Rotation Law Research Articles

Simulation analysis of an impeller percussive drilling tool based on rotation law

Simulation analysis of an impeller percussive drilling tool based on rotation law

Toroidal magnetic fields in self-gravitating disks around black holes

We investigate stationary models of magnetized, self-gravitating disks around black holes. The disks are assumed to rotate according to a recently introduced Keplerian rotation law. We consider different prescriptions of the toroidal magnetic field. Similarly to the purely hydrodynamical case (i.e., with no magnetic field), we observe a bifurcation in the parameter space of solutions. There are usually two branches of solutions: a branch corresponding to relatively light disks and a branch for which the disk can be more massive than the black hole. The existence of this latter branch can be explained by geometric properties of the spacetime. We investigate the influence of the magnetic field in the disk on these effects.

Jupiter and Saturn Multi-layer Models Rotating Differentially

In a past work, models for Jupiter were constructed in base to a set of concentric distorted spheroids (“spheroidals”) rotating differentially—whose semi-axes are independent of one another—a task that was achieved with a law of rotation deduced from a generalization of Bernoulli’s theorem, and which holds exclusively for axial-symmetric masses. The shape of the mass is that of a spheroid whose surface equation contains an extra term, d/z4, where d is a parameter which measures the degree of distortion. Each layer rotates with its own profile of angular velocity. The rotation law has a simple dependence on the derivative of the gravitational potential. No magnetic fields or equations of state were involved. The multi- structures were demanded, firstly, to reproduce the gravitational moments of the planets, as surveyed by space missions; and, secondly, to be equilibrium figures. For the calculation of the gravitational moments, a minimization procedure was employed. Paying attention on the outermost laye—the relevant one in the present context—of the formerly reported models for Jupiter, we became aware that they all share an angular velocity profile that decreases from the pole towards the equator, an event that, so far, has not been verified observationally. Since figures with profiles of the opposite tendency turned out to be also possible, they should be included as candidates for our purpose, as effectively they are herein as a complement of that work. The same procedure is here entailed to Saturn, for which figures to show one or the other tendencies are as well obtained. The dual behavior of the rotation profiles may be explained by arguments involving the centripetal force. According to this standpoint, the double behavior is a consequence of the algebraic sign assigned to d: if positive, so that the surface is more bloated than that of a spheroid, the decreasing tendency results; whereas if negative, so that the surface is more depressed, the increasing tendency shows up. This, in turn, is because for d negative the radial force increases more rapidly from pole to the equator than for d positive. We point out that the rotation profiles of the current figures are determined from their equilibrium, rather than being imposed ad initio.

Stationary massive disks around black holes: Realistic equation of state and bifurcation

We study stationary and axially symmetric black hole-disk systems, assuming a combination of the DD2 and Timmes-Swesty equations of state and a three-parameter family of rotation laws. There exist two branches of solutions that are shown to bifurcate, for a suitable specific entropy and a parameter in the rotation law. Low entropy nuclear matter allows for the existence of moderately massive Keplerian disks.

Multiaxial stress-fractional plasticity model for anisotropically overconsolidated clay

Clays in the field can experience various consolidation histories, e.g., isotropic or anisotropic overconsolidation, before subjected to three-dimensional loads exerted by the neighbouring geotechnical infrastructures. Correct representation of the multiaxial strength and deformation behaivour of anisotropically overconsolidated clay is a prerequisite for engineering design. Accordingly, a multiaxial constitutive model is developed in this study, by employing the anisotropic stress-fractional plasticity two surfaces. The consolidation history is represented by using an inclined bounding surface, while the loading behaviour in multiaxial stress space is captured through the stress transformation of an inclined loading surface. The incorporation of such stress transformation method overcomes the difficulty in obtaining the fractional derivative of the Lode's angle. To capture the dilatancy behaviour of anisotropically overconsolidated clay, a multiaxial state-dependant nonassociated plastic flow rule is developed by only using the stress-fractional gradient of the loading surface, which significantly differs from the prior attempts using traditional plasticity. In addition, a multiaxial rotational hardening law for the bounding/loading surface is suggested to characterise the shearing-induced fabric destruction of anisotropically overconsolidated clay. Finally, test results of two different clays under various consolidation histories and stress paths are adopted to validate the developed model. It is found that the predicted strength and deformation behaviour of clay depends the Lode's angle and anisotropic consolidation path, which agrees with the corresponding test results. Specifically speaking, the hardening and softening behaviour of clay induced at seven different overconsolidation ratios ranging from 1 to 10 can be quantified, and the multiaxial strength behaviour of clay loaded from a wide range of Lode's angles ranging from 0° to 60° can be also quantified.

