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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 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 adaptive control of walking is often studied on a split-belt treadmill, where people gradually reduce their step length asymmetries (SLAs) by modulating foot placement and timing. Although it is proposed that this adaptation may be driven in part by a desire to reduce instability, it is unknown if changes in asymmetry impact people's ability to maintain balance in response to destabilizing perturbations. Here, we used intermittent perturbations to determine if changes in SLA affect reactive balance control as measured by whole-body angular momentum (WBAM) in the sagittal and frontal planes. Sixteen neurotypical older adults (70.0 ± 5.3 years old; 6 males) walked on a treadmill at a 2:1 belt speed ratio with real-time visual feedback of their achieved and target step lengths. We used mixed-effects models to determine if there were associations between SLA or foot placement and WBAM during the applied perturbations. Walking with more positive SLAs was associated with small reductions in forward WBAM (p < 0.001 for fast and slow belts) but increased lateral WBAM (p = 0.045 for fast belt; p = 0.003 for slow belt) during perturbations. When participants walked with more positive SLAs, they shortened their foot placement on the slow belt, and this shortening was associated with moderate reductions in forward WBAM (p < 0.001) and small increases in lateral WBAM (p = 0.008) during slow-belt perturbations. Our findings suggest that spatiotemporal changes that occur during split-belt treadmill walking may improve sagittal-plane stability by reducing people's susceptibility to losses of balance, but this may come at the expense of frontal-plane stability. [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]

• 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]

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]

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]

Rotation is a challenging riddle for the relationalist. In early versions of the absolute-relational debate for example, Newton's rotating bucket poured cold water on the relationalist position. While the parameters of the debate have changed, a more recent analysis in 1999 by Belot proclaimed rotation to be "the downfall of relationalism." In this paper, we provide a relational response to the riddle of rotation. We present a theory that, contrary to orthodoxy, can account for all rotational effects without introducing, as the absolutist does, a fixed standard of rotation. Instead, our theory posits a universal SO (3) charge that plays the role of global angular momentum and couples to inter-particle relations via terms commonly seen in standard gauge theories such as electromagnetism and the Standard Model of particle physics. Our theory makes use of an enriched form of relationalism: it adds an SO (3) structure to the traditional relational description. Our construction is made possible by the modern tools of gauge theory, which reveal a simple relational law describing rotational effects. In this way, we can save all the phenomena of Newtonian mechanics using conserved charges and relationalism. In a second paper, we will further explore the ontological and explanatory implications of the theory developed here. [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]

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]

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]

Granular mixing is important to many industries, but the mixing process is still poorly understood. In this study, motion of a single intruder particle introduced in a shallow bed of native particles was investigated. A parametric investigation was carried out to quantify the effects of initial intruder particle location, blade speed, and density difference between similarly sized native and intruder particles on the motion of the intruder particle during the mixing process. Intruder particles were color-tagged and videos were obtained from the top free surface of the shallow bed throughout the mixing duration. Additional experiments were performed to investigate the effect of density ratio between the intruder and native particles on the mean radial location (MRL) of the intruder particle. In the shallow bed system, all particles were found to be consistently under the direct influence of the blade and moved in discrete tracks unless randomly excited by the blade or neighboring particles. Intruder particles that were denser than the native particles were found to rotate closer to the hub with a smaller mean radial location, whereas less dense intruders were found to be further away from the mixer center on average. Initial location was important only for the first few rotations, and the blade speed had a negligible impact on the intruder particle flow behavior. Unlabelled Image • Density ratio between a tagged particle and its native counterparts determines its radial location in a bladed mixer. • Particles heavier than the native particles tend to move closer to the hub (and vice versa). • A simple angular momentum model can predict the mean radial location of tagged intruder particles. • Initial location and blade speed have little influence on tagged particles' mean radial location. [ABSTRACT FROM AUTHOR]

The angular momentum of radiation related to the passage of relativistic particles in a cylindrical channel is studied theoretically. To enhance the angular momentum of radiation, it is proposed to place the channel in a strong magnetic field parallel to the channel axis. The trajectories of the particles in the channel, the conditions for trapping particles in the channeling mode are investigated and equations for calculating the orbital angular momentum of radiation are obtained. It is shown that the angular momentum of radiation of a uniform beam of particles in the channel is not equal to zero only if the particles enter the channel at an angle greater than the critical angle. A significant difference between vortex radiation from a bunch of cylindrical channels (for example bunch of carbon nanotubes) from laser or undulator radiation is that the radiation beam of the latter has only one vortex axis. While the radiation from the beam of cylindrical channels has one vortex axis per each channel. Dependence of the angular momentum of radiation on the value of magnetic field and on the incident angle is studied. [ABSTRACT FROM AUTHOR]

