Moment Components Research Articles

Thermodynamics and spectroscopic properties of C2H5CONH2 found in Sagittarius B2(N1)

Thermodynamics and spectroscopic properties of low-lying isomers of propionamide (C2H5CONH2) have been investigated employing density functional theory and high-level coupled-cluster (CC) method. Isomer 1 (Propionamide) is found to be the thermodynamically most stable, while 2 (N, N-dimethylformamide) and 3 (1-aminopropan-2-one) lie 0.63 and 0.79 eV, respectively above 1 at CCSD/cc-pVTZ level of theory. Spectroscopic parameters such as rotational and centrifugal distortion constants, inertial axis dipole moment components, net dipole moments have been calculated using ωB97XD/cc-pVQZ and ae-CCSD(T)/cc-pVTZ methods. Molecular properties such as ionization potential, electron affinity, chemical potential, electronegativity, global hardness and softness, electrophilicity index, etc. have also been evaluated at ae-CCSD(T)/cc-pVTZ level.

Effect of yaw angle on aerodynamics of square inclined flat plates in ground effect

Aerodynamics of finite-span inclined square flat plates is experimentally investigated at a chord-based Reynolds number of 50 000 in ground effect. The minimum ground height is varied between gap ratios of 0.1 to 1.0 in chord lengths. All components of forces and moments are measured using a load cell for yaw angles between 0° and 180° at an angle of attack of 30°. In addition, surface flow visualization and planar, three-component particle image velocimetry are used to relate the main trends in structural loadings to changes in flow development. The results show that ground effect is significantly modified by yaw angle. As the gap ratio is decreased, a relatively invariant suction side flow and moderate increase in total force and moment driven by ram effect are observed for yaw angles less than 90°. Between yaw angles of 90° and 120°, the suction side flow is also insensitive to gap ratio variations, however, the loading is constant due to absence of ram effect. The suction side sting placement resulted in notable sting effect on both loading and flow for yaw angles between 120° and 150°, obfuscating the impact of ground proximity. For yaw angles above 150°, the onset of stall with decreasing gap ratio leads to a decrease in total loading, with the effect becoming more pronounced at higher yaw angles. These results may be utilized to drive targeted designs of photovoltaic support structures based on site surveys of wind direction and ground clearances.

Нетривиальная динамика спинов под действием взаимно перпендикулярных постоянных и переменных магнитных полей

The paper considers the nontrivial dynamics of a spin when it is simultaneously affected by a constant magnetic field directed along the Z axis and a variable one applied to the XOY plane. It is shown that coupled oscillations of all components of the magnetic moment (or magnetization) arise in this case. In other words, it becomes possible to control the orientation of the magnetic moment. Further, it was found that this possibility remains even in the case of two constant magnetic fields – when they are perpendicular to each other. In the latter case, elliptical precessions of magnetic moments occur in planes perpendicular to the applied fields, the amplitudes of which can be changed by means of constant magnetic fields.

Diminazene Ameliorates Neuroinflammation by Suppression of Astrocytic miRNA-224-5p/NLRP3 Axis in Alzheimer’s Disease Model

ACE2/Ang(1-7)/Mas Receptor, the momentous component of the renin-angiotensin system, has been shown to be involved in Alzheimer's disease (AD). We had previously found that enhancing brain ACE2 activity ameliorated cognitive impairment and attenuated brain neuroinflammation in SAMP8 mice, an animal model of AD. However, the exact mechanism of action of Diminazene (DIZE) has not been revealed. APP/PS1 mice were injected intraperitoneally with DIZE. Cognitive functions, neuronal and synaptic integrity, and inflammation-related markers were assessed by Morris water maze, Nissl staining, Western blotting and ELISA, respectively. Since astrocytes played a crucial role in AD-related neuroinflammation whilst miRNAs were reported to participate in modulating inflammatory responses, astrocytes of APP/PS1 mice were then isolated for high-throughput miRNAs sequencing to identify the most differentially expressed miRNA following DIZE treatment. Afterward, the downstream pathway of this miRNA in the anti-inflammatory action of DIZE was investigated using primary astrocytes. The results showed that DIZE alleviated cognitive impairment and neuronal and synaptic damage in APP/PS1 mice. Simultaneously, DIZE suppressed the secretion of pro-inflammatory cytokines and the expression of NLRP3 inflammasome. Importantly, miR-224-5p was significantly up-regulated in the astrocytes of APP/PS1 mice treated by DIZE, and NLRP3 is one of the targets of miR-224-5p. Upregulation of miR-224-5p inhibited the expression of NLRP3 in Aβ1-42-stimulated cells, whereas miR-224-5p downregulation reversed this effect. Furthermore, the inhibition of miR-224-5p could reverse the inhibitory effect of DIZE on astrocytic NLRP3 inflammasome. These findings firstly suggested that DIZE could inhibit astrocyte-regulated neuroinflammation via miRNA-224-5p/NLRP3 pathway. Furthermore, our study reveals the underlying mechanism by which DIZE suppresses neuroinflammatory responses in AD mice and uncovers the potential of DIZE in AD treatment.

