PLIC) volume-of-fluid (VOF) advection method, which is three-dimensional, unsplit, and discretely conservative and bounded. The approach is developed with reference to a collocated node-based finite-volume two-phase flow solver that utilizes the median-dual mesh constructed from non-convex polyhedra. The proposed advection algorithm satisfies conservation and boundedness of the liquid volume fraction irrespective of the underlying flux polyhedron geometry, which differs from contemporary unsplit VOF schemes that prescribe topologically complicated flux polyhedron geometries in efforts to satisfy conservation. Instead of prescribing complicated flux-polyhedron geometries, which are prone to topological failures, our VOF advection scheme, the non-intersecting flux polyhedron advection (NIFPA) method, builds the flux polyhedron iteratively such that its intersection with neighboring flux polyhedra, and any other unavailable volume, is empty and its total volume matches the calculated flux volume. During each iteration, a candidate nominal flux polyhedron is extruded using an iteration dependent scalar. The candidate is subsequently intersected with the volume guaranteed available to it at the time of the flux calculation to generate the candidate flux polyhedron. The difference in the volume of the candidate flux polyhedron and the actual flux volume is used to calculate extrusion during the next iteration. The choice in nominal flux polyhedron impacts the cost and accuracy of the scheme; however, it does not impact the methods underlying conservation and boundedness. As such, various robust nominal flux polyhedron are proposed and tested using canonical periodic kinematic test cases: Zalesak's disk and two- and three-dimensional deformation. The tests are conducted on the median duals of a quadrilateral and triangular primal mesh, in two-dimensions, and on the median duals of a hexahedral, wedge and tetrahedral primal mesh, in three-dimensions. Comparisons are made with the adaptation of a conventional unsplit VOF advection scheme to our collocated node-based flow solver. Depending on the choice in the nominal flux polyhedron, the NIFPA scheme presented accuracies ranging from zeroth to second order and calculation times that differed by orders of magnitude. For the nominal flux polyhedra which demonstrate second-order accuracy on all tests and meshes, the NIFPA method's cost was comparable to the traditional topologically complex second-order accurate VOF advection scheme.

Structure and thermodynamics of a simple fluid

NASA Astrophysics Data System (ADS)

Stell, G.; Weis, J. J.

1980-02-01

Monte Carlo results are found for a simple fluid with a pair potential consisting of a hard-sphere core and a Lennard-Jones attractive tail. They are compared with several of the most promising recent theoretical treatments of simple fluids, all of which involve the decomposition of the pair potential into a hard-sphere-core term and an attractive-tail term. This direct comparison avoids the use of a second perturbation scheme associated with softening the core, which would introduce an ambiguity in the significance of the differences found between the theoretical and Monte Carlo results. The study includes the optimized random-phase approximation (ORPA) and exponential (EXP) approximations of Andersen and Chandler, an extension of the latter approximation to nodal order three (the N3 approximation), the linear-plus-square (LIN + SQ) approximation of Høye and Stell, the renormalized hypernetted chain (RHNC) approximation of Lado, and the quadratic (QUAD) approximation suggested by second-order self-consistent Γ ordering, the lowest order of which is identical to the ORPA. As anticipated on the basis of earlier studies, it is found that the EXP approximation yields radial distribution functions and structure factors of excellent overall accuracy in the liquid state, where the RHNC results are also excellent and the EXP, QUAD, and LIN + SQ results prove to be virtually indistinguishable from one another. For all the approximations, however, the thermodynamics from the compressibility relation are poor and the virial-theorem results are not uniformly reliable. Somewhat more surprisingly, it is found that the EXP results yield a negative structure factor S(k) for very small k in the liquid state and poor radial distribution functions at low densities. The RHNC results are nowhere worse than the EXP results and in some states (e.g., at low densities) much better. In contrast, the N3 results are better in some respects than the EXP results but worse in others. The authors briefly comment on the RHNC and EXP approximations applied to the full Lennard-Jones potential, for which the EXP approximation appears somewhat improved in the liquid state as a result of the softening of the potential core.

