Rotational Properties Research Articles

Rotational wave velocity of protons

The angular momentum of particles is the result of rotational waves, which are believed not to rotate in a classical sense. Therefore, the rotational wave properties of protons or nucleons, which should be comparable to De Broglie matter waves, have never been attributed to a wavelength, frequency or energy, but solely to their spin, which is a quantized property and probably does not reflect the true angular momentum as the product of radius and rotational impulse of a particle. Using data that originates from the hadron accelerator CERN in Switzerland, the true, not quantized velocity of the rotational wave of protons could be, however, measured. Thereby, its frequency is 2072.18 Hz, hence, it is unexpectedly low. The spike in the polarizability curve of protons at Q^2 = 0.33 GeV^2, published currently in the journal Nature, together with the rotational wave frequency obtained from CERN data, provides reliable evidence that this might be an interference in terms of superposition of the particle wave of the scattered electrons with the rotational wave of the protons at the same energy level, doubling the expected curve value, which, since there are no other possible explanations, proves the determined rotating wave velocity of protons.

Asymmetric rotations and dimerization driven by normal to modulated phase transition in 4-biphenylcarboxy coupled L-phenylalaninate.

Amongst the derivatives of 4-biphenylcarboxylic acid and amino acid esters, the crystal structure of 4-biphenylcarboxy-(L)-phenylalaninate is unusual owing to its monoclinic symmetry within a pseudo-orthorhombic crystal system. The distortion is described by a disparate rotational property around the chiral centers (ϕchiral ≃ -129° and 58°) of the two molecules in the asymmetric unit. Each of these molecules comprises planar biphenyl moieties (ϕbiphenyl = 0°). Using temperature-dependent single-crystal X-ray diffraction experiments we show that the compound undergoes a phase transition below T ∼ 124 K that is characterized by a commensurate modulation wavevector, q = δ(101), δ = ½. The (3+1)-dimensional modulated structure at T = 100 K suggests that the phase transition drives the biphenyl moieties towards noncoplanar conformations with significant variation of internal torsion angle (ϕmaxbiphenyl ≤ 20°). These intramolecular rotations lead to dimerization of the molecular stacks that are described predominantly by distortions in intermolecular tilts (θmax ≤ 20°) and small variations in intermolecular distances (Δdmax ≃ 0.05 Å) between biphenyl molecules. Atypical of modulated structures and superstructures of biphenyl and other polyphenyls, the rotations of individual molecules are asymmetric (Δϕbiphenyl ≈ 5°) while ϕbiphenyl of one independent molecule is two to four times larger than the other. Crystal-chemical analysis and phase relations in superspace suggest multiple competing factors involving intramolecular steric factors, intermolecular H-C...C-H contacts and weak C-H...O hydrogen bonds that govern the distinctively unequal torsional properties of the molecules.

NaRb6(B4O5(OH)4)3(BO2) Featuring Noncentrosymmetry, Chirality, and the Linear Anionic Group BO2.

Noncentrosymmetric (NCS) structures are of particular interest owing to their symmetry-dependent physical properties, e.g., pyroelectricity, ferroelectricity, piezoelectricity, and nonlinear optical (NLO) behavior. Among them, chiral materials exhibit polarization rotation and host topological properties. Borates often contribute to NCS and chiral structures via their triangular [BO3] and tetrahedral [BO4] units and their numerous superstructure motifs. However, no chiral compound with the linear [BO2] unit has been reported to date. Herein, an NCS and chiral mixed-alkali-metal borate, NaRb6(B4O5(OH)4)3(BO2), with a linear BO2- unit in the structure was synthesized and characterized. The structure features a combination of three types of basic building units (BBUs), [BO2], [BO3], and [BO4] with sp-, sp2-, and sp3-hybridization of boron atoms, respectively. It crystallizes in the trigonal space group R32 (No. 155), one of the 65 Sohncke space groups. Two enantiomers of NaRb6(B4O5(OH)4)3(BO2) were found, and their crystallographic relationships are discussed. These results not only expand the small family of NCS structures with the rare linear BO2- unit but also prompt recognition to the fact that NLO materials have generally overlooked the existence of two enantiomers in achiral Sohncke space groups.

