Showing papers on "Equations of motion published in 2021"

Generating Spin Polarization from Vorticity through Nonlocal Collisions.

Abstract: We derive the collision term in the Boltzmann equation using the equation of motion for the Wigner function of massive spin-$1/2$ particles. To next-to-lowest order in $\ensuremath{\hbar}$, it contains a nonlocal contribution, which is responsible for the conversion of orbital into spin angular momentum. In a proper choice of pseudogauge, the antisymmetric part of the energy-momentum tensor arises solely from this nonlocal contribution. We show that the collision term vanishes in global equilibrium and that the spin potential is, then, equal to the thermal vorticity. In the nonrelativistic limit, the equations of motion for the energy-momentum and spin tensors reduce to the well-known form for hydrodynamics for micropolar fluids.

A worldsheet for Kerr

Abstract: We show that the Newman-Janis shift property of the exact Kerr solution can be interpreted in terms of a worldsheet effective action. This holds both in gravity, and for the single-copy $$ \sqrt{\mathrm{Kerr}} $$ solution in electrodynamics. At the level of equations of motion, we show that the Newman-Janis shift holds also for the leading interactions of the Kerr black hole. These leading interactions are conveniently described using chiral classical equations of motion with the help of the spinor-helicity method familiar from scattering amplitudes.

Evolution of Einstein-scalar-Gauss-Bonnet gravity using a modified harmonic formulation

Abstract: We present numerical solutions of several spacetimes of physical interest, including binary black hole mergers, in shift-symmetric Einstein-scalar-Gauss-Bonnet (ESGB) gravity, and describe our methods for solving the full equations of motion, without approximation, for general spacetimes. While we concentrate on the specific example of shift-symmetric ESGB, our methods, which make use of a recently proposed modification to the generalized harmonic formulation, should be generally applicable to all Horndeski theories of gravity (including general relativity). We demonstrate that these methods can stably follow the formation of scalar clouds about initially vacuum nonspinning and spinning black holes for values of the Gauss-Bonnet coupling approaching the maximum value above which the hyperbolicity of the theory breaks down in spherical symmetry. We study the collision of black holes with scalar hair, finding that the theory remains hyperbolic in the spacetime region exterior to the black hole horizons in a similar regime, which includes cases where the deviations from general relativity in the gravitational radiation is appreciable. Finally, we demonstrate that these methods can be used to follow the inspiral and merger of binary black holes in full ESGB gravity. This allows for making predictions for Horndeski theories of gravity in the strong-field and nonperturbative regime, which can confronted with gravitational wave observations, and compared to approximate treatments of modifications to general relativity.

From chiral kinetic theory to relativistic viscous spin hydrodynamics

Abstract: In this paper, we start with chiral kinetic theory and construct the spin hydrodynamic framework for a chiral spinor system. Using the 14-moment expansion formalism, we obtain the equations of motion of second-order dissipative relativistic fluid dynamics with nontrivial spin-polarization density. In a chiral spinor system, the spin-alignment effect could be treated in the same framework as the chiral vortical effect (CVE). However, the quantum corrections due to fluid vorticity induce not only CVE terms in the vector/axial charge currents, but also corrections to the stress tensor. In this framework, viscous corrections to the hadron spin polarization are self-consistently obtained, which will be important for precise prediction of the polarization rate for the observed hadrons, e.g., $\mathrm{\ensuremath{\Lambda}}$ hyperon.

Extended corner symmetry, charge bracket and Einstein's equations

Abstract: We develop the covariant phase space formalism allowing for non-vanishing flux, anomalies, and field dependence in the vector field generators. We construct a charge bracket that generalizes the one introduced by Barnich and Troessaert and includes contributions from the Lagrangian and its anomaly. This bracket is uniquely determined by the choice of Lagrangian representative of the theory. We then extend the notion of corner symmetry algebra to include the surface translation symmetries and prove that the charge bracket provides a canonical representation of the extended corner symmetry algebra. This representation property is shown to be equivalent to the projection of the gravitational equations of motion on the corner, providing us with an encoding of the bulk dynamics in a locally holographic manner.