Aeroservoelastic modeling and applications using minimum-state approximations of the unsteady aerodynamics

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Karpel, Mordechay

1989-01-01

Various control analysis, design, and simulation techniques for aeroelastic applications require the equations of motion to be cast in a linear time-invariant state-space form. Unsteady aerodynamics forces have to be approximated as rational functions of the Laplace variable in order to put them in this framework. For the minimum-state method, the number of denominator roots in the rational approximation. Results are shown of applying various approximation enhancements (including optimization, frequency dependent weighting of the tabular data, and constraint selection) with the minimum-state formulation to the active flexible wing wind-tunnel model. The results demonstrate that good models can be developed which have an order of magnitude fewer augmenting aerodynamic equations more than traditional approaches. This reduction facilitates the design of lower order control systems, analysis of control system performance, and near real-time simulation of aeroservoelastic phenomena.

Magnetic field homogeneity perturbations in finite Halbach dipole magnets.

PubMed

Turek, Krzysztof; Liszkowski, Piotr

2014-01-01

Halbach hollow cylinder dipole magnets of a low or relatively low aspect ratio attract considerable attention due to their applications, among others, in compact NMR and MRI systems for investigating small objects. However, a complete mathematical framework for the analysis of magnetic fields in these magnets has been developed only for their infinitely long precursors. In such a case the analysis is reduced to two-dimensions (2D). The paper details the analysis of the 3D magnetic field in the Halbach dipole cylinders of a finite length. The analysis is based on three equations in which the components of the magnetic flux density Bx, By and Bz are expanded to infinite power series of the radial coordinate r. The zeroth term in the series corresponds to a homogeneous magnetic field Bc, which is perturbed by the higher order terms due to a finite magnet length. This set of equations is supplemented with an equation for the field profile B(z) along the magnet axis, presented for the first time. It is demonstrated that the geometrical factors in the coefficients of particular powers of r, defined by intricate integrals are the coefficients of the Taylor expansion of the homogeneity profile (B(z)-Bc)/Bc. As a consequence, the components of B can be easily calculated with an arbitrary accuracy. In order to describe perturbations of the field due to segmentation, two additional equations are borrowed from the 2D theory. It is shown that the 2D approach to the perturbations generated by the segmentation can be applied to the 3D Halbach structures unless r is not too close to the inner radius of the cylinder ri. The mathematical framework presented in the paper was verified with great precision by computations of B by a highly accurate integration of the magnetostatic Coulomb law and utilized to analyze the inhomogeneity of the magnetic field in the magnet with the accuracy better than 1 ppm. Copyright © 2013 Elsevier Inc. All rights reserved.

The Approximation of Two-Mode Proximity Matrices by Sums of Order-Constrained Matrices.

ERIC Educational Resources Information Center

Hubert, Lawrence; Arabie, Phipps

1995-01-01

A least-squares strategy is proposed for representing a two-mode proximity matrix as an approximate sum of a small number of matrices that satisfy certain simple order constraints on their entries. The primary class of constraints considered defines Q-forms for particular conditions in a two-mode matrix. (SLD)

Nuclear magnetic resonance signal dynamics of liquids in the presence of distant dipolar fields, revisited

PubMed Central

Barros, Wilson; Gochberg, Daniel F.; Gore, John C.

2009-01-01

The description of the nuclear magnetic resonance magnetization dynamics in the presence of long-range dipolar interactions, which is based upon approximate solutions of Bloch–Torrey equations including the effect of a distant dipolar field, has been revisited. New experiments show that approximate analytic solutions have a broader regime of validity as well as dependencies on pulse-sequence parameters that seem to have been overlooked. In order to explain these experimental results, we developed a new method consisting of calculating the magnetization via an iterative formalism where both diffusion and distant dipolar field contributions are treated as integral operators incorporated into the Bloch–Torrey equations. The solution can be organized as a perturbative series, whereby access to higher order terms allows one to set better boundaries on validity regimes for analytic first-order approximations. Finally, the method legitimizes the use of simple analytic first-order approximations under less demanding experimental conditions, it predicts new pulse-sequence parameter dependencies for the range of validity, and clarifies weak points in previous calculations. PMID:19425789

