Search

In the constrained Cosserat theory of a rod with a rigid cross-section, the balance of angular momentum is satisfied by a restriction on the constitutive equations that requires a second order tensor to be symmetric. The kinematics of the rod are determined by satisfying the balances of linear and director momentum and kinematic constraints. In contrast, the Antman model for a special Cosserat theory of rods proposes constitutive equations directly for the force and mechanical moment applied to the rod and the kinematics are determined by the balances of linear and angular momentum. These two models differ by their treatment of angular momentum. This note poses and answers the question: Are the solutions of these two models identical for the same strain energy? [ABSTRACT FROM AUTHOR]

To win a taekwondo competition, more points must be scored, and the key to scoring points is to improve the motor performance of the kick. However, the relationship between core stability and the effectiveness of athletic performance, particularly in executing the wing kick, remains ambiguous, impeding coaches and athletes in their efforts to improve athletic performance. A total of 26 male participants (height: 167.21 ± 7.29 cm; weight: 62.07 ± 8.03 kg; age: 24.69 ± 2.53 years) participated, and they have been practicing Taekwondo for more than 10 years. Kinematic and kinetic data were collected using 13 infrared cameras at 120 Hz, muscle activity data were collected using epidermal electromyography, and participants’ core stability level were measured using the Sahrmann Core Stability Test (SCST) for correlation with other variables. Core stability levels showed a strong negative correlation with execution time (r = −0.7144, p < 0.001) of the aerial phase of the wing kick as did angular momentum in most lower limb segments (thigh X axis, r = −0.6435, p < 0.001, shank X axis, r = −0.62008, p < 0.001, foot X axis, r = −0.7033, p < 0.001). Bilateral rectus abdominis (RA) showed strong correlations with muscle activation (left rectus abdominis (LRA) of left foot take off-left knee max extension (LTO-LKMF) phase, r = 0.5351, p < 0.001, right rectus abdominis (RRA) of LTO-LKMF phase, r = −0.5628, p < 0.001), and high levels of core stability were associated with better core-muscle coupling. We conclude that incorporating core stability training into taekwondo training has the potential to improve wing kick performance.

A novel physical effect has been found to be illuminated of being physically self-consistent to take into account in further calculating the dynamics of magnetically-induced asteroid rotation, surface of which has mostly a conducting structure (whereas such mostly metallic-formed asteroid is assumed to be moving in an external magnetic field of planet but in the meantime to be orbiting preferably outside its sphere of effective attraction). The last condition of asteroid surface's having conducting structure means the existence of the applied external torques stemming from the physical interactions between external magnetic field and iron asteroid itself (including long-term effect due to torques stemming from arising eddy-currents on metallic surface of asteroid). Such eddy-currents should heat the conducting surface of asteroid with further non-uniformly re-directing the heat flow from surface of asteroid into outer space via fluxes of thermal photons which carry momentum (in orthogonal direction to the surface which is in most cases far from the ideal surface of sphere). This leads by taking into account the overall outcome of heat flow (from the non-ideal surface of asteroid) to a kind of long-term magnetic second-grade YORP effect. System of Euler equations for aforementioned dynamics of asteroid magnetic rotation has been investigated in regard to existence of semi-analytical solution. Various perturbations (such as collisions, YORP effect) may destabilize the rotation of asteroid deviating it from the current spin state, whereas the electric(eddy)current-induced dissipation of energy reduces kinetic one of asteroid spin. So, dynamics of the asteroid rotation should result in a spinning about maximal-inertia axis with the proper spin state corresponding to minimal energy with a fixed angular momentum. • New physical effect is found for magnetically-induced metallic asteroid rotation. • Metallic-formed asteroid is assumed to be moving in an external magnetic field. • Conducting structure means torques stemming from an eddy-currents on its surface. • Overall outcome of non-iniform heat flow forms magnetic second-grade YORP effect. • Evolution of spin towards rotation about maximal-inertia axis is approximated. [ABSTRACT FROM AUTHOR]

The flywheel is a widespread mechanical component used for the storage of kinetic energy and angular momentum. It typically consists of cylindrical inertia rotating about its axis on rolling bearings, which involves undesired friction, lubrication, and wear. This paper presents an alternative mechanism that is functionally equivalent to a classical flywheel while relying exclusively on limited-stroke flexure joints. This novel one-degree-of-freedom zero-force mechanism has no wear and requires no lubrication: it is thus compatible with extreme environments, such as vacuum, cryogenics, or ionizing radiation. The mechanism is composed of two coupled pivoting rigid bodies whose individual angular momenta vary during motion but whose sum is constant at all times when the pivoting rate is constant. The quantitative comparison of the flexure-based flywheel to classical ones based on a hollow cylinder as inertia shows that the former typically stores 6 times less angular momentum and kinetic energy for the same mass while typically occupying 10 times more volume. The freedom of design of the shape of the rigid bodies offers the possibility of modifying the ratio of the stored kinetic energy versus angular momentum, which is not possible with classical flywheels. For example, a flexure-based flywheel with rigid pivoting bodies in the shape of thin discs stores 100 times more kinetic energy than a classical flywheel with the same angular momentum. A proof-of-concept prototype was successfully built and characterized in terms of reaction moment generation, which validates the presented analytical model. [ABSTRACT FROM AUTHOR]

While walking, ground reaction forces point from the centre of pressure to the neighbourhood of a focal point, namely the virtual pivot point (VPP), that adjusts angular momentum around the centre of mass (CoM). This study explores how age and speed affect the VPP quality and position during walking. Analysing an experimental dataset reveals high quality of the VPP in the sagittal plane for both young and elderly groups, regardless of speed. However, in the frontal plane, the VPP quality decreases with increasing speed, with elderly participants exhibiting significantly lower quality. Although not a direct measure of balance, VPP quality reflects changes in whole-body angular momentum owing to ageing and speed. Additionally, a template model is used to reproduce the VPP quality and position trends observed in the experiment. Simulation results highlight the sensitivity of VPP quality to leg force feedback and show that changing VPP height has minimal effect on gait speed. Furthermore, energy redistribution occurs through increased hip extension and leg damping, associated with a greater horizontal VPP distance from the CoM, observed in elderly walking. This study shows promise for analysing gait based on VPP, potentially aiding clinical interventions and supporting locomotion in the elderly.

