Dissipative Torque Research Articles

Analysis of nonlinear vibration of lateral-torsional coupling for drill string in deviated well

To clarify the motion characteristic of the drill string in deviated well, the nonlinear dynamic model of lateral-torsional coupling for drill string system is established by the Lagrange equation. This model incorporates the contact between the drill string and borehole wall, torque dissipation, and borehole trajectory effects. Additionally, the contact behavior using linear elastic contact model is simulated. Meanwhile, the torque transfer law in the drill string system is described by a discrete torque-drag model. Finally, numerical simulations are employed to determine the dynamic properties of the drill string system. The results reveal that friction losses in drill string systems are increased with higher well inclination angles. The motion of BHA along the x direction is predominantly concentrated near the wellhole center at inclination angle of 65°, while in the y direction it primarily focuses on the low side of the wellhole. An increase in inclination angle leads to a more prominent occurrence of stick-slip motion in the drill string. When inclination angle more than 25°, there is a slightly higher collision frequency observed between the BHA and the low side of the borehole wall compared to that with the upper side. When increasing the WOB (weight on bit) to 160 kN, stick-slip motion becomes more pronounced within the drill string. Through parametric dynamics analysis of the drill string system, the rotary speed can be controlled in range from 40 to 70 r/min, and the WOB should be restricted in range from 20 to 40 kN in well depth 5000 m.

Matrix projective synchronization and mechanical analysis of unified chaotic system

This article explores the mechanical analysis of a unified chaotic system and matrix projective synchronization (MPS). The sufficient conditions to achieve MPS of unified chaotic system have derived. The mechanics of unified chaotic system have been examined in contrast with Kolmogorov system, Euler equation, and Hamiltonian function. The Casimir energy function is also introduced to analyze the system dynamics. The unified chaotic system has been transformed into Kolmogorov type system and decomposed into four types of torques: inertial, internal, dissipation, and external torque. In order to view the mechanics behind the unified chaotic system, different particular cases have been discussed. Five scenarios are examined using combinations of various torques in order to identify the key elements in chaos creation and their physical significance. The bifurcation diagram, Lyapunov exponent and Lyapunov dimension validates the generation of chaos for different particular cases.

Accurate Computations up to Breakdown of Quasi-Periodic Attractors in the Dissipative Spin–Orbit Problem

We consider a Celestial Mechanics model: the spin–orbit problem with a dissipative tidal torque, which is a singular perturbation of a conservative system. The goal of this paper is to show that it is possible to maintain the accuracy and reliability of the computation of quasi-periodic attractors for parameter values extremely close to the breakdown and, therefore, it is possible to obtain information on the breakdown mechanism of these quasi-periodic attractors. The method uses at the same time numerical and rigorous improvements to provide (i) a very accurate computation of the time-1 map of the spin–orbit problem (which reduces the dimensionality of the problem); (ii) a very efficient KAM method for maps which computes the attractor and its tangent spaces (by quadratically convergent, low storage requirements, and low operation count); (iii) explicit algorithms backed by a rigorous a posteriori KAM theorem, which establishes that if the algorithm is successful and produces a small residual, then there is a true solution nearby; and (iv) guaranteed algorithms to reach arbitrarily close to the border of existence as long as there are enough computer resources. As a by-product of the accuracy that we maintain till breakdown, we study several scale-invariant observables of the tori used in the renormalization group of infinite-dimensional spaces. In contrast with previously studied simple models, the behavior at breakdown of the spin–orbit problem does not satisfy standard scaling relations which implies that the spin–orbit problem is not described by a hyperbolic fixed point of the renormalization operator.

