Nonzero Frequency Research Articles

Response probability density of a single-degree-of-freedom linear system under non-Gaussian random excitation with dominant frequency

Abstract The response probability density function (PDF) of a single-degree-of-freedom linear system under non-Gaussian random excitation with a non-zero dominant frequency is investigated. The non-Gaussian excitation is a zero-mean stationary stochastic process prescribed by a first-order PDF and a power spectral density (PSD) with bandwidth and dominant frequency parameters. Uniform and Laplace distributions are considered for the excitation PDF. Monte Carlo simulations are performed to obtain the stationary displacement and velocity PDFs of the system. The simulation results indicate that the effects of excitation non-Gaussianity on the response PDFs vary greatly, depending on the bandwidth and dominant frequency of the excitation PSD. Particularly, the excitation non-Gaussianity appears strongly in the response PDFs when the excitation has a narrow bandwidth and the excitation dominant frequency matches the natural frequency of the system. Next, it is shown that when the excitation and response waveforms are similar, the response PDFs take a shape similar to the excitation PDF; on the other hand, when the waveforms are different, the response PDFs are nearly Gaussian, irrespective of the shape of the excitation PDF. Furthermore, as a quantitative index of waveform similarity, the maximum absolute value of the normalized cross-correlation function of excitation and response is introduced. The correspondence between the index value and the non-Gaussianity of the response PDF is revealed.

On the origin of circular rolls in rotor-stator flow

Rotor-stator flows are known to exhibit instabilities in the form of circular and spiral rolls. While the spirals are known to emanate from a supercritical Hopf bifurcation, the origin of the circular rolls is still unclear. In the present work we suggest a quantitative scenario for the circular rolls as a response of the system to external forcing. We consider two types of axisymmetric forcing: bulk forcing (based on the resolvent analysis) and boundary forcing using direct numerical simulation. Using the singular value decomposition of the resolvent operator the optimal response is shown to take the form of circular rolls. The linear gain curve shows strong amplification at non-zero frequencies following a pseudo-resonance mechanism. The optimal energy gain is found to scale exponentially with the Reynolds number $Re$ (for $Re$ based on the rotation rate and interdisc spacing $H$ ). The results for both types of forcing are compared with former experimental works and previous numerical studies. Our findings suggest that the circular rolls observed experimentally are the effect of the high forcing gain together with the roll-like form of the leading response of the linearised operator. For high enough Reynolds number it is possible to delineate between linear and nonlinear responses. For sufficiently strong forcing amplitudes, the nonlinear response is consistent with the self-sustained states found recently for the unforced problem. The onset of such non-trivial dynamics is shown to correspond in state space to a deterministic leaky attractor, as in other subcritical wall-bounded shear flows.

Klein-Gordon oscillators and Bergman spaces

We consider classical and quantum dynamics of relativistic oscillator in Minkowski space R3,1. It is shown that for a non-zero frequency parameter ω the covariant phase space of the classical Klein-Gordon oscillator is a homogeneous Kähler-Einstein manifold Z6=AdS7/U(1)=U(3,1)/U(3)×U(1). In the limit ω→0, this manifold is deformed into the covariant phase space T⁎H3 of a free relativistic particle, where H3=H+3∪H−3 is a two-sheeted hyperboloid in momentum space. Quantization of this model with ω≠0 leads to the Klein-Gordon oscillator equation which we consider in the Segal-Bargmann representation. It is shown that the general solution of this model is given by functions from the weighted Bergman space of square-integrable holomorphic (for particles) and antiholomorphic (for antiparticles) functions on the Kähler-Einstein manifold Z6. This relativistic model is Lorentz covariant, unitary and does not contain non-physical states.

Dissipative split-charge formalism: Ohm's law, Nyquist noise, and non-contact friction.

The split-charge equilibration method is extended to describe dissipative charge transfer similarly as the Drude model, whereby the complex-valued frequency-dependent dielectric permittivities or conductivities of dielectrics and metals can be mimicked at non-zero frequencies. To demonstrate its feasibility, a resistor-capacitor circuit is simulated using an all-atom representation for the resistor and capacitor. The dynamics reproduce the expected charging process and Nyquist noise, the latter resulting from the thermal voltages acting on individual split charges. The method bears promise to model friction caused by the motion of charged particles past metallic or highly polarizable media.

