Angular Excitations Research Articles

Monocular Vision-Based Multiparameter Dynamic Calibration Method Used for the Low-Frequency Linear and Angular Vibration Sensors

The low-frequency linear and angular vibration sensors have been gradually used in many applications of vibration monitoring because they can measure dynamic displacement and angle. These sensors must be calibrated before they are used and after they have been used for a period to ensure their measurement accuracy. Currently, the laser interferometry (LI) and sensor-based comparison method are commonly used to calibrate their sensitivities. However, the former suffers inevitably drawbacks in low- frequency range, while the latter usually has only a limited range, these undoubtedly limit their wide application. In this study, a new monocular vision-based multi-parameter calibration method is investigated, which can determine the sensitivities of these sensors in a broad low-frequency range. The monocular vision method with improved line segment detector (LSD) is applied to measure the linear and angular vibration excitations by extracting the motion feature edges with sub-pixel accuracy. This investigated method strongly promotes the perfection and unification of linear and angular vibration calibration. Many comparison experiments with the LI, the Earth's graviation (EG) method, and the circular grating (CG)-based method confirm that the investigated method gets the satisfactory accuracies in the linear and angular vibration calibration with an efficient, flexible, and low-cost system in the low-frequency range.

Influence of surface grooving methods on steady and dynamic performance of spiral groove gas face seals

In this paper, a structural form called double-sided spiral groove gas face seal is considered. Steady-state performances, such as film load-carrying capacity and film stiffness, of gas face seals with single-sided groove on the stator, single-sided groove on the rotor, and double-sided groove are compared. Introducing axial and angular excitations, coupled with gas lubrication, seal rings vibration, contact mechanics, and instantaneous changes in fluid film thickness, the complete dynamic behavior history is obtained. Two dynamic performance indicators, logarithmic decrement and period valley, are defined. The effects of groove depths and equilibrium film thickness on the dynamic performance of gas face seals with three different surface grooving methods are studied. Combined with the transient sealing performance and film dynamic coefficients, the mechanisms of several typical unstable conditions are analyzed. The results show that the double-sided grooving method has both high gas film load-carrying capacity and gas film stiffness when the equilibrium film thickness is relatively large. In addition, double-sided grooving has both advantages of high gas film damping of single-sided grooving on the stator and high gas film stiffness of single-sided grooving on the rotor, which can ensure stable operation under various operation conditions.

Roton Excitations in an Oblate Dipolar Quantum Gas.

We observe signatures of radial and angular roton excitations around a droplet crystallization transition in dipolar Bose-Einstein condensates. In situ measurements are used to characterize the density fluctuations near this transition. The static structure factor is extracted and used to identify the radial and angular roton excitations by their characteristic symmetries. These fluctuations peak as a function of the interaction strength indicating the crystallization transition of the system. We compare our observations to a theoretically calculated excitation spectrum allowing us to connect the crystallization mechanism with the softening of the angular roton modes.

Lightest flavor-singlet qqq baryons as witnesses to color

We present a new computation in a field-theoretical model of Coulomb gauge QCD of the first radial and angular excitations of a qqq system in a SU(3) flavor singlet state, Lambda_S. The traditional motivation for the study is that the absence of flavor singlets in the lowest-lying spectrum is a direct consequence of the color degree of freedom. (The calculation is tested with decuplet baryons Delta(1232) and Omega(1672).) We also analyze decay branching fractions of the flavor singlet baryon for various masses with the simplest effective Lagrangians.

Normal modes for [formula omitted] identical particles: A study of the evolution of collective behavior from few-body to many-body

