Search Results (48)

The stable rotation of young pulsars is often interrupted by two non-deterministic phenomena: glitches and red timing noise. Timing noise provides insights into plasma and nuclear physics under extreme conditions. The framework leverages rotational symmetry in pulsar spin-down models and temporal symmetry in noise processes to achieve computational efficiency, aligning with the journal’s focus on symmetry principles in physical systems. In this paper, we apply a novel frequentist framework developed within the PINT software package (v0.9.8) to analyze single-pulsar noise processes. Using 17.5 years of pulse time-of-arrival (TOA) data for the young pulsar PSR J1741—3016, observed with the Nanshan 26 m radio telescope, we investigate its timing properties. In this study, we employed the Downhill Weighted Least-Squares Fitter to estimate the pulsar’s spin parameters and position. The Akaike Information Criterion (AIC) was used for model parameter selection. The results obtained with PINT were compared to those from ENTERPRISE and TEMPONEST, two Bayesian-based frameworks. We demonstrate that PINT achieves comparable results with significantly reduced computational costs. Additionally, the adequacy of the noise model can be readily verified through visual inspection tools. Future research will utilize this framework to analyze timing noise across a large sample of young pulsars. Full article

The aim of this work is to demonstrate that all linear derivatives of the tensor algebra over a smooth manifold M can be viewed as specific cases of a broader concept—the operation of derivation. This approach reveals the universal role of differentiation, which simplifies and generalizes the study of tensor derivatives, making it a powerful tool in Differential Geometry and related fields. To perform this, the generic derivative is introduced, which is defined in terms of the quantities $Q_k^{\left(i\right)}\left(X\right)$. Subsequently, the transformation law of these quantities is determined by the requirement that the generic derivative of a tensor is a tensor. The quantities $Q_k^{\left(i\right)}\left(X\right)$ and their transformation law define a specific geometric object on M, and consequently, a geometric structure on M. Using the generic derivative, one defines the tensor fields of torsion and curvature and computes them for all linear derivatives in terms of the quantities $Q_k^{\left(i\right)}\left(X\right)$. The general model is applied to the cases of Lie derivative, covariant derivative, and Fermi derivative. It is shown that the Lie derivative has non-zero torsion and zero curvature due to the Jacobi identity. For the covariant derivative, the standard results follow without any further calculations. Concerning the Fermi derivative, this is defined in a new way, i.e., as a higher-order derivative defined in terms of two derivatives: a given derivative and the Lie derivative. Being linear derivative, it has torsion and curvature tensor. These fields are computed in a general affine space from the corresponding general expressions of the generic derivative. Applications of the above considerations are discussed in a number of cases. Concerning the Lie derivative, it is been shown that the Poisson bracket is in fact a Lie derivative. Concerning the Fermi derivative, two applications are considered: (a) the explicit computation of the Fermi derivative in a general affine space and (b) the consideration of Freedman–Robertson–Walker spacetime endowed with a scalar torsion field, which satisfies the Cosmological Principle and the computation of Fermi derivative of the spatial directions defining a spatial frame along the cosmological fluid of comoving observers. It is found that torsion, even in this highly symmetric case, induces a kinematic rotation of the space axes, questioning the interpretation of torsion as a spin. Finally it is shown that the Lie derivative of the dynamical equations of an autonomous conservative dynamical system is equivalent to the standard Lie symmetry method. Full article

Spin Hamiltonians, like the Heisenberg model, are used to describe the magnetic properties of exchange-coupled molecules and solids. For finite clusters, physical quantities, such as heat capacities, magnetic susceptibilities or neutron-scattering spectra, can be calculated based on energies and eigenstates obtained by exact diagonalization (ED). Utilizing spin-rotational symmetry SU(2) to factor the Hamiltonian with respect to total spin S facilitates ED, but the conventional approach to spin-adapting the basis is more intricate than selecting states with a given magnetic quantum number M (the spin z-component), as it relies on irreducible tensor-operator techniques and spin-coupling coefficients. Here, we present a simpler technique based on applying a spin projector to uncoupled basis states. As an alternative to Löwdin’s projection operator, we consider a group-theoretical formulation of the projector, which can be evaluated either exactly or approximately using an integration grid. An important aspect is the choice of uncoupled basis states. We present an extension of Löwdin’s theorem for $s=\frac{1}{2}$ to arbitrary local spin quantum numbers s, which allows for the direct selection of configurations that span a complete, linearly independent basis in an S sector upon the spin projection. We illustrate the procedure with a few examples. Full article

