Quadrupolar Parameters Research Articles

33S NMR: Recent Advances and Applications.

The purpose of this review is to present advances and applications of 33S NMR, which is an underutilized NMR spectroscopy. Experimental NMR aspects in solution, chemical shift tendencies, and quadrupolar relaxation parameters will be briefly summarized. Emphasis will be given to advances and applications in the emerging fields of solid-state and DFT computations of 33S NMR parameters. The majority of the examples were taken from the last twenty years and were selected on the basis of their importance to provide structural, electronic, and dynamic information that is difficult to obtain by other techniques.

Quasi-periodic oscillations in rotating and deformed space–times

ABSTRACT Quasi-periodic oscillation (QPOs) analysis is important for understanding the dynamical behaviour of many astrophysical objects during transient events such as gamma-ray bursts, solar flares, magnetar flares, and fast radio bursts. In this paper, we analyse QPO data in low-mass X-ray binary (LMXB) systems, using the Lense-Thirring, Kerr, and approximate Zipoy-Voorhees metrics. We demonstrate that the inclusion of spin and quadrupole parameters modifies the well-established results for the fundamental frequencies in the Schwarzschild space–time. We interpret the QPO data within the framework of the standard relativistic precession model, allowing us to infer the values of the mass, spin, and quadrupole parameters of neutron stars in LMXBs. We explore recent QPO data sets from eight distinct LMXBs, assess their optimal parameters, and compare our findings with results in the existing literature. Finally, we discuss the astrophysical implications of our findings.

The Shock Cone Instabilities and Quasi-Periodic Oscillations around the Hartle–Thorne Black Hole

To explain the observed X-ray data in a black hole–accreting matter system and understand the physical mechanisms behind QPOs, we have numerically modeled the dynamical and oscillation properties of the shock cone formed around both slowly and rapidly rotating Hartle–Thorne black holes, resulting from the mechanism of Bondi–Hoyle–Lyttleton (BHL). According to the numerical simulations, an increase in the quadrupole parameter leads to a decrease in the shock cone opening angle around the black hole. A larger quadrupole parameter results in more matter falling into the black hole within the cone. The combination of the quadrupole parameter and black hole rotation causes the matter inside the cone to exhibit chaotic motion. These dynamical changes and chaotic behavior of the shock cones excite the fundamental oscillation modes. Moreover, new frequencies have been formed due to the nonlinear coupling of the fundamental modes. Conversely, we have numerically studied the behavior of cones formed around rapidly rotating Hartle–Thorne black holes and found differences and similarities to those obtained from slowly rotating cases. Finally, comparing the outcomes obtained fromHartle–Thorne gravity with the results fromKerr and Einstein–Gauss–Bonnet (EGB) gravities reveals the impact of the quadrupole parameter on the shock cone and QPOs.

The germanides ScTGe2 (T = Fe, Co, Ru, Rh) – crystal chemistry, 45Sc solid-state NMR and 57Fe Mössbauer spectroscopy

Abstract The TiMnSi2-type (space group Pbam) germanides ScTGe2 (T = Fe, Co, Ru, Rh) were synthesized from the elements by arc-melting. Single crystals were grown by annealing sequences of the arc-melted buttons in an induction furnace. The structures of ScFeGe2, ScRuGe2 and ScRhGe2 were refined from single-crystal X-ray diffraction data. In ScRuGe2, the ruthenium atoms have distorted octahedral germanium coordination (242–268 pm Ru–Ge). Three trans-face-sharing octahedra form a sub-unit which is condensed via common edges in c direction and connected via common corners with four adjacent blocks, forming a three-dimensional [RuGe2 type] substructure. The two crystallographically independent scandium sites have coordination numbers 15 (Sc1@Ge8Ru4Sc3) and 17 (Sc2@Ge7Ru6Sc4). Electronic band structure calculations for ScCoGe2 and ScRuGe2 show a net charge transfer from the scandium to the transition metal and germanium atoms, leading to a description with polyanionic networks Sc δ+[TGe2]δ−. The two crystallographically independent Sc sites are easily distinguishable by 45Sc magic-angle spinning (MAS)-NMR spectroscopy. Isotropic chemical shift values and nuclear electric quadrupolar interaction parameters were deduced from an analysis of the triple-quantum (TQ)-MAS NMR spectra. The electric field gradient parameters deduced from these experiments are in good agreement with quantum-chemical calculations using the Wien2k code. Likewise, the two crystallographically independent iron sites in ScFeGe2 could be discriminated in the 57Fe Mößbauer spectra through their isomer shifts and quadrupole splitting parameters: δ = 0.369(1) mm s−1 and ∆E Q = 0.232(2) mm s−1 for Fe1 and δ = 0.375(2) mm s−1 and ∆E Q = 0.435(4) mm s−1 for Fe2 (data at T = 78 K).