Experiment study on reactive powder concrete beams using spirals reinforcement under torsion

This paper investigates the torsional behavior of reactive powder concrete (RPC) beams using spiral reinforcement. The influences of parameters, including different spiral reinforcement configuration, spiral reinforcement ratio, and the steel fiber content on the torsional performance of the nine RPC beams, were investigated and discussed. The experimental results showed that the failure mode, ultimate torque, torsional stiffness, and energy dissipation of the RPC beams were not affected by longitudinal reinforcement alone, but it improved the ductility. Compared to commonly used stirrups, the locked spiral reinforcement exhibits more torsional ductility, stiffness, and ultimate torque of the RPC beams. But the torsional ductility, stiffness, and ultimate torque decreased when the spiral reinforcement was unlocked. The cracking torque and pre-cracking torsional stiffness of beams were less affected by the locking and unlocking of spiral reinforcement. Greater steel fiber content and spiral reinforcement ratio resulted in higher torsional ductility, torsional stiffness, energy dissipation and ultimate torque of the locked spiral reinforcement reinforced beams. The pre-yielding torsional stiffness and plastic dissipation capacity were strongly influenced by spiral reinforcement states and spiral reinforcement ratio. The pre-cracking torsional stiffness and energy dissipation of RPC beam were determined by the steel fiber content. Considering the torsional contribution of steel fiber and concrete tensile strength, a new formula for calculating the ultimate torque of RPC beam was proposed, and the calculated value was closer to the experimental value.

Torques and Moments of Inertia Models for Horizontal Axis Hydrokinetic Turbine Driveline

The quantification of torques and moments of inertia of horizontal axis hydrokinetic turbine driveline is important to precisely predict the dynamic behavior of the complete system. Initially, this paper presents different models used in the literature for describing torques and moments of inertia of turbine components. A dynamic model of a small hydrokinetic turbine using belt transmission is developed. The model uses the Blade Element Momentum (BEM) for determining the power coefficient of the turbine rotor and considers the inertial effects and dissipative torques of whole system using some of the torque models and moments of inertia described previously. The results for the dynamical behavior of the turbine model are compared with experimental data, showing good agreement. In order to numerically analyze a more efficient drivetrain, the belt transmission is replaced by a planetary gearbox in the dynamic model, and the new results are also assessed. As a result, it was found that with planetary gears, a more compact transmission can be used, reducing the inertial effects, which brings a better efficiency in the starting of the machine and shortening the transient regime time.

The differential precession of Earth’s fluid and solid cores

The Earth’s spin axis is inclined by ∊=23.4° with respect to the ecliptic normal and precesses in space with a period of 26 kyr. The fluid core and solid inner core precess at slightly different angles. Here, we compute their differential precession angles on the basis of an elastically deforming Earth and dissipative torques inferred from nutation observations. We show that the precession angle of the fluid core is larger than that of the mantle by 1.714 arcsec and lags behind it by 0.0124 arcsec. The precession angle of the spin (and figure) axis of the inner core is smaller than that of the mantle by 1.861 arcsec and trails behind it by 3.660 arcsec. These correspond to differential velocities (Δv) at the core mantle boundary (CMB) and inner core boundary (ICB) of 2.11 and 2.21 mm/s, to associated boundary layer Reynolds (Re) numbers of 247 and 258, and to dissipations D of 4.6 and 14.5 GW. At such Re values the flow in the core should feature wavelike instabilities but should not be in a fully developed turbulent regime. Δv and Re at the CMB have remained approximately constant in the past 4 Gyr, and D has been steadily decreasing from a maximum of approximately double its present-day value. At the ICB, Δv,Re and D have all increased since inner core formation. Future projections indicate that Re and D at the ICB may reach 500 and 100 GW, respectively, in a few Gyr. Our results suggest that, for the whole of Earth’s history, dissipation from the misaligned precession of the fluid and solid cores has contributed only a small fraction of the total heat flux out of the core and has not provided an important power source for maintaining the geodynamo.

