Angular Fluctuations Research Articles

Research on Precise Attitude Measurement Technology for Satellite Extension Booms Based on the Star Tracker

This paper reports the successful application of a self-developed, miniaturized, low-power nano-star tracker for precise attitude measurement of a 5-m-long satellite extension boom. Such extension booms are widely used in space science missions to extend and support payloads like magnetometers. The nano-star tracker, based on a CMOS image sensor, weighs 150 g (including the baffle), has a total power consumption of approximately 0.85 W, and achieves a pointing accuracy of about 5 arcseconds. It is paired with a low-cost, commercial lens and utilizes automated calibration techniques for measurement correction of the collected data. This system has been successfully applied to the precise attitude measurement of the 5-m magnetometer boom on the Chinese Advanced Space Technology Demonstration Satellite (SATech-01). Analysis of the in-orbit measurement data shows that within shadowed regions, the extension boom remains stable relative to the satellite, with a standard deviation of 30′′ (1σ). The average Euler angles for the “X-Y-Z” rotation sequence from the extension boom to the satellite are [−89.49°, 0.08°, 90.11°]. In the transition zone from shadow to sunlight, influenced by vibrations and thermal factors during satellite attitude adjustments, the maximum angular fluctuation of the extension boom relative to the satellite is approximately ±2°. These data and the accuracy of the measurements can effectively correct magnetic field vector measurements.

The Jittering Jets Explosion Mechanism in Electron Capture Supernovae

We conduct one-dimensional stellar-evolution simulations of stars with zero-age main-sequence (ZAMS) masses of M ZAMS = 8.8 − 9.45 M ⊙ toward core collapse by electron capture and find that the convective zone of the precollapse core can supply the required stochastic angular momentum fluctuations to set a jet-driven electron capture supernova explosion in the frame of the jittering jets explosion mechanism. By our assumed criteria of a minimum convective specific angular momentum and an accreted mass during jet launching of M acc ≃ 0.001−0.01 M ⊙, the layer in the convective zone that when accreted launches the exploding jittering jets resides in the helium-rich zone. Depending on the model, this exploding layer is accreted at about a minute to a few hours after core collapse occurs, much shorter than the time the exploding shock crosses the star. The final (gravitational) mass of the neutron star (NS) remnant is in the range of M NS = 1.25−1.43 M ⊙.

Stochastic modulation of the Montgomery’s rings to generate the self-imaging effect with revival features

The synthesis of optical fields that follows a stochastic process and whose statistical mean values generate the self-imaging-revivals effect is analyzed. A sufficient condition for optical fields to exhibit the self-imaging effect occurs when the frequency representation is located on the Montgomery’s rings. The study is performed by implementing stationary random fluctuations on the Montgomery’s rings of additive and multiplicative types. The additive noise is of the stochastic radial walk type with zero mean. Multiplicative noise generates stochastic angular fluctuations in the rings and is implemented using the Karhunen–Loève theorem. The modal representation implicit in the theorem is obtained by interpreting the self-imaging planes as an optical cavity, assuring the statistical periodicity of the noise. A time consonance of the random fluctuations for each ring allows to determine the revivals period for the self-imaging optical fields. The model is corroborated by computer simulations.

A novel 3-DOF active vibration isolation method for TBM’s laser target

In the process of full-face tunnel boring machine (TBM) tunneling, pitch angle measurement accuracy of the laser target is greatly reduced by low frequency vibrations with large amplitude and multiple degrees of freedom. In order to improve pitch angle measurement accuracy of laser target under vibration, a three-degree-of-freedom (3-DOF) active vibration isolation system is designed in this paper. A plate-type voice coil motor with large air gap and large thrust is designed based on genetic algorithm. In order to increase damping of the vibration isolation system, an eddy current damper is designed by combining copper plate and permanent magnet of the voice coil motor. An active vibration isolation device for laser target was built by using the designed plate-type voice coil motor and eddy current damper, and the dynamic model of the system was established. Aiming at control and stability problems caused by the nonlinear factors, a High-Frequency sliding mode controller which can ensure system asymptotically stable is designed in this paper. A 1–30 Hz sinusoidal sweep excitation experiment was performed on a shaking table. The experimental results show that the active vibration isolation system has a good damping effect. The root mean square (RMS) of acceleration in Y direction can be attenuated by 90.5%, in Z direction can be attenuated by 95.8%. The active isolation system effectively attenuates the vibration transmitted to the laser target, and pitch angular fluctuation of the laser target is reduced by 75.8%. The designed active vibration isolation system improves the pitch angle measurement accuracy of the laser target.