Cooperative hydrogen bonding in thiazole⋯(H2O)2 revealed by microwave spectroscopy.

Two isomers of a complex formed between thiazole and two water molecules, thi⋯(H2O)2, have been identified through Fourier transform microwave spectroscopy between 7.0 and 18.5GHz. The complex was generated by the co-expansion of a gas sample containing trace amounts of thiazole and water in an inert buffer gas. For each isomer, rotational constants, A0, B0, and C0; centrifugal distortion constants, DJ, DJK, d1, and d2; and nuclear quadrupole coupling constants, χaa(N) and [χbb(N) - χcc(N)], have been determined through fitting of a rotational Hamiltonian to the frequencies of observed transitions. The molecular geometry, energy, and components of the dipole moment of each isomer have been calculated using Density Functional Theory (DFT). The experimental results for four isotopologues of isomer I allow for accurate determinations of atomic coordinates of oxygen atoms by r0 and rs methods. Isomer II has been assigned as the carrier of an observed spectrum on the basis of very good agreement between DFT-calculated results and a set of spectroscopic parameters (including A0, B0, and C0 rotational constants) determined by fitting to measured transition frequencies. Non-covalent interaction and natural bond orbital analyses reveal that two strong hydrogen bonding interactions are present within each of the identified isomers of thi⋯(H2O)2. The first of these binds H2O to the nitrogen of thiazole (OH⋯N), and the second binds the two water molecules (OH⋯O). A third, weaker interaction binds the H2O sub-unit to the hydrogen atom that is attached to C2 (for isomer I) or C4 (for isomer II) of the thiazole ring (CH⋯O).

Sign reversal of the spontaneous and induced polarisation in a mixture of achiral liquid crystal host and chiral azo dopant

ABSTRACT Achiral liquid crystal, possessing orthogonal smectic A and tilted smectic C phases in its phase sequence, was doped with a chiral photochromic azo dopant. It was found that the spontaneous and induced polarisation in the tilted smectic C* phase and in the orthogonal smectic A phase, respectively, change their sign, as well as their magnitude, under illumination with UV light. The origin of this sign reversal effect is considered to be the different sign of the molecular net dipole moment component µy of trans- and cis-isomers of the photochromic azo dopant, respectively. This light-induced sign reversal effect seems to have large potential for applications in the light-light controlled photonic liquid crystal devices, based on this effect.