Effect of anisotropy on the onset of convection in rotating bi-disperse Brinkman porous media

Thermal convection in a horizontally isotropic bi-disperse porous medium (BDPM) uniformly heated from below is analysed. The combined effects of uniform vertical rotation and Brinkman law on the stability of the steady state of the momentum equations in a BDPM are investigated. Linear and nonlinear stability analysis of the conduction solution is performed, and the coincidence between linear instability and nonlinear stability thresholds in the L^2-norm is obtained.

General relativistic rotational energy extraction from black holes-accretion disk systems

The determination of mass and spin parameters of the black holes (BHs) is crucial in the analysis of the merger of BHs and BHs formation and evolution, including accretion. Here we constrain the BH spin with the evaluation of the dimensionless parameter ξ representing the total rotational energy extracted versus the mass of the BH, following procedure introduced by Daly (2009 Astrophys. J. 691 L72–6) that is independent from the details of the specific extraction process. The energy extraction can power an outflow which can be then observed. We relate the energy extraction to the accreting configurations and the accretion processes occurring in a cluster of agglomerate corotating and counter-rotating tori orbiting one central Kerr SMBH, associating ξ to the characteristics of the accretion processes. We relate the regions of tori parameters to features of the energy extraction processes, binding ξ to properties of light surfaces by using the bundles developed by Pugliese and Quevedo (2019 Eur. Phys. J. C 79 209), relating measures in different regions of the spacetimes. We evaluate properties of the BH accretions disks, and correlate spacetimes prior and after their transition due to the energy extraction. Light surfaces are related to the generators of Killing horizons, proving limiting frequency of the stationary observers of the geometries. We consider the photon limiting curves of the stationary observers as constraints for various processes regulated by these frequencies, to relate different BH states, prior and after the energy extraction, investigating regions close to the BH horizons and rotational axis. From methodological view-point we used a naked singularity—BH correspondence defined with metric bundles to predict observational characteristics of the BH—accretion disk system. The analysis points relevant BH spins a ≈ 0.94M, a ≈ 0.7M and a ≈ 0.3M. We show the relation between the rotational law of the tori, the characteristic frequency of the bundle and the relativistic velocity defining the von Zeipel surfaces. The inferior limit on the formation of corotating tori is ℓ/a ⩾ 2, for counter-rotating tori ℓ/a ⩽ −22/5 (ℓ is the fluids specific angular momentum).

A computational method for rotating, multi-layer spheroids with internal jumps

Abstract We discuss the structure of differentially rotating, multilayer spheroids containing mass-density jumps and rotational discontinuities at the interfaces. The study is based upon a scale-free, numerical method. Polytropic equations of state and cylindrical rotation profiles are assumed. The Bernoulli equation and the Poisson equation for the gravitational potential are solved for each layer separately on a common computational grid. The 2-layer (core-envelope) case is first investigated in detail. We find that the core and the envelope are not, in general, homothetical in shape (cores are more than spherical than the envelope). Besides, the occurence of a mass-density jump all along the interface is prone to a rotational discontinuity (unless the polytropic indices are the same). In particular, for given rotation laws, the mass-density jump is not uniform along the interface. Tests, trends and examples (e.g. false bipolytrope, critical rotation, degenerate configurations) are given. Next, we consider the general case of systems made of ${\cal L}>2$ layers. This includes the full equation set, the virial equation, a comprehensive step-by-step procedure and two examples of tripolytropic systems. The properties observed in the 2-layer case hold for any pairs of adjacent layers. In spite of a different internal structure, two multilayer configurations can share the same mass, same axis ratio, same size and same surface velocity (which is measured through a degeneracy parameter). Applications concern the determination of the interior of planets, exoplanets, stars and compact objects.