A Fokker–Planck Framework for Studying the Variability of the Magnetic Field Direction in the Alfvénic Streams of the Solar Wind

Turbulent rotations of the magnetic field vector are observed in the Alfvénic streams of the solar wind where the magnetic field strength remains close to a constant. They can lead to reversals of the radial magnetic field component or switchbacks. It is not ruled out from the data that the rotations are divisible into the sum of small random angular deflections. In this work, we develop tools aimed at the analysis of the one-point statistical properties of the directional fluctuations of the magnetic field vector in the solar wind. The angular fluctuations are modeled by a drift-diffusion process which admits the exponential distribution as steady-state solution. Realizations of the stochastic process are obtained by solving the corresponding Langevin equation. It is shown that the cumulative effects of consecutive small-angle deflections can yield frequent reversals of the magnetic field vector even when the concentration parameter of the directional data is large. The majority of the rotations are associated with nearly transverse magnetic field fluctuations in this case.

Fallback onto kicked neutron stars and its effect on spin-kick alignment

ABSTRACT Fallback in core-collapse supernova explosions is potentially of significant importance for the birth spins of neutron stars and black holes. It has recently been pointed out that the angular momentum imparted onto a compact remnant by fallback material is subtly intertwined with its kick because fallback onto a moving neutron star or black hole will preferentially come for a conical region around its direction of travel. We show that contrary to earlier expectations such one-sided fallback accretion onto a neutron star will tend to produce spin-kick misalignment. Since the baroclinic driving term in the vorticity equation is perpendicular to the nearly radial pressure gradient, convective eddies in the progenitor as well as Rayleigh–Taylor plumes growing during the explosion primarily carry angular momentum perpendicular to the radial direction. Fallback material from the accretion volume of a moving neutron star therefore carries substantial angular momentum perpendicular to the kick velocity. We estimate the seed angular momentum fluctuations from convective motions in core-collapse supernova progenitors and argue that accreted fallback material will almost invariably be accreted with the maximum permissible specific angular momentum for reaching the Alfvén radius. This imposes a limit of ${\sim }10^{-2}\, \mathrm{M}_\odot$ of fallback accretion for fast-spinning young neutron stars with periods of ${\sim }20\, \mathrm{ms}$ and less for longer birth spin periods.

A Hydraulic Axial Piston Pump Fault Diagnosis Based on Instantaneous Angular Speed under Non-Stationary Conditions

Due to the intense noise interference in hydraulic systems, it is extremely difficult to detect component faults through vibration signals. Diagnostic performance is also constrained by highly time-varying and non-stationary operating conditions. This study proposes to use instantaneous angular speed (IAS) signals that are both operational and state parameters as sources of information. Firstly, the instantaneous angular speed fluctuation (IASF) of a piston pump is analyzed theoretically, and it is concluded that its fluctuating components contain the health status information of the components. The IASF can then be obtained by subtracting the speed trend term from IAS signals obtained via a magneto-electric speed sensor. A synchro-extraction of the normal S transform (SNST) is proposed to process it via line-pass filtering. Finally, the filtered and reconstructed IASF signal is utilized to draw a two-dimensional polar coordinate map online. A non-stationary-condition test is carried out on the test platform to monitor the morphological characteristics of the valve plate under normal, slight, and severe wear conditions. The polar plot shows significant increases in speed fluctuations and oscillation times within a range from 180° to 270°. The relevant research results reflect that the IAS signal can provide a new method for monitoring the operating status of and conducting fault diagnoses for hydraulic equipment.