Normal mode dynamics are ubiquitous in nature underlying the motions of diverse interacting systems from the behavior of rotating stars to the vibration of crystal structures. These behaviors are composed of simple collective motions of the N interacting particles which move with the same frequency and phase, thus encapsulating many-body effects into simple dynamic motions. In this study, I investigate the evolution of collective motion as a function of N for five types of normal modes previously obtained from an L=0 group theoretic solution of a general Hamiltonian for confined, identical particles. I show using simple analytic forms for the N-body normal modes that the collective behavior of few-body systems, which have the well known motions of molecular equivalents such as ammonia and methane, evolves smoothly as N increases to the collective motions expected for large N ensembles (breathing, center of mass, particle–hole radial and angular excitations and phonon). Furthermore, the transition from few-body behavior (symmetric stretch, symmetric bend, asymmetric stretch, asymmetric bend and the opening and closing of alternative interparticle angles) to large N behavior occurs at quite low values of N. I extend this investigation to a Hamiltonian known to support collective behavior, the Hamiltonian for Fermi gases in the unitary regime. This analysis reveals two phenomena that could contribute to the viability of collective behavior. With the recent success using normal modes to describe the emergence of collective behavior in the form of superfluidity in ultracold Fermi gases in the unitary regime, understanding the character of these normal modes and the evolution of their behavior as a function of N has become of some interest due to the possibility of offering insight into the dynamics of regimes supporting collective behavior. In this study, I investigate both the macroscopic behavior associated with these N-body normal modes, as well as the microscopic motions underlying this behavior, and study the evolution of their collective behavior as a function of N.

Two-dimensional orbital Hall insulators

The orbital-Hall effect (OHE), similarly to the spin-Hall effect (SHE), refers to the creation of a transverse flow of orbital angular momentum that is induced by a longitudinally applied electric field. For systems in which the spin-orbit coupling (SOC) is sizeable, the orbital and spin angular momentum degrees of freedom are coupled, and an interrelationship between charge, spin and orbital angular momentum excitations is naturally established. The OHE has been explored mostly in metallic systems, where it can be quite strong. However, several of its features remain unexplored in two-dimensional (2D) materials. Here, we investigate the role of orbital textures for the OHE displayed by multi-orbital 2D materials. We predict the appearance of a rather large orbital Hall effect in these systems both in their metallic and insulating phases. In some cases, the orbital Hall currents are larger than the spin Hall ones, and their use as information carriers widens the development possibilities of novel spin-orbitronic devices.

Higher hybrid bottomonia in an extended potential model

Using our extension of the quark potential model to hybrid mesons that fits well with the available lattice results, we now calculate the masses, radii, wave functions at the origin, leptonic and two-photon decay widths, and $E1$ and $M1$ radiative transitions for a significant number of bottomonium mesons. These mesons include both conventional and hybrid ones with radial and angular excitations. Our numerical solutions of the Schr\"odinger equation are related to QCD through the Born-Oppenheimer approach. Relativistic corrections in masses and decay widths are also calculated by applying the leading-order perturbation theory. The calculated results are compared with available experimental data and the theoretical results by other groups. We also identify the states of $\mathrm{\ensuremath{\Upsilon}}(10860)$, $\mathrm{\ensuremath{\Upsilon}}(11020)$, and ${Y}_{b}(10890)$ mesons by comparing their experimental masses and decay widths to our results.

Mapping chiral symmetry breaking in the excited baryon spectrum

We study the conjectured "Insensitivity to Chiral Symmetry Breaking" in the highly excited light baryon spectrum. While the experimental spectrum is being measured at JLab and CBELSA/TAPS, this insensitivity remains to be computed theoretically in detail. As the only existing option to have both confinement, highly excited states and chiral symmetry, we adopt the truncated Coulomb gauge formulation of QCD, considering a linearly confining Coulomb term. Adopting a systematic and numerically intensive variational treatment up to 12 harmonic oscillator shells we are able to access several angular and radial excitations. We compute both the excited spectra of $I=1/2$ and $I=3/2$ baryons, up to large spin $J=13/2$, and study in detail the proposed chiral multiplets. While the static-light and light-light spectra clearly show chiral symmetry restoration high in the spectrum, the realization of chiral symmetry is more complicated in the baryon spectrum than earlier expected.

