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Journal articles on the topic 'Spectral flow'

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Published: 4 June 2021

Last updated: 4 February 2022

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1

Carey, A. L., V. Gayral, J. Phillips, A. Rennie, and F. A. Sukochev. "Spectral Flow for Nonunital Spectral Triples." Canadian Journal of Mathematics 67, no. 4 (August 1, 2015): 759–94. http://dx.doi.org/10.4153/cjm-2014-042-x.

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AbstractWe prove two results about nonunital index theory left open in a previous paper. The first is that the spectral triple arising from an action of the reals on a C*-algebra with invariant trace satisûes the hypotheses of the nonunital local index formula. The second result concerns the meaning of spectral flow in the nonunital case. For the special case of paths arising from the odd index pairing for smooth spectral triples in the nonunital setting, we are able to connect with earlier approaches to the analytic definition of spectral flow

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2

Dai, Xianzhe, and Weiping Zhang. "Higher Spectral Flow." Mathematical Research Letters 3, no. 1 (1996): 93–102. http://dx.doi.org/10.4310/mrl.1996.v3.n1.a9.

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3

Dai, Xianzhe, and Weiping Zhang. "Higher Spectral Flow." Journal of Functional Analysis 157, no. 2 (August 1998): 432–69. http://dx.doi.org/10.1006/jfan.1998.3273.

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4

GATO-RIVERA, BEATRIZ, and JOSE IGNACIO ROSADO. "THE OTHER SPECTRAL FLOW." Modern Physics Letters A 11, no. 05 (February 20, 1996): 423–29. http://dx.doi.org/10.1142/s0217732396000461.

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Recently we showed that the spectral flow acting on the N=2 twisted topological theories gives rise to a topological algebra automorphism. Here we point out that the untwisting of that automorphism leads to a spectral flow on the untwisted N=2 super-conformal algebra which is different from the usual one. This “other” spectral flow does not interpolate between the chiral ring and the antichiral ring. In particular it maps the chiral ring into the chiral ring and the antichiral ring into the antichiral ring. We discuss the similarities and differences between these two spectral flows. We also analyze their action on null states.

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5

Azamov, N. A., A. L. Carey, P. G. Dodds, and F. A. Sukochev. "Operator Integrals, Spectral Shift, and Spectral Flow." Canadian Journal of Mathematics 61, no. 2 (April 1, 2009): 241–63. http://dx.doi.org/10.4153/cjm-2009-012-0.

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Abstract. We present a new and simple approach to the theory of multiple operator integrals that applies to unbounded operators affiliated with general von Neumann algebras. For semifinite von Neumann algebras we give applications to the Fréchet differentiation of operator functions that sharpen existing results, and establish the Birman–Solomyak representation of the spectral shift function of M.G. Krein in terms of an average of spectral measures in the type II setting. We also exhibit a surprising connection between the spectral shift function and spectral flow.

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6

Azamov, N. A., A. L. Carey, and F. A. Sukochev. "The Spectral Shift Function and Spectral Flow." Communications in Mathematical Physics 276, no. 1 (August 28, 2007): 51–91. http://dx.doi.org/10.1007/s00220-007-0329-9.

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7

Burd, S. W., and T. W. Simon. "Turbulence Spectra and Length Scales Measured in Film Coolant Flows Emerging From Discrete Holes." Journal of Turbomachinery 121, no. 3 (July 1, 1999): 551–57. http://dx.doi.org/10.1115/1.2841350.

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To date, very little attention has been devoted to the scales and turbulence energy spectra of coolant exiting from film cooling holes. Length-scale documentation and spectral measurements have primarily been concerned with the free-stream flow with which the coolant interacts. Documentation of scales and energy decomposition of the coolant flow leads to more complete understanding of this important flow and the mechanisms by which it disperses and mixes with the free stream. CFD modeling of the emerging flow can use these data as verification that flow computations are accurate. To address this need, spectral measurements were taken with single-sensor, hot-wire anemometry at the exit plane of film cooling holes. Energy spectral distributions and length scales calculated from these distributions are presented for film cooling holes of different lengths and for coolant supply plenums of different geometries. Measurements are presented on the hole streamwise centerline at the center of the hole, one-half diameter upstream of center, and one-half diameter downstream of center. The data highlight some fundamental differences in energy content, dominant frequencies, and scales with changes in the hole and plenum geometries. Coolant flowing through long holes exhibits smoothly distributed spectra as might be anticipated in fully developed tube flows. Spectra from short-hole flows, however, show dominant frequencies.

