Uniform Rotation Research Articles

Про стійкість обертання вільної системи двох пружно зв’язаних гіроскопів Лагранжа, один з яких має ідеальну рідину

On the basis of the known equations of motion of the system of coupled gyrostats by P. V. Kharlamov and the state function by S. L. Sobolev, the equations of rotation of a free system of two elastically coupled Lagrange gyroscopes were derived, one of which has an arbitrary axisymmetric cavity completely filled with an ideal incompressible fluid. The rigid bodies are connected by an elastic restoring spherical hinge. A transcendental characteristic equation of the perturbed uniform rotation of the mechanical system under consideration is derived. Taking into account the fundamental tone of the fluid oscillation, a characteristic equation of the fifth order is obtained. On the basis of the Liénard – Chipart criterion written in the inor form, the necessary conditions for the stability of the uniform rotation of the Lagrange gyroscopes and the fluid are written out as a system of four inequalities. With respect to the elasticity coefficient, these inequalities have degrees 1, 3, 6 and 8, respectively. Analytical studies of the leading coefficients of these stability conditions are carried out. It is shown that when the center of mass of the first solid body with liquid or the second does not coincide with the common point of these bodies, then at sufficiently large values of the elasticity coefficient the necessary stability conditions will always be satisfied. In the absence of elasticity in the hinge, the characteristic equation has a double zero root and in this case the stability conditions require additional studies. The obtained stability conditions are exact for an ellipsoidal cavity and approximate for other axisymmetric cavities. To clarify the obtained glass conditions for these voids, it is necessary to take into account additional tones of oscillation of an ideal liquid.

Quantum-based PRNG for image encryption: a comprehensive study

Quantum computing, grounded in the principles of quantum mechanics, has ushered in a new era of intriguing possibilities and fresh scientific insights. In this document, we present an innovative algorithm tailored for the encryption and decryption of images. This algorithm harnesses the quasi-probability values extracted from each state within the quantum system, represented as | ψ 〉 . These numerical values are seamlessly integrated with conventional data to facilitate image encryption and decryption processes. Our methodology undergoes comprehensive validation and evaluation through extensive simulations performed on the IBM Qiskit Aer simulator. We subject the generated numerical sequence to rigorous statistical scrutiny using the NIST SP 800-22 suite, ensuring its authenticity and reliability. Employing a quantum system comprising 3 qubits and uniform rotation gates, our algorithm produces a dataset consisting of 41,943,040 binary digits. Additionally, we conduct a thorough assessment encompassing both visual and statistical analyses to ascertain the effectiveness and robustness of our proposed algorithm. Furthermore, we emphasize the critical importance of achieving a quasi-probability error rate of 10 − 6 for real-world implementation, highlighting the practical viability and scalability of our approach. Through comparative analysis and meticulous examination of correlation patterns, our study provides invaluable insights into the distinctive characteristics and efficacy of our encryption scheme.

Averaged flow in a rotating flat layer at librations

Abstract One of the important areas in fluid mechanics is thermal convection; its study is an urgent task from the point of view of effective control of heat and mass transfer. With increasing energy consumption worldwide, improved energy transfer methods are required. Various complicating factors can either strengthen or weaken energy transport mechanisms. In the current work, attention is paid to the libration effect as one of the effective ways to control heat transfer in a rotating cavity. The experiments are aimed at a study of convective flows generated in a flat layer unevenly rotating around a horizontal axis. The flat boundaries are kept at different temperatures. It is found that the cavity librations noticeably intensify the heat transfer in a layer. The flow structure obtained using the PIV method for the cases of uniform and non-uniform rotation of the cavity is presented for the first time. The effectiveness of librations for the intensifying heat and mass transfer in a rotating hydrodynamic system is shown.