ДЕЯКІ ЗАДАЧІ ПРО РУХ ТВЕРДОГО ТІЛА У СЕРЕДОВИЩІ З ОПОРОМ

The dynamics of rotating rigid bodies is a classical topic of study in mechanics. In the eighteenth and nineteenth centuries, several aspects of a rotating rigid body motion were studied by famous mathematicians as Euler, Jacobi, Poinsot, Lagrange, and Kovalevskya. However, the study of the dynamics of rotating bodies of still important for aplications such as the dynamics of satellite-gyrostat, spacecraft, re-entry vehicles, theory of gyroscopes, modern technology, navigation, space engineering and many other areas. A number of studies are devoted to the dynamics of a rigid body in a resistive medium. The presence of the velocity of proper rotation of the rigid body leads to the apearance of dissipative torques causing the braking of the body rotation. These torques depend on the properties of resistant medium in which the rigid body motions occur, on the body shape, on the properties of the surface of the rigid body and the distribution of mass in the body and on the characters of the rigid body motion. Therefore, the dependence of the resistant torque on the orientation of the rigid body and its angular velocity can de quite complicated and requires consideration of the motion of the medium around the body in the general case. We confine ourselves in this paper to some simple relations that can qualitative describe the resistance to rigid body rotation at small angular velocities and are used in the literature. In setting up the equations of motion of a rigid body moving in viscous medium, we need to consider the nature of the resisting force generated by the motion of the rigid body. The evolution of rotations of a rigid body influenced by dissipative disturbing torques were studied in many papers and books. The problems of motion of a rigid body about fixed point in a resistive medium described by nonlinear dynamic Euler equations. An analytical solution of the problem when the torques of external resistance forces are proportional to the corresponding projections of the angular velocity of the rigid body is obtain in several works. The dependence of the dissipative torque of the resistant forces on the angular velocity vector of rotation of the rigid body is assumed to be linear. We consider dynamics of a rigid body with arbitrary moments of inertia subjected to external torques include small dissipative torques.

KAM quasi-periodic tori for the dissipative spin–orbit problem

We provide evidence of the existence of KAM quasi-periodic attractors for a dissipative model in Celestial Mechanics. We compute the attractors extremely close to the breakdown threshold.We consider the spin–orbit problem describing the motion of a triaxial satellite around a central planet under the simplifying assumption that the center of mass of the satellite moves on a Keplerian orbit, the spin-axis is perpendicular to the orbit plane and coincides with the shortest physical axis. We also assume that the satellite is non-rigid; as a consequence, the problem is affected by a dissipative tidal torque that can be modeled as a time-dependent friction, which depends linearly upon the velocity.Our goal is to fix a frequency and compute the embedding of a smooth attractor with this frequency. This task requires to adjust a drift parameter.We have shown in Calleja et al. (2020) that it is numerically efficient to study Poincaré maps; the resulting spin–orbit map is conformally symplectic, namely it transforms the symplectic form into a multiple of itself. In Calleja et al. (2020), we have developed an extremely efficient (quadratically convergent, low storage requirements and low operation count per step) algorithm to construct quasi-periodic solutions and we have implemented it in extended precision. Furthermore, in Calleja et al. (2020) we have provided an “a-posteriori” KAM theorem that shows that if we have an embedding and a drift parameter that satisfy the invariance equation up to an error which is small enough with respect to some explicit condition numbers, then there is a true solution of the invariance equation. This a-posteriori result is based on a Nash–Moser hard implicit function theorem, since the Newton method incurs losses of derivatives.The goal of this paper is to provide numerical calculations of the condition numbers and verify that, when they are applied to the numerical solutions, they will lead to the existence of the torus for values of the parameters extremely close to the parameters of breakdown. Computing reliably close to the breakdown allows to discover several interesting phenomena, which we will report in Calleja et al. (2020).The numerical calculations of the condition numbers presented here are not completely rigorous, since we do not use interval arithmetic to estimate the round off error and we do not estimate rigorously the truncation error, but we implement the usual standards in numerical analysis (using extended precision, checking that the results are not affected by the level of precision, truncation, etc.). Hence, we do not claim a computer-assisted proof, but the verification is more convincing than a standard numerics. We hope that our work could stimulate a computer-assisted proof.

