Momentum Change Research Articles

Spin–orbit interaction in non-paraxial Gaussian beams and the spin-only measurement of optical torque

A circularly polarized focussed Gaussian beam carries total angular momentum of per photon about the beam axis, but less than spin per photon, due to the focussing of the beam. The remainder of the angular momentum is carried as orbital angular momentum. When such beams are used to rotate microscopic birefringent particles in optical tweezers, the change in angular momentum can be optically measured. However, this measurement is made using the collimated transmitted beam, rather than the focussed beam. Therefore, the conversion of spin to orbital angular momentum by focussing or collimating the beam is expected to affect the measurement. We show that for the typical cases where rotating optical tweezers are used for such measurements, the error due to spin–orbit conversion is unimportant, but there exist cases where a spin-only torque measurement would be completely erroneous.

Effects of Trunk Functional Capacity on the Control of Angular Momentum During Manual Wheelchair Braking

Background: Manual wheelchair braking induces an upper body angular impulse which must be controlled by joint moments to prevent a forward fall. Objective: The purpose of this study was to determine the effects of trunk functional capacity (low, high) on the rate of change in sagittal plane upper body angular momentum during manual wheelchair braking. Methods: Eight wheelchair users (4 low function, 4 high function) completed 10 trials of abrupt wheelchair braking. Trunk segment angles and abdominal joint angles, and normalized upper-body angular impulses were computed for each trial. Linear mixed effects models with initial velocity as a covariate were used to determine differences between groups. Results: The low function group had a higher angular impulse than the high function group with a mean difference (MD) ± SE of 1.59 ± 0.65 N∙m∙s/kg/m2, with a 95% CI 0.287 to 2.89, p = 0.018. The low function group also had a higher trunk segment extension angle, MD = –13.98 degrees, 95% CI: –26.27 to –1.69, p = .027. The low function group employed a greater trunk segment range of motion during braking when compared to the high function group, MD = 12.14 degrees, 95% CI: –24.48 to 0.21, p = 0.054. Lower trunk functional capacity wheelchair users had a higher fall risk during braking. Conclusion: Wheelchair users with less trunk function may be at increased risk of suffering a fall when bringing their wheelchair to an abrupt stop due to an impaired ability to arrest angular momentum.

Correlated Product Distributions in the Photodissociation of à State NO-CH4 and NO-N2 van der Waals Complexes.

This paper reports correlated product distributions for dissociation of the van der Waals complexes NO-CH4 and NO-N2 on their à state surfaces, providing detailed data sets against which calculations can be benchmarked. NO-CH4 dissociation strongly favors small changes in the CH4 angular momentum, with ΔJ = 0 and 1 providing the bulk of the products. Conversely, the associated NO products show little constraint in terms of the rotational angular momentum transfer, with the full range of energetically accessible angular momentum states populated, although the distributions show minima. The lack of angular momentum transfer to methane accompanied by broad, structured, angular momentum transfer to NO gives the NO-CH4 dissociation some qualitative similarities to NO-Rg complex dissociation. In contrast, for NO-N2, the cluster of highest probability products corresponds to high N2 angular momentum and low NO angular momentum, with a sharp drop in the probability for populating the highest energetically accessible J states. For both the NO and N2 products, there appears to be a constraint limiting angular momentum transfer at the highest energetically accessible rotational states. Both complexes show product distributions that include a component attributed to excitation from warm complexes, which provides insight into their internal energies. Interestingly, for NO-N2, the 44,475 cm-1 photolysis translational energy release distribution for N = 8 extends to energies beyond those accessible from the highest bound X̃ states. This indicates either that there are long-lived (>100 μs) states above the X̃ state binding energy or that there is another mechanism that also contributes to this distribution.