The impact of radiative levitation on mode excitation of main-sequence B-type pulsators

Context. Numerical computations of stellar oscillations for models representative of B-type stars predict fewer modes to be excited than observations reveal from modern space-based photometric data. One shortcoming of state-of-the-art evolution models of B-type stars that may cause a lack of excited modes is the absence of microscopic diffusion in most such models. Aims. We investigate whether the inclusion of microscopic diffusion in stellar models of B-type stars, notably radiative levitation experienced by isotopes, leads to extra mode driving by the opacity mechanism compared to the case of models that do not include microscopic diffusion. Methods. We consider the case of slowly to moderately rotating stars and use non-rotating equilibrium models, while we account for (uniform) rotation in the computations of the pulsation frequencies. We calculate 1D stellar structure and evolution models with and without microscopic diffusion and examine the effect of radiative levitation on mode excitation, for both low-radial order pressure and gravity modes and for high-radial order gravity modes. As is common practice in asteroseismology, rotation is included in the pulsation computations according to the mode’s frequency regime. For modes having frequencies below twice the rotation frequency, that is, modes in the sub-inertial regime, we adopt the traditional approximation of rotation. For modes in the super-inertial regime with frequency above twice the rotation frequency, rotation is treated perturbatively up to first order in the rotation. We consider macroscopic envelope mixing induced by internal gravity waves to compute the modes and study its effect on the surface abundances. Results. We find systematically more modes to be excited for the stellar models including microscopic diffusion compared to those without it, in agreement with observational findings of pulsating B-type dwarfs. Furthermore, the models with microscopic diffusion predict that excited modes occur earlier on in the evolution compared to modes without it. In order to maintain realistic surface abundances during the main sequence, we include macroscopic envelope mixing by internal gravity waves. Along with microscopic diffusion, such macroscopic envelope mixing ensures both more excited modes and surface abundances consistent with spectroscopic studies of B-type stars. Conclusions. While radiative levitation has so far largely been neglected in stellar evolution computations of B-type stars for computational convenience, it impacts mode excitation predictions for stellar models of such stars. We conclude that the process of radiative levitation is able to reduce the discrepancy between predicted and observed excited pulsation modes in B-type stars.

Cosserat-phase-field modeling of grain nucleation in plastically deformed single crystals

Thermomechanical processing of crystalline materials induces microstructural evolution such as grain nucleation and growth. In the numerical simulation of these processes, grain nucleation is generally treated as an additional ad hoc step in which circular or spherical grains are added in regions where a critical dislocation density, stress or strain are reached. In this paper, systematic finite element simulations are performed showing that the Kobayashi–Warren–Carter (KWC) phase field model and its coupling with Cosserat crystal plasticity predict spontaneous nucleation of new grains in single crystals in the presence of lattice orientation/rotation gradients. The numerical analysis of the stability of gradients of lattice rotation and dislocation-based stored energy indicates that a gradient of stored energy alone is not sufficient to trigger grain formation. As an application, the KWC–Cosserat model is used to simulate the torsion and annealing of a copper single crystal bar with a circular cross section. This mechanical loading produces a large, fairly uniform axial rotation gradient which induces nucleation in the form of a stack of cylindrical grains. Plastic strain gradients in cross-sections predicted by the 3D finite element simulation, are not strong enough to compete with the longitudinal nucleation process, as confirmed by experimental observations from the literature.

A mechanical device to demonstrate the composition of two simple harmonic motions

The slot link mechanism can project uniform rotation to a simple harmonic motion (SHM), based on which, the device including two sliding table systems has been prepared. These two sliding table systems can be stacked up and down, and each of them can produce a tunable mechanical SHM using a stepper motor. When the upper sliding table system is attached to the lower one and both are turned on, the motion of the sliding table of the upper component is the composition of the two SHMs. With the help of a self-powered LED, a violet laser, and a movable phosphorescent foil, this mechanical device can visualize the composition of the SHMs in the same and mutual perpendicular directions including the beat phenomenon and Lissajous figures. In addition to demonstrating several typical compositions of two SHMs, this device can also highlight the vector characteristics of mechanical vibration and demonstrate the tilted Lissajous figures.

A spectropolarimetric study of the radio galaxy Pictor A using MeerKAT

ABSTRACT We present the results of a polarimetric study from our new high-sensitivity L-band (0.8–1.7 GHz) observation of Pictor A using the MeerKAT radio telescope. We confirm the presence of the radio jet extending from the nucleus to the western hotspot of this source. Additionally, we show the radio emission expected to coincide with previously observed X-ray emission in the radio lobes, confirming that the emission mechanism is of inverse Compton origin, as suggested by a previous study. Our spectropolarimetric analysis using the rotation measure synthesis technique reveals a relatively uniform mean rotation measure distribution across the lobes of Pictor A, with most lines of sight exhibiting single-peaked Faraday spectra. However, a number of the lines of sight exhibit single peaked spectra with a wide base or multiple peaks, suggesting the presence of multiple Faraday components or a Faraday thick structure along Pictor A’s lines of sight. We also confirm the asymmetry in rotation measure variability and depolarization between the two lobes of this source, as reported in a previous study.