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8

Ciriza, E., P. M. Fitzpatrick, and J. Pejsachowicz. "Uniqueness of spectral flow." Mathematical and Computer Modelling 32, no. 11-13 (December 2000): 1495–501. http://dx.doi.org/10.1016/s0895-7177(00)00221-1.

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9

Heinzl, Thomas, and Anton Ilderton. "Noncommutativity from spectral flow." Journal of Physics A: Mathematical and Theoretical 40, no. 30 (July 12, 2007): 9097–123. http://dx.doi.org/10.1088/1751-8113/40/30/029.

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10

Barmpalias, Konstantinos G., Ndaona Chokani, Anestis I. Kalfas, and Reza S. Abhari. "Data Adaptive Spectral Analysis of Unsteady Leakage Flow in an Axial Turbine." International Journal of Rotating Machinery 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/121695.

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A data adaptive spectral analysis method is applied to characterize the unsteady loss generation in the leakage flow of an axial turbine. Unlike conventional spectral analysis, this method adapts a model dataset to the actual data. The method is illustrated from the analysis of the unsteady wall pressures in the labyrinth seal of an axial turbine. Spectra from the method are shown to be in good agreement with conventional spectral estimates. Furthermore, the spectra using the method are obtained with data records that are 16 times shorter than for conventional spectral analysis, indicating that the unsteady processes in turbomachines can be studied with substantially shorter measurement schedules than is presently the norm.

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11

Thompson, R. S., and G. K. Aldis. "Flow spectra from spectral power density calculations for pulsed Doppler." Ultrasonics 40, no. 1-8 (May 2002): 835–41. http://dx.doi.org/10.1016/s0041-624x(02)00223-8.

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12

Layton, H. E., E. Bruce Pitman, and Leon C. Moore. "Spectral properties of the tubuloglomerular feedback system." American Journal of Physiology-Renal Physiology 273, no. 4 (October 1, 1997): F635—F649. http://dx.doi.org/10.1152/ajprenal.1997.273.4.f635.

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A simple mathematical model was used to investigate the spectral properties of the tubuloglomerular feedback (TGF) system. A perturbation, consisting of small-amplitude broad-band forcing, was applied to simulated thick ascending limb (TAL) flow, and the resulting spectral response of the TGF pathway was assessed by computing a power spectrum from resulting TGF-regulated TAL flow. Power spectra were computed for both open- and closed-feedback-loop cases. Open-feedback-loop power spectra are consistent with a mathematical analysis that predicts a nodal pattern in TAL frequency response, with nodes corresponding to frequencies where oscillatory flow has a TAL transit time that equals the steady-state fluid transit time. Closed-feedback-loop spectra are dominated by the open-loop spectral response, provided that γ, the magnitude of feedback gain, is less than the critical value γc required for emergence of a sustained TGF-mediated oscillation. For γ exceeding γc, closed-loop spectra have peaks corresponding to the fundamental frequency of the TGF-mediated oscillation and its harmonics. The harmonics, expressed in a nonsinusoidal waveform for tubular flow, are introduced by nonlinear elements of the TGF pathway, notably TAL transit time and the TGF response curve. The effect of transit time on the flow waveform leads to crests that are broader than troughs and to an asymmetry in the magnitudes of increasing and decreasing slopes. For feedback gain magnitude that is sufficiently large, the TGF response curve tends to give a square waveshape to the waveform. Published waveforms and power spectra of in vivo TGF oscillations have features consistent with the predictions of this analysis.

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13

Azamov, Nurulla. "Spectral flow and resonance index." Dissertationes Mathematicae 528 (2017): 1–91. http://dx.doi.org/10.4064/dm756-6-2017.