Orbits and action changes during star-clump encounters responsible for the origin of exponential discs in dwarf galaxies

ABSTRACT Previous studies found that stellar scattering by massive clumps can lead to the formation of exponential profiles in galaxy discs, but details on how a star is moved around have not been fully explained. We use a gadget-2 simulation where an exponential profile forms from an initially Gaussian disc in about 4 Gyr for a low-mass galaxy like a dwarf irregular. We find that nearly all large angular momentum changes of stars are caused by star-clump encounters with the closest approach less than 0.5 kpc. During star-clump encounters, stars may increase their random motions, resulting in an increase in the average radial and vertical actions of the whole stellar population. The angular momentum change and the radial action change of an individual star are influenced by the direction from which the star approaches a clump. A star initially at a higher galactic radius relative to the scattering clump usually gets pulled inwards and loses its angular momentum during the encounter, and one at a lower radius tends to shift outwards and gains angular momentum. The increase in the radial action is the largest if a star encounters a clump from the azimuthal direction, and is the smallest from a radial approach. The angular momentum change due to encounters has an inward bias when the clump profile has a steep radial decline, and a shallow decline can make the bias outwards. The stellar profile evolution towards an exponential seems to occur regardless of the direction of the bias.

Influence of honeycomb structures on labyrinth seal aerodynamics

Shroud cavities in aero engines are typically formed by a labyrinth seal between the rotating turbine shroud and the stationary casing wall. To mitigate rub-in and reduce weight, the casing often features honeycomb structures above the rotor seal fins. In this paper, the aerodynamic performance of such honeycomb structures is experimentally investigated using a rotating test rig featuring both smooth and honeycomb-tapered casing walls. Measurements show that the discharge coefficient decreases for the honeycomb configuration while losses and subsequent windage heating of the flow increase. A variation in rotational speed reveals additional sensitivities to the local flow field in the swirl chamber. Numerical simulations are conducted and validated using the experiments. A good agreement between the prediction and measurements of the jet via the evolution of pressure across the sealing fins is identified. In contrast, the prediction of losses and integral parameters reveals larger deficits. Empirical correlations from available literature satisfactorily predict the leakage mass flow rate if rotation is low and if the casing is smooth. High rotation and the presence of honeycombs, however, prove challenging and reveal the potential for further improvements. We propose a simple a-posteriori correction that can capture the effect of honeycomb structures on seal discharge by accounting for changes in momentum and flow area.

Momentum based classification for robotic active debris removal

Recent spacecraft collisions with debris and various near misses have highlighted the need for pursuing Active Debris Removal (ADR) of space debris. Robotic manipulators provide a versatile way to capture, detumble, and eventually deorbit the debris. This paper explores the classification of space debris and robotic manipulators based on angular momentum. Previous classifications have considered the tumble rates, size, and orbit of the debris. However, a momentum-based classification gives an additional insight into the method selection for debris removal as shown in this paper. A study on the momentum capture capabilities of previously flown robotic manipulators is performed. This gives an impression of the capabilities of the flight-heritage robotic manipulators for their use in ADR missions. Furthermore, an analysis is also performed on the momentum of cylindrical space debris as it closely represents the spent rocket upper stages which could be prime targets for a robotic ADR mission. The change in momentum due to the tumble rate and inertia is analysed for such cylindrical debris and they are then categorized based on their momentum. These analyses provide the data required to perform a matching of the momentum of the debris with the momentum capabilities of the existing robotic manipulators and thus classify the debris based on momentum. The classification is then applied to real debris objects and the results are discussed. The comparison of the momentum of debris and manipulators is also used to provide input for future manipulator development for ADR missions.