Spin angular momentum (SAM) and Orbital angular momentum (OAM) are two distinct forms of electromagnetic angular momentum (AM). Generally, circularly-polarized (CP) wave is deemed as the typical form of spin wave, which carries SAM only. In this work, the OAM characteristic of spin wave is found after stating the CP wave into the cylindrical coordinate: the spin wave contains two components along r and ϕ directions, which carry both SAM and OAM. Based on the OAM character of spin wave, an electromagnetic waveform with SAM in the center and SAM-OAM beside is demonstrated. In addition, since spin wave carries OAM naturally, a spin–orbit coupling mechanism is performed, which demands no spin Pancharatnam–Berry phase nor any phase modulation structure. All the results have been experimentally verified. Our research can be utilized in the theoretical studies of rotational electromagnetic and may be potentially applied in metamaterial, information and quantum research areas.

Background In classical electrodynamics, light-matter interactions are modelled using Maxwell equations. The solution of Maxwell equations, which is typically given by means of the electric and magnetic field, is vectorial in nature. Yet it is well known that light-matter interactions can be approximately described in a scalar (polarization independent) way for many optical applications. While the accuracy of the scalar approximation can be theoretically computed, to the best of our knowledge, it has never been determined experimentally. Here, we introduce Vortex Circular Dichroism (VCD), an optical measurement that has the required features to assess the vectoriality of diffraction. Methods VCD is measured as the differential transmission (or absorption) of left and right circularly polarized vortex beams. We test the VCD measurement with two different systems: i) an experimental set of single circular nano-apertures drilled in a gold film with diameters ranging from 150 to 1950 nm; and ii) a theoretical set of golden spheres with the same diameters as the nano-apertures. Results We observe that in both systems, VCD > 0 for smaller diameters, VCD ≲ 0 for intermediate values and VCD ≈ 0 for larger values of the diameter. Furthermore, the simulations show that a diffraction process characterized by a VCD ≈ 0 (VCD ≠ 0) is polarization-independent (polarization-dependent). As a result, we relate VCD ≠ 0 to a vectorial diffraction, and VCD ≈ 0 to a scalar one. Conclusions Overall, our results show compelling evidence that it is possible to experimentally assess the scalar/vectorial regime of a diffraction process, and that the VCD technique possesses the required features to measure the vectoriality of diffraction processes involving plasmonic cylindrically symmetric structures.

The Jordan–Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator creation and annihilation operators acting in the Hilbert space of quantum oscillator states. Then, to describe quantum states in the probability representation of quantum oscillator states, we express their density operators in terms of conditional probability distributions (symplectic tomograms) or Husimi-like probability distributions. We illustrate this general scheme by examples of qubit states (spin-1/2 s u (2) -group states) and even and odd Schrödinger cat states related to the other representation of s u (2) -algebra (spin-j representation). The two-mode coherent-state superpositions associated with cyclic groups are studied, using the Jordan–Schwinger map. This map allows us to visualize and compare different properties of the mentioned states. For this, the s u (2) coherent states for different angular momenta j are used to define a Husimi-like Q representation. Some properties of these states are explicitly presented for the cyclic groups C 2 and C 3 . Also, their use in quantum information and computing is mentioned. [ABSTRACT FROM AUTHOR]

Since the 1970s, astronomers have struggled with the issue of how matter can be accreted to promote black-hole growth. While low-angular-momentum stars may be devoured by a black hole, they are not a sustainable source of fuel. Gas, which could potentially provide an abundant fuel source, presents another challenge due to its enormous angular momentum. While viscous torques are not significant, gas is subject to gravity torques from non-axisymmetric potentials such as bars and spirals. Primary bars can exchange angular momentum with the gas within corotation, causing it to spiral inwards until reaching the inner Lindblad resonance. An embedded nuclear bar can then take over. As the gas reaches the black hole's sphere of influence, the torque becomes negative, fueling the center. Dynamical friction also accelerates the infall of gas clouds closer to the nucleus. However, because of the Eddington limit, growing a black hole from a stellar-mass seed is a slow process. The existence of very massive black holes in the early universe remains a puzzle that could potentially be solved through direct collapse of massive clouds into black holes or super-Eddington accretion. [ABSTRACT FROM AUTHOR]

Featured Application: This study is a first step for real-time monitoring the risk of falls during gait. The goal of this study was to analyze instability during stepping at different speeds in young and older adults. To this aim, the anteroposterior and the mediolateral distances between the body center of mass (COM) and the minimum moment axis (MMA) were computed. A total of 15 young adults (25 y.o. [19–29]) and 15 older adults (68.7 y.o. [63–77]) volunteered for this study. For the computation of the distances, a complete biomechanical protocol combining two force platforms and a 3D motion capture analysis system was setup. The subjects were equipped with 47 reflective markers and were modeled as a frictionless multibody system with 19 segments, 18 joints and 42 degrees of freedom. They were asked to perform a series of stepping tasks at fast and spontaneous speeds. The stepping was divided into five phases, with successive swing and double-stance phases. Greater instability was observed during the swing phases. The distances reveal a significant higher instability at fast speed for both groups (p < 0.001) for all the phases compared with spontaneous speeds. The anteroposterior distance was significantly greater for older adults, highlighting greater instability compared to young adults, while no differences were observed for the mediolateral distance all along the five phases, suggesting higher risks of backward and forward falls during stepping. [ABSTRACT FROM AUTHOR]

Complex numbers were created by introducing the imaginary unit i to represent the square root of -1, allowing solutions to equations that involved square roots of negative numbers. Complex numbers were further extended to quaternionic numbers by introducing additional imaginary units, namely “j” and “k”. Quaternions are non-commutative and involve four components, with each component being a real number or a multiple of an imaginary unit. Usually complex numbers are used to represent wave functions in quantum mechanics. Solutions using quaternions to square well, spin and angular momentum, Dirac equations have been obtained by many researchers. In this article, we have made use of quaternions to study the generalization of adding angular momenta, the digital signal processing of a quaternionic function and circular potential of a particle in real Hilbert space and have obtained quaternionic solutions in terms of Bessel functions.

