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Showing papers on "Equations of motion published in 2020"


Journal ArticleDOI
TL;DR: The HEOM theory has been used to treat systems of practical interest, in particular, to account for various linear and nonlinear spectra in molecular and solid state materials, to evaluate charge and exciton transfer rates in biological systems, to simulate resonant tunneling and quantum ratchet processes in nanodevices, and to explore quantum entanglement states in quantum information theories.
Abstract: An open quantum system refers to a system that is further coupled to a bath system consisting of surrounding radiation fields, atoms, molecules, or proteins. The bath system is typically modeled by an infinite number of harmonic oscillators. This system-bath model can describe the time-irreversible dynamics through which the system evolves toward a thermal equilibrium state at finite temperature. In nuclear magnetic resonance and atomic spectroscopy, dynamics can be studied easily by using simple quantum master equations under the assumption that the system-bath interaction is weak (perturbative approximation) and the bath fluctuations are very fast (Markovian approximation). However, such approximations cannot be applied in chemical physics and biochemical physics problems, where environmental materials are complex and strongly coupled with environments. The hierarchical equations of motion (HEOM) can describe the numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system-bath interactions, which has been verified on the basis of exact analytical solutions (non-Markovian tests) with any desired numerical accuracy. The HEOM theory has been used to treat systems of practical interest, in particular, to account for various linear and nonlinear spectra in molecular and solid state materials, to evaluate charge and exciton transfer rates in biological systems, to simulate resonant tunneling and quantum ratchet processes in nanodevices, and to explore quantum entanglement states in quantum information theories. This article presents an overview of the HEOM theory, focusing on its theoretical background and applications, to help further the development of the study of open quantum dynamics.

223 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the D → 4 limit of the D-dimensional Einstein-Gauss-Bonnet gravity, where the limit is taken with α ˜ = (D − 4 ) α kept fixed and α is the original Gauss- Bonnet coupling.

157 citations


Journal ArticleDOI
TL;DR: In this paper, a 4D Einstein-Gauss-Bonnet gravity has been proposed by Glavan and Lin (2020 Phys. Rev. Lett. 124 081301) by rescaling the coupling and taking the limit at the level of equations of motion.
Abstract: Recently, a novel 4D Einstein–Gauss–Bonnet gravity has been proposed by Glavan and Lin (2020 Phys. Rev. Lett. 124 081301) by rescaling the coupling and taking the limit at the level of equations of motion. This prescription, though was shown to bring non-trivial effects for some spacetimes with particular symmetries, remains mysterious and calls for scrutiny. Indeed, there is no continuous way to take the limit in the higher D-dimensional equations of motion because the tensor indices depend on the spacetime dimension and behave discretely. On the other hand, if one works with 4D spacetime indices the contribution corresponding to the Gauss–Bonnet term vanishes identically in the equations of motion. A necessary condition (but may not be sufficient) for this procedure to work is that there is an embedding of the 4D spacetime into the higher D-dimensional spacetime so that the equations in the latter can be properly interpreted after taking the limit. In this note, working with 2D Einstein gravity, we show several subtleties when applying the method used in (2020 Phys. Rev. Lett. 124 081301).

151 citations


Journal ArticleDOI
TL;DR: In this article, the free vibration and buckling responses of functionally graded nanoplates with magneto-electro-elastic coupling are studied for the first time using a nonlocal modified sinusoidal shear deformation plate theory including the thickness stretching effect.
Abstract: In this study, the free vibration and buckling responses of functionally graded nanoplates with magneto-electro-elastic coupling are studied for the first time using a nonlocal modified sinusoidal shear deformation plate theory including the thickness stretching effect. The constitutive relations for these kind of structures are defined. The equations of motion for rectangular sandwich plates in macro and nano scale are derived using a modified dynamic version of Hamilton's principle including a contribution of the electric and magnetic fields. The closed-form analytical solution to simply supported plates is obtained using Navier solution technique. A power-law distribution and a half cosine variation are used to model the variation of materials properties and electric/magnetic potentials, respectively. The analytical solutions are verified with well-known solutions in the literature. A parametric study was conducted to show the effect of nonlocal parameter, power-law index, predefined electric and magnetic fields, axial compressive and tensile forces, the aspect ratio of plates, and volume ratio of functionally graded and piezomagnetic layers on mechanical behaviors of nanoplates. Obtained numerical results can be used as benchmark values for validation of correctness of diverse analytical and numerical methods applied for design and analysis of composite nanoelectromechanical systems.

