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The purpose of this study was to determine the effects of thrower-discus system rotation on performance in discus throwing. The resultant angular momentum of the thrower-discus system and direction cosines of the angular momentum vector were calculated from kinematic data at five critical instants of discus throwing for 28 female and 15 male elite discus throwers, and compared between their long and short trials in actual competition. Compared to short trials, elite female throwers' long trials had significantly less angular momentum at right foot takeoff and left foot takeoff (P ≤ 0.023), and significantly less top-to-left rotation at right foot takeoff, left foot takeoff, left foot touchdown, and release (P ≤ 0.007), and significantly greater right-to-left rotation at left foot touchdown and release (P ≤ 0.009) in long trials. Compared to their short trials, elite male throwers had significantly less top-to-left and top-to-front rotations at left foot touchdown (P ≤ 0.042), and significantly less total angular momentum at release (P = 0.043) in long trials. Elite discus throwers should control the amount of rotations of the thrower-discus system to reduce the top-to-left roll of the discus during the flight to extend the aerodynamic distance. [ABSTRACT FROM AUTHOR]

This study developed a teaching material that makes the conservation of angular momentum, which students find very difficult, more concrete. The fact that angular momentum is a vector concept, the direction of the vector and the importance of this vector direction in angular momentum conservation are visualized. The teaching material consists of a table mounted on a freely rotating shaft, two electric motors mutually connected to the table, and a speed adjuster circuit used to change the rotation speeds of the motors. When electric motors begin to rotate, the angular momentum of the motors changes. How the angular momentum of the system is preserved thanks to the changing angular momentum of the parts interacting with each other, the directions of the vectors formed, the inertia torque, angular velocity, angular momentum relationship, and the relationship of the parts forming a system with each other have been tried to be explained in detail through the teaching material. When the motors were operated in different directions and speeds, the change in the rotation direction of the table was observed. This observation concretizes that angular momentum and angular momentum conservation are vector concepts. The right-hand rule, which describes the angular momentum vector direction with the material, can be demonstrated to students in practice. Video recordings showing how the teaching material works have been shared with readers. [ABSTRACT FROM AUTHOR]

Sorting orbital angular momentum (OAM) and spin angular momentum (SAM) of photons is crucial for optical communications, optical storage, and quantum information processing, wherein complicated optical setups or bulky devices are conventionally utilized to determine the angular momentum via repetitive interference or diffractive projection measurements. Recently, advancements in compact and single‐shot OAM detection have been made via coordinate transformation metasurfaces. Nevertheless, most of these strategies require precise separation and alignment between multiple components and cannot simultaneously distinguish full angular momentum states. Besides, the single‐shot maximum identifiable OAM mode numbers are generally limited to 60 due to the tradeoff between the mode space and reduced‐cross‐talk mode interval. Here, this work puts forward and experimentally demonstrates a monolithic spiral metalens (SML) for ultrahigh‐capacity sorting full angular momentum states. The SML focus the incident vortex beam into multiple‐turn spiral ring rather than a circle ring on the focal plane according to its topological charge, with the mode order ranging from −250 to 250. Consequently, the maximum identifiable OAM mode number is up to 168 under a single‐shot measurement, which largely surpass the best results reported hitherto. The experimental results obtained in the telecom band underpin the design approach, which may find great potential in high‐capacity communication and storage applications. [ABSTRACT FROM AUTHOR]

Recently, Ahn et al. created dumbbell-shaped silica nanoparticles, then optically levitated in vacuum, capable of spinning at 300 billion revolutions per minute, driven only by the force and torque of laser. This is by far the fastest spinning object in the world. We show that in this system, there is an additional change in momentum (or extra force) that is proportional to the change in the angular momentum of the particle (or torque). We suggest that this effect also applies to microscopic particles. In the experiment of Ahn et al., although the angular momentum of the particle itself L is large, the rate of change of the angular momentum L ̇ may not be large. Therefore, experimentally, the physical effects associated with changes in angular momentum can be verified either by applying very strong force and torque to the particle, or by allowing the axis of rotation of the particle to find a way to change very quickly. [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 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]

The global perspective presented here is built on earlier papers discussing the dynamics of the upper branch of the Hadley cell in the two solsticial seasons. The role of the tropics is made explicit in a conceptual model that is presented and evaluated. The fluctuation of deep tropical convection in longitude and time is seen as crucial. The filamentary outflows from such convective events move westward and across the equator deep into the winter hemisphere. The horizontal tilt of the cross-equatorial flow implies a significant upper-tropospheric flux of westerly momentum from the winter tropics to the summer hemisphere. These properties are related to the cross-equatorial propagation of wave activity triggered by deep tropical convection in the summer hemisphere. The filaments carry with them near-equatorial values of absolute vorticity and potential vorticity. After turning anticyclonically, some filaments move eastward and poleward to the equatorial edge of the winter subtropical jet. There is strong evidence they can interact with the eddies on this jet and enhance their poleward westerly momentum flux. In the global perspective, tropical and extratropical systems and the interaction between them are all important for the dynamics of the upper branch of the Hadley cell. significance statement: The Hadley cell is the large-scale overturning in the atmosphere with air in the upper troposphere moving from the equatorial region to near 30° in the winter hemisphere. In the standard view it is midlatitude weather systems that are responsible for removing angular momentum from this upper branch of the Hadley cell. Here it is proposed that tropical systems and their interaction with the midlatitude systems are also important. Insight into the role of the tropics in the dynamics of the Hadley cell can be obtained by considering it as the sum of many events of active deep convection occurring in different longitudes and at different times. [ABSTRACT FROM AUTHOR]