Modelling of the torsional IR spectra of the HSSSH, DSSSH, and DSSSD molecules

Equilibrium configurations of trans- and cis- conformers of the HSSSH molecule (trisulfane), as well as the vibrational spectra of both conformers, were calculated at the MP2/Aug-cc-pVTZ, level of theory in the harmonic and anharmonic approximations. A more accurate analysis of torsional vibrations of thiol groups was performed by constructing 2D surfaces of a) potential energy, b) kinetic coefficients, and c) dipole moment components as functions of torsional coordinates of S-H groups. The values of b) and c) were calculated at the MP2/Aug-cc-pVTZ level of theory while the values of a) were calculated at the B3LYP/Aug-cc-pVTZ, MP2/cc-pVTZ, MP2/Aug-cc-pVTZ, MP2/cc-pVQZ, MP2/CBS(T,Q) and CCSD(T)/Aug-cc-pVTZ levels of theory. The energies of the stationary torsional states of the trisulfane molecule conformers were determined by numerically solving the vibrational Schrödinger equation of restricted dimensionality. The frequencies of torsional vibrations of S-H groups, as well as the splittings of torsional energy levels in trans- and cis-conformers due to tunneling between equivalent configurations of the molecule, were determined. The calculated values of tunneling frequencies in the ground torsional state of HSSSH and DSSSD trans-conformers (2.3 * 10−22 and 7.5 * 10−27 cm−1, respectively) are of particular interest due to the fact that trisulfane is considered to be one of the best candidates for establishing the effect of violation of parity conservation law in chiral molecules.

Electric Dipole Moments from Stark Effect in Supersonic Expansion: n-Propanol, n-Butanol, and n-Butyl Cyanide.

The orientation and magnitude of the molecular electric dipole moment are key properties relevant to topics ranging from the nature of intermolecular interactions to the quantitative analysis of complex gas-phase mixtures, such as chemistry in astrophysical environments. Stark effect measurements on rotational spectra have been the method of choice for isolated molecules but have become less common with the practical disappearance of Stark modulation spectrometers. Their role has been taken over by supersonic expansion measurements within a Fabry-Perot resonator cavity, which introduces specific technical problems that need to be overcome. Several of the adopted solutions are described and compared. Presently, we report precise electric dipole moment determinations for the two most stable conformers of the selected molecules of confirmed or potential astrophysical relevance: n-propanol, n-butanol, and n-butyl cyanide. All dipole moment components have been precisely determined at supersonic expansion conditions by employing specially designed Stark electrodes and a computer program for fitting the measured Stark shifts, inclusive of cases with resolved nuclear quadrupole hyperfine structure. The experimental values are compared with suitable quantum chemistry computations. It is found that, among the tested levels of computation, vibrationally averaged dipole moments are the closest to the observation and the molecular values are, as in the lighter molecules in the series, largely determined by the hydroxyl or nitrile groups.

Large Orbital Magnetic Moment in VI3.

The existence of the V3+-ion orbital moment is an open issue of the nature of magnetism in the van der Waals ferromagnet VI3. The huge magnetocrystalline anisotropy in conjunction with the significantly reduced ordered magnetic moment compared to the spin-only value provides strong but indirect evidence of a large V orbital moment. We used the unique capability of X-ray magnetic circular dichroism to determine the orbital component of the total magnetic moment and provide a direct proof of an exceptionally sizable orbital moment of the V3+ ion in VI3. Our ligand field multiplet simulations of the XMCD spectra in synergy with the results of DFT calculations agree with the existence of two V sites with different orbital occupations and OM magnitudes in the ground state.

Human Lumbar Spine Injury Risk in Dynamic Combined Compression and Flexion Loading.

Anticipating changes to vehicle interiors with future automated driving systems, the automobile industry recently has focused attention on crash response in novel postures with increased seatback recline. Prior research found that this posture may result in greater risk of lumbar spine injury in the event of a frontal crash. This study developed a lumbar spine injury risk function (IRF) that estimated injury risk as a function of simultaneously applied compression force and flexion moment. Force and moment failure data from 40 compression-flexion tests were utilized in a Weibull survival model, including appropriate data censoring. A mechanics-based injury metric was formulated, where lumbar spine compression force and flexion moment were normalized by specimen geometry. Subject age was incorporated as a covariate to further improve model fit. A weighting factor was included to adjust the influence of force and moment, and parameter optimization yielded a value of 0.11. Thus, the normalized compression force component had a greater effect on injury risk than the normalized flexion moment component. Additionally, as force was nominally increased, less moment was required to produce injury for a given age and specimen geometry. The resulting IRF may be utilized to improve occupant safety in the future.