140 citations


Journal ArticleDOI
TL;DR: The hierarchical equations of motion (HEOM) theory as discussed by the authors can describe numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system.
Abstract: An open quantum system refers to a system that is further coupled to a bath system consisting of surrounding radiation fields, atoms, molecules, or proteins. The bath system is typically modeled by an infinite number of harmonic oscillators. This system-bath model can describe the time-irreversible dynamics through which the system evolves toward a thermal equilibrium state at finite temperature. In nuclear magnetic resonance and atomic spectroscopy, dynamics can be studied easily by using simple quantum master equations under the assumption that the system-bath interaction is weak (perturbative approximation) and the bath fluctuations are very fast (Markovian approximation). However, such approximations cannot be applied in chemical physics and biochemical physics problems, where environmental materials are complex and strongly coupled with environments. The hierarchical equations of motion (HEOM) can describe numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system--bath interactions, which has been verified on the basis of exact analytical solutions (non-Markovian tests) with any desired numerical accuracy. The HEOM theory has been used to treat systems of practical interest, in particular to account for various linear and nonlinear spectra in molecular and solid state materials, to evaluate charge and exciton transfer rates in biological systems, to simulate resonant tunneling and quantum ratchet processes in nanodevices, and to explore quantum entanglement states in quantum information theories. This article, presents an overview of the HEOM theory, focusing on its theoretical background and applications, to help further the development of the study of open quantum dynamics.

139 citations


Journal ArticleDOI
TL;DR: In this paper, a fundamental study on the nonlinear vibrations considering large amplitude in multi-sized hybrid nano-composites (MHC) disk (MHCD) relying on nonlinear elastic media and located in an environment with gradually changed temperature feature is presented.
Abstract: This is a fundamental study on the nonlinear vibrations considering large amplitude in multi-sized hybrid Nano-composites (MHC) disk (MHCD) relying on nonlinear elastic media and located in an environment with gradually changed temperature feature. Carbon fibers (CF) or carbon nanotubes (CNTs) in the macro or nano sizes respectively are responsible for reinforcing the matrix. For prediction of the efficiency of the properties MHCD's modified Halpin-Tsai theory has been presented. The strain-displacement relation in multi-sized laminated disk's nonlinear dynamics through applying Von Karman nonlinear shell-theory and using third-order-shear-deformation-theory (TSDT) is determined. The energy methods called Hamilton's principle is applied for deriving the motion equations along with Boundary Conditions (BCs), which has ultimately been solved using the perturbation approach (PA) and generalized differential quadrature method (GDQM). At the final stage, the outcomes illustrate that patterns of FG, fibers' various directions, the WCNT and VF factors, top surface's applied temperature and temperature gradient have considerable impact on the MHCD's nonlinear dynamics. Another important consequence is that, the influences of the θ, WCNT and VF amounts on the disk's nonlinear vibrations may be taken into account at the larger amounts of the high deflection element and the negative axial load's impact on the structure's nonlinear dynamics is more extreme. A more general conclusion of this study is that for designing the MHCD should be more attention to the nonlinearity parameter.

136 citations


Journal ArticleDOI
TL;DR: In this article, a quasi-3D hyperbolic shear deformation theory is proposed to analyze the statics and free vibration of functionally graded porous plates resting on elastic foundations, and the equations of motion are derived from the Hamilton principle.
Abstract: This work investigates a new type of quasi-3D hyperbolic shear deformation theory is proposed in this study to discuss the statics and free vibration of functionally graded porous plates resting on elastic foundations. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. By including indeterminate integral variables, the number of unknowns and governing equations of the present theory is reduced, and therefore, it is easy to use. The present approach to plate theory takes into account both transverse shear and normal deformations and satisfies the boundary conditions of zero tensile stress on the plate surfaces. The equations of motion are derived from the Hamilton principle. Analytical solutions are obtained for a simply supported plate. Contrary to any other theory, the number of unknown functions involved in the displacement field is only five, as compared to six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to verify the accuracy and efficiency of the present theory. The influences of the porosity parameter, power-law index, aspect ratio, thickness ratio and the foundation parameters on bending and vibration of porous FG plate.

134 citations


Journal ArticleDOI
TL;DR: In this paper, a new theoretical framework for the Einstein-Gauss-Bonnet theories of gravity is introduced, which results to particularly elegant, functionally simple and transparent gravitational equations of motion, slow-roll indices and the corresponding observational indices.