Extremely large magnetoresistance and anisotropic transport in the multipolar Kondo system PrTi2Al20

Multipolar Kondo systems offer unprecedented opportunities to design astonishing quantum phases and functionalities beyond spin-only descriptions. A model material platform of this kind is the cubic heavy fermion system PrT2Al20 (T=Ti, V), which hosts a nonmagnetic crystal-electric-field ground state and substantial Kondo entanglement of the local quadrupolar and octopolar moments with the conduction electron sea. Here, we explore the magnetoresistance (MR) and Hall effect of PrTi2Al20, which develops ferroquadrupolar (FQ) order below TQ∼2 K, and compare their behavior with that of the MR and Hall effect of the non-4f analog, LaTi2Al20. In the FQ ordered phase, PrTi2Al20 displays extremely large magnetoresistance (XMR) of ∼103%. The unsaturated, quasilinear field (B) dependence of the XMR violates Kohler's scaling and defies description based on carrier compensation alone. By comparing the MR and the Hall effect observed in PrTi2Al20 and LaTi2Al20, we conclude that the open-orbit topology on the electron-type Fermi surface sheet is key for the observed XMR. The low-temperature MR and the Hall resistivity in PrTi2Al20 display pronounced anisotropy in the [111] and [001] magnetic fields, which is absent in LaTi2Al20, suggesting that the transport anisotropy ties in with the anisotropic magnetic field response of the quadrupolar order parameter. Published by the American Physical Society 2024

Collisional Penrose process of extended test particles near an extremal Kerr black hole

We investigate the collisional Penrose process of extended test particles near an extremal Kerr black hole using the pole-dipole-quadrupole approximation. We analyze the motion of the test particles and examine the dynamics and maximal efficiency of energy extraction in this process. Our results demonstrate that the maximal extracted energy in the collisional Penrose process is influenced by the spin s and quadrupolar parameter C of the test particles. Specifically, we observe that, at a fixed collisional position, the energy extraction efficiency decreases as the spin increases for either the pole-dipole or the pole-dipole-quadrupole approximation case. Furthermore, for a fixed spin, the energy extraction efficiency is higher in the pole-dipole-quadrupole approximation compared to the pole-dipole approximation. These findings provide insight into the role of the internal structures of the test particles in the collisional Penrose process.

From the EFT of spinning gravitating objects to Poincaré and gauge invariance at the 4.5PN precision frontier