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14

Carey, Alan, John Phillips, and Fyodor Sukochev. "Spectral flow and Dixmier traces." Advances in Mathematics 173, no. 1 (January 2003): 68–113. http://dx.doi.org/10.1016/s0001-8708(02)00015-4.

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15

Liszewski, Kathy. "Spectral Flow Cytometry Makes Debut." Genetic Engineering & Biotechnology News 33, no. 21 (December 2013): 1, 20–21. http://dx.doi.org/10.1089/gen.33.21.08.

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16

Collado, Jaime, Alvaro A. Aidama, and José L. Acosta‐Rodríguez. "Optimal Spectral Base‐Flow Estimation." Journal of Hydraulic Engineering 116, no. 12 (December 1990): 1540–46. http://dx.doi.org/10.1061/(asce)0733-9429(1990)116:12(1540).

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17

Giribet, Gastón, Ari Pakman, and Leonardo Rastelli. "Spectral flow in AdS3/CFT2." Journal of High Energy Physics 2008, no. 06 (June 10, 2008): 013. http://dx.doi.org/10.1088/1126-6708/2008/06/013.

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18

Klinkhamer, Frans R., and Christian Rupp. "Sphalerons, spectral flow, and anomalies." Journal of Mathematical Physics 44, no. 8 (August 2003): 3619–39. http://dx.doi.org/10.1063/1.1590420.

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19

Furutani, Kenro, and Nobukazu Otsuki. "Spectral flow and intersection number." Journal of Mathematics of Kyoto University 33, no. 1 (1993): 261–83. http://dx.doi.org/10.1215/kjm/1250519347.

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20

Zúñiga Zamalloa, Carlo, Henry Chi-Hin Ng, Pinaki Chakraborty, and Gustavo Gioia. "Spectral analogues of the law of the wall, the defect law and the log law." Journal of Fluid Mechanics 757 (September 19, 2014): 498–513. http://dx.doi.org/10.1017/jfm.2014.497.

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AbstractUnlike the classical scaling relations for the mean-velocity profiles of wall-bounded uniform turbulent flows (the law of the wall, the defect law and the log law), which are predicated solely on dimensional analysis and similarity assumptions, scaling relations for the turbulent-energy spectra have been informed by specific models of wall turbulence, notably the attached-eddy hypothesis. In this paper, we use dimensional analysis and similarity assumptions to derive three scaling relations for the turbulent-energy spectra, namely the spectral analogues of the law of the wall, the defect law and the log law. By design, each spectral analogue applies in the same spatial domain as the attendant scaling relation for the mean-velocity profiles: the spectral analogue of the law of the wall in the inner layer, the spectral analogue of the defect law in the outer layer and the spectral analogue of the log law in the overlap layer. In addition, as we are able to show without invoking any model of wall turbulence, each spectral analogue applies in a specific spectral domain (the spectral analogue of the law of the wall in the high-wavenumber spectral domain, where viscosity is active, the spectral analogue of the defect law in the low-wavenumber spectral domain, where viscosity is negligible, and the spectral analogue of the log law in a transitional intermediate-wavenumber spectral domain, which may become sizable only at ultra-high$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}_{\tau }$), with the implication that there exist model-independent one-to-one links between the spatial domains and the spectral domains. We test the spectral analogues using experimental and computational data on pipe flow and channel flow.

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21

Burgess, B. H., Andre R. Erler, and Theodore G. Shepherd. "The Troposphere-to-Stratosphere Transition in Kinetic Energy Spectra and Nonlinear Spectral Fluxes as Seen in ECMWF Analyses." Journal of the Atmospheric Sciences 70, no. 2 (February 1, 2013): 669–87. http://dx.doi.org/10.1175/jas-d-12-0129.1.

