Low-frequency Limit Research Articles

Finite-frequency spin conductance of the interface between a ferro- or ferrimagnetic insulator and a normal metal

The interface between a ferro-/ferrimagnetic insulator and a normal metal can support spin currents polarized collinear with and perpendicular to the magnetization direction. The flow of angular momentum perpendicular to the magnetization direction ("transverse" spin current) takes place via spin torque and spin pumping. The flow of angular momentum collinear with the magnetization ("longitudinal" spin current) requires the excitation of magnons. In this article we extend the existing theory of longitudinal spin transport [Bender and Tserkovnyak, Phys. Rev. B 91, 140402(R) (2015)] in the zero-frequency weak-coupling limit in two directions: We calculate the longitudinal spin conductance non-perturbatively (but in the low-frequency limit) and at finite frequency (but in the limit of low interface transparency). For the paradigmatic spintronic material system YIG|Pt, we find that non-perturbative effects lead to a longitudinal spin conductance that is ca. 40% smaller than the perturbative limit, whereas finite-frequency corrections are relevant at low temperatures < 100 K only, when only few magnon modes are thermally occupied.

Physics-informed recurrent neural networks for linear and nonlinear flame dynamics

This paper demonstrates the ability of recurrent neural networks (RNNs) to predict the linear and the nonlinear response of a premixed laminar flame to incoming velocity perturbations. We develop data-driven models, which require the velocity and heat release rate fluctuations as input data. Both time series are obtained from Direct Numerical Simulations (DNS) of a laminar flame. The length of the signals, and, hence, the cost of the simulation, is comparable to those used in the linear framework of System Identification. A more robust type of RNNs, namely long short term memory (LSTM), is employed to reduce the dependency on large datasets. The LSTM framework is modeled as a time series regression problem and four models are trained with decreasing data set lengths. All purely data-driven models accurately predict the unsteady time series of the heat release rate and, hence, the Flame Transfer Functions (FTFs). We further improve the model accuracy by incorporating a physical constraint, namely the low-frequency limit for perfectly-premixed flames, into the LSTM model. This step reduces the required data length compared to the purely data-driven approach. The proposed model, called PI-LSTM, is able to reproduce the linear and the nonlinear FTFs for amplitudes up to 50% of the laminar flame based on one numerical simulation, where the length of the time series is 100 ms.

Dynamical charge susceptibility in nonequilibrium double quantum dots

Double quantum dots are one of the promising two-state quantum systems for realizing qubits. In the quest of successfully manipulating and reading information in qubit systems, it is of prime interest to control the charge response of the system to a gate voltage, as filled in by the dynamical charge susceptibility. We theoretically study this quantity for a nonequilibrium double quantum dot by using the functional integral approach and derive its general analytical expression. One highlights the existence of two lines of maxima as a function of the dot level energies, each of them being split under the action of a bias voltage. In the low frequency limit, we derive the capacitance and the charge relaxation resistance of the equivalent quantum RC-circuit with a notable difference in the range of variation for $R$ depending on whether the system is connected in series or in parallel. By incorporating an additional triplet state in order to describe the situation of a double quantum dot with spin, we obtain results for the resonator phase response which are in qualitative agreement with recent experimental observations in spin qubit systems. These results show the wealth of information brought by the knowledge of dynamical charge susceptibility in double quantum dots with potential applications for spin qubits.

Limitations of the asymptotic equations for exterior sound waves

The determination of exterior sound field due to incident plane waves on a cylinder may be of importance in many areas of acoustics. Applications in acoustics include detecting, locating and classifying objects that generate a scattered sound field excited by the incident sound waves. The exterior sound field in the acoustic domain due to incident plane waves on a cylinder can be determined analytically and numerically. However, it has been observed that for convergence the asymptotic expressions of the analytical models used in the literature required infinite number of terms in the series calculations or are seldom restricted either by low or high frequency limit or the requirement of near-field and far-field approximations. This paper investigates the reasons that caused the nonconformity of the asymptotic analytical expressions. The investigation thus carried out based on the numerically determined exterior sound field using the boundary element method (BEM) and compared with the results obtained using the governing expressions. The comparisons showed good agreement when the governing expressions are not restricted, but nonconformity occurs when they are restricted.