The Neutron Star to Black Hole Mass Gap in the Frame of the Jittering Jets Explosion Mechanism (JJEM)

I build a toy model in the frame of the jittering jets explosion mechanism (JJEM) of core collapse supernovae that incorporates both the stochastically varying angular momentum component of the material that the newly born neutron star (NS) accretes and the constant angular momentum component, and show that the JJEM can account for the ≃2.5–5M ⊙ mass gap between NSs and black holes (BHs). The random component of the angular momentum results from pre-collapse core convection fluctuations that are amplified by post-collapse instabilities. The fixed angular momentum component results from pre-collapse core rotation. For slowly rotating pre-collapse cores the stochastic angular momentum fluctuations form intermittent accretion disks (or belts) around the NS with varying angular momentum axes in all directions. The intermittent accretion disk/belt launches jets in all directions that expel the core material in all directions early on, hence leaving an NS remnant. Rapidly rotating pre-collapse cores form an accretion disk with angular momentum axis that is about the same as the pre-collapse core rotation. The NS launches jets along this axis and hence the jets avoid the equatorial plane region. Inflowing core material continues to feed the central object from the equatorial plane increasing the NS mass to form a BH. The narrow transition from slow to rapid pre-collapse core rotation, i.e., from an efficient to inefficient jet feedback mechanism, accounts for the sparsely populated mass gap.

The collective burst mechanism of angular jumps in liquid water

Understanding the microscopic origins of collective reorientational motions in aqueous systems requires techniques that allow us to reach beyond our chemical imagination. Herein, we elucidate a mechanism using a protocol that automatically detects abrupt motions in reorientational dynamics, showing that large angular jumps in liquid water involve highly cooperative orchestrated motions. Our automatized detection of angular fluctuations, unravels a heterogeneity in the type of angular jumps occurring concertedly in the system. We show that large orientational motions require a highly collective dynamical process involving correlated motion of many water molecules in the hydrogen-bond network that form spatially connected clusters going beyond the local angular jump mechanism. This phenomenon is rooted in the collective fluctuations of the network topology which results in the creation of defects in waves on the THz timescale. The mechanism we propose involves a cascade of hydrogen-bond fluctuations underlying angular jumps and provides new insights into the current localized picture of angular jumps, and its wide use in the interpretations of numerous spectroscopies as well in reorientational dynamics of water near biological and inorganic systems. The role of finite size effects, as well as of the chosen water model, on the collective reorientation is also elucidated.

Implications of post-kick jets in core-collapse supernovae

ABSTRACTI examine the assumption that the jets that shape the axisymmetrical morphological features of core-collapse supernova (CCSN) remnants are post-kick jets, i.e. the neutron star (NS) launches these jets after the explosion and after it acquired its natal kick velocity. I find that this assumption implies that the pre-collapse cores of CCSN progenitors have sufficient angular momentum fluctuations to support jittering jets that explode the star. From the finding that the shaping-jets neither tend to be aligned with the kick velocity nor to be perpendicular to it I argue that the assumption that the shaping-jets are post-kick jets has the following implications. (1) The NS accretes mass at a radius of $r_{\rm acc} \approx 5000 {~\rm km}$ from the centre of the explosion at $\approx 10 {~\rm s}$ after explosion. (2) The required angular momentum fluctuations of the accreted gas to explain the medium values of jets-kick angles are also sufficient to support an intermittent pre-kick accretion disc, just before and during the explosion. Such an intermittent accretion disc is likely to launch jets that explode the star in the frame of the jittering jets explosion mechanism. This suggests that most likely the shaping-jets are the last jets in the jittering jets explosion mechanism rather than post-kick jets. (3) The jittering jets explosion mechanism expects that black holes have small natal kick velocities.

Molecular dynamics simulations of F1-ATPase's angular fluctuations and associated restoring force.

Molecular dynamics (MD) is a computational method that allows researchers to analyze the movement of atoms and molecules on the nanosecond timescale. The runtime for these simulations is limited to the hardware specifications of the computers. One frame at a time, fluctuations in the positions of organic molecules can be recorded with a image resolutions far beyond what can be seen by single-molecule imaging. In this poster, we examine a rotary motor enzyme, F1-ATPase. The rotor's angular displacement can be tracked and associated with an instantaneous velocity at each timestep. By analyzing such data, we found that a restoring force exists to regulate the rotation around a dwell angle. As fluctuations drive the angular position of the rotor to deviate from the center of the dwell angle, the restoring force motivates the rotor to return to the original position. We hope to combine our present data with measurements collected from single-molecule imaging to calculate mathematical model from the atomistic fluctuations.