We have presented in this communication a new solving procedure for Kelvin–Kirchhoff equations, considering the dynamics of rising the quasi-rigid ellipsoid of rotation in an ideal incompressible fluid (up to the surface), assuming additionally the dynamical symmetry of rotation for the rising body, I 1 = I 2 . Fundamental law of angular momentum conservation has been used for the aforementioned solving procedure. The system of Euler equations for dynamics of non-rigid ellipsoid rotation has been explored in regard to the existence of an analytic way of presentation for the approximated solution (where we suppose that components of fluid's torque vector { T i } are approximately proportional to the appropriate components of angular velocity { Ω i }). The results of calculations for the components of angular velocity { Ω i } should then be used for solving momentum equation of Kelvin–Kirchhoff system. Thus, the full system of equations of Kelvin–Kirchhoff problem has been explored with respect to the existence of an analytic way of presentation of the general solution. The last but not least, we have pointed out the 1-st integral of Kelvin–Kirchhoff system under the aforesaid additional assumption for fluid's torque vector { T i } when { I i } = const (but without the additional restriction of dynamical symmetry onto the form of the rising body, I 1 = I 2 ). [ABSTRACT FROM AUTHOR]

This paper presents a simplified model of the viscous transport of angular momentum and sets up a simplified expression of the rate of specific angular momentum transfer from the planet to the disk. Thanks to Whittaker's functions, we have found an analytic solution for the disk surface density. [ABSTRACT FROM AUTHOR]

The energy-momentum tensor form factors contain a wealth of information about the nucleon. It is insightful to visualize this information in terms of 3D or 2D densities related by Fourier transformations to the form factors. The densities associated with the angular momentum distribution were recently shown to receive monopole and quadrupole contributions. We show that these two contributions are uniquely related to each other. The quadrupole contribution can be viewed as induced by the monopole contribution, and contains no independent information. Both contributions however play important roles for the visualization of the angular momentum density. [ABSTRACT FROM AUTHOR]

This paper investigates the feasibility of using four movable masses distributed in a plane to realize three-axis attitude stabilization. With the proposed distribution and moving the paired masses in the same or opposite direction simultaneously, aerodynamic torque or internal momentum exchange torque is acted on the spacecraft. Then the spacecraft is gradually stabilized under a three-phase control strategy. Each of the three control phases is designed based on optimal control, nonlinear and sliding mode control, respectively. The stability of the proposed controller is given. Furthermore, numerical simulation matches the analytical results presented in this paper. Results show that three-axis attitude stabilization is possible using only in-plane movable masses which weigh less than 10 percent of spacecraft mass. Finally, the proposed control system can be a viable alternative for three-axis attitude stabilization of spacecraft orbiting in low Earth orbit. [ABSTRACT FROM AUTHOR]

We study theoretically the vortex radiation of a relativistic charged particle. General expressions for the spectral and angular distributions of angular momentum of radiation are derived for an arbitrary moving charge. Special attention is given to calculation of the angular momentum of synchrotron radiation. We obtain the spectrum and the angular distribution of angular momentum carried by synchrotron radiation. Similar expressions for the angular momentum of radiation of a charge moving on a spiral trajectory are derived by use of Lorentz transformations. It is shown that the main part of angular momentum in this case is emitted at a small angle to the vortex axis. Relativistic charged particles at spiral motion are effective source of the vortex photon beams at wave lengths ranging from radio waves to gamma rays. The obtained equations can be used for calculations of the angular momentum emitted by charged particles in the helical undulators and at axial channeling in solid crystal. • Spectral and angular properties of vortex radiation of relativistic charged particle are calculated. • Angular momentum transferred by synchrotron radiation is calculated. • The same properties are calculated for a charged particle moving along a spiral. • Vortex photon beams produced by the relativistic particles range from radio waves to gamma rays. [ABSTRACT FROM AUTHOR]