Circumbinary discs for stellar population models

ABSTRACT We develop a rapid algorithm for the evolution of stable, circular, circumbinary discs suitable for parameter estimation and population synthesis modelling. Our model includes disc mass and angular momentum changes, accretion on to the binary stars, and binary orbital eccentricity pumping. We fit our model to the post-asymptotic giant branch (post-AGB) circumbinary disc around IRAS 08544−4431, finding reasonable agreement despite the simplicity of our model. Our best-fitting disc has a mass of about $0.01\, \mathrm{M}_{\odot }$ and angular momentum $2.7\times 10^{52}\, \mathrm{g}\, \mathrm{cm}^{2}\, \mathrm{s}^{-1}\simeq 9 \,\mathrm{M}_{\odot }\, \mathrm{km}\, \mathrm{s}^{-1}\, \mathrm{au}$, corresponding to 0.0079 and 0.16 of the common-envelope mass and angular momentum, respectively. The best-fitting disc viscosity is αdisc = 5 × 10−3 and our tidal torque algorithm can be constrained such that the inner edge of the disc Rin ∼ 2a. The inner binary eccentricity reaches about 0.13 in our best-fitting model of IRAS 08544−4431, short of the observed 0.22. The circumbinary disc evaporates quickly when the post-AGB star reaches a temperature of $\sim \! 6\times 10^4\, \mathrm{K}$, suggesting that planetismals must form in the disc in about $10^{4}\, \mathrm{yr}$ if secondary planet formation is to occur, while accretion from the disc on to the stars at ∼10 times the inner-edge viscous rate can double the disc lifetime.

Stabilized Rotator for Mechatronic Automatic Systems

The aim of the work is to find a mechanical analogue of cyclotron motion and to determine the scheme of the corresponding device, which is appropriate to call a stabilized rotator. From the key circumstance that determines the possibility of generalizing cyclotron motion to mechanics, which consists in the fact that the Lagrangian of an electron is twice as large as its kinetic energy, which, as applied to a stabilized rotator, should be interpreted as the equality of kinetic and potential energies, it follows that the composition of a stabilized rotator should include elements, which are able to store both of these types of energy, namely, the load and the spring. The natural frequency of rotation of a stabilized rotator is strictly fixed (it does not depend on either the moment of inertia or the moment of momentum) and remarkably coincides with the natural frequency of oscillations of a pendulum with identical parameters. When the angular momentum changes, the radius and tangential velocity change (the rotation frequency does not change and is equal to its own). The position of the load, in which its center of mass coincides with the axis of rotation, corresponds to a state of indefinite equilibrium. During rotation, the load can deviate with equal probability in any of the two directions and, accordingly, both compression and extension of the spring can develop. The state of indefinite equilibrium can be eliminated by providing the initial (static) displacement of the load and the initial deformation of the spring equal to it. Just as the frequency does not coincide with the natural frequency during forced oscillations of the pendulum, the rotation frequency of a stabilized rotator under loading does not coincide with the natural rotation frequency. At zero torque in the stationary mode, the rotational speed of the stabilized rotator cannot be arbitrary and takes on a single value. A stabilized rotator can be used to control the natural frequency of a radial oscillator, although in this capacity it may have strong competition from mechatronic systems. On the contrary, as a rotation stabilizer, its competitive capabilities are undeniable and are determined by the extreme simplicity of the design.

A review of atmospheric vortex engines for power generation

A review has been conducted to understand buoyancy-induced vortex flow behaviour, establish control parameters, and to assess the possibility of harnessing kinetic energy in the flow for electricity production. To create and maintain a vortex, a buoyancy force generated by a relatively large heat flux over a large surface area is required, such that warmed air is concentrated at the centre and rise. This flow induces an inward swirl and large angular momentum. These two contributions need to overcome surface friction and ambient shear flow. A single-cell vortex possesses the highest energy flux to circulation strength ratio. Even though a two-cell vortex at the base corner possesses a higher incoming tangential velocity which would translate to a larger change in angular momentum for higher aerodynamic torque, it is less stable due to high shear between the core downdraft and peripheral updraft swirl. The atmospheric vortex engine should be designed and controlled such that the buoyancy vortex can be generated and anchored, the guide vanes and other vortex station features create minimal flow shear, and the vortex stability is minimally affected by the physical presence of the turbine, saturated steam, air influx and energy extraction.

