Quadrupole Term Research Articles

Mass octupole and current quadrupole corrections to gravitational wave emission from close hyperbolic encounters

Abstract In this paper, we study the next-to-leading order corrections in the mass multipole expansion, i.e. the mass octupole and current quadrupole, to gravitational wave production by close hyperbolic encounters of compact objects. We find that the signal is again, as in the simple quadrupole case, a burst event with the majority of the released energy occurring during the closest approach. In particular, we investigate the relative contribution to the power, both in the time and frequency domains, and total energy emitted by each order in the mass multipole expansion in gravitational waves. To do so, we include in the quadrupole term its first order post-Newtonian correction, giving this a contribution to the power of the same order as that of the mass octupole and the current quadrupole. We find specific configurations of systems where these corrections could be important and should be taken into account when analysing burst events.

Metamaterial-induced-transparency engineering through quasi-bound states in the continuum by using dielectric cross-shaped trimers

This study presents a novel approach to activate a narrowband transparency line within a reflecting broadband window in all-dielectric metasurfaces, in analogy to the electromagnetically-induced transparency effect, by means of a quasi-bound state in the continuum (qBIC). We demonstrate that the resonance overlapping of a bright mode and a qBIC-based nearly-dark mode with distinct Q-factor can be fully governed by a silicon trimer-based unit cell with broken-inversion-symmetry cross shape, thus providing the required response under normal incidence of a linearly-polarized light. Our analysis that is derived from the far-field multipolar decomposition and near-field electromagnetic distributions uncovers the main contributions of different multipoles on the qBIC resonance, with governing magnetic dipole and electric quadrupole terms supplied by distinct parts of the dielectric “molecule”. The findings extracted from this research open up new avenues for the development of polarization-dependent technologies, with particular interest in its capabilities for sensing and biosensing.

On the northward shift of the heliospheric current sheet at the end of solar cycle 24

ABSTRACT Since solar cycle 16, the heliospheric current sheet (HCS) has been found to be shifted southward during the late declining to minimum phase. However, this trend is broken at the end of solar cycle 24. In this paper, we analyse the shift of the HCS by using information obtained from coronal model and in situ data provided by the near-Earth OMNI data base and the Parker Solar Probe (PSP). Coronal potential field source surface modelling results show that the northward shift is established at the beginning of 2018 and remains stable for about 2 yr. Interplanetary magnetic field data obtained from and within 1 au also support the northward shift, as the southern polarity T appears more frequently than the northern polarity A between 2018 and 2020. Both model results and in situ observation obtained by PSP imply that the HCS shift is established in the corona, and then propagates into the heliosphere. The quadrupole term still has a significant influence on the formation of the HCS shift.

Frequency-domain quadrupole correction for the permeable-surface Ffowcs Williams and Hawkings integration

The permeable-surface Ffowcs Williams and Hawkings (FW–H) integration for computing the far-field sound has the advantage of encapsulating the sources and nonlinear propagation inside the integral surface. However, it suffers from spurious sound when the volume integral for quadrupole term outside the permeable surface is conventionally ignored. The spurious sound is often suppressed by using two distinct approaches, which modifies the FW–H integration and acoustic variables/sources, respectively. This work clarifies the connection between the two approaches by analyzing the integral of the quadrupole sources. We show that the modification of the acoustic sources can be reformulated as a modification of the FW–H integration, which means that the two distinct approaches are interconvertible. A new quadrupole correction model for the FW–H integration is proposed by delicately modifying the acoustic sources. The modified acoustic sources consist of the filtered Lighthill stress tensor, where a convection operator is used to filter out the acoustically inefficient components. The proposed quadrupole correction model is consistent with the previous work on the modification of the FW–H integration under special conditions with the uniform convection velocity. The proposed model is validated by computing the sound pressure generated by laminar and turbulent flows over bluff bodies. It is found that the sensitivity of the acoustic pressure to the FW–H surface's position is suppressed and the accuracy of the predicted sound is improved. The results suggest that the modification of acoustic variables/sources can be a powerful method to construct new quadrupole correction models for the permeable FW–H integration.

