Conservation Of Angular Momentum Research Articles

Weak (non)conservation and stochastic dynamics of angular momentum

Angular momentum conservation influences equilibrium statistical mechanics, leading to a generalized microcanonical density for an isolated system and a generalized Gibbs density for a weakly coupled system. We study the stochastic decay of angular momentum due to the weakly imperfect rotational symmetry of the external potential that confines the isolated many-particle system. We present a mesoscopic description of the system, deriving Langevin and Fokker–Planck equations, which are consistent with equilibrium statistical mechanics when rotational symmetry is maintained. When the symmetry is weakly violated, we formulate a coarse-grained stochastic differential equation governing the decay of total angular momentum over time. To validate our analytical predictions, we conduct numerical simulations of the microcanonical ensemble, an isolated system undergoing thermalization due to weak two-body interactions. Our coarse-grained Langevin equation accurately characterizes both the decay of the angular momentum and its fluctuations in a steady state. Furthermore, we estimate the parameters of our mesoscopic model directly from simulations, providing insights into the dissipative phenomenological coefficients, such as friction. More generally, this study contributes to a deeper understanding of the behavior of the integrals of motion when the corresponding symmetry is weakly violated.

Spatial Mode conversion of a Reflected Polarized Beam from an Isotropic Medium at Brewster angle

Abstract In this study, the spatial mode evolution of a chiral polarized beam during
reflection on an isotropic medium surface at Brewster angle is both theoretically and
experimentally investigated. In this process, the topological charge of the reflection
field’s horizontal component increases (decreases) by one, relative to the specific left
(right) elliptical polarization incident beam. While incident li-order vortex beam is in
a certain polarization state, the intensity distribution of the reflection field’s horizontal
component appears as the interference pattern of the li±1-order output vortex beams.
The conversion occurs between the spin and orbital angular momentum and does not
violate the conservation of the total angular momentum. We explain the physical
mechanism of this phenomenon using phase shift theorem, and analyze the effect of
ellipticity and polarization angle on this physical phenomenon.

Shooting stars on schedule: synchronising re-entry of particles launched from a satellite

Abstract The ALE-3 mission plans to create artificial “shooting stars” in the upper atmosphere by launching pellets sequentially from a satellite in low Earth orbit. How does one arrange for all pellets to re-enter over the intended location simultaneously? Starting with conservation of energy and angular momentum, I derive a version of Kepler’s equation that gives time as a function of radial distance in an orbit, which can be used to find the transfer time from the pellet’s ejection to its re-entry as a function of its launch velocity. I show that for a given pellet ejection speed, there is a launch angle from the satellite that results in the fastest transfer time. I use these results to determine the pellets’ launch times and velocities for simultaneous arrival at a desired re-entry point. These results can be applied to de-orbiting any set of objects launched from a satellite, and use concepts that can be covered in an advanced undergraduate course in physics or aerospace engineering. Supplementary materials are provided online.

Three-body binary formation in clusters: analytical theory

ABSTRACT Binary formation in clusters through triple encounters between three unbound stars, ‘three-body’ binary formation, is one of the main dynamical formation processes of binary systems in dense environments. In this paper, we use an analytical probabilistic approach to study the process for the equal mass case and calculate a probability distribution for the orbital parameters of three-body-formed binaries, as well as their formation rate. For the first time, we give closed-form analytical expressions to the full orbital parameter distribution, accounting for both energy and angular momentum conservation. This calculation relies on the sensitive dependence of the outcomes of three-body scatterings on the initial conditions: here we compute the rate of three-body binaries from ergodic interactions, which allow for an analytical derivation of the distribution of orbital parameters of the binaries thus created. We find that soft binaries are highly favoured in this process and that these binaries have a superthermal eccentricity distribution, while the few hard three-body binaries have an eccentricity distribution much closer to thermal. The analytical results predict and reproduce simulation results of three-body scattering experiments in the literature well.