Effects of rotation and temperature‐dependent viscosity on thermal convection in Oldroydian fluid saturating porous media: A modified stability analysis

AbstractThe onset of thermal convection in an incompressible Oldroydian fluid‐saturating porous media is examined to study the combined impact of uniform rotation and temperature‐dependent viscosity. A characteristic equation from the basic hydrodynamic equations governing the Brinkman–Oldroyd model is derived using linear stability theory and modified Boussinesq approximation. For various combinations of stress‐free and slip‐free boundaries, the expressions for the Darcy–Rayleigh numbers for both non‐oscillatory as well as oscillatory convection with linear and exponential temperature‐dependent viscosity are derived, using the “weighted residual method.” The effects of rotation, variable viscosity parameter, strain retardation and stress relaxation time parameters and other fluid parameters on non‐oscillatory and oscillatory convection are investigated numerically and the results are presented graphically. From the analysis, it is found that overstability is the preferred mode of onset of convection. The rotation, the coefficient of specific heat variations (due to temperature variation), and the strain retardation time have a stabilizing influence on the stability of the system, whereas the stress relaxation imparts a destabilizing effect. Additionally, it is noticed that the variable viscosity parameter and Brinkman‐Darcy number stabilize the system for each set of boundary conditions.

Continuous TOA Measurement Based Single-Anchor Indoor Localization

On the premise of guaranteeing high-quality measurement data, active wireless localization (A-WL) locates the target by at least three anchor nodes (ANs) with known coordinates, while passive wireless localization (P-WL) requires more ANs. In addition, P-WL requires a cumbersome training process to maintain the robustness in application scenarios as much as possible. However, the optimal deployment of ANs is not an easy task, and the application scenario will not remain unchanged. Therefore, a lightweight localization system that satisfies the localization accuracy requirements and can be quickly deployed should be one of the preferred solutions for WL. In this paper, we propose a single-anchor localization system based on continuous time-of-arrival (TOA) measurement. Specifically, we fix the AN on the blade with uniform rotation, construct the time-length distribution map by using the cyclically varying TOA caused by blade rotation, and intercept it according to the rotation period. We extract the change angle and distance information from the intercepted data in real time to achieve single-anchor localization. Meanwhile, we also construct a support vector machine classifier to identify the line-of-sight state of each interception period to assist the angle estimation in harsh environments and further improve the adaptability of the system. Experimental results show that the line-of-sight recognition accuracy of higher than 92% under continuous movement, and the average localization error of less than 0.6m. The average localization error is less than 0.3m in the mixed motion state.

Распространение магнитогидродинамических волн и гравитационная неустойчивость в астрофизической анизотропной и теплопроводной плазме

The hydrodynamic instability of a magnetised, self-gravitating rotating anisotropic plasma is analysed in the collisionless approximation and taking into account the heat flux vector on the basis of the modified Chew-Goldberger-Low equations. The dispersion relation is derived and simplified cases of propagation of small-amplitude perturbation waves are discussed, with modified analytical criteria for hydrodynamic instability obtained. In accordance with the general dispersion relation, three cases when the propagation of the perturbation wave passes across, along, and obliquely to the magnetic field vector are specifically considered. It is shown that anisotropic pressure and heat flux not only modify the classical Jeans instability criterion but also induce new unstable regions. It is found that the presence of uniform plasma rotation reduces the critical wave number and has a stabilising effect on the gravitational instability criterion for transverse propagation of the perturbation wave and has no effect in the case of its longitudinal propagation. The inclusion of thermal flows leads to the appearance of two additional wave modes. The results obtained are important for the construction of evolutionary magnetohydrodynamic models of collisionless astrophysical plasma.

High-Resolution Imaging and Morphological Phenotyping of C. elegans through Stable Robotic Sample Rotation and Artificial Intelligence-Based 3-Dimensional Reconstruction.