A novel Short-time Fourier transform-based algorithm for detection of wandering in the patients with Alzheimer’s disease

ABSTRACT As the elderly population rises, the growth rate of age-related diseases such as Alzheimer’s disease and cognitive impairments increases. Wandering is one of the first and the most progressive and challenging behaviors; that manifest with certain patterns in the mobility behavior of the patients in the early stages of the disease. Timely diagnosis of wandering can prevent irreparable damages, including the risk of losing the patient, severe physical injuries caused by accidents, and even death. So far, numerous studies have focused on the development of wandering detection algorithms. Most of these mainly rely on two approaches of extracting features from patients’ trajectory history and estimating the path complexity. Motion signal processing methods have rarely been used in this area. An important consideration for these patients is the instability in their movement behaviors, which has received limited attention in previous research, leading to less compatibility of models with this feature. Therefore, this paper proposes an algorithm based on motion signal processing using the Short-time Fourier transform (STFT). This algorithm detects wandering patterns only by using the patient’s trajectory data and changes in their zero and non-zero frequency components. The efficiency of the proposed algorithm has been evaluated using the Geolife open-source dataset, considering the macro-average of metrics such as accuracy, precision, specificity, recall, and F-score, achieving respective values of 96.38%, 94.89%, 96.36%, 96.36%, and 95.58%. The results have validated the proposed algorithm’s strong performance in diagnosing wandering behavior, which, on one hand, helps prevent adverse consequences and, on the other hand, aids in the diagnosis and predicting the progression of the disease to severe Alzheimer’s stage.

Baryonic thermal screening mass at NLO

We determine the resummed 1-loop correction to a baryonic thermal screening mass. The calculation is carried out in the framework of a dimensionally reduced effective theory, where quarks are heavy fields due to their non-zero Matsubara frequencies. The correction due to interactions is computed at O(g2) in the coupling constant. In order to solve a 3-body Schrödinger equation, we exploit a two-dimensional generalization of the hyperspherical harmonics method. At electroweak scale temperatures, the NLO correction represents a ∼ 4.6% increase of the free-theory value 3πT of the screening mass.

Different Fractional Charges from Auto- and Cross-Correlation Noise in Quantum Hall States without Upstream Modes.

Fractional charges of anyons can be extracted from shot noise in two ways. One can use either the autocorrelation noise of the current in one drain or the cross-correlation noise between two drains on the two sides of the device. The former approach typically overestimates the charge. This may happen due to upstream edge modes. We propose a mechanism for the excess autocorrelation noise without upstream modes. It applies to systems with multiple copropagating edge modes and assumes that the noise is measured at a low but nonzero frequency.

Dynamics and active mixing of a droplet in a Stokes trap

Particle trapping and manipulation have a wide range of applications in biotechnology and engineering. Recently, a flow-based, particle-trapping device called the Stokes trap was developed for trapping and control of small particles in the intersection of multiple branches in a microfluidic channel. This device can also be used to perform rheological experiments to determine the viscoelastic response of an emulsion or suspension. We show that besides these applications, the various flow modes produced by the Stokes trap are able to manipulate drop shapes and induce active mixing inside droplets. To this end, we analyse the dynamics of a droplet in a Stokes trap through boundary-integral simulations. We also explore the dynamic response of drop shape with respect to distinct external flow modes, which allows us to perform numerical experiments such as step strain and oscillatory extension. A linear controller is used to manipulate drop position, and the drop deformation is characterized by a spherical-harmonic decomposition. For small drop deformations, we observe a linear superposition of harmonics, which, surprisingly, seems to hold even for moderate deformations. This result indicates that such a device can be used for shape control of droplets. We also investigate how the different flow modes may be combined to induce mixing inside the droplets. The transient combination of modes produces an effective chaotic mixing, which is characterized by a mixing number. The mixing inside the droplet can be further enhanced for lower viscosity ratios and low, but non-zero capillary number and flow frequencies.

Willis coupling in one-dimensional poroelastic laminates

We employ the Baker–Campbell–Hausdorff formula to derive closed-form expressions for the effective properties, including emergent Willis coupling, of a one-dimensional heterogeneous poroelastic medium consisting of a periodically repeating two-layer unit-cell. In contrast to the elastic and fluidic analogs, the Willis coupling of this periodic poroelastic medium does not vanish in the low-frequency limit. However, the effective wavenumber and impedance of this asymmetric lamellar material demonstrate symmetric reflection and absorption behavior that is indicative of symmetric structures in the low-frequency limit due to the effect of Darcy’s law on the dynamic effective density, which is inversely proportional to frequency. These closed-form expressions are validated against results obtained by direct numerical evaluation. The scattering coefficients, particularly the two reflection coefficients for incidence from either side of a finite length asymmetric structure, are different at non-zero frequencies but still in the metamaterial limit and are correct when the Willis coupling is included. The results show that asymmetry in poroelastic layers results in direction-dependent absorption coefficients, one of which could be optimized based on layer properties and asymmetry factors. As a consequence, the frequency range of validity of these scattering coefficients is wider when the Willis coupling matrix is accounted for than in its absence. This work paves the way for better control of elastic and acoustic waves in multiphase materials by considering poroelastic behavior.