Effect of bearing dissipative torques on the dynamic behavior of H-Darrieus wind turbines

Effect of bearing dissipative torques on the dynamic behavior of H-Darrieus wind turbines

Self-induced spin-orbit torques in metallic ferromagnets

We present a phenomenological theory of spin-orbit torques in a metallic ferromagnet with spin-relaxing boundaries. The model is rooted in the coupled diffusion of charge and spin in the bulk of the ferromagnet, where we account for the anomalous Hall effects as well as the anisotropic magnetoresistance in the corresponding constitutive relations for both charge and spin sectors. The diffusion equations are supplemented with suitable boundary conditions reflecting the spin-sink capacity of the environment. In inversion-asymmetric heterostructures, the uncompensated spin accumulation exerts a dissipative torque on the order parameter, giving rise to a current-dependent linewidth in the ferromagnetic resonance with a characteristic angular dependence. We compare our model to recent spin-torque ferromagnetic resonance measurements, illustrating how rich self-induced spin-torque phenomenology can arise even in simple magnetic structures.

Voltage-control of damping constant in magnetic-insulator/topological-insulator bilayers

The magnetic damping constant is a critical parameter for magnetization dynamics and the efficiency of memory devices and magnon transport. Therefore, its manipulation by electric fields is crucial in spintronics. Here, we theoretically demonstrate the voltage-control of magnetic damping in ferro- and ferrimagnetic-insulator (FI)/topological-insulator (TI) bilayers. Assuming a capacitor-like setup, we formulate an effective dissipation torque induced by spin-charge pumping at the FI/TI interface as a function of an applied voltage. By using realistic material parameters, we find that the effective damping for a FI with 10 nm thickness can be tuned by one order of magnitude under the voltage of 0.25 V. Also, we provide perspectives on the voltage-induced modulation of the magnon spin transport on proximity-coupled FIs.

Microscopic calculation of spin torques in textured antiferromagnets

A microscopic calculation is presented for the spin-transfer torques (STT) and damping torques in metallic antiferromagnets (AF). It is found that the sign of the STT is opposite to that in ferromagnets because of the AF transport character, and the current-to-STT conversion factor is enhanced near the AF gap edge. The dissipative torque parameter $\beta_n$ and the damping parameter $\alpha_n$ for the N\'eel vector arise from spin relaxation of electrons. Physical consequences are demonstrated for the AF domain wall motion using collective coordinates, and some similarities to the ferromagnetic case are pointed out such as intrinsic pinning and the specialty of $\alpha_n = \beta_n$. A recent experiment on a ferrimagnetic GdFeCo near its angular-momentum compensation temperature is discussed.

Spin-orbit torques and magnetotransport of two-dimensional Dirac electrons without particle-hole symmetry

We study spin-orbit torques and transport properties of Dirac electrons on the surface of ferromagnetic topological insulators. A focus is on the effects of deviation from the ideal Dirac model with linear dispersion, which takes an additional scalar form, quadratic in wave vector, and breaks particle-hole symmetry. This term removes some peculiar features of the linear Dirac model, and, combined with in-plane magnetization, gives rise to in-plane anisotropies. We study in detail the chemical potential dependence of longitudinal/transverse conductivities and reactive/dissipative spin-orbit torques, including the out-of-plane spin polarization. It is found that the in-plane anisotropy is generally stronger for $p$-type carriers than $n$-type carriers (for positive curvature of the quadratic term). It is also found that the in-plane anisotropy of the dissipative spin-orbit torque changes sign across the Dirac point. Because of the similarity of the model, we also study the magnetic Rashba model focusing on its Dirac-like parameter region. In this model, with an in-plane magnetization, a curious discontinuity is found at the Dirac point in the current-induced out-of-plane spin polarization.