Performance investigation for CRMC and CPM ejectors applied in refrigeration under equivalent ejector geometry by CFD simulation

In this paper, one of the remaining questions for ejector design, “Does the constant rate of momentum change (CRMC) ejector provide better performance than the constant pressure mixing (CPM) ejector under identical ejector area ratio, ejector length, and operating conditions?”, has been answered. Two steam ejector designs operating with the various boiler and evaporator temperatures were simulated by the SST k-omega turbulence model. The present computational fluid dynamics (CFD) model produced a reasonable agreement with our previous published experimental data. The upstream operating conditions were simultaneously considered to assess the better performance ejector design with the help of the primary expansion coefficient. The predicted results revealed that the CRMC ejector showed an advantage in entrainment ratio and a disadvantage in critical condenser pressure. However, the ejector efficiency comparison confirmed that the CRMC ejector design provided better performance than the CPM ejector design for a primary expansion coefficient greater than unity. The maximum percentage improvement of ejector efficiency was 32.418%.

Stellar angular momentum can be controlled from cosmological initial conditions

ABSTRACT The angular momentum of galaxies controls the kinematics of their stars, which in turn drives observable quantities such as the apparent radius, the bulge fraction, and the alignment with other nearby structures. To show how angular momentum of galaxies is determined, we build high (35 pc) resolution numerical experiments in which we increase or decrease the angular momentum of the Lagrangian patches in the early universe. We perform cosmological zoom-in simulations of three galaxies over their histories from z = 200 to z = 2, each with five different choices for the angular momentum (15 simulations in total). Our results show that altering early universe angular momentum changes the timing and orbital parameters of mergers, which in turn changes the total stellar angular momentum within a galaxy’s virial radius in a predictable manner. Of our three galaxies, one has no large satellite at z = 2; in this case, the specific angular momentum is concentrated in the central galaxy. Our changes to the initial conditions result in its stellar angular momentum changing over 0.7 dex (from 61 to ${320}\, {\rm kpc\, km\, s}^{-1}$) at z = 2. This causes its effective radius to grow by 40 per cent, its v/σ parameter to grow by a factor of 2.6, and its bulge fraction to decrease from 0.72 to 0.57. This proof of concept illustrates how causal studies can contribute to a better understanding of the origin of galaxy scaling relations and intrinsic alignments.

Mechanism of Ultrafast Triplet Exciton Formation in Single Cocrystals of π-Stacked Electron Donors and Acceptors.

Ultrafast triplet formation in donor-acceptor (D-A) systems typically occurs by spin-orbit charge-transfer intersystem crossing (SOCT-ISC), which requires a significant orbital angular momentum change and is thus usually observed when the adjacent π systems of D and A are orthogonal; however, the results presented here show that subnanosecond triplet formation occurs in a series of D-A cocrystals that form one-dimensional cofacial π stacks. Using ultrafast transient absorption microscopy, photoexcitation of D-A single cocrystals, where D is coronene (Cor) or pyrene (Pyr) and A is N,N-bis(3'-pentyl)-perylene-3,4:9,10-bis(dicarboximide) (C5PDI) or naphthalene-1,4:5,8-tetracarboxydianhydride (NDA), results in formation of the charge transfer (CT) excitons Cor•+-C5PDI•-, Pyr•+-C5PDI•-, Cor•+-NDA•-, and Pyr•+-NDA•- in <300 fs, while triplet exciton formation occurs in τ = 125, 106, 484, and 958 ps, respectively. TDDFT calculations show that the SOCT-ISC rates correlate with charge delocalization in the CT exciton state. In addition, time-resolved EPR spectroscopy shows that Cor•+-C5PDI•- and Pyr•+-C5PDI•- recombine to form localized 3*C5PDI excitons with zero-field splittings of |D| = 1170 and 1250 MHz, respectively. In contrast, Cor•+-NDA•- and Pyr•+-NDA•- give triplet excitons in which |D| is only 1240 and 690 MHz, respectively, compared to that of NDA (2091 MHz), which is the lowest energy localized triplet exciton, indicating that the Cor-NDA and Pyr-NDA triplet excitons have significant CT character. These results show that charge delocalization in CT excitons impacts both ultrafast triplet formation as well as the CT character of the resultant triplet states.