131 citations


Journal ArticleDOI
TL;DR: The covariant phase space method of Iyer, Lee, Wald, and Zoupas as discussed by the authors gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance.
Abstract: The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance. The original literature however does not systematically treat total derivatives and boundary terms, which has led to some confusion about how exactly to apply the formalism in the presence of boundaries. In particular the original construction of the canonical Hamiltonian relies on the assumed existence of a certain boundary quantity “B”, whose physical interpretation has not been clear. We here give an algorithmic procedure for applying the covariant phase space formalism to field theories with spatial boundaries, from which the term in the Hamiltonian involving B emerges naturally. Our procedure also produces an additional boundary term, which was not present in the original literature and which so far has only appeared implicitly in specific examples, and which is already nonvanishing even in general relativity with sufficiently permissive boundary conditions. The only requirement we impose is that at solutions of the equations of motion the action is stationary modulo future/past boundary terms under arbitrary variations obeying the spatial boundary conditions; from this the symplectic structure and the Hamiltonian for any diffeomorphism that preserves the theory are unambiguously constructed. We show in examples that the Hamiltonian so constructed agrees with previous results. We also show that the Poisson bracket on covariant phase space directly coincides with the Peierls bracket, without any need for non-covariant intermediate steps, and we discuss possible implications for the entropy of dynamical black hole horizons.

121 citations


Journal ArticleDOI
TL;DR: In this article, the buckling and vibrational behavior of the composite beam armed with single-walled carbon nanotubes (SW-CNT) resting on Winkler-Pasternak elastic foundation are investigated.
Abstract: In this work, the buckling and vibrational behavior of the composite beam armed with single-walled carbon nanotubes (SW-CNT) resting on Winkler-Pasternak elastic foundation are investigated. The CNT-RC beam is modeled by a novel integral first order shear deformation theory. The current theory contains three variables and uses the shear correction factors. The equivalent properties of the CNT-RC beam are computed using the mixture rule. The equations of motion are derived and resolved by Applying the Hamilton\'s principle and Navier solution on the current model. The accuracy of the current model is verified by comparison studies with others models found in the literature. Also, several parametric studies and their discussions are presented.

121 citations


Journal ArticleDOI
TL;DR: In this article, a harmonic oscillator with position-dependent mass is investigated, and the classical Euler-Lagrange equations of motion are derived from the classical Lagrangian.
Abstract: In this study, a harmonic oscillator with position-dependent mass is investigated. Firstly, as an introduction, we give a full description of the system by constructing its classical Lagrangian; thereupon, we derive the related classical equations of motion such as the classical Euler–Lagrange equations. Secondly, we fractionalize the classical Lagrangian of the system, and then we obtain the corresponding fractional Euler–Lagrange equations (FELEs). As a final step, we give the numerical simulations corresponding to the FELEs within different fractional operators. Numerical results based on the Caputo and the Atangana-Baleanu-Caputo (ABC) fractional derivatives are given to verify the theoretical analysis.

Journal ArticleDOI
TL;DR: In this paper, a dynamic analysis of the FG-sandwich plate seated on elastic foundation with various kinds of support using refined shear deformation theory is presented, in which the unknowns number is reduced.
Abstract: The current work, present dynamic analysis of the FG-sandwich plate seated on elastic foundation with various kinds of support using refined shear deformation theory. The present analytical model is simplified which the unknowns number are reduced. The zero-shear stresses at the free surfaces of the FG-sandwich plate are ensured without introducing any correction factors. The four equations of motion are determined via Hamilton\' principle and solved by Galerkin\'s approach for FG-sandwich plate with three kinds of the support. The proposed analytical model is verified by comparing the results with those obtained by other theories existing in the literature. The parametric studies are presented to detect the various parameters influencing the fundamental frequencies of the symmetric and non-symmetric FG-sandwich plate with various boundary conditions.

Journal ArticleDOI
TL;DR: In this article, the Coulomb solution in gauge theory is compared to the two-parameter Janis-Newman-Winicour solution in gravity, which is a static, spherically symmetric, asymptotically fiat solution that generically includes a dilaton field, but admits the Schwarzschild solution as a special case.
Abstract: The classical double copy relates solutions to the equations of motion in gauge theory and in gravity. In this paper, we present two double-copy formalisms for relating the Coulomb solution in gauge theory to the two-parameter Janis-Newman-Winicour solution in gravity. The latter is a static, spherically symmetric, asymptotically fiat solution that generically includes a dilaton field, but also admits the Schwarzschild solution as a special case. We first present the classical double copy as a perturbative construction, similar to its formulation for scattering amplitudes, and then present it as an exact map, with a novel generalisation of the Kerr-Schild double copy motivated by double field theory. The latter formalism exhibits the relation between the Kerr-Schild classical double copy and the string theory origin of the double copy for scattering amplitudes.