Atmospheric angular momentum (AAM) is used to study the variability of Earth's atmospheric circulation during the past 45 years, a time of considerable climate change. Using global AAM, two interdecadal states are defined covering the periods 1977–98 (hereinafter P1) and 1999–2022 (P2). Global AAM decreased from P1 to P2 and was accompanied by weakened subtropical jet streams in both hemispheres, strong convection around the northern Maritime Continent, and a strengthened sea surface temperature (SST) gradient across the tropical Pacific Ocean. The period differences project onto 1) internal interdecadal Pacific variability (IPV), 2) a postulated transient ocean thermostat response to greenhouse gas and aerosol emissions, and 3) circulation anomalies related to the ozone hole. During 1977–2023, the first two processes are forcing the climate toward larger Pacific Ocean SST gradients and a poleward expansion of the Indo-Pacific warm pool (IPWP), especially into the Northern Hemisphere. The ozone hole produces its own distinct pattern of anomalies in the Southern Hemisphere that tend to become persistent in the early 1990s. The zonal and vertical mean AAM variations during P1 have frequent westerly wind anomalies between 40°N and 40°S with poleward propagation on interannual time scales. During P2, the circulation is dominated by subtropical easterly wind anomalies, poleward-shifted jets, and weaker propagation. Locally, the zonal mean anomalies manifest as midlatitude ridges that lead to continental droughts. Case studies illustrate the weakened subtropical jet streams of P2 and examine the factors behind a transition to La Niña in early 2020 that maintains the P2 pattern. [ABSTRACT FROM AUTHOR]

We consider the focusing mass supercritical nonlinear Schrödinger equation with rotation i u t = - 1 2 Δ u + 1 2 V (x) u - | u | p - 1 u + L Ω u , (x , t) ∈ R N × R , where N = 2 or 3 and V(x) is an anisotropic harmonic potential. Here L Ω is the quantum mechanical angular momentum operator. We establish conditions for global existence and blow-up in the energy space. Moreover, we prove strong instability of standing waves under certain conditions on the rotation and the frequency of the wave. Finally, we construct orbitally stable standing waves solutions by considering a suitable local minimization problem. Those results are obtained for nonlinearities which are L 2 -supercritical. [ABSTRACT FROM AUTHOR]

The statistical mechanics and thermodynamics of a system of symmetric rigid quantum rotors in the field of centrifugal forces are considered. Using the theory of canonical ensembles, we find one-particle distribution function, and the partition function and thermodynamic potential are expressed as a function of temperature and angular velocity. The equation of state in the angular velocity–angular momentum–temperature coordinates is explicitly found in the high-temperature and ultra-cold cases. The macroscopic parameters of the system show a dependence on the angular velocity, so the chiral effects are present in the system. The magnitude of chiral effects is estimated. The entropy and angular momentum graphs are plotted in the ultra-cold case. [ABSTRACT FROM AUTHOR]

Photonic spin‐orbit interactions describe the interactions between spin angular momentum and orbital angular momentum of photons, which play essential roles in subwavelength optics. However, the influence of frequency dispersion on photonic angular‐momentum coupling is rarely studied. Here, by elaborately designing the contribution of the geometric phase and waveguide propagation phase, the dispersion‐enabled symmetry switching of photonic angular‐momentum coupling is experimentally demonstrated. This notion may induce many exotic phenomena and be found in enormous applications, such as the spin‐Hall effect, optical calculation, and wavelength division multiplexing systems. As a proof‐of‐concept demonstration, two metadevices, a multi‐channel vectorial vortex beam generator and a phase‐only hologram, are applied to experimentally display optical double convolution, which may offer additional degrees of freedom to accelerate computing and a miniaturization configuration for optical convolution without collimation operation. These results may provide a new opportunity for complex vector optical field manipulation and calculation, optical information coding, light‐matter interaction manipulation, and optical communication. [ABSTRACT FROM AUTHOR]

In this study, persistent rainfall (PR) over South China (SC) is divided into two types. One type occurs multiple times in succession [defined as multiple PR (MPR)]; another type represents isolated PR (IPR), for which no new PR occurs for 10 days after the previous PR. The spatiotemporal structures of the 10-30-day intraseasonal oscillations (ISOs) associated with the two types of PR are compared and analyzed. The results reveal that the low-level moisture and air temperature perturbations always have a leading phase relative to the anomalous precipitation. In addition, the positive low-level moisture tendency appears in the MPR ending phase, whereas that in the IPR is close to zero. This difference results in convective development after the MPR ending phase, though not after the IPR. The moisture budget shows that the difference in moisture tendency between MPR and IPR is mainly due to meridional advection, including advections by the mean meridional flow across the perturbation moisture gradient and by the perturbation meridional flow across the mean moisture gradient. For the former, the difference is attributed to the perturbation moisture gradients, while the mean moisture gradients are responsible for the difference of the latter. Furthermore, an essential cause of the difference is the influence of higher-latitude disturbances that affect the IPR more significantly than the MPR. Two associated mechanisms are proposed. One is the perturbation stacking effect, and the other is the effect of angular momentum conservation. By contrast, the low-level temperature anomalies are not the key factor causing the difference between MPR and IPR. [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]

For modern Earth, the annual-mean equatorial winds in the upper troposphere are flowing from east to west (i.e., easterly winds). This is mainly due to the deceleration effect of the seasonal cross-equatorial Hadley cells, against the relatively weaker acceleration effect of coupled Rossby and Kelvin waves excited from tropical convection and latent heat release. In this work, we examine the evolution of equatorial winds during the past 250 million years using one global Earth system model, the Community Earth System Model version 1.2.2 (CESM1.2.2). Three climatic factors different from the modern Earth—solar constant, atmospheric CO2 concentration, and land–sea configuration—are considered in the simulations. We find that the upper-tropospheric equatorial winds change sign to westerly flows (called equatorial superrotation) in certain eras, such as 250–230 and 150–50 Ma. The strength of the superrotation is below 4 m s−1, comparable to the magnitude of the present-day easterly winds. In general, this phenomenon occurs in a warmer climate within which the tropical atmospheric circulation shifts upward in altitude, stationary and/or transient eddies are relatively stronger, and/or the Hadley cells are relatively weaker, which in turn are due to the changes of the three factors, especially CO2 concentration and land–sea configuration. [ABSTRACT FROM AUTHOR]