Accurate visualization and 3-dimensional (3D) morphological profiling of small model organisms can provide quantitative phenotypes benefiting genetic analysis and modeling of human diseases in tractable organisms. However, in the highly studied nematode Caenorhabditis elegans, accurate morphological phenotyping remains challenging because of notable decrease in image resolution of distant signal under high magnification and complexity in the 3D reconstruction of microscale samples with irregular shapes. Here, we develop a robust robotic system that enables the contactless, stable, and uniform rotation of C. elegans for multi-view fluorescent imaging and 3D morphological phenotyping via the precise reconstruction of 3D models. Contactless animal rotation accommodates a variety of body shapes and sizes found at different developmental stages and in mutant strains. Through controlled rotation, high-resolution fluorescent imaging of C. elegans structures is obtained by overcoming the limitations inherent in both widefield and confocal microscopy. Combining our robotic system with machine learning, we create, for the first time, precise 3D reconstructions of C. elegans at the embryonic and adult stages, enabling 3D morphological phenotyping of mutant strains in an accurate and comprehensive fashion. Intriguingly, our morphological phenotyping discovered a genetic interaction between 2 RNA binding proteins (UNC-75/CELF and MBL-1/MBNL), which are highly conserved between C. elegans and humans and implicated in neurological and muscular disorders. Our system can thus generate quantitative morphological readouts facilitating the investigation of genetic variations and disease mechanisms. More broadly, our method will also be amenable for 3D phenotypic analysis of other biological samples, like zebrafish and Drosophila larvae.

A two-dimensional friction-decoupling method based on numerical integration method and momentum theorem

This article introduces a simplified Two-Dimensional Friction-Coupling Model (TDFC) designed for typical surface-to-surface contact friction systems in engineering structures. With the assumption of a constant friction force magnitude within each calculation time step, the alteration of the friction direction of TDFC within each calculation time step can be visualized as the rotation of a circular radius under horizontal bidirectional dynamic loads. This dynamic force analysis approach is referred to as the “Circular making”. It is noteworthy that the friction direction change in each calculation time step demonstrates unidirectional rotatability. Leveraging this rotatability and assuming uniform rotation, the momentum theorem accurately determines the direction of the plane friction acting on the TDFC model at the end of each calculation time step. This allows for the decoupled calculation of plane friction and precise response calculation of the TDFC model. The study verifies the reliability of theoretical assumptions, such as constant friction force magnitude and uniform rotation, with a time step of 0.01 s. Additionally, by introducing an equivalent spring effect to modify the TDFC model, it is observed that the modified TDFC effectively simulates the behavior of the Friction Pendulum Bearing (FPB) under horizontal bidirectional seismic loads. Compared to the ABAQUS finite element model of FPB, the modified TDFC model provides a more efficient approach for rapidly and accurately calculating the response of various FPB types under horizontal bidirectional seismic loads by adjusting parameter values of the modified TDFC model.

A numerical analysis of fluid flow and heat transfer between two rotating disks with induced porous medium

In this article, fluid flow between rotating disks is a fundamental topic in fluid dynamics and has various practical applications in engineering and technology. The primary motivation for studying fluid flow between two rotating disk includes its applications in heat exchanger design, generating energy, designing aircraft components like helicopter blades, propellers, wind turbine rotors, fluid pumping, stirring, etc. Authors have considered radially stretching and rotating disks simultaneously under the spiraling motion of a couple stress fluid. This type of motion is developed by radial stretching in addition to the disk’s uniform rotation. This study gives information about the effect of various physical parameters on radial, tangential velocities, and temperature profiles. The similarity transformation resulted in coupled nonlinear ordinary differential equations from the constitutive flow rules of nonlinear partial differential equations. For getting numerical solutions, the authors have used the in-build NDSolve command in MATHEMATICA software, which uses the finite difference method for discretizing and solving differential equations. The outcomes of the above study depict how the fluid flow pattern between the rotating disks is affected by Darcy’s parameter, and other parameters, like Prandtl number, rotation parameter, stretching parameter, couple stress parameter, etc. on the flow, have been thoroughly analyzed, with the physical relevance illustrated. Radial and tangential velocity profiles decrease whenever the Darcy parameter increases. An increase in rotation parameter enhances the radial and tangential velocity due to rotation of the disks.

