Spectral Transfers Research Articles

2D Fourier series representation of gravitational functionals in spherical coordinates

2D Fourier series representation of a scalar field like gravitational potential is conventionally derived by making use of the Fourier series of the Legendre functions in the spherical harmonic representation. This representation has been employed so far only in the case of a scalar field or the functionals that are related to it through a radial derivative. This paper provides a unified scheme to represent any gravitational functional in terms of spherical coordinates using a 2D Fourier series representation. The 2D Fourier series representation for each individual point is derived by transforming the spherical harmonics from the geocentric Earth-fixed frame to a rotated frame so that its equator coincides with the local meridian plane of that point. In the obtained formulation, each functional is linked to the potential in the spectral domain using a spectral transfer. We provide the spectral transfers of the first-, second- and third-order gradients of the gravitational potential in the local north-oriented reference frame and also those of some functionals of frequent use in the physical geodesy. The obtained representation is verified numerically. Moreover, spherical harmonic analysis of anisotropic functionals and contribution analysis of the third-order gradient tensor are provided as two numerical examples to show the power of the formulation. In conclusion, the 2D Fourier series representation on the sphere is generalized to functionals of the potential. In addition, the set of the spectral transfers can be considered as a pocket guide that provides the spectral characteristics of the functionals. Therefore, it extends the so-called Meissl scheme.

REPRESENTATION OF GRADIENTS OF A SCALAR FIELD ON THE SPHERE USING A 2D FOURIER EXPRESSION

Abstract. Representation of data on the sphere is conventionally done using spherical harmonics. Making use of the Fourier series of the Legendre function in the SH representation results in a 2D Fourier expression. So far the 2D Fourier series representation on the sphere has been confined to a scalar field like geopotential or relief data. We show that if one views the 2D Fourier formulation as a representation in a rotated frame, instead of the original Earth-fixed frame, one can easily generalize the representation to any gradient of the scalar field. Indeed, the gradient and the scalar field itself are simply linked in the spectral domain using spectral transfers. We provide the spectral transfers of the first-, second- and third-order gradients of a scalar field in a local frame. Using three numerical examples based on gravity and geometrical quantities, we show the applicability of the presented formulation.

Toward an internal gravity wave spectrum in global ocean models

AbstractHigh‐resolution global ocean models forced by atmospheric fields and tides are beginning to display realistic internal gravity wave spectra, especially as model resolution increases. This paper examines internal waves in global simulations with 0.08° and 0.04° (~8 and 4 km) horizontal resolutions, respectively. Frequency spectra of internal wave horizontal kinetic energy in the North Pacific lie closer to observations in the 0.04° simulation than in the 0.08° simulation. The horizontal wave number and frequency (K‐ω) kinetic energy spectra contain peaks in the semidiurnal tidal band and near‐inertial band, along with a broadband frequency continuum aligned along the linear dispersion relations of low‐vertical‐mode internal waves. Spectral kinetic energy transfers describe the rate at which nonlinear mechanisms remove or supply kinetic energy in specific K‐ω ranges. Energy is transferred out of low‐mode inertial and semidiurnal internal waves into a broad continuum of higher‐frequency and higher‐wave number internal waves.

Spectral changes in layeredf-electron systems induced by Kondo hole substitution in the boundary layer

We investigate the effect of disorder on the dynamical spectrum of layered $f$-electron systems. With random dilution of $f$ sites in a single Kondo insulating layer, we explore the range and extent to which Kondo hole incoherence can penetrate into adjacent layers. We consider three cases of neighboring layers: band insulator, Kondo insulator, and simple metal. The disorder-induced spectral weight transfer, used here for quantification of the proximity effect, decays algebraically with distance from the boundary layer. Further, we show that the spectral weight transfer is highly dependent on the frequency range considered as well as the presence of interactions in the clean adjacent layers. The changes in the low-frequency spectrum are very similar when the adjacent layers are either metallic or Kondo insulating, and hence are independent of interactions. In stark contrast, a distinct picture emerges for the spectral weight transfers across large energy scales. The spectral weight transfer over all energy scales is much higher when the adjacent layers are noninteracting as compared to when they are strongly interacting Kondo insulators. Thus, over all scales, interactions screen the disorder effects significantly. We discuss the possibility of a crossover from non-Fermi-liquid to Fermi-liquid behavior upon increasing the ratio of clean to disordered layers in particle-hole asymmetric systems.

