Equations Of Motion Research Articles

Equation-of-motion regularized orbital-optimized second-order perturbation theory with the density-fitting approximation.

The density-fitted equation-of-motion (EOM) orbital-optimized second-order perturbation theory (DF-EOM-OMP2) method is presented for the first time. In addition, κ-DF-EOM-MP2 and κ-DF-EOM-OMP2 methods are implemented with the addition of κ-regularization. The accuracy of the DF-EOM-OMP2, κ-DF-EOM-MP2, and κ-DF-EOM-OMP2 methods are compared to the density-fitted EOM-MP2 (DF-EOM-MP2), EOM coupled-cluster (CC) singles and doubles (DF-EOM-CCSD), and EOM-CCSD with the triples excitation correction model [EOM-CCSD(fT)] for excitation energies of many closed- and open-shell chemical systems. The excitation energies computed using different test cases and methods were compared to the EOM-CCSD(fT) method and mean absolute errors (MAEs) are presented. The MAE values of closed- and open-shell cases (closed-shell organic chromophores set, open-shell set, peptide radicals set, and radical set) according to the EOM-CCSD(fT) method show that the κ-regularization technique yields highly accurate results for the first excited states. Our results indicate that the κ-DF-EOM-MP2 and κ-DF-EOM-OMP2 methods perform noticeably better than the DF-EOM-MP2 and DF-EOM-OMP2 methods. They approach the EOM-CCSD quality, at a significantly reduced cost, for the computation of excitation energies. Especially, the κ-DF-EOM-MP2 method provides outstanding results for most test cases considered. Overall, we conclude that the κ-versions of DF-EOM-MP2 and DF-EOM-OMP2 emerge as a useful computational tool for the study of excited-state molecular properties.

Theory of high-temperature superfluorescence in hybrid perovskite thin films.

The recent discovery of high-temperature superfluorescence in hybrid perovskite thin films has opened new possibilities for harnessing macroscopic quantum phenomena in nanotechnology. This study aimed to elucidate the mechanism that enables high-temperature superfluorescence in these systems. The proposed model describes a quasi-2D Wannier exciton in a thin film that interacts with phonons via the longitudinal optical phonon-exciton Fröhlich interaction. We show that the super-radiant properties of the coherent state in hybrid perovskites are stable against perturbations caused by the longitudinal optical phonon-exciton Fröhlich interaction. Using the multiconfiguration Hartree approach, we derive semiclassical equations of motion for a single-exciton wavefunction, where the vibrational degrees of freedom interact with the Wannier exciton through a mean-field Hartree term. Super-radiance is effectively described by a non-Hermitian term in the Hamiltonian. The analysis was then extended to multiple excited states using the semiclassical Hamiltonian as the basic model. We demonstrate that the ground state of the model exciton Hamiltonian with long-range interactions is a symmetric Dicke super-radiant state, where the Fröhlich interaction is nullified. The additional density matrix-based consideration draws an analogy between this system and stable systems, where the conservation laws determine the nullification of the constant (momentum-independent) decay rate part. In the exciton-phonon system, nullification is associated with the absence of a momentum-independent component in the Wannier exciton-phonon interaction coupling function.

Stability and vibration control of electrostatically excited functionally graded microresonator using nonlinear observer based sliding mode controller

The dynamic stability analysis of microsystems is an important aspect in understanding the critical operating regions under different excitations. Present study proposes an observer-based adaptive back-stepping sliding mode controller (ABSMC) model to control and stabilize an electrostatically excited functionally graded microresonator. The dynamic model of a microsystem subjected to random disturbances is derived using modified couple stress theory and Euler–Bernoulli’s beam model. The effective material properties are obtained from Mori-Tanaka scheme and the equations of motion are derived using Hamilton principle and solved by Galerkin’s method. A trained neural network estimator predicts the disturbances and the adaptive back-stepping sliding mode controller is designed for improving the system stability. The results of the proposed controller are compared with conventional sliding mode control (SMC) and proportional-derivative (PD) control solutions and it is found that ABSMC reduces settling time and input control force by 52.42% and 88.40%, respectively, with minimal chattering. The proposed control methodology effectively extends the travelling range of FG microsystems within and beyond the pull-in voltage.