The effects of the theoretical formalism and data selection on mantle models derived from waveform tomography

NASA Astrophysics Data System (ADS)

Mégnin, Charles; Romanowicz, Barbara

1999-08-01

Most global tomographic models to date are derived using a combination of surface wave (or normal-mode) data and body wave traveltime data. The traveltime approach limits the number of phases available for inversion by requiring them to be isolated on the seismogram. This may ultimately result in limiting the resolution of 3-D structure, at least in some depth ranges in the mantle. In a previous study, we successfully derived a degree 12 whole-mantle SH-velocity tomographic model (SAW12D) using exclusively waveform data. In that inversion, a normal-mode formalism suitable for body waveforms, the non-linear asymptotic coupling theory (NACT), was combined with a body wave windowing scheme, referred to as the `individual wavepacket' (IW) technique, which allows one to assign individual weights to different body wave energy packets. We here compare the relative merits of this choice of theoretical formalism and windowing scheme at different depth ranges in the mantle. Choosing as the reference a model obtained using 7500 transverse-component body wave and 8000 surface wave seismograms and the NACT and IW approaches, we discuss the relative performance of the path average approximation (PAVA), a zeroth-order theoretical approximation appropriate for single-mode surface waves, relative to NACT, and compare the IW windowing scheme with a more standard `full window' (FW) approach, in which a single time window is considered from the first body wave arrival to the fundamental-mode surface waves. The combination PAVA/FW is often used in global tomography to supplement the traveltime data. We show that although the quality of the image derived under the PAVA/FW formalism is very similar to that derived under NACT/IW in the first 300 km of the upper mantle, where the resolution is dominated by surface waves, it deteriorates at greater depths. Images of the lower mantle are shown to be strongly sensitive to the theoretical formalism. In contrast, the resolution of structure near the core-mantle boundary depends mostly on the windowing scheme. This is because this resolution is controlled by low-amplitude phases such as S_diff, which are downweighted in the FW scheme. Whilst the image obtained in D'' using the combination NACT/IW is in good agreement with images obtained by other authors using both waveforms and traveltimes, we show that, when using FW, uppermost mantle structure can be mapped into D''. This result is confirmed by synthetic tests performed on a composite of the upper-mantle geodynamic model 3SMAC. We also show, based on synthetic tests, that for structures in the upper mantle with sharp boundaries, differences are observed between NACT and PAVA. Whilst a combination of traveltimes and surface wave data is adequate for resolving relatively smooth features in the mantle, our results show that by potentially increasing the achievable sampling, the waveform approach shows great promise for future high-resolution tomographic modelling of mantle structure, if cast in an appropriate theoretical framework.

A general moment expansion method for stochastic kinetic models

NASA Astrophysics Data System (ADS)

Ale, Angelique; Kirk, Paul; Stumpf, Michael P. H.

2013-05-01

Moment approximation methods are gaining increasing attention for their use in the approximation of the stochastic kinetics of chemical reaction systems. In this paper we derive a general moment expansion method for any type of propensities and which allows expansion up to any number of moments. For some chemical reaction systems, more than two moments are necessary to describe the dynamic properties of the system, which the linear noise approximation is unable to provide. Moreover, also for systems for which the mean does not have a strong dependence on higher order moments, moment approximation methods give information about higher order moments of the underlying probability distribution. We demonstrate the method using a dimerisation reaction, Michaelis-Menten kinetics and a model of an oscillating p53 system. We show that for the dimerisation reaction and Michaelis-Menten enzyme kinetics system higher order moments have limited influence on the estimation of the mean, while for the p53 system, the solution for the mean can require several moments to converge to the average obtained from many stochastic simulations. We also find that agreement between lower order moments does not guarantee that higher moments will agree. Compared to stochastic simulations, our approach is numerically highly efficient at capturing the behaviour of stochastic systems in terms of the average and higher moments, and we provide expressions for the computational cost for different system sizes and orders of approximation. We show how the moment expansion method can be employed to efficiently quantify parameter sensitivity. Finally we investigate the effects of using too few moments on parameter estimation, and provide guidance on how to estimate if the distribution can be accurately approximated using only a few moments.