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Abstract Global horizontal wavenumber kinetic energy spectra and spectral fluxes of rotational kinetic energy and enstrophy are computed for a range of vertical levels using a T799 ECMWF operational analysis. Above 250 hPa, the kinetic energy spectra exhibit a distinct break between steep and shallow spectral ranges, reminiscent of dual power-law spectra seen in aircraft data and high-resolution general circulation models. The break separates a large-scale “balanced” regime in which rotational flow strongly dominates divergent flow and a mesoscale “unbalanced” regime where divergent energy is comparable to or larger than rotational energy. Between 230 and 100 hPa, the spectral break shifts to larger scales (from n = 60 to n = 20, where n is spherical harmonic index) as the balanced component of the flow preferentially decays. The location of the break remains fairly stable throughout the stratosphere. The spectral break in the analysis occurs at somewhat larger scales than the break seen in aircraft data. Nonlinear spectral fluxes defined for the rotational component of the flow maximize between about 300 and 200 hPa. Large-scale turbulence thus centers on the extratropical tropopause region, within which there are two distinct mechanisms of upscale energy transfer: eddy–eddy interactions sourcing the transient energy peak in synoptic scales, and zonal mean–eddy interactions forcing the zonal flow. A well-defined downscale enstrophy flux is clearly evident at these altitudes. In the stratosphere, the transient energy peak moves to planetary scales and zonal mean–eddy interactions become dominant.

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22

Siji, Siji, Sanju Alias K. Varghese, Jayaraj U. Kidav, and Shiny C. Shiny C. "Design & Development of Spectral Doppler System for Blood Flow Measurement." International Journal of Scientific Research 3, no. 5 (June 1, 2012): 210–12. http://dx.doi.org/10.15373/22778179/may2014/63.

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23

da Cunha Lima, A. T., I. C. da Cunha Lima, and M. P. de Almeida. "Analysis of turbulence power spectra and velocity correlations in a pipeline with obstructions." International Journal of Modern Physics C 28, no. 02 (February 2017): 1750019. http://dx.doi.org/10.1142/s012918311750019x.

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We calculate the power spectral density and velocity correlations for a turbulent flow of a fluid inside a duct. Turbulence is induced by obstructions placed near the entrance of the flow. The power spectral density is obtained for several points at cross-sections along the duct axis, and an analysis is made on the way the spectra changes according to the distance to the obstruction. We show that the differences on the power spectral density are important in the lower frequency range, while in the higher frequency range, the spectra are very similar to each other. Our results suggest the use of the changes on the low frequency power spectral density to identify the occurrence of obstructions in pipelines. Our results show some frequency regions where the power spectral density behaves according to the Kolmogorov hypothesis. At the same time, the calculation of the power spectral densities at increasing distances from the obstructions indicates an energy cascade where the spectra evolves in frequency space by spreading the frequency amplitude.

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24

Motsa, S. S., P. G. Dlamini, and M. Khumalo. "Spectral Relaxation Method and Spectral Quasilinearization Method for Solving Unsteady Boundary Layer Flow Problems." Advances in Mathematical Physics 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/341964.

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Nonlinear partial differential equations (PDEs) modelling unsteady boundary-layer flows are solved by the spectral relaxation method (SRM) and the spectral quasilinearization method (SQLM). The SRM and SQLM are Chebyshev pseudospectral based methods that have been successfully used to solve nonlinear boundary layer flow problems described by systems of ordinary differential equations. In this paper application of these methods is extended, for the first time, to systems of nonlinear PDEs that model unsteady boundary layer flow. The new extension is tested on two problems: boundary layer flow caused by an impulsively stretching plate and a coupled four-equation system that models the problem of unsteady MHD flow and mass transfer in a porous space. Numerous simulation experiments are conducted to determine the accuracy and compare the computational performance of the proposed methods against the popular Keller-box finite difference scheme which is widely accepted as being one of the ideal tools for solving nonlinear PDEs that model boundary layer flow problems. The results indicate that the methods are more efficient in terms of computational accuracy and speed compared with the Keller-box.

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25

Chait, Arnon, and Seppo A. Korpela. "The secondary flow and its stability for natural convection in a tall vertical enclosure." Journal of Fluid Mechanics 200 (March 1989): 189–216. http://dx.doi.org/10.1017/s0022112089000625.