The collinear helium atom: adiabatic potential curves and quasi-separable approximation in hyperspherical coordinates

The collinear models of the helium atom, where the electrons reside on the opposite sides of the nucleus (eZe configuration) and on the same side (Zee configuration), are studied using the adiabatic approach in hyperspherical coordinates. Adiabatic potential curves are evaluated for both configurations and related to hyperspherical channels. The eigenenergies are calculated by applying the quasi-separable (single-channel) approximation and found to be in good agreement with those obtained using other methods. It is demonstrated that the widths of autoionizing states can be estimated by taking into account the coupling between different channels. The adiabatic potential curves and energy levels for the collinear atom are compared to those for the full three-dimensional (3D) model. It is shown that the S states of the 3D model with minimal and maximal angular excitations, as well as the corresponding adiabatic potential curves at large values of the hyperradius, can be related to the eZe and Zee collinear configurations, respectively. It is demonstrated that a set of curves of the 3D atom converging to the same ionization threshold is then confined in the area delimited by the pair of eZe/Zee curves also converging to this threshold. A class of anticrossings of the adiabatic potential curves in the 3D model, located along the eZe adiabatic curves at small values of the hyperradius, is observed and related to the unstable character of the classical configuration corresponding to the eZe collinear model in this domain.

Dynamics of a Bose–Einstein condensate in a symmetric triple-well trap

We present a complete analysis of the dynamics of a Bose–Einstein condensate trapped in a symmetric triple-well potential. Our classical analogue treatment, based on a time-dependent variational method using SU(3) coherent states, includes the parameter dependence analysis of the equilibrium points and their local stability, which is closely related to the condensate collective behaviour. We also consider the effects of off-site interactions, and how these ‘cross-collisions’ may become relevant for a large number of trapped bosons. Even in the presence of cross-collisional terms, the model still features an integrable sub-regime, known as the twin-condensate dynamics, which corresponds to invariant surfaces in the classical phase space. However, the quantum dynamics preserves the twin-condensate defining characteristics only partially, thus breaking the invariance of the associated quantum subspace. Moreover, the periodic geometry of the trapping potential allowed us to investigate the dynamics of finite angular momentum collective excitations, which can be suppressed by the emergence of chaos. Finally, using the generalized purity associated with the su(3) algebra, we were able to quantify the dynamical classicality of a quantum evolved system, as compared to the corresponding classical trajectory.

Position Error Predictions of a Hard Disk Drive Undergoing a Large Seeking Motion With Shock Excitations

In this paper, we present numerical simulations to predict position errors of a hard disk drive (HDD) undergoing a long seeking-and-settling process while experiencing a shock excitation. The HDD model for simulations consists of a rotating spindle motor carrying multiple disks, a stationary base with a top cover, and a swinging head-stack assembly (HSA). The rotating part, stationary part, and swinging HSA are connected to one another via fluid-dynamic bearings, pivot bearings, and air bearings. The seeking-and-settling process consists of four segments: acceleration, coasting, deceleration, and settling. A 2-ms shock excitation is applied to each segment of the seeking-and-settling process, respectively, to evaluate severity of the shock excitations to position errors. Both linear and angular shock excitations are considered. Simulation results lead to the following significant conclusions. First, shock excitations generally result in two types of response: spindle vibration [e.g., half-speed whirls or (0,1) unbalanced modes in the form of rocking] and HSA vibration (e.g., torsional vibration of the voice coil or bending of the suspension arms). Moreover, spindle vibration response usually appears with large amplitude (per unit g) but damps out quickly due to its large damping. In contrast, HSA response usually appears with small amplitude (per unit g) but decays slowly due to its small damping. As a result, shock excitations applied near the beginning of the seeking-and-settling process are less detrimental because the larger spindle response has enough time to damp out before the heads settle on the desired tracks. In contrast, shock excitations applied to the end of the seeking-and-settling process tend to present large spindle response leading to significant position errors. In this case, the ability to rapidly reduce the position errors relies on performance and properties of the fluid-dynamic spindle motor.

Mass spectra and Regge trajectories of light mesons in the relativistic quark model

Masses of the ground state and the orbitally and radially excited states of quark-antiquark mesons composed of light $(u,d,s)$ quarks are calculated within the framework of the relativistic quark model based on the quasipotential approach. The relativistic treatment of the light quark dynamics results in mass spectra which agree well with available experimental data for the masses of the most well-established states. The Regge trajectories for angular and radial excitations are constructed, and their linearity, parallelism, and equidistance are verified. The assignment of experimentally observed light mesons to particular Regge trajectories is based on their masses and quantum numbers.