Effects of Nonzero-frequency Fluctuations on Turbulence Spectral Observations

In situ observations of turbulence spectra in space plasmas are usually interpreted as wavenumber spectra, assuming that the fluctuation frequency is negligible in the plasma flow frame. We explore the effects of nonzero frequency in the plasma flow frame on turbulence spectral observations. The finite frequency can be caused by either propagating waves or nonlinear broadening of nonpropagating structures. We show that the observed frequency spectrum can be modified by the nonzero frequency of turbulent fluctuations in several ways. Specifically, (i) frequency broadening results in a minor modification to the observed spectrum, primarily acting as a smoothing kernel of the spectrum near the spectral break, while the asymptotic spectral index remains unchanged; (ii) wave propagation can affect the observed spectral index for anisotropic turbulence. The effect is significant at low frequencies and weaker at high frequencies, leading to a “concave” shape of the observed perpendicular spectrum; (iii) the Doppler shift for forward- and backward-propagating Elsasser modes can result in a nonzero cross helicity for critical-balanced turbulence since the effect of the Doppler shift favors outward-propagating waves systematically, resulting in an observed imbalance. These results may have important implications for the interpretation of solar wind flows observed by Parker Solar Probe.

Measuring axion gradients with photon interferometry

We propose a novel search technique for axions with a CP-violating monopole coupling g˜Q to bulk Standard Model charges Q∈{B,L,B−L}. Gradients in the static axion field configurations sourced by matter induce achromatic circular photon birefringence via the axion-photon coupling gϕγ. Circularly polarized light fed into an optical or (open) radio-frequency (RF) Fabry-Pérot (FP) cavity develops a phase shift that accumulates up to the cavity finesse: the fixed axion spatial gradient prevents a cancellation known to occur for an axion dark-matter search. The relative phase shift between two FP cavities fed with opposite circular polarizations can be detected interferometrically. This time-independent signal can be modulated up to nonzero frequency by altering the cavity orientations with respect to the field gradient. Multiwavelength co-metrology techniques can be used to address chromatic measurement systematics and noise sources. With Earth as the axion source, we project reach beyond current constraints on the product of couplings g˜Qgϕγ for axion masses mϕ≲10−5 eV. If shot-noise-limited sensitivity can be achieved, an experiment using high-finesse RF FP cavities could reach a factor of ∼105 into new parameter space for g˜Qgϕγ for masses mϕ≲4×10−11 eV. Published by the American Physical Society 2024

Numerical Evaluation of the Frequency-Dependent Impedance of Hemispherical Ground Electrodes through Finite Element Analysis

Metallic electrodes are widely used in many applications, the analysis of their frequency-domain behavior is an important subject, particularly in applications related to earthing/grounding systems, from dc up into the MHz range. In this paper, a numerical evaluation of the frequency-dependent complex impedance of the hemispherical ground electrode is implemented. A closed-form solution for non-zero frequencies is still a difficult task to achieve as evidenced in a previous paper dedicated to the subject and, therefore, numerical approaches should be an alternative option. The aim of this article is to present a solution based on a numerical method using finite element analysis. In typical commercial FE tools, electric currents exhibit azimuthal orientation and, as such, the magnetic field has a null azimuthal component but non-null axial and radial components. On the contrary, a dual problem is considered in this work, with a purely azimuthal magnetic field. To overcome the difficulty of directly using a commercial FE tool, a novel formulation is developed. An innovative 2D formulation, the ι-form, is developed as a modification of the H-formulation applied to axisymmetric magnetic field problems. The results are validated using a classical 3D H-formulation; comparisons showed very good agreement. The electrode complex impedance is analyzed considering two different cases. Firstly, the grounding system is constituted by a hemispherical electrode surrounded by a remote concentric electrode; in the second case, the grounding system is constituted by two identical thin hemispherical electrodes. Computed results are presented and discussed, showing how the grounding impedance depends on the frequency and, also, on the radius of the remote concentric electrode (first case) or on the distance between the two hemispherical electrodes (second case).