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The multicellular flow between two vertical parallel plates is numerically simulated using a time-splitting pseudospectral method. The steady flow of air, and the time-periodic flow of oil (Prandtl numbers of 0.71 and 1000, respectively) are investigated and descriptions of these flows using both physical and spectral approaches are presented. The details of the time dependency of the flow and temperature fields of oil are shown, and the dynamics of the process is discussed. The spectral transfer of energy among the axial modes comprising the flow is explored. The spectra of kinetic energy and thermal variance for air are found to be smooth and viscously dominated. Similar spectra for oil are bumpier, and the dynamics of the time-dependent flow are determined to be confined to the lower end of the spectrum alone.The three-dimensional linear stability of the multicellular flow of air is parametrically studied. The domain of stable two-dimensional cellular motion was found to be constrained by the Eckhaus instability and by two types of monotone instability. The two-dimensional multicellular flow is unstable above a Grashof number of about 8550 (with the critical Grashof number for the base flow being 8037). Therefore the flow of air in a sufficiently tall vertical enclosure should be considered to be three-dimensional for most practical applications.

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26

HENNINGSON, DAN S. "Description of complex flow behaviour using global dynamic modes." Journal of Fluid Mechanics 656 (July 20, 2010): 1–4. http://dx.doi.org/10.1017/s0022112010002776.

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A novel method for performing spectral analysis of a fluid flow solely based on snapshot sequences from numerical simulations or experimental data is presented by Schmid (J. Fluid Mech., 2010, this issue, vol. 656, pp. 5–28). Dominant frequencies and wavenumbers are extracted together with dynamic modes which represent the associated flow structures. The mathematics underlying this decomposition is related to the Koopman operator which provides a linear representation of a nonlinear dynamical system. The procedure to calculate the spectra and dynamic modes is based on Krylov subspace methods; the dynamic modes reduce to global linear eigenmodes for linearized problems or to Fourier modes for (nonlinear) periodic problems. Schmid (2010) also generalizes the analysis to the propagation of flow variables in space which produces spatial growth rates with associated dynamic modes, and an application of the decomposition to subdomains of the flow region allows the extraction of localized stability information. For finite-amplitude flows this spectral analysis identifies relevant frequencies more effectively than global eigenvalue analysis and decouples frequency information more clearly than proper orthogonal decomposition.

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27

Doll, Nora, Hermann Schulz‐Baldes, and Nils Waterstraat. "Parity as Z2‐valued spectral flow." Bulletin of the London Mathematical Society 51, no. 5 (August 26, 2019): 836–52. http://dx.doi.org/10.1112/blms.12282.

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28

Clercx, H. J. H. "Spectral Methods for Incompressible Viscous Flow." European Journal of Mechanics - B/Fluids 22, no. 2 (March 2003): 199. http://dx.doi.org/10.1016/s0997-7546(03)00003-7.

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29

BALACHANDRAN, A. P., and SACHINDEO VAIDYA. "SKYRMIONS, SPECTRAL FLOW AND PARITY DOUBLES." International Journal of Modern Physics A 14, no. 03 (January 30, 1999): 445–61. http://dx.doi.org/10.1142/s0217751x99000221.

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It is well-known that the winding number of the Skyrmion can be identified as the baryon number. We show in this paper that this result can also be established using the Atiyah–Singer index theorem and spectral flow arguments. We argue that this proof suggests that there are light quarks moving in the field of the Skyrmion. We then show that if these light degrees of freedom are averaged out, the low energy excitations of the Skyrmion are in fact spinorial. A natural consequence of our approach is the prediction of a [Formula: see text] state and its excitations in addition to the nucleon and delta. Using the recent numerical evidence for the existence of Skyrmions with discrete spatial symmetries, we further suggest that the the low energy spectrum of many light nuclei may possess a parity doublet structure arising from a subtle topological interaction between the slow Skyrmion and the fast quarks. We also present tentative experimental evidence supporting our arguments.

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30

Lee, Matthew E., and Mark J. T. Smith. "Spectral analysis of glottal flow models." Journal of the Acoustical Society of America 115, no. 5 (May 2004): 2609–10. http://dx.doi.org/10.1121/1.4784738.