We confirm the generalized actions of the complete NLO cubic-in-spin interactions for generic compact binaries which were first tackled via an extension of the EFT of spinning gravitating objects. We first reduce these generalized actions to standard actions with spins, where the interaction potentials are found to consist of 6 independent sectors, including a new unique sector that is proportional to the square of the quadrupolar deformation parameter, CES2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {C}_{{\ extrm{ES}}^2} $$\\end{document}. We derive the general Hamiltonians in an arbitrary reference frame, and for generic kinematic configurations. With these most general Hamiltonians we construct the full Poincaré algebra of all the sectors at the fourth and a half post-Newtonian (4.5PN) order, including the third subleading spin-orbit sector, recently accomplished uniquely via our framework, thus proving the Poincaré invariance of all relevant sectors. We then derive the binding energies with gauge-invariant relations useful for gravitational-wave applications. Finally, we also derive the extrapolated scattering angles in the aligned-spins configuration for the scattering problem. Yet, as made clear already as of quadratic-in-spin sectors, the aligned-spins simplification inherent to the scattering-angle observable, entails a great loss of physical information, that is only growing with higher-spin sectors. Our completion of the full Poincaré algebra at the present 4.5PN order provides strong confidence that this new precision frontier in PN theory has now been established.

Deformation studies on thorium isotopes

The study of the deformation on thorium nuclei are important in nuclear physics due to its fissile nature. Thermally fissile isotopes have importance in energy production. The quadrupole and hexadecapole deformation parameters are important as they provide information on nuclear shape, size and moments of nuclei. The shape degree of freedom plays an important role in determining the fission barrier. In the present study, the quadrupole and hexadecapole deformation parameters of thorium nuclei were estimated by using the relativistic mean-field theory, with density dependent meson exchange interaction DD-ME2 and the density dependent point-coupling interaction DD-PC1. The estimated results of quadrupole deformation parameter are comparable with the available data and the minima point towards the neutron numbers N=126 and 184. The hexadecapole deformation parameter of thorium nuclei are positive along the stability line, negative towards the drip lines and zero at neutron number N=126 and 184.

Axisymmetric oscillation modes of relativistic tori in the vicinity of a distorted, deformed compact object

ABSTRACT This paper studies the oscillation properties of relativistic, non-self-gravitating tori in the background of a distorted, deformed compact object. This work concentrates on a static and axially symmetric metric containing two quadrupole parameters; relating to the central object and the external fields. This metric may associate the observable effects of these parameters as dynamical degrees of freedom. The astrophysical motivation for choosing such a field is the possibility of constituting a reasonable model for an actual scenario occurring in the vicinity of compact objects. Following our previous works, this paper aims to investigate the radial epicyclic frequency in a perfect fluid disc and not a test particle scenario via a local analysis. To achieve this goal, we employ the vertically integrated technique to be able to treat the equations analytically. The tori configuration is also modelled with Keplerian and non-Keplerian distributions of specific angular momentum. In this set-up, we also discuss the dependence of oscillation properties on the model’s variables related to angular momentum distribution and quadrupoles. In the present contribution, we further explore these properties with the possibility of relating oscillatory frequencies to some high-frequency quasi-periodic oscillations models and observed data in some microquasar and neutron star sources, and test the ability of this fluid approach to fit with observational data.

Thermodynamic properties of anisotropic antiferromagnets with four-spin exchange

Magnetic semiconductors are widely used in microelectronics, which is used to control spacecraft. The transport and electrical properties depend on the magnetic structure, which can be changed by the action of the magnetic field and controlled by the current. The magnetic structure of semiconductors with a strong spin-lattice interaction, which is reduced to a four-spin exchange interaction, is investigated. The magnetic characteristics are calculated in a classical Heisenberg model constructed from equivalent magnetic atoms forming a simple cubic and square lattice. The Hamiltonian of the system contains the exchange interaction between the nearest neighbors, the four-spin exchange, and the one-ion anisotropy of the light axis type. The Monte Carlo method calculates the thermodynamic characteristics: the sublattice magnetization, the quadrupole parameter, the pairwise spin-spin correlation functions, the spontaneous moment at the node directed along the light axis and in the basis plane, the internal energy, and the magnetic susceptibility. The magnetic order type was found to change from a collinear antiferromagnet (AFM) to a noncollinear (NAF) as the four-spin exchange constant increases. The dependence of the spin correlation functions on the distance has a weakly damped oscillatory character. In the AFM-NAP transition region, the near antiferromagnetic order is replaced by the ferromagnetic one, while the far antiferromagnetic order is preserved. A phase diagram of the antiferromagnetic (AFM) and non-collinear (NAF) on square and cubic lattices is constructed on the four-spin exchange-single-axis anisotropy plane. The longitudinal and transverse susceptibility of the NAF from temperature for different parameters of the four-spin exchange is calculated. The region of anisotropy and quadrupole exchange parameters in noncollinear NAF with a first-order phase transition, the sublattice magnetization jump, and the quadrupole parameter from temperature are determined. The anisotropy and four-spin exchange constants in a classical antiferromagnet with spontaneous momentum and far- and near-order parameters were found.