Probing the cosmological principle using the slope of log N-log S relationship for quasars

We study the dipole signal in the slope x of the log N–log S relationship for quasars using the CatWISE2020 catalog of infrared sources. Here N is the number of sources with flux density greater than S. The slope is extracted by using a maximized log-likelihood method as well as Bayesian analysis. We obtain the value x = 1.579 ± 0.001 for a quasar sample of 1355352 sources. We extract the dipole signal in this parameter by employing χ 2 minimization, assuming a sky model of x up to the quadrupole term. We find that the dipole amplitude |D| is 0.005 ± 0.002 and dipole direction (l, b) in Galactic coordinate system equal to (201.50° ± 27.87°, -29.37° ± 19.86°). The direction of dipole anisotropy is found to be very close to the hemispherical power asymmetry (l, b)=(221°,-27°) in the Cosmic Microwave Background (CMB). The dipole signal is also extracted using Bayesian analysis and found to be in good agreement with that obtained using χ 2 minimization. We also obtain a signal of quadrupole anisotropy which is found to be correlated with the ecliptic poles and can be attributed to ecliptic bias.

Measuring a Gravitomagnetic Effect with the Triple Pulsar PSR J0337+1715

Measuring a Gravitomagnetic Effect with the Triple Pulsar PSR J0337+1715

Modified Complex Robert-Bonamy calculations of line shape parameters for the CO2-H2O collision system

Modified Complex Robert-Bonamy calculations were made for the CO2-H2O collision system using an intermolecular potential comprised of quadrupole-dipole, quadrupole-quadrupole, Lennard-Jones atom-atom, induction, and London dispersion terms. The initial atom-atom parameters were obtained using combination rules and the other parameters from taken from the literature. The intermolecular potential was then adjusted to give results that agree with the measurements of Sung et al. [Can. J. Phys. 87,469-484, 2009]. The final potential results (pot 46) compared with the data of Sung et al. have an average percent difference of 0.07 and a standard deviation of 1.096 %. Calculations were then made for all transitions in the 00011-00001 band with J” from 0 to 120 at 13 temperatures from 200 to 3000 K. The speed dependence of the half-width and line shift were computed for use in more advanced line shape models. The temperature dependence of the half-widths and line shifts were determined using the double power-law (DPL) model of Gamache and Vispoel [JQSRT 217, 440-452, 2018].

On the physical significance of non-local material parameters in optical metamaterials

When light interacts with a material made from subwavelength periodically arranged constituents, non-local effects can emerge. They occur because of either a complicated response of the constituents or possible lattice interactions. In lowest-order approximations of a general non-local response function, phenomena like an artificial magnetism and a bi-anisotropic response emerge. However, investigations beyond these lowest-order descriptions of non-local effects are needed for optical metamaterials (MMs) where a significant long-range interaction becomes evident. This highlights the need for additional material parameters to account for spatial non-locality in an effective medium description. These material parameters emerge from a Taylor expansion of the general and exact non-local response function. Even though these non-local parameters improve the effective description, their physical significance is yet to be understood. To improve the situation, we consider a conceptional MM consisting of scatterers characterized by a prescribed multipolar response arranged on a square lattice. Lorentzian polarizabilities describe the scatterers in the electric dipolar, electric quadrupolar, and magnetic dipolar terms. A slab of such a MM is homogenized while considering an increasing number of non-local terms in the constitutive relations at the effective level. We show that the effective permittivity and permeability are linked to the electric and magnetic dipole moments of the scatterers. The non-local material parameters are related to the higher-order multipolar moments and their interaction with the dipolar terms. Studying the effective material parameters with the knowledge of the induced multipolar moments in the lattice facilitates our understanding of the significance of each material parameter. Our insights aid in deciding on the order to truncate the Taylor expansion of the considered constitutive relations for a given MM.