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31

Kirk, Paul, and Eric Klassen. "Computing spectral flow via cup products." Journal of Differential Geometry 40, no. 3 (1994): 505–62. http://dx.doi.org/10.4310/jdg/1214455777.

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32

Carey, Alan, and John Phillips. "Unbounded Fredholm Modules and Spectral Flow." Canadian Journal of Mathematics 50, no. 4 (August 1, 1998): 673–718. http://dx.doi.org/10.4153/cjm-1998-038-x.

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AbstractAn odd unbounded (respectively, p-summable) Fredholm module for a unital Banach *-algebra, A, is a pair (H,D) where A is represented on the Hilbert space, H, and D is an unbounded self-adjoint operator on H satisfying:(1) (1 + D2)-1 is compact (respectively, Trace_(1 + D2)-(p/2)_∞), and(2) ﹛a ∈ A | [D, a] is bounded﹜ is a dense *- subalgebra of A.If u is a unitary in the dense *-subalgebra mentioned in (2) thenuDu* = D + u[D, u*] = D + Bwhere B is a bounded self-adjoint operator. The pathis a “continuous” path of unbounded self-adjoint “Fredholm” operators. More precisely, we show thatis a norm-continuous path of (bounded) self-adjoint Fredholm operators. The spectral flow of this path is roughly speaking the net number of eigenvalues that pass through 0 in the positive direction as t runs from 0 to 1. This integer,recovers the pairing of the K-homology class [D] with the K-theory class [u].We use I.M. Singer's idea (as did E. Getzler in the θ-summable case) to consider the operator B as a parameter in the Banach manifold, Bsa(H), so that spectral flow can be exhibited as the integral of a closed 1-formon this manifold. Now, for B in ourmanifold, any X ∈ TB_Bsa(H)_ is given by an X in Bsa(H) as the derivative at B along the curve t→ B + tX in the manifold. Then we show that for m a sufficiently large half-integer:is a closed 1-form. For any piecewise smooth path {Dt = D + Bt} with D0 and D1 unitarily equivalent we show thatthe integral of the 1-form ã. If D0 and D1 are not unitarily equivalent, wemust add a pair of correction terms to the right-hand side. We also prove a bounded finitely summable version of the form:for an integer. The unbounded case is proved by reducing to the bounded case via the map . We prove simultaneously a type II version of our results.

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33

Booss-Bavnbek, Bernhelm, Matthias Lesch, and John Phillips. "Unbounded Fredholm Operators and Spectral Flow." Canadian Journal of Mathematics 57, no. 2 (April 1, 2005): 225–50. http://dx.doi.org/10.4153/cjm-2005-010-1.

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AbstractWe study the gap (= “projection norm” = “graph distance”) topology of the space of all (not necessarily bounded) self-adjoint Fredholm operators in a separable Hilbert space by the Cayley transformand direct methods. In particular, we show the surprising result that this space is connected in contrast to the bounded case. Moreover, we present a rigorous definition of spectral flow of a path of such operators (actually alternative but mutually equivalent definitions) and prove the homotopy invariance. As an example, we discuss operator curves on manifolds with boundary.

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34

Taubes, Clifford Henry. "Asymptotic spectral flow for Dirac operators." Communications in Analysis and Geometry 15, no. 3 (2007): 569–87. http://dx.doi.org/10.4310/cag.2007.v15.n3.a5.

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35

Kopnin, N. B., and V. M. Vinokur. "Spectral flow in superconducting point contacts." Europhysics Letters (EPL) 61, no. 6 (March 2003): 824–30. http://dx.doi.org/10.1209/epl/i2003-00308-1.

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36

Ming-de, Dong. "The spectral problem of Poiseuille flow." Applied Mathematics and Mechanics 6, no. 3 (March 1985): 213–18. http://dx.doi.org/10.1007/bf01895516.

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37

Kovtun, S. N., A. I. Mogil'ner, S. A. Morozov, Yu P. Trubakov, and A. Yu Uralets. "Spectral method of flow-velocity measurement." Soviet Atomic Energy 60, no. 3 (1986): 265–67. http://dx.doi.org/10.1007/bf01132318.