Dynamically stable negative-energy states induced by spin-transfer torques

We investigate instabilities of the magnetic ground state in ferromagnetic metals that are induced by uniform electrical currents, and, in particular, go beyond previous analyses by including dipolar interactions. These instabilities arise from spin-transfer torques that lead to Doppler shifted spin waves. For sufficiently large electrical currents, spin-wave excitations have negative energy with respect to the uniform magnetic ground state, while remaining dynamically stable due to dissipative spin-transfer torques. Hence, the uniform magnetic ground state is energetically unstable, but is not able to dynamically reach the new ground state. We estimate this to happen for current densities $ j\gtrsim (1-D/D_c)10^{13} \mathrm{A/m^2} $ in typical thin film experiments, with $ D $ the Dzyaloshinskii-Moriya interaction constant, and $ D_c $ the Dzyaloshinskii-Moriya interaction that is required for spontaneous formation of spirals or skyrmions. These current densities can be made arbitrarily small for ultrathin film thicknesses at the order of nanometers, due to surface- and interlayer effects. From an analogue gravity perspective, the stable negative energy states are an essential ingredient to implement event horizons for magnons -- the quanta of spin waves -- giving rise to e.g. Hawking radiation and can be used to significantly amplify spin waves in a so-called black-hole laser.

Nonlinear Control for Attitude Stabilization of a Rigid Body Forced by Nonstationary Disturbances with Zero Mean Values

A rigid body forced by a nonstationary perturbing torque with zero mean value is under consideration. The control strategy for attitude stabilization of the rigid body is based on the usage of dissipative and restoring torques. It is assumed that the dissipative torque is linear, while restoring and perturbing torques are purely nonlinear. A theorem on sufficient conditions for asymptotic stability of the body angular position is proved on the basis of the decomposition method, the Lyapunov direct method and the averaging technique. Computer simulation results illustrating the theorem are presented.

Dynamical torque from Shiba states ins-wave superconductors

Magnetic impurities inserted in a $s$-wave superconductor give rise to spin-polarized in-gap states called Shiba states. We study the back-action of these induced states on the dynamics of the classical moments. We show that the Shiba state pertains to both reactive and dissipative torques acting on the precessing classical spin that can be detected through ferromagnetic resonance measurements. Moreover, we highlight the influence of the bulk states as well as the effect of the finite linewidth of the Shiba state on the magnetization dynamics. Finally, we demonstrate that the torques are a direct measure of the even and odd frequency triplet pairings generated by the dynamics of the magnetic impurity. Our approach offers non-invasive alternative to the STM techniques used to probe the Shiba states.

The spin–spin model and the capture into the double synchronous resonance

The aim of this article is to propose a model, that is a planar version of the full two-body problem, and discuss the existence and stability of a relevant periodic solution. Consider two homogeneous ellipsoids orbiting around each other in fixed coplanar Keplerian orbits. Moreover, their respective spin axes are assumed to be perpendicular to the orbital plane, that is also a common equatorial plane. The spin–spin model deals with the coupled rotational dynamics of both ellipsoids. For a non-zero orbital eccentricity, it has the structure of a non-autonomous system of coupled pendula. This model is a natural extension of the classical spin–orbit problem for two extended bodies. In addition, we consider dissipative tidal torques, that can trigger the capture of the system into spin–orbit and spin–spin resonances. In this paper we give some theoretical results for both the conservative model and the dissipative one. The conservative model has a Hamiltonian structure. We use properties of Hamiltonian systems to give some sufficient conditions in the space of parameters of the model, that guarantee existence, uniqueness and linear stability of an odd periodic solution. This solution represents a double synchronous resonance in the conservative regime. Such solution can be continued to the dissipative regime, where it becomes asymptotically stable. We see asymptotic stability as a dynamical mechanism for the capture into the double synchronous resonance. Finally we apply our results to several cases including the Pluto–Charon binary system and the Trojan binary asteroid 617 Patroclus, target of the LUCY mission.