The paper focuses on applying the octonions to explore the influence of the external torque on the angular momentum of fluid elements, revealing the interconnection of the external torque and the vortices of vortex streets. J. C. Maxwell was the first to introduce the quaternions to study the physical properties of electromagnetic fields. The contemporary scholars utilize the quaternions and octonions to investigate the electromagnetic theory, gravitational theory, quantum mechanics, special relativity, general relativity, curved spaces, and so forth. The paper adopts the octonions to describe the electromagnetic and gravitational theories, including the octonionic field potential, field strength, linear momentum, angular momentum, torque, and force. In case the octonion force is equal to zero, it is able to deduce eight independent equations, including the fluid continuity equation, current continuity equation, and force equilibrium equation. Especially, one of the eight independent equations will uncover the interrelation of the external torque and angular momentums of fluid elements. One of its inferences is that the direction, magnitude, and frequency of the external torque must impact the direction and curl of the angular momentum of fluid elements, altering the frequencies of Karman vortex streets within the fluids. It means that the external torque is interrelated with the velocity circulation, by means of the liquid viscosity. The external torque is able to exert an influence on the direction of downwash flows, improving the lift and drag characteristics generated by the fluids. [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]

Using noncommutative infinitesimal rotations, we work out a formulation for angular momentum which leads to an expression for nuclear magnetic resonance (NMR). We also indicate a cosmic footprint of these considerations, much like the 21 cm radio signal of cosmic Hydrogen. Here, the motivation is that there are a number of "second-order effects" which provide results over and above the usual well-known results. [ABSTRACT FROM AUTHOR]

The interactions between electromagnetic (EM) waves and Metamaterials have always been considered as research focus of electronic information science and technology. In this work, we focus on the dynamical properties of EM waves with vortex structure propagating in left-handed materials (LHMs) exhibiting dispersive characteristics. The analytical expressions for the electric and magnetic field components of vortex EM waves without the limitation of the paraxial condition are derived using the spectral domain method. A canonical approach is utilized to explore the dynamical properties, including the energy, momentum, spin and orbital angular momentum, of vortex EM waves in dispersive LHMs. Numerical results show that the orientation of transverse energy flow in the LHM is reversed compared to that in the free space. The waves with higher angular frequency are beneficial to improve the dynamical characteristics. Furthermore, the topological charge and polarization state have a significant effect on the dynamical quantities. This study is expected to provide useful insights into the interactions of vortex EM waves with metamaterials, and their further applications. [ABSTRACT FROM AUTHOR]

Forward and reverse springboard somersaulting dives use similar approaches with a hurdle step prior to the final board contact phase during which forward rotation is produced in forward takeoffs and backward rotation in reverse takeoffs. This study compared forward and reverse takeoffs for joint strength, activation complexity, technique kinematics, and rotation potential. A planar 8-segment torque-driven computer simulation model of springboard diving takeoff was used to determine isometric joint strength by matching performances of a forward 2½ somersault dive and a reverse 1½ somersault dive. Activation complexity for the reverse takeoff was increased to achieve a similar closeness of match as for the forward takeoff. Takeoff technique was optimised to maximise rotation potential of forward and reverse somersaulting dives. Kinematics at touchdown, lowest point and takeoff were compared for the optimised forward and reverse takeoff simulations. It was found that the optimised reverse somersaulting dive exhibited greater isometric strength for ankle plantarflexion and shoulder flexion, greater joint torque activation complexity for ankle plantarflexion and for knee flexion. There was also less forward motion during board depression, more hip extension and knee flexion during the later stages of board recoil, less capacity for rotation potential, and greater vertical velocity at takeoff. [ABSTRACT FROM AUTHOR]

It is shown that, in some non-QCD theories, there are effects shared by QCD: (i) in SU(2) Yang–Mills theory containing a nonlinear spinor field, there is a mass gap; (ii) in SU(3) Proca–Higgs theory, there are flux tube solutions with a longitudinal electric field required for producing a force binding quarks; (iii) in non-Abelian Proca–Higgs theories, there exist flux tube solutions with a momentum directed along the tube axis and particlelike solutions with a nonvanishing total angular momentum created by crossed color electric and magnetic fields; in QCD, such configurations may contribute to the proton spin. We discuss the conjecture that such non-QCD theories might be a consequence of approximate solution of an infinite set of Dyson–Schwinger equations describing the procedure of nonperturbative quantization. The phenomenon of dimensional transmutation for nonperturbative quantization and the analogy between nonperturbative quantization and turbulence modeling are also discussed. [ABSTRACT FROM AUTHOR]

The central theme of this study is to explore if and how the intensity of a tropical cyclone (TC) is related to its size. This subject has puzzled atmospheric scientists since the work of Deppermann, but the existence of this relationship still remains elusive. The improved understanding of the intensity–size relationship of TCs will help coastal communities to prepare for the maximum potential damage as both the intensity and size have important impacts on wind damages, storm surges, and flooding. This study considers 33 years (1988–2020) of TC records of maximum surface winds and radii of maximum and gale-force winds over the North Atlantic basin derived from the Extended Best Track Dataset. Analysis of these TC records reveals a robust positive correlation between loss of Earth and relative angular momentum. This finding together with the inspiration from the seminal work of Emanuel and his collaborators leads us to combine absolute angular momentum and its frictional loss as a radially invariant quantity, referred to as "effective absolute angular momentum" (eAAM), for radial profiles of TC surface winds. It is demonstrated that the eAAM model can reproduce the observed complex intensity–size relationship of TCs, which can be further reduced to a quasi-linear one after factoring out the angular momentum loss and the radius of maximum surface winds. The findings of this study would not only advance our understanding of the complex TC intensity–size relation, but also allow for operational assessments of TC severity and potential damage just using its outer wind information. [ABSTRACT FROM AUTHOR]