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38

Eglitis, P., I. W. McCrea, T. R. Robinson, T. B. Jones, K. Schlegel, and T. Nygren. "Flow dependence of COSCAT spectral characteristics." Journal of Atmospheric and Terrestrial Physics 58, no. 1-4 (January 1996): 189–203. http://dx.doi.org/10.1016/0021-9169(95)00029-1.

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39

Heinrichs, Wilhelm. "Spectral viscosity for convection dominated flow." Journal of Scientific Computing 9, no. 2 (June 1994): 137–48. http://dx.doi.org/10.1007/bf01578384.

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40

Candy, J., and E. A. Belli. "Spectral treatment of gyrokinetic shear flow." Journal of Computational Physics 356 (March 2018): 448–57. http://dx.doi.org/10.1016/j.jcp.2017.12.020.

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41

Romero, Xabier, and Juan A. Hernández. "Spectral problem for water flow glazings." Energy and Buildings 145 (June 2017): 67–78. http://dx.doi.org/10.1016/j.enbuild.2017.03.013.

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42

Thiang, Guo Chuan. "On Spectral Flow and Fermi Arcs." Communications in Mathematical Physics 385, no. 1 (February 8, 2021): 465–93. http://dx.doi.org/10.1007/s00220-021-04007-z.

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43

Lange, Andrew J., and Peter R. Griffiths. "Use of Buffered Solvent Systems with Concentric Flow Nebulization Liquid Chromatography/Fourier Transform Infrared Spectrometry." Applied Spectroscopy 47, no. 4 (April 1993): 403–10. http://dx.doi.org/10.1366/0003702934335047.

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Identifiable Fourier transform infrared (FT-IR) spectra of species eluting from a high-performance liquid Chromatograph (HPLC) in buffered mobile phases are shown. The spectra are measured with the use of an online solvent-elimination HPLC/FT-IR interface based on direct-deposition concentric flow nebulization. Both volatile and nonvolatile buffers were used, in mobile phases consisting of 63–100% water. Examples of spectra of components separated by microbore HPLC using these buffered systems are shown. For the systems using nonvolatile buffers, spectral subtraction is needed to obtain analyte spectra, and absorption bands due to the buffer are rarely completely eliminated. For systems using volatile buffers, very little or no spectral subtraction is needed at low buffer concentrations. Minimum identifiable quantities in the low-nanogram range were achieved.

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44

Sieber, Moritz, C. Oliver Paschereit, and Kilian Oberleithner. "Spectral proper orthogonal decomposition." Journal of Fluid Mechanics 792 (March 4, 2016): 798–828. http://dx.doi.org/10.1017/jfm.2016.103.

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The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures the dominant flow structures. The most prominent candidates are the energy-ranked proper orthogonal decomposition (POD) and the frequency-ranked Fourier decomposition and dynamic mode decomposition (DMD). However, these methods are not suitable when the relevant coherent structures occur at low energies or at multiple frequencies, which is often the case. To overcome the deficit of these ‘rigid’ approaches, we propose a new method termed spectral proper orthogonal decomposition (SPOD). It is based on classical POD and it can be applied to spatially and temporally resolved data. The new method involves an additional temporal constraint that enables a clear separation of phenomena that occur at multiple frequencies and energies. SPOD allows for a continuous shifting from the energetically optimal POD to the spectrally pure Fourier decomposition by changing a single parameter. In this article, SPOD is motivated from phenomenological considerations of the POD autocorrelation matrix and justified from dynamical systems theory. The new method is further applied to three sets of PIV measurements of flows from very different engineering problems. We consider the flow of a swirl-stabilized combustor, the wake of an airfoil with a Gurney flap and the flow field of the sweeping jet behind a fluidic oscillator. For these examples, the commonly used methods fail to assign the relevant coherent structures to single modes. The SPOD, however, achieves a proper separation of spatially and temporally coherent structures, which are either hidden in stochastic turbulent fluctuations or spread over a wide frequency range. The SPOD requires only one additional parameter, which can be estimated from the basic time scales of the flow. In spite of all these benefits, the algorithmic complexity and computational cost of the SPOD are only marginally greater than those of the snapshot POD.