Large time existence and asymptotic stability of the generalized solution to flow and thermal explosion model of reactive real micropolar gas

We study the long time behavior of the generalized solution of the flow and thermal explosion model of the reactive real micropolar gas. The dynamics of the chemical reaction involved and the usual laws of conservation of mass, momentum, angular momentum, and energy generate a complex governing system of partial differential equations. The fluid is nonideal and non‐Newtonian. In this work, we prove that the problem can be solved in an infinite time domain and establish the asymptotic properties of the solution. Namely, we conclude that for certain parameter values, the solution stabilizes exponentially to a steady‐state solution, while for others the stabilization occurs but at power decay rate. At the end, we conducted a few numerical tests whereby we experimentally confirmed theoretical findings about long‐term behavior of the solution.

Conservation of Angular Momentum with a 3D-Printed Launcher

Conservation of Angular Momentum with a 3D-Printed Launcher

Dynamics of charged particles in a solenoid and the accurate determination of the magnetic axis of a solenoid using measured field data.

A fundamental understanding of the theory and measurement procedures for characterizing a solenoid is crucial for making a project cost-effective and achieving the desired performance for its use in a LINAC. This paper attempts to comprehend the beam dynamics of charged particles by considering the conservation of canonical angular momentum, which can take on positive, negative, and zero values. The analytical expression to generate a parallel beam using a solenoid is derived. The effect of the final beam size on the values of a solenoid's spherical aberration coefficient and the position of the minimum beam size with respect to the focal length is studied using electron trajectories. A practical procedure to tune the above two parameters of a solenoid is demonstrated by simply modifying the demountable disks connected at each end. A mathematical model is proposed to accurately determine the axis of a solenoid and the magnetic centre using the measured magnetic field data, which is validated experimentally. Several solenoids, used in the 9.5MeV 10kW electron LINAC suitable for sterilizing medical products and food irradiation, have been characterised using this procedure.

Efficient multimode vectorial nonlinear propagation solver beyond the weak guidance approximation

In this paper, we present an efficient numerical model able to solve the vectorial nonlinear pulse propagation equation in circularly symmetric multimode waveguides. The algorithm takes advantage of the conservation of total angular momentum of light upon propagation and takes into account the vectorial nature of the propagating modes, making it particularly relevant for studies in ring-core fibers. While conventional propagation solvers exhibit a computational complexity scaling as Nmode4, where Nmode is the number of considered modes, the present solver scales as Nmode3/2. As a first example, it is shown that orbital angular momentum modulation instability processes take place in ring-core fibers in realistic conditions. Finally, it is predicted that the modulation instability process is followed by the appearance of breather-like angular structures.

The torsion of stellar streams and the overall shape of galactic gravity's source

Flat rotation curves, $v(r)$, are naturally explained by elongated (prolate) dark matter (DM) distributions, and we have provided competitive fits to the SPARC database. To further probe the geometry of the halo, or the equivalent source of gravity in other formulations, one needs observables outside the galactic plane. Stellar streams, poetically analogous to airplane contrails, but caused by tidal dispersion of massive substructures such as satellite dwarf galaxies, would lie on their own plane (consistently with angular momentum conservation) should the DM-halo gravitational field be spherically symmetric. Tracks resembling entire orbits are seldom available because their periods are commensurable with Hubble time, with streams often presenting themselves as short segments. Therefore, we aim to establish stellar stream torsion, a local observable that measures the deviation from planarity in differential curve geometry, as a diagnostic providing sensitivity to aspherical DM distributions and ensuring the use of even relatively short streams. We performed small-scale simulations of tidally distorted star clusters to check that indeed a central force center produces negligible torsion, while distorted halos can generate it. Turning to observational data, we identified among the known streams those that are at the largest distance from the Galactic center, and that are likely not affected by the Magellanic clouds, as the most promising for the study, and by means of polynomial fits we extracted their differential torsion. We find that the torsion of the few known streams that should be sensitive to most of the Milky Way's DM halo is much larger than expected for a central spherical bulb alone. This is consistent with the nonsphericity of the halo. Future studies of stellar stream torsion with larger samples and further out of the galactic plane should be able to extract the ellipticity of the halo to see whether it is just a slight distortion of a spherical shape or whether it rather resembles a more elongated cigar.