Parity-doublet bands in the odd- A isotones U237 and Pu239 investigated by a particle-number-conserving method based on the cranked shell model

Based on the reflection-asymmetric Nilsson potential, the parity-doublet rotational bands in odd-$A$ isotones \element{237}U and \element{239}Pu have been investigated by using the particle-number-conserving (PNC) method in the framework of the cranked shell model (CSM). The experimental kinematic moments of inertia (MOIs) and angular momentum alignments are reproduced very well by the PNC-CSM calculations. The significant differences of rotational properties between \element{237}U and \element{239}Pu are explained with the contribution of nucleons occupying proton octupole-correlation pairs of $\pi ^{2} i_{13/2}f_{7/2}$. The upbendings of moments of inertia of the parity-doublet bands in \element{237}U are due to the interference terms of alignments of protons occupying $\pi f_{7/2}$ (${1/2}$) and the high-$j$ intruder $\pi i_{13/2}$ $(1/2, 3/2)$ orbitals. The splittings between the simplex partner bands of the parity-doublet bands in both \element{237}U and \element{239}Pu result from the contribution of alignment of neutron occupying the $\nu d_{5/2}$ ($1/2$) orbital.

A Comparison of Millisecond Pulsar Populations between Globular Clusters and the Galactic Field

We have performed a systematic study of the rotational, orbital, and X-ray properties of millisecond pulsars (MSPs) in globular clusters (GCs) and compared their nature with those of the MSPs in the Galactic field (GF). We found that GC MSPs generally rotate slower than their counterparts in the GF. Different from the expectation of a simple recycling scenario, no evidence for the correlation between the orbital period and the rotation period can be found in the MSP binaries in GCs. There is also an indication that the surface magnetic field of GC MSPs is stronger than those in the GF. All these suggest dynamical interactions in GCs can alter the evolution of MSPs/their progenitors, which can leave an imprint on their X-ray emission properties. While the MSPs in both GF and GCs have similar distributions of X-ray luminosity and hardness, our sample supports the notion that these two populations follow different relations between the X-ray luminosity and spin-down power. We discuss this in terms of both the pulsar emission model and the observational bias.

Low-lying state investigations of odd-A Mn isotopes around N = 28

Based on the systematic studies for low-lying states of the odd-A 49−57Mn isotopes, the ground-states inversion and the rotational properties of a ground-state-based sequence are revealed and discussed. The energy levels of low-lying states and electromagnetic moments in odd-A 49−57Mn isotopes have been well reproduced in shell-model calculations, and the above phenomena could be understood with obviously different occupation numbers in proton orbitals such as π f 7/2 and π p 3/2, which changes similarly with the obtained quadrupole deformation in covariant density functional theory (CDFT). After considering the coupling of collective rotation and intrinsic single-particle motion, the available experimental magnetic moments in 53Mn and adjacent nuclei can be well explained with CDFT. The present calculations suggest that the 5/2− and 7/2− states in 53Mn are formed by π5/2−[312] and π7/2−[303] respectively. Together with the behavior of levels, this provides proofs for the level sequences of low-lying states in 53Mn distinct from the K π = 5/2− rotational band in 49Cr and other odd-A Mn isotopes.

Real-time six-dimensional spatiotemporal tracking of single anisotropic nanoparticles in live cells by integrated multifunctional light-sheet nanoscopy

An integrated multifunctional light-sheet nanoscopy (iMLSN) combined with differential interference contrast, total internal reflection, epifluorescence, a super-resolution radial fluctuation-stream module, and a wavelength-dependent light sheet was developed to simultaneously realize the six-dimensional (6D) vector-valued (three coordinates + rotational dynamics (azimuth and elevation angles) + transport speed) tracking of anisotropic nanoparticles in single living cells. The wavelength-dependent asymmetric scattering of light by gold nanorods was used to trigger signals depending on the polarizer angle, and real-time photo-switching was achieved by turning the polarizer, obtaining a series of super-resolution images, and tracking using different polarization directions and two channels. This technique was employed to directly observe native gold nanorods (AuNRs; 5 nm diameter × 15 nm length) and surface-functionalized AuNRs during their endocytosis and transport at the upper and attaching side membrane regions of single living cells, revealing that the AuNRs bound to the membrane receptors. The nanorods were subsequently internalized and transported away from the original entry spots. Detailed dynamic information regarding the rotation properties and endocytosis speed during the transmembrane process was also acquired for each region. The developed technique can be considered useful for the real-time monitoring of intracellular transport at various regions in single living cells, as well as for 6D vector-valued non-fluorescence super-resolution imaging and tracking.Graphical

Fibula Nail versus Locking Plate Fixation-A Biomechanical Study.