We have presented in this communication a new solving procedure for the dynamics of non-rigid asteroid rotation, considering the final spin state of rotation for a small celestial body (asteroid). The last condition means the ultimate absence of the applied external torques (including short-term effect from torques during collisions, long-term YORP effect, etc.). Fundamental law of angular momentum conservation has been used for the aforementioned solving procedure. The system of Euler equations for dynamics of non-rigid asteroid rotation has been explored with regard to the existence of an analytic way of presentation of the approximated solution. Despite of various perturbations (such as collisions, YORP effect) which destabilize the rotation of asteroid via deviating from the current spin state, the inelastic (mainly, tidal) dissipation reduces kinetic energy of asteroid. So, evolution of the spinning asteroid should be resulting by the rotation about maximal-inertia axis with the proper spin state corresponding to minimal energy with a fixed angular momentum. Basing on the aforesaid assumption (component K 1 is supposed to be fluctuating near the given appropriate constant of the fixed angular momentum), we have obtained that 2-nd component K 2 is the solution of appropriate Riccati ordinary differential equation of 1-st order, whereas component K 3 should be determined via expression for K 2. • The dynamics of asteroid rotation moving along the elliptic orbit is explored. • New type of solutions for dynamics of non-rigid asteroid rotation are obtained. • New method for solving Euler's equations of non-rigid body rotation is suggested. • Evolution of spin towards rotation about maximal-inertia axis is approximated. • The 2-nd component of angular momentum is proved to be solution of Riccati ODE. [ABSTRACT FROM AUTHOR]

Slow walking speed and lack of balance control are common impairments post-stroke. While locomotor training often improves walking speed, its influence on dynamic balance is unclear. The goal of this study was to assess the influence of a locomotor training program on dynamic balance in individuals post-stroke during steady-state walking and determine if improvements in walking speed are associated with improved balance control. Kinematic and kinetic data were collected pre- and post-training from seventeen participants who completed a 12-week locomotor training program. Dynamic balance was quantified biomechanically (peak-to-peak range of frontal plane whole-body angular-momentum) and clinically (Berg-Balance-Scale and Dynamic-Gait-Index). To understand the underlying biomechanical mechanisms associated with changes in angular-momentum, foot placement and ground-reaction-forces were quantified. As a group, biomechanical assessments of dynamic balance did not reveal any improvements after locomotor training. However, improved dynamic balance post-training, observed in a sub-group of 10 participants (i.e., Responders), was associated with a narrowed paretic foot placement and higher paretic leg vertical ground-reaction-force impulse during late stance. Dynamic balance was not improved post-training in the remaining seven participants (i.e., Non-responders), who did not alter their foot placement and had an increased reliance on their nonparetic leg during weight-bearing. As a group, increased walking speed was not correlated with improved dynamic balance. However, a higher pre-training walking speed was associated with higher gains in dynamic balance post-training. These findings highlight the importance of the paretic leg weight bearing and mediolateral foot placement in improving frontal plane dynamic balance post-stroke. [ABSTRACT FROM AUTHOR]

Employing the quaternionic fundamental commutator bracket between position and momentum and the electromagnetic quaternion as a wavefunction, we have found new Maxwell's equations where the orbital angular momentum L → of the photon induces additional electric and magnetic fields, and that it is perpendicular to the magnetic field (L → · B → = 0), but makes an angle with the electric field (L → · E → = − (3 ℏ c / 2) Λ), if the photon were massive, where Λ is some scalar function. The photon, as a particle, has its own electric and magnetic fields analogous to that of a uniformly moving charged particle. The angular momentum of the photon points a long the direction of the wave motion allowing us to connect it with the spin angular momentum. The photon angular momentum induces electric and magnetic fields, and electric and magnetic charged densities given by, ρ e = − 4 c ε 0 3 ℏ B → T · p → and ρ m = 4 3 ℏ c E → · p → , where B → T is the total magnetic field, p is the photon momentum vector, c and ℏ are the speed of light, and the reduced Planck's constant. Representing the photon by its vector potential as a wavefunction led to different set of equations. New Electric and magnetic fields coupled with their potentials are found to satisfy Maxwell's equations. [ABSTRACT FROM AUTHOR]