Nonlinear squeezing of stochastic motion

Linearized stochastic nanomechanical systems operating at nonzero temperatures and constant frequency and damping are restricted in their capacity to reduce noise in nonlinear combinations of the canonical variables. Nonlinear dynamics are then required in order to overcome these limits. Here we demonstrate how to make these limits explicit in the form of a threshold for nonlinear squeezing of the motional variables. Noise suppression below the threshold cannot be explained by linearized dynamics and is helpful in low-noise nonlinear devices at an ambient temperature. We predict that a state of the art levitating particle, exposed to cubic or quartic trapping potentials for a short interval will display nonlinear squeezing of stochastic motion that cannot be replicated by linear motion.

Vibrational Analysis of Constrained Molecular Systems.

Vibrational spectroscopy, including infrared (IR), Raman spectroscopy, and vibrational circular dichroism, is instrumental in determining the structure and composition of molecules. These techniques are highly sensitive to molecular conformations. However, full molecular optimization, necessary for theoretical vibrational spectra, can lead to unintended conformational changes, especially in large biomolecules like polypeptides. To address this, dihedral angle constraints can be imposed during optimization to preserve the molecule's native conformation. Constraint-optimized molecular geometries, not being true stationary points in the full configurational space, pose challenges for traditional vibrational analysis. We address this by considering such geometries as subspace minima, reformulating vibrational analysis to incorporate constraints. Normal modes and spectra consistent with these constraints are obtained by projecting the force constant matrix onto a space orthogonal to the constrained coordinates. This method, illustrated by the example of enkephalin, yields 3N - 6 - m nonzero frequencies after constraint projection, demonstrating its applicability to biomolecules with flexible conformations. Our approach offers a comprehensive mathematical framework to compute vibrational spectra of molecules with conformationally flexible subunits under environmental constraints.

Modal Analysis of 15 MW Semi-Submersible Floating Wind Turbine: Investigation on the Main Influences in Natural Vibration

One of the sources of sustainable energy with great, still untapped potential is wind power. One way to harness such potential is to develop technology for offshore use, more specifically at high depths with floating turbines. It is always critical that their structural designs guarantee that their natural frequencies of vibration do not match the frequencies of the most important oscillatory loads to which they will be subjected. This avoids resonance and its excessive undesired oscillatory responses. Based on that, a 3D finite element model of a 15 MW semi-submersible floating offshore wind turbine was developed in the commercial software ANSYS Mechanical ® to study its dynamic behavior and contribute to the in-depth analysis of structural modeling of FOWTs. A tower and floating platform were individually modeled and coupled together. The natural frequencies and modes of vibration of the coupled system and of its components were obtained by modal analysis, not only to verify the resonance, but also to investigate the determinant factors affecting such behaviors, which are not extensively discussed in literature. It was found that there is strong coupling between the components and that the tower affects the system as a result of its stiffness, and the floater as a result of its rotational inertia. The platform’s inertia comes mainly from the ballast and the effects of added mass, which was considered to be a literal increase in mass and was modeled in two manners: first, it was approximately calculated and distributed along the submerged flexible platform members and then as a nodal inertial element with the floater being considered as a rigid body. The second approach allowed an iterative analysis for non-zero frequencies of vibration, which showed that a first approximation with an infinite period is sufficiently accurate. Furthermore, the effects of the mooring lines was studied based on a linear model, which showed that they do not affect the boundary conditions at the bottom of the tower in a significant way.

Energy transport induced by transition from the weak to the strong coupling regime between non-Hermitian optical systems

The strong coupling between non-Hermitian physical systems of different natures has been widely investigated recently since it endows them with new properties. In this work, we consider energy transport through an open quantum optical system consisting of strongly coupled subsystems. We use a partial-secular approach for the description of an open quantum system to investigate the system dynamics during the transition from a weak to a strong coupling regime with an increase of coupling between subsystems. On the example of strongly coupled two-level atoms, we show that during the transition to the strong coupling regime, the enhancement of energy transport through the open quantum system takes place. Namely, starting from zero value, when the coupling constant equals zero, the stationary energy flow increases and tends to an approximately constant value at the high values of the coupling constant. As a result, the specific energy flow—the stationary energy flow normalized to the coupling constant—reaches the maximum at some value of the coupling constant. This behavior takes place even in the case of the non-zero frequency detuning when there is no clear transition point from the weak to the strong coupling regime in the spectrum of system eigenvalues. Thus, to achieve significant energy flow through the compound open quantum system, it is sufficient to restrict the value of the coupling constant at which the specific energy flow is maximized. Also, we demonstrate the suppression of the stationary energy flow at high dissipation rates. The obtained results can be used in the design of quantum thermal devices.