Angularly excited and interacting boson stars andQballs

We study angularly excited as well as interacting nontopological solitons, the so-called $Q$ balls, and their gravitating counterparts, the so-called boson stars, in $3+1$ dimensions. $Q$ balls and boson stars carry a nonvanishing Noether charge and arise as solutions of complex scalar field models in a flat space-time background and coupled minimally to gravity, respectively. We present examples of interacting $Q$ balls that arise due to angular excitations, which are closely related to the spherical harmonics. We also construct explicit examples of rotating boson stars that interact with nonrotating boson stars. We observe that rotating boson stars tend to absorb the nonrotating ones for increasing, but reasonably small gravitational coupling. This is a new phenomenon as compared to the flat space-time limit and is related to the negative contribution of the rotation term to the energy density of the solutions. In addition, our results indicate that a system of a rotating and nonrotating boson star can become unstable if the direct interaction term in the potential is large enough. This instability is related to the appearance of ergoregions.

Interacting Q-balls

We study non-topological solitons, so-called Q-balls, which carry a non-vanishing Noether charge and arise as lump solutions of self-interacting complex scalar field models. Explicit examples of new axially symmetric non-spinning Q-ball solutions that have not been studied so far are constructed numerically. These solutions can be interpreted as angular excitations of the fundamental Q-balls and are related to the spherical harmonics. Correspondingly, they have higher energy and their energy densities possess two local maxima on the positive z-axis.We also study two Q-balls interacting via a potential term in 3 + 1 dimensions and construct examples of stationary, solitonic-like objects in (3 + 1)-dimensional flat space–time that consist of two interacting global scalar fields. We concentrate on configurations composed of one spinning and one non-spinning Q-ball and study the parameter-dependence of the energy and charges of the configuration.In addition, we present numerical evidence that for fixed values of the coupling constants two different types of 2-Q-ball solutions exist: solutions with defined parity, but also solutions that are asymmetric with respect to reflection through the x–y plane.

Excitation levels and magic numbers of small parahydrogen clusters (N⩽40)

The excitation energies of parahydrogen clusters have been systematically calculated by the diffusion Monte Carlo technique in steps of 1molecule from 3to40molecules. These clusters possess a very rich spectra, with angular momentum excitations arriving up to L=13 for the heavier ones. No regular pattern can be guessed in terms of the angular momenta and the size of the cluster. Clusters with N=13 and 36 are characterized by a peak in the chemical potential and a large energy gap of the first excited level, which indicate the magical character of these clusters. From the calculated excitation energies, the partition function has been obtained, thus allowing for an estimate of thermal effects. An enhanced production is predicted for cluster sizes of N=13, 31, and 36, which is in agreement with the experiment.

Large degeneracy of excited hadrons and quark models

The pattern of a large approximate degeneracy of the excited hadron spectra (larger than the chiral restoration degeneracy) is present in the recent experimental report of Bugg. Here we try to model this degeneracy with state of the art quark models. We review how the Coulomb Gauge chiral invariant and confining Bethe-Salpeter equation simplifies in the case of very excited quark-antiquark mesons, including angular or radial excitations, to a Salpeter equation with an ultrarelativistic kinetic energy with the spin-independent part of the potential. The resulting meson spectrum is solved, and the excited chiral restoration is recovered, for all mesons with $J>0$. Applying the ultrarelativistic simplification to a linear equal-time potential, linear Regge trajectories are obtained, for both angular and radial excitations. The spectrum is also compared with the semiclassical Bohr-Sommerfeld quantization relation. However, the excited angular and radial spectra do not coincide exactly. We then search, with the classical Bertrand theorem, for central potentials producing always classical closed orbits with the ultrarelativistic kinetic energy. We find that no such potential exists, and this implies that no exact larger degeneracy can be obtained in our equal-time framework, with a single principal quantum number comparable to the nonrelativistic Coulomb or harmonic oscillator potentials. Nevertheless we find it plausible that the large experimental approximate degeneracy will be modeled in the future by quark models beyond the present state of the art.

