Angular Momentum Constraints Research Articles

A position-based method for detecting orbital angular momentum modes

Abstract Due to the inherent limitations of current Orbital Angular Momentum (OAM) mode detection methods and constraints posed by the physical size of receiving antennas, accurately identifying higher-order OAM modes represents a significant challenge. Therefore, there is a pressing necessity to overcome these hurdles. This paper introduces a new approach to OAM mode detection that exploits positional information. Our methodology ascertains the OAM mode by examining the phase and position data of the electric field at any two randomly chosen points within the energy's spatial distribution radiated by vortex electromagnetic waves. This innovation promises not only to precisely detect higher-order OAM modes but also grants greater versatility in the placement of receiving antennas. Moreover, the study delves into the correlation between the electric field phase of vortex electromagnetic waves, the azimuth angle, and the receiving distance. The validity of our approach is confirmed through both simulation outcomes and experimental data derived from physical tests.

Deciphering the Kinematic Substructure of Local Dark Matter with LAMOST K Giants

Numerical simulations indicate that correlations exist between the velocity distributions of stars and dark matter (DM). We study the local DM velocity distribution based on these correlations. We select K giants from LAMOST DR8 cross-matched with Gaia DR3, which have robust measurements of velocity and metallicity, and separate them into the disk, halo substructure, and isotropic halo components in the chemodynamical space utilizing the Gaussian mixture model. The substructure component is highly radially anisotropic and possibly related to the Gaia–Enceladus–Sausage (GES) merger event, while the isotropic halo component is accreted from the earliest mergers following the Maxwell–Boltzmann distribution (standard halo model [SHM]). We find that the GES-like substructure contributes ∼85% of the local nondisk stars in the solar neighborhood, which is nearly invariant when applying different volume cuts or additional angular momentum constraints. Utilizing the metallicity–stellar mass relation and the stellar mass–halo mass relation, we find that ∼25−15+24% of local DM is in the kinematic substructure. Combined with the stellar distributions of nondisk components, we modify the heliocentric velocity distribution of local DM. It shifts to a lower speed with a sharper peak compared to the SHM and updates the detection limits of DM direct detection experiments. We discuss extensively the degeneracies present in the GMM fitting and propose that more kinematic and chemical information such as α abundance could help to break the degeneracy in the future. Our work confirms that the local DM velocity distribution deviates significantly from the SHM and needs to be properly accounted for in the DM detection experiments.

Quasi-time-optimal steering law for low-thrust orbit transfer considering angular momentum and torque constraints

In this study, a quasi-time-optimal steering law for low-thrust orbit transfer is investigated. In the proposed steering law, the satellite attitude is controlled to suppress its error with respect to the ideal thruster direction under the orthogonality constraint between the Sun direction and the solar array driving mechanism's rotational axis as well as the angular momentum and torque constraints. All these constraints are satisfied by introducing a structure similar to Baumgarte's stabilization method and by formulating a quadratically constrained quadratic programming problem which can be analytically solved to obtain the control torque. Several numerical simulations show that the transfer time difference from the ideal unconstrained transfer is less than a few percent.

Sun-Avoidance Slew Planning with Keep-Out Cone and Actuator Constraints

This paper presents a geometric approach for a sun (or any bright object) avoidance slew maneuver with pointing and actuator constraints. It is assumed that a gyrostat has a single light-sensitive payload with control-torque and reaction wheels’ angular momentum constraints. Furthermore, it is assumed that the initial and final attitudes, an instrument’s line-of-sight vector, and sun vector are known. Then Pontryagin’s minimum principle is used, and the desired or target-frame quaternions, angular velocity, and acceleration are derived. In the end, numerical simulations are performed to show the viability of the proposed algorithm with control-torque and angular momentum constraints.

Vertical angular momentum constraint on lunar formation and orbital history

The Moon likely formed in a giant impact that left behind a fast-rotating Earth, but the details are still uncertain. Here, we examine the implications of a constraint that has not been fully exploited: The component of the Earth-Moon system's angular momentum that is perpendicular to the Earth's orbital plane is nearly conserved in Earth-Moon history, except for possible intervals when the lunar orbit is in resonance with the Earth's motion about the Sun. This condition sharply constrains the postimpact Earth orientation and the subsequent lunar orbital history. In particular, the scenario involving an initial high-obliquity Earth cannot produce the present Earth-Moon system. A low-obliquity postimpact Earth followed by the evection limit cycle in orbital evolution remains a possible pathway for producing the present angular momentum and observed lunar composition.