In this review, the process of extracting precise values for NMR interaction tensors from single crystal samples is systematically explored. Starting with a description of the orientation dependence of the considered interactions, i.e., chemical shift, dipolar, and quadrupole interaction, the techniques for acquiring and analysing single-crystal spectra are outlined. This includes the ‘classical’ approach, which requires the acquisition of three rotation patterns around three rotation axes that are orthogonal to each other, as well as more recent strategies aimed at reducing the number of required NMR spectra. One such strategy is the ‘single-rotation method’, which exploits the symmetry relations between tensors in the crystal structure to reduce the necessary amount of orientation-dependent data. This concept may be extended to additionally include the orientation of the goniometer axis itself in the data fit, which may be termed the ‘minimal-rotation method’. Other, more exotic schemes, such as the use of specialised probe designs or the investigation of single crystals under magic-angle-spinning, are also briefly discussed. Actual values of NMR interaction tensors as determined from the various single-crystal methods have been collected and are provided in tables for spin $I=1/2$, $I=1$, and half-integer spins with $I>1/2$. Full article

Metasurfaces can flexibly manipulate electromagnetic waves by engineering subwavelength structures, which have attracted enormous attention in holography, cloaking, and functional multiplexing. For structures with n-fold (n > 2) rotational symmetry, they have been utilized to realize broadband and high-efficiency wavefront manipulation with generalized Pancharatnam–Berry phase, whereas spin-selective wavefront manipulation is still a challenge limited by their symmetrical spin–orbit interactions. Here, we demonstrate the spin-selective wavefront manipulations with generalized Pancharatnam–Berry phase in the range of 560–660 nm with a metal–insulator–metal metasurface consisting of the chiral C3 logarithmic spiral nanostructures. As a proof of concept, two deflectors and a bifocal metalens are designed. This configuration may provide a platform for various applications in polarimetry, polarization-selective images, and nonlinear optical responses. Full article

In this paper, the concept of symmetry is utilized in the promising trajectory planning design of autonomous ground vehicles—that is, the construction and the solution of improved artificial potential field-based trajectory planning approach are symmetrical. Despite existing artificial potential fields (APF) achievements on trajectory planning in autonomous ground vehicles (AGV), applying the traditional approach to dynamic traffic scenarios is inappropriate without considering vehicle dynamics environment and road regulations. This paper introduces a highly efficient approach for planning trajectories using improved artificial potential fields (IAPF) to handle dynamic road participants and address the issue of local minima in artificial potential fields. To begin with, potential fields are created with data obtained from other sensors. By incorporating rotational factors, the potential field will spin when the obstacle executes a maneuver; then, a safety distance model is also developed to limit the range of influence in order to minimize the computational burden. Furthermore, during the planning process, virtual forces using the gradient descent method are generated to direct the vehicle’s movement. During each timestep, the vehicle will assess whether it is likely to encounter a local minimum in the future. Once a local minimum is discovered, the method will create multiple temporary objectives to guide the vehicle toward the global minimum. Consequently, a trajectory that is both collision-free and feasible is planned. Traffic scenarios are carried out to validate the effectiveness of the proposed approach. The simulation results demonstrate that the improved artificial potential field approach is capable of generating a secure trajectory with both comfort and stability. Full article

Binary droplet collision is a basic fluid phenomenon for many spray processes in nature and industry involving lots of discrete droplets. It exists an inherent mirror symmetry between two colliding droplets. For specific cases of the collision between two identical droplets, the head-on collision and the off-center collision, respectively, show the axisymmetric and rotational symmetry characteristics, which is useful for the simplification of droplet collision modeling. However, for more general cases of the collision between two droplets involving the disparities of size ratio, surface tension, viscosity, and self-spin motions, the axisymmetric and rotational symmetry droplet deformation and inner flow tend to be broken, leading to many distinct phenomena that cannot occur for the collision between two identical droplets owing to the mirror symmetry. This review focused on interpreting the asymmetric droplet deformation and the collision-induced internal mixing that was affected by those symmetry breaking factors, such as size ratio effects, Marangoni Effects, non-Newtonian effects, and droplet self-spin motion. It helps to understand the droplet internal mixing for hypergolic propellants in the rocket engineering and microscale droplet reactors in the biological engineering, and the modeling of droplet collision in real combustion spray processes. Full article