Modeling of 2D seismic wave propagation in heterogeneous porous media: a frequency-domain finite-element method formulated by variational principles

Summary We propose a frequency-domain finite-element (FDFE) method to model the 2D P-SV waves propagating in porous media. This specific finite element method (FEM) is based on the framework of variational principles, which differ from previously widely used FEMs that rely on the weak formulations of the governing equations. By applying the calculus of variations, we establish the equivalence between solving the stress-strain relations, equations of motion and boundary conditions that govern the propagation of P-SV waves, and determining the extremum or stationarity of a properly defined functional. The structured rectangular element is utilized to partition the entire computational region. We validate the FDFE method by conducting a comparison with an analytically-based method for models of a horizontal planar contact of two poroelastic half-spaces, and a poroelastic half-space with a free surface. The excellent agreements between the analytically-based solutions and the FDFE solutions indicate the effectiveness of the FDFE method in modeling the poroelastic waves. Modeling results manifest that both propagative and diffusive natures of the Biot slow P-wave can be effectively modeled. The proposed FDFE method simulates wave fields in the frequency domain, allowing for easily incorporation of frequency-dependent parameters and enabling parallel computational capabilities at each frequency point (sample). We further employ the developed FDFE method to model two simplified poroelastic reservoirs, one with gas-saturated sandstone and the other with oil-saturated sandstone. The results suggest that changing the fluid phase of the sandstone reservoir from gas to oil can substantially impact the recorded solid and relative fluid-solid displacements. The modeling suggests that the proposed FDFE algorithm is a useful tool for studying the propagation of poroelastic waves.

Intelligent Trajectory Prediction Algorithm for Hypersonic Vehicle Based on Sparse Associative Structure Model

The Hypersonic Glide Vehicle (HGV) has become a focal point in military competitions among nations. Predicting the real-time trajectory of an HGV is of significant importance for aerospace defense interception and assessing enemy combat intentions. Existing prediction methods are limited by the need for large data samples and poor general applicability. To address these challenges, this paper presents a novel trajectory forecasting approach based on the Sparse Association Structure Model (SASM). The SASM can uncover the relationship among known data, transfer associative relationships to unknown data, and improve the generalization of the model. Firstly, a trajectory database is established for different maneuvering modes based on the six-degree-of-freedom motion equations and models of attack and bank angles of the HGV. Subsequently, three trajectory parameters are selected as prediction variables according to the maneuvering characteristics of the HGV. A parameters prediction model based on the SASM is then constructed to predict trajectory parameters. The SASM model demonstrates high accuracy and generalization in forecasting the trajectories of three different HGV types. Experimental results show a 50.35% reduction in prediction error and a 48.7% decrease in average processing time compared to the LSTM model, highlighting the effectiveness of the proposed method for real-time trajectory forecasting.

Proper orthogonal decomposition reduced-order model of the global oceans

AbstractA reduced-order model (ROM) of the global oceans is developed by projecting the hydrostatic Boussinesq equations of motion onto a proper orthogonal decomposition (POD) basis. Three-dimensional POD modes are calculated from the ocean fields of an ensemble climate reanalysis dataset. The coefficients in the POD ROM are calculated using a regression approach. The performance of various POD ROM configurations are assessed. Each configuration is derived from an alternate sea-water equation of state, linking the density and temperature fields. POD ROM variants incorporating an equation of state in which density is a quadratic function of temperature, are able to reproduce the statistics of the large-scale structures at a fraction of the computational cost required to numerically simulate this flow. Due to the speed and efficiency of calculation, such reduced-order models of the global geophysical system will enable researchers and policy makers to assess the physical risk for a broader range of potential future climate scenarios.