An approximation theory for the identification of linear thermoelastic systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Su, Chien-Hua Frank

1990-01-01

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

Dynamical cluster approximation plus semiclassical approximation study for a Mott insulator and d-wave pairing

NASA Astrophysics Data System (ADS)

Kim, SungKun; Lee, Hunpyo

2017-06-01

Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.

Approximate analysis for repeated eigenvalue problems with applications to controls-structure integrated design

NASA Technical Reports Server (NTRS)

Kenny, Sean P.; Hou, Gene J. W.

1994-01-01

A method for eigenvalue and eigenvector approximate analysis for the case of repeated eigenvalues with distinct first derivatives is presented. The approximate analysis method developed involves a reparameterization of the multivariable structural eigenvalue problem in terms of a single positive-valued parameter. The resulting equations yield first-order approximations to changes in the eigenvalues and the eigenvectors associated with the repeated eigenvalue problem. This work also presents a numerical technique that facilitates the definition of an eigenvector derivative for the case of repeated eigenvalues with repeated eigenvalue derivatives (of all orders). Examples are given which demonstrate the application of such equations for sensitivity and approximate analysis. Emphasis is placed on the application of sensitivity analysis to large-scale structural and controls-structures optimization problems.

Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization

NASA Technical Reports Server (NTRS)

Simpson, Timothy W.; Korte, John J.; Mauery, Timothy M.; Mistree, Farrokh

1998-01-01

In this paper, we compare and contrast the use of second-order response surface models and kriging models for approximating non-random, deterministic computer analyses. After reviewing the response surface method for constructing polynomial approximations, kriging is presented as an alternative approximation method for the design and analysis of computer experiments. Both methods are applied to the multidisciplinary design of an aerospike nozzle which consists of a computational fluid dynamics model and a finite-element model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations, and four optimization problems m formulated and solved using both sets of approximation models. The second-order response surface models and kriging models-using a constant underlying global model and a Gaussian correlation function-yield comparable results.

Reduced linear noise approximation for biochemical reaction networks with time-scale separation: The stochastic tQSSA+

NASA Astrophysics Data System (ADS)

Herath, Narmada; Del Vecchio, Domitilla

2018-03-01

Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA+". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.

Two-body perturbation theory versus first order perturbation theory: A comparison based on the square-well fluid.

PubMed

Mercier Franco, Luís Fernando; Castier, Marcelo; Economou, Ioannis G

2017-12-07

We show that the Zwanzig first-order perturbation theory can be obtained directly from a truncated Taylor series expansion of a two-body perturbation theory and that such truncation provides a more accurate prediction of thermodynamic properties than the full two-body perturbation theory. This unexpected result is explained by the quality of the resulting approximation for the fluid radial distribution function. We prove that the first-order and the two-body perturbation theories are based on different approximations for the fluid radial distribution function. To illustrate the calculations, the square-well fluid is adopted. We develop an analytical expression for the two-body perturbed Helmholtz free energy for the square-well fluid. The equation of state obtained using such an expression is compared to the equation of state obtained from the first-order approximation. The vapor-liquid coexistence curve and the supercritical compressibility factor of a square-well fluid are calculated using both equations of state and compared to Monte Carlo simulation data. Finally, we show that the approximation for the fluid radial distribution function given by the first-order perturbation theory provides closer values to the ones calculated via Monte Carlo simulations. This explains why such theory gives a better description of the fluid thermodynamic behavior.

Numerical solution of the unsteady Navier-Stokes equation

NASA Technical Reports Server (NTRS)

Osher, Stanley J.; Engquist, Bjoern

1985-01-01

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws are discussed. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first-order accuracy, in the sense of truncation error, at extrema of the solution. In this paper a uniformly second-order approximation is constructed, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Physical Applications of a Simple Approximation of Bessel Functions of Integer Order

ERIC Educational Resources Information Center

Barsan, V.; Cojocaru, S.

