Quadratic Theory Research Articles

Thermalization dynamics of two correlated bosonic quantum wires after a split

Coherently splitting a one-dimensional Bose gas provides an attractive, experimentally estab- lished platform to investigate many-body quantum dynamics. At short enough times, the dynamics is dominated by the dephasing of single quasi-particles, and well described by the relaxation to- wards a generalized Gibbs ensemble corresponding to the free Luttinger theory. At later times on the other hand, the approach to a thermal Gibbs ensemble is expected for a generic, interacting quantum system. Here, we go one step beyond the quadratic Luttinger theory and include the lead- ing phonon-phonon interactions. By applying kinetic theory and non-equilibrium Dyson-Schwinger equations, we analyze the full relaxation dynamics beyond dephasing and determine the asymptotic thermalization process in the two-wire system for a symmetric splitting protocol. The major ob- servables are the different phonon occupation functions and the experimentally accessible coherence factor, as well as the phase correlations between the two wires. We demonstrate that, depending on the splitting protocol, the presence of phonon collisions can have significant influence on the asymptotic evolution of these observables, which makes the corresponding thermalization dynamics experimentally accessible.

The theory of spherically symmetric thin shells in conformal gravity

The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy–momentum tensor of the thin shell is proportional to Diracs delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl–Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in detail the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless ([Formula: see text] massless) shell, it is shown that their dynamics cannot be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl–Einstein gravity, the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.

Application of optimal control law to laser guided bomb

ABSTRACTThe paper presents a laser guided bomb guidance law based on the linear quadratic differential game theory, where a case of two perpendicular planes with two state variables in each plane has been considered. The Kalman filtering method has been used for noise removal from the measured signals and for estimation of the missing state variable values needed for the optimal guidance law. Optimisation has been conducted with respect to minimisation of the performance index. Comparative analysis of different guidance laws is done. A statistical analysis is performed to obtain the terminal miss distance in dependence on total flight time.

On the Subsystem Level Gain Scheduled Controller Design for MIMO Systems

This paper presents a unique approach to design in the frequency domain a gain scheduled controller (GSC) to nonlinear Lipschitz MIMO system model. The proposed design procedure is based on the Method of Equivalent subsystems and Integral Quadratic Constraints-Small Gain Theory. The feasible design procedures provide a subsystem equivalent frequency characteristic and frequency design method to obtain design procedure for GSC design. The obtained design results and their properties are illustrated in the simultaneously design of controllers for nonlinear turbogenerator model (6-order). The results of the obtained design procedure are a PI automatic gain scheduled voltage regulator (AVR) for synchronous generator, and a PI governor gain scheduled controller.

Gregory\u2013Laflamme analysis of MGD black strings

The minimal geometric deformation (MGD), associated with the 4D Schwarzschild solution of the Einstein equations, is shown to be a solution of the pure 4D Ricci quadratic gravity theory, whose linear perturbations are then implemented by the Gregory–Laflamme eigentensors of the Lichnerowicz operator. The stability of MGD black strings is hence studied, through the correspondence between their Lichnerowicz eigenmodes and the ones associated with the 4D MGD solutions. It is shown that there exists a critical mass driving the MGD black strings stability, above which the MGD black string is precluded from any Gregory–Laflamme instability. The general-relativistic limit shows the MGD black string to be unstable, as expected, corresponding to the standard Gregory–Laflamme black string instability.

Using block pulse functions for seismic vibration semi-active control of structures with MR dampers

Abstract This article applied the idea of block pulse functions in the semi-active control of structures. The BP functions give effective tools to approximate complex problems. The applied control algorithm has a major effect on the performance of the controlled system and the requirements of the control devices. In control problems, it is important to devise an accurate analytical technique with less computational cost. It is proved that the BP functions are fundamental tools in approximation problems which have been applied in disparate areas in last decades. This study focuses on the employment of BP functions in control algorithm concerning reduction the computational cost. Magneto-rheological (MR) dampers are one of the well-known semi-active tools that can be used to control the response of civil Structures during earthquake. For validation purposes, numerical simulations of a 5-story shear building frame with MR dampers are presented. The results of suggested method were compared with results obtained by controlling the frame by the optimal control method based on linear quadratic regulator theory. It can be seen from simulation results that the suggested method can be helpful in reducing seismic structural responses. Besides, this method has acceptable accuracy and is in agreement with optimal control method with less computational costs.