Bulk ideal flows constitute a wide class of solutions in plasticity theory. Ideal flow solutions concern inverse problems. In particular, the solution determines part of the boundary of a region where it is valid. Bulk planar ideal flows exist in the case of (i) isotropic rigid/plastic material obeying an arbitrary pressure-independent yield criterion and its associated flow rule and (ii) the double sliding and rotation model based on the Mohr–Coulomb yield criterion. In the latter case, the intrinsic spin must vanish. Both models are perfectly plastic, and the complete equation systems are hyperbolic. All available specific solutions for both models describe flows with a symmetry axis. The present paper aims at general solutions for flows with no symmetry axis. The general structure of the solutions consists of two rigid regions connected by a plastic region. The characteristic lines between the plastic and rigid regions must be straight, which partly dictates the general structure of the characteristic nets. The solutions employ Riemann’s method in regions where the characteristics of both families are curvilinear. Special solutions that do not have such regions are considered separately. In any case, the solutions are practically analytical. A numerical technique is only necessary to evaluate ordinary integrals. The solutions found determine the tool shapes that produce ideal flows. In addition, the distribution of pressure over the tool’s surface is calculated, which is important for predicting the wear of tools. Full article

In this paper, different aspects of the concept of spin are studied. The most well-established one is, of course, the quantum mechanical aspect: spin is a broken symmetry in the sense that the solutions of the Dirac equation tend to have directional properties that cannot be seen in the equation itself. It has been clear since the early days of quantum mechanics that this has something to do with the indefinite metric in Lorentz geometry, but the mechanism behind this connection is elusive. Although spin is not the same as rotation in the usual sense, there must certainly be a close relationship between these concepts. And, a possible way to investigate this connection is to instead start from the underlying geometry in general relativity. Is there a reason why rotating motion in Lorentz geometry should be more natural than non-rotating motion? In a certain sense, the answer turns out to be yes. But, it is by no means easy to see what this should correspond to in the usual quantum mechanical picture. On the other hand, it seems very unlikely that the similarities should be just coincidental. The interpretation of the author is that this can be a golden opportunity to investigate the interplay between these two theories. Full article

An optical interference test rig with spinning elastohydrodynamic lubrication (EHL) was established to investigate the spinning lubrication performance under different oil-supply conditions. Variations in the shape and thickness of the film versus the velocity, the load, and the spinning factor under fully flooded lubrication were discussed, and the effects of the inlet-starvation position and oil-supply quantity were analyzed. The results show that the symmetry for the classical horseshoe shape does not exist under both spinning–rolling and spinning–sliding EHL conditions. Different from spinning–rolling, a dimple is generated more easily under the spinning–sliding condition. The dimple is related to the load and the speed. The effects of the inlet-starvation position on spinning EHL are different. When the inlet starvation is on the low-speed side of the contact, that is, proximal to the center of rotation, the inlet-starvation position extends from the proximal side to the center of rotation to the distal side to the center of rotation, i.e., the high-speed side of the contact, which is starved easily. When the starvation happens on the high-speed side, i.e., distal to the center of rotation, the starvation at this position becomes much more severe, and lubrication failure and a risk of wear will occur. In addition, the effects of oil-supply quantity on spinning EHL are important. Full article

We study the sharp focusing of the input structured light field that has a non-uniform elliptical polarization: the parameters of the ellipse depend on the position in the input plane (we limited ourselves to the dependence only on the angular variable). Two types of non-uniformity were considered. The first type corresponds to the situation when the semi-axes of the polarization ellipse are fixed while the slope of the major semi-axis changes. The second type is determined by the situation when the slope of the major semi-axis of the polarization ellipse is constant, and the ratio between the semi-axis changes (we limited ourselves to the trigonometric dependence of this ratio on the polar angle). Theoretical and numerical calculations show that in the case of the first type of non-uniformity, if the tilt angle is a multiple of the polar angle with an integer coefficient, then the intensity distribution has rotational symmetry, and the energy flow is radially symmetric and has the negative direction near the optical axis. In this second case, the intensity symmetry is not very pronounced, but with an odd dependence of the ratio of the semi-axes of the polarization ellipse, the focused field at each point has a local linear polarization, despite the rather complex form of the input field. In addition, we investigate the distribution of the longitudinal component of the Poynting vector. The obtained results may be used for the formation of focused light fields with the desired distributions of polarization, Poynting vector density, or spin angular momentum density in the field of laser manipulation and laser matter interaction. Full article