Quantum phase transition in the one-dimensional Dicke-Hubbard model with coupled qubits

We study the ground state phase diagram of a one-dimensional two qubits Dicke-Hubbard model with XY qubit-qubit interaction. We use a numerical method combing the cluster mean-field theory and the matrix product state(MPS) to obtain the exact wave function of the ground state. When counter-rotating wave terms(CRTs) in the qubit-cavity coupling are neglected, we observe a rich phase diagram including a quantum phase transition between the Mott-insulating phase and the superfluid phase. This phase transition can be either the first-order or the second-order type depending on whether the total angular momentum changes across the phase diagram. Moreover, we observe two quantum triple points, at which three different phases coexist, with both positive and negative XY interactions. By further considering the effect of CRTs, we find that the main feature in the previous phase diagram, including the existence of quantum triple points, is retained. We also show that CRTs extremely demolish the non-local correlations in the coherent phase.

Study of eccentric binaries in Horndeski gravity

We study the orbital evolution of eccentric binary systems in Horndeski gravity. This particular theory provides a testbed to give insightful comparisons with data. We compute the rate of energy loss and the rate of change of angular momentum for the binaries by calculating the multipole moments of the radiation fields. We have used appropriate parameters for the eccentric binaries to compute the decay rates of its orbital eccentricity and semi-major axis. We then compare this decay rate with that of GR.

Speed Self-Stabilization

The aim of the work is to find a mechanical analogue of cyclotron motion and to determine the scheme of the corresponding device, which is appropriate to call a stabilized rotator. From the key circumstance that determines the possibility of generalizing cyclotron motion to mechanics, which consists in the fact that the Lagrangian of an electron is twice as large as its kinetic energy, which, as applied to a stabilized rotator, should be interpreted as the equality of kinetic and potential energies, it follows that the composition of a stabilized rotator should include elements, which are able to store both of these types of energy, namely, the load and the spring. The natural frequency of rotation of a stabilized rotator is strictly fixed (it does not depend on either the moment of inertia or the moment of momentum) and remarkably coincides with the natural frequency of oscillations of a pendulum with identical parameters. When the angular momentum changes, the radius and tangential velocity change (the rotation frequency does not change and is equal to its own). The position of the load, in which its center of mass coincides with the axis of rotation, corresponds to a state of indefinite equilibrium. During rotation, the load can deviate with equal probability in any of the two directions and, accordingly, both compression and extension of the spring can develop. The state of indefinite equilibrium can be eliminated by providing the initial (static) displacement of the load and the initial deformation of the spring equal to it. Just as the frequency does not coincide with the natural frequency during forced oscillations of the pendulum, the rotation frequency of a stabilized rotator under loading does not coincide with the natural rotation frequency. At zero torque in the stationary mode, the rotational speed of the stabilized rotator cannot be arbitrary and takes on a single value. A stabilized rotator can be used to control the natural frequency of a radial oscillator, although in this capacity it may have strong competition from mechatronic systems. On the contrary, as a rotation stabilizer, its competitive capabilities are undeniable and are determined by the extreme simplicity of the design.

Changes in orbital angular momentum distribution of a twisted partially coherent array beam in anisotropic turbulence.

Based on the generalized Huygens Fresnel integral, we derive the analytical formula of the cross-spectral density of a twisted partially coherent array beam propagating in non-Kolmogorov anisotropic turbulence, and investigate the changes in orbital angular momentum (OAM). The results show that the anisotropy of the turbulence causes different effects in horizontal and vertical directions. The spectral density distribution of twisted partially coherent array beam in turbulence presents self-splitting and rotation, which combines the interesting effects of the twist phase and coherent structure. Although OAM is conserved, the spatial distribution of OAM flux density can be changed by changing the propagation distance, power and anisotropy of turbulence, and the modulation of the twist phase affects not only the magnitude of OAM but also its distribution. Our work is helpful for exploring new forms of OAM sources, and promote the application of free-space optical communications and optical field modulation.