Decay analysis of compound nuclei such as 9 6 Zr ∗ and 9 8 Ru ∗ formed in 4 8 Ca + 4 8 Ca and 3 4 S + 6 4 Ni reactions, respectively, is studied using two theoretical frameworks, dynamical cluster-decay model (DCM) and PACE4. To explore the decay dynamics in a relatively lighter mass region ( A CN ≈ 6 0) , two more reactions are picked (i) 3 4 S + 2 6 Mg forming the 6 0 Ni ∗ compound nucleus, (ii) another one involving the odd mass projectile, 3 5 Cl + 2 7 Al → 6 2 Zn ∗ . In DCM, the fusion excitation functions are calculated using sticking (I S) and nonsticking (I NS ) limits of the moment of inertia. For the chosen reactions, fusion cross-sections are equivalent to evaporation residue (ER) cross-sections (σ fus = σ ER ) as fission cross-sections are negligible. A lower magnitude of maximum angular momentum (ℓ max ) is obtained via the I NS approach in comparison to the I S approach and the angular momentum obtained via the I NS approach is closer to the experimental observations. The structure and magnitude of fragmentation potential and preformation probability (P 0) depend on the choice of moment of inertia and the magnitude of angular momentum involved. Besides this, PACE4 is employed to address the fusion cross-section of chosen reactions. The most probable decay channel is identified using both DCM and PACE4 approaches. [ABSTRACT FROM AUTHOR]

In this paper, a novel magnetohydrodynamic attitude adjustment method is proposed, which only uses a spherical magnetohydrodynamic attitude controller for three-axis attitude adjustment. The electromagnetic field equations and fluid flow equations are simultaneously solved using a finite volume method. The purpose of the simulation is to analyze the influences of changing parameters of geometric design of the proposed mechanism on the magnetic field distribution, flow field distribution, angular momentum, and output torque. Also, the influences of different numbers of poles and slots on the magnetic field distribution, flow field distribution, and attitude adjustment parameters are studied. It was found that the magnetic induction intensity, fluid velocity, angular momentum, and torque produced by the electromagnetic actuator with 4 poles and 24 slots are almost the largest in the proposed mechanism. Therefore, 4 poles and 24 slots are selected as the design parameter of the electromagnetic actuator. Furthermore, the magnetic field distribution, flow field distribution, angular momentum, and the output torque in four different fluid domains are studied. It was found that the angular momentum increases with the increase in the range of flow field. However, for a certain range of flow, the increase in angular momentum is minimum. In addition, the output torque produced by the fluid does not change basically with the flow field range. According to the numerical results, a combination of pole and slot numbers and the range of flow field are proposed for the physical design of the proposed mechanism. Note that this study can provide a reference for the optimal design of the proposed mechanism. [ABSTRACT FROM AUTHOR]

An analytical solution for the gyroscopic effect of the spinning rotor-blades assembly on the dynamic response of offshore wind turbines (OWT) is presented. A continuous coupled model is rigorously developed to form the partial differential equations of fore-aft, side-side, and yaw motions. The gyroscopic moments caused by the angular momentum of the spinning rotor-blades assembly are formulated and handled into the three boundary conditions at the nacelle. The procedure for obtaining the operational natural frequencies of the structure including these coupled boundary conditions is developed. Furthermore, a response function for each fore-aft and yaw motions is obtained by solving the equations of motion under a wave load applied in only the fore-aft direction. Finally, the operational natural frequencies are calculated and compared to the idling ones for the considered example of OWT. The response of the structure under different values of the rotor-blades assembly's angular velocity is investigated. The proposed solution in this study unfolds a revelational procedure in capturing the gyroscopic effect in wind turbine industries which also can be a guideline for developing the floating OWT models. • An analytical procedure is presented to formulate the gyroscopic effect of rotor-blades assembly at the nacelle level. • An 3D analytical model is created based on the Euler-Bernoulli beam theory to take account the flexural stiffness of the structure in the formulation. • Generator reaction and breaking force on the nacelle is considered in the formulation. [ABSTRACT FROM AUTHOR]

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]

Numerical simulations of a laboratory model of a tropical cyclone are carried out for different rotation rates. Particular attention is paid to the non-stationary stage of intensive cyclonic vortex formation. The transfer of angular momentum plays a key role in the formation of cyclonic and anticyclonic flows; therefore, a detailed analysis of the redistribution and variation of angular momentum is given. The time evolution of angular momentum fluxes and total angular momentum strongly depend on the rotation rate. It is shown that intensive cyclonic motion with velocity exceeding initial values substantially (ten or more times) is a result of accumulation in the centre of a small fraction of global angular momentum of a fluid layer (from 0.25% at fast rotation to 2% at slow rotation). The integral angular momentum of the anticyclonic flow is significantly larger than that of the cyclonic flow, mainly because of the relatively large fluid volume of the anticyclonic flow. Another important result is that the rotating fluid layer very quickly adapts to new boundary conditions (heating and cooling). Approximately two rotation periods are required to reach a quasi-stationary state. The application of the obtained results to the evolution of real tropical cyclones is discussed. [ABSTRACT FROM AUTHOR]