Digital design and experimental testing of a compressor's suction muffler transmission loss

Abstract The purpose of this paper is to provide a fast, efficient, and low-cost digital design method for the design of suction mufflers in refrigerator compressor plants. The main content of this paper is to establish a three-dimensional acoustic model of the compressor suction muffler by using Solidedge software, combine the upper suction port of the muffler with the valve group, then use Hypermesh to mesh the acoustic model and carry out the theoretical calculation, transform the control differential equation in the solution domain into the integral equation on the boundary by Green's function, discretize the boundary and carry out the numerical solution. The boundary is discretized and solved numerically. The transfer matrix quadrupole parameters are used to describe the acoustic components, and the transfer matrix of the discontinuous cross section is obtained to transform the complex system into a chain superposition of simple systems. The dependent variable in the partial differential equation to be solved is changed to a linear system of equations, and the transmission loss is calculated from the incident and transmitted sound pressure. The theoretical calculation of the transmission loss of the muffler is performed using LMS. Virtual. Lab software and the design solution is continuously optimized using this software. The experimental analysis shows that the designed muffler is printed and trimmed by 3D printing equipment and loaded onto the transmission loss test bench for experimental testing, and the highest theoretical value differs from the test result by 10dB.

Near-continuous isotropic – nematic transition in compressed rod-like liquid crystal based nanocolloid

Landau-de Gennes mean-field model predicts the discontinuous transition for the isotropic – nematic (I-N) transition, associated with uniaxial ordering and a quadrupolar order parameter in three dimensions. This report shows pressure-related dielectric studies for rod-like nematogenic pentylcyanobiphenyl (5CB) and its nanocolloids with BaTiO3 nanoparticles. The scan of the dielectric constant revealed the near-continuous I-N phase transition in the compressed nanocolloid with a tiny amount of nanoparticles (x = 0.1%).For the nematic phase in 5CB and its x = 1% nanocolloid the enormous values of the dielectric constant and the bending–type, long-range pretransitional behavior were detected. The impact of prenematic fluctuations was also noted for the ionic-related contribution to dielectric permittivity in the isotropic liquid phase. For the high-frequency relaxation domain, this impact was tested for the primary relaxation time pressure evolution and the translational–orientational decoupling.

Indirectly detected satellite-transition quadrupolar NMR via progressive saturation of the proton reservoir

Static satellite-transitions (ST) NMR line shapes from half-integer quadrupolar nuclei could be very informative: they can deliver insight about local motions over a wide range of timescales, and can report on small changes in the local electronic environments as reflected by variations in the quadrupolar parameters. Satellite transitions, however, are typically “invisible” for half-integer quadrupolar nuclei due to their sheer breadth, leading to low signal-to-noise ratio –especially for unreceptive low-gamma or dilute quadrupolar nuclei. Very recently we have introduced a method for enhancing the NMR sensitivity of unreceptive X nuclei in static solids dubbed PROgressive Saturation of the Proton Reservoir (PROSPR), which opens the possibility of magnifying the signals from such spins by repeatedly imprinting frequency-selective X-driven depolarizations on the much more sensitive 1H NMR signal. Here, we show that PROSPR's efficacy is high enough for enabling the detection of static ST NMR for challenging species like 35Cl, 33S and even 17O –all at natural-abundance. The ensuing ST-PROSPR NMR experiment thus opens new approaches to probe ultra-wideline (6–8 MHz wide) spectra. These highly pronounced anisotropies can in turn deliver new vistas about dynamic changes in solids, as here illustrated by tracking ST line shapes as a function of temperature during thermally-driven events.