Journal ArticleDOI
TL;DR: The present plate theory approach accounts for both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor.
Abstract: This work presents an efficient and original high-order shear and normal deformation theory for the static and free vibration analysis of functionally graded plates. The Hamilton’s principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. The present plate theory approach accounts for both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.

Journal ArticleDOI
TL;DR: In this article, the influence of boundary conditions on the bending and free vibration behavior of functionally graded sandwich plates resting on a two-parameter elastic foundation is examined using an original high order shear theory.
Abstract: The influence of boundary conditions on the bending and free vibration behavior of functionally graded sandwich plates resting on a two-parameter elastic foundation is examined using an original novel high order shear theory. The Hamilton\'s principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. This theory includes indeterminate integral variables and contains only four unknowns in which any shear correction factor not used, with even less than the conventional theory of first shear strain (FSDT). Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five, six or more in the case of other shear deformation theories. Galerkin\'s approach is utilized for FGM sandwich plates with six different boundary conditions. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.

Journal ArticleDOI
TL;DR: In this paper, the impact of the induced magnetic field of peristaltic flow for an incompressible Williamson fluid in the curved channel is examined and the effects of embedded parameters portrayed and discussed using graphical approach.
Abstract: Examination has been made to explore the impact of the induced magnetic field of peristaltic flow for an incompressible Williamson fluid in the curved channel. Formulation of problem is constructed in wave frame of reference. HPM (homotopy perturbation method) is utilized for explaining the continuity equation, induction equation and equation of motion after utilizing the approximations of long-wavelength and low-Reynolds number. Explicit analytical expressions for pressure gradient and stream function, magnetic force function, induced magnetic field and current density are developed. The effects of embedded parameters portrayed and discussed by using graphical approach.

Journal ArticleDOI
TL;DR: In this paper, the authors apply the method of Maggi's equations to realize the assembly of the equations of motion for a planar mechanical systems using finite two-dimensional elements.
Abstract: An important stage in an analysis of a multibody system (MBS) with elastic elements by the finite element method is the assembly of the equations of motion for the whole system. This assembly, which seems like an empirical process as it is applied and described, is in fact the result of applying variational formulations to the whole considered system, putting together all the finite elements used in modeling and introducing constraints between the elements, which are, in general, nonholonomic. In the paper, we apply the method of Maggi’s equations to realize the assembly of the equations of motion for a planar mechanical systems using finite two-dimensional elements. This presents some advantages in the case of mechanical systems with nonholonomic liaisons.

Journal ArticleDOI
TL;DR: In this paper, the effects of activation energy and thermophoretic diffusion on steady micropolar fluid along with Brownian motion are discussed, and a famous shooting scheme is used to present the numerical solutions.
Abstract: The present study is related to the effects of activation energy and thermophoretic diffusion on steady micropolar fluid along with Brownian motion. The activation energy and thermal conductivity of steady micropolar fluid are also discussed. The equation of motion, angular momentum, temperature, concentration, and their boundary conditions are presented for the micropolar fluid. The detail of geometry reveals the effects of several parameters on the parts of the system. The nonlinear partial differential equations are converted into nonlinear ordinary differential equations, and a famous shooting scheme is used to present the numerical solutions. The comparison of the obtained results by the shooting technique and the numerical bvp4c technique is presented. The behavior of local skin friction numbers and couple stress number is tabulated for different parameters, and some figures are plotted to present the different parameters. For uplifting the values of AE for parameter , the concentration profile is increased because of the Arrhenius function, and AE increases with the reduction of this function. The increasing values of the parameter of rotation G show the decrement in velocity because of the rotation of the particle of the fluid, so the linear motion decreases. Thermophoresis is responsible for shifting the molecules within the fluid, and due to this, an increment in boundary layer thickness is found, so by a greater value of , the concentration profile decreases and temperature profile goes down.

Journal ArticleDOI
TL;DR: In this article, a dynamic analysis of functionally graded graphene nanoplatelets reinforced composite (FG-GNPRC) cylindrical nanoshell subjected to a moving harmonic load is investigated.