New design for unconventional timing silent chain system of inline engine

More and more unconventional timing silent chain systems are used in the low-emission vehicles or hybrid vehicles, but engineering practices show that the classical design method cannot ensure the stability and the feasibility anymore. According to the angular velocity fluctuations of crankshaft, the maximum accumulation length is calculated to design the ideal path of the tension side chain. The tension rate is defined to determine the ideal chain path at the loose side. In order to match the ideal chain paths with the actual chain length, the pitch variation algorithm is proposed. Based on a specific inline engine, the unconventional timing silent chain system is designed by the classical design method and the new design method respectively. The design process proves that the new method is belonging to a real parametric design, and it can expediently and quickly obtain the results. With the dynamics simulation comparison, the results show that the operation performance of the unconventional timing system can be roundly and significantly improved by using the new design method. Furtherly, this new design method is not only suitable for the unconventional timing system, but also suitable for the other types of timing systems.

Relativistic angular redshift fluctuations embedded in large scale varying gravitational potentials

We compute the linear order, general relativistic corrections to angular redshift fluctuations (ARF), a new cosmological observable built upon density-weighted two-dimensional (2D) maps of galaxy redshifts. We start with an existing approach for galaxy/source counts developed in the Newtonian gauge, and generalize it to ARF, modifying for this purpose a standard Boltzmann code. Our calculations allow us identifying the velocity terms as the leading corrections on large scales, emphasizing the sensitivity of ARF to peculiar, cosmological velocity fields. Just like for standard 2D clustering, the impact of gravitational lensing on ARF is dominant on small angular scales and for wide redshift shells, while the signatures associated to gravitational potentials are extremely small and hardly detectable. The ARF also present interesting correlation properties to anisotropies of the Cosmic Microwave Background (CMB): they are highly correlated to CMB lensing potential fluctuations, while also exhibiting a significant (S/N∼ 4–5) anti-correlation with the Integrated Sachs-Wolfe effect (ISW). This negative ARF×ISW signal is quite complementary to the standard 2D clustering×ISW correlation, since the former appears mostly at higher redshift (z ∼ 2) than the latter (z ≲ 1), and the combination of the two observables significantly increases the χ 2 statistics testing the null (no ISW) hypothesis. We conclude that ARF constitute a novel, alternative, and potentially powerful tool to constrain the nature of Dark Energy component that gives rise to the ISW.

High-Precision Angular Speed Tracking Control of Gimbal System With Harmonic Reducer

In this article, a composite controller based on an extended state observer (ESO) and sliding-mode control (SMC) is presented in order to deal with the angular speed fluctuation caused by the kinematic error of a harmonic reducer in the gimbal system of a control moment gyro. First, based on the analysis of the kinematic error derived from the relationship between the angular speed of the motor and that of the load, a second-order gimbal system model is established based on the Lagrange function and the Rayleigh dissipation function. Second, a three-order linear ESO is designed to observe the uncertain disturbances of the gimbal system, and the disturbances are rejected via the proposed composite controller combining the ESO with SMC. Third, we prove the overall system stability by using the Lyapunov approach and the final value theorem. Finally, both simulation and experimental results verify the effectiveness of the proposed method in attenuating gimbal system disturbances.