Previous studies have shown that Kelvin–Rossby instability is a viable mechanism for producing equatorial superrotation in small and/or slowly rotating planets. It is shown in this paper that this mechanism can also produce superrotation with terrestrial parameters when the baroclinic forcing moves to low latitudes, explaining previous results by Williams. The transition between superrotating and subrotating flow occurs abruptly as the baroclinic forcing moves poleward. Although Kelvin–Rossby instability weakens when the baroclinic zone moves away from the equator, the key factor explaining the abrupt transition is the change in the baroclinic eddies. When differential heating is contained within the tropics, baroclinic eddies do not decelerate the subtropical jet and the upper-tropospheric flow approximately conserves angular momentum, providing conditions favorable for Kelvin–Rossby instability. In contrast, when baroclinic eddies are generated in the extratropics, they decelerate the subtropical jet and prevent the Kelvin–Rossby coupling. Due to this sensitivity to baroclinic eddies, the system exhibits hysteresis: near the transition parameter, extratropical eddies can prevent superrotation when they are initially present. [ABSTRACT FROM AUTHOR]

Background: Individuals with obesity demonstrate deficits in postural stability, leading to increased fall risks. Controlling whole-body angular momentum is essential for maintaining postural stability during walking and preventing falls. However, it is unknown how obesity impacts whole-body angular momentum during walking.Research Purpose: To investigate the change in angular momentum about the body's COM during walking in individuals with different degrees of obesity.Methods: Thirty-eight young adults with different body mass index (BMI) scores walked barefoot at their preferred speed on a treadmill for 2 min. The whole-body angular momentum has been quantified from ground reaction force and moment data to capture the rotational behavior of walking in individuals with obesity without relying solely on placing markers on anatomical landmarks.Results: We found that adults with higher BMI scores walked slower with shorter step length, wider step width, and longer double support time (ps<.01). Ranges of the frontal- and transverse-plane angular momentum were greater in adults with higher BMI scores (ps<.01), while no difference was observed between BMI groups in the total sum of changes in whole-body angular momentum in any plane (ps>.05).Significance: Obesity not only decreased walking speed but also limited the ability to control mediolateral stability during walking. Investigating how obesity affects whole-body angular momentum may help better understand why adults with obesity have atypical gait with poor balance, address fall risk factors, and facilitate participation in physical activities. [ABSTRACT FROM AUTHOR]

This paper presents theoretical arguments that certain virtual bound states carry the trace component of affine torsion. The motivation for this work is that Einstein–Cartan theory, which extends general relativity by including torsion to model intrinsic angular momentum, is becoming more credible. We are not aware of any situation for which there is evidence or substantial argument for the presence of torsion trace, except in the continuum theory of edge dislocations in crystals. The main evidence for the hypothesis consists of analogies between the structure of virtual bound states and (a) geometry of dislocations in crystal lattices, which are modeled with torsion; and (b) modeling of intrinsic angular momentum by torsion in Einstein–Cartan theory and the theory of micro-elasticity. The work focuses on conjectured presence of torsion in para-positronium, which intermediates annihilation of an electron and a positron with opposite z-spins. If the virtual bound state carries torsion, then the local law of conservation of angular momentum can hold over the spacelike separation during annihilation. [ABSTRACT FROM AUTHOR]

A pirouette en dehors (PeDh) is multiple turns using the angular momentum generated by swinging the arms with both feet on the ground. The purpose of this study was to investigate how the arm swing facilitates increasing peak angular momenta of both arms during multiple PeDh. Upper body movements in single to six-revolutions clockwise (as seen from above) PeDhs were analysed to determine arm’s angular momentum induced by the individual joint torque, gravitational force and motion-dependent terms. The horizontal abduction and adduction torques of the right and left shoulder joints, respectively, and clockwise torsional torque of the upper torso induced the clockwise angular momentum (CWAM) of the arms in the horizontal plane, about the vertically upward axis. The motion-dependent term induced the CWAMs after joint torques and contributed to the maximum total CWAM of both arms substantially. The CWAMs induced by the motion-dependent term increased with joint torques up to the triple PeDh in the right arm but independently from the left shoulder joint torque up to the sextuple PeDh in the left arm. Using a whip-like motion of the arm, increasing the arm joint torques would not be required necessarily when performing, i.e., more than quaruple PeDhs. [ABSTRACT FROM AUTHOR]

Successful performance of difficult, multi-revolution jumps is a critical aspect of singles and pairs figure skating. Key determinants of quality jumps include jump height, angular momentum at takeoff (L_BodyTO) and total body moment of inertia (I_Body). The purpose of this study was to determine the effect of weighted gloves on L_BodyTO of figure skating jumps. Kinematic data was collected from thirteen skaters during on-ice testing sessions conducted before and after one week of training with weighted gloves. A one-way repeated measures ANOVA was used to compare metrics from jumps performed pre-training without weights (PreNW), post-training without weights (PostNW) and post-training with weights (PostW). No significant differences were found between kinematics in PreNW and PostNW. Skaters did not pull their arms in as tightly while wearing the weighted gloves (distance from the wrists to the axis of rotation were 13.6% and 12.1% greater in PostW than PreNW and PreW, respectively). A post hoc simulation showed that the added mass affected I_Body in the air. While theoretical evidence supports the use of weighted gloves in figure skating jumps, compensations negated their effectiveness in jumps the skaters could already perform well. Optimal implementation may be when skaters are learning new jumps. [ABSTRACT FROM AUTHOR]

In this paper, the contributions of gravitational instantons to the temperature of the cosmic background radiation are evaluated. The comoving number density in the radiation-dominated and matter-dominated eras is derived. In addition to the temperature resulting from expansion of the universe, the mass of the microscopic black holes required to create the thermal energy of the cosmic microwave background radiation is derived. [ABSTRACT FROM AUTHOR]