Quantum focusing conjecture in two-dimensional evaporating black holes

We consider the quantum focusing conjecture (QFC) for two-dimensional evaporating black holes in the Russo-Susskind-Thorlacius (RST) model. The QFC is closely related to the behavior of the generalized entropy. In the context of the black hole evaporation, the entanglement entropy of the Hawking radiation is decreasing after the Page time, and therefore it is not obvious whether the QFC holds. One of the present authors previously addressed this problem in a four-dimensional spherically symmetric dynamical black hole model and showed that the QFC is satisfied. However, the background spacetime considered was approximated by the Vaidya metric, and quantum effects of matters in the semiclassical regime were not fully taken into consideration. It remains to be seen if the QFC in fact holds for exact solutions of the semiclassical Einstein equations. In this paper, we address this problem in the RST model, which allows us to solve the semiclassical equations of motion exactly. We prove that the QFC is satisfied for evaporating black holes in the RST model with the island formation taken into account.

Thermoelastic damping in asymmetric vibrations of nonlocal circular plate resonators with Moore-Gibson-Thompson heat conduction

Precise estimation of the amount of thermoelastic damping (TED) in small-sized resonators is one of the crucial issues in their optimal design. According to several experimental, numerical and theoretical findings, the behavior of structures with such small dimensions in structural and thermal domains does not follow classical elasticity theory and the Fourier law of heat conduction. The objective of this work is to develop a nonclassical formulation for computing TED in asymmetric vibrations of circular nanoplates according to nonlocal theory (NT) and Moore-Gibson-Thompson (MGT) heat transfer model. To do so, first, the coupled equations of motion and heat are derived in the purview of NT and MGT model. Then, the real and imaginary parts of the system frequency are extracted from the frequency equation affected by thermoelastic coupling. Finally, by means of the existing definition for TED, a mathematical expression including nonlocal parameter of NT and nonclassical constants of MGT model is obtained to make an estimate of TED value. In the numerical examples section, to ensure the credibility of the provided formulation, the results obtained through this model are compared with those reported in the literature in the context of simpler models. Then, by presenting various graphical data, the type and extent of the role of different factors in TED changes are appraised. The obtained results indicate that employing NT and MGT model can substantially impact the amount of TED compared to the estimations of the classical formulation. Furthermore, the comparison of results reveals that the magnitude of TED in asymmetric vibration modes surpasses that in symmetric ones, and consequently incorporating asymmetric vibration modes is crucial for thorough analysis of TED in circular nanoplates. Thus, the formulation presented in this article can aid in achieving an optimal design for such plates, particularly in terms of minimizing energy loss.

New Angular Momentum Conservation Laws for Electromagnetic Waves Interacting with Dirac fields

Abstract Global conservation laws of angular momentum are well-known in the theory of light-matter interaction. However, local conservation laws, i.e. the conservation law of angular momentum at every point in space, remain unexplored especially in the context of relativistic Dirac-Maxwell fields. Here, we use the QED Lagrangian and Noether's theorem to derive a new local conservation law of angular momentum for Dirac-Maxwell fields in the form of the continuity relation for linear momentum. We separate this local conservation law into four coupled motion equations for spin and orbital angular momentum (OAM) densities. We introduce a helicity current tensor, OAM current tensor, and spin-orbit torque in the motion equations to shed light on the local dynamics of spin-OAM interaction and angular momentum exchange between Maxwell and Dirac fields. We elucidate how our results translate to classical electrodynamics using the example of plane wave interference as well as a dual-mode optical fiber. Our results shine light on angular momentum phenomena related to the relativistic interaction of electromagnetic waves and Dirac fields.

Time-dependent orbital-optimized coupled-cluster methods families for fermion-mixtures dynamics.

Five time-dependent orbital optimized coupled-cluster methods, of which four can converge to the time-dependent complete active space self-consistent-field method, are presented for fermion-mixtures with arbitrary fermion kinds and numbers. Truncation schemes maintaining the intragroup orbital rotation invariance, as well as equations of motion of coupled-cluster (CC) amplitudes and orbitals, are derived. Present methods are compact CC-parameterization alternatives to the time-dependent multiconfiguration self-consistent-field method for systems consisting of arbitrarily different kinds and numbers of interacting fermions. Theoretical analysis of applications of present methods to various chemical systems is reported.