Intensity Modulated Photocurrent Microspectrosopy for Next Generation Photovoltaics.

In this report, a large-area laser beam induced current microscope that has been adapted to perform intensity modulated photocurrent spectroscopy (IMPS) in an imaging mode is described. Microscopy-based IMPS method provides a spatial resolution of the frequency domain response of the solar cell, allowing correlation of the optoelectronic response with a particular interface, bulk material, specific transport layer, or transport parameter. The system is applied to study degradation effects in back-contact perovskite cells where it is found to readily differentiate areas based on their markedly different frequency response. Using the diffusion-recombination model, the IMPS response is modeled for a sandwich structure and extended for the special case of lateral diffusion in a back-contact cell. In the low-frequency limit, the model is used to calculate spatial maps of the carrier ambipolar diffusion length. The observed frequency response of IMPS images is then discussed.

Firmness evaluation of watermelon and melon using velocity dispersion of surface-acoustic-wave

The surface-acoustic-wave (SAW) velocity was measured in the frequency range of 400–7000 Hz in watermelon and melon to evaluate the firmness nondestructively. We showed that the positive velocity dispersion (velocity increases with increasing frequency) observed was caused by the fruit structure, which consists of a hard pericarp and underlying soft flesh. In watermelon, the low-frequency limit of the velocity dispersion curve observed for the pericarp predicted the SAW velocity in watermelon flesh, which was measured to be independent of frequency. In melon, the positive velocity dispersions observed for the pericarp as well as the flesh suggested a distribution of elasticity in the depth direction. Ripening for fourteen days caused a decrease in the SAW velocity by 34%–57% depending on the frequency. The present results demonstrate that the SAW velocity dispersion is a good measure of the firmness and ripening of fruits.

Space Charge Limited Current and Induced Particle Reflection With a Time-Varying Current Injection

Properties of space charge limited current and induced particle reflection with a time-varying current injection are investigated by an efficient grid-free numerical approach. Considering a planar diode with a single-frequency current emitted parallel to the upstream electrode surface, we study the current transmission characteristics between two dc biased electrodes and the influence of current frequency and magnitude on the limiting current first leading to electrons reflection. It is found that on account of the time-varying current injection, the limiting current strongly depends on the current frequency and magnitude, as well as the emission velocity of electrons. For the low-frequency limit, the dc component of the limiting current is approximately equal to half of that obtained from the time-independent model. The limiting current increases monotonically with increasing the frequency, and the dc component has a maximum equal to the limiting current obtained from the time-independent model.

Dynamical chemistry: non-equilibrium effective actions for reactive fluids

We present two approaches for describing chemical reactions taking place in fluid phase. The first method mirrors the usual derivation of the hydrodynamic equations of motion by relating conserved—or to account for chemical reactions, non-conserved—currents to local-equilibrium parameters. The second method involves a higher-brow approach in which we attack the same problem from the perspective of non-equilibrium effective field theory (EFT). Non-equilibrium effective actions are defined using the in–in formalism on the Schwinger–Keldysh contour and are therefore capable of describing thermal fluctuations and dissipation as well as quantum effects. The non-equilibrium EFT approach is especially powerful as all terms in the action are fully specified by the symmetries of the system; in particular the second law of thermodynamics does not need to be included by hand, but is instead derived from the action itself. We find that the equations of motion generated by both methods agree, but the EFT approach yields certain advantages. To demonstrate some of these advantages we construct a quadratic action that is valid to very small distance scales—much smaller than the scales at which ordinary hydrodynamic theories break down. Such an action captures the full thermodynamic and quantum behavior of reactions and diffusion at quadratic order. Finally, taking the low-frequency and low-wavenumber limit, we reproduce the linearized version of the well-known reaction–diffusion equations as a final coherence check.