The Relativistic Rotation Transformation and the Observer Manifold

We show that relativistic rotation transformations represent transfer maps between the laboratory system and a local observer on an observer manifold, rather than an event manifold, in the spirit of C-equivalence. Rotation is, therefore, not a parameterised motion on a background space or spacetime, but is determined by a particular sequence of tetrads related by specific special Lorentz transformations or boosts. Because such Lorentz boosts do not form a group, these tetrads represent distinct observers that cannot put together their local descriptions into a manifold in the usual sense. The choice of observer manifold depends on the dynamical situation under consideration, and is not solely determined by the kinematics. Three examples are given: Franklin’s rotation transformation for uniform plane rotation, the Thomas precession of a vector attached to an electron, and the motion of a charged particle in an electromagnetic field. In each case, at each point of its trajectory, there is a distinguished tetrad and a special Lorentz transformation that maps Minkowski space to the spacetime of the local observer on the curve.

Constraining the long-lived supramassive neutron stars by magnetar boosted kilonovae

ABSTRACT Kilonovae are optical transients following the merger of neutron star binaries, which are powered by the r-process heating of merger ejecta. However, if a merger remnant is a long-lived supramassive neutron star supported by its uniform rotation, it will inject energy into the ejecta through spin-down power. The energy injection can boost the peak luminosity of a kilonova by many orders of magnitudes, thus significantly increasing the detectable volume. Therefore, even if such events are only a small fraction of the kilonova population, they could dominate the detection rates. However, after many years of optical sky surveys, no such event has been confirmed. In this work, we build a boosted kilonova model with rich physical details, including the description of the evolution and stability of a proto neutron star, and the energy absorption through X-ray photoionization. We simulate the observation prospects and find the only way to match the absence of detection is to limit the energy injection by the newly born magnetar to only a small fraction of the neutron star rotational energy, thus they should collapse soon after the merger. Our result indicates that most supramassive neutron stars resulting from binary neutron star mergers are short lived and they are likely to be rare in the Universe.

Jeans Gravitational Instability of a Rotating Collisionless Magnetized Plasma with Anisotropic Pressure

The problem of self-gravitational instability of an astrophysical rotating plasma in a strong magnetic field with an anisotropic pressure tensor is studied on the basis of the Chew–Goldberger–Low (CGL) quasi-hydrodynamic equations modified by generalized polytropic laws. Using the general form of a dispersion relation obtained by the normal-mode perturbation method, a discussion is provided of the propagation of small-amplitude perturbation waves in an infinite homogeneous plasma medium for transverse, longitudinal, and oblique directions with respect to the magnetic field vector. It is shown that different polytropic indices and anisotropic pressures not only change the classical Jeans instability condition but also cause the appearance of new unstable regions. Modified Jeans instability criteria are obtained for isotropic MHD equations and anisotropic CGL equations owing to the influence of the polytropic indices on gravitational and firehose instabilities for astrophysical plasma. It is shown that in the case of a longitudinal mode of perturbation wave propagation, the Jeans instability criterion does not depend on uniform rotation. In the case of the transverse propagation regime, the presence of rotation reduces the critical wave number and exerts a stabilizing effect on the growth rate of the unstable regime.

Insights into the thermodynamic efficiency of Homann-Agrawal hybrid nanofluid flow

In this study, we investigate the characteristics of axisymmetric Homann and Agrawal flows over a stretching and spiraling surface at the stagnation point flow. The effects of uniform rotation and linear radial stretching of the disk are considered, along with the utilization of hybrid nanofluids. Specifically, titanium oxide and multi-walled carbon nanotubes are dispersed in engine oil to form the nanofluid. The surface velocity adopts a spiral logarithmic shape due to the combined influence of uniform rotation and radial stretching, while a perpendicular magnetic field is applied to the flow. Furthermore, we analyze the entropy generation of the hybrid nanofluid flow. To solve the problem, we employ a similarity transformation technique to convert partial differential equations (PDEs) into ordinary differential equations (ODEs) and utilize the bvp4c technique available in MATLAB. Graphical representations are employed to illustrate the impact of relevant parameters. This analysis yields valuable insights into the thermodynamic efficiency of fluid flow systems, enabling optimization of their design and performance. Understanding the influence of nanoparticle concentration and flow parameters on system efficiency is of utmost importance in developing more effective and efficient fluid flow systems. The study offers crucial insights applicable to a wide range of engineering applications, including heat exchangers, cooling systems, and other fluid flow systems.