Chaotic Assessment of the Heave and Pitch Dynamics Motions of Air Cushion Vehicles

In this study, a three degrees of freedom nonlinear air cushion vehicle (ACV) model is introduced to examine the dynamic behavior of the heave and pitch responses in addition to the cushion pressure of the ACV in both time and frequency domains. The model is based on the compressible flow Bernoulli’s equation and the thermodynamics nonlinear isentropic relations along with the Newton second law of translation and rotation. In this study, the dynamical investigation was based on a numerical simulation using the stiff ODE solvers of the Matlab software. The chaotic investigations of the proposed model are provided using the Fast Fourier Transform (FFT), the Poincaré maps, and the regression analysis. Three control design parameters are investigated for the chaotic studies. These parameters are: ACV mass (<i>M</i>), the mass flow rate entering the cushion volume (<i>ṁin</i>), and the ACV base radius (r). Chaos behavior was observed for heave, and pitch responses as well as the cushion pressure.

Angular momentum transport by magnetoconvection and the magnetic modulation of the solar differential rotation

In order to explain the variance of the solar rotation law during the activity minima and maxima, the angular momentum transport by rotating magnetoconvection is simulated in a convective box penetrated by an inclined azimuthal magnetic field. Turbulence-induced kinetic and magnetic stresses and the Lorentz force of the large-scale magnetic background field are the basic transporters of angular momentum. Without rotation, the sign of the magnetic stresses naturally depends on the signs of the field components as positive (negative) BθBϕ transport the angular momentum poleward (equatorward). For fast enough rotation, however, the turbulence-originated Reynolds stresses start to dominate the transport of the angular momentum flux. The simulations show that positive ratios of the two meridional magnetic field components to the azimuthal field reduce the inward radial as well as the equatorward latitudinal transport, which result from hydrodynamic calculations. Only for BθBϕ > 0 (generated by solar-type rotation laws with an accelerated equator) does the magnetic-influenced rotation at the solar surface prove to be flatter than the nonmagnetic profile together with the observed slight spin-down of the equator. The latter phenomenon does not appear for antisolar rotation with polar vortex as well as for rotation laws with prevailing radial shear.

A control-orientated analytical model for a cyclorotor wave energy device with N hydrofoils

We present a new analytical model from which a model-based controller can be derived for a cyclorotor-based wave energy converter (WEC). Few cyclorotor-based WEC concepts and models have previously been studied and only one control strategy for the entire wave cancellation has been tested. Our model is derived for a horizontal cyclorotor with N hydrofoils and is suitable for the application of various control algorithms and the calculation of various performance metrics. The mechanical model is based on Newton’s second law for rotation. The cyclorotor operates in two dimensional potential flow. This paper modeled the velocity field in detail around the turbine with N hydrofoils by explaining each velocity term and estimated the generated torque using two methods (point source method and thin-chord method). The developed model is very convenient for control design, using the power take off torque and hydrofoil pitch angles as control inputs. The authors of this work have derived new, exact analytic functions for the free surface perturbation and induced fluid velocity field caused by hydrofoil rotation. These new formulae significantly decrease the model calculation time and increase the accuracy of the results. The new equations also provide useful insight into the nature of the associated variables, and are successfully validated against the results of physical experiments and numerical calculations previously published by two independent research groups. Representation of hydrofoils as both a point source and a thin chord were analysed, with both models cross-validated for the case of free rotation in monochromatic waves.