This study formulates three-dimensional (3D) residual flow, treating both stationary and transient waves. The zonal and meridional momentum equations contain four terms: the geostrophic wind tendency, Coriolis force for the residual horizontal flow, product of the geostrophic wind and potential vorticity other than the constant planetary vorticity, and friction. The thermodynamic equation contains three terms: the potential temperature tendency, advection of the basic potential temperature by the residual vertical flow, and diabatic heating. The zonal mean of the 3D residual flow equals the time mean of the residual flow of the transformed Eulerian-mean equations. The new residual flow is the sum of that derived by Plumb for transient waves and the quadratic terms of the time-mean fields, which correspond approximately to the Stokes correction due to stationary waves. The 3D residual flow and momentum equations are symmetric in the zonal and meridional directions, in contrast with those formulated by Kinoshita et al., which treat the time-mean zonal-mean zonal wind as the basic wind. The newly derived formulas are applied to the climatology of the 3D structure of the deep branch of the Brewer–Dobson circulation. In the Northern Hemisphere in December–February, the residual flows are directed inward toward the polar vortex strongly over east Siberia, where the downward flow is maximized, and weakly over the Atlantic; meanwhile, they are directed outward from the vortex over North America and Europe. A longitudinal dependence of the poleward flow is also observed in the Southern Hemisphere in June–August. [ABSTRACT FROM AUTHOR]

Constitutive models exhibiting viscoelastic and micro-inertia with vortex viscosity effects are used for modeling of transport of heat energy, (angular and linear) with conservation laws for dust phase flow. The governing models are solved via the finite element method. The convergence of numerical solutions is guaranteed and mesh-free results are computed in view of a variation of physical parameters. Micro-rotations have shown a remarkable impact on shear stress and wall heat flux. The momentum relaxation (memory effects) time has shown a remarkable decrease in velocity associated with macro-flow. An increase in vortex viscosity increases angular motion. The Deborah number has shown a decreasing trend on flow. This causes a significant decrease in convective transport of heat energy. The temperature of dust particles increases when the ratio of specific heat and fluid particle interaction parameter for temperature is increased. However, the opposite behavior is noted for the case of increasing the relaxation time of the particle phase. The hybrid nanofluid transports much momentum than the momentum transported by mono-nanofluid. [ABSTRACT FROM AUTHOR]

Atomic cluster expansion (ACE) methods provide a systematic way to describe particle local environments of arbitrary body order. For practical applications it is often required that the basis of cluster functions be symmetrized with respect to rotations and permutations. Existing methodologies yield sets of symmetrized functions that are over-complete. These methodologies thus require an additional numerical procedure, such as singular value decomposition (SVD), to eliminate redundant functions. In this work, it is shown that analytical linear relationships for subsets of cluster functions may be derived using recursion and permutation properties of generalized Wigner symbols. From these relationships, subsets (blocks) of cluster functions can be selected such that, within each block, functions are guaranteed to be linearly independent. It is conjectured that this block-wise independent set of permutation-adapted rotation and permutation invariant (PA-RPI) functions forms a complete, independent basis for ACE. Along with the first analytical proofs of block-wise linear dependence of ACE cluster functions and other theoretical arguments, numerical results are offered to demonstrate this. The utility of the method is demonstrated in the development of an ACE interatomic potential for tantalum. Using the new basis functions in combination with Bayesian compressive sensing sparse regression, some high degree descriptors are observed to persist and help achieve high-accuracy models. • We elucidate connections between atomic cluster expansion (ACE) descriptors and quantum angular momentum. • New recursion relationships and permutation properties of generalized Wigner symbols are derived. • Wigner symbol properties are used to expose linear relationships within subsets of ACE descriptors. • Recurrence relationships for independent descriptors are defined by adapting ACE to permutation properties of Wigner symbols. • We conjecture that an independent rotationally and permutationally invariant basis of ACE descriptors may be constructed. [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]

Balance studies usually focus on quantities describing the global body motion. Assessing such quantities using classical marker-based approach can be tedious and modify the participant's behaviour. The recent development of markerless motion capture methods could bypass the issues related to the use of markers. This work compared dynamic balance related quantities obtained with markers and videos. Sixteen young healthy participants performed four different motor tasks: walking at self-selected speed, balance loss, walking on a narrow beam and countermovement jumps. Their movements were recorded simultaneously by marker-based and markerless motion capture systems. Videos were processed using a commercial markerless pose estimation software, Theia3D. The centre of mass position (CoM) was computed, and the associated extrapolated centre of mass position (XCoM) and whole-body angular momentum (WBAM) were derived. Bland-Altman analysis was performed and root mean square difference (RMSD) and coefficient of correlation were computed to compare the results obtained with marker-based and markerless methods. Bias remained of the magnitude of a few mm for CoM and XCoM positions, and RMSD of CoM and XCoM was around 1 cm. RMSD of the WBAM was less than 10 % of the total amplitude in any direction, and bias was less than 1 %. Results suggest that outcomes of balance studies will be similar whether marker-based or markerless motion capture system are used. Nevertheless, one should be careful when assessing dynamic movements such as jumping, as they displayed the biggest differences (both bias and RMSD), although it is unclear whether these differences are due to errors in markerless or marker-based motion capture system. [ABSTRACT FROM AUTHOR]

• Circumferential ultrasonic waves in a piezoelectric tube generate a static torque. • This effect is explained on the basis of lattice dynamics and simulated with FEM. • The magnitude of the torque strongly depends on the ultrasound attenuation. • The influence of different loss channels in the piezoelectric has been quantified. The excitation of acoustic waves by a unidirectional transducer, integrated in a piezoelectric cylindrical tube or disk, can lead to a time-independent torque. This phenomenon, demonstrated earlier in experiments and analyzed with coupling-of mode theory, is explained in detail, starting on the level of lattice dynamics of a piezoelectric crystal. Expressions are derived for the stationary torque in the form of integrals over the volume or surface of the piezoelectric, involving the electric potential and displacement field associated with the acoustic waves generated by the transducer. Simulations have been carried out with the help of the finite element method for a tube made of PZT for two cases: A pre-defined potential on the surface of the tube and metal electrodes buried in the piezoelectric. The displacement field and electric potential of the high-frequency acoustic waves (between 200 and 300 kHz) were computed and used in the evaluation of the integrals. The attenuation due to various loss channels of the acoustic waves in the system has been analyzed in detail, as this plays a crucial role for the efficiency of torque generation. It is conjectured that time-reversal symmetry, present in the absence of attenuation, prohibits the generation of a static torque at least in the linear limit. A qualitative comparison is made between the simulations and earlier experiments. Discrepancies are attributed to lack of knowledge of the relevant material constants of the piezoelectric and to a simplified modeling of the electrode geometry in the cylindrical tube, which was necessary for reasons of numerical accuracy. [ABSTRACT FROM AUTHOR]