Journal ArticleDOI
TL;DR: In this paper, the classical sub-leading soft graviton theorem was derived for the electromagnetic wave-form generated during scattering of charged particles, and a new conjecture was presented on subsubleading corrections to the gravitational waveform at early and late retarded time.
Abstract: Classical subleading soft graviton theorem in four space-time dimensions determines the gravitational wave-form at late and early retarded time, generated during a scattering or explosion, in terms of the four momenta of the ingoing and outgoing objects. This result was ‘derived’ earlier by taking the classical limit of the quantum soft graviton theorem, and making some assumptions about how to deal with the infrared divergences of the soft factor. In this paper we give a direct proof of this result by analyzing the classical equations of motion of gravity coupled to matter. We also extend the result to the electromagnetic wave-form generated during scattering of charged particles, and present a new conjecture on subsubleading corrections to the gravitational wave-form at early and late retarded time.

Journal ArticleDOI
TL;DR: In this paper, a model for quasi-two-dimensional MHD flows between two planes with small magnetic Reynolds number and constant transverse magnetic field orthogonal to the planes is presented.
Abstract: This paper presents a model for quasi two-dimensional MHD flows between two planes with small magnetic Reynolds number and constant transverse magnetic field orthogonal to the planes. A method is presented that allows to take 3D effects into account in a 2D equation of motion thanks to a model for the transverse velocity profile. The latter is obtained by using a double perturbation asymptotic development both in the core flow and in the Hartmann layers arising along the planes. A new model is thus built that describes inertial effects in these two regions. Two separate classes of phenomena are thus pointed out : the one related to inertial effects in the Hartmann layer gives a model for recirculating flows and the other introduces the possibility of having a transverse dependence of the velocity profile in the core flow. The ''recirculating'' velocity profile is then introduced in the transversally averaged equation of motion in order to provide an effective 2D equation of motion. Analytical solutions of this model are obtained for two experimental configurations : isolated vortices aroused by a point electrode and axisymmetric parallel layers occurring in the MATUR (MAgneticTURbulence) experiment. The theory is found to give a satisfactory agreement with the experiment so that it can be concluded that recirculating flows are actually responsible for both vortices core spreading and excessive dissipative behavior of the axisymmetric side wall layers.

Journal ArticleDOI
TL;DR: In this paper, a 4D Einstein-Gauss-Bonnet gravity has been proposed by Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020), which rescales the coupling and takes the limit $D\rightarrow 4$ at the level of equations of motion.
Abstract: Recently, a novel 4D Einstein-Gauss-Bonnet gravity has been proposed by Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)] by rescaling the coupling $\alpha \rightarrow \alpha/(D-4)$ and taking the limit $D\rightarrow 4$ at the level of equations of motion. This prescription, though was shown to bring non-trivial effects for some spacetimes with particular symmetries, remains mysterious and calls for scrutiny. Indeed, there is no continuous way to take the limit $D\rightarrow 4$ in the higher $D$-dimensional equations of motion because the tensor indices depend on the spacetime dimension and behave discretely. On the other hand, if one works with four-dimensional spacetime indices the contribution corresponding to the Gauss-Bonnet term vanishes identically in the equations of motion. A necessary condition (but may not be sufficient) for this procedure to work is that there is an embedding of the four-dimensional spacetime into the higher $D$-dimensional spacetime so that the equations in the latter can be properly interpreted after taking the limit. In this note, working with 2D Einstein gravity, we show several subtleties when applying the method used in [Phys. Rev. Lett. 124, 081301 (2020)].

Journal ArticleDOI
TL;DR: In this paper, the wave propagation and vibration of a porous beam embedded via nanocomposite piezoelectric layers were considered through modified Halpin-Tsai micromechanics model to approximate the Young modulus and Poisson's ratio of graphene/pieziolectric polymer layers.
Abstract: This paper deals with wave propagation and vibration of a porous beam embedded via nanocomposite piezoelectric layers Various patterns of reinforcement of the face sheets by non-uniform graphene nanoplatelets (GPLs) are considered through modified Halpin-Tsai micromechanics model to approximate the Young modulus and Poisson's ratio of graphene/piezoelectric polymer layers The sandwich's face sheets, due to their characteristics, are regarded as sensor and actuator with which the wave velocity and frequency of structure can be controlled and for this reason, a proportional-differential (PD) controller is handled So as to model the structure much more realistic, the material characteristic of whole system are hypothesized as viscoelastic state according to Kelvin-Voigt model and Kerr viscoelastic foundation is developed which include two springs, two dampers and one shear elements as well For mathematical modelling of system, refined zigzag theory (RZT) is exercised and using energy method, the motion equations are obtained Analytical procedure is utilized for solving the governing equations as well as calculating the wave velocity and frequency of the sandwich structure A precise parametric study is carried out focusing GPLs volume percent and distribution pattern, geometrical parameter of every layer, piezoelectric properties of GPLs, porosity dispersion of the core, exerted voltage and structural damping and their effects on the wave propagation and vibration of system Results show that increase in the porous coefficient lead to decline in the wave velocity and frequency In addition, considering the piezoelectric properties of GPLs enhances the wave velocity and frequency of the sandwich structure