Destabilization of super-rotating Taylor–Couette flows by current-free helical magnetic fields

In an earlier paper we showed that the combination of azimuthal magnetic fields and super-rotation in Taylor–Couette flows of conducting fluids can be unstable against non-axisymmetric perturbations if the magnetic Prandtl number of the fluid is $\textrm {Pm}\neq 1$ . Here we demonstrate that the addition of a weak axial field component allows axisymmetric perturbation patterns for $\textrm {Pm}$ of order unity depending on the boundary conditions. The axisymmetric modes only occur for magnetic Mach numbers (of the azimuthal field) of order unity, while higher values are necessary for the non-axisymmetric modes. The typical growth time of the instability and the characteristic time scale of the axial migration of the axisymmetric mode are long compared with the rotation period, but short compared with the magnetic diffusion time. The modes travel in the positive or negative $z$ direction along the rotation axis depending on the sign of $B_\phi B_z$ . We also demonstrate that the azimuthal components of flow and field perturbations travel in phase if $|B_\phi |\gg |B_z|$ , independent of the form of the rotation law. Within a short-wave approximation for thin gaps it is also shown (in an appendix) that for ideal fluids the considered helical magnetorotational instability only exists for rotation laws with negative shear.

Axisymmetric models for neutron star merger remnants with realistic thermal and rotational profiles

Merging neutron stars are expected to produce hot, metastable remnants in rapid differential rotation, which subsequently cool and evolve into rigidly rotating neutron stars or collapse to black holes. Studying this metastable phase and its further evolution is essential for the prediction and interpretation of the electromagnetic, neutrino, and gravitational signals from such a merger. In this work, we model binary neutron star merger remnants and propose new rotation and thermal laws that describe post-merger remnants. Our framework is capable to reproduce quasi-equilibrium configurations for generic equations of state, rotation and temperature profiles, including nonbarotropic ones. We demonstrate that our results are in agreement with numerical relativity simulations concerning bulk remnant properties like the mass, angular momentum, and the formation of a massive accretion disk. Because of the low computational cost for our axisymmetric code compared to full 3+1-dimensional simulations, we can perform an extensive exploration of the binary neutron star remnant parameter space studying several hundred thousand configurations for different equation of states.

Clearance-Induced Orientation Uncertainty of Spherical Linkages

Abstract This paper proposes a kinematic model to evaluate the orientation uncertainty range of spherical linkages caused by the joint clearances. Based on the concepts of imaginary clearance link, spherical N-bar rotatability laws, and the invariant link rotatability, the uncertainty of the output angle can be treated as a mobility problem. The uncertainty region of the end-effector is treated as a workspace problem for the remodeled linkage. This paper highlights the orientation error by isolating the kinematic effects of joint clearance from other error factors. The discussion is carried out through spherical four-bar linkages and five-bar linkages. Numeric examples are presented to demonstrate the uncertainty range of the output angle and the uncertainty region of the end-effector. The result shows that, in the worst case, the error of each joint clearance will be magnified in a closed-loop structure compared with linearly adding all the clearance error. This implies that from a kinematics point of view, closed-loop spherical linkages or parallel manipulators will lead to a greater deviation on the end-effector than their open-loop counterparts. Using more passive joints in the manipulator may result in bigger error possibilities.

Применение программного обеспечения Simulink при проектировании судна

The article considers different types of controllers and regulators used in industry, laboratories and for daily tasks. In practice, the most commonly used controllers are discrete state controllers, PID controllers, fuzzy and neural controllers. The last two use more sophisticated concepts, such as artificial intelligence. Controllers can be divided into feed-forward and feedback controllers. The feed-forward controller works by giving a result based on waiting for the next step, while the feedback controller works to give an observable result that changes the processing value of the later step. PID controllers are very popular in the design of a ship's main power plant. There is considered a schematic diagram of the PID controller. The description of the ship model in the Simulink environment is presented, the specified model of the diesel engine, the mechanical regulator, areas of restrictions of the engine are illustrated. The model of the turbocharger is analyzed in detail. It consists of a turbine resting on the exhaust gases coming out of the cylinders, due to which the compressor starts and compresses the air at the inlet to the cylinders. There is given the equation formed by the ratio of integral to time. In accordance with the original model of the diesel engine Diesel Engine Module, the nominal efficiency is defined. A model of shaft dynamics based on Newton's second law for rotation is considered. The actual Simulink model is illustrated, which introduces transmission losses and saturation associated with the load capacity of the engine. The model uses three designs of propellers. The characteristics of the propellers on the container ship MSC Caitlin, the tanker “Ivan Poddubny” and the ferry “Olympiad” are given. The general model of the propeller is made and resistance of calm water is simulated. The additional model of wave resistance is presented.