Background: Turning is a frequently performed, asymmetric task of daily living. The asymmetric nature makes turning challenging to perform while maintaining balance.Research Question: How do healthy individuals maintain dynamic balance, quantified as whole-body angular momentum, during a 90-degree turn compared to straight-line walking?Methods: The kinematics of sixteen healthy individuals were tracked during walking in a straight-line and during left and right 90-degree turns at a comfortable pace. Whole-body and segment angular momenta were calculated and the relative contributions of the legs, arms, pelvis and head/trunk to whole-body angular momentum were evaluated.Results: Average whole-body angular momentum was different during turning compared to straight-line walking in all planes of motion. The initiation of a turn required generation of whole body angular momentum in all three planes of motion, which was counteracted at the end of the turn by a generation of angular momentum in the opposite direction in the frontal and sagittal planes. Transverse plane momentum was always directed in the turn direction. All segment groups, except for the inside leg, had a greater magnitude of angular momentum during turning compared to straight-line walking. The outside leg and head/trunk segments were the largest contributors to frontal and transverse plane whole-body angular momentum.Significance: Understanding how body segments contribute to maintaining balance during a 90-degree turn can be useful for designing rehabilitation paradigms for people who have difficulty turning or impaired balance. [ABSTRACT FROM AUTHOR]

Abstract Performance in the flight phase of springboard diving is limited by the amounts of linear and angular momentum generated during the takeoff phase. A planar 8-segment torque-driven simulation model combined with a springboard model was used to investigate optimum takeoff technique for maximising rotation in forward dives from the one metre springboard. Optimisations were run by varying the torque activation parameters to maximise forward rotation potential (angular momentum × flight time) while allowing for movement constraints, anatomical constraints, and execution variability. With a constraint to ensure realistic board clearance and anatomical constraints to prevent joint hyperextension, the optimised simulation produced 24% more rotation potential than a simulation matching a 2½ somersault piked dive. When 2 ms perturbations to the torque onset timings were included for the ankle, knee and hip torques within the optimisation process, the model was only able to produce 87% of the rotation potential achieved in the matching simulation. This implies that a pre-planned technique cannot produce a sufficiently good takeoff and that adjustments must be made during takeoff. When the initial onset timings of the torque generators were unperturbed and 10 ms perturbations were introduced into the torque onset timings in the board recoil phase, the optimisation produced 8% more rotation potential than the matching simulation. The optimised simulation had more hip flexion and less shoulder extension at takeoff than the matching simulation. This study illustrates the difficulty of including movement variability within performance optimisation when the movement duration is sufficiently long to allow feedback corrections. [ABSTRACT FROM AUTHOR]

Abstract In this work the influence of isospin and angular momentum on two versions of Ren formula has been studied by adding the asymmetry and angular momentum terms for α -decay half-lives. We obtain coefficients for the two new formulae (New Ren A, New Ren B) and previous Ren (Ren B) formula, the coefficient are determined by least square fitting method of 356 nuclei for the even–even, even–odd, odd–even and odd–odd sets of nuclei. For each formula, the average and standard deviations have been evaluated. The new expressions provide good agreement between the calculated and experimental data for the α -decay half-lives when we consider the influence of nuclear isospin and angular momentum. [ABSTRACT FROM AUTHOR]

Abstract Running is beneficial for physical, social, and emotional health, and participating in physical activity, including running, is becoming more popular for people with an amputation. However, this population has a greater risk of falling relative to people without an amputation, which may be a barrier to running. Understanding how dynamic balance is maintained during running is important for removing this barrier. To investigate dynamic balance, we quantified whole-body angular momentum in eight people with a unilateral transtibial amputation (TTA) using running-specific prostheses (RSPs) compared to eight people without TTA during running at 2.5, 3.0, and 3.5 m/s. People with TTA had greater ranges of whole-body angular momentum compared to people without TTA in the frontal and sagittal planes (p < 0.01). These greater ranges resulted from smaller peak medial, lateral, and braking ground reaction forces from the amputated leg compared to the intact leg and people without TTA. Reduced RSP mass relative to the biological leg also influenced whole-body angular momentum as evidenced by smaller ranges of amputated leg angular momentum compared to the intact leg in the frontal and sagittal planes. Smaller amputated leg angular momentum corresponded with smaller contralateral arm angular momentum in the sagittal plane (p < 0.01). People with TTA maintain balance during running with altered muscle coordination and prosthesis characteristics. Restoring mediolateral force generation through prosthetic design advances may help in regulating the frontal plane component of whole-body angular momentum for people with TTA, with potential to improve their ability to maintain balance during running. [ABSTRACT FROM AUTHOR]