Based on the Richards-Wolf formalism, we obtain two different exact expressions for the angular momentum (AM) density in the focus of a vortex beam with the topological charge n and with right circular polarization. One expression for the AM density is derived as the cross product of the position vector and the Poynting vector and has a nonzero value at the focus for an arbitrary integer number n. The other expression for the AM density is deduced as a sum of the orbital angular momentum (OAM) and the spin angular momentum (SAM). We reveal that at the focus of the light field under analysis, the latter turns zero at n = –1. While both these expressions are not equal to each other at each point of space, 3D integrals thereof are equal. Thus, exact expressions are obtained for densities of AM, SAM and OAM at the focus of a vortex beam with right-hand circular polarization and the identity for the densities AM = SAM + OAM is shown to be violated. Besides, it is shown that the expressions for the strength vectors of the electric and magnetic fields near the sharp focus, obtained by adopting the Richards-Wolf formalism, are exact solutions of the Maxwell's equations. Thus, Richards–Wolf theory exactly describes the behavior of light near the sharp focus in free space.

The study of spin–orbit coupling (SOC) of light is crucial to explore the light–matter interactions in sub-wavelength structures. By designing a plasmonic lattice with chiral configuration that provides parallel angular momentum and spin components, one can trigger the strength of the SOC phenomena in photonic or plasmonic crystals. Herein, we explore the SOC in a plasmonic crystal, both theoretically and experimentally. Cathodoluminescence (CL) spectroscopy combined with the numerically calculated photonic band structure reveals an energy band splitting that is ascribed to the peculiar spin–orbit interaction of light in the proposed plasmonic crystal. Moreover, we exploit angle-resolved CL and dark-field polarimetry to demonstrate circular-polarization-dependent scattering of surface plasmon waves interacting with the plasmonic crystal. This further confirms that the scattering direction of a given polarization is determined by the transverse spin angular momentum inherently carried by the SP wave, which is in turn locked to the direction of SP propagation. We further propose an interaction Hamiltonian based on axion electrodynamics that underpins the degeneracy breaking of the surface plasmons due to the spin–orbit interaction of light. Our study gives insight into the design of novel plasmonic devices with polarization-dependent directionality of the Bloch plasmons. We expect spin–orbit interactions in plasmonics will find much more scientific interests and potential applications with the continuous development of nanofabrication methodologies and uncovering new aspects of spin–orbit interactions.

Formation of a compound nucleus and production of its evaporation residue are hindered by quasi-fission process. It reduces the evaporation residue cross section since it takes place before the target and projectile combines to form a composite nucleus. We study the quasifission barriers (Bqf) for 14 fusion reactions in the formation of superheavy element 298Og within the framework of the di-nuclear system model. In particular, the influence of entrance channel parameters on quasifission barriers has been investigated. We notice that the quasifission barriers decreases with an increase in angular momentum and fusion barrier height. We constructed semi-empirical formulae for Bqf as a function of mean fissility. The fusion reaction 48Ca+250Cf poses larger Bqf. The larger evaporation cross section is observed for this fusion reaction for 3n evaporation channel with the cross-section of 0.81pb. Similarly, a smaller evaporation cross-section of about 0.033pb is observed for 51Cr+247Pu fusion reaction for 4n evaporation channel with both projectile and target being deformed, unlike to the previous reaction with spherical projectile and deformed target.

Transfemoral prosthesis users (TFPUs) typically have a high risk of balance loss and falling. Whole-body angular momentum ( ${\overrightarrow {H}}_{{\text {WB}}}{)}$ is a common measure for assessing dynamic balance during human walking. However, little is known about how unilateral TFPUs maintain this dynamic balance through segment-to-segment cancellation strategies. Better understanding of the underlying mechanisms of dynamic balance control in TFPUs is required to improve gait safety. Thus, this study aimed to evaluate dynamic balance in unilateral TFPUs during walking at a self-selected constant speed. Fourteen unilateral TFPUs and fourteen matched controls performed level-ground walking at a comfortable speed on a straight, 10-m-long walkway. In the sagittal plane, the TFPUs had a greater and smaller range of $\overrightarrow {H}_{{\text {WB}}}$ compared to controls during intact and prosthetic steps, respectively. Further, the TFPUs generated greater average positive and negative $\overrightarrow {H}_{{\text {WB}}}$ than did the controls during intact and prosthetic steps, respectively, which may necessitate larger step-to-step postural changes in the forward and backward rotation about the body center of mass (COM). In the transverse plane, no significant difference was observed in the range of $\overrightarrow {H}_{{\text {WB}}}$ between groups. However, the TFPUs displayed smaller negative average $\overrightarrow {H}_{{\text {WB}}}$ in the transverse plane than did the controls. In the frontal plane, the TFPUs and controls demonstrated similar range of $\overrightarrow {H}_{{\text {WB}}}$ and step-to-step whole-body dynamic balance owing to the employment of different segment-to-segment cancellation strategies. Our findings should be interpreted and generalized with caution for the demographic features in our participants.

The flywheel is a widespread mechanical component used for the storage of kinetic energy and angular momentum. It typically consists of cylindrical inertia rotating about its axis on rolling bearings, which involves undesired friction, lubrication, and wear. This paper presents an alternative mechanism that is functionally equivalent to a classical flywheel while relying exclusively on limited-stroke flexure joints. This novel one-degree-of-freedom zero-force mechanism has no wear and requires no lubrication: it is thus compatible with extreme environments, such as vacuum, cryogenics, or ionizing radiation. The mechanism is composed of two coupled pivoting rigid bodies whose individual angular momenta vary during motion but whose sum is constant at all times when the pivoting rate is constant. The quantitative comparison of the flexure-based flywheel to classical ones based on a hollow cylinder as inertia shows that the former typically stores 6 times less angular momentum and kinetic energy for the same mass while typically occupying 10 times more volume. The freedom of design of the shape of the rigid bodies offers the possibility of modifying the ratio of the stored kinetic energy versus angular momentum, which is not possible with classical flywheels. For example, a flexure-based flywheel with rigid pivoting bodies in the shape of thin discs stores 100 times more kinetic energy than a classical flywheel with the same angular momentum. A proof-of-concept prototype was successfully built and characterized in terms of reaction moment generation, which validates the presented analytical model.