2007-01-01

Applications of a simple approximation of Bessel functions of integer order, in terms of trigonometric functions, are discussed for several examples from electromagnetism and optics. The method may be applied in the intermediate regime, bridging the "small values regime" and the "asymptotic" one, and covering, in this way, an area of great…

The arbitrary order mixed mimetic finite difference method for the diffusion equation

DOE PAGES

Gyrya, Vitaliy; Lipnikov, Konstantin; Manzini, Gianmarco

2016-05-01

Here, we propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux andmore » scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.« less

On the convergence of difference approximations to scalar conservation laws

NASA Technical Reports Server (NTRS)

Osher, S.; Tadmor, E.

1985-01-01

A unified treatment of explicit in time, two level, second order resolution, total variation diminishing, approximations to scalar conservation laws are presented. The schemes are assumed only to have conservation form and incremental form. A modified flux and a viscosity coefficient are introduced and results in terms of the latter are obtained. The existence of a cell entropy inequality is discussed and such an equality for all entropies is shown to imply that the scheme is an E scheme on monotone (actually more general) data, hence at most only first order accurate in general. Convergence for total variation diminishing-second order resolution schemes approximating convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.

Relaxation approximations to second-order traffic flow models by high-resolution schemes

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

Nikolos, I.K.; Delis, A.I.; Papageorgiou, M.

2015-03-10

A relaxation-type approximation of second-order non-equilibrium traffic models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms with the attractive feature that neither Riemann solvers nor characteristic decompositions are in need. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. To discretize the resulting relaxation system, high-resolution reconstructions in space are considered. Emphasis is given on a fifth-order WENO scheme and its performance. The computations reportedmore » demonstrate the simplicity and versatility of relaxation schemes as numerical solvers.« less

Numerical Solution of Time-Dependent Problems with a Fractional-Power Elliptic Operator

NASA Astrophysics Data System (ADS)

Vabishchevich, P. N.

2018-03-01

A time-dependent problem in a bounded domain for a fractional diffusion equation is considered. The first-order evolution equation involves a fractional-power second-order elliptic operator with Robin boundary conditions. A finite-element spatial approximation with an additive approximation of the operator of the problem is used. The time approximation is based on a vector scheme. The transition to a new time level is ensured by solving a sequence of standard elliptic boundary value problems. Numerical results obtained for a two-dimensional model problem are presented.

On High-Order Radiation Boundary Conditions

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas

1995-01-01

In this paper we develop the theory of high-order radiation boundary conditions for wave propagation problems. In particular, we study the convergence of sequences of time-local approximate conditions to the exact boundary condition, and subsequently estimate the error in the solutions obtained using these approximations. We show that for finite times the Pade approximants proposed by Engquist and Majda lead to exponential convergence if the solution is smooth, but that good long-time error estimates cannot hold for spatially local conditions. Applications in fluid dynamics are also discussed.

Approximate Dispersion Relations for Waves on Arbitrary Shear Flows

NASA Astrophysics Data System (ADS)

Ellingsen, S. À.; Li, Y.

2017-12-01

An approximate dispersion relation is derived and presented for linear surface waves atop a shear current whose magnitude and direction can vary arbitrarily with depth. The approximation, derived to first order of deviation from potential flow, is shown to produce good approximations at all wavelengths for a wide range of naturally occuring shear flows as well as widely used model flows. The relation reduces in many cases to a 3-D generalization of the much used approximation by Skop (1987), developed further by Kirby and Chen (1989), but is shown to be more robust, succeeding in situations where the Kirby and Chen model fails. The two approximations incur the same numerical cost and difficulty. While the Kirby and Chen approximation is excellent for a wide range of currents, the exact criteria for its applicability have not been known. We explain the apparently serendipitous success of the latter and derive proper conditions of applicability for both approximate dispersion relations. Our new model has a greater range of applicability. A second order approximation is also derived. It greatly improves accuracy, which is shown to be important in difficult cases. It has an advantage over the corresponding second-order expression proposed by Kirby and Chen that its criterion of accuracy is explicitly known, which is not currently the case for the latter to our knowledge. Our second-order term is also arguably significantly simpler to implement, and more physically transparent, than its sibling due to Kirby and Chen.