Classical observables from coherent-spin amplitudes

Abstract: The quantum field-theoretic approach to classical observables due to Kosower, Maybee and O’Connell provides a rigorous pathway from on-shell scattering amplitudes to classical perturbation theory. In this paper, we promote this formalism to describe general classical spinning objects by using coherent spin states. Our approach is fully covariant with respect to the massive little group SU(2) and is therefore completely synergistic with the massive spinor-helicity formalism. We apply this approach to classical two-body scattering due gravitational interaction. Starting from the coherent-spin elastic-scattering amplitude, we derive the classical impulse and spin kick observables to first post-Minkowskian order but to all orders in the angular momenta of the massive spinning objects. From the same amplitude, we also extract an effective two-body Hamiltonian, which can be used beyond the scattering setting. As a cross-check, we rederive the classical observables in the center-of-mass frame by integrating the Hamiltonian equations of motion to the leading order in Newton’s constant.

A non-relativistic limit of NS-NS gravity.

Abstract: We discuss a particular non-relativistic limit of NS-NS gravity that can be taken at the level of the action and equations of motion, without imposing any geometric constraints by hand. This relies on the fact that terms that diverge in the limit and that come from the Vielbein in the Einstein-Hilbert term and from the kinetic term of the Kalb-Ramond two-form field cancel against each other. This cancelling of divergences is the target space analogue of a similar cancellation that takes place at the level of the string sigma model between the Vielbein in the kinetic term and the Kalb-Ramond field in the Wess-Zumino term. The limit of the equations of motion leads to one equation more than the limit of the action, due to the emergence of a local target space scale invariance in the limit. Some of the equations of motion can be solved by scale invariant geometric constraints. These constraints define a so-called Dilatation invariant String Newton-Cartan geometry.

Covariant color-kinematics duality

Abstract: We show that color-kinematics duality is a manifest property of the equations of motion governing currents and field strengths. For the nonlinear sigma model (NLSM), this insight enables an implementation of the double copy at the level of fields, as well as an explicit construction of the kinematic algebra and associated kinematic current. As a byproduct, we also derive new formulations of the special Galileon (SG) and Born-Infeld (BI) theory. For Yang-Mills (YM) theory, this same approach reveals a novel structure — covariant color-kinematics duality — whose only difference from the conventional duality is that 1/□ is replaced with covariant 1/D2. Remarkably, this structure implies that YM theory is itself the covariant double copy of gauged biadjoint scalar (GBAS) theory and an F3 theory of field strengths encoding a corresponding kinematic algebra and current. Directly applying the double copy to equations of motion, we derive general relativity (GR) from the product of Einstein-YM and F3 theory. This exercise reveals a trivial variant of the classical double copy that recasts any solution of GR as a solution of YM theory in a curved background. Covariant color-kinematics duality also implies a new decomposition of tree-level amplitudes in YM theory into those of GBAS theory. Using this representation we derive a closed-form, analytic expression for all BCJ numerators in YM theory and the NLSM for any number of particles in any spacetime dimension. By virtue of the double copy, this constitutes an explicit formula for all tree-level scattering amplitudes in YM, GR, NLSM, SG, and BI.