The space–time line element for static ellipsoidal objects

In this paper, we solved the Einstein’s field equation and obtained a line element for static, ellipsoidal objects characterized by the linear eccentricity ( $$\eta $$ ) instead of quadrupole parameter (q). This line element recovers the Schwarzschild line element when $$\eta $$ is zero. In addition to that it also reduces to the Schwarzschild line element, if we neglect terms of the order of $$r^{-2}$$ or higher which are present within the expressions for metric elements for large distances. Furthermore, as the ellipsoidal character of the derived line element is maintained by the linear eccentricity ( $$\eta $$ ), which is an easily measurable parameter, this line element could be more suitable for various analytical as well as observational studies.

Impact of updated multipole Love numbers and f -Love universal relations in the context of binary neutron stars

Neutron star (NS) equation of state (EoS) insensitive relations or universal relations (UR) involving neutron star bulk properties play a crucial role in gravitational-wave astronomy. Considering a wide range of equations of state originating from (i) phenomenological relativistic mean field models, (ii) realistic EoS models based on different physical motivations, and (iii) polytropic EoSs described by spectral decomposition method, we update the EoS-insensitive relations involving NS tidal deformability (Multipole Love relation) and the UR between f-mode frequency and tidal deformability (f-Love relation). We analyze the binary neutron star (BNS) event GW170817 using the frequency domain TaylorF2 waveform model with updated universal relations and find that the additional contribution of the octupolar electric tidal parameter and quadrupolar magnetic tidal parameter or the change of multipole Love relation has no significant impact on the inferred NS properties. However, adding the f-mode dynamical phase lowers the 90% upper bound on $\tilde{\Lambda}$ by 16-20% as well as lowers the upper bound of NSs radii by $\sim$500m. The combined URs (multipole Love and f-Love) developed in this work predict a higher median (also a higher 90% upper bound) for $\tilde{\Lambda}$ by 6% and also predict higher radii for the binary components of GW170817 by 200-300m compared to the URs used previously in the literature. We further perform injection and recovery studies on simulated events with different EoSs in $\rm A+$ detector configuration as well as with third generation (3G) Einstein telescope. In agreement with the literature, we find that neglecting f-mode dynamical tides can significantly bias the inferred NS properties, especially for low mass NSs. However, we also find that the impact of the URs is within statistical errors.

Relativistic equilibrium fluid configurations around rotating deformed compact objects

The main goal of this paper is to investigate the physical properties of equilibrium sequences of non-self-gravitating surfaces that characterize Thick disks around a rotating deformed compact object described by a stationary generalization of the static mathrm q-metric. The space-time corresponds to an exact solution of Einstein’s field equations so that we can perform the analysis for arbitrary values of the quadrupole moment and rotation parameter. To study the properties of this disk model, we analyze bounded trajectories in this space-time. Further, we find that depending on the values of the parameters, we can have various disk structures that can easily be distinguished from the static case and also from the Schwarzschild background. We argue that this study may be used to evaluate the rotation and quadrupole parameters of the central compact object.

Residue-Specific High-Resolution 17O Solid-State Nuclear Magnetic Resonance of Peptides: Multidimensional Indirect 1H Detection and Magic-Angle Spinning.