Legged robots excel in navigating challenging natural environments, such as steep obstructions or wide gaps in the ground. In addition to rough terrain, they may confront unexpected impact forces during their leaping gaits. While facing external disturbances, legged robots should maintain and (if necessary) restore their stability while completing their gaits. To this end, external disturbances and body orientation errors should be identified, and appropriate actions have to be taken to restore the balance of the robot and to provide advantageous landing circumstances. This paper briefly surveys the developments for balance and posture control of legged robots. The primary focus of these studies is on balancing legged robots under external disturbances or performing dynamic gaits. This paper also includes a brief focus on the literature that present research on balance and posture control strategies using the angular momentum approach. [ABSTRACT FROM AUTHOR]

In this paper, a novel magnetohydrodynamic attitude adjustment method is proposed, which uses a spherical magnetohydrodynamic attitude control device for the three-axis attitude adjustment. This paper mainly studies the distribution characteristics of the magnetic field and liquid flow field, and it does not involve attitude control performance and other contents. The magnetohydrodynamic method is used to solve the liquid flow field, which is coupled with the magnetic field. Then, the angular momentum and output torque of the attitude controller are calculated. The calculations aim to investigate the effects of current intensity and frequency on the magnetic induction intensity, flow velocity, angular momentum, and output torque in the spherical magnetohydrodynamic attitude control device. It was found that the velocity, angular momentum, and output torque increased when the current frequency and intensity increased. In addition, to achieve a larger flow rate and more efficient performance of the output angular momentum, priority should be given to increasing the current intensity rather than the current frequency. Thus, an optimal combination of the current intensity and frequency is proposed based on the numerical results. Finally, some implications of the proposed method are further discussed. [ABSTRACT FROM AUTHOR]

The tight focusing of an optical vortex with an integer topological charge (TC) and linear polarization was considered. We showed that the longitudinal components of the spin angular momentum (SAM) (it was equal to zero) and orbital angular momentum (OAM) (it was equal to the product of the beam power and the TC) vectors averaged over the beam cross-section were separately preserved during the beam propagation. This conservation led to the spin and orbital Hall effects. The spin Hall effect was expressed in the fact that the areas with different signs of the SAM longitudinal component were separated from each other. The orbital Hall effect was marked by the separation of the regions with different rotation directions of the transverse energy flow (clockwise and counterclockwise). There were only four such local regions near the optical axis for any TC. We showed that the total energy flux crossing the focus plane was less than the total beam power since part of the power propagated along the focus surface, while the other part crossed the focus plane in the opposite direction. We also showed that the longitudinal component of the angular momentum (AM) vector was not equal to the sum of the SAM and the OAM. Moreover, there was no summand SAM in the expression for the density of the AM. These quantities were independent of each other. The distributions of the AM and the SAM longitudinal components characterized the orbital and spin Hall effects at the focus, respectively. [ABSTRACT FROM AUTHOR]

We have considered here a novel particular model for dynamics of a non-rigid asteroid rotation, assuming the added mass model instead of the concept of Viscoelastic Oblate Rotators to describe the physically reasonable response of a 'rubble pile' volumetric material of asteroid with respect to the action of a projectile impacting its surface. In such a model, the response is approximated as an inelastic collision in which the projectile pushes the 'rubble pile' parts of the asteroid together to form a mostly solidified plug in the crater during the sudden impact on the asteroid's surface. Afterwards, the aforementioned 'solidified plug' (having no sufficient adhesion inside the after-impact crater) will be pushed outside the asteroid's surface by centrifugal forces, forming a secondary rotating companion around the asteroid. Thus, according to the fundamental law of angular momentum conservation, the regime of the asteroid's rotation should be changed properly. Namely, changes in rotational dynamics stem from decreasing the asteroid's mass (due to the fundamental law of angular momentum conservation). As the main finding, we have presented a new solving procedure for a semi-analytical estimation of the total mass of the aforementioned 'solidified plug', considering the final spin state of rotation for the asteroid with minimal kinetic energy reduced during a long time period by the inelastic (mainly, tidal) dissipation. The asteroid is assumed to be rotating mainly along the maximal inertia axis with a proper spin state corresponding to minimal energy with a fixed angular momentum. [ABSTRACT FROM AUTHOR]

Biped robots swing their legs alternately to achieve highly dynamic walking, which is the basic ability required for them to perform tasks. However, swinging of the swinging leg in the air will disturb the interaction between the supporting leg and the ground and affect the upper body's balance during dynamic walking. To allow the robot to use its own intrinsic motion characteristics to maintain stable movement like a human when its lower limbs are affected by unknown disturbances during dynamic walking, the ability to use its arms to resist disturbances is essential. This article presents a hybrid momentum compensation control method for torque-controlled biped robots to adapt to unknown disturbances during dynamic walking. First, a hybrid angular momentum and linear momentum regulator is designed to compensate for the disturbance caused by the swinging leg. Second, based on real-time dynamic state changes of the legs, a mixed-momentum quadratic programming controller is designed to realize stable dynamic walking. The proposed method allows the force-controlled robot to maintain its balance while walking down an unknown platform, and it maintains good straightness in the forward direction of dynamic motion. The proposed method's effectiveness is verified experimentally on the BHR-B2 force-controlled biped robot platform. [ABSTRACT FROM AUTHOR]

Based on the Richards-Wolf (RW) formalism, we obtain two different exact expressions for the angular momentum (AM) density of light in the focus of an optical vortex with a topological charge n and right circular polarization. One expression for the AM density is derived as the cross product of the position vector and the Poynting vector and has a nonzero value in the focus for an arbitrary integer n. Another expression for the AM density is equal to a sum of the orbital angular momentum (OAM) and the spin angular momentum (SAM) and, in the focus of a considered light field, is equal to zero at n = −1. These expressions are not equal at each point in space, but their 3D integrals are equal. Thus, we derive exact expressions for the AM, SAM and OAM densities in the focus of an optical vortex with right circular polarization and demonstrate that the identity for the densities AM = SAM + OAM is not valid. In addition, we show that the expressions for the strength vectors of the electric and magnetic field near the tight focus, obtained on the basis of the RW formalism, are exact solutions of Maxwell's equations. Thus, the RW theory exactly describes the behavior of light near the tight focus in free space. [ABSTRACT FROM AUTHOR]

The Jordan–Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator creation and annihilation operators acting in the Hilbert space of quantum oscillator states. Then, to describe quantum states in the probability representation of quantum oscillator states, we express their density operators in terms of conditional probability distributions (symplectic tomograms) or Husimi-like probability distributions. We illustrate this general scheme by examples of qubit states (spin-1/2 su(2)-group states) and even and odd Schrödinger cat states related to the other representation of su(2)-algebra (spin-j representation). The two-mode coherent-state superpositions associated with cyclic groups are studied, using the Jordan–Schwinger map. This map allows us to visualize and compare different properties of the mentioned states. For this, the su(2) coherent states for different angular momenta j are used to define a Husimi-like Q representation. Some properties of these states are explicitly presented for the cyclic groups C2 and C3. Also, their use in quantum information and computing is mentioned.