In the treatment of ankle fractures, complications such as wound healing problems following open reduction and internal fixation are a major problem. An innovative alternative to this procedure offers a more minimally invasive nail stabilization. The purpose of this biomechanical study was to clarify whether this method was biomechanically comparable to the established method. First, the stability (range of motion, diastasis) and rotational stiffness of the native upper ankle were evaluated in eight pairs of native geriatric specimens. Subsequently, an unstable ankle fracture was created and fixed with a locking plate or a nail in a pairwise manner. The ankles showed significantly less stability and rotational stiffness properties after nail and plate fixations than the corresponding native ankles (p < 0.001 for all parameters). When comparing the two methods, both showed no differences in their range of motion (p = 0.694) and diastasis (p = 0.166). The nail also presented significantly greater rotational stiffness compared to the plate (p = 0.001). However, both fixations remained behind the native stability and rotational stiffness. Due to the comparable biomechanical properties of the nail and plate fixations, an early weight-bearing following nail fixation should be assessed on a case-by-case basis considering the severity of fractures.

Nuclear Structure Investigations of Even–Even Hf Isotopes

The mass region of rare-earth nuclei in the nuclear chart is riddled with well-deformed nuclei, exhibiting rotational properties and many interesting nuclear structure-related phenomena. The scarcity of experimental data as the neutron number increases and the exotic phenomena such as shape coexistence, which are strongly connected with the underlying symmetries of the Hamiltonian and are predicted to take place in this region, make this mass region a fertile ground for experimental and theoretical studies of nuclear structure. In this work, we investigate the structure of the even–even 162–184Hf (hafnium) isotopes through a calculation of various observables such as B(E2;01+→21+) reduced transition matrix elements and quadrupole moments. Six different nuclear models are employed in the calculations of the observables for these nuclei, the shapes of which deviate from spherical symmetry, and as such, are characterized by Hamiltonians, which break the rotational invariance of the exact nuclear many-body Hamiltonian. The results of the present study are expected to establish some concrete guidelines for current and future experimental endeavors. Along these lines, the results for the 162–180Hf isotopes are compared with existing experimental data where available, showing an overall good agreement.

Physical and dynamical properties of selected Earth co-orbital asteroids

We present our investigations of the physical and dynamical properties of selected Earth co-orbital asteroids. The photometric optical light curves as well as rotation periods and pole solutions for a sample of four Earth co-orbital asteroids, namely (138175) 2000 EE104 (P=13.9476+/-0.0051 hrs), (418849) 2008 WM64 (P=2.4077+/-0.0001 hrs), 2016 CA138 (P=5.3137+/-0.0016 hrs) and 2017 SL16 (P=0.3188+/-0.0053 hrs), are determined or improved and presented in this work. For this investigation, we combine observations carried out at the Bulgarian National Astronomical Observatory - Rozhen using the FoReRo2 instrument attached to the 2mRCC telescope as well as sparse data from AstDys2 database. Parallel to the rotational properties we did numerical dynamical simulations to investigate the orbital stability of those objects and to find out if there is a relation with their rotational properties. Our results show that the orbit stability is affected by the orbit itself and mainly its eccentricity and inclination, which are responsible for the close encounters with other Solar system planets. We cannot make a definitive conclusion about the relation between orbit stability and the rotational state of the asteroids, so we need further investigations and observations in order to prove or disprove it.