Flutter of a finite rectangular Wing’D mill in pitch and heave

Exact solutions of flutter are explored for a mode suitable for an oscillating 2D hydrofoil version of the summarised FlutterWing windpump which radically surpasses the old rotary fanpump. The imaginary part G of the 1D Theodorsen wake lift factor T rises singularly from the steady to allow 1D pure pitch flutter around the leading edge at low frequency. But its logarithmic infinite negative pitch damping by the shed vorticity is capped by the log of the 2D span. The downwash of an oscillating trailing (tip) vortex is reduced by a function of the reduced frequency based on spanwise distance. Its lag damps pitch and further raises the pitch unstable aspect ratio A to above 36. All binary pitch &amp; heave neutral flutter frequency contours in (inertia, imbalance) space still pass through a nexus of the same total pitch inertia and imbalance as the corrected virtual mass concentrated at ¾ chord, a very high total in water. The internal bound windwise vortex from ¼ chord to trailing edge reduces as A−2 the 1D lift slope at all frequencies. It expands the 1D T = ½ double root of high frequency elliptical contours kissing the low frequency limit line at the nexus to make them dip below the line to the right of the nexus as hyperbolae with the nexal ray as left asymptote. Thus low A discovers a new wedge of high frequency binary flutter with real mass moments less than the virtual, as in water.

Two-photon annihilation of positrons with K -shell electrons of H-like ions

The two-photon annihilation of a positron with an electron bound in the $1s$ state of a H-like ion is calculated within the fully relativistic QED framework. The interaction with the nucleus is treated nonperturbatively, thus allowing the calculations to be carried out for the annihilation with strongly bound inner shells of heavy ions. Infrared divergences, appearing when one of the emitted photons approaches the low-frequency limit, are accurately eliminated from final expressions. The total cross section of the two-photon and one-photon annihilation processes are compared for a wide range of collision energies and nuclear charge numbers. It is demonstrated that the two-photon annihilation channel dominates over the one-photon channel for the low- and medium-$Z$ ions, whereas for the high-$Z$ ions the situation reverses.

Energy Flux in Thin Plates

Summary A formula for energy flux due to vibrations in a thin plate modelled by Kirchhoff theory is derived by considering a Mindlin plate and taking the low frequency (or low thickness) limit. It is shown that a term that is usually neglected in Kirchhoff theory persists close to free edges. This term does not affect the transverse displacement, but it does affect the energy flux. The new flux formula conserves energy and evaluates to zero along fixed, free and simply supported edges. An example problem, in which edge waves are excited by a point source located in a semi-infinite plate, is considered. Numerical calculations show that the energy radiated into the far field matches the energy introduced by the source.

Parametric description of power loss in soft magnetic materials with unbiased, rate-independent hysteresis loops

This paper develops a parametric model describing power loss per unit volume, PV, on unbiased minor loops, in the low frequency limit, using the corresponding remanence Br, coercivity Hc, saturated field value BS and power loss per unit volume PVS, from the major loop. In the saturating regime where Hmax>Hc, PV scales as BSHc, and depends on BrHmax/(BSHc), with Hmax the maximum value H on the minor loop. In the intermediate regime where Hmax<Hc, PV scales as μ0μiHc2, and depends on Hmax/Hc. For composite magnetic materials, a major loop may be inaccessible, in which case an expression is obtained for the low field regime, where PV scales as Hmax2, and depends on the initial relative permeability μi. The models are in good agreement with published experimental data. Observed deviations are explained through experimental uncertainties and limitations of the model.

Identification and reconstruction of high-frequency fluctuations evolving on a low-frequency periodic limit cycle: application to turbulent cylinder flow