Stepped pressure equilibrium with relaxed flow and applications in reversed-field pinch plasmas

The multi-region relaxed magnetohydrodynamics (MRxMHD) has been successful in the construction of equilibria in three-dimensional (3D) configurations. In MRxMHD, the plasma is sliced into sub-volumes separated by ideal interfaces, each undergoing relaxation, allowing the formation of islands and chaos. The resulting equilibrium has a stepped pressure profile across sub-volumes. The stepped pressure equilibrium code (SPEC) (S R Hudson et al, Phys. Plasmas 19, 112502 (2012)) was developed to calculate MRxMHD equilibria numerically. In this work, we have extended the SPEC code to compute MRxMHD equilibria with field-aligned flow and rotation, following the theoretical development to incorporate cross-helicity and angular momentum constraints. The code has been verified for convergence and compared to a Grad–Shafranov solver in 2D. We apply our new tool to study the flow profile change before and after the sawtooth crash of a reversed-field pinch discharge, in which data of the parallel flow is available. We find the promising result that under the constraints of cross-helicity and angular momentum, the parallel flow profile in post-crash SPEC equilibrium is flat in the plasma core and the amplitude of the flow matches experimental observations. Finally, we provide an example equilibrium with a 3D helical field structure as the favoured lower energy state. This will be the first 3D numerical equilibrium in which the flow effects are self-consistently calculated.

Orbital angular momentum constraints in the variational optimization of the two-electron reduced-density matrix

The direct variational determination of the two-electron reduced-density matrix (2-RDM) is usually carried out under the assumption that the 2-RDM is a real-valued quantity. However, in systems that possess orbital angular momentum symmetry, the description of states with a well-defined, non-zero z-projection of the orbital angular momentum requires a complex-valued 2-RDM. We consider a semidefinite program suitable for the direct optimization of a complex-valued 2-RDM and explore the role of orbital angular momentum constraints in systems that possess the relevant symmetries. For atomic systems, constraints on the expectation values of the square and z-projection of the orbital angular momentum operator allow one to optimize 2-RDMs for multiple orbital angular momentum states. Similarly, in linear molecules, orbital angular momentum projection constraints enable the description of multiple electronic states, and, moreover, for states with a non-zero z-projection of the orbital angular momentum, the use of complex-valued quantities is essential for a qualitatively correct description of the electronic structure. For example, in the case of molecular oxygen, we demonstrate that orbital angular momentum constraints are necessary to recover the correct energy ordering of the lowest-energy singlet and triplet states near the equilibrium geometry. However, care must still be taken in the description of the dissociation limit, as the 2-RDM-based approach is not size consistent, and the size-consistency error varies dramatically, depending on the z-projections of the spin and orbital angular momenta.

Terrestrial magma ocean origin of the Moon

A conceptual framework for the origin of the Moon must explain both the chemical and the mechanical characteristics of the Earth–Moon system to be viable. The classic concept of an oblique giant impact explains the large angular momentum and the lack of a large iron-rich core to the Moon, but in this scenario it is difficult to explain the similarity in the isotopic compositions of the Earth and Moon without violating the angular momentum constraint. Here we propose that a giant, solid impactor hit the proto-Earth while it was covered with a magma ocean, under the conventional collision conditions. We perform density-independent smoothed particle hydrodynamic collision simulations with an equation of state appropriate for molten silicates. These calculations demonstrate that, because of the large difference in shock heating between silicate melts and solids (rocks), a substantial fraction of the ejected, Moon-forming material is derived from the magma ocean, even in a highly oblique collision. We show that this model reconciles the compositional similarities and differences between the Moon and Earth while satisfying the angular momentum constraint. Moon formation by a giant impact ejecting material from a magma ocean on Earth reconciles geochemical and dynamical constraints on its formation, according to numerical simulations.