ГОРИЗОНТАЛЬНОЕ ВРАЩЕНИЕ ДЕФОРМИРОВАННЫХ ЭЛЕМЕНТОВ ЗЕМНОЙ ПОВЕРХНОСТИ

The structural composition and properties of the horizontal rotation of the elements of the Earth's surface, which is part of the skew-symmetric part of the geomechanical distortion tensor, are investigated. It is established that it consists of a real rotation, showing the rotation of a deformed area element in geospatial space, and a virtual one, displaying its artificial rotation. The decomposition of angular deformations into components leading to real and virtual rotation, as well as the calculation of their angles, is carried out according to the presented nomogram and the formulas attached to it. Practical examples show the deformation and rotation of complex contours of man-made mining facilities located on differently moving blocks of the Earth's surface.

Computational Super-Resolution Imaging With a Sparse Rotational Camera Array

A sparse camera array utilizes several identical cameras for multi-frame super-resolution. However, the influence of camera layout on super-resolution performance remains unclear. In conventional camera arrays, all cameras share a similar observation model, resulting in redundancy during information collection. This study presents a novel super-resolution framework that actively controls cameras in a sparse camera array to rotate to certain degrees. Through a detailed analysis of the forward imaging model, it is shown that the rotation of cameras uses the rotational asymmetry property of pixel layouts and shape. The proposed camera layout method provides more diverse and informative spatial sampling than a conventional camera array with only translations between cameras. A physics-enabled deep neural network was introduced for multi-frame super-resolution. With the explicitly defined gradients and affine models as guidance, it can effectively decode additional information collected by the rotational camera array and overcome the large-scale spatial feature alignment problem. The experimental results on synthetic and real prototype datasets validated the proposed theory and solution. We believe our study can inspire innovations for future task-specific camera array system design.

Torsional vibrations of a rotating viskoelastic rod

A homogeneous and isotropic round viscoelastic rod rotating around its axis of symmetry with a constant angular velocity is considered in a cylindrical coordinate system. It is believed that the behavior of the rod is described within the framework of the linear theory of viscoelasticity, where the relationship between stresses and deformations is given in the form of relations Boltzmann-Volterra. In this case, the condition of its reversibility is imposed on the kernel of the integral operator. The equations of motion of the rod concerning non-zero stress components are written, taking into account the centrifugal force caused by the rotation. It is assumed that torsional vibrations are caused by given stress on its surface. A general equation of torsional vibrations of such a rod is obtained, which is an integral-differential equation of infinitely high order for the main part of the torsional displacement. Limiting the general equations to the zero and first approximations, the equations of the second and fourth orders are obtained, which, in the case of the absence of rotation, exactly coincide with the known equations of other authors. The resulting refined equation of the fourth order in its structure considers the angular velocity of rotation, the deformation of the transverse shear, and the inertia of rotation. Based on the derived oscillation equations, a particular problem is solved to study the influence of rotation and viscoelastic properties of the material on the stress-strain state of the rod, according to the results of which graphs of the dependencies of elastic and viscoelastic changes on time at points of three different sections of the rod are constructed. A comparative analysis of the results obtained with the results of other authors is performed.

Study of the High Rotational Bands of Moderately Heavy Nuclei

Abstract: This paper provides a study of the rotational properties of heavy and medium nuclei, particularly the paired nuclei existing in the rare-earth, including Gd, Er, …, first to have a good representation of the intrinsic prolate fundamentals of the considered nuclei. The most important residual nuclear interaction is the pairing force which makes it possible to couple the nucleons in pairs. To take it into account, we introduce the Bardeen-Cooper-Shrie formalism (BCS), developed to describe the phenomenon of superconductivity. The test wave function is then more elaborate than that of Hartree-Fock and corresponds to a state no longer of independent particles, but of independent quasi-particles. A quasi-particle state (qp) is a linear combination of particles and holes. The Routhian Hartree-Fock model through the analysis of the experimental spectra of rotation of the deformed nucleus was usewd. Knowing that this was originally expanded by Bohr-Mottelson by applying I(I+1) expansion, we modified an existing fixed code (HF) with axial symmetry, which extended in a way that allows us to add constraints on the angular momentum and kelvin rotation to the Hamiltonian known as Cr.HF (cranking version of this formalism), initially studied by P. Quentin. This modification led to good results, especially the spectra of rotation and the angular velocities as a function of the angular momentum. Besides, it led to a decrease in the moment of inertia after it was large in some models, such as in the Hartree-Fock-Bogoliubov (HFB) model. The rotational properties and the moments of inertia of the super-deformed bands of some deformed nuclei have been studied as well as in the mass regions A=190; A=160. The results were compared with experimental results which gave good agreement. This work will offer an interesting perspective necessary for certain improvements or extensions of the Cr.HF. Keywords: Microscopic mean field, Collective nuclear rotation, Angular momentum Routhian Hartree-Fock (RHF) model, Inertia moments, Angular velocity.