On opto-thermally excited parametric oscillations of microbeam resonators. I

The present article is the first part of the work devoted to investigation of the nonlinear dynamics of parametrically excited flexural vibrations of a clamped-clamped microbeam - the basic sensitive element of a promising class of microsensors of various physical quantities - under laser thermooptical action in the form of periodically generated pulses acting on a certain part of the surface of the beam element. An analytical solution of the heat transfer problem is found for the steady harmonic distribution of temperature in the volume of the resonator. The static and dynamic components of temperature-induced axial force and bending moment are determined. Using the Galerkin method, the discretization of nonlinear coupled partial differential equations describing the longitudinal-flexural oscillations of the resonator is performed. Using the asymptotic method of multiple time-scales, an approximate analytical solution is obtained for the nonlinear dynamics problem under the conditions of primary parametric resonance.

Rotational spectroscopy of hydrogen-bonded binary trifluoro-propanol conformers: conformational diversity, preference and abundances in a jet expansion.

The rich conformational landscape including the associated conformational conversion paths of the hydrogen-bonded binary 3,3,3-trifluoropropanol (TFP) aggregate was explored using chirped pulse Fourier transform microwave spectroscopy and computational chemistry. To appropriately identify the binary TFP conformers responsible for the five sets of candidate rotational transitions assigned, we established a set of important conformational assignment criteria. These include an extensive conformational search, good agreement between the experimental and theoretical rotational constants, relative magnitude of the three dipole moment components, and quartic centrifugal distortion constants, and observation and non-observation of the predicted conformers. Extensive conformational searches were carried out using CREST, a conformational search tool, producing hundreds of structural candidates. The CREST candidates were screened using a multitier approach and subsequently the low energy conformers (<25 kJ mol-1) were optimized at the B3LYP-D3BJ/def2-TZVP level, leading to 62 minima within an energy window of 10 kJ mol-1. Good agreement with the predicted spectroscopic properties mentioned above allowed us to clearly identify five binary TFP conformers as the molecular carriers. Particularly, a combined kinetic and thermodynamic model was developed, which provides a satisfactory explanation for the observation and non-observation of the low energy conformers predicted. The role of the intra- and intermolecular hydrogen bonding interactions in the stability ordering of the binary conformers is discussed.

Formulation and Numerical Solution of the Stability Loss Problem of Elastic-Plastic Shells of Revolution with an Elastic Filler under Combined Axisymmetric and Torsional Loadings

A dynamic statement and a method for numerically solving the buckling problems of elastoplastic shells of revolution with filler in axisymmetric and non-axisymmetric shapes under quasi-static and dynamic loading are presented within the framework of two approaches. In the first approach, the problem of elastic-plastic deformation and buckling of shells of revolution with an elastic filler under combined axisymmetric loading with torsion is formulated in a two-dimensional (generalized axisymmetric) formulation based on the hypotheses of the shells theory of the Timoshenko type and the Winkler foundation. The constitutive relations are written in the cylindrical system of Euler coordinates. For each shell element, a local Lagrangian coordinate system is introduced. Kinematic relations are recorded in the current state metric. The distribution of the displacement velocity components over the shell thickness and strain rate tensors in the local basis is written as the sum of the momentless and moment components, which, in turn, are written as the sum of the symmetric and asymmetric parts in the local and in the general basis. The elastoplastic properties of the shell material are taken into account within the framework of the theory of flow with nonlinear isotropic hardening. To take into account non-axisymmetric forms of buckling, the desired functions (both displacements and forces, moments, contact pressure) are expanded into a Fourier series in the circumferential direction. The variational equations of shell motion are derived from the general equation of dynamics. The contact between the shell and the deformable filler is modeled based on the conditions of non-penetration along the normal and free slip along the tangent. The variational equations of shell dynamics for axisymmetric and nonaxisymmetric processes are interconnected through the physical relations of the theory of plasticity. They take into account large axisymmetric shape changes and the instantaneous stress-strain state of the shell. At the initial stage of the nonaxisymmetric buckling process, the deflections are small; therefore, the equations of nonaxisymmetric buckling are obtained as linearized with respect to nonaxisymmetric forms. To initiate nonaxisymmetric buckling modes, initial nonaxisymmetric deflections are introduced. To solve the defining system of equations, a finite-difference method and an explicit time integration scheme of the “cross” type are used. The second approach is based on continuum mechanics hypotheses and implemented in a three-dimensional setting. Both approaches make it possible to simulate the nonlinear subcritical deformation of shells of revolution with an elastic filler, to determine the ultimate (critical) loads in a wide range of loading rates, taking into account geometric shape imperfections, to study the processes of buckling in axisymmetric and non-axisymmetric shapes under dynamic and quasi-static complex loading by tension, compression, torsion, internal and external pressure. The results of numerical simulation are compared with experimental data on the torsion of steel cylindrical elastoplastic shells ( R / h = 1.45) with an elastic filler.