Engineering Mechanics: Statics & Dynamics

Abstract: STATICS 1. General Principles. Mechanics. Fundamental Concepts. Units of Measurement. The International System of Units. Numerical Calculations. 2. Force Vectors. Scalars and Vectors. Vector Operations. Vector Addition of Forces. Addition of a System of Coplanar Forces. Cartesian Vectors. Addition and Subtraction of Cartesian Vectors. Position Vectors. Force Vector Directed Along a Line. Dot Product. 3. Equilibrium of a Particle. Condition for the Equilibrium of a Particle. The Free-Body Diagram. Coplanar Force Systems. Three-Dimensional Force Systems. 4. Force System Resultants. Moment of a Force-Scalar Formation. Cross Product. Moment of a Force-Vector Formulation. Principle of Moments. Moment of a Force About a Specified Axis. Moment of a Couple. Equivalent System. Resultants of a Force and Couple System. Further Reduction of a Force and Couple System. Reduction of a Simple Distributed Loading. 5. Equilibrium of a Rigid Body. Conditions for Rigid-Body Equilibrium. Equilibrium in Two Dimensions. Free-Body Diagrams. Equations of Equilibrium. Two- and Three-Force Members. Equilibrium in Three Dimensions. Free-Body Diagrams. Equations of Equilibrium. Constraints for a Rigid Body. 6. Structural Analysis. Simple Trusses. The Method of Joints. Zero-Force Members. The Method of Sections. Space Trusses. Frames and Machines. 7. Internal Forces. Internal Forces Developed in Structural Members. Shear and Moment Equations and Diagrams. Relations Between Distributed Load, Shear, and Moment. Cables. 8. Friction. Characteristics of Dry Friction. Problems Involving Dry Friction. Wedges. Frictional Forces on Screws. Frictional Forces on Flat Belts. Frictional Forces on Collar Bearings, Pivot Bearings, and Disks. Frictional Forces on Journal Bearings. Rolling Resistance. 9. Center of Gravity and Centroid. Center of Gravity and Center of Mass for a System of Particles. Center of Gravity, Center of Mass, and Centroid for a Body. Composite Bodies. Theorems of Pappus and Guldinus. Resultant of a General Distributed Force System. Fluid Pressure. 10. Moments of Inertia. Definitions of Moments of Inertia for Areas. Parallel-Axis Theorem for an Area. Radius of Gyration of an Area. Moments of Inertia for an Area by Integration. Moments of Inertia for Composite Areas. Product of Inertia for an Area. Moments of Inertia for an Area About Inclined Axes. Mohr's Circle for Moments of Inertia. Mass Moment of Inertia. 11. Virtual Work. Definition of Work and Virtual Work. Principle of Virtual Work for a Particle and a Rigid Body. Principle of Virtual Work for a System of Connected Rigid Bodies. Conservative Forces. Potential Energy. Potential Energy Criterion for Equilibrium. Stability of Equilibrium. Appendixes. A. Mathematical Expressions. B. Numerical and Computer Analysis. Answers. Index. DYNAMICS 12. Kinematics of a Particle. Introduction. Rectilinear Kinematics: Continuous Motion. Rectilinear Kinematics: Erratic Motion. General Curvilinear Motion. Curvilinear Motion: Rectangular Components. Motion of a Projectile. Curvilinear Motion: Normal and Tangential Components. Curvilinear Motion: Cylindrical Components. Absolute Dependent Motion Analysis of Two Particles. Relative-Motion Analysis of Two Particles Using Translating Axes. 13. Kinetics of a Particle: Force and Acceleration. Newton's Laws of Motion. The Equation of Motion. Equation of Motion for a System of Particles. Equations of Motion: Rectangular Coordinates. Equations of Motion: Normal and Tangential Coordinates. Equations of Motion: Cylindrical Coordinates. Central-Force Motion and Space Mechanics. 14. Kinetics of a Particle: Work and Energy. The Work of a Force. Principle of Work and Energy. Principle of Work and Energy for a System of Particles. Power and Efficiency. Conservative Forces and Potential Energy. Conservation of Energy. 15. Kinetics of a Particle: Impulse and Momentum. Principle of Linear Impulse and Momentum. Principle of Linear Impulse and Momentum for a System of Particles. Conservation of Linear Momentum for a System of Particles. Impact. Angular Momentum. Relation Between Moment of a Force and Angular Momentum. Angular Impulse and Momentum Principles. Steady Fluid Streams. Propulsion with Variable Mass. REVIEW 1: KINEMATICS AND KINETICS OF A PARTICLE. 16. Planar Kinematics of a Rigid Body. Rigid-Body Motion. Translation. Rotation About a Fixed Axis. Absolute General Plane Motion Analysis. Relative-Motion Analysis: Velocity. Instantaneous Center of Zero Velocity. Relative-Motion Analysis: Acceleration. Relative-Motion Analysis Using Rotating Axes. 17. Planar Kinetics of a Rigid Body: Force and Acceleration. Moment of Inertia. Planar Kinetic Equations of Motion. Equations of Motion: Translation. Equations of Motion: Rotation About a Fixed Axis. Equations of Motion: General Plane Motion. 18. Planar Kinetics of a Rigid Body: Work and Energy. Kinetic Energy. The Work of a Force. The Work of a Couple. Principle of Work and Energy. Conservation of Energy. 19. Planar Kinetics of a Rigid Body: Impulse and Momentum. Linear and Angular Momentum. Principle of Impulse and Momentum. Conservation of Momentum. Eccentric Impact. REVIEW 2: PLANAR KINEMATICS AND KINETICS OF A RIGID BODY. 20. Three-Dimensional Kinematics of a Rigid Body. Rotation About a Fixed Point. The Time Derivative of a Vector Measured from a Fixed and Translating-Rotating System. General Motion. Relative-Motion Analysis Using Translating and Rotating Axes. 21. Three-Dimensional Kinetics of a Rigid Body. Moments and Products of Inertia. Angular Momentum. Kinetic Energy. Equations of Motion. Gyroscopic Motion. Torque-Free Motion. 22. Vibrations. Undamped Free Vibration. Energy Methods. Undamped Forced Vibration. Viscous Damped Free Vibration. Viscous Damped Forced Vibration. Electrical Circuit Analogs. Appendixes. A. Mathematical Expressions. B. Numerical and Computer Analysis. C. Vector Analysis. D. Review for the Fundamentals of Engineering Examination. Answers to Selected Problems. Index.