A note on noncompact and nonmetricit quadratic curvature gravity theories

In this note, we evaluate the Weyl-invariant quadratic curvature tensors for the particular Weyl gauge field constructed in the $3+1$-dimensional noncompact Weyl-Einstein-Yang-Mills model. We subsequently extend the model to its higher curvature version. We also compute the Weyl-invariant extension of the topological Gauss-Bonnet term for this specific choice of vector field.

Nonlinear Control for Spacecraft Pursuit-Evasion Game Using the State-Dependent Riccati Equation Method

Spacecraft pursuit-evasion game is formulated as a two-player zero-sum differential game. The Hill reference frame is used to describe the dynamics of the game. The goal is to derive feedback control law which forms a saddle point solution to the game. Both spacecraft use continuous-thrust engines. The linear quadratic differential game theory is applied to derive a linear control law. This theory is extended to derive a nonlinear control law using the state-dependent Riccati equation method. A state-dependent coefficient matrix is developed for this purpose. Various scenarios are considered for comparing the performance of the linear and nonlinear laws. In all the scenarios, the efficacy of the nonlinear control law is found to be superior to that of the linear control law with computation cost similar to the linear law.

Progressive damage and failure analysis of three-dimensional braided composites subjected to biaxial tension and compression

This paper investigates the failure behavior of three-dimensional (3D) braided composites subjected to biaxial tension and compression through an improved micromechanical computational method and the finite element (FE) method. The yarns and the out-of-yarn matrix in the composites are modeled by an extended Hashin criterion and an extended Drucker-Prager criterion, respectively. The uniaxial mechanical properties are analyzed based on the available experimental data as a verification of the models. The biaxial progressive damage and failure behavior are investigated using the models. The braiding structure, whose diversity results in the difference in failure modes during damage evolution, has significant influence on the biaxial failure correlation of the composites. The predicting formulae for failure envelopes are suggested in this study. The failure envelopes of 3D four-directional and five-directional braided composites can be described by quadratic tensor theories, and the envelopes of 3D six-directional and seven-directional braided composites can be predicted by the maximum strain criterion.

Coordination control of multiple micro sources in islanded microgrid based on differential games theory

To deal with the deviations of frequency of microgrid system composed of multiple micro sources caused by load disturbance, the load frequency control of islanded microgrid system is studied based onlinear quadratic differential games theory in this paper. Considering the operating characteristics of each micro source, different objective function weighting matrix is selected, and the control strategy of non-cooperative feedback Nash equilibrium of each micro source in microgrid system is researched. The simulation results show that the control strategy can accomplish system control targets, make full use of the various of characteristics of each micro source and balance the benefit of them. At the same time, the control strategy has good robustness to external disturbance and parameter variation of the internal unit.

Stability in quadratic torsion theories

We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier.

Fourier transform and particle swarm optimization based modified LQR algorithm for mitigation of vibrations using magnetorheological dampers

Structural control has gained significant attention in recent times. The standalone issue of power requirement during an earthquake has already been solved up to a large extent by designing semi-active control systems using conventional linear quadratic control theory, and many other intelligent control algorithms such as fuzzy controllers, artificial neural networks, etc. In conventional linear–quadratic regulator (LQR) theory, it is customary to note that the values of the design parameters are decided at the time of designing the controller and cannot be subsequently altered. During an earthquake event, the response of the structure may increase or decrease, depending the quasi-resonance occurring between the structure and the earthquake. In this case, it is essential to modify the value of the design parameters of the conventional LQR controller to obtain optimum control force to mitigate the vibrations due to the earthquake. A few studies have been done to sort out this issue but in all these studies it was necessary to maintain a database of the earthquake. To solve this problem and to find the optimized design parameters of the LQR controller in real time, a fast Fourier transform and particle swarm optimization based modified linear quadratic regulator method is presented here. This method comprises four different algorithms: particle swarm optimization (PSO), the fast Fourier transform (FFT), clipped control algorithm and the LQR. The FFT helps to obtain the dominant frequency for every time window. PSO finds the optimum gain matrix through the real-time update of the weighting matrix R, thereby, dispensing with the experimentation. The clipped control law is employed to match the magnetorheological (MR) damper force with the desired force given by the controller. The modified Bouc–Wen phenomenological model is taken to recognize the nonlinearities in the MR damper. The assessment of the advised method is done by simulation of a three-story structure having an MR damper at the ground floor level subjected to three different near-fault historical earthquake time histories, and the outcomes are equated with those of simple conventional LQR. The results establish that the advised methodology is more effective than conventional LQR controllers in reducing inter-storey drift, relative displacement, and acceleration response.

Zames–Falb Multipliers for Invariance

This letter provides a comprehensive framework for local stability analysis of uncertain feedback interconnections within the integral quadratic constraints theory using general dynamic multipliers. It is shown how so-called hard and soft constraints can be effectively combined in order to (locally) capture the action of the uncertainty. This is illustrated for Zames–Falb multipliers, where it is proven that the subclasses of causal and anticausal multipliers can easily be factorized into hard constraints and thus individually be incorporated into the framework without introducing conservatism.

A general method for closed-loop inverse simulation of helicopter maneuver flight

Maneuverability is a key factor to determine whether a helicopter could finish certain flight missions successfully or not. Inverse simulation is commonly used to calculate the pilot controls of a helicopter to complete a certain kind of maneuver flight and to assess its maneuverability. A general method for inverse simulation of maneuver flight for helicopters with the flight control system online is developed in this paper. A general mathematical describing function is established to provide mathematical descriptions of different kinds of maneuvers. A comprehensive control solver based on the optimal linear quadratic regulator theory is developed to calculate the pilot controls of different maneuvers. The coupling problem between pilot controls and flight control system outputs is well solved by taking the flight control system model into the control solver. Inverse simulation of three different kinds of maneuvers with different agility requirements defined in the ADS-33E-PRF is implemented based on the developed method for a UH-60 helicopter. The results show that the method developed in this paper can solve the closed-loop inverse simulation problem of helicopter maneuver flight with high reliability as well as efficiency.

Prediction of the wave induced second order vertical bending moment due to the variation of the ship side angle by using the quadratic strip theory

In this study, the second order bending moment induced by sea waves is calculated using the quadratic strip theory. The theory has the fluid forcing terms including the quadratic terms of the hydrodynamic forces and the Froude–Krylov forces. They are applied to a ship as the external forces in order to estimate the second order ship responses by fluid forces. The sensitivity of the second order bending moment is investigated by implementing the quadratic terms by varying the ship side angle for two example ships. As a result, it was found that the second order bending moment changes significantly by the variation of the ship side angle. It implies that increased flare angles at the bow and the stern of ships being enlarged would amplify their vertical bending moments considerably due to the quadratic terms and may make them vulnerable to the fatigue.

To design high efficient red-emitting iridium complexes by variation of ancillary ligand: Emissive rule and quantum yield

The scarcity of high efficient red-emitting phosphorescent emitters, especially for deeply red emitter, has become the major road stone to block the further development of organic light-emitting diodes. Most of studies have been devoted to developing new Ir(III) complexes by variation of primary ligands. The ancillary ligand has attracted less attention. Four Ir(III) complexes, (DPQ)2Ir(pic) (1), (DPQ)2Ir(tmd) (2), (DPQ)2Ir(ozl) (3), and (DPQ)2Ir(iml) (4) with different ancillary ligands are explored from both emissive rule and quantum yields, where DPQ is 2,4-diphenylquinoline with a CF3 group at meta position of the phenyl ring, pic is picolinate, tmd is 2,2,6,6-tetramethylheptane-3,5-diketonate, ozl is 2-(4,5-dihydrooxazol-2-yl)phenol, and iml is 2-(1-ethyl-4,5-dihydro-1H-imidazol-2-yl)phenol. Radiative rate constant for phosphorescence (kr) is calculated by quadratic response time-dependent density functional theory (QR-TDDFT). The transition dipole moment, spin-orbit coupling matrix element, and singlet-triplet splitting energy related with the kr are also analyzed to further uncover the crucial factors to affect the kr. While the nonradiative rate constant for phosphorescence (knr) is qualitatively estimated from both temperature-independent nonradiative rate constant (k′nr) and temperature-dependent nonradiative rate constant (knr(T)) viewpoints. The emissive wavelength of new designed Ir(III) complex 4 locates in the deeply red region. Moreover, it has the larger quantum yield because of both larger kr and smaller knr. The variation of ancillary ligand is also an advisable choice to develop red-emitting Ir(III) complex with ideal quantum efficiency.

On Stabilizing Control of Gaussian Processes for Unknown Nonlinear Systems

This paper proposes a novel controller design to stabilize Gaussian process (GP) dynamical models for partially unknown nonlinear systems. The unknown system is identified as the GP model. Because existing GP models are difficult to analyze in terms of controller design, a novel GP identification method is proposed that obtains the state dependent coefficient matrix of the system, making the controller design more efficient. The GP model is represented as a piecewise linear system with a bounded uncertainty that is derived based on the characteristics of the GP. Extending quadratic stability theory derives a novel stabilizing controller for such systems.

Forming of Space Charge Wave with Broad Frequency Spectrum in Helical Relativistic Two-Stream Electron Beams**Supported by the Ministry of Education and Science of Ukraine under Grant No 0117U002253.

We elaborate a quadratic nonlinear theory of plural interactions of growing space charge wave (SCW) harmonics during the development of the two-stream instability in helical relativistic electron beams. It is found that in helical two-stream electron beams the growth rate of the two-stream instability increases with the beam entrance angle. An SCW with the broad frequency spectrum, in which higher harmonics have higher amplitudes, forms when the frequency of the first SCW harmonic is much less than the critical frequency of the two-stream instability. For helical electron beams the spectrum expands with the increase of the beam entrance angle. Moreover, we obtain that utilizing helical electron beams in multiharmonic two-stream superheterodyne free-electron lasers leads to the improvement of their amplification characteristics, the frequency spectrum broadening in multiharmonic signal generation mode, and the reduction of the overall system dimensions.

A Method for Angular Super-Resolution via Big Data Radar System

This paper proposes a novel method for enhancing angular resolution in multimedia big data navigation radar system. A new radar scanning model is designed on the basis of quadratic programming theory, by which the proposed Gradient Projection (GP) algorithm is used for solving the optimal solution of this model, and then the target information can be restored successfully at low signal to noise ratio (SNR). Simulations further confirm our theoretical discussion, and manifest that the efficiency and applicability of the proposed method is favorable that the resolution ratio reaches 4~11 times under our proposed scanning model framework if SNR is above 10dB. Moreover, the designed model is suitable for some other angular super-resolution methods, the restoration ratio of which can be improved while SNR is be equal or greater than 10dB. In this case, a higher signal to reconstructed error ratio (SRER) is provided by our method.

Black hole continuum spectra as a test of general relativity: quadratic gravity

Observations of the continuum spectrum emitted by accretion disks around black holes allows us to infer their properties, including possibly whether black holes are described by the Kerr metric. Some modified gravity theories do not admit the Kerr metric as a solution, and thus, continuum spectrum observations could be used to constrain these theories. We here investigate whether current and next generation x-ray observations of the black hole continuum spectrum can constrain such deviations from Einstein’s theory, focusing on two well-motivated modified quadratic gravity theories: dynamical Chern–Simons gravity and Einstein-dilaton-Gauss–Bonnet gravity. We do so by determining whether the non-Kerr deviations in the continuum spectrum introduced by these theories are larger than the observational error intrinsic to the observations. We find that dynamical Chern–Simons gravity cannot be constrained better than current bounds with current or next generation continuum spectrum observations. Einstein-dilaton-Gauss–Bonnet gravity, however, may be constrained better than current bounds with next generation telescopes, as long as the systematic error inherent in the accretion disk modeling is decreased below the predicted observational error.