Continuation of Bianchi spacetimes through the big bang

In this paper we present a framework in which the relational description of general relativity can be used to smoothly continue cosmological dynamical systems through the big bang without invoking quantum gravity effects. Cosmological spacetimes contain as a key dynamical variable a notion of scale through the volume factor ν. However, no cosmological observer is ever able to separate their measuring apparatus from the system they are measuring, in that sense every measurement is a relative one, and measurable dynamical variables are, in fact, dimensionless ratios. This is manifest in the identification of a scaling symmetry or “dynamical similarity” in the Einstein-Hilbert action associated with the volume factor. By quotienting out this scaling symmetry, we form a relational system defined on a contact manifold whose dynamical variables are decoupled from scale. When the phase space is reduced to shape space, we show that there exists unique solutions to the equations of motion that pass smoothly through the initial cosmological singularity in flat Friedmann-Lemaître-Robertson-Walker, Bianchi I, and Quiescent Bianchi IX cosmologies. Published by the American Physical Society 2024

On the sausage magnetohydrodynamic waves in magnetic flux tubes: finite plasma beta and phase mixing

Abstract Over the past twenty years, there has been increasing evidence of the existence of sausage waves in the solar atmosphere. These observations make them useful tools in the context of atmospheric seismology. Here, we study sausage magnetohydrodynamic waves in a magnetic flux tube of non-zero plasma beta with a circular cross-section and a radially inhomogeneous plasma density. Solving numerically the equations of motion for an initial value problem, the spatio-temporal evolution of the velocity perturbations is obtained for different sets of parameters. We show that the ratio of the amplitudes of the longitudinal and radial perturbations is determined by the amount of plasma beta. Additionally, the longitudinal component of the velocity perturbation experiences phase-mixing within a layer surrounding the boundary of the flux tube with a rate depending on the amount of plasma beta. The results revealed that in the presence of a non-zero plasma beta, the flux tube exhibits oscillations in both the radial and longitudinal directions, characterized by a combination of two frequencies: one belonging to the slow continuum and the other to the Alfvén continuum. Also, the period of radial oscillation is obtained for different sets of parameters. The dependence of the period of the radial oscillation on the wavenumber confirms the results obtained in previous studies.

Research on the change of the combined moment of inertia for two-link manipulator with angular coordinate system

The main of the problems of the development of two-link manipulators with an angular coordinate system is the lack of effective and universal control systems capable of implementing energy-intensive modes of movement. This is due to the design features of the pointer system of such manipulators and the methods of their use. During the operation of the manipulator, significant dynamic loads occur in its drive system, which create oscillations of the mechanical system and reduce the accuracy of work. The control system must also effectively compensate for such dynamic variations. Dynamic equations of motion used to build manipulator control controllers, which allow taking into account various features of using manipulators. These mathematical models necessarily contain one of the characteristics in the form of the combined moment of inertia of the mechanical system, which is important in the calculation of differential equations and the determination of kinematic parameters of motion. In this article, the combined moments of inertia of the boom system of a two-link manipulator with an angular coordinate system are determined. A study was carry out and it shown that the nature of the change in the combined moments of inertia influenced by the modes of movement of the boom system links. The results of the study showed that the combined moment of inertia of the boom system of the manipulator is not a constant value, which does not change uniformly under special operating conditions of the machine. To determine the combined moments of inertia, the method of bringing the kinetic energy of the moving system to the drive mechanism was apply. This is relevant, because in the future it will be necessary to adjust the unevenness of the movement of the manipulator links by the drive itself. The study was conduct for a typical linear motion mode and a motion mode with a change in speed along a parabolic trajectory.