Using Car-Parrinello simulations and microscopic order descriptors to reveal two locally favored structures with distinct molecular dipole moments and dynamics in ambient liquid water

Water is essential for life and technological applications, mainly for its unique thermodynamic and dynamic properties, often anomalous or counterintuitive. These anomalies result from the hydrogen-bonds fluctuations, as evidenced by studies for supercooled water. However, it is difficult to characterize these fluctuations under ambient conditions. Here, we fill this knowledge gap thanks to the Car-Parrinello ab initio molecular dynamics (MD) simulation technique. We calculate the local structural order parameter ζ, quantifying the coordination shells separation, and find two locally-favored structures or states: High-ζ and Low-ζ. On average, High-ζ molecules have a tetrahedral arrangement, with four hydrogen bonds, and the first and the second coordination shell well separated. The Low-ζ molecules are less connected, partially merging the first and the second shells. The appearance of isosbestic points in the radial distribution functions and the collective density fluctuations at different length scales and timescales reveal that the two-state model, consistent with available experimental data for supercooled water, also holds under ambient conditions, as we confirm by analyzing the vibrational spectrum of both types of water molecules. Significant consequences of the structural differences between the two states are that High-ζ molecules have a dipole moment 6 % higher than Low-ζ. At the same time, Low-ζ structures are more disordered and with more significant angular fluctuations. These differences are also reflected in the dynamics under ambient conditions. The Low-ζ molecules decorrelate their reorientation faster than High-ζ and merge their coordination shells within 0.2 ps, while the High-ζ preserve the shell separation for longer times. Our analysis shows that first-principle calculations make predictions under ambient conditions calling for new and definitive experiments confirming the two-state model.

Kinematics and shear-induced alignment in confined granular flows of elongated particles

The kinematics and the shear-induced alignment of elongated particles in confined, heterogeneous flow conditions are investigated experimentally. Experiments are conducted in an annular shear cell with a rotating bottom wall and a top wall permitting confinement of the flow. Flow kinematics and particle orientation statistics are computed by particle tracking using optical imaging. Translational velocity profiles show an exponential decay, and surprisingly, only the slip velocity at the bottom is influenced by the particle shape. Rotations are highly frustrated by particle shape, more elongated particles showing, on average, a lower angular velocity. In addition, a clear shear-rate dependency of the proneness of a particle to rotate is observed, with a stronger inhibition in low shear zones. The average orientation of the particles does not correspond to the main flow direction, they are slightly tilted downwards. The corresponding angle decreases with the particles’ elongation. Orientational order was observed to increase with particles’ elongation, and surprisingly was not affected by the applied confinement. A weak but systematic decrease of the orientational order was observed in regions of higher shear rate. At the particle-scale, angular velocity fluctuations show a strong correlation with local particle orientation, particles being strongly misaligned with the preferential particles’ orientation rotating faster. This correlation becomes stronger for more elongated particles, while is almost unaffected by the applied confinement.

Soft modes in Fermi liquids at arbitrary temperatures

We use kinetic-theory methods to analyze Landau Fermi-liquid theory, and in particular to investigate the number and nature of modes in Fermi liquids that are soft in the long-wavelength limit, both in the hydrodynamic and the collisionless regimes. In the hydrodynamic regime we show that Fermi-liquid theory is consistent with Navier-Stokes hydrodynamics at all temperatures, as expected. The soft modes are the ones familiar from classical hydrodynamics that are controlled by the five conservation laws; namely, two first-sound modes, two shear diffusion modes, and one heat diffusion mode. These modes have a particle-like spectrum and are soft, or scale invariant, at all temperatures. In the collisionless regime we show that the entire single-particle distribution function is soft with a continuous part of the spectrum. This continuous soft mode, which is well known but often not emphasized, has important physical consequences, e.g., for certain quantum phase transitions. In addition, there are the well-known soft zero-sound excitations that describe angular fluctuations of the Fermi surface; their spectra are particle-like. They are unrelated to conservation laws, acquire a mass at any nonzero temperature, and their number depends on the strength of the quasiparticle interaction. We also discuss the fates of these two families of soft modes as the temperature changes. With increasing temperature the size of the collisionless regime shrinks, the damping of the modes grows, and eventually all of the collisionless modes become overdamped. In their stead the five hydrodynamic modes appear in the hydrodynamic regime at asymptotically low frequencies. The two families of soft modes are unrelated and have very different physical origins. In charged Fermi liquids the first-sound modes in the hydrodynamic regime and the $\ensuremath{\ell}=0$ zero-sound modes in the collisionless regime get replaced by plasmons, all other modes remain soft.