The free vibration analysis of hybrid porous nanocomposite joined hemispherical–cylindrical–conical shells

Abstract: In this research, the natural frequency responses of joined hemispherical–cylindrical–conical shells made of composite three-phase materials have been dealt with in the framework of First-Order Shear Deformation Theory (FOSDT). The joined hemispherical–cylindrical–conical shells are assumed to be made of hybrid porous nanocomposite material with three phases including a matrix of epoxy, macroscale carbon fiber, and nanoscale 3D Graphene Foams (3GFs). For getting the equivalent mechanical properties of the Hybrid Matrix (HM) including polymer epoxy and 3GFs, the well-known rule of the mixture is used. In addition, the effect of porosity throughout the HM is considered using two novel and one well-known porosity distribution pattern. Moreover, the HM is reinforced with transversely isotropic macroscale carbon fibers in which the Halpin–Tsai scheme is used for multiscale homogenization procedure. The governing equations of motion associated with hybrid porous nanocomposite joined hemispherical–cylindrical–conical structures are figured out by implementing Donnell-type shell formulation and Hamilton’s approach. Moreover, an efficient and well-known semi-analytical solution method entitled Generalized Differential Quadrature Method (GDQM) is employed to solve the governing differential equations. To verify the proposed formulation some well-known benchmarks, especially those are composed of homogenous materials have been analyzed, and a good agreement has been achieved. Besides, some other new and applicable problems are considered to investigate the effects of different parameters including various boundary conditions, patterns of porosity distributions, and geometric properties of structure on the vibration behavior of joined shells.

Buckling and post-buckling behaviors of higher order carbon nanotubes using energy-equivalent model