Feedback Stability of Generalized Positive Real and Negative Imaginary Systems

This paper derives necessary and sufficient conditions for robust stability of a feedback interconnection of linear time-invariant (LTI) systems that exhibit positive realness on finite nonzero frequencies (excluding pole locations) through a weighting function, i.e. a multiplier. This class of LTI systems importantly includes the well-studied negative imaginary systems without poles at the origin as a subset. Under the assumption that the instantaneous gain of the loop transfer function is zero, it is shown that the aforementioned feedback interconnection is stable if and only if the static (a.k.a. DC) loop gain is less than unity. This condition is identical to the one that guarantees feedback stability of negative imaginary systems, but is applicable to a much wider class of systems beyond negative imaginariness. Our proof is based entirely on the multivariable Nyquist stability criterion — it does not make use of realisations of the transfer functions. Comparisons with integral quadratic constraint based robust stability results are also made.

Asymptotic formulations of anti-plane problems in pre-stressed compressible elastic laminates

Abstract This article investigates the long-wave anti-plane shear motion in a symmetric three-layered laminate composed of pre-stressed compressible elastic layers. The layers of the laminate are perfectly bonded, while traction-free and fixed boundary conditions are considered on the outer faces of the laminate. In both cases, the dispersion relation is obtained in terms of symmetric and anti-symmetric decompositions. Numerical results and an asymptotic long-wave analysis are presented, corresponding to the three possible vibration modes. It is revealed that a low-frequency mode only exists in respect of symmetric motion with free-faces, while all other cases pose a series of non-zero cut-off frequencies. Comparisons between the exact and approximate asymptotic results are presented, and excellent agreement is observed.

Tunable electronic and optical properties of GeC/PtO2 vdW hetero-bilayer using first-principles study

The detailed optical and electronic characteristics of 2D GeC and 2D PtO2 under biaxial strains and electric fields across the plane are studied systematically using the density functional theory (DFT) based first-principles framework. The six different stacking patterns of the stacked van der Waals (vdW) GeC/PtO2 hetero-bilayers were DFT screened, and HBL 4 and HBL 5 are found both dynamically stable and energetically favorable, evident from the non-zero phonon frequency and negative binding energy from phonon dispersion and binding energy calculations, respectively. The bandgap of 2D GeC and 2D PtO2 is found to be ∼2.08 eV (direct) and ∼1.63 eV (indirect), while the bandgaps in vdW HBL 4 (HBL 5) are found to be 0.51 eV (0.49 eV). Biaxial strain lowered the bandgap by ∼11.13 (∼1.81) times at 6% compressive (tensile) biaxial strain in HBL 4 (HBL 5). Semiconductor-to-metal switching is found in both HBLs at ±0.6 V/Å of the cross-plane electric field. All the HBLs show type-II band-alignment, evident from the difference in charge density and projected density of state contour, indicating spatial carrier separation capability. The peak of the optical absorption coefficient is found to be ∼3.1 × 105 cm−1 at 310 nm for both HBL 4 and HBL 5, which is comparable to high-absorbing perovskite material. Moreover, the optical absorption is sensitive to the biaxial strains and electric fields, and increased visible band optical absorption is found for tensile strains in both HBLs. These exceptional findings and engineered bandgap in GeC/PtO2 vdW HBL indicate the promising application of this material in 2D advanced nanoelectronics.

Loop current fluctuations and quantum critical transport

We study electrical transport at quantum critical points (QCPs) associated with loop current ordering in a metal, focusing specifically on models of the “Hertz-Millis” type. At the infrared (IR) fixed point and in the absence of disorder, the simplest such models have infinite DC conductivity and zero incoherent conductivity at nonzero frequencies. However, we find that a particular deformation, involving NN species of bosons and fermions with random couplings in flavor space, admits a finite incoherent, frequency-dependent conductivity at the IR fixed point, \sigma(\omega>0)\sim\omega^{-2/z}σ(ω>0)∼ω−2/z, where zz is the boson dynamical exponent. Leveraging the non-perturbative structure of quantum anomalies, we develop a powerful calculational method for transport. The resulting "anomaly-assisted large NN expansion" allows us to extract the conductivity systematically. Although our results imply that such random-flavor models are problematic as a description of the physical N = 1N=1 system, they serve to illustrate some general conditions for quantum critical transport as well as the anomaly-assisted calculational methods. In addition, we revisit an old result that irrelevant operators generate a frequency-dependent conductivity, \sigma(\omega>0) \sim \omega^{-2(z-2)/z}σ(ω>0)∼ω−2(z−2)/z, in problems of this kind. We show explicitly, within the scope of the original calculation, that this result does not hold for any order parameter.