Generation of Strict Stealth Walking Gait Using Upper Body and Reaction Wheel

This paper proposes a novel method for easily generating a strict stealth walking gait of an underactuated rimless wheel (URW) by temporally controlling the stance-leg angle using an additional control torque. First, we introduce a 3-DOF URW model with a reaction wheel that can utilize two control torques, and describe the equation of motion. Second, we develop a controller for achieving strict output-following control of the stance-leg angle and angular momentum constraint control simultaneously. Third, we derive an approximate analytical solution of the target initial states of the upper body and reaction wheel. Furthermore, we propose a simple numerical procedure for identifying the target initial state of the nonlinear model, and show the effectiveness through numerical simulations.

Generation of Stealth Walking Gait on Frictionless Level Surface Utilizing Upper Body and Reaction Wheel

This paper proposes a new model of an underactuated rimless wheel (URW) that added a reaction wheel for easily generating a non-slippery stealth walking gait. First, we introduce a 3-DOF URW model that can utilize two control torques, and describe the equation of motion. Second, we develop a controller for achieving strict output-following control of the stance-leg angle and angular momentum constraint control simultaneously. Third, we derive an approximate analytical solution of the target initial states of the upper body and reaction wheel. Furthermore, we propose a simple numerical procedure for identifying the target initial state of the nonlinear model, and investigate the effectiveness through numerical simulations.

Generation of Stealth Walking Gait on Frictionless Descending Stairs Utilizing Upper Body and Reaction Wheel

Towards adaptation to slippery ground surface for underactuated locomotion robots, the authors proposed the method of stealth walking, which avoids energy loss at landing of swing foot. Moreover, they proposed angular momentum constraint control (AMCC), which constraints the horizontal ground reaction force to zero, to make the robots walk on the frictionless road surface stably. In this paper, we investigate a more severe situation, i.e., stable walking on frictionless descending stairs. First, we introduce a mathematical model of an underactuated rimless wheel with an upper body and a reaction wheel for analysis, and develop the control law for achieving trajectory tracking control of the stance-leg angle and AMCC simultaneously. Second, we investigate the validity of the proposed method and discuss the nonlinearity of zero dynamics through numerical simulations.

Evolution of cyclic mixmaster universes with noncomoving radiation

We study a model of a cyclic, spatially homogeneous, anisotropic 'mixmaster' universe of Bianchi type IX, containing a radiation field with non-comoving ('tilted' with respect to the tetrad frame of reference) velocities and vorticity. We employ a combination of numerical and approximate analytic methods to investigate the consequences of the second law of thermodynamics on the evolution. We model a smooth cycle-to-cycle evolution of the mixmaster universe, bouncing at a finite minimum, by the device of adding a comoving 'ghost' field with negative energy density. In the absence of a cosmological constant, an increase in entropy, injected at the start of each cycle, causes an increase in the volume maxima, increasing approach to flatness, falling velocities and vorticities, and growing anisotropy at the expansion maxima of successive cycles. We find that the velocities oscillate rapidly as they evolve and change logarithmically in time relative to the expansion volume. When the conservation of momentum and angular momentum constraints are imposed, the spatial components of these velocities fall to smaller values when the entropy density increases, and vice versa. Isotropisation is found to occur when a positive cosmological constant is added because the sequence of oscillations ends and the dynamics expand forever, evolving towards a quasi de Sitter asymptote with constant velocity amplitudes. The case of a single cycle of evolution with a negative cosmological constant added is also studied.