A new effective dipole moment model for the XY₂ ($C_{2v}$−symmetry) molecule in a doublet electronic state is derived that includes (as special cases) all currently known models of effective dipole moments for such types of molecules, and allows us to take into account the influence of spin–rotation interactions on the effective dipole moment operator that were not considered in the preceding studies. Necessary for the analysis of absolute line strengths, the matrix elements of this dipole moment operator are derived. A comparison with the previous analog models is made and discussed. The efficiency of the obtained results is illustrated, which have been applied to a set of the “forbidden” $\Delta K_a=2$ transitions of the ${\nu }_3$ band of the OClO free radical molecule. Full article

Although electrons (fermions)and photons (bosons) produce the same interference patterns in the two-slit experiments, known in optics for photons since the 17th Century, the description of these patterns for electrons and photons thus far was markedly different. Photons are spin one, relativistic and massless particles while electrons are spin half massive particles producing the same interference patterns irrespective to their speed. Experiments with other massive particles demonstrate the same kind of interference patterns. In spite of these differences, in the early 1930s of the 20th Century, the isomorphism between the source-free Maxwell and Dirac equations was established. In this work, we were permitted replace the Born probabilistic interpretation of quantum mechanics with the optical. In 1925, Rainich combined source-free Maxwell equations with Einstein’s equations for gravity. His results were rediscovered in the late 1950s by Misner and Wheeler, who introduced the word "geometrodynamics” as a description of the unified field theory of gravity and electromagnetism. An absence of sources remained a problem in this unified theory until Ranada’s work of the late 1980s. However, his results required the existence of null electromagnetic fields. These were absent in Rainich–Misner–Wheeler’s geometrodynamics. They were added to it in the 1960s by Geroch. Ranada’s solutions of source-free Maxwell’s equations came out as knots and links. In this work, we establish that, due to their topology, these knots/links acquire masses and charges. They live on the Dupin cyclides—the invariants of Lie sphere geometry. Symmetries of Minkowski space-time also belong to this geometry. Using these symmetries, Varlamov recently demonstrated group-theoretically that the experimentally known mass spectrum for all mesons and baryons is obtainable with one formula, containing electron mass as an input. In this work, using some facts from polymer physics and differential geometry, a new proof of the knotty nature of the electron is established. The obtained result perfectly blends with the description of a rotating and charged black hole. Full article

We investigate the gap symmetry of the topological superconductor candidate HfRuP, which crystallizes in a noncentrosymmetric hexagonal crystal structure, using muon spin rotation/relaxation ($\mu$SR) measurements in transverse-field (TF) geometry. The temperature and magnetic field dependencies of the superconducting relaxation rate derived from the TF-$\mu$SR spectra can be well described by an isotropic s-wave gap. The superconducting carrier density $n_s$ = 1.41(1) × 10${}^{26}$ m${}^{-3}$ and the magnetic penetration depth, $\lambda$(0) = 603(2) nm, were calculated from the TF-$\mu$SR data. Interestingly, the ratio between the superconducting transition temperature and the superfluid density, $T_c$/$\lambda$${}^{-2}$(0) ∼ 3.3, is very close to those of unconventional superconductors. Further, our zero-field (ZF) $\mu$SR results do not show any considerable change in the muon spin relaxation above and below the superconducting transition temperature, suggesting that time-reversal symmetry is preserved in the superconducting state of this superconductor. Full article

The ability of bumblebee gravity models to explain dark energy, which is the phenomenon responsible for the universe’s observed accelerated expansion, is one of their most significant applications. An effect that causes faster expansion can be linked to how much the Lorentz symmetry of our universe is violated. Moreover, since we do not know what generates dark energy, the bumblebee gravity theory seems highly plausible. By utilizing the physical changes happening around a rotating bumblebee black hole (RBBH), we aim to obtain more specific details about the bumblebee black hole’s spacetime and our universe. However, as researched in the literature, slow-spinning RBBH (SRBBH) spacetime, which has a higher accuracy, will be considered instead of general RBBH. To this end, we first employ the Rindler–Ishak method (RIM), which enables us to study how light is bent in the vicinity of a gravitational lens. We evaluate the deflection angle of null geodesics in the equatorial plane of the SRBBH spacetime. Then, we use astrophysical data to see the effect of the Lorentz symmetry breaking (LSB) parameter on the bending angle of light for numerous astrophysical stars and black holes. We also acquire the analytical greybody factors (GFs) and quasinormal modes (QNMs) of the SRBBH. Finally, we visualize and discuss the results obtained in the conclusion section. Full article