Abstract: This paper aims to investigate the size scale effect on the buckling and post-buckling of single-walled carbon nanotube (SWCNT) rested on nonlinear elastic foundations using energy-equivalent model (EEM). CNTs are modelled as a beam with higher order shear deformation to consider a shear effect and eliminate the shear correction factor, which appeared in Timoshenko and missed in Euler–Bernoulli beam theories. Energy-equivalent model is proposed to bridge the chemical energy between atoms with mechanical strain energy of beam structure. Therefore, Young’s and shear moduli and Poisson’s ratio for zigzag (n, 0), and armchair (n, n) carbon nanotubes (CNTs) are presented as functions of orientation and force constants. Conservation energy principle is exploited to derive governing equations of motion in terms of primary displacement variable. The differential–integral quadrature method (DIQM) is exploited to discretize the problem in spatial domain and transformed the integro-differential equilibrium equations to algebraic equations. The static problem is solved for critical buckling loads and the post-buckling deformation as a function of applied axial load, CNT length, orientations and elastic foundation parameters. Numerical results show that effects of chirality angle, boundary conditions, tube length and elastic foundation constants on buckling and post-buckling behaviors of armchair and zigzag CNTs are significant. This model is helpful especially in mechanical design of NEMS manufactured from CNTs.

Extended corner symmetry, charge bracket and Einstein's equations

Abstract: We develop the covariant phase space formalism allowing for non-vanishing flux, anomalies and field dependence in the vector field generators. We construct a charge bracket that generalizes the one introduced by Barnich and Troessaert and includes contributions from the Lagrangian and its anomaly. This bracket is uniquely determined by the choice of Lagrangian representative of the theory. We then extend the notion of corner symmetry algebra to include the surface translation symmetries and prove that the charge bracket provides a canonical representation of the extended corner symmetry algebra. This representation property is shown to be equivalent to the projection of the gravitational equations of motion on the corner, providing us with an encoding of the bulk dynamics in a locally holographic manner.

Hydrodynamics of spin currents

Abstract: We study relativistic hydrodynamics in the presence of a non vanishing spin chemical potential. Using a variety of techniques we carry out an exhaustive analysis, and identify the constitutive relations for the stress tensor and spin current in such a setup, allowing us to write the hydrodynamic equations of motion to second order in derivatives. We then solve the equations of motion in a perturbative setup and find surprisingly good agreement with measurements of global $\Lambda$-hyperon polarization carried out at RHIC.

Free vibration of FGM conical–spherical shells

Abstract: Natural frequencies of a conical–spherical functionally graded material (FGM) shell are obtained in this study. It is assumed that the conical and spherical shell components have identical thickness. The system of joined shell is made from FGMs, where properties of the shell are graded through the thickness direction. The first order shear deformation theory of shells is used to investigate the effects of shear strains and rotary inertia. The Donnel type of kinematic assumptions are adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton’s principle. The resulting system of equations are discretized using the semi-analytical generalized differential quadrature (GDQ) method. Considering various types of boundary conditions for the shell ends and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells with the data of conventional finite element software, parametric studies are carried out for the system of combined moderately thick conical–spherical joined shells made of FGMs and various types of end supports.

Vertical time-harmonic coupling vibration of an impermeable, rigid, circular plate resting on a finite, poroelastic soil layer

Abstract: Studies associated with dynamic plate–medium interactions generally assumed the plate structures to be permeable for the sake of convenience. But the effect and applicability of such an assumption are still unclear, and then the pore fluid pressure on the plate and medium interfaces cannot be obtained. In this paper, the mentioned problems are discussed by studying the coupling steady-state vibration of an impermeable, rigid, circular plate resting on a finite, fluid-saturated, poroelastic soil layer underlain by rigid base and subjected to a vertical time-harmonic loading. The semi-analytical solutions for the dynamic compliance, displacements, stresses, especially the contact stress including effective stress and pore fluid pressure of the plate and the layer, are proposed. In developing these solutions, the linearly poroelastic model established by de Boer is used to describe the mechanical behaviour of the porous medium. By means of four scalar displacement potentials and the Fourier–Hankel transformation to solve the equations of motion of the poroelastic layer, and then imposing boundary and interfacial conditions, a pair of coupling Fredholm’s integral equations of the second kind formulating the plate–medium interaction are derived and evaluated with numerical methods. The proposed solutions are then verified by comparing with the existing special solutions and the FEM calculation results. Numerical examples are also performed to examine the effects of the permeability of both the plate and the poroelastic layer and the thickness of the layer on the dynamic response of the coupling system.