Since the 1970s, astronomers have struggled with the issue of how matter can be accreted to promote black-hole growth. While low-angular-momentum stars may be devoured by a black hole, they are not a sustainable source of fuel. Gas, which could potentially provide an abundant fuel source, presents another challenge due to its enormous angular momentum. While viscous torques are not significant, gas is subject to gravity torques from non-axisymmetric potentials such as bars and spirals. Primary bars can exchange angular momentum with the gas within corotation, causing it to spiral inwards until reaching the inner Lindblad resonance. An embedded nuclear bar can then take over. As the gas reaches the black hole’s sphere of influence, the torque becomes negative, fueling the center. Dynamical friction also accelerates the infall of gas clouds closer to the nucleus. However, because of the Eddington limit, growing a black hole from a stellar-mass seed is a slow process. The existence of very massive black holes in the early universe remains a puzzle that could potentially be solved through direct collapse of massive clouds into black holes or super-Eddington accretion.

Legged robots can walk stably down slopes without any actuation or control. The locomotion is called passive dynamic walking. Its dynamics at foot strike are governed by impact forces. The impulsive dynamics have been modelled in several approaches, where all the approaches assume that the stance leg instantaneously loses contact with the ground at foot strike. The loss-of-contact assumption has been introduced so as to guarantee conservation of angular momentum at foot strike; however, it is shown in this paper that the loss-of-contact assumption is neither necessary nor sufficient for that purpose. This paper provides a necessary and sufficient condition for conservation of angular momentum at foot strike in a modelling framework for multibody dynamics with impact. A compass-like biped robot is considered in this paper. Its impulsive dynamics are modelled by the relationship between impact forces and change of momentum with constraints. A necessary and sufficient condition for conservation of angular momentum is derived by examining the validity of foot velocities and impact forces in the impulsive model.

Based on the novel prescription for the power function, (x+iy)m, the new expression for Ψ(x,y|m), the eigenfunction of the operator of the third component of the angular momentum, M^z, is presented. These functions are normalizable, single valued and, distinct to the traditional presentation, (x+iy)m=ρmeimϕ, are invariant under the rotations at 2π for any, not necessarily integer, m—the eigenvalue of M^z. For any real m the functions Ψ(x,y|m) form an orthonormal set, therefore they may serve as a quantum mechanical eigenfunction of M^z. The eigenfunctions and eigenvalues of the angular momentum operator squared, M^2, derived for the two different prescriptions for the square root, (m2)1/2, (m2)1/2=|m| and (m2)1/2=±m, are reported. The normalizable eigenfunctions of M^2 are presented in terms of hypergeometric functions, admitting integer as well as non-integer eigenvalues. It is shown that the purely integer spectrum is not the most general solution but is just the artifact of a particular choice of the Legendre functions as the pair of linearly independent solutions of the eigenvalue problem for the M^2.

Though interstellar dust mass is negligible compared to the stars and the interstellar gas, it is in continuous contact with the rest of the world instead of being an isolated entity. Interstellar dust mass significantly influences the star formation process and its appearance. Hence it is important to study how it interacts with its environment. Here, we try to understand the motion of interstellar dust grains in the presence of the forces, viz., the drag force due to the interstellar gas and the radiation pressure due to a nearby star. [ABSTRACT FROM AUTHOR]

The structures of the Southwest Vortex (SWV) differ depending on the different environmental conditions, ultimately resulting in various types of disasters. Based on SWV Year Book during 20122017, this paper mainly makes statistical analysis on the characteristics of summer SWV and winter SWV. The radius and vertical depth between summer and winter SWVs are compared. Using composite method, PV tendency equation and angular momentum, the differences of both types of SWV scales are analyzed to reveal environmental conditions and the mechanism of different scales. The result shows that:(1) approximately 90% of winter SWVs are characterized by shallow pattern, but the percentage of summer SWVs sharing the similar pattern drops below 50%. Additionally, the average radius of SWVs in both seasons exhibits distinct variations with summer SWVs and winter SWVs reaching 100 km and 130 km, respectively. (2) Higher levels of environment angular momentum are exhibited in summer compared to winter, resulting in lager radius of winter SWV than summer SWV. (3) The PV tendency equation suggests that the diabatic heating effect is benefited to transport PV to higher level and strong convergence resulting in higher vertical extension height and radius contraction. (4) Winter SWV exhibits a wide range of inertial stability, which negatively affects the transport of angular momentum to the vortex core, consequently causing a maximum tangential wind and transport of angular momentum to appear outside the core. • Compared to the winter Southwest Vortex (SWV), the summer SWV is deeper on vertical scale but narrower on horizontal scale. • Winter conditions, such as lack of water vapor and more angular momentum, are more conducive to generating larger but not deeper SWV. • A mechanism contributing to the differences in summer and winter SWV scales is proposed. [ABSTRACT FROM AUTHOR]

The goal of this study was to analyze instability during stepping at different speeds in young and older adults. To this aim, the anteroposterior and the mediolateral distances between the body center of mass (COM) and the minimum moment axis (MMA) were computed. A total of 15 young adults (25 y.o. [19–29]) and 15 older adults (68.7 y.o. [63–77]) volunteered for this study. For the computation of the distances, a complete biomechanical protocol combining two force platforms and a 3D motion capture analysis system was setup. The subjects were equipped with 47 reflective markers and were modeled as a frictionless multibody system with 19 segments, 18 joints and 42 degrees of freedom. They were asked to perform a series of stepping tasks at fast and spontaneous speeds. The stepping was divided into five phases, with successive swing and double-stance phases. Greater instability was observed during the swing phases. The distances reveal a significant higher instability at fast speed for both groups (p < 0.001) for all the phases compared with spontaneous speeds. The anteroposterior distance was significantly greater for older adults, highlighting greater instability compared to young adults, while no differences were observed for the mediolateral distance all along the five phases, suggesting higher risks of backward and forward falls during stepping.