Stability of hierarchical triples – II. The inclination ι = 140° resonance in the stability surface

ABSTRACT The stability of a hierarchical triple star may be decided by a simple criterion, which was derived in Paper I. However, there is a region in the phase space where the stability limit Qmax is raised by a factor of two in a small region of the phase space with respect to the surrounding phase space. The phase space is defined by the inner and outer eccentricities ein and eout, respectively, as well as by the inclination ιtot between the inner and outer orbits. Additional parameters of the phase space are the masses of the three bodies. We study by numerical integration the orbits of over 100 000 triple systems in the resonance region. We find that the instability that causes the high value of Qmax arises from the octupole Kozai–Lidov resonance. This resonance region has rather equal contributions from the quadrupole and octupole terms and leads to secular evolution with an amplitude larger than either of the two oscillations in isolation. The conditions for this situation are best satisfied near the relative inclination ι = 140°. Additionally, the relative orientation of the two orbits plays a decisive role: the resonance is found only at certain values of the orbit’s node line longitude Ω. An analytical approximation of the energy change in a single close encounter between the inner and outer systems suggests a cos 2Ω dependence of Qmax on Ω, which seems to be qualitatively valid. We model Qmax as a function of cos ι and ein by a Gaussian function.

Numerical Investigation of Self-Propulsion Performance and Noise Level of DARPA Suboff Model

Propulsion noise is an enduring problem of significant military and environmental importance. Hence, it is crucial to investigate propeller noise characteristics. In this study, the hydrodynamic performance and noise level of the DARPA (Defense Advanced Research Projects Agency) Suboff submarine with the E1619 propeller were analyzed. The hull resistance and propeller hydrodynamics were studied separately, and the numerical results were validated using available experimental values. The self-propulsion point was determined by matching the hull resistance and propeller thrust following ITTC (International Towing Tank Conference) convention. Based on hydrodynamics and acoustic Ffowcs Williams–Hawkings (FW–H) models, the underwater-radiated noise characteristics in the self-propulsion state were simulated. The calculations indicated that the contribution of the quadrupole term in the FW–H equation is not negligible in the high-frequency band. Compared with the noise of open-water propellers, the spectrum of the E1619 propeller in its self-propulsion state is more complex, and the upstream noise is amplified.

Strain-induced magnetic anisotropy in Heusler alloys studied from first principles

We report the microscopic origin of strain-mediated changes in the magnetocrystalline anisotropy energy of the Co2FeSi, Co2MnSi, and Fe3Si Heusler alloys from the viewpoint of first-principles electron theory. Both Co2FeSi and Co2MnSi have similar anisotropy changes upon induced strain within the (001) plane, where the quadrupole moment due to Co minority-spin states dominates the anisotropy modulation, and, thus, giant magnetoelectric couplings in multiferroic heterointerfaces containing these compounds. In contrast, the strain-induced anisotropy modulation in Fe3Si has mixed contributing factors not limited to the anisotropy term of the orbital magnetic moment and the quadrupole term.

Electromagnetic scattering by arbitrary-shaped magnetic particles and multipole decomposition: Analytical and numerical approaches

We develop a theoretical approach that makes it possible to analyze the role of multipole contributions in the scattering spectra of arbitrarily shaped magnetic particles with the relative permittivity and permeability given in a general tensor-valued form. The method for calculating the exact multipole moments with the inclusion of induced electric polarization and magnetization is suggested and explicitly applied for dipole and quadrupole terms. The final expressions for the dipole and quadrupole moments are obtained in such a form that they can be easily implemented in numerical solvers. Successful verification of the analytical expressions for multipole moments and the multipole decomposition of the scattered field and scattering cross section is provided by comparing the results obtained for differently shaped magnetic particles using the analytical Mie theory, numerical discrete dipole approximation, and comsol multiphysics software. As a particular example, the manifestation of the Faraday effect for fields scattered by a ferrite sphere is discussed in the framework of the multipole decomposition method with the derived magnetization terms. Accounting for the magnetic properties of particles in the multipole analysis of the electromagnetic scattering significantly expands the method's capabilities for studying and modeling metamaterial properties in the spectral ranges where natural materials can have a relative permeability different from unity.

On the nature of the Schottky anomaly in endohedral water.