Modeling the secular evolution of embedded protoplanetary disks

Protoplanetary disks are known to form around nascent stars from their parent molecular cloud as a result of angular momentum conservation. As they progressively evolve and dissipate, they also form planets. While a lot of modeling efforts have been dedicated to their formation, the question of their secular evolution, from the so-called class 0 embedded phase to the class II phase where disks are believed to be isolated, remains poorly understood. We aim to explore the evolution between the embedded stages and the class II stage. We focus on the magnetic field evolution and the long-term interaction between the disk and the envelope. We used the GPU accelerated code Idefix to perform a 3D, barotropic, non ideal magnetohydrodynamic (MHD) secular core collapse simulation that covers the system evolution from the collapse of the pre-stellar core until $100 \ kyr $ after the first hydrostatic core formation and the disk settling while ensuring sufficient vertical and azimuthal resolutions (down to $10^ $ au) to properly resolve the disk internal dynamics and non axisymmetric perturbations. The disk evolution leads to a power-law gas surface density in Keplerian rotation that extends up to a few $10 \ au $. The magnetic flux trapped in the disk during the initial collapse decreases from $100 \ mG $ at disk formation down to $1 \ mG $ by the end of the simulation. After the formation of the first hydrostatic core, the system evolves in three phases. A first phase with a small ($ au $), unstable, strongly accreting ($ disk that loses magnetic flux over the first $15 \ kyr $, a second phase where the magnetic flux is advected with a smooth, expanding disk fed by the angular momentum of the infalling material, and a final phase with a gravitationally regulated $ au $ disk accreting at at few $10^ The initial isotropic envelope eventually feeds large-scale vertically extended accretion streamers, with accretion rates similar to that onto the protostar ($ Some of the streamer material collides with the disk's outer edge and produces accretion shocks, but a significant fraction of the material lands on the disk surface without producing any noticeable discontinuity. While the initial disk size and magnetization are set by magnetic braking, self-gravity eventually drives accretion, so that the disk ends up in a gravitationally regulated state. This evolution from magnetic braking to self-gravity is due to the weak coupling between the gas and the magnetic field once the disk has settled. The weak magnetic field at the end of the class I phase ($B_z mG $) is a result of the magnetic flux dilution in the disk as it expands from its initial relatively small size. This expansion should not be interpreted as a viscous expansion, as it is driven by newly accreted material from large-scale streamers with large specific angular momentum.

Dynamical complexity in microscale disk-wind systems

Powerful winds at accretion-disk scales have been observed in the past 20 years in many active galactic nuclei (AGN). These are the so-called ultrafast outflows (UFOs). Outflows are intimately related to mass accretion through the conservation of angular momentum, and they are therefore a key ingredient of most accretion disk models around black holes (BHs). At the same time, nuclear winds and outflows can provide the feedback that regulates the joint BH and galaxy growth. We reconsidered UFO observations in the framework of disk-wind scenarios, both magnetohydrodynamic disk winds and radiatively driven winds. We studied the statistical properties of observed UFOs from the literature and derived the distribution functions of the ratio $ of the mass-outflow and -inflow rates and the ratio $ of the mass-outflow and the Eddington accretion rates. We studied the links between $ and $ and the Eddington ratio $ L_ bol L_ Edd $. We derived the typical wind-activity history in our sources by assuming that it can be statistically described by population functions. We find that the distribution functions of $ and $ can be described as power laws above some thresholds, suggesting that there may be many wind subevents for each major wind event in each AGN activity cycle, which is a fractal behavior. We then introduced a simple cellular automaton to investigate how the dynamical properties of an idealized disk-wind system change following the introduction of simple feedback rules. We find that without feedback, the system is overcritical. Conversely, when feedback is present, regardless of whether it is magnetic or radiation driven, the system can be driven toward a self-organized critical state. Our results corroborate the hypothesis that AGN feedback is a necessary key ingredient in disk-wind systems, and following this, in shaping the coevolution of galaxies and supermassive BHs.