Highlights • The key idea is to place the channel into the magnetic field. • The magnetic field ensures the preferred helicity of the particle trajectories. • The angular momentum of radiation is calculated. • Conditions of channeling, such as critical incident angle are found. • The critical incident angle can be greater than the Lindhard critical angle. Abstract We study theoretically the angular momentum of radiation emitted at axial channeling of the fast particles in a crystal or in a bunch of micro- or nanotubes placed in strong magnetic field. It is shown that high energy particles channeled in the presence of magnetic field are effective source of vortex radiation in the X-ray and gamma-range of photons energies. We show that there are two factors that increase the angular momentum of emitted radiation in the presence of magnetic field. First, the magnetic field favours additional "twisting" of the channeled particles in a certain direction and, secondly, the particles that have the corresponding initial angular momentum are predominantly captured into the channeling mode. Dependence of the angular momentum of radiation on the value of magnetic field and on the incident angle is studied. [ABSTRACT FROM AUTHOR]

We have presented here our reply on the comments on our recent article "ON THE DYNAMICS OF NON-RIGID ASTEROID ROTATION". We would restate again: our partial solution stems from fundamental law of angular momentum conservation for the non-rigid asteroid rotation (where asteroids were considered preferably as deformed 'rubble pile' asteroids , not as elastic bodies), meanwhile authors of the aforementioned comments have considered other partial solving procedure which can be associated with commensurable elongations of the asteroid during the deformations. This assumption contradicts the physical nature of most known asteroids ('rubble pile' asteroids are known to have a non-elastic internal rheology), therefore as such the solutions of Euler equations for dynamics of non-rigid asteroid rotation, obtained by authors of the comments, does not have real meaning in astrophysical sense. Despite the fact that it is useless in astrophysical area, the suggested strategy or solving procedure for the constructing a new class of special kind of solutions for Euler equations (dynamics of non-rigid elastic body's rotation) can be of partial interest to a journals for theoretical mechanics but not first-class astrophysical journals or journal in the field of celestial mechanics. So, we wish the best for the authors to possible publishing their full solution (not a simple a note, which seems to be "following-in-wake" in regard to our article) where they could discuss additionally the stability of solutions if it is deemed required. • The proposed criticism in comments to article is based on unphysical assumption. • 'Rubble pile' asteroids structure & rheology should be taken into consideration. • New type of solutions for dynamics of non-rigid asteroid rotation is defended. • New method for solving Euler's equations of non-rigid body rotation is defended. • Evolution of spin towards rotation about maximal-inertia axis is circa constant. AMS Subject Classification: 70F15, 70F07 (Celestial mechanics). [ABSTRACT FROM AUTHOR]

[Display omitted] • Angular momentum constraint distorts chain conformation in molecular dynamics (MD) simulation. • A reweighting factor for distortion correction was theoretically derived. • Distortion can also be caused by insufficient thermalization of the angular momentum. The effect of angular momentum on single-chain conformation in an implicit solvent model was investigated by molecular dynamics simulation. The distribution of the end-to-end distance depends on whether the angular momentum of the entire molecule is fixed or thermalized, and these two distributions can be transformed from the one to the other through the reweighting method. In addition, depending on the thermostat, the thermalization of the angular momentum becomes insufficient even if no constraint is imposed on the angular momentum, resulting in the distortion of the distribution of chain conformation. These results suggest the importance of the choice of thermostat that enables the thermalization of the angular momentum. [ABSTRACT FROM AUTHOR]

The purpose of this wok is to obtain a complete description of the entropy production within the framework of non equilibrium thermodynamics for the case of an isotropic material interface between two one-component immiscible fluids when both of them are magnetizable and polarizable and external and internal angular momentum are included. All physical variables are allowed to be singular along the interface with the exception of the magnetic field and electric field. The set of conservation laws for the interface are derived and the explicit form of the entropy production is obtained. Taking into account spacial and time reversal symmetries, we establish the phenomenological relations between the fluxes and thermodynamic forces. We conclude by providing an example where constraints for the values of the transport coefficients are obtained as a consequence of conditions which must be fulfilled to guarantee that the matrix of transport coefficients remains positive definite. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence conditions of bounded motions of an infinitesimally small particle in the spatial circular restricted three-body problem. In particular, by using the Jacobi integral that corresponds to the inertial coordinate system, we prove a theorem on boundedness of motion that enables us to supplement the Hill approach in the study of motion of an infinitesimally small particle. [ABSTRACT FROM AUTHOR]