Unusual spin dynamics

The paper considers the dynamics of a spin when it is simultaneously affected by a constant magnetic field directed along the Z axis and a variable one applied to the X0Y plane. It is shown that coupled oscillations of all components of the magnetic moment (or magnetization) arise in this case. In other words, it becomes possible to control the orientation of the magnetic moment. Further, it was found that this possibility remains even in the case of two constant magnetic fields - when they are perpendicular to each other.

Dynamic response and energy absorption performance of aluminum foam-filled sandwich circular tubes under internal blast loading

The dynamic response and energy absorption properties of an aluminum foam-filled sandwich circular tube under internal blast loading is investigated by experimental, theoretical, and numerical simulations. A series of blast experiments were performed using spherical emulsion explosives of different masses. Three axially deformed regions are obtained for the internal and external tubes: a region with large plastic deformation, a rigid section moving around the plastic hinge, and an undistorted boundary region. Explosive mass, the internal and external tube wall thickness have a significant influence on the final deformation of a foam-filled sandwich circular tube. A theoretical explicit calculation method including the circumferential plastic membrane forces and the axial moment components has been developed to predict the internal blast response of a foam-filled sandwich circular tube. The FE model, based on a 3D Voronoi algorithm for the foam core, was developed to investigate the deformation mechanism of a foam-filled sandwich circular tube. Both numerical and experimental results are consistent with the theoretical predictions. In addition, the impact of the explosive mass, the diameter and the wall thickness of the internal and external tubes, and the axial arrangement of the core on the dynamic response and energy absorption properties are investigated. It is found that the sandwich circular tube with negative gradient core has the best anti-blasting performance among the sandwich circular tubes with gradient arrangement.

Using Laurent’s series in the theoretical solution to estimate the stress resultants of FG-CNTRC plates weakened by a central cutout at different temperatures

Conventional ordinary materials have many weaknesses when exposed to extreme loadings. Hence, scientists develop novel engineered materials to address these weaknesses. Functionally Graded Carbon Nanotube Reinforced Composites (FG-CNTRCs) are a modern group of materials that have recently flourished thanks to their excellent and unique mechanical properties. One common loading condition is subjecting FG-CNTRC plates containing cutouts to in-plane loadings. The presence of an opening disturbs the stress field, especially in the proximity of the cutout, and creates stress concentration. This study estimates the stress and moment resultants on the edge of elliptical cutouts in asymmetric FG-CNTRC plates under various loading conditions using a new analysis based on Lekhnitskii’s complex variables method, mapping function, and Laurent series. Unlike previous studies on perforated asymmetric plates, which were based on numerical methods or the Schwartz formulations, this study presents a new solution using Laurent’s series to represent the holomorphic function. In calculating the stress and moment components around the opening, the effect of determining variables is studied. This approach can be generalized to solve different anisotropic body problems (FG_CNTRC, FGM, Laminate composites). Thus, stress and moment components in perforated anisotropic plates can be determined simply and systematically using this method.