Remnant masses of core collapse supernovae in the jittering jets explosion mechanism

ABSTRACT We conduct one-dimensional (1D) stellar evolution simulations of non-rotating stars with initial masses in the range of $11\!-\!48 \, \mathrm{M}_{\odot }$ to the time of core collapse and, using a criterion on the specific angular momentum fluctuations in the inner convective zones, estimate the masses of the neutron star (NS) remnants according to the jittering jets explosion mechanism. From the 1D simulations, we find that several convective zones with specific angular momentum fluctuations of $j_{\rm {conv}} \gtrsim 2.5 \times 10^{15} {\, \rm cm}^2 {\, \rm s}^{-1}$ develop near the edge of the iron core in all models. For this condition for explosion, we find the NS remnant masses to be in the range of $1.3\!-\!1.8 \, \mathrm{M}_\odot$, while if we require twice as large values, i.e. $j_{\rm {conv}} \gtrsim 5 \times 10^{15} {\, \rm cm}^2 {\, \rm s}^{-1}$, we find the NS remnant masses to be in the range of $1.4\!-\!2.8 \, \mathrm{M}_\odot$ (the upper values here might form black holes). Note that in general, the formation of black holes in the jittering jets explosion mechanism requires a rapidly rotating pre-collapse core, while we simulate non-rotating stars.

Effective and robust rocking centrifugal pendulum vibration absorbers

In this work, a design methodology for robust and effective centrifugal pendulum absorbers is presented with a relative center of mass translation along a given path and angular body rotation. This type of absorber is used in rotatory machines with rotor angle synchronous excitation, allowing for a reduction of angular rotor fluctuations over the entire speed range. The main areas of application are aircraft drives and automotive drive trains with internal combustion engines. Since the requirements placed on absorbers are increasingly demanding in terms of reducing their mass without sacrificing effectiveness, new design approaches must be pursued. The linear theory used in the past has been replaced by the nonlinear tautochronic design philosophy that provides an increased working range of the pendula. This approach has been extended in recent years with regard to nonlinear detuning in order to obtain effective and robust absorbers. It is known that, in addition to the translation of the pendula, the rotation of the pendulum bodies, contributes to absorber performance, and the nonlinear design tools are extended to this case. The proposed unified design approach allows one to apply existing tuning methodologies of centrifugal pendulum absorbers with their relative rotational movement, referred to as “rocking” absorbers. Maintaining generality, the equations of motion are derived for a system with multiple absorbers and prepared for the application of simulations and continuation algorithms for parameter studies. Additionally, a state transformation is presented, which allows the application of perturbation methods and averaging under the assumption of small parameters. The increased effectiveness of these rocking absorber class when compared to non-rocking absorbers is quantified and demonstrated by numerical case studies.

Joint motion planning of industrial robot based on hybrid polynomial interpolation

To plan an industrial robot's point-to-point joint motion that has velocity constraints, the cubic polynomial interpolation planning method has angular acceleration discontinuity. The quintic polynomial interpolation planning method needs to set in advance the angular acceleration values of target points and easily causes angular velocity fluctuation. Because of the existence of quintic polynomials, hybrid polynomial planning 3-5-…-5-3 also easily causes large angular velocity fluctuation. To solve these problems, a hybrid polynomial interpolation planning method based on cubic and quartic polynomial interpolation is proposed. Cubic polynomial interpolation planning is applied to the first planning, and quartic polynomial interpolation planning is used for the rest of planning. The planning method can not only specify the angular velocities of intermediate target points but also ensure the continuity of angular acceleration. In addition, there is no need to set in advance the angular acceleration values of target points so as to avoid the angular velocity fluctuation caused by the unreasonable presetting of angular acceleration. Furthermore, in order to avoid excessive peaks of angular velocity during the joint motion planning, a calculation method for finding out reasonable motion time is put forward, under which the larger speed at two target points is taken as maximum, thus making the planned angular velocity fluctuation small. A case study is performed to verify the rationality and effectiveness of the planning method. Compared with the other two planning methods used for the case study, our planning method can effectively solve the problems of point-to-point joint motion planning with velocity constrains, therefore being beneficial to the working performance and service life of an industrial robot.