An electric field propagating along a non-planar path can acquire geometric phases. Previously, geometric phases have been linked to spin redirection and independently to spatial mode transformation, resulting in the rotation of polarisation and intensity profiles, respectively. We investigate the non-planar propagation of scalar and vector light fields and demonstrate that polarisation and intensity profiles rotate by the same angle. The geometric phase acquired is proportional to j = ℓ + σ, where ℓ is the topological charge and σ is the helicity. Radial and azimuthally polarised beams with j = 0 are eigenmodes of the system and are not affected by the geometric path. The effects considered here are relevant for systems relying on photonic spin Hall effects, polarisation and vector microscopy, as well as topological optics in communication systems.

Spin angular momentum associated with circular polarization is a fundamental and important aspect of photons both in classical and quantum optics. The interaction of this optical spin with matter and structures results in many intriguing optical effects and state-of-the-art applications covered under the emerging subject of spin optics. Distinct from longitudinal optical spin along the mean wavevector, transverse spin, the corresponding vector of which is perpendicular to the mean wavevector, prevails and plays a significant role in confined electromagnetic waves such as focused beams, guided waves, and evanescent waves. In the optical near-field, these transverse spins are generated owing to the spatial variation of the kinetic momentum of confined electromagnetic waves, where the spin and orbital angular momenta are strongly coupled, leading to many interesting topological spin structures and properties. Several reviews on optical transverse spins have been published in recent years in which their concepts and the various configurations producing them were introduced systematically. Here, we introduce in this review the underlying physics and dynamics of transverse spin and the resultant topological structures and properties such as the photonic skyrmions and merons. We term this sub-area ‘spin photonics’, its scope being to cover the design and research of spin structures in strongly confined electromagnetic fields with unique properties and applications. The concepts and framework reviewed have importance in optics, topological photonics, metrology, and quantum technologies and may be used to extend spin-dynamics concepts to fluidic, acoustic, and gravitational waves.

Recently there have been analytical studies concerning the threshold on the instability for a rotating BEC under a trapping potential. In this note, we obtain a critical lower bound μ∗that ensures the existence of ground state solutions for the L2-critical RNLS in 2dand 3d, where an anisotropic harmonic potential is present. In addition, we perform numerical estimation for the corresponding stationary equation for the ground state and the vortex state solutions. Our findings indicate agreement on the sharp bound from both analytical and numerical demonstration. Among others we prove a blowup alternative result for RNLS with an inhomogeneous nonlinearity.

People post-stroke have an increased risk of falls compared to neurotypical individuals, partly resulting from an inability to generate appropriate reactions to restore balance. However, few studies investigated the effect of paretic deficits on the mechanics of reactive control strategies following forward losses of balance during walking. Here, we characterized the biomechanical consequences of reactive control strategies following perturbations induced by the treadmill belt accelerations. Thirty-eight post-stroke participants and thirteen age-matched and speed-matched neurotypical participants walked on a dual-belt treadmill while receiving perturbations that induced a forward loss of balance. We computed whole-body angular momentum and angular impulse using segment kinematics and reaction forces to quantify the effect of impulse generation by both the leading and trailing limbs in response to perturbations in the sagittal plane. We found that perturbations to the paretic limb led to larger increases in forward angular momentum during the perturbation step than perturbations to the non-paretic limb or to neurotypical individuals. To recover from the forward loss of balance, neurotypical individuals coordinated reaction forces generated by both legs to decrease the forward angular impulse relative to the pre-perturbation step. They first decreased the forward pitch angular impulse during the perturbation step. Then, during the first recovery step, they increased the backward angular impulse by the leading limb and decreased the forward angular impulse by the trailing limb. In contrast to neurotypical participants, people post-stroke did not reduce the forward angular impulse generated by the stance limb during the perturbed step. They also did not increase leading limb angular impulse or decrease the forward trailing limb angular impulse using their paretic limb during the first recovery step. Lastly, post-stroke individuals who scored poorer on clinical assessments of balance and had greater motor impairment made less use of the paretic limb to reduce forward momentum. Overall, these results suggest that paretic deficits limit the ability to recover from forward loss of balance. Future perturbation-based balance training targeting reactive stepping response in stroke populations may benefit from improving the ability to modulate paretic ground reaction forces to better control whole-body dynamics.

The chirality‐dependent forces can offer new possibilities for passive optical separation and identification of chiral particles, which opens great opportunities to develop the technologies of pharmaceutics, chemicals, and biomedicine. Here, a robust enantioselective rotation of subwavelength chiral particles using lateral optical forces induced by a tightly focused azimuthally polarized beam is demonstrated. Although this focused field carries neither optical orbital angular momentum nor optical chirality, the lateral optical force can rotate the particle with opposite chirality around opposite directions, achieving an effective optical enantioseparation. Such a counterintuitive phenomenon is closely related to the transformation of the magnetic spin angular momentum of the focused field into the mechanical orbital angular momentum of the particle. In addition, the particle with different chirality parameters will be trapped in different orbits while with opposite chirality trapped in the same orbit, meanwhile its rotation direction is determined by the sign of the chirality parameter, which can realize an efficient chiral identification of single particles. The investigations may open up a new path toward light‐induced rotation or probing of objects with different chirality parameters.