Modelling of non-linear elastic constitutive relationship and numerical simulation of rocks based on the Preisach-Mayergoyz space model

Summary The existence of pores, cracks, and cleavage in rocks results in significant non-linear elastic phenomena. One important non-linear elastic characteristic is the deviation of the stress-strain curve from the linear path predicted by Hooke's law. To provide a more accurate description of the non-linear elastic characteristics of rocks and to characterize the propagation of non-linear elastic waves, we introduce the Preisach-Mayergoyz space model. This model effectively captures the non-linear mesoscopic elasticity of rocks, allowing us to observe the stress-strain and modulus-stress relationships under different stress protocols. Additionally, we analyze the discrete memory characteristics of rocks subjected to cyclic loading. Based on the Preisach-Mayergoyz space model, we develop a new non-linear elastic constitutive relationship in the form of an exponential function. The new constitutive relationship is validated through copropagating acousto-elastic testing, and the experimental result is highly consistent with the data predicted by the theoretical non-linear elastic constitutive relationship. By combining the new non-linear elastic constitutive relationship with the strain-displacement formula and the differential equation of motion, we derive the non-linear elastic wave equation. We numerically solve the non-linear elastic wave equation with the finite difference method and observe two important deformations during the propagation of non-linear elastic waves: amplitude attenuation and dispersion. We also observe wavefront discontinuities and uneven energy distribution in the 2-D wavefield snapshot, which are different from those of linear elastic waves. We qualitatively explain these special manifestations of non-linear elastic wave propagation.

A flow-field integrated flight control: dynamic wind tunnel testing and simulation

Abstract Abrupt changes in aircraft attitude due to encountering terrain turbulence or wind shear at low altitudes can directly lead to serious accidents. Therefore, a highly responsive and reliable active attitude stabiliser on board is necessary to counteract low-level severe atmospheric disturbances. However, gust environments caused by local terrain and structures are difficult to represent with typical models, such as the Dryden continuous gust model in free space. As a result, an optimal model-based control design cannot be applied. To address this problem, this paper introduces an adaptive mechanism for updating motion equations based on atmospheric conditions using in-flight surface pressure-field sensing. Additionally, a dynamic wind tunnel experiment system, which can be constructed at universities at a low cost, is developed and described in detail. The effectiveness of the proposed scheme is evaluated through wind tunnel experiments and numerical simulations using a large number of gust samples.

Carroll geodesics

Using effective field theory methods, we derive the Carrollian analog of the geodesic action. We find that it contains both “electric” and “magnetic” contributions that are in general coupled to each other. The equations of motion descending from this action are the Carrollian pendant of geodesics, allowing surprisingly rich dynamics. As an example, we derive Carrollian geodesics on a Carroll–Schwarzschild background and discover an effective potential similar to the one appearing in geodesics on Schwarzschild backgrounds. However, the Newton term in the potential turns out to depend on the Carroll particle’s energy. As a consequence, there is only one circular orbit localized at the Carroll extremal surface, and this orbit is unstable. For large impact parameters, the deflection angle is half the value of the general relativistic light-bending result. For impact parameters slightly bigger than the Schwarzschild radius, orbits wind around the Carroll extremal surface. For small impact parameters, geodesics get reflected by the Carroll black hole, which acts as a perfect mirror.

Dynamic stability and response of morphing wing structure with time-varying stiffness

Abstract Morphing, adaptable or smart structures are being used in mechanical and aerospace applications in recent years. These structures often have the property of time-varying stiffness or inertial properties, which can cause parametric instability issues that are not well understood. This paper examines the dynamic stability and response of a morphing aircraft wing with periodically time-varying structural stiffness. The wing is modeled as a beam with coupled bending-torsion motion, and parametrically excited stiffness. Aerodynamic loads introduce aerodynamic damping and aerodynamic stiffness to the wing structure. The dynamic and aeroelastic equation of motion resembles a coupled, damped Mathieu-type equation but differs with asymmetric damping and stiffness matrices, and symmetric inertial matrix. Further, these equations are functions of airspeed, magnitude and frequency of parametric excitation. Initially, dynamic stability of the wing is analyzed using Floquet theory, and the instability regions are numerically quantified by stability charts. Subsequently, dynamic responses in the stable and unstable regions are investigated with a Floquet-based Harmonic balance method. The findings reveal that, at zero airspeed, the combination instabilities are eliminated by varying the bending and torsional stiffness with equal magnitudes and frequency. However, as airspeed increases, instability regions shift unevenly, leading to the emergence of new instabilities. Furthermore, the response analysis within stable regions uncovers several unfavorable zones for operating the variable stiffness, where response decay is slower. The results clearly show that parametric excitation can cause unusual phenomena that significantly impact the operation of morphing wings with variable stiffness, which needs to be thoroughly investigated for successful implementation.