Magneto-Rotatory Convection in Couple-Stress Fluid

Background: Thermal convection is the most convective instability when crystals are produced from a single element like silicon and the thermal instability of a fluid layer heated from below plays an important role in geophysics, oceanography, atmospheric physics, etc. The flow through porous media is of considerable interest for petroleum engineers, for geophysical fluid dynamicists and has importance in chemical technology and industry. Many of the flow problems in fluids with couple-stresses indicate some possible experiments, that could be used for determining the material constants, and the results are found to differ from those of Newtonian fluid. Keeping this in view, the present work was to study the effect of a uniform vertical magnetic field on the couple-stress fluid heated from below in the presence of a uniform vertical rotation through permeable media. Methodology: The present problem is studied using the linearized stability theory, Boussinesq approximation, normal mode analysis, and the dispersion relation is obtained. Results: The stationary convection, stability of the system, and oscillatory modes are discussed. In the case of stationary convection, the rotation postpones the onset of convection. The magnetic field and couple-stress may hasten the onset of convection in the presence of rotation while in the absence of rotation; they always postpone the onset of convection. The medium permeability hastens the onset of convection in the absence of rotation while in the presence of rotation, it may postpone the onset of convection. The rotation and magnetic field are found to introduce oscillatory modes in the system which was non-existent in their absence. A sufficient condition for the non-existence of overstability is also obtained.

Разработка ветрового устройства специальной конструкции для отдаленных сельскохозяйственных объектов

The object of the study is a wind turbine with a vertical axis of rotation. The main problem of operating wind farms with a horizontal axis of rotation includes: the need for constant guidance to the wind, cantilever tension at the attachment point of the blades, uneven rotation of the wind wheel. A vortex wind device with a vertical axis of rotation eliminates wind guidance mechanisms, cantilever tension of the blades, ensures uniform rotation of the wind wheel. The wind device has a concentrator with curved channels that concentrate the flow onto the blades of the wind wheel and create a vortex motion, which is enhanced by the thrust of the vertical pipe. A feature of the development is the steady vortex motion created inside the concentrator, which ensures uniform and stable rotational movement of the wind wheel in unstable wind flow. Based on mathematical modeling and experimental studies, an experimental model and a semi-industrial installation were developed.

Calibrating angular momentum transport in intermediate-mass stars from gravity-mode asteroseismology

Context. The physical mechanisms driving the transport of angular momentum in stars are not fully understood, as current models cannot explain the observed stellar rotation profiles across all stages of evolution. Aims. By making use of pulsating F-type dwarfs, we aim to (i) observationally calibrate the efficiency of angular momentum transport, assuming a constant uniform viscosity, and (ii) test how well state-of-the-art rotating stellar models with angular momentum (AM) transport by rotationally induced processes can explain observed rotation profiles. In both cases, the aim is to simultaneously reproduce the measured near-core rotation and core-to-surface rotation ratio. Methods. Asteroseismic modelling is applied to a sample of seven slowly rotating pulsators in order to derive (core) masses and ages from their gravity-mode oscillations. This work focuses on the main sequence (MS), using models that start with an initial uniform rotation frequency at the start of core-hydrogen burning, which is a free parameter. Two treatments of AM transport are considered: (i) a constant uniform viscosity, and (ii) rotationally induced processes (including the Spruit-Tayler dynamo). Next, the initial rotation frequency of each star is derived from the observed present-day near-core rotation frequency for both treatments. Results. Asteroseismic modelling of gravity mode periods reveals that all seven slowly rotating stars (one of which is not further modelled) in the sample are near the end of core-hydrogen burning. To explain the near-core rotation rate at the inferred age, initial rotation frequencies at the zero-age main sequence need to be below 10% of the initial critical break-up frequency. The derived initial rotation frequencies are consistent with previous works. Conclusions. A diffusive approximation of angular momentum transport can in general explain the observed rotation profiles of the six slowly rotating F-type dwarfs for average values of the viscosity of between 2 × 105 and 5 × 107 cm2 s−1 or when the viscosity is computed from rotationally induced mechanisms. Yet, for three stars in the sample, the core-to-surface rotation fraction from rotationally induced mechanisms is predicted to be higher than observed.