Light beams possess three types of angular momentum. They are the spin angular momentum, the extrinsic orbital angular momentum, and the intrinsic orbital angular momentum. Interaction of these momenta due to translational or cylindrical symmetry breaking leads to effects of the spin-orbit interaction of light, including topological effects. Topological optical activity or topological circular phase anisotropy, known as Rytov-Vladimirsky-Berry-Chao-Tomita plane polarization rotation, is the result of the extrinsic orbital angular momentum influence on the spin angular momentum. The effect manifests under linear polarized light propagation along a curved trajectory when the translational symmetry is breaking. We predict a new topological effect under the cylindrical symmetry breaking. This effect is the result of the extrinsic orbital angular momentum influence on the spin angular momentum in the converging asymmetrical light beam. It manifests as the transformation of linear polarized light into elliptically polarized one when an asymmetrical in the vertical direction beam passes through the left or right half of the focal plane. We have estimated the value of the ellipticity and proposed an experimental setup. We successfully observed the ellipticity change of 10 (− 3) using our method of small ellipticity determination. We have considered this transformation as the topological circular dichroism (topological circular amplitude anisotropy). We have demonstrated the connection of the ellipticity change with the value of the topological circular amplitude anisotropy R. The measured value of the topological circular amplitude anisotropy R turned out to be R = ± (0.60 ± 0.08) × 10 − 3. This new effect of the spin-orbit interaction of light contributes to our understanding of the nature of light. It can be used to develop new sensors in optics, including nano and quantum optics. • The effects of the spin-orbit interaction of light are the result of the pair interactions between the beam angular momenta. • The effects can be observed in fibers, in light beams, in liquid crystals, and under light scattering. • The influence of the extrinsic angular momentum on the spin angular momentum was observed only in fibers. • We proposed and experimentally observed that influence in asymmetrical converged light beams. • The effect can be considered as topological circular dichroism. [ABSTRACT FROM AUTHOR]

Precision in optical micromanipulation is critical for non-invasive, non-contact control of objects with light and for using light to measure forces and torques. We demonstrate the control of birefringent objects over three translational directions and three rotational degrees of freedom. Our work trapping and rotating calcite, a unique crystal with no axis of symmetry, extends the positioning abilities of optical tweezers. We trap and levitate a single crystal in linearly polarized light and position it in three rotational directions relative to the polarization. Our model of the torque on the crystals is based on determining the induced polarization and its interaction with the incident electric field. Crystals are shown to rest in equilibrium with their optic axis along the beam axis and one extraordinary axis along the direction of polarization. The calculated equilibrium positions align with our observations of stable trapped calcite. [ABSTRACT FROM AUTHOR]

After stroke, deficits in paretic single limb stance (SLS) are commonly observed and affect walking performance. During SLS, the hip abductor musculature is critical in providing vertical support and regulating balance. Although disrupted paretic hip abduction torque production has been identified in individuals post-stroke, interpretation of previous results is limited due to the discrepancies in weight-bearing conditions. Using a novel perturbation-based assessment that could induce SLS by removing the support surface underneath one limb, we aim to investigate whether deficits in hip abduction torque production, vertical body support, and balance regulation remain detectable during SLS when controlling for weight-bearing, and whether these measures are associated with gait performance. Our results showed that during the perturbation-induced SLS, individuals post-stroke had lower hip abduction torque, less vertical stiffness, and increased frontal plane angular impulse at the paretic limb compared to the non-paretic limb, while no differences were found between the paretic limb and healthy controls. In addition, vertical stiffness during perturbation-induced SLS was positively correlated with single support duration during gait at the paretic limb and predicted self-selected and fast walking speeds in individuals post-stroke. The findings indicate that reduced paretic hip abduction torque during SLS likely affects vertical support and balance control. Enhancing SLS hip abduction torque production could be an important rehabilitation target to improve walking function for individuals post-stroke. [ABSTRACT FROM AUTHOR]

The redistribution of angular momentum density can be achieved by tightly focusing the special vector optical fields, which can induce the orbital motion of the microscopic particles. Here, we investigate the focusing properties of radial-variant hybridly polarized vector optical fields with the polarization state varying along the different circular trajectories of the Poincaré sphere. It is found that the redistribution of local angular momentum is induced by the assembling of asymmetric spin flow derived from the orthogonal circularly polarized components of the vector optical field. On this basis, we present an effective method for flexibly manipulating the angular momentum density distribution by customizing the variations of polarization corresponding to different circular trajectories on the Poincaré sphere. These works may promote the applications of vector optical field in optical microfabrication and micro-manipulation. [ABSTRACT FROM AUTHOR]