Comparisons between full molecular dynamics simulation and Zhang's multiscale scheme for nanochannel flows.

In a very small surface separation, the fluid flow is actually multiscale consisting of both the molecular scale non-continuum adsorbed layer flow and the intermediate macroscopic continuum fluid flow. Classical simulation of this flow often takes over large computational source and is not affordable owing to using molecular dynamics simulation (MDS) to model the adsorbed layer flow, if the flow field size is on the engineering size scale such as of 0.01-10mm or even bigger like occurring in micro or macro hydrodynamic bearings. The present paper uses full MDS to validate Zhang's multiscale flow model, which yields the closed-form explicit flow equations respectively for the adsorbed layer flow and the intermediate continuum fluid flow. Here, full MDS was carried out for the pressure-driven flow of methane in the nano slit pore made of silicon respectively with the channel heights 5.79nm, 11.57nm, and 17.36nm. According to the number density distribution, the flow areas were respectively discriminated as the adsorbed layer zone and the intermediate fluid zone. The values of the characteristic parameters for Zhang's multiscale scheme were extracted from full MDS and input to Zhang's multiscale flow equations respectively for calculating the flow velocity profile and the volume flow rates of the adsorbed layers and the intermediate fluid. It was found that for these three channel heights, the flow velocity profiles calculated from Zhang's model approximate those calculated from full MDS, while the total flow rates through the channel calculated from Zhang's model are close to those calculated from full MDS. The accuracy of Zhang's multiscale flow model is improved with the increase of the channel height. The recent modification of the optimized potential for liquid simulation (MOPLS) model was used to calculate the interaction force between two methane molecules. In order to calculate the interaction force between the wall atoms and the methane molecules accurately, our previous non-equilibrium multiscale MDS was used. The interaction forces between the methane molecule and the wall atom were obtained from the coupled potential function by the L-B mixing rule when the fluid molecules arrived at near wall. The methane molecule diameter was obtained from the radial distribution function by using equilibrium MDS under the same initial conditions. The local viscosities across the adsorbed layer were obtained from the local velocity profile by using the Poiseuille flow method. The motion equation of the methane molecule was solved by the leapfrog method. The temperature of the simulation system was checked by Bhadauria's method, i.e., the system temperature was rectified by the velocities in the y- and z-directions. The flow velocity distributions across the channel height and the volume flow rates through the channel were also calculated from Zhang's closed-form explicit flow equations respectively for the adsorbed layer flow and the intermediate fluid flow. The results respectively obtained from full MDS and Zhang's multiscale flow equations were then compared.

Calculation of Some Low-Lying Electronic Excitations of Barium Monofluoride Using the Equation of Motion (EOM)-CC3 Method with an Effective Core Potential Approach

Calculation of Some Low-Lying Electronic Excitations of Barium Monofluoride Using the Equation of Motion (EOM)-CC3 Method with an Effective Core Potential Approach

Complex electromagnetism and coupled gravitational-electromagnetic waves in the interstellar medium

Gravito-electromagnetism is an approximation of general relativity that has significant analogies to electromagnetism. We show that the remained asymmetry in those two field equations and the equations of motion can be alleviated through appropriate scaling on the complex plane, thereby allowing gravity and electromagnetism to be combined into a single set of equations for analysis. This enables a more concise and intuitive interpretation of mixed-field interactions of the interstellar medium. The interstellar medium, composed of ionized gas, interacts with both gravitational and electromagnetic fields, and within this medium, gravitational and electromagnetic waves exist in a coupled form. We derive the dispersion relation of these coupled waves tied by the interstellar medium and discuss two branches of wave solutions. These two solutions correspond to the well-known pure gravitational and electromagnetic waves in the classical limit. Based on the characteristics of this coupled wave, we discuss the possible generation of gravitational waves in the interstellar medium and the abnormal behaviors in a medium composed of dark matter that may provide a new methodology for dark matter detection.