Advances in light-front quantization and new perspectives for QCD from AdS/CFT

The light-front quantization of gauge theories in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a Fock space built on a trivial vacuum. The AdS/CFT correspondence has led to important insights into the properties of quantum chromodynamics even though QCD is a broken conformal theory. We have recently shown how a model based on a truncated AdS space can be used to obtain the hadronic spectrum of q q ¯ , qqq and gg bound states, as well as their respective light-front wavefunctions. Specific hadrons are identified by the correspondence of string modes with the dimension of the interpolating operator of the hadron's valence Fock state, including orbital angular momentum excitations. The predicted mass spectrum is linear M ∝ L at high orbital angular momentum, in contrast to the quadratic dependence M 2 ∝ L found in the description of spinning strings. Since only one parameter, the QCD scale Λ Q C D , is introduced, the agreement with the pattern of physical states is remarkable. In particular, the ratio of Δ to nucleon trajectories is determined by the ratio of zeros of Bessel functions. As a specific application of QCD dynamics from AdS/CFT duality, we describe a computation of the proton magnetic form factor in both the space-like and time-like regions. The extended AdS/CFT space-time theory also provides an analytic model for hadronic light-front wavefunctions, thus providing a relativistic description of hadrons in QCD at the amplitude level. The model wavefunctions display confinement at large inter-quark separation and conformal symmetry at short distances. In particular, the scaling and conformal properties of the LFWFs at high relative momenta agree with perturbative QCD. These AdS/CFT model wavefunctions could be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian.

Vibration of rotating disk/spindle systems with flexible housing/stator assemblies

The subject of study in this paper is a rotating spindle carrying multiple flexible disks mounted on a flexible housing/stator assembly through ball bearings or hydrodynamic bearings. The disk/spindle system is subjected to prescribed force excitations, and the housing/stator assembly is subjected to prescribed linear and angular base excitations. This paper has two specific goals. The first goal is to derive linearized equations of motion governing free and forced vibration of the spindle/housing system using a Lagrangian formulation. The second goal is to verify the mathematical model through calibrated experiments. Theoretical predictions of natural frequencies agree well with experimental measurements within 5% of difference for spindle motors using ball bearings. Numerical simulations on spindle motors with hydrodynamic bearings indicate that base flexibility could lead to significant spindle vibration.

Analysis of dynamical corrections to baryon magnetic moments

We present and analyze QCD corrections to the baryon magnetic moments in terms of the one-, two-, and three-body operators which appear in the effective field theory developed in our recent papers. The main corrections are extended Thomas-type corrections associated with the confining interactions in the baryon. We investigate the contributions of low-lying angular excitations to the moments quantitatively and show that they are completely negligible. When the QCD corrections are combined with the non-quark model contributions of the meson loops, we obtain a model which describes the moments within a mean deviation of 0.04 $\mu_N$. The nontrivial interplay of the two types of corrections to the quark-model moments is analyzed in detail, and explains why the quark model is so successful. In the course of these calculations, we parametrize the general spin structure of the $j={1/2}^+$ baryon wave functions in a form which clearly displays the symmetry properties and the internal angular momentum content of the wave functions, and allows us to use spin-trace methods to calculate the many spin matrix elements which appear in the expressions for the moments. This representation may be useful elsewhere.

Mass formula for baryon resonances

Light-baryon resonances with u,d, and s quarks only can be classified using the non-relativistic quark model. When we assign to baryon resonances with total angular momenta J intrinsic orbital angular momenta L and spin S we make the following observations: plotting the squared masses of the light-baryon resonances against these intrinsic orbital angular momenta L, Delta's with even and odd parity can be described by the same Regge trajectory. For a given L, nucleon resonances with spin S=3/2 are approximately degenerate in mass with Delta resonances of same total orbital momentum L. To which total angular momentum L and S couple has no significant impact on the baryon mass. Nucleons with spin 1/2 are shifted in mass; the shift is - in units of squared masses - proportional to the component in the wave function which is antisymmetric in spin and flavor. Sequential resonances in the same partial wave are separated in mass square by the same spacing as observed in orbital angular momentum excitations. Based on these observations, a new baryon mass formula is proposed which reproduces nearly all known baryon masses.