Wind-Induced Impact Behavior of Base-Isolated High-Rise Buildings with Adjacent Structures

The base-isolation technology has been increasingly applied in high-rise buildings in recent years. Previous studies have shown that the unfavorable wind-induced response can be effectively reduced by a certain degree of hysteretic energy dissipation after the yielding of the isolation system under strong wind load. However, a large relative inelastic displacement at the isolation level will occur under this condition, which is likely to exceed the width of seismic gap, and cause a structural impact with the adjacent structures (i.e. retaining wall or other barriers). Such wind-induced impacts may have detrimental consequences on the structural performance and have not been investigated much before. This study prospectively investigated the wind-induced impact behavior of base-isolated high-rise buildings with adjacent structures. The multi-story superstructure is modeled as a linear elastic shear building, while the isolation system is represented by bilinear hysteresis restoring force model. An impact element combined with linear spring and damper is used. The story wind load is determined by its cross power spectral density (PSD). Responses for two kinds of typical impact including crosswind and along-wind impact are examined by time history analysis. The results demonstrate that the impact will increase the fluctuation components of superstructure displacement, shear force and bending moment to some extent compared with that of the base-isolated building without impact. The floor accelerations, especially floors close to the base, are significantly increased during impact. The impact has no effect on the mean component of each response. At last, a parametric analysis is carried out to explore the influences of various impact parameters on the inelastic impact response. The results of this study can help to better understand the impact behavior of base-isolated high-rise buildings under strong wind excitation and be useful for performance-based wind resistance design.

Optimization of manipulator's motion mode on elastic base according to the criteria of the minimum central square value of drive torque

The results of studies of optimizing the mode of movement of the manipulator boom, mounted on an elastic base with a known stiffness the paper presents. The purpose of this scientific research is to reduce the oscillations of the manipulator turnout system, which will increase the overall efficiency of the manipulator, durability and reliability of the metal structure elements. The implementation of this goal have achieved by applying a controlled mode of operation of the drive with dynamic balancing of the drive mechanism. Using the Lagrange equation of the second kind, the equation of motion of the manipulator boom was compile and the expression for the generalized driving moment of the drive mechanism of the manipulator boom system was determined. This study considers only the angular displacement of the manipulator boom. The unbalanced drive driving moment of the manipulator boom had estimated by the component of the total inertial moment of the moving mass of the boom and load and the static load from the mass of the boom and load on the drive mechanism. The elastic base of the manipulator was present in the form of a linear spring with a given coefficient of elasticity. Since the main external factor of oscillation, perturbation in the metal structure of the manipulator is the driving moment of the drive, so we used the target optimization function, which estimates the root mean square value of the driving moment of the drive mechanism. The main criterion for optimizing the mode of motion was present in the form of an integral functional, and the search for its minimum value is carried out using the methods of calculus of variations.&#x0D; The results of this work can used by the drive control system at the design stage of the manipulator and during its operation. The dynamics of oscillations of such structural elements of boom systems of cranes is also estimated. The implementation of the obtained optimal modes of movement can be carried out using a hydraulic drive.

Inadvertent side effects of fixed lingual retainers : An in vitro study.

To better understand the side effects of fixed lingual retainers by means of an in vitro study in atwo-tooth model determining the three-dimensional (3D) force-moment components acting at adjacent teeth combined with different composite-wire interfaces. Triple-stranded round retainer wires were embedded in cured disks of flowable composite. At one side the composite-wire interface was untreated and checked to be absolutely fix. At the other side the composite-wire interface was configured as either an isolated compound with (1)petroleum jelly coating, or an adhered compound with (2)no manipulation, (3)ethanol degreasing or (4)ethanol degreasing and rectangular bending of the wire ends. The 3D force-moment components were registered, while the intertooth distance was increased in steps of 0.01 mm leading to increasing tension of the wire. Measurements were repeated after artificially aging the specimens. Retainer wire specimens with adhered compound (2, 3, 4) showed negative vestibulo-oral moments ranging maximally each between -0.3 and -0.9 Nmm in opposite direction to positive moments of 1.9 Nmm for specimens with isolated compound1. Significant tipping moments occurred in the group with isolated compound at lower forces than in those groups with adhered compound. Similar effects were observed after artificial aging. Side effects emerge under specific circumstances: an altered adhesive compound combined with the presence of oral forces. Compounds with lost adhesion at the composite-wire interface showed rotational moments in the direction of the wire windings even during low tensile forces similar to those that may occur in clinical settings. Opposite rotational moments leading to unwinding of the wire may occur in cases with adhered compounds at higher tensile forces. Utilization of round triple-stranded retainer wires without bent ends are of higher risk to induce inadvertent side effects.

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.