Equilibrium sequences of differentially rotating stars with post-merger-like rotational profiles

ABSTRACT We present equilibrium sequences of rotating relativistic stars, constructed with a new rotation law that was proposed by Uryū et al. (2017). We choose rotational parameters motivated by simulations of binary neutron star merger remnants, but otherwise adopt a cold, relativistic N = 1 polytropic EOS, in order to perform a detailed comparison to published equilibrium sequences that used the Komatsu, Eriguchi and Hachisu (1989) rotation law. We find a small influence of the choice of rotation law on the mass of the equilibrium models and a somewhat larger influence on their radius. The versatility of the new rotation law allows us to construct models that have a similar rotational profile and axial ratio as observed for merger remnants, while at the same time being quasi-spherical. More specifically, we construct equilibrium sequence variations with different degrees of differential rotation and identify type A and type C solutions, similar to the corresponding types in the classification of Ansorg, Gondek-Rosińska and Villain (2009). While our models are highly accurate solutions of the fully general relativistic structure equations, we demonstrate that for models relevant to merger remnants the IWM-CFC approximation still maintains an acceptable accuracy.

On construction of the control that provides the desired trajectory of the movement of the single-link manipulator with elastic joint

The law of rotation of the electric motor, which ensures a global asymptotic direction of the trajectory of the model of a single-link manipulator with an elastic joint to a given program trajectory is obtained The elasticity of the joint is modeled by a torsion spring, the elastic force of which is considered to be nonlinearly dependent on the displacement. This fact makes it impossible to apply the usual approach and greatly complicates the task of control construction. The fact that some parameters of the model can be uncertain and, in some way, depend on some numerical parameter, the area of change of which is unknown in advance, also adds complexity. However, the use of DSC (Dynamic Surface Control) technique allows us to get the desired control. The development of the DSC technique, which consists in a specific choice of parameters and constants of filters, is proposed. It avoids the growth of the order of the auxiliary system, as well as a significant complication of the form of both the auxiliary system of differential equations and the control law, the so-called “explosion of terms”. It allows us to obtain explicitly the corresponding auxiliary function and to prove that the proposed control law solves the control problem. The robustness of such control is also proved, and the region of robustness in the system parameters space is defined. The obtained results are illustrated by the example of a mechanical model.

"Temple complexes" in the religious life of the trypillia community

In the period 4800-3600 BC. in the eastern part of the Trypillia area arose "giant settlements" or "megasites" / "mega-settlements" (working term of modern archaeologists) with thousands of buildings. In the central parts of these living conglomerates, scientists found special buildings that were recognized as sanctuaries, sacred complexes or temples. In the late period of the Trypillia culture they disappeared. These religious buildings were built with a focus visible processes of celestial bodies and the laws of cyclic rotation of the Earth in space, and included in their internal filling usually cruciform altars, ritual utensils, troughs with graters for the preparation of ritual bread and numerous other ceremonial and religious artifacts. There were also unique finds, such as gold jewelry (an element of prestige) and a perforated clay disk with tockins to it from the space of the Nebelivka Temple. The interior and exterior walls of the Trypillia sacral centers were painted with natural colors with a predominance of red. The wood carving for decoration of elements of a skeleton of a construction was investigated also. The first Temples on the European continent show that even at that time there was a cult of architecture. In general, it is clear that such Trypillia objects of religious worship carried encoded astronomical information in symbolic form. The building itself was oriented with regard to worldsides and designed relative to visible celestial bodies. This indicates that the people of Trypillia had a fairly clear worldview, which allowed them to reach the level of understanding the structure and mechanisms of many natural cyclical processes on Earth. Trypillia cosmology united the celestial and terrestrial spheres, and the Temple was the point of contact of the earth with the visible Universe.
 In his work, the author traces the existing analogies in the structure of construction of Trypillia and sacred complexes of the ancient Middle East and biblical ideas about the Tabernacle and the House of the Lord in the ancient Jews, given the fact, that the Trypillia temple building is known from 4,000 years BC. and several thousand years older than the Middle Eastern counterparts. There are also significant parallels in the construction of temples in the context of Indo-European religious heritage.
 It is noted that the Temple was not only a metaphysical reflection of the annual cycle with a focus on the points of the equinoxes and solstices, but also had a higher religious function, which consisted in the combination of the terrestrial sphere with the celestial, the connection of man with the mystery of the cosmos.