Very few physicists who laid the foundation stone of quantum mechanics have played as important a role in chemistry as Friedrich Hund [1]. The following two significant contributions bear his name. (i) 'Hund's rules' dealing with the electronic configuration of atoms and the atomic term symbols. These rules are now a part of high school chemistry worldwide and have been generalized to diatomic molecules by Hund himself. (ii) 'Hund's coupling cases' called by him as (a) to (d) addressing the ways in which various quantum mechanical angular momenta (electron spin, orbital angular momentum, rotation) couple to form the total angular momentum via vector addition. Another early and pioneering work by Hund was on the quantum mechanical tunneling effect. However, the most significant and long-lasting contribution of Hund, together with Mulliken, was to establish the molecular orbital (MO) theory on a firm footing. In view of this, the MO theory became known as the Mulliken—Hund MO theory. [ABSTRACT FROM AUTHOR]

In this paper, we review what mechanisms are used to stabilize human bipedal walking. Based on mechanical reasoning, potential mechanisms to control the body center of mass trajectory are modulation of foot placement, stance leg control by modulation of ankle moments and push-off forces, and modulations of the body's angular momentum. The first two mechanisms and especially the first are dominant in controlling center of mass accelerations during gait, while angular momentum control plays a lesser role, but may be important to control body alignment and orientation. The same control mechanisms stabilize both steady-state and perturbed gait in both the mediolateral and antero-posterior directions. Control is at least in part active and is affected by proprioceptive, visual and vestibular information. Results support that this reflects a feedback process in which sensory information is used to obtain an estimate of the center of mass state based on which foot placement and ankle moments are modulated. These active feedback mechanisms suggest training approaches for populations at risk of falling, through perturbations, augmented feedback, or constraining one mechanism to train the other mechanisms. [ABSTRACT FROM AUTHOR]

While walking, ground reaction forces point from the centre of pressure to the neighbourhood of a focal point, namely the virtual pivot point (VPP), that adjusts angular momentum around the centre of mass (CoM). This study explores how age and speed affect the VPP quality and position during walking. Analysing an experimental dataset reveals high quality of the VPP in the sagittal plane for both young and elderly groups, regardless of speed. However, in the frontal plane, the VPP quality decreases with increasing speed, with elderly participants exhibiting significantly lower quality. Although not a direct measure of balance, VPP quality reflects changes in whole-body angular momentum owing to ageing and speed. Additionally, a template model is used to reproduce the VPP quality and position trends observed in the experiment. Simulation results highlight the sensitivity of VPP quality to leg force feedback and show that changing VPP height has minimal effect on gait speed. Furthermore, energy redistribution occurs through increased hip extension and leg damping, associated with a greater horizontal VPP distance from the CoM, observed in elderly walking. This study shows promise for analysing gait based on VPP, potentially aiding clinical interventions and supporting locomotion in the elderly., Competing Interests: We declare we have no competing interests., (© 2024 The Authors.)

Based on the novel prescription for the power function, (x + i y) m , the new expression for Ψ (x , y | m) , the eigenfunction of the operator of the third component of the angular momentum, M ^ z , is presented. These functions are normalizable, single valued and, distinct to the traditional presentation, (x + i y) m = ρ m e i m ϕ , are invariant under the rotations at 2 π for any, not necessarily integer, m—the eigenvalue of M ^ z . For any real m the functions Ψ (x , y | m) form an orthonormal set, therefore they may serve as a quantum mechanical eigenfunction of M ^ z . The eigenfunctions and eigenvalues of the angular momentum operator squared, M ^ 2 , derived for the two different prescriptions for the square root, (m 2) 1 / 2 , (m 2) 1 / 2 = | m | and (m 2) 1 / 2 = ± m , are reported. The normalizable eigenfunctions of M ^ 2 are presented in terms of hypergeometric functions, admitting integer as well as non-integer eigenvalues. It is shown that the purely integer spectrum is not the most general solution but is just the artifact of a particular choice of the Legendre functions as the pair of linearly independent solutions of the eigenvalue problem for the M ^ 2 . [ABSTRACT FROM AUTHOR]

Background. Measures of whole-body angular momentum in the sagittal plane are commonly used to characterize dynamic balance during human walking. To compute angular momentum, one must specify a reference point about which momentum is calculated. Although biomechanists primarily compute angular momentum about the center of mass (CoM), momentum-based controllers for humanoid robots often use the center of pressure. Here, we asked if the choice of the reference point influences interpretations of how dynamic balance is controlled in the sagittal plane during perturbed walking. Methods. Eleven healthy young individuals walked on a dual-belt treadmill at their self-selected speed. Balance disturbances were generated by treadmill accelerations of varying magnitudes and directions. We computed angular momentum about two reference points: (1) the CoM or (2) the leading edge of the base of support and then projected it along the mediolateral axes that pass through either of the reference points as the sagittal plane angular momentum. We also performed principal component analysis to determine if the choice of reference point influences our interpretations of how intersegmental coordination patterns contribute to perturbation recovery. Results. We found that the peak angular momentum was correlated with perturbation amplitude and the slope of this relationship did not differ between reference points. One advantage of using a reference point at the CoM is that one can easily determine how the momenta from contralateral limbs, such as the left and right legs, offset one another to regulate the whole-body angular momentum. Alternatively, analysis of coordination patterns referenced to the leading edge of the base of support may provide more insight into the inverted-pendulum dynamics of walking during responses to sudden losses of balance. [ABSTRACT FROM AUTHOR]

In this article, gyroscopes and flywheels are used to prevent the rollover of a vehicle due to external forces. The rollover preventing performance of the flywheels for a heavy trailer (an inverted pendulum problem) is investigated at a high road bank angle risk. Two control moment gyroscopes (CMG) and a reaction wheel are controlled by proportional torques to keep the vehicle in a stable motion in the vertical position. The reaction wheel was used only to eliminate the dissipation energy of damper. By using the energy stored in the flywheels of gyroscopes, the sprung mass of a vehicle can make a stable oscillating motion of small amplitude, standing upright without tipping over. The optimum flywheel speed was derived from the frequency equations with the appropriate controller gain. Most importantly, the required angular momentum to keep the vehicle upright without tipping over depends on the amplitude of the gimbal oscillation and the frequency. It has also been observed that Matlab simulations of Lagrangian equations and simulations modeled in RecurDyn software are in perfect harmony. [ABSTRACT FROM AUTHOR]

The theory of curves has a very long history. Moving frames defined on curves are important parts of this theory. They have never lost their importance. A point particle of constant mass moving along a trajectory in space may be seen as a point of the trajectory. Therefore, there is a very close relationship between the differential geometry of the trajectory and the kinematics of the particle moving on it. One of the most important elements of the particle kinematics is the jerk vector of the moving particle. Recently, a new resolution of the jerk vector, along the tangential direction and two special radial directions, has been presented by \"Ozen et al. (JTAM 57(2)(2019)). By means of these two special radial directions, we introduce a new moving frame for the trajectory of a moving particle with non vanishing angular momentum in this study. Then, according to this frame, some characterizations for the trajectory to be a rectifying curve, an osculating curve, a normal curve, a planar curve and a general helix are given. Also, slant helical trajectories are defined with respect to this frame. Afterwards, the necessary and sufficient conditions for the trajectory to be a slant helical trajectory (according to this frame) are obtained and some special cases of these trajectories are investigated. Moreover, we provide an illustrative numerical example to explain how this frame is constructed. This frame is a new contribution to the field and it may be useful in some specific applications of differential geometry, kinematics and robotics in the future.