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Milan, S. E., and M. Lester. "Simultaneous observations at different altitudes of ionospheric backscatter in the eastward electrojet." Annales Geophysicae 16, no. 1 (January 31, 1998): 55–68. http://dx.doi.org/10.1007/s00585-997-0055-9.

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Abstract. A common feature of evening near-range ionospheric backscatter in the CUTLASS Iceland radar field of view is two parallel, approximately L-shell-aligned regions of westward flow which are attributed to irregularities in the auroral eastward electrojet region of the ionosphere. These backscatter channels are separated by approximately 100–200 km in range. The orientation of the CUTLASS Iceland radar beams and the zonally aligned nature of the flow allows an approximate determination of flow angle to be made without the necessity of bistatic measurements. The two flow channels have different azimuthal variations in flow velocity and spectral width. The nearer of the two regions has two distinct spectral signatures. The eastern beams detect spectra with velocities which saturate at or near the ion-acoustic speed, and have low spectral widths (less than 100 m s–1), while the western beams detect lower velocities and higher spectral widths (above 200 m s–1). The more distant of the two channels has only one spectral signature with velocities above the ion-acoustic speed and high spectral widths. The spectral characteristics of the backscatter are consistent with E-region scatter in the nearer channel and upper-E-region or F-region scatter in the further channel. Temporal variations in the characteristics of both channels support current theories of E-region turbulent heating and previous observations of velocity-dependent backscatter cross-section. In future, observations of this nature will provide a powerful tool for the investigation of simultaneous E- and F-region irregularity generation under similar (nearly co-located or magnetically conjugate) electric field conditions.Key words. Auroral ionosphere · Ionospheric irregularities · Plasma convection

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AZZALI, SARA, and CHARLOTTE WAHL. "SPECTRAL FLOW, INDEX AND THE SIGNATURE OPERATOR." Journal of Topology and Analysis 03, no. 01 (March 2011): 37–67. http://dx.doi.org/10.1142/s1793525311000477.

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We relate the spectral flow to the index for paths of selfadjoint Breuer–Fredholm operators affiliated to a semifinite von Neumann algebra, generalizing results of Robbin–Salamon and Pushnitski. Then we prove the vanishing of the von Neumann spectral flow for the tangential signature operator of a foliated manifold when the metric is varied. We conclude that the tangential signature of a foliated manifold with boundary does not depend on the metric. In the Appendix we reconsider integral formulas for the spectral flow of paths of bounded operators.

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Kaad, J., R. Nest, and A. Rennie. "KK-Theory and Spectral Flow in von Neumann Algebras." Journal of K-Theory 10, no. 2 (April 4, 2012): 241–77. http://dx.doi.org/10.1017/is012003003jkt185.

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AbstractWe present a definition of spectral flow for any norm closed ideal J in any von Neumann algebra N. Given a path of selfadjoint operators in N which are invertible in N/J, the spectral flow produces a class in Ko(J).Given a semifinite spectral triple (A, H, D) relative to (N, τ) with A separable, we construct a class [D] ∈ KK1(A, K(N)). For a unitary u ∈ A, the von Neumann spectral flow between D and u*Du is equal to the Kasparov product [u]A[D], and is simply related to the numerical spectral flow, and a refined C*-spectral flow.

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Goffeng, Magnus, and Elmar Schrohe. "Spectral flow of exterior Landau–Robin hamiltonians." Journal of Spectral Theory 7, no. 3 (2017): 847–79. http://dx.doi.org/10.4171/jst/179.

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Carey, Alan, John Phillips, and Hermann Schulz-Baldes. "Spectral flow for skew-adjoint Fredholm operators." Journal of Spectral Theory 9, no. 1 (October 23, 2018): 137–70. http://dx.doi.org/10.4171/jst/243.

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Isaacson, LaVar King. "Spectral Entropy in a Boundary-Layer Flow." Entropy 13, no. 9 (August 26, 2011): 1555–83. http://dx.doi.org/10.3390/e13091555.

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