Oftentimes, turbulent flows exhibit a high-frequency turbulent component developing on a strong low-frequency periodic motion. In such cases, the low-frequency motion may strongly influence the spatio-temporal features of the high-frequency component. A typical example of such behaviour is the flow around bluff bodies, for which the high-frequency turbulent component, characterized by Kelvin–Helmholtz structures associated with thin shear layers, depends on the phase of the low-frequency vortex-shedding motion. In this paper, we propose extended versions of spectral proper orthogonal decomposition (SPOD) and of resolvent analysis that respectively extract and reconstruct the high-frequency turbulent fluctuation field as a function of the phase of the low-frequency periodic motion. These approaches are based on a quasi-steady (QS) assumption, which may be justified by the supposedly large separation between the frequencies of the periodic and turbulent components. After discussing their relationship to more classical Floquet-like analyses, the new tools are illustrated on a simple periodically varying linear Ginzburg–Landau model, mimicking the overall characteristics of a turbulent bluff-body flow. In this simple model, we in particular assess the validity of the QS approximation. Then, we consider the case of turbulent flow around a squared-section cylinder at a Reynolds number of $Re=22\,000$ , for which we show reasonable agreement between the extracted spatio-temporal fluctuation field and the prediction of QS resolvent analysis at the various phases of the periodic vortex-shedding motion.

Ferromagnetic resonance modulation in d -wave superconductor/ferromagnetic insulator bilayer systems

We investigate ferromagnetic resonance (FMR) modulation in $d$-wave superconductor (SC)/ferromagnetic insulator (FI) bilayer systems theoretically. The modulation of the Gilbert damping in these systems reflects the existence of nodes in the $d$-wave SC and shows power-law decay characteristics within the low-temperature and low-frequency limit. Our results indicate the effectiveness of use of spin pumping as a probe technique to determine the symmetry of unconventional SCs with high sensitivity for nanoscale thin films.

Asymptotically exact photonic approximations of chiral symmetric topological tight-binding models

Topological photonic edge states, protected by chiral symmetry, are attractive for guiding wave energy as they can allow for more robust guiding and greater control of light than alternatives; however, for photonics, chiral symmetry is often broken by long-range interactions. We look to overcome this difficulty by exploiting the topology of networks, consisting of voids and narrow connecting channels, formed by the spaces between closely spaced perfect conductors. In the limit of low frequencies and narrow channels, these void–channel systems have a direct mapping to analogous discrete mass–spring systems in an asymptotically rigorous manner and therefore only have short-range interactions. We demonstrate that topological tight-binding models that are protected by chiral symmetries, such as the SSH model and square-root semimetals, are reproduced for these void–channel networks with appropriate boundary conditions. We anticipate, moving forward, that this paper provides a basis from which to explore continuum photonic topological systems, in an asymptotically exact manner, through the lens of a simplified tight-binding model.

Supergravity black holes, Love numbers, and harmonic coordinates

To perform realistic tests of theories of gravity, we need to be able to look beyond general relativity and evaluate the consistency of alternative theories with observational data from, especially, gravitational wave detections using, for example, an agnostic Bayesian approach. In this paper we further examine properties of one class of such viable, alternative theories, based on metrics arising from ungauged supergravity. In particular, we examine the massless, neutral, minimally coupled scalar wave equation in a general stationary, axisymmetric background metric such as that of a charged rotating black hole, when the scalar field is either time independent or in the low-frequency, near-zone limit, with a view to calculating the Love numbers of tidal perturbations, and of obtaining harmonic coordinates for the background metric. For a four-parameter family of charged asymptotically flat rotating black hole solutions of ungauged supergravity theory known as STU black holes, which includes Kaluza-Klein black holes and the Kerr-Sen black hole as special cases, we find that all time-independent solutions, and hence the harmonic coordinates of the metrics, are identical to those of the Kerr solution. In the low-frequency limit we find the scalar fields exhibit the same $SL(2,R)$ symmetry as holds in the case of the Kerr solution. We point out extensions of our results to a wider class of metrics, which includes solutions of Einstein-Maxwell-Dilaton theory.

Nonadiabatic Born Effective Charges in Metals and the Drude Weight.

In insulators, Born effective charges describe the electrical polarization induced by the displacement of individual atomic sublattices. Such a physical property is at first sight irrelevant for metals and doped semiconductors, where the macroscopic polarization is ill defined. Here we show that, in clean conductors, going beyond the adiabatic approximation results in nonadiabatic Born effective charges that are well defined in the low-frequency limit. In addition, we find that the sublattice sum of the nonadiabatic Born effective charges does not vanish as it does in the insulating case, but instead is proportional to the Drude weight. We demonstrate these formal results with density functional perturbation theory calculations of Al and electron-doped SnS_{2} and SrTiO_{3}.