In this work, we study the heat capacity contribution of a rigid water molecule encapsulated in C60 by performing six-dimensional eigenstate calculations with the inclusion of its quantized rotational and translational degrees of freedom. Two confinement model potentials are considered: in the first, confinement is described using distributed pairwise Lennard-Jones interactions, while in the second, the water molecule is trapped within an eccentric but isotropic 3D harmonic effective confinement potential [Wespiser et al., J. Chem. Phys. 156, 074304 (2022)]. Contributions to the heat capacity from both the ortho and para nuclear spin isomers of water are considered to enable the effects of their interconversion to be assessed. By including a symmetry-breaking quadrupolar potential energy term in the Hamiltonian, we can reproduce the experimentally observed Schottky anomaly at ∼2K [Suzuki et al., J. Phys. Chem. Lett. 10, 1306 (2019)]. Furthermore, our calculations predict a second Schottky anomaly at ∼0.1K resulting from the H configuration, a different orientational arrangement of the fullerene cages in crystalline solid C60. Contributions from the H configuration to CV also explain the second peak observed at ∼7K in the experimentally measured heat capacity.

Dual Mesh Technique for Hydroacoustic Prediction of Cavitating Flows around a Three-Dimensional Bullet

Nowadays, hydroacoustics is of great importance. A major source of underwater noise is cavitation noise. One of the difficulties in cavitation noise prediction is its complex formation mechanism. In this paper, a cavitating bullet is taken as the research object, and detailed numerical simulation research of the local cavitation for this three-dimensional model is carried out. Ffowcs Williams and Hawkings equation (FW-H) is adopted. The quadrupole term is obtained by the direct volume integration method. Furthermore, dual mesh technique is adopted to achieve fast calculation. The results show that the dual mesh technology reduces the computational complexity of the nonlinear sound pressure significantly. With the appropriate acoustic grid size, the dual mesh method can ensure the same accuracy as the CFD grid. This provides a reliable way for the calculation of nonlinear sound pressure in the cavitation phenomenon.

Gravitational Waves and Electromagnetic Radiation from Charged Black Hole Binaries

In this manuscript, we investigate the electromagnetic radiation of a binary system of electrically charged black holes. Using the results of previous works, we compute the analytical expression for the waveform, the phase, and the Fourier transform during the inspiral phase for both the electromagnetic and gravitational radiations. To do so, we consider the quasi-circular approximation and small values for the charge-to-mass ratio in each black hole. In the case of electromagnetic radiation, we focus on the dipole contribution, but we also include the quadrupole term to complete our discussion. We found that the gravitational and electromagnetic waveforms contain two terms, and so does the Fourier transform. However, the behavior is dominated only by one of them. In the frequency-domain waves, for example, the dipole and quadrupole contributions and the gravitational wave are dominated by terms proportional to f−3/6, f−1/6, and f−7/6, respectively. As expected, the gravitational radiation and the quadrupole contribution have the same phase, in contrast to the dipole contribution. Moreover, the electromagnetic wave is more sensitive to changes in the charge-to-mass ratio than the gravitational wave.

Effective two-body approach to the hierarchical three-body problem: Quadrupole to 1PN

Many binary systems of interest for gravitational-wave astronomy are orbited by a third distant body, which can considerably alter their relativistic dynamics. Precision computations are needed to understand the interplay between relativistic corrections and three-body interactions. We use an effective field theory approach to derive the effective action describing the long time-scale dynamics of hierarchical three-body systems up to 1PN quadrupole order. At this level of approximation, computations are complicated by the backreaction of small oscillations on orbital time-scales as well as deviations from the adiabatic approximation. We address these difficulties by eliminating the fast modes through the method of near-identity transformations. This allows us to compute for the first time the complete expression of the 1PN quadrupole cross-terms in generic configurations of three-body systems. We numerically integrate the resulting equations of motion and show that 1PN quadrupole terms can affect the long term dynamics of relativistic three-body systems.