Journal ArticleDOI
TL;DR: In this paper, the role of electromagnetic field in f ( R, T ) gravity was analyzed and the behavior of electric charge on the length of the thin shell, energy content, and entropy of gravastar was studied graphically.

Journal ArticleDOI
TL;DR: In this paper, the effect of porosity distributions on the mechanics of nanostructures is investigated based on the higher-order nonlocal strain gradient theory, where the displacements gradients are assumed to be small so that the components of the Green-Lagrange strain tensor are linear and infinitesimal.

Journal ArticleDOI
TL;DR: In this paper, an active control of nonlinear free vibration of viscoelastic orthotropic piezoelectric doubly-curved smart nanoshells with surface effects is studied.

Journal ArticleDOI
TL;DR: In this paper, the authors generalize the worldline EFT formalism developed in [4-9] to calculate the non-conservative tidal effects on spinning black holes in a long wavelength approximation that is valid to all orders in the magnitude of the spin.
Abstract: We generalize the worldline EFT formalism developed in [4-9] to calculate the non-conservative tidal effects on spinning black holes in a long wavelength approximation that is valid to all orders in the magnitude of the spin. We present results for the rate of change of mass and angular momentum in a background field and find agreement with previous calculations obtained by different techniques. We also present new results for both the non-conservative equations of motion and power loss/gain for a binary inspiral, which start at 5PN and 2.5PN order respectively and manifest the Penrose process.

Journal ArticleDOI
TL;DR: In this article, the authors investigated nonlinear harmonic resonance behaviors of graded graphene-reinforced composite spinning thin cylindrical shells subjected to a thermal load and an external excitation.
Abstract: This work investigates nonlinear harmonic resonance behaviors of graded graphene-reinforced composite spinning thin cylindrical shells subjected to a thermal load and an external excitation. The volume fraction of graphene platelets varies continuously in the shell’s thickness direction, which generates position-dependent useful material properties. Natural frequencies of shell traveling waves are derived by considering influences of the initial hoop tension, centrifugal and Coriolis forces, thermal expansion deformation, and thermal conductivity. A new Airy stress function is introduced. Harmonic resonance behaviors and their stable solutions for the spinning cylindrical shell are analyzed based on an equation of motion which is established by adopting Donnell’s nonlinear shell theory. The necessary and sufficient conditions for the existence of the subharmonic resonance of the spinning composite cylindrical shell are given. Besides the shell’s intrinsic structural damping, the Coriolis effect due to the spinning motion has a contribution to the damping terms of the system as well. Comparisons between the present analytical results and those in other papers are made to validate the existing solutions. Influences of main factors on vibration characteristics, primary resonance, and subharmonic resonance behaviors of the novel composite cylindrical shell are discussed. Furthermore, the mechanism of how the spinning motion affects the amplitude–frequency curves of harmonic resonances of the cylindrical shell is analyzed.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the classical dynamics of colour-charged particle scattering from the perspective of amplitudes, rather than equations of motion, and explained how to compute the change of colour and the radiation of colour, during a classical collision.
Abstract: The double copy suggests that the basis of the dynamics of general relativity is Yang-Mills theory. Motivated by the importance of the relativistic two-body problem, we study the classical dynamics of colour-charged particle scattering from the perspective of amplitudes, rather than equations of motion. We explain how to compute the change of colour, and the radiation of colour, during a classical collision. We apply our formalism at next-to-leading order for the colour change and at leading order for colour radiation.

Journal ArticleDOI
TL;DR: This method can be used to provide a Hamiltonian derivation of recently found dual charges and is observed that the first order formalism is best suited to an analysis of asymptotic charges.
Abstract: We present a method for finding, in principle, all asymptotic gravitational charges The basic idea is that one must consider all possible contributions to the action that do not affect the equations of motion for the theory of interest; such terms include topological terms As a result we observe that the first order formalism is best suited to an analysis of asymptotic charges In particular, this method can be used to provide a Hamiltonian derivation of recently found dual charges