Metasurface absorber for ultra-broadband sound via over-damped modes coupling

Highly efficient absorption of broadband low-frequency sound with a slim subwavelength meta-structure promises extensive applications in acoustic engineering, which remains a major challenge due to the weak coupling of strong scattering resonant modes. Here, we formulate the interaction of resonant modes in different damping states on the basis of a coupled-mode theory and draw the conclusion that couplings between over-damped modes demonstrate superiority to under-damped or critically coupled states in sound absorption. Furthermore, we theoretically propose and experimentally demonstrate an ultra-broadband sound absorber by hybridizing multi-order Helmholtz resonators, which support a series of over-damped modes in a single element with flexible key acoustic parameters, including operating frequencies and loss and leakage factors decorated at will. Due to the intense coupling between these elaborated over-damped modes, the designed absorber demonstrates 81% average absorptance for airborne sound ranging from 100 to 1000 Hz (exceeding three octaves) with a thickness down to 1/18.8 of wavelength at the lower-limit frequency. We envision the design methodology to push forward more versatile functional devices.

Acoustic characteristics of impingement cooling sheets; effect of bias-grazing flow interaction on the liner impedance in a thin annulus

This study investigates the acoustic characteristics of impingement sheets that are typically installed around can-combustors in stationary gas turbines for cooling purposes. From an acoustic point of view the impingement sheet is a perforated liner backed by the large compressor plenum of the gas turbine. The annular gap between the can and the liner is often only a few millimeters wide to allow for a strong jet impingement on the outer combustor wall. Due to the small cross sectional area of the annular gap, the grazing flow is strongly accelerated along the perforated liner. In this study, we present an acoustic model for impingement sheets, which accounts for bias-grazing flow effects. We experimentally investigate liners with four different porosities between 2% and 5%, in the frequency range between 60Hz and 700Hz. The bias flow Mach number is varied between 0.03 and 0.25, the axially varying grazing flow Mach number between 0 and 0.14 and setups with and without jet impingement on a solid center-body are investigated. Measured reflection coefficients agree well with predictions of the presented model. A significantly increased influence of grazing flow on aperture resistance, compared to existing studies without jet impingement, is noted. The acoustic damping potential of impingement sheets is elaborated and a condition of maximum damping in the low frequency limit is derived, which agrees well with the experimental observations. The results of this work provide the fundamentals for the acoustic analysis and acoustic design of impingement cooling sheets.

Magnetic Flux Synchronous Motion Modulation for Improving the Low-Frequency Magnetic Field Detection Limit of Magnetoresistive Sensor Using MEMS Resonators

MEMS-based magnetoresistive (MR) sensors have attracted considerable attention for years due to their small weight, low power consumption, and high sensitivity, whereas the 1/<inline-formula> <tex-math notation="LaTeX">$f$ </tex-math></inline-formula> noise is larger in the low-frequency region and degrades the low-frequency magnetic field detection limit. To reduce the impact of 1/<inline-formula> <tex-math notation="LaTeX">$f$ </tex-math></inline-formula> noise, MEMS resonators are utilized to modulate the low-frequency field to a high-frequency region where the 1/<inline-formula> <tex-math notation="LaTeX">$f$ </tex-math></inline-formula> noise vanishes. This article proposes a novel modulation method called synchronous motion modulation (SMM) using a comb-driven resonator and a piezoelectric cantilever resonator; meanwhile, it analyzes the relationship of modulation efficiency of SMM, vertical motion modulation (VMM), and gap change modulation (GCM) theoretically and with finite element method (FEM) simulation. It is found that the theoretical analysis is coincident with numerical simulation, and the SMM is the optimal modulation method for improving the low-frequency magnetic field detection limit due to its modulation efficiency is the sum of that of VMM and GCM.