Chiral effects in classical spinning gas

We consider a statistical mechanics of rotating ideal gas consisting of classical non-relativistic spinning particles. The microscopic structure elements of the system are massive point particles with a nonzero proper angular momentum. The norm of proper angular momentum is determined by spin. The direction of proper angular momentum changes continuously. Applying the Gibbs canonical formalism for the rotating system, we construct the one-particle distribution function, generalising the usual Maxwell–Boltzmann distribution, and the partition function of the system. The model demonstrates a set of chiral effects caused by interaction of spin and macroscopic rotation, including the change of entropy, heat capacity, chemical potential and angular momentum.

Experimental investigation of 40 kW[formula omitted] methane-assisted and self-sustained pulverized biomass flames

This paper presents an assessment of the effects of methane assistance on pulverized biomass swirl flames specifically regarding flow fields and flame structure. Experiments are carried out using a pilot-scale down-fired cylindrical combustion chamber equipped with a swirl burner and biomass/methane fuel mixtures. Studied conditions have an identical thermal output of 40 kW, with the thermal output share of methane gradually decreasing from 50% to 0% while the biomass share (walnut shells) increased from 50% to 100% (self-sustained condition). A detailed flow field characterization of the respective flames is conducted by in-flame, two-dimensional laser Doppler velocimetry measurements. These measurements are complemented by narrow-band flame imaging conducted at two different wavelengths (OH* and CH* radical band heads). Results show that the methane flames have a significant influence on the ignition and the determination of the flame flow field structure, including higher peak and overall velocities, as well as major changes in the ratio of tangential over axial velocity component. Further on, flame attachment of the self-sustained flame can be permanently achieved by the initial, short-term assistance of a methane flame with comparatively low thermal output. These observations are analysed and discussed, where higher measured velocities and overall changes in the flame structure between the self-sustained and the methane-assisted flames are attributed to important local expansion and momentum changes of the combustion gases introduced by the combustion of methane.

Versatile Tool for Parametric Smooth Turbomachinery Blades

Designing blades for efficient energy transfer by turning the flow and angular momentum change is both an art and iterative multidisciplinary engineering process. A robust parametric design tool with few inputs to create 3D blades for turbomachinery and rotating or non-rotating energy converters is described in this paper. The parameters include axial–radial coordinates of the leading/trailing edges, construction lines (streamlines), metal angles, thickness-to-chord ratio, standard, and user-defined airfoil type among others. Using these, 2D airfoils are created, conformally mapped to 3D stream surfaces, stacked radially with multiple options, and they are transformed to a 3D Cartesian coordinate system. Smooth changes in blade curvature are essential to ensure a smooth pressure distribution and attached flow. B-splines are used to control meanline curvature, thickness, leading edge shape, sweep-lean, and other parameters chordwise and spanwise, making the design iteration quick and easy. C2 curve continuity is achieved through parametric segments of cubic and quartic B-splines and is better than G2. New geometries using an efficient parametric scheme and minimal CAD interaction create watertight solid bodies and optional fluid domains. Several examples of ducted axial and radial turbomachinery with special airfoil shapes or otherwise, unducted rotors including propellers and wind and hydrokinetic turbines are presented to demonstrate versatility and robustness of the tool and can be easily tied to any automation chain and optimizer.

Optimal Estimation of Conjugate Shifts in Position and Momentum by Classically Correlated Probes and Measurements

Multiparameter estimation is necessary for force sensing due to simultaneous and nontrivial small changes of position and momentum. The design of quantum probes that allow simultaneous estimation of all parameters is therefore an important task. The optimal methods for estimation of the conjugate changes of position and momentum of quantum harmonic oscillator employ probes in entangled or quantum non-Gaussian states. We show that the same results can be obtained in a significantly more feasible fashion by employing independent sets of differently squeezed Gaussian states classically correlated with position or momentum measurements. This result demonstrates an unexplored power of a classical correlation between the probe states and measurements directly applicable to force sensing.