• The multiple droplets impact is compared under symmetrical and asymmetrical impact condition. • Distinct rebound modes are found under symmetrical and asymmetrical impact condition. • The contact time of multiple droplets impact is analyzed under various rebound modes. • The effect of angular momentums on the contact time is revealed for multiple droplets impacts. The rebound dynamics of multiple impinging droplets is investigated and compared under the symmetrical and asymmetrical impact conditions. The result shows that at various relative velocities, when multiple droplets symmetrically impinge macrotextured superhydrophobic surfaces, the rebound modes consist of the left–right non-simultaneous rebound (LRNSR), the coalescence-split simultaneous rebound (CSSR) and the right-left non-simultaneous rebound (RLNSR). With the transition of rebound modes, the contact time is first reduced under the LRNSR mode and then constant under the CSSR and RLNSR modes as the relative velocity is increased. Whereas when multiple droplets asymmetrically impinge macrotextured superhydrophobic surfaces, the rebound modes consist of the left-ridge-right rebound (LRIRR), the left–right-ridge rebound (LRRIR) and LRNSR. When the relative velocity is increased, the contact time is first reduced under the LRIRR mode and then constant under the LRRIR mode. But under the LRNSR mode, the first reduced and then constant contact time appears with increased relative-velocities. [ABSTRACT FROM AUTHOR]

The time-dependent acceleration of fluid particles in an arbitrary superposition of multipolar spherical and cylindrical vortices in presence of a background rotational rigid flow is the gradient of the difference between their kinetic energy and the product of their total axial angular momentum times the angular velocity of the background flow. If the potential energy is defined as the time-dependent field whose minus gradient equals the acceleration of the flow, then the total energy, defined as the sum of kinetic and potential energies, equals the total axial angular momentum times the angular velocity of the background flow. The total energy of a fluid particle has therefore a linear relationship with the azimuthal velocity field. The role of the axial angular momentum in these oscillating flows is explained also in the classical Lagrangian and Hamiltonian descriptions of motion. The linear relation between total energy and angular momentum makes possible that the free parameters of these flows may be obtained, in a way similar to that developed in the quantum mechanics description of motion, as the eigenvalues of linear operators acting on some components of the spherical modes. Beltrami flow solutions in prolate spheroidal geometry for axisymmetric flows are also discussed. • The total energy of fluid particles has a linear relationship with the azimuthal velocity. • The axial angular momentum in oscillating flows is explained in the Lagrangian and Hamiltonian theories. • The free parameters of the oscillating flow may be obtained using linear operators. • There is an analogy to the quantum mechanics description of motion. [ABSTRACT FROM AUTHOR]

Localization technology is mostly achieved through Global Navigation Satellite Systems (GNSS). However, in mountainous areas where leaves and trees block signals from satellites, getting an appropriate location with GNSS positioning sometimes becomes difficult. In this paper, a localization algorithm based on altitude profiles with angular momentum (yaw rate) profile is proposed. It is a kind of landmark-based localization algorithm in which altitude and angular momentum (yaw rate) profiles are treated as landmarks. The proposed localization algorithm attempts to identify the current position by matching altitude and angular momentum (yaw rate) reference data prepared in advance with altitude and angular momentum (yaw rate) data currently acquired. The effectiveness of the algorithm is presented with several experimental results obtained with real data. This paper is an extension to the previous paper presented at the SICE Annual Conference 2020 [Yokota. Localization algorithm based on altitude time series in GNSS-denied environment. In: 2020 Proceedings of the SICE Annual Conference; Chiang Mai, Thailand; 2020 Sep 23–26. p. 952–957], in which vehicle localization was carried out by using only altitude profile matching. This paper used both altitude and angular momentum (yaw rate) for sensor fusion to improve the accuracy of the localization.

Spin angular momentum (SAM) and Orbital angular momentum (OAM) are two distinct forms of electromagnetic angular momentum (AM). Generally, circularly-polarized (CP) wave is deemed as the typical form of spin wave, which carries SAM only. In this work, the OAM characteristic of spin wave is found after stating the CP wave into the cylindrical coordinate: the spin wave contains two components along r and ϕ directions, which carry both SAM and OAM. Based on the OAM character of spin wave, an electromagnetic waveform with SAM in the center and SAM-OAM beside is demonstrated. In addition, since spin wave carries OAM naturally, a spin–orbit coupling mechanism is performed, which demands no spin Pancharatnam–Berry phase nor any phase modulation structure. All the results have been experimentally verified. Our research can be utilized in the theoretical studies of rotational electromagnetic and may be potentially applied in metamaterial, information and quantum research areas. [ABSTRACT FROM AUTHOR]

The tight focusing of an optical vortex with an integer topological charge (TC) and linear polarization was considered. We showed that the longitudinal components of the spin angular momentum (SAM) (it was equal to zero) and orbital angular momentum (OAM) (it was equal to the product of the beam power and the TC) vectors averaged over the beam cross-section were separately preserved during the beam propagation. This conservation led to the spin and orbital Hall effects. The spin Hall effect was expressed in the fact that the areas with different signs of the SAM longitudinal component were separated from each other. The orbital Hall effect was marked by the separation of the regions with different rotation directions of the transverse energy flow (clockwise and counterclockwise). There were only four such local regions near the optical axis for any TC. We showed that the total energy flux crossing the focus plane was less than the total beam power since part of the power propagated along the focus surface, while the other part crossed the focus plane in the opposite direction. We also showed that the longitudinal component of the angular momentum (AM) vector was not equal to the sum of the SAM and the OAM. Moreover, there was no summand SAM in the expression for the density of the AM. These quantities were independent of each other. The distributions of the AM and the SAM longitudinal components characterized the orbital and spin Hall effects at the focus, respectively.