Optical spectral weight: Comparison of weak and strong spin-orbit coupling

The Fermi velocity ($v_{F}$) associated with the spin-orbit coupling is two orders of magnitude smaller for spintronic semiconductors than it is for topological insulators. Both families can be treated with the same Hamiltonian which contains a relativistic (Dirac) linear in momentum term proportional to $v_{F}$ and a non-relativistic quadratic contribution with Schr\"{o}dinger mass (m). We find that the AC dynamic longitudinal and transverse (Hall) magneto-conductivities are strongly dependent on the size of $v_{F}$. When the Dirac fermi velocity is small, the absorption background provided by the interband optical transitions is finite only over a very limited range of photon energies as compared with topological insulators. Its onset depends on the value of the chemical potential ($\mu$) and on the magnetic field (B), as does its upper cut off. Within this limited range its magnitude is however constant and has the same magnitude of $e^{2}\pi/(8h)$ as is found in topological insulators and also in graphene noting a difference in degeneracy factor. The total optical spectral weight under the universal interband background is $e^{2}\pi/(8h)4mv_{F}^{2}$. In contrast to the known result for graphene no strict conservation law applies to the spectral weight transfers between inter and intra band transition brought about by variations in the magnitude of the chemical potential when a non-relativistic contribution is present in the Hamiltonian whatever size it may have.

Brain Transfer: Spectral Analysis of Cortical Surfaces and Functional Maps.

The study of brain functions using fMRI often requires an accurate alignment of cortical data across a population. Particular challenges are surface inflation for cortical visualizations and measurements, and surface matching or alignment of functional data on surfaces for group-level analyses. Present methods typically treat each step separately and can be computationally expensive. For instance, smoothing and matching of cortices often require several hours. Conventional methods also rely on anatomical features to drive the alignment of functional data between cortices, whereas anatomy and function can vary across individuals. To address these issues, we propose BrainTransfer, a spectral framework that unifies cortical smoothing, point matching with confidence regions, and transfer of functional maps, all within minutes of computation. Spectral methods decompose shapes into intrinsic geometrical harmonics, but suffer from the inherent instability of eigenbasis. This limits their accuracy when matching eigenbasis, and prevents the spectral transfer of functions. Our contributions consist of, first, the optimization of a spectral transformation matrix, which combines both, point correspondence and change of eigenbasis, and second, focused harmonics, which localize the spectral decomposition of functional data. BrainTransfer enables the transfer of surface functions across interchangeable cortical spaces, accounts for localized confidence, and gives a new way to perform statistics directly on surfaces. Benefits of spectral transfers are illustrated with a variability study on shape and functional data. Matching accuracy on retinotopy is increased over conventional methods.

Kondo-hole substitution in heavy fermions: Dynamics and transport

Kondo-hole substitution is a unique probe for exploring the interplay of interactions, f-electron dilution and disorder in heavy fermion materials. Within the diluted periodic Anderson model, we investigate the changes in single-particle dynamics as well as response functions, as a function of Kondo hole concentration ($x$) and temperature. We show that the spectral weight transfers due to Kondo hole substitution has characteristics that are different from those induced by temperature; The dc resistivity crosses over from a highly non-monotonic form with a coherence peak in the $x\rightarrow 0$ limit to a monotonic single-impurity like form that saturates at low temperature. The thermopower exhibits a characteristic maximum as a function of temperature, the value of which changes sign with increasing $x$, and its location is shown to correspond to a low energy scale of the system. The Hall coefficient also changes sign with increasing $x$ at zero temperature and is highly temperature dependent for all $x$. As $x$ is increased beyond a certain $x_c$, the Drude peak and the mid-infrared peak in the optical conductivity vanish almost completely; A peak in the optical scattering rate melts and disappears eventually. We discuss the above-mentioned changes in the properties in terms of a crossover from coherent, Kondo lattice behaviour to single impurity like, incoherent behaviour with increasing $x$. A comparison of theory with experiments carried out for the dc resistivity and the thermopower of Ce$_{1-x}$La$_x$B$_6$ yields good agreement.