Hemispherically asymmetric trade wind changes as signatures of past ITCZ shifts

The atmospheric Hadley cells, which meet at the Intertropical Convergence Zone (ITCZ), play critical roles in transporting heat, driving ocean circulation and supplying precipitation to the most heavily populated regions of the globe. Paleo-reconstructions can provide concrete evidence of how these major features of the atmospheric circulation can change in response to climate perturbations. While most such reconstructions have focused on ITCZ-related rainfall, here we show that trade wind proxies can document dynamical aspects of meridional ITCZ shifts. Theoretical expectations based on angular momentum constraints and results from freshwater hosing simulations with two different climate models predict that ITCZ shifts due to anomalous cooling of one hemisphere would be accompanied by a strengthening of the Hadley cell and trade winds in the colder hemisphere, with an opposite response in the warmer hemisphere. This expectation of hemispherically asymmetric trade wind changes is confirmed by proxy data of coastal upwelling and windblown dust from the Atlantic basin during Heinrich stadials, showing trade wind strengthening in the Northern Hemisphere and weakening in the Southern Hemisphere subtropics in concert with southward ITCZ shifts. Data from other basins show broadly similar patterns, though improved constraints on past trade wind changes are needed outside the Atlantic Basin. The asymmetric trade wind changes identified here suggest that ITCZ shifts are also marked by intensification of the ocean's wind-driven subtropical cells in the cooler hemisphere and a weakening in the warmer hemisphere, which induces cross-equatorial oceanic heat transport into the colder hemisphere. This response would be expected to prevent extreme meridional ITCZ shifts in response to asymmetric heating or cooling. Understanding trade wind changes and their coupling to cross-equatorial ocean cells is key to better constraining ITCZ shifts and ocean and atmosphere dynamical changes in the past, especially for regions and time periods for which few paleodata exist, and also improves our understanding of what changes may occur in the future.

A Synoptic Climatology of Northern Hemisphere, Cold Season Polar and Subtropical Jet Superposition Events

AbstractNarrow, tropopause-level wind speed maxima known as jet streams or jets are among the most ubiquitous structural characteristics of Earth’s atmosphere. Two species, the polar and subtropical jets, can be observed on any given day. The polar jet is tied, via eddy momentum flux convergence associated with extratropical wave development, to the troposphere-deep baroclinicity of the midlatitudes, while the subtropical jet is tied, by angular momentum constraints, to the poleward edge of the tropical Hadley cell. As a consequence of their different origins, the polar and subtropical jets are separated by both latitude and elevation. However, there are times when these two usually separate features become vertically superposed to form a single, intense jet core designated as a jet superposition or superposed jet. An objective method for identifying tropopause-level jets is employed in the construction of 50-yr cold season (November–March) synoptic climatologies of the Northern Hemisphere polar jet, subtropical jet, and jet superpositions. The analysis demonstrates that while superposition events are relatively rare, there are clear geographical maxima. Superpositions are most frequent in the western Pacific from December through February, with a secondary peak in southern North America and along its eastern seaboard. Consistent with expectations, the spatiotemporal maxima in jet superpositions appear to be coincident with maxima in the polar and subtropical jets.

Stability of the wobbling motion in an odd-mass nucleus and the analysis of Pr135

We apply alternative representations of Holstein-Primakoff boson expansion to the particle-rotor model as useful probes to test the stability and the physical contents of the exact solution. The diagonal representations with the total and single-particle angular momenta along the same axis (longitudinal case) and along two perpendicular axes (transverse case) are employed according to the system with rigid or hydrodynamical moments of inertia (MoI). The longitudinal case gives the normal wobbling mode for rigid MoI, but does not give a stable solution for hydrodynamical MoI. The transverse case applied for hydrodynamical MoI describes a few low spin states with reduced alignment of the total spin in the parallel direction to the single-particle spin, but these states differ from the wobbling mode which involves a quantized unit of rotational angular momentum. Employing the angular-momentum-dependent rigid MoI which is derived from the self-consistent Hartree-Fock-Bogoliubov equation together with angular momentum and particle-number constraints, we obtain good fitting not only to the energy-level scheme, but also to the electromagnetic transition rates and the mixing ratio for $^{135}\mathrm{Pr}$.

A multiple-impact origin for the Moon

The hypothesis of lunar origin by a single giant impact can explain some aspects of the Earth-Moon system. However, it is difficult to reconcile giant impact models with the compositional similarity of the Earth and Moon without violating angular momentum constraints. Furthermore, successful giant impact scenarios require very specific conditions such that they have a low probability of occurring. Here we present numerical simulations suggesting that the Moon could instead be the product of a succession of a variety of smaller collisions. In this scenario, each collision forms a debris disk around the proto-Earth that then accretes to form a moonlet. The moonlets tidally advance outward, and may coalesce to form the Moon. We find that sub-lunar moonlets are a common result of impacts expected onto the proto-Earth in the early solar system and find that the planetary rotation is limited by impact angular momentum drain. We conclude that, assuming efficient merger of moonlets, a multiple impact scenario can account for the formation of the Earth-Moon system with its present properties.