The experimental verification of compound nucleus theory has successfully been performed for light ion induced reactions using proton and α -particle beams on different targets. However, such studies using the heavy ion beams are scarce due to the complex nature of heavy ion interaction process. The present work is an attempt to validate the Bohr's independent hypothesis using heavy ion beam of 18O beam on 159Tb targets and 12C on 165Ho targets, forming the same compound nucleus 177Ta. A channel wise analysis of cross section data for evaporation residues produced in 18O+159Tb and 12C+165Ho systems has been performed within the framework of statistical model code PACE4 and found to reasonably agree with the experimental data. Further, a comparison of reaction cross section data for the same evaporation residues produced in the two different systems has been found to follow Bohr's compound nucleus hypothesis at relatively higher excitation energies. However, at relatively lower excitation energies, a significant deviation in the measured cross section data of the same residues in the above mentioned systems have been observed and is attributed to the discrepancies in angular momentum values. Such discrepancies are well explained on the basis of input angular momentum involved in the reactions. [ABSTRACT FROM AUTHOR]

This work proposes a machine learning detection scheme for wireless orbital angular momentum (OAM) communication systems. The new scheme works for single‐input–single‐output (SISO) and multiple‐input–single‐output (MISO) wireless communication between the transmitter and the receiver. The transmitter encodes its data in OAM modes which are constructed using Laguerre–Gaussian beam form. The transmitted beams travel through a wireless channel with weak to medium turbulence strength and they arrive at random positions on the same receiver area. The authors proposed detection scheme allows the reception of multiple overlapping beams without prior knowledge of beams centre positions. The proposed scheme uses a novel technique of receiver segmentation and space filtering along with neural network to decode the received beams. Simulations show the detection efficiency and the enhanced performance of their proposed scheme for the SISO case and the MISO case with 2, 4, and 16 beams. [ABSTRACT FROM AUTHOR]

A weakly focused light beam is studied numerically in the focal plane, to observe the linear polarization separation and circular polarization accumulation in the beam cross section. This is an example of spin-orbit interaction of light, where the extrinsic orbital angular momentum of light encountered due to focusing is converted into spin angular momentum and causes circular polarization generation and linear polarization separation in different parts of the beam cross section. This effect is studied by evaluating the polarization vector and Stokes vector and angle parameters in the beam cross section in detail. Because of the lens’s spherical geometry and origination of geometric phase, the accumulation of the spin component in the beam cross section is observed to be circularly symmetric, while the linear polarization shows splitting into orthogonal polarization components in the beam cross section. The underlying results may have an important role for understanding the spin-orbit interaction in a weakly focused system at a fundamental level and can be useful in many applications of nanophotonics. [ABSTRACT FROM AUTHOR]

Among a high number of concepts taught in physical sciences, some of them are not formulated correctly in an adequate way, which allows that their comprehension by students can be ambiguous and lead to a false representation. The concept of spin in general and that of electronic spin are part of this topic. For this reason, the main aim of this paper is to clarify from students' life the effect of teaching the spin concept in its fuzzy way; this is included in the didactics of science in teaching quantum mechanics. Then, we will suggest how to behave vigilantly when we are responsible for teaching such concepts. [ABSTRACT FROM AUTHOR]

In this paper, Smarandache trajectory curves of constant mass point particles are described and evaluated as they move along the trajectory curve in Euclidean 3-space E³ using its position adapted frame (PAF). We also look at the Frenet apparatus of these unique trajectories. We anticipate a new way of analysing particle kinematics that could be useful in some application areas of differential geometry and particle physics. We then give a computational examples to illustrate these curves. [ABSTRACT FROM AUTHOR]

The electric field of an orbiting charge or electron observed in the rotating frame takes on a circular trajectory with a maximum radius of R = c ω ′ . The resultant extended electromagnetic structure is used to derive the spin–orbit energy of the orbiting electron. A surprising result of the derived expression is that the orbital velocity has a specific value ( β 0 = 1 136.96 ) in close agreement ( 99.94 % ) with the experimentally determined value for the fine structure constant ( ħ = k e 2 c 1 α exp = k e 2 c 1 β 0 → α exp = β 0 ). Furthermore, the derived spin–orbit expression does not include a g-factor (i.e g = 1 ) which means that the Larmor and Thomas precessions are equal and opposite, resulting in zero net precession in the lab frame. These results suggest that the quantised fine structure constant and by extension Planck’s constant, are a natural extension of classical electromagnetism and conservation of energy in a rotating frame. [ABSTRACT FROM AUTHOR]

Two new configurations of superposition of quantum states corresponding to the angular momentum of spin-1 quantum system is proposed in this article. One is a trivial state, |β, α⊥〉≡ (I −|α〉〈α|)|β〉, which consists of two Klauder's type of spin coherent state |α〉 and |β〉 that is also perpendicular to |α〉, and the other is a non-trivial case composed of vector product of two different copies of spin states, |α〉 and |β, α⊥〉, i.e. |vps〉 := |α〉×|β, α⊥〉. Some properties of such quantum states are discussed. For instance, depending on the particular choice of parameters, we show that they minimize both the Heisenberg and Robertson-Schr ö dinger uncertainty relations (RSUR) of each pair of the angular momentum components while the standard spin-coherent states do not satisfy. We have also shown that preparing the system state as a |β, α⊥〉 and choosing one of the mentioned orthogonal states, |vps〉, one can find a minimum lower bound for the Maccone-Pati uncertainty relations (MPUR) which is stronger than the other uncertainties. We also establish an irreducible and unitary representation of Lie algebra su(2) through the introduced states. [ABSTRACT FROM AUTHOR]

The paper focuses on a winch drum winding a heavy rope to present the variety of issues related to the dynamics of systems with rotating parts of time-varying mass. The dynamic motion equations for such systems are frequently either incorrect or derived under the assumption of mass constancy. When the mass variability is taken into account, simpler cases are discussed. The considerations on the angular momentum theorem enables formulating a new two time parameters form of the rotational motion equation for the system with time varying mass. Four cases are considered and different approaches of motion equations derivation are applied. The assumptions and solution methods of the analyzed systems as well as ambiguities and possible contradictions that may arise as a result of the trial of the problem formulation on the grounds of rigid body mechanics are discussed. The numerical simulations are presented. [ABSTRACT FROM AUTHOR]