Geostrophic Turbulence in the Frequency–Wavenumber Domain: Eddy-Driven Low-Frequency Variability*

Abstract Motivated by the potential of oceanic mesoscale eddies to drive intrinsic low-frequency variability, this paper examines geostrophic turbulence in the frequency–wavenumber domain. Frequency–wavenumber spectra, spectral fluxes, and spectral transfers are computed from an idealized two-layer quasigeostrophic (QG) turbulence model, a realistic high-resolution global ocean general circulation model, and gridded satellite altimeter products. In the idealized QG model, energy in low wavenumbers, arising from nonlinear interactions via the well-known inverse cascade, is associated with energy in low frequencies and vice versa, although not in a simple way. The range of frequencies that are highly energized and engaged in nonlinear transfer is much greater than the range of highly energized and engaged wavenumbers. Low-frequency, low-wavenumber energy is maintained primarily by nonlinearities in the QG model, with forcing and friction playing important but secondary roles. In the high-resolution ocean model, nonlinearities also generally drive kinetic energy to low frequencies as well as to low wavenumbers. Implications for the maintenance of low-frequency oceanic variability are discussed. The cascade of surface kinetic energy to low frequencies that predominates in idealized and realistic models is seen in some regions of the gridded altimeter product, but not in others. Exercises conducted with the general circulation model suggest that the spatial and temporal filtering inherent in the construction of gridded satellite altimeter maps may contribute to the discrepancies between the direction of the frequency cascade in models versus gridded altimeter maps seen in some regions. Of course, another potential reason for the discrepancy is missing physics in the models utilized here.

Dynamic Mott gap from holographic fermions in geometries with hyperscaling violation

We investigate a dynamically generated Mott gap from holographic fermions in asymptotically geometries with hyperscaling violation by employing a bulk dipole coupling for the fermion field. We find that when the coupling strength increases the spectral function first transfers to the negative frequency region but soon redistributes to the positive region. A stable gap and two bands emerges for all momentum when the coupling strength beyonds a critical value. Generally, The upper band on the positive frequency axis is much sharper than the lower band on the negative side. When the diploe coupling increases further, the gap becomes larger and the up band still keeps sharp while the lower band disperses and widens, concentrating on the small momentum region. We also find that the bands will be smoothed out gradually with the increasing of hyperscaling violation.

Hund and pair-hopping signatures in transport properties of degenerate nanoscale devices

We investigate the signature of a complete Coulomb interaction in transport properties of double-orbital nanoscale devices. We analyze the specific effects of Hund exchange and pair hopping terms, calculating in particular stability diagrams. It turns out that a crude model, with partial Coulomb interaction, may lead to a misinterpretation of experiments. In addition, it is shown that spectral weight transfers induced by gate and bias voltages strongly influence charge current. The low temperature regime is also investigated, displaying inelastic cotunneling associated with the exchange term, as well as Kondo conductance enhancement.