This study examined how dancers regulate the hip joint kinetics to coordinate the upper and lower body angular momenta with the increased rotation of pirouette en dehors (pirouette) during the preparation. During the preparation of the pirouette, the upper body rotates greatly about the vertical axis; however, the lower extremity remains relatively stationary. Therefore, there must be specific control at the hip to coordinate the upper and lower body angular momenta in turns of increased rotation. Kinematics and kinetics of single to quadruple pirouettes performed by eight ballet dancers were analysed using a motion capture system and force plates. Peak angular momentum of the upper body around the vertical axis increased from the single to the quadruple pirouettes. The vertical components of hip abductor torque of the anterior lower limb and hip adductor and flexor torques of the posterior lower limb contributed to generating the clockwise moment acting on the upper body around the vertical axis, which was reduced by the vertical components of the hip internal and external rotator torques. Thigh flexion angles of the posterior and anterior lower limbs, respectively, at the peak adductor and abductor torques at the corresponding hip joints changed with the number of revolutions and changed the percent contribution of the relevant hip joint torques about the vertical axis. The results suggest that dancers need to regulate hip joint torques along with the thigh angles in the pirouettes depending on the number of revolutions. [ABSTRACT FROM AUTHOR]

Orientation factor (κ 2 ) for FRET from a rotating donor dipole, transferred helicity of the donor field and torque exerted on the acceptor by the donor have been investigated in the framework of classical electrodynamics. It is shown that for rotating dipole, κ 2 is significantly higher as compared to linear dipole independently of the orientation distribution of the donor and acceptor and whether the static or the dynamic rotational regimes are used for averaging κ 2 . By this property of κ 2 , FRET serves as an example for a phenomenon where local field interference may take place in a “natural” way for emitters possessing rotating dipoles in their excited states by nature. The overlapping spatial distributions for the helicity of donor local field, torque exerted on the acceptor by the donor and for the FRET orientational factor suggest that transfer of both energy and helicity take place predominantly in the plane of rotation by keeping the original direction of helicity, i.e. in accordance with the conservation law for helicity. Orienting FRET has been proposed by engineering local field structure by using elliptically polarized light for donor excitation or by using linearly polarized light coupled with electromagnetic modification of the donor environment. The phenomenon of increased κ 2 can be exploited for checking helicity conservation for different FRET donors without the need for polarized detection optics. Modulation of FRET with changing ellipticity of the excited donor state might supply structural and dynamical information on the orientational distribution of dye-holding matrices even on the surface of living cells, e.g. on the level of cell surface receptor clusters. Furthermore, it might also be exploited in sensing local electromagnetic fields. Rotating excited donor states might also facilitate turning on photoswitchable acceptors. [ABSTRACT FROM AUTHOR]

The α -decay half-lives for the even–even, even–odd, odd–even and odd–odd of 356 nuclei in the range 52 ≤ Z p ≤ 118 have been studied within the analytical formula of Royer and also within the modified analytical formula of Royer. We calculated the new coefficient of the Royer by fitting 356 isotopes. Also, we considered the Denisov and Khudenko formula and obtained the new coefficient for the modified Denisov and Khudenko formula. We calculated the standard deviation and the average deviation. Analytical results are compared with the experimental data. The results are in better agreement with the experimental data when the effect of the isospin considered for the parent nuclei. [ABSTRACT FROM AUTHOR]

Maintaining dynamic balance during community ambulation is a major challenge post-stroke. Community ambulation requires performance of steady-state level walking as well as tasks that require walking adaptability. Prior studies on balance control post-stroke have mainly focused on steady-state walking, but walking adaptability tasks have received little attention. The purpose of this study was to quantify and compare dynamic balance requirements during common walking adaptability tasks post-stroke and in healthy adults and identify differences in underlying mechanisms used for maintaining dynamic balance. Kinematic data were collected from fifteen individuals with post-stroke hemiparesis during steady-state forward and backward walking, obstacle negotiation, and step-up tasks. In addition, data from ten healthy adults provided the basis for comparison. Dynamic balance was quantified using the peak-to-peak range of whole-body angular-momentum in each anatomical plane during the paretic, nonparetic and healthy control single-leg-stance phase of the gait cycle. To understand differences in some of the key underlying mechanisms for maintaining dynamic balance, foot placement and plantarflexor muscle activation were examined. Individuals post-stroke had significant dynamic balance deficits in the frontal plane across most tasks, particularly during the paretic single-leg-stance. Frontal plane balance deficits were associated with wider paretic foot placement, elevated body center-of-mass, and lower soleus activity. Further, the obstacle negotiation task imposed a higher balance requirement, particularly during the trailing leg single-stance. Thus, improving paretic foot placement and ankle plantarflexor activity, particularly during obstacle negotiation, may be important rehabilitation targets to enhance dynamic balance during post-stroke community ambulation. [ABSTRACT FROM AUTHOR]