Time-varying optical spin-orbit Hall effect in tightly focused femtosecond optical field.

The spin-orbit Hall effect (HE) is dominated by the law of conservation of angular momentum of a beam and is highly significant in light-matter interactions. The electromagnetic field, phase, topological structure, and spin-orbit HE of an azimuthally polarized vortex pulse beam in a tightly focused system are studied theoretically here. Calculations show that the focal field has ultrafast bright-dark alternating characteristics and a distorted phase distribution. Furthermore, the time evolution of the polarization singularity in the focused light field is explained using Stokes parameters. Importantly, the spin-orbit HE of the pulsed beam is shown to be time-varying in a tightly focused system. This time-varying spin-orbit HE is particularly sensitive to the pulse width and central wavelength. Our method has important applications in particle manipulation.

Relative Motion Estimation Algorithm for Noncooperative Targets Considering Multiple Solutions of Rotational Parameters.

On-orbit servicing using a space robot is gaining popularity among the space community for both economic and safety aspects. In particular, the estimation of the relative motion of a noncooperative target is a challenging problem. This study presents a relative motion estimation scheme based on stereovision for noncooperative targets considering multiple solutions of rotational parameters. Specifically, the mass distribution of the target is identified based on the least-square method and the principle of conservation of angular momentum. Then, the determination of a unique principal axis coordinate frame of the target is employed to resolve the multiple-solution problem. In addition, an EKF (extended Kalman filter)-based filter with global observability is designed to estimate the full motion states and inertia parameters of the target. The convergence performance of the proposed method is verified by numerical simulation. The results also demonstrate that the method is robust to occlusion.

Simulation of Human Movement in Zero Gravity.

In the era of expanding manned space missions, understanding the biomechanical impacts of zero gravity on human movement is pivotal. This study introduces a novel and cost-effective framework that demonstrates the application of Microsoft's Azure Kinect body tracking technology as a motion input generator for subsequent OpenSim simulations in weightlessness. Testing rotations, locomotion, coordination, and martial arts movements, we validate the results' realism under the constraints of angular and linear momentum conservation. While complex, full-body coordination tasks face limitations in a zero gravity environment, our findings suggest possible approaches to device-free exercise routines for astronauts and reveal insights into the feasibility of hand-to-hand combat in space. However, some challenges remain in distinguishing zero gravity effects in the simulations from discrepancies in the captured motion input or forward dynamics calculations, making a comprehensive validation difficult. The paper concludes by highlighting the framework's practical potential for the future of space mission planning and related research endeavors, while also providing recommendations for further refinement.

Indicating the direction in conservation of angular momentum

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

Fluid–rigid body coupling simulations with the passively moving solid model based on a physically consistent particle method

Fluid–rigid body interaction is a significant topic in research on particle methods. This study developed a fluid–rigid body coupling method based on a physically consistent particle method, i.e., the moving particle hydrodynamics (MPH) method, incorporating the passively moving solid (PMS) model. When the discrete particle system satisfies the fundamental laws of physics, i.e., mass conservation, linear and angular momentum conservation, and the second law of thermodynamics, the method is asserted physically consistent, and this feature is important for robust dynamic calculations. The PMS model is a pioneering approach that is practical for particle methods in which fluid and rigid-body particles are initially calculated as a fluid. Then, only rigid-body particles are modified to restore the initial shape by applying rigid-body constraints. Thus, combining the MPH method and the PMS model realizes a fluid–rigid body coupling method that satisfies fundamental physical laws. The proposed method was first verified via the fundamental rigid body and fluid–rigid body coupling problems: the Dzhanibekov effect on a T-shaped rigid body, a floating rectangular solid, a floating cylinder, and water entry of a two-dimensional cylinder. Second, the proposed method was validated via calculating a cylinder rolling on a liquid film as a fluid–rigid body coupling problem with rotation. By using a potential-based surface tension model, the computed results showed reasonable agreement with the experimental data obtained in this study. Overall, it was confirmed that the proposed method is a promising fluid–rigid body coupling approach, in which the surface tension and wettability can be considered as well.