MAGNETIC ENERGY CASCADE IN SPHERICAL GEOMETRY. I. THE STELLAR CONVECTIVE DYNAMO CASE

We present a method to characterize the spectral transfers of magnetic energy between scales in simulations of stellar convective dynamos. The full triadic transfer functions are computed thanks to analytical coupling relations of spherical harmonics based on the Clebsch-Gordan coefficients. The method is applied to mean field $\alpha\Omega$ dynamo models as benchmark tests. From the physical standpoint, the decomposition of the dynamo field into primary and secondary dynamo families proves very instructive in the $\alpha\Omega$ case. The same method is then applied to a fully turbulent dynamo in a solar convection zone, modeled with the 3D MHD ASH code. The initial growth of the magnetic energy spectrum is shown to be non-local. It mainly reproduces the kinetic energy spectrum of convection at intermediate scales. During the saturation phase, two kinds of direct magnetic energy cascades are observed in regions encompassing the smallest scales involved in the simulation. The first cascade is obtained through the shearing of magnetic field by the large scale differential rotation that effectively cascades magnetic energy. The second is a generalized cascade that involves a range of local magnetic and velocity scales. Non-local transfers appear to be significant, such that the net transfers cannot be reduced to the dynamics of a small set of modes. The saturation of the large scale axisymmetric dipole and quadrupole are detailed. In particular, the dipole is saturated by a non-local interaction involving the most energetic scale of the magnetic energy spectrum, which points out the importance of the magnetic Prandtl number for large-scale dynamos.

A framework for the evaluation of turbulence closures used in mesoscale ocean large-eddy simulations

We present a methodology to determine the best turbulence closure for an eddy-permitting ocean model through measurement of the error-landscape of the closure’s subgrid spectral transfers and flux. We apply this method to 6 different closures for forced-dissipative simulations of the barotropic vorticity equation on an f-plane (2D Navier–Stokes equation). Using a high-resolution benchmark, we compare each closure’s model of energy and enstrophy transfer to the actual transfer observed in the benchmark run. The error-landscape norm enables us to both make objective comparisons between the closures and to optimize each closure’s free parameter for a fair comparison. The hyper-viscous closure most closely reproduces the enstrophy cascade, especially at larger scales due to the concentration of its dissipative effects to the very smallest scales. The viscous and Leith closures perform nearly as well, especially at smaller scales where all three models were dissipative. The Smagorinsky closure dissipates enstrophy at the wrong scales. The anticipated potential vorticity closure was the only model to reproduce the upscale transfer of kinetic energy from the unresolved scales, but would require high-order Laplacian corrections in order to concentrate dissipation at the smallest scales. The Lagrangian-averaged α-model closure did not perform successfully for forced 2D isotropic Navier–Stokes: small-scale filamentation is only slightly reduced by the model while small-scale roll-up is prevented. Together, this reduces the effects of diffusion.

Infrared spectroscopy and the ferromagnetic transition in Gd

The low energy electronic structure of Gd has been investigated experimentally by infrared reflectance spectroscopy, and theoretically from first principles, using the fully relativistic Dirac linear-muffin-tin-orbital (LMTO) method in the local spin density approximation (LSDA) as well as within the LSDA + U approach. The reflectance of a Gd single crystal was measured with the electric field in the plane perpendicular to the c-axis for temperatures between 50 K and slightly above the Curie temperature (293 K) in the frequency range between 100 and 12 000 cm−1 (0.013–1.5 eV). As Gd enters the ferromagnetic state, the dissipative part of the optical conductivity exhibits interesting spectral weight transfers over the whole spectral range measured. It is shown that the ab initio calculations reproduce well the experimental spectra for the ferromagnetic state and allow one to explain the microscopic origin of the optical response of Gd in terms of interband transitions.