Semi-analytical vibrational analysis of functionally graded carbon nanotubes coupled conical-conical shells

Abstract: This article is dedicated to predict the vibrational behavior of composite coupled conical-conical shell structures. The structural material is composed of two phases, including polymer epoxy matrix and Carbon NanoTube (CNT) fibers. To improve the vibrational structural behavior, the distributions of CNTs throughout the thickness of shells are assumed to be Functionally Graded. In order to enhance the research, five different patterns are considered for distribution of the CNT fibers within the matrix. The governing equations of motion associated with conical shells are obtained by using Donnell's theory and Hamilton method. In addition, the five-parameter shell theory is utilized in this article. As a result, five differential equations are achieved by using variation calculation. To solve the system of differential equations, an efficient and modified Generalized Differential Quadrature Method (GDQM) is employed. All the natural frequencies of shell structures are found for different states. By considering continuity conditions, the required modification is applied to GDQM. To validate the proposed formulation, some well-known benchmarks are solved. Moreover, several numerical examples and parametric studies are implemented to show the high accuracy and capability of the authors' scheme for analyzing coupled shells. To obtain accurate responses, 15 grid points are required for using in GDQM. Besides, it is observed that the minimum and maximum dimensionless frequency parameters are obtained by the patterns F G − O and F G − X , respectively.

Non-conservative effects on spinning black holes from world-line effective field theory

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.

On the time evolution of cosmological correlators

Abstract: Developing our understanding of how correlations evolve during inflation is crucial if we are to extract information about the early Universe from our late-time observables. To that end, we revisit the time evolution of scalar field correlators on de Sitter spacetime in the Schrodinger picture. By direct manipulation of the Schrodinger equation, we write down simple “equations of motion” for the coefficients which determine the wavefunction. Rather than specify a particular interaction Hamiltonian, we assume only very basic properties (unitarity, de Sitter invariance and locality) to derive general consequences for the wavefunction’s evolution. In particular, we identify a number of “constants of motion” — properties of the initial state which are conserved by any unitary dynamics — and show how this can be used to partially fix the cubic and quartic wavefunction coefficients at weak coupling. We further constrain the time evolution by deriving constraints from the de Sitter isometries and show that these reduce to the familiar conformal Ward identities at late times. Finally, we show how the evolution of a state from the conformal boundary into the bulk can be described via a number of “transfer functions” which are analytic outside the horizon for any local interaction. These objects exhibit divergences for particular values of the scalar mass, and we show how such divergences can be removed by a renormalisation of the boundary wavefunction — this is equivalent to performing a “Boundary Operator Expansion” which expresses the bulk operators in terms of regulated boundary operators. Altogether, this improved understanding of the wavefunction in the bulk of de Sitter complements recent advances from a purely boundary perspective, and reveals new structure in cosmological correlators.

Symbolic pregression: Discovering physical laws from distorted video.

Abstract: We present a method for unsupervised learning of equations of motion for objects in raw and optionally distorted unlabeled synthetic video (or, more generally, for discovering and modeling predictable features in time-series data). We first train an autoencoder that maps each video frame into a low-dimensional latent space where the laws of motion are as simple as possible, by minimizing a combination of nonlinearity, acceleration, and prediction error. Differential equations describing the motion are then discovered using Pareto-optimal symbolic regression. We find that our pre-regression ("pregression") step is able to rediscover Cartesian coordinates of unlabeled moving objects even when the video is distorted by a generalized lens. Using intuition from multidimensional knot theory, we find that the pregression step is facilitated by first adding extra latent space dimensions to avoid topological problems during training and then removing these extra dimensions via principal component analysis. An inertial frame is autodiscovered by minimizing the combined equation complexity for multiple experiments.