Measurement and Modeling of Magnetic Materials under 3D Vectorial Magnetization for Electrical Machine Design and Analysis

The magnetic properties of magnetic cores are essential for the design of electrical machines, and consequently appropriate mathematical modeling is needed. Usually, the design and analysis of electrical machines consider only the one-dimensional (1D) magnetic properties of core materials, i.e., the relationship of magnetic flux density (B) versus magnetic field strength (H), and their associated power loss under 1D magnetization, in which the B and H are constrained in the same orientation. Some studies have also been performed with the two-dimensional (2D) magnetizations in which the B and H are vectorial, rotating on a plane, and they may not be in the same direction. It has been discovered that the 2D rotational property is very different from its 1D alternating counterpart. However, the magnetic fields in an electrical machine, in particular claw pole and transverse flux machines, are naturally three-dimensional (3D), and the B and H vectors are rotational and may not lie on the same plane. It can be expected that the 3D vectorial property might be different from its 2D or 1D counterpart, and hence it should be investigated for the interests of both academic research and engineering application. This paper targets at a general summary about the magnetic material characterization with 3D vectorial magnetization, and their application prospect in electrical machine design and analysis.

Optical scheme of developing Hamming code-based error detection and correction using Toffoli gates with frequency encoded data

Bit-error detection and correction is a very important part of a data communication network. In this article, we propose an optical approach to designing an error detection and correction circuit using Hamming code-based frequency encoded binary data and Toffoli gates. Here, the Toffoli gates are made of semiconductor optical amplifiers (SOAs) that work based on the nonlinear polarization rotation property. The characteristics of SOA, including very fast switching action (about 0.01 ns), low power consumption, frequency independent cross-polarization gain in the C-band, cascading property, etc., make the scheme attractive. The frequency encoded data-based proposed scheme will be effective for WDM communication networks. MATLAB simulation results testify to the feasibility of the proposed scheme.

Investigation of the high-spin yrast band structure of Pu236–246 isotopes

The available data on some actinide nuclei point to certain significant features of the rotational yrast band and other excited bands. The rotational properties of plutonium isotopes ($^{236--346}\mathrm{Pu}$) were studied via projected shell model (PSM). Calculations are based on the Hamiltonian of the PSM which includes the formed part of a single particle, the $Q\ensuremath{-}Q$ force, and the residual interaction of monopole and quadrupole pairings. The results of the calculated energy levels of the yrast band are then compared with available experimental data and a good agreement has been found. The crossing between two-quasiparticle (2qp) excited bands and the ground state band (g band) in the high-spin regions has been analyzed in terms of band diagrams. The upbendings observed in the kinematic moments of inertia (${j}^{(1)}$ MOI) curves for $^{236--346}\mathrm{Pu}$ isotopes are due to the effect of two aligning nucleons that occupy excited bands and the $\ensuremath{\nu}({j}_{15/2}$), $\ensuremath{\pi}({i}_{13/2}$) high-$j$ intruder orbits. The PSM successfully reproduces the observed upbending in ${j}^{(1)}$ as well as the upturning and downturning in ${j}^{(2)}$. For the $^{240}\mathrm{Pu}$ isotope, the PSM predicts a simultaneous alignment of neutrons ${\ensuremath{\nu}}^{2} [1/2,\ensuremath{-}7/2] {K}^{\ensuremath{\pi}}$ = ${4}^{+}$ and protons ${\ensuremath{\pi}}^{2} [\ensuremath{-}3/2,5/2] {K}^{\ensuremath{\pi}}$ = ${1}^{+}$ bands cross the g band at spin $I=22$. We expect it to be mainly responsible for the disagreement at $I=22$. Furthermore, electric quadrupole transition probabilities $B(E2)$ and the gyromagnetic factor ($g$ factor) for the yrast band energy levels are also studied.