Collective spin dynamics under dissipative spin Hall torque

Current-induced spin torques in layered magnetic heterostructures have many commonalities across broad classes of magnetic materials. These include not only collinear ferromagnets, ferrimagnets, and antiferromagnets but also more complex noncollinear spin systems. We develop a general Lagrangian–Rayleigh approach for studying the role of dissipative torques, which can pump energy into long-wavelength magnetic dynamics, causing dynamic instabilities. While the Rayleigh structure of such torques is similar for different magnetic materials, their consequences depend sensitively on the nature of the order and, in particular, on whether there is a net magnetic moment. The latter endows the system with a unipolar switching capability, while magnetically compensated materials tend to evolve toward limit cycles, at large torques, with chirality dependent on the torque sign. Apart from the ferromagnetic and antiferromagnetic cases, we discuss ferrimagnets, which display an intricate competition between switching and limit cycles. As a simple case for compensated noncollinear order, we consider isotropic spin glasses and a scenario of their coexistence with a collinear magnetic order.

Evolution of a heavy rigid body rotation under the action of unsteady restoring and perturbation torques

The paper develops an approximate solution to the system of Euler’s equations with additional perturbation term for dynamically symmetric rotating rigid body. The perturbed motions of a rigid body, close to Lagrange’s case, under the action of restoring and perturbation torques that are slowly varying in time are investigated. We describe an averaging procedure for slow variables of a rigid body perturbed motion, similar to Lagrange top. Conditions for the possibility of averaging the equations of motion with respect to the nutation phase angle are presented. The averaging technique reduces the system order from 6 to 3 and does not contain fast oscillations. An example of motion of the body using linearly dissipative torques is worked out to demonstrate the use of general equations. The numerical integration of the averaged system of equations is conducted of the body motion. The graphical presentations of the solutions are represented and discussed. A new class of rotations of a dynamically symmetric rigid body about a fixed point with account for a nonstationary perturbation torque, as well as for a restoring torque that slowly varies with time, is studied. The main objective of this paper is to extend the previous results for problem of the dynamic motion of a symmetric rigid body subjected to perturbation and restoring torques. The proposed averaging method is implemented to receive the averaging system of equations of motion. The graphical representations of the solutions are presented and discussed. The attained results are a generalization of our former works where µ and Mi are independent of the slow time τ and Mi depend on the slow time only.

Spintronics Meets Nonadiabatic Molecular Dynamics: Geometric Spin Torque and Damping on Dynamical Classical Magnetic Texture due to an Electronic Open Quantum System.

We analyze a quantum-classical hybrid system of steadily precessing around the fixed axis slow classical localized magnetic moments (LMMs), forming a head-to-head domain wall, surrounded by fast electrons driven out of equilibrium by LMMs and residing within a metallic wire whose connection to macroscopic reservoirs makes electronic quantum system an open one. The model captures the essence of dynamical noncollinear magnetic textures encountered in spintronics, while making it possible to obtain the exact time-dependent nonequilibrium density matrix of electronic systems and split it into four contributions. The Fermi surface contribution generates dissipative (or dampinglike in spintronics terminology) spin torque on LMMs, as the counterpart of electronic friction in nonadiabatic molecular dynamics (MD). Among two Fermi sea contributions, one generates geometric torque dominating in the adiabatic regime, which remains as the only nonzero contribution in a closed system with disconnected reservoirs. Locally geometric torque can have nondissipative (or fieldlike in spintronics terminology) component, acting as the counterpart of geometric magnetism force in nonadiabatic MD, as well as a much smaller dampinglike component acting as "geometric friction." Such current-independent geometric torque is absent from widely used micromagnetics or atomistic spin dynamics modeling of magnetization dynamics based on the Landau-Lifshitz-Gilbert equation, while previous analyses of how to include our Fermi-surface dampinglike torque have severely underestimated its total magnitude.