Oxygen is an integral component of proteins but remains sparsely studied because its only NMR active isotope, 17O, has low sensitivity, low resolution, and large quadrupolar couplings. These issues are addressed here with efficient isotopic labeling, high magnetic fields, fast sample spinning, and 1H detection in conjunction with multidimensional experiments to observe oxygen sites specific to each amino acid residue. Notably, cross-polarization at high sample spinning frequencies provides efficient 13C ↔ 17O polarization transfer. The use of 17O for initial polarization is found to provide better sensitivity per unit time compared to 1H. Sharp isotropic 17O peaks are obtained by using a low-power multiple-quantum sequence, which in turn allows extraction of quadrupolar parameters for each oxygen site. Finally, the potential to determine sequential assignments and long-range distance restraints is demonstrated by using 3D 1H/13C/17O experiments, suggesting that such methods can become an essential tool for biomolecular structure determination.

Second order Zeeman interaction and ferroquadrupolar order in TmVO4

TmVO4 exhibits ferroquadrupolar order of the Tm 4f electronic orbitals at low temperatures, and is a model system for Ising nematicity. A magnetic field oriented along the c-axis constitutes a transverse effective field for the quadrupolar order parameter, continuously tuning the system to a quantum phase transition as the field is increased from zero. In contrast, in-plane magnetic fields couple to the order parameter only at second order, such that orienting along the primary axes of the quadrupole order results in an effective longitudinal field, whereas orienting at 45 degrees results in a second effective transverse field. Not only do in-plane fields engender a marked in-plane anisotropy of the critical magnetic and quadrupole fluctuations above the ferroquadrupolar ordering temperature, but in-plane transverse fields initially enhance the ferroquadrupolar order, before eventually suppressing it, an effect that we attribute to admixing of the higher crystalline electric field levels.

Half-integer-spin quadrupolar nuclei in magic-angle spinning paramagnetic NMR: The case of NaMnO2

A combination of solid-state NMR methods for the extraction of 23Na shift and quadrupolar parameters in the as-synthesized, structurally complex NaMnO2 Na-ion cathode material, under magic-angle spinning (MAS) is presented. We show that the integration of the Magic-Angle Turning experiment with Rotor-Assisted Population transfer (RAPT) can be used both to identify shifts and to extract a range of magnitudes for their quadrupolar couplings. We also demonstrate the applicability of the two-dimensional one pulse (TOP) based double-sheared Satellite Transition Magic-Angle Spinning (TOP-STMAS) showing how it can yield a spectrum with separated shift and second-order quadrupolar anisotropies, which in turn can be used to analyze a quadrupolar lineshape free of anisotropic bulk magnetic susceptibility (ABMS) induced shift dispersion and determine both isotropic shift and quadrupolar products. Combining all these experiments, the shift and quadrupolar parameters for all observed Na environments were extracted and yielded excellent agreement with the density functional theory (DFT) based models that were reported in previous literature. We expect these methods to open the door for new possibilities for solid-state NMR to probe half-integer quadrupolar nuclei in paramagnetic materials and other systems exhibiting large shift dispersion.

Dynamics of charged particles and quasi-periodic oscillations in the vicinity of a distorted, deformed compact object embedded in a uniform magnetic field

ABSTRACT This work presents the dynamic properties of charged test particles influenced by the gravitational and electromagnetic fields. Accordingly in this work, we concentrate on the static and axially symmetric metric containing two quadrupole parameters. One relates to the central object, and another relates to the external distribution of matter. This metric may associate the observable effects to these parameters as dynamical degrees of freedom. The astrophysical motivation for choosing such a field is the possibility to constitute a reasonable model for an actual situation occurring in the objects’ vicinity. To test the role of large-scale magnetic fields in accretion processes, we start by analysing different time-like bound orbits under the influence of the system’s different parameters. This leads to examining their stability concerning radial and/or vertical oscillations. The main focus is to discuss the effect of magnetic field on the oscillation modes’ resonant phenomena using different resonant models for disc-oscillation modes. In the present contribution, we further explore the possibility of relating oscillatory frequencies of charged particles to the frequencies of the high-frequency quasi-periodic oscillations observed in the microquasars GRS 1915+105, XTE 1550-564, and GRO 1655-40 via assuming relevance of resonant phenomena on the radial and vertical oscillations.