The crater-induced YORP effect

Context. The Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect plays an important role in the rotational properties and evolution of asteroids. While the YORP effect induced by the macroscopic shape of the asteroid and by the presence of surface boulders has been well studied, no investigation has been performed yet regarding how craters with given properties influence this effect. Aims. We introduce and estimate the crater-induced YORP effect (CYORP), which arises from the concave structure of the crater, to investigate the magnitude of the resulting torques as a function of varying properties of the crater and the asteroid by a semi-analytical method. Methods. By using a simple spherical shape model of the crater and assuming zero thermal inertia, we calculated the total YORP torque due to the crater, which was averaged over the spin and orbital motions of the asteroid, accounting for self-sheltering and self-sheltering effects. Results. The general form of the CYORP torque can be expressed in terms of the crater radius R0 and the asteroid radius Rast: 〈TCYORP〉 ~ WR02RastΦ/c, where W is an efficiency factor. We find that the typical values of W are about 0.04 and 0.025 for the spin and obliquity component, respectively, which indicates that the CYORP can be comparable to the normal YORP torque when the size of the crater is about one-tenth of the size of the asteroid, or equivalently when the crater/roughness covers one-tenth of the asteroid surface. Although the torque decreases with the crater size R0 as ~R02, the combined contribution of all small craters can become non-negligible due to their large number when the commonly used power-law crater size distribution is considered. The CYORP torque of small concave structures, usually considered as surface roughness, is essential to the accurate calculation of the complete YORP torque. Under the CYORP effect that is produced by collisions, asteroids go through a random walk in spin rate and obliquity, with a YORP reset timescale typically of 0.4 Myr. This has strong implications for the rotational evolution and orbital evolution of asteroids. Conclusions. Craters and roughness on asteroid surfaces, which correspond to concave structures, can influence the YORP torques and therefore the rotational properties and evolution of asteroids. We suggest that the CYORP effect should be considered in the future investigation of the YORP effect on asteroids.

The VLT-FLAMES Tarantula Survey

Context. The origin of massive runaway stars is an important unsolved problem in astrophysics. Two main scenarios have been proposed, namely: dynamical ejection or release from a binary at the first core collapse. However, their relative contribution remains heavily debated. Aims. Taking advantage of two large spectroscopic campaigns towards massive stars in 30 Doradus, we aim to provide observational constraints on the properties of the O-type runaway population in the most massive active star-forming region in the Local Group. Methods. We used radial velocity measurements of the O-type star populations in 30 Doradus obtained by the VLT-FLAMES Tarantula Survey and the Tarantula Massive Binary Monitoring to identify single and binary O-type runaways. Here, we discuss the rotational properties of the detected runaways and qualitatively compare the observations with expectations of ejection scenarios. Results. We identified 23 single and one binary O-type runaway objects, most of them located outside the main star-forming regions in 30 Doradus. We find an overabundance of rapid rotators (ve sin i > 200 km s−1) among the runaway population, thus providing an explanation for the observed overabundance of rapidly rotating stars in the 30 Doradus field. Considerations of the projected rotation rates and runaway line-of-sight velocities reveal a conspicuous absence of rapidly rotating (ve sin i > 210 km s−1), fast-moving (vlos > 60 km s−1) runaway stars in our sample, strongly suggesting the presence of two different populations of runaway stars: a population of rapidly spinning but slowly moving runaway stars and a population of fast-moving but slowly rotating ones. These are detected with a ratio close to 2:1 in our sample. Conclusions. We argue that slowly moving but rapidly spinning runaway stars result from binary ejections, while rapidly moving but slowly spinning runaways could result from dynamical ejections. Given that detection biases will more strongly impact the slow-moving runaway population, our results suggest that the binary evolution scenario dominates the current massive runaway star population in 30 Doradus.

Existence of a periodic solution for superlinear second order ODEs

We prove a necessary and sufficient condition for the existence of a T-periodic solution for the time-periodic second order differential equation x¨+f(t,x)+p(t,x,x˙)=0, where f grows superlinearly in x uniformly in time, while p is bounded. Our method is based on a fixed-point theorem which uses the rotational properties of the dynamics.