Quadratic Theory Research Articles

Nonlinear chiral forms in the Sen formulation

The Sen formulation for chiral (2p)-form in 4p+2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4p+2$$\\end{document} dimensions describes a system with two separate sectors, one is physical while the other is unphysical. Each contains a chiral form and a metric. In this paper, we focus on the cases where the self-duality condition for the unphysical sector is linear while for the physical sector can be nonlinear. We show the decoupling at the Hamiltonian and Lagrangian levels. The decoupling at the Hamiltonian level follows the idea in the literature. Then by an appropriate field redefinition of the corresponding first-order Lagrangian, the separation at the Lagrangian level follows. We derive the diffeomorphism of the theory in the case where the chiral form in the physical sector has nonlinear self-dual field strength and couples to external (2p+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2p+1)$$\\end{document}-form field. Explicit forms of Sen theories are also discussed. The Lagrangian for the quadratic theory is separated into two Henneaux–Teitelboim Lagrangians. We also discuss the method of generating explicit nonlinear theories with p=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p=1$$\\end{document}. Finally, we also show that the M5-brane action in the Sen formulation is separated into a Henneaux–Teitelboim action in unphysical sector and a gauge-fixed PST in physical sector.

Quantum backreactions in (A)dS3 massive gravity and logarithmic asymptotic behavior

We study the interplay between higher-curvature terms and the backreaction of quantum fluctuations in three-dimensional massive gravity in asymptotically (anti–)de Sitter space. We focus on the theory at the special point of the parameter space where the two maximally symmetric vacua coincide. In the case of positive cosmological constant, this corresponds to the partially massless point, at which the classical theory admits de Sitter black holes and exhibits an extra conformal symmetry at linear level. We explicitly find the quantum corrected black hole geometry in the semiclassical approximation and show that it induces a relaxation of the standard asymptotic conditions. Nonetheless, the new asymptotic behavior is still preserved by an infinite-dimensional algebra, which, in addition to Virasoro, contains logarithmic supertranslations. Finally, we show that all the results we obtain for the quadratic massive gravity theory can be extended to theories including cubic and quartic terms in the curvature. Published by the American Physical Society 2024

Effectiveness of Weyl gravity in probing quantum corrections to AdS black holes

Computing leading higher curvature contributions to thermodynamic quantities of AdS black hole is drastically simplified once the higher curvature terms are expressed in terms of powers of Weyl tensor by applying proper field redefinitions, avoiding the usual complications caused by higher derivative Gibbons-Hawking-York term or surface counterterms. We establish the method by computing the Euclidean action of general rotating anti–de Sitter (AdS) black holes in five-dimensional quadratic curvature theories with or without supersymmetry and verifying the results numerically. Our result is the state of the art for charged rotating AdS black holes in five-dimensional minimal gauged supergravity including corrections from all three supersymmetric curvature squared terms. Our approach facilitates precision tests in the AdS/CFT correspondence and should be applicable in diverse dimensions. Published by the American Physical Society 2024

Coupling Constants as Conserved Charges in Black Hole Thermodynamics.

In a generic theory of gravity coupled to matter fields, the Smarr formula for black holes does not work properly if the contributions of the coupling constants defining the theory are not incorporated. However, these couplings, such as the cosmological constant or the dimensionful parameters that appear in the Lagrangian, are fixed parameters defining the theory, and they cannot be varied. Here, we present a robust method, applicable to any covariant Lagrangian, that upgrades the role of the couplings from being constants in the theory to being free parameters of the solutions. To this end, for each one of the couplings in a theory, a pair of auxiliary scalar and gauge fields is introduced. The couplings are shown to be conserved charges of the global part of the implemented gauge symmetry. Besides, their conjugate chemical potentials are defined as the electric potential of the corresponding gauge fields on the black hole horizon. Using this method, we systematically extend the first law and the Smarr formula by coupling conserved charges and their conjugate potentials. The thermodynamics of a black hole solution in a quadratic gravity theory is given as an example.