Long–Term Variations in Solar Differential Rotation and Sunspot Activity, II: Differential Rotation Around the Maxima and Minima of Solar Cycles 12 – 24

Studies of variations in the solar differential rotation are important for understanding the underlying mechanism of solar cycle and other variations of solar activity. We analyzed the sunspot-group daily data that were reported by Greenwich Photoheliographic Results (GPR) during the period 1874 – 1976 and Debrecen Photoheliographic Data (DPD) during the period 1977 – 2017. We determined the equatorial rotation rate [ $A$ ] and the latitude gradient [ $B$ ] components of the solar differential rotation by fitting the data in each of the 3-year moving time intervals (3-year MTIs) successively shifted by one year during the period 1874 – 2017 to the standard law of differential rotation. The values of $A$ and $B$ around the years of maxima and minima of Solar Cycles 12 – 24 are obtained from the 3-year MTIs series of $A$ and $B$ and studied the long-term cycle-to-cycle modulations in these coefficients. Here we have used the epochs of the maxima and minima of the Solar Cycles 12 – 24 that were recently determined from the revised Version-2 international sunspot-number series. We find that there exits a considerably significant secular decreasing-trend in $A$ around the maxima of solar cycles. There exist no secular trends in both $A$ and $B$ around the minima of solar cycles. The secular trend in $B$ around the maxima of solar cycles is also found to be statistically insignificant. We fitted a cosine function to the values of $A$ , and also to those of $B$ , after removing the corresponding linear trends. The cosine-fits suggest that there exist ≈54-year (≈94-year) and ≈82-year (≈79-year) periodicities in $A$ ( $B$ ) around the maxima and minima of solar cycles, respectively. The amplitude of the cosine-profile of $A$ ( $B$ ) around the minima of solar cycles is about 41% (65%) larger than that of $A$ ( $B$ ) around the maxima. In addition, the cosine profiles of $A$ and $B$ suggest a large (up to $180^{\circ }$ ) phase difference between the long-term variations of $A$ , and also between those of $B$ , around maxima and minima of solar cycles. Implications of all these results are discussed briefly.

Effect of the Problem-based Learning (PBL) Method with the Integration of Interactive Simulation on the Physical Sciences Conceptual Understanding of the Moroccan Common Core Learners

Thanks to its advantages in improving the learning, the understanding and the performance of learners, the interactive simulations have become among the main tools recommended by many researches as an alternative to the traditional pedagogical tools. Indeed, the forms and the objectives of the integration of simulations in teaching and learning process are varied depending on the pedagogical needs of the user, as well as according to the adopted learning methods and activities. In this contribution we aim to study the impact of problem-based learning (PBL) using interactive simulation, on the understanding of the concepts related to the rotational equilibrium, taught in common core science level. The concepts covered by this study are force and inventory, torque and Newton's second law for rotation. We first propose a selection grid to help teachers to choose the appropriate simulation product for a given problem-based learning activity, we later perform the experience to compare the performance of the students in the control group (who solve the problem using traditional method) and the students in the experimental group (who use the simulation tool) based on the pre-test and post-test methodology. The simulation tool used in the experimental part is determined using the grid that we have developed. Obtained results have shown that the use of interactive simulation has a positive effect on student's conceptual understanding, if it was properly integrated into an educational context.