Interaction of two Rydberg atoms in the vicinity of an optical nanofibre

We consider two rubidium atoms, prepared in the same S or P Rydberg states, near an optical nanofibre, and we determine their van der Waals interaction potential as a function of their separation along the nanofibre axis, their distance to the nanofibre axis, and their relative azimuthal angle. We compare results obtained through direct diagonalisation of the Hamiltonian (including quadrupolar interaction terms) with second-order perturbation calculations, and we identify which couplings mainly contribute to the potential in the presence of the nanofibre and in free-space. We relate the appearance of new allowed couplings to the broken rotation symmetry around the interatomic axis due to the presence of the fibre. These couplings induce novel features and cause a reshaping of the interaction anisotropy and formation of an interaction potential well for P states near the nanofibre. Our work constitutes an important step in the assessment of Rydberg atom-nanofibre quantum interfaces and devices.

Optical activity of solids from first principles

Within the framework of independent particle approximation, the optical activity tensor of solids is formulated as from different contributions: the magnetic dipole, electric quadrupole, and band dispersion terms. The first two terms have similar counterparts in the theory of finite systems, while the last term is unique for crystals. The magnetic dipole and electric quadrupole transition moments are calculated with a sum-over-states formulation. We apply the formulation to calculate and analyze the optical rotation of elemental tellurium and the circular dichroism of $(6,4)$ carbon nanotube. Decomposed optical activity into different contributions are discussed. The calculated spectra agree well with experiments. As a showcase of achiral crystals, we calculate the optical activity of wurtzite GaN.

The quadrupole in the local Hubble parameter: first constraints using Type Ia supernova data and forecasts for future surveys

ABSTRACT The cosmological principle asserts that the Universe looks spatially homogeneous and isotropic on sufficiently large scales. Given its fundamental implications, it is important to empirically test its validity. In this paper, we use the Type Ia supernova (SN Ia) magnitude–redshift relation, from both the Pantheon and joint light-curve analysis compilations, to constrain theoretically motivated anisotropies in the Hubble flow. In particular, we constrain the quadrupole in the effective Hubble parameter and the dipole in the effective deceleration parameter. We find no significant quadrupole term regardless of the redshift frame used. Our results are consistent with the theoretical expectation of a quadrupole moment of a few percent at scales of ∼100 h−1 Mpc. We place an upper limit of an $\sim 10{{\%}}$ quadrupole amplitude relative to the monopole, H0, at these scales. We find that we can detect an $\sim 7{{\%}}$ quadrupole at the 5σ level, for a forecast low-z sample of 1055 SNe Ia. We find the signficance of an exponentially decaying dipole of the deceleration parameter depends on the redshift frame used. In the heliocentric frame, as expected, it is detected at ∼3σ significance. In the cosmic microwave background (CMB) rest frame, we find a marginal ∼2σ dipole, however, after applying peculiar velocity (PV) corrections, the dipole is insignificant. Finally, we find the best-fitting frame of rest relative to the supernovae to differ from that of the CMB at ∼2σ for both compilations, which reduces to <1σ when including PV covariance.

Origin of eclipsing time variations in post-common-envelope binaries: Role of the centrifugal force

Eclipsing time variations in post-common-envelope binaries were proposed to be due to the time-varying component of the stellar gravitational quadrupole moment. This is suggested to be produced by changes in the stellar structure due to an internal redistribution of angular momentum and the effect of the centrifugal force. We examined this hypothesis and present 3D simulations of compressible magnetohydrodynamics performed with the PENCIL CODE. We modeled the stellar dynamo for a solar-mass star with angular velocities of 20 and 30 times solar. We included and varied the strength of the centrifugal force and compared the results with reference simulations without the centrifugal force and with a simulation in which its effect is enhanced. The centrifugal force causes perturbations in the evolution of the numerical model, so that the outcome in the details becomes different as a result of nonlinear evolution. While the average density profile is unaffected by the centrifugal force, a relative change in the density difference between high latitudes and the equator of ∼10−4 is found. The power spectrum of the convective velocity is found to be more sensitive to the angular velocity than to the strength of the centrifugal force. The quadrupole moment of the stars includes a fluctuating and a time-independent component, which vary with the rotation rate. As very similar behavior is produced in absence of the centrifugal force, we conclude that it is not the main ingredient for producing the time-averaged and fluctuating quadrupole moment of the star. In a real physical system, we thus expect contributions from both components, that is, from the time-dependent gravitational force from the variation in the quadrupole term and from the spin-orbit coupling that is due to the persistent part of the quadrupole.