Dynamical screening effects in correlated materials: Plasmon satellites and spectral weight transfers from a Green's function ansatz to extended dynamical mean field theory

Dynamical screening of the Coulomb interactions in correlated electron systems results in a low-energy effective problem with a dynamical Hubbard interaction U(omega). We propose a Green's function ansatz for the Anderson impurity problem with retarded interactions, in which the Green's function factorizes into a contribution stemming from an effective static-U problem and a bosonic high-energy part introducing collective plasmon excitations. Our approach relies on the scale separation of the low-energy properties, related to the instantaneous static U, from the intermediate to high energy features originating from the retarded part of the interaction. We argue that for correlated materials where retarded interactions arise from downfolding higher-energy degrees of freedom, the characteristic frequencies are typically in the antiadiabatic regime. In this case, accurate approximations to the bosonic factor are relatively easy to construct, with the most simple being the boson factor of the dynamical atomic limit problem. We benchmark the quality of our method against numerically exact continuous time quantum Monte Carlo results for the Anderson-Holstein model both, at half- and quarter-filling. Furthermore we study the Mott transition within the Hubbard-Holstein model within extended dynamical mean field theory. Finally, we apply our technique to a realistic three-band Hamiltonian for SrVO3. We show that our approach reproduces both, the effective mass renormalization and the position of the lower Hubbard band by means of a dynamically screened U, previously determined ab initio within the constrained random phase approximation. Our approach could also be used within schemes beyond dynamical mean field theory, opening a quite general way of describing satellites and plasmon excitations in correlated materials.

Spin dynamics near the critical doping in weakly superconducting underdopedYBa2Cu3O6.35(Tc=18K)

From neutron inelastic and elastic scattering we have determined the magnetic structure and fluctuations in the $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.35}$ (YBCO) superconductor $({T}_{c}=18\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ near the boundary of the superconducting phase. The long-range ordered collinear spins of the insulating antiferromagnet are replaced by a commensurate central mode arising from slow, isotropically polarized, short-range spin correlations extending over four planar unit cells. The inelastic spectrum up to $30\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ is also broad in wave vector and commensurate. In contrast to the resonance peak of higher-${T}_{c}$ superconductors, the spins exhibit a single overdamped spectrum whose rate of relaxation $\ensuremath{\Gamma}$ decreases on cooling and saturates at $2\ensuremath{\Gamma}=5\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ below $\ensuremath{\sim}50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. As the relaxation rate saturates, the quasistatic spin correlations grow and become resolution limited in energy. The spin susceptibility above $\ensuremath{\sim}50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ follows the same $\ensuremath{\omega}∕T$ scaling relation found for the monolayer ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$ system, indicating that the dominant energy scale is set by the temperature. Below $50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ the scale length is geometric and not linked by velocity to dynamic widths. Despite the large differences from an antiferromagnet, we show that integrated intensity conserves the total moment sum rule, and that on cooling the spectral weight transfers from the inelastic spin relaxation to the elastic central peak. There is no observable suppression of the spin fluctuations or central mode upon the onset of superconductivity. The spins respond not to coherent charge pairs but to hole doping, allowing coexistence of glassy short-range spin order with superconductivity. Since the physics of the weakly superconducting system ${\mathrm{YBCO}}_{6.35}$ must connect continuously with that in more strongly superconducting ${\mathrm{YBCO}}_{6.5}$, we find that neither incommensurate stripe-like spin modulations nor a well-defined neutron spin resonance are essential for the onset with doping of pairing in a high-temperature cuprate superconductor.

Spectral transfers and zonal flow dynamics in the generalized Charney-Hasegawa-Mima model

The mechanism of four nonlinearly interacting drift or Rossby waves is used as the basic process underlying the turbulent evolution of both the Charney-Hasegawa-Mima-equation (CHME) and its generalized modification (GCHME). Hasegawa and Kodama’s concept of equivalent action (or quanta) is applied to the four-wave system and shown to control the distribution of energy and enstrophy between the modes. A numerical study of the GCHME is described in which the initial state contains a single finite-amplitude drift wave (the pump wave), and all the modulationally unstable modes are present at the same low level (10−6 times the pump amplitude). The simulation shows that at first the fastest-growing modulationally unstable modes dominate but reveals that at a later time, before pump depletion occurs, long- and short-wavelength modes, driven by pairs of fast-growing modes, grow at 2γmax. The numerical simulation illustrates the development of a spectrum of turbulent modes from a finite-amplitude pump wave.