Particle nature of the photonic spin Hall effect.

It is widely recognized that light exhibits a wave-particle duality. However, the explanation for the photonic spin Hall effect (PSHE) primarily relies on the wave nature of light as dictated by Maxwell's Equations. There is a lack of exploration into the particle nature of light in this regard. In this context, we offer a fresh interpretation of the PSHE from the perspective of particle nature of light. For the out-of-plane PSHE, the spin shifts result from the macroscopic manifestation of the conservation of spin-orbital angular momentum of one photon. For the in-plane PSHE, the spin shifts arise from the spread of in-plane wavevector. Based on the wave nature of light, we also obtain the same spin shifts, confirming the consistency of the wave-particle duality of light. Furthermore, we find that the spin shifts of the PSHE are not the overall displacement of photons with the same handedness, but the outcome of coherent superposition among photons of the same handedness. These discoveries further enhance our comprehension of the fundamental nature of the PSHE.

A slowly evolving conical pendulum

The idea of this work originally arose from a question pertaining to a laboratory experiment on circular motion in our departmental lab manual. The experiment itself involves rotating a bob along a horizontal circle (Figure 1), where the tension in the string attached to the bob provides the centripetal acceleration of the bob, the string itself passing through a smooth vertical pipe. It is assumed that the rotation is fast enough for the effect of gravity to be neglected and therefore the orientation of the part of the string between the top end of the pipe and the bob can be taken to be horizontal. The abovementioned question enquires what happens to the speed of the bob in the case that the bottom end of the string is hand-held and pulled slowly so that the radius of the circular orbit decreases. The answer to the question is straightforward. Either a work-energy argument or an argument involving the conservation of angular momentum provides the same correct answer.

Inhomogeneity of the Ideal Gas of a Finite Number of Particles with Angular Momentum Conservation

We continue to study various aspects of the behavior of a classical ideal gas in a stationary axisymmetric container. The symmetry of the vessel leads to the conservation of the gas’s angular momentum and, hence, the state of gas rotation. We consider the case of a nonrotating two-dimensional gas of a finite number of colliding particles. In this case, the gas statistical distributions differ from the classical ones found in the nineteenth century. We will show that the filling of the axisymmetric vessel with a nonrotating gas is not uniform and provide the exact spatial distribution of gas particles. This previously unknown distribution depends on all the particle masses and is found explicitly. The absence of a rotation in gas layers is shown through the investigation of the distributions of the tangential components of particle momenta. We also show that, for any number of particles in a container, the behavior of a massive enough particle may be unusual. The analytic results are confirmed by simple numerical experiments.

Total angular momentum conservation in Ehrenfest dynamics with a truncated basis of adiabatic states.

We show that standard Ehrenfest dynamics does not conserve linear and angular momentum when using a basis of truncated adiabatic states. However, we also show that previously proposed effective Ehrenfest equations of motion [M. Amano and K. Takatsuka, "Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions," J. Chem. Phys. 122, 084113 (2005) and V. Krishna, "Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum classical limit," J. Chem. Phys. 126, 134107 (2007)] involving the non-Abelian Berry force do maintain momentum conservation. As a numerical example, we investigate the Kramers doublet of the methoxy radical using generalized Hartree-Fock with spin-orbit coupling and confirm that angular momentum is conserved with the proper equations of motion. Our work makes clear some of the limitations of the Born-Oppenheimer approximation when using abinitio electronic structure theory to treat systems with unpaired electronic spin degrees of freedom, and we demonstrate that Ehrenfest dynamics can offer much improved, qualitatively correct results.