We discuss in detail the spatial distribution of angular momentum inside the nucleon. We show that the discrepancies between different definitions originate from terms that integrate to zero. Even though these terms can safely be dropped at the integrated level, they have to be taken into account when discussing distributions. Using the scalar diquark model, we illustrate our results and, for the first time, check explicitly that the equivalence between kinetic and canonical orbital angular momentum persists at the level of distributions, as expected in a system without gauge degrees of freedom. [ABSTRACT FROM AUTHOR]

Understanding the dynamic processes of a real game system requires an appropriate dynamics model, and rigorously testing a dynamics model is nontrivial. In our methodological research, we develop an approach to testing the validity of game dynamics models that considers the dynamic patterns of angular momentum and speed as measurement variables. Using Rock–Paper–Scissors (RPS) games as an example, we illustrate the geometric patterns in the experiment data. We then derive the related theoretical patterns from a series of typical dynamics models. By testing the goodness-of-fit between the experimental and theoretical patterns, we show that the validity of these models can be evaluated quantitatively. Our approach establishes a link between dynamics models and experimental systems, which is, to the best of our knowledge, the most effective and rigorous strategy for ascertaining the testability of evolutionary game dynamics models. [ABSTRACT FROM AUTHOR]

We give a brief overview about recent developments in theories and experiments on the global and local spin polarization in heavy ion collisions. [ABSTRACT FROM AUTHOR]

Preparation of various concentrations of Dy 3+ doped borosilicate glasses using melt quenching technique and their optical characterizations are presented. Based on the measured optical spectra, Judd-Ofelt approach is used to determine the optical parameters such as oscillator strengths, optical intensity parameters and transition lifetime. The impact of the total angular momentum on the transition lifetime is theoretically investigated. The lifetime decreases as the angular momentum increases until J = 7 / 2 , for the atomic terms F J 6 , then its value increases at higher values of angular momentum. The same behavior occurs for the H J 6 states, but longer lifetime starts at J = 11 / 2 to J = 13 / 2 . The free ion collision strengths and cross sections are evaluated to asses an interpretation of the presented radiative results. The cross sections show a decrease trend with the J -increasing while the collision strengths show the opposite behavior. Calculated data of electric dipole transition probabilities and branching ratio of several transitions of Dy 3+ are reported. [ABSTRACT FROM AUTHOR]

Background Patients with transtibial amputation adopt trunk movement compensations that alter effort and increase the risk of developing low back pain. However, the effort required to achieve high-demand tasks, such as step ascent and descent, remains unknown. Methods Kinematics were collected during bilateral step ascent and descent tasks from two groups: 1) seven patients with unilateral transtibial amputation and 2) seven healthy control subjects. Trunk kinetic effort was quantified using translational and rotational segmental moments (time rate of change of segmental angular momentum). Peak moments during the loading period were compared across limbs and across groups. Findings During step ascent, patients with transtibial amputation generated larger sagittal trunk translational moments when leading with the amputated limb compared to the intact limb ( P = 0.01). The amputation group also generated larger trunk rotational moments in the frontal and transverse planes when leading with either limb compared to the healthy group ( P = 0.01, P < 0.01, respectively). During step descent, the amputation group generated larger trunk translational and rotational moments in all three planes when leading with the intact limb compared to the healthy group ( P < 0.017). Interpretation This investigation identifies how differing trunk movement compensations, identified using the separation of angular momentum, require higher kinetic effort during stepping tasks in patients with transtibial amputation compared to healthy individuals. Compensations that produce identified increased and asymmetric trunk segmental moments, may increase the risk of the development of low back pain in patients with amputation. [ABSTRACT FROM AUTHOR]

It is well-known that the fields of pure radially-polarised optical vortex modes do not possess the usual phase function e i ℓ ϕ of typical twisted light and so they do not carry angular momentum. However, recent work has confirmed that radially-polarised modes with helical wave fronts have been created in the laboratory by several groups and they can now be readily generated using commercially available devices. They are endowed with the phase function e i ℓ ϕ for arbitrary values of the winding number ℓ. Crucially, the original theoretical treatments disregard the longitudinal electric and magnetic field components. We show here that the longitudinal components must be included, not just for the consistency of the treatment, but because only this can lead to angular momentum. We show that for such created modes the cycle-averaged angular momentum is α ħ ℓ where α = (P w 0 2) / (ħ c 2) is a dimensionless constant, with P the power in the mode and w 0 the mode width at focus. • It is well-known that radially-polarised vortex modes do not carry angular momentum (AM). • Recently, angular momentum-carrying modes have been realised and they possess AM. [ABSTRACT FROM AUTHOR]