Boundary layer flow with forced convective heat transfer and viscous dissipation past a porous rotating disk

Abstract: The Coriolis effect with forced convective heat transfer on steady ferrohydrodynamic flow past a rotating porous disk in the presence of viscous dissipation has been investigated. The basic idea of the Neuringer-Rosensweig model has been used for the equation of motion of the nanofluid flow. With help of suitable transformations, the governing non-linear system of coupled partial differential equations is simplified into the dimensionless system of ordinary differential equations. Further, the dimensionless system of equations is solved numerically by the MATLAB routine bvp4c solver package. The findings for the motivating parameters of physical interest are expressed by the table and discussed with graphs. The outcomes show that heat transfer rate and thermal boundary layer thickness increase due to the higher value of the dissipation parameter.

Time-dependent inertia of self-propelled particles: The Langevin rocket.

Abstract: Many self-propelled objects are large enough to exhibit inertial effects but still suffer from environmental fluctuations. The corresponding basic equations of motion are governed by active Langevin dynamics, which involve inertia, friction, and stochastic noise for both the translational and orientational degrees of freedom coupled via the self-propulsion along the particle orientation. In this paper, we generalize the active Langevin model to time-dependent parameters and explicitly discuss the effect of time-dependent inertia for achiral and chiral particles. Realizations of this situation are manifold, ranging from minirockets (which are self-propelled by burning their own mass), to dust particles in plasma (which lose mass by evaporating material), to walkers with expiring activity. Here we present analytical solutions for several dynamical correlation functions, such as mean-square displacement and orientational and velocity autocorrelation functions. If the parameters exhibit a slow power law in time, we obtain anomalous superdiffusion with a nontrivial dynamical exponent. Finally, we constitute the ``Langevin rocket'' model by including orientational fluctuations in the traditional Tsiolkovsky rocket equation. We calculate the mean reach of the Langevin rocket and discuss different mass ejection strategies to maximize it. Our results can be tested in experiments on macroscopic robotic or living particles or in self-propelled mesoscopic objects moving in media of low viscosity, such as complex plasma.

Response regimes of nonlinear energy harvesters with a resistor-inductor resonant circuit by complexification-averaging method

Abstract: In this paper, the steady-state response regimes of nonlinear energy harvesters with a resistor-inductor resonant circuit are theoretically investigated. The complexification averaging (CA) method is used to theoretically analyze the energy harvesting performance and reduce the motion equations into a set of first-order differential equations. The amplitudes and phases of both the response displacement and the output voltage are derived, and the corresponding stability conditions are determined. The response regimes are studied with the variation of nonlinear stiffness coefficients and coupling parameters, which are verified by the time domain analysis. The frequency island phenomenon is found and analyzed. Additionally, the backbone curve for deducing the extreme vibration frequency and amplitude is derived. Simultaneously, the analytical expressions of the switching points (critical amplitude and frequency) to identify the hardening and softening properties are established. Accordingly, a criterion is given to determine the occurrence of the jump phenomenon, and its effectiveness is verified. Overall, this paper presents an in-depth theoretical analysis of nonlinear energy harvesters with a resistor-inductor resonant circuit. It presents the theoretical framework and guidance for more extensive evaluations and understanding the theoretical analysis of nonlinear energy harvesters with external circuits.

On wave dispersion characteristics of magnetostrictive sandwich nanoplates in thermal environments

Abstract: Present manuscript undergoes with the investigation of the wave propagation features of smart magnetostrictive sandwich nanoplates (MSNPs) with regard to the influences of small scale in the context of the so-called nonlocal strain gradient theory (NSGT) of elasticity. The under observation continuous system, i.e. a thin-type one, is modeled via the Kirchhoff-Love theorem incorporated with the dynamic form of the principle of virtual work considering the impacts of both thermal and viscose losses on the dispersion characteristics of the nanostructure. Once the modified size-dependent constitutive equations are inserted into the motion equations, the final governing equations of the problem are attained. Thereafter, an analytical dispersion solution will be employed for the purpose of solving the dynamic problem to extract the wave response of the system. In order to examine the accuracy of the presented results, the natural frequencies obtained from this methodology are compared with those reported in the open literature. According to the presented illustrations, it can be declared that the magnetostriction can affect the dispersion responses of the smart nanoplate in low wave numbers.