The Response of the Lower Stratosphere to Zonally Symmetric Thermal and Mechanical Forcing

Abstract The response of the atmosphere to zonally symmetric applied heating and mechanical forcing is considered, allowing for the fact that the response may include a change in the wave force (or “wave drag”). A scaling argument shows that an applied zonally symmetric heating is effective in driving a steady meridional circulation provided that the wave force (required to satisfy angular momentum constraints) is sufficiently sensitive to changes in the mean flow in the sense that the ratio is large, where K is a measure of the sensitivity of the wave force; α, N, and f are the radiative damping rate, buoyancy frequency, and Coriolis parameter, respectively; and and are the horizontal and vertical length scales of the heating, respectively. Furthermore, in the “narrow heating” regime where this ratio is large, the structure of the meridional circulation response is only weakly dependent on the details of the wave force. The scaling arguments are verified by experiments in a dry dynamical circulation model. Consistent with the scaling prediction, the regime does not apply when the width of the imposed heating is increased. The narrow-heating regime is demonstrated to be relevant to the double peak in tropical lower-stratospheric upwelling considered in a companion paper, supporting the hypothesis that this feature is radiatively driven. Similar arguments are applied to show that a narrow zonally symmetric applied mechanical forcing is primarily balanced by a change in wave force. This provides an explanation for the recently identified compensation between resolved and parameterized waves in driving modeled trends in the Brewer–Dobson circulation.

A novel study on Kepler’s law and inverse square law of gravitation

The Udwadia–Kalaba equation is a simple, aesthetic, and thought-provoking description of the world at a very fundamental level. It is about the way systems move. In this paper, we creatively apply the Udwadia–Kalaba approach to study heavenly bodies’ movements (especially on Kepler’s law and the inverse square law of gravitation). In an alternative way, we show that a heavenly body’s motion orbit can be an ellipse, a circle, a hyperbola, or a parabola and show the conservation of angular momentum. Furthermore, by applying the Udwadia–Kalaba approach, we use the constraint of motion orbit (ellipse, circle, hyperbola, or parabola) and the conservation of angular momentum constraint (or energy conservation constraint) and easily verify that any heavenly body’s motion complies with the inverse square law of gravitation. That is, we study Kepler’s law and Newton’s inverse square law in an analytical way, which makes the dynamicist more clear about the way heavenly bodies move and also makes the celestial mechanician more clear about the analytical mechanics (the Udwadia–Kalaba approach). Furthermore, for the students of dynamics and celestial physics, a different unique perspective is provided for them to study. At the end, we present the detailed process of applying the Udwadia–Kalaba approach to two imaginary cases to show its simplicity and efficiency.

Bipedal Hopping Pattern Generation for Passively Compliant Humanoids: Exploiting the Resonance

This paper describes a novel technique to analytically generate feasible hopping trajectories that can be applied to passively compliant bipedal humanoid robots. The proposed method is based on exploiting the inherent passive compliance through a reduced model, while the dynamic balance is maintained via the zero moment point (ZMP) criterion. To begin with, a computational resonance frequency analysis and a system identification routine are performed for the actual robot so as to determine the base resonance frequency, which is of special interest. Subsequently, the vertical component of the center of mass trajectory is generated by using a periodic function in which the aforementioned resonance frequency is utilized. The horizontal component of the center of mass trajectory is generated via the ZMP concept to ensure the dynamic balance. Having analytically generated both vertical and horizontal elements of the center of mass trajectory, joint motions are computed through the utilization of translational and angular momentum constraints. Applying the proposed method, a series of periodic forward hopping experiments is conducted on our actual compliant bipedal robot. As a result, we observe repetitive, continuous, and dynamically equilibrated forward hopping cycles with successful landing phases.

OBSERVATIONS OF CHIRAL ODD GPDs AND THEIR IMPLICATIONS

Our original suggestion to investigate exclusive π0 electroproduction as a method for extracting the tensor charge, transversity, and other quantities related to chiral odd generalized parton distributions from cross section and asymmetry data is reviewed. We explain some of the details of the process: i) the connection between the helicity description and the cartesian basis; ii) the dependence on the momentum transfer squared, Q2, and iii) the angular momentum, parity, and charge conjugation constraints (JPC quantum numbers).