The Mott transition: Unconventional transport, spectral weight transfers, and critical behaviour

Strongly correlated metals close to the Mott transition display unusual transport regimes, together with large spectral weight transfers in optics and photoemission. We briefly review the theoretical understanding of these effects, based on the dynamical mean-field theory, and emphasize the key role played by the two energy scales associated with quasiparticle coherence scale and with the Mott gap. Recent experimental results on two-dimensional organic compounds and transition metal oxides are considered in this perspective. The liquid-gas critical behaviour at the Mott critical endpoint is also discussed. Transport calculations using the numerical renormalization group are presented.

For a morphology of interaction

In mixed electroacoustic music it is common to find the erroneous conception according to which interaction should base itself exclusively on the fusion between instrumental writing and electronic devices, whereas the contrast between these sound spheres is as significant as the fusional states. Although fusion may be seen as the most important ingredient for an efficacious compositional strategy concerning interaction, it is actually through contrast that the identities of spectral transfers in mixed composition can be evaluated by the listener. This text intends to introduce a discussion about the many possibilities offered by the morphology of interaction between acoustic sources and electroacoustic resources and structures. In this sense it tries to identify intermediate types between the extremes of pure fusion and pure contrast, which can be established by the composer that sees in interactive music one of the most advantageous poetic realms of electroacoustic music.

Ultraviolet photoelectron spectroscopy study of colossal magnetoresistive La 0.7− xPr xCa 0.3MnO 3

We have investigated the electronic structure of colossal magnetoresistive perovskite manganites La 0.7− x Pr x Ca 0.3MnO 3 using ultraviolet photoelectron spectroscopy as a function of temperature and Pr concentration x ( x=0.13, 0.3, and 0.4). Unusual temperature-dependent and x-dependent spectral changes are observed in the entire valence band region. Since Pr doping does not introduce carriers into the system but brings about strong lattice distortion effects which exert significant influence on the p–d hybridization, the degree of mixing between Mn 3d and O2p levels is considered to be the major factor responsible for the spectral weight transfers with temperature and Pr doping level. The observed changes are not consistent with the results of local-density-approximation (LDA) band calculation, but can be understood by the density-of-states from the LDA+U calculation or configuration-interaction cluster calculations. This implies that a strong correlation effect between d electrons plays an important role in these manganites. High resolution spectra near the Fermi level shows a clear metallic edge at low temperature for low Pr concentration sample ( x=0.13), but the metallic Fermi edge disappears at higher Pr doping levels ( x=0.3 and 0.4) even at the temperature below T c where the bulk metal–insulator transition occurs. This may be due to the low effective carrier density resulting from the reduced ferromagnetic ordering and the lattice distortion, or the pseudo-gap phenomena and the surface effect.

A Two-Time-Scale Model for Turbulent Mixing Flows Induced by Rayleigh–Taylor and Richtmyer–Meshkov Instabilities

A two-time-scale closure model for compressible flows previously developed is extended to turbulent Rayleigh-Taylor and Richtmyer-Meshkov driven flows where mixing coexists with mean pressure gradients. Two model coefficients are calibrated with the help of Canuto-Goldman's model. For several Rayleigh-Taylor configurations, it is shown that the characteristic lengths scale as t 2 while the kinetic energies and spectral transfers behave as t 2 and t, respectively. The computed phenomenological coefficients of Youngs' scaling law are compared with experimental data ones. Comparisons with Youngs' three-dimensional numerical simulation (The Physics of Fluids A 3 (1991) 1312) are also performed. Finally three shock tube experiments, where the Richtmyer-Meshkov instability initiates the mixing, are simulated. The mixing thickness evolution is well reproduced while the turbulence levels seem to be overestimated with such first order models. The capability of the two-time-sale model to recover available data for different turbulent flows allows us to conclude to a more universal behavior in comparison with single-time-scale models.