Backward walking training has been reported to improve gait speed and balance post-stroke. However, it is not known if gains are achieved through recovery of the paretic limb or compensations from the nonparetic limb. The purpose of this study was to compare the influence of backward locomotor training (BLT) versus forward locomotor training (FLT) on gait speed and dynamic balance control, and to quantify the underlying mechanisms used to achieve any gains. Eighteen participants post chronic stroke were randomly assigned to receive 18 sessions of either FLT (n = 8) or BLT (n = 10). Pre- and post-intervention outcomes included gait speed (10-meter Walk Test) and forward propulsion (time integral of anterior-posterior ground-reaction-forces during late stance for each limb). Dynamic balance control was assessed using clinical (Functional Gait Assessment) and biomechanical (peak-to-peak range of whole-body angular-momentum in the frontal plane) measures. Balance confidence was assessed using the Activities-Specific Balance Confidence scale. While gait speed and balance confidence improved significantly within the BLT group, these improvements were associated with an increased nonparetic limb propulsion generation, suggesting use of compensatory mechanisms. Although there were no improvements in gait speed within the FLT group, paretic limb propulsion generation significantly improved post-FLT, suggesting recovery of the paretic limb. Neither training group improved in dynamic balance control, implying the need of balance specific training along with locomotor training to improve balance control post-stroke. Despite the within-group differences, there were no significant differences between the FLT and BLT groups in the achieved gains in any of the outcomes. [ABSTRACT FROM AUTHOR]

We study theoretically by means of quantum electrodynamics the vortex radiation of a relativistic electron in a uniform magnetic field. The exact expressions for the probability of emission of a photon with a certain angular momentum are found. The classical asymptotics ħ → 0 of this probability does not match the angular momentum flux density calculated by the classical method using the symmetrized energy-momentum tensor. Although the flux of angular momentum integrated over the radiation directions is the same in both cases. We found the angular momentum flux of the radiation field using the canonical (not symmetrized) energy-momentum tensor and showed that the flux obtained in this way coincides with the classical limit for the probability of photon emission. • Orbital angular momentum of radiation from relativistic charged particle at circular and spiral motion is calculated. • Angular momentum of radiation calculated by use of quantum and classical electrodynamics is compared. • The difference between the angular momentum due to symmetrized and canonical energy-momentum tensors is discussed. • The angular momentum due to the canonical energy-momentum tensor coincides with that obtained by quantum electrodynamics. [ABSTRACT FROM AUTHOR]

An elliptically polarized electromagnetic wave transports linear and angular momentums, and exerts force and torque on an exposed surface. The angular momentums associated with the left- ( L ) and right-handed ( R ) circularly polarized waves are parallel and opposite to the direction of propagation, respectively. Applying the principle of superposition, an algorithm is constructed to decompose the elliptically polarized wave into L - and R -components. The relationship between the resultant angular momentum and the electrical energy of the elliptically polarized wave is completely determined by Stokes parameters. Utilizing the proposed relation to study the propagation of the polarized wave through an anisotropic crystal, it is found that the angular momentum brings the ordinary and the extraordinary waves to produce self-modulation effect, working as a pilot wave, or a hidden-variable, as suggested by de Broglie and Bohm. [ABSTRACT FROM AUTHOR]

The number of times spin s appears in the Kronecker product of n spin j representations is computed, and the large n asymptotic behavior of the result is obtained. Applications are briefly sketched. [ABSTRACT FROM AUTHOR]

• A simplified rigid body model to calculation of full body angular momentum. • Only 7 IMU sensors are needed to calculate the full body angular momentum using this simplified model. • The model was validated on both able-bodied subjects and transfemoral amputees. The capability to monitor gait stability during everyday life could provide key information to guide clinical intervention to patients with lower limb disabilities. Whole body angular momentum (L body) is a convenient stability indicator for wearable motion capture systems. However, L body is costly to estimate, because it requires monitoring all major body segment using expensive sensor elements. In this study, we developed a simplified rigid body model by merging connected body segments to reduce the number of body segments, which need to be monitored. We demonstrated that the L body could be estimated by a seven-segment model accurately for both people with and without lower extremity amputation. [ABSTRACT FROM AUTHOR]