Singular space-times with bounded algebraic curvature scalars

We show that the absence of unbounded algebraic curvature invariants constructed from polynomials of the Riemann tensor cannot guarantee the absence of strong singularities. As a consequence, it is not sufficient to rely solely on the analysis of such scalars to assess the regularity of a given space-time. This conclusion follows from the analysis of incomplete geodesics within the internal region of asymmetric wormholes supported by scalar matter which arise in two distinct metric-affine gravity theories. These wormholes have bounded algebraic curvature scalars everywhere, which highlights that their finiteness does not prevent the emergence of pathologies (singularities) in the geodesic structure of space-time. By analyzing the tidal forces in the internal wormhole region, we find that the angular components are unbounded along incomplete radial time-like geodesics. The strength of the singularity is determined by the evolution of Jacobi fields along such geodesics, finding that it is of strong type, as volume elements are torn apart as the singularity is approached. Lastly, and for completeness, we consider the wormhole of the quadratic Palatini theory and present an analysis of the tidal forces in the entire space-time.

Merger estimates for a disformal Kerr black hole in quadratic degenerate higher-order scalar-tensor theories* *Supported by the National Key Research and Development Program of China (2020YFC2201400), and the National Natural Science Foundation of China (12275079, 12035005, 12275078)

We investigate the main features of a disformal Kerr black hole merger in quadratic degenerate higher-order scalar-tensor theories. In the ringdown stage of the black hole merger, for the prograde orbit, the real part of the quasinormal modes decreases with an increase in the disformal parameter, and the imaginary part also decreases, except in the Kerr case for a large spin parameter. However, for the retrograde orbit, the real part increases with an increase in the disformal parameter, and the imaginary part always decreases with it. For the approximate final spin, regardless of an equal spin, unequal spin, or generic spin configuration merger, the final black hole spin always increases with an increase in the disformal parameter. Our results show that the disformal parameter in the disformal Kerr solution and the MOG parameter in the Kerr-MOG case have obviously different effects on the black hole merger, which suggests the differences between these two spacetime structures.

Kalman state estimator for aircraft structural load alleviation using eigenpair assignment

Process of finding the “best estimate” from noisy signals amounts to “filtering out” the noise. Many methods exist to filter the unwanted noise. A tried and tested method is to use a Kalman Filter which not only cleans up the signals but can also be used to provide signal estimates, for use in reduced order feedback control. Typically, Kalman filter gains are computed using the Linear Quadratic Regulator theory. Reduced order feedback control has been applied in aircraft control problems. One such application area is in synthetic load alleviation, structural loads that arise due to gusts and or control surface deflections. Aircraft structural load alleviation necessitates the use of robust feedback control. The controllers are required to provide load alleviation in cases where the feedback signals are contaminated with noise or missing due to sensor failures. In this paper a method of computing the Kalman gains for the purposes of reduced order feedback is presented, which completely specifies the error dynamics of the estimator in terms of its eigenvalues and associated eigenvectors. The state estimator synthesized using the proposed approach has excellent noise rejection properties and shown to be robust and can be successfully used in reduced order state feedback control, specifically in Aircraft Structural Load Alleviation control schemes. The proposed scheme demonstrates reduction in structural loads.

Optimal Control Strategy of Electro-hydraulic Position Servo System Using Genetic Algorithm

Background: The optimal control strategy has been widely used in electro-hydraulic position servo systems to achieve high-precision position tracking. However, the difficulty of selecting the weighted matrices in optimal control often leads to poor tracking accuracy. Objective: This patent proposes an optimal control strategy using a genetic algorithm to improve the tracking accuracy of the electro-hydraulic servo system. Methods: The patent first established the system state equation of the valve-controlled asymmetric cylinder. Secondly, based on linear quadratic optimal control theory and genetic algorithm, an optimal control strategy using a genetic algorithm was proposed. Finally, the simulation and experimental results showed that the designed controller has high position tracking accuracy . Results: The optimal controller using a genetic algorithm was designed using Matlab/Simulink, and the effectiveness of the controller was verified through simulation. Additionally, experimental results showed that the proposed optimal control controller using a genetic algorithm had higher tracking accuracy than the proportional-integral-derivative controller and traditional backstepping controller for a given reference signal. Conclusion: The control technology of the optimal controller using a genetic algorithm was found to be superior to proportional-integral-derivative and traditional backstepping controllers, and the tracking error of the linear quadratic regulator controller was reported to be relatively small. This demonstrated the effectiveness of the optimal control strategy using a genetic algorithm in this patent.

Spin current generation in an organic antiferromagnet via photo-excitation

We investigate the spin current generation in a one-dimensional organic antiferromagnetic system under light illumination via the quadratic response theory. We show that when the light energy is greater than the band gap of the system, a finite DC spin current of the shift type can be excited while the charge current remains zero. The spin conductivity is found to be an even function of the chemical potential μ, and can take comparatively large values around μ=0. The estimated nonlinear spin conductivity might be on the order of 10−6ħe⋅A/V2, which is comparable to the values reported recently for some inorganic systems, indicating that the optical approach may be an efficient way to generate spin currents in organic materials.

Toward Accurate Two-Photon Absorption Spectrum Simulations: Exploring the Landscape beyond the Generalized Gradient Approximation.

In this Letter, we present a pioneering analysis of the density functional approximations (DFAs) beyond the generalized gradient approximation (GGA) for predicting two-photon absorption (2PA) strengths of a set of push-pull π-conjugated molecules. In more detail, we have employed a variety of meta-generalized gradient approximation (meta-GGA) functionals, including SCAN, MN15, and M06-2X, to assess their accuracy in describing the 2PA properties of a chosen set of 48 organic molecules. Analytic quadratic response theory is employed for these functionals, and their performance is compared against the previously studied DFAs and reference data obtained at the coupled-cluster CC2 level combined with the resolution-of-identity approximation (RI-CC2). A detailed analysis of the meta-GGA functional performance is provided, demonstrating that they improve upon their predecessors in capturing the key electronic features of the π-conjugated two-photon absorbers. In particular, the Minnesota functional MN15 shows very promising results as it delivers pleasingly accurate chemical rankings for two-photon transition strengths and excited-state dipole moments.

Trajectory control of Mars probe based on fuzzy variable parameter theory

The longitudinal dynamics model of the Mars probe's entry phase is a time-varying and nonlinear model. The study of time-varying nonlinear systems is complex. When the system is processed with a T–S fuzzy system, there is a limitation that the number of fuzzy rules increases dramatically. In this paper, the dynamic model of the Mars probe in the entry phase is treated with a fuzzy variable parameter system to overcome this shortcoming. By the process of local linearisation, a fuzzy variable parameter model of the Mars probe is established according to the time-varying characteristics of atmospheric density. Next, the full-state feedback and dynamic output feedback gain-scheduling controllers are designed based on the quadratic Lyapunov stability theory. Finally, Simulink simulation verifies that the fuzzy variable parameter system of the Mars probe's entry phase can be asymptotically stabilised by the designed controllers.

Controller Design for Congestion Avoidance Based on Several Optimization Techniques

The world has become more like a small community thanks to the internet, which connects millions of people, businesses, and pieces of technology for a variety of uses. Because of the significant influence these networks have on our lives, maintaining their efficiency is important, which necessitates addressing issues like congestion. In this study, PI-controller gains are adjusted using a variety of optimization strategies to regulate the nonlinear TCPAQM model. This controller commits controlled pressured signaling characteristics and modifies computer network congestion. First manual tune PI-Controller are used; then several optimization techniques were used to tune PI-controller gains (Particle Swarm Optimization (PSO), Ant-Colony Optimization (ACO) and Simulated Annealing algorithm (SA)) and then Linear Quadratic Regulator theory are used. To test the reliability and effectiveness of each of the suggested controllers, several tests utilizing varied network parameter values, different queue sizes, and extra disturbances were conducted. MATLAB was used for all experiments., the results show the superiority of the LQR controller over PI controller with both manual and optimal tuning techniques.

A comparison of finiteness conditions in quadratic form theory

We discuss and relate finiteness conditions for certain field invariants which are studied in quadratic form theory. This includes the [Formula: see text]-invariant, the reduced stability index and the symbol lengths for Galois cohomology groups with coefficients in [Formula: see text], as well as a new invariant called the splitting height.

Robustness analysis of uncertain time‐varying systems with unknown initial conditions

SummaryThis paper focuses on the robustness analysis of discrete‐time, linear time‐varying (LTV) systems subject to various uncertainties, such as static and dynamic, time‐invariant and time‐varying, linear perturbations, and unknown initial conditions. The proposed approach is based on integral quadratic constraint theory and allows for a potentially more accurate characterization of the set in which the initial state resides by imposing separate constraints on the initial values of the state variables as opposed to simply requiring the initial state to lie in some ellipsoid. The adopted problem formulation facilitates the analysis of uncertain LTV systems subject to disturbance inputs that are bounded pointwise in time, and the developed results enable determining useful pointwise bounds on the performance outputs given such inputs. The main analysis result is given for eventually periodic nominal systems, which include linear time‐invariant, finite horizon, and periodic systems as special cases. The analysis conditions are expressed as linear matrix inequalities. Two additional results stemming from the main analysis theorem are provided that can be used to determine overapproximated ellipsoidal reachable sets. Finally, the utility of the proposed approach is demonstrated in an illustrative example.

Frequency-Dependent Quadratic Response Properties and Two-Photon Absorption from Relativistic Equation-of-Motion Coupled Cluster Theory.

We present the implementation of quadratic response theory based upon the relativistic equation-of-motion coupled cluster method. We showcase our implementation, whose generality allows us to consider both time-dependent and time-independent electric and magnetic perturbations, by considering the static and frequency-dependent hyperpolarizability of hydrogen halides (HX, X = F-At), providing comprehensive insights into their electronic response characteristics. Additionally, we evaluated the Verdet constant for noble gases Xe and Rn and discussed the relative importance of relativistic and electron correlation effects for these magneto-optical properties. Finally, we calculate the two-photon absorption cross sections of transition [ns1S0 → (n + 1)s1S0] of Ga+ and In+, which are suggested as candidates for new ion clocks. As our implementation allows for the use of nonrelativistic Hamiltonians as well, we have compared our EOM-QRCC results to the QR-CC implementation in the DALTON code and show that the differences between CC and EOMCC response are in general smaller than 5% for the properties considered. Collectively, the results underscore the versatility of our implementation and its potential as a benchmark tool for other approximated models, such as density functional theory for higher-order properties.

Design of automatic tobacco trash detection system based on quadratic fuzzy theory

Abstract Fuzzy sets and deep learning models have accurate recognition accuracy in automatic detection. To be able to accurately identify tobacco debris and improve the quality of cigarettes, this paper proposes the design of a tobacco debris detection system with a deep learning model and fuzzy quadratic theory. The collected data is stored to AL422B by quadratic fuzzy set timing conversion, the cached image data is read by the microcontroller, the image pixel points are output, and the external controller and internal registers are set to read the tobacco image. The integrated Thumb extended instruction set to obtain the CPU clock frequency makes the controller interrupt and ensures PWM output. Integrate the internal fixed oscillator and external integrated control circuit to debug the program interface circuit to prevent power on and off misoperation. The negative log-likelihood function is obtained by following the activation rules given by the visible layer and hidden layer activation functions. The RBM is trained by quadratic fuzzy set estimation to optimize the parameters; test sample sets appear overfitting, combined with DBN pre-training and fine-tuning, iterative output, and labeling target data to meet the preset requirements to achieve intelligent detection of tobacco debris. The result analysis shows that the deep learning model and the quadratic fuzzy set generalization ability and accuracy are high, the highest F-value in tobacco clutter detection reaches 100%, and the system is designed to detect tobacco clutter automatically with high accuracy and good detection of clutter.

Second response theory: a theoretical formalism for the propagation of quantum superpositions

The propagation of general electronic quantum states provides information of the interaction of molecular systems with external driving fields. These can also offer understandings regarding non-adiabatic quantum phenomena. Well established methods focus mainly on propagating a quantum system that is initially described exclusively by the ground state wavefunction. In this work, we expand a previously developed size-extensive formalism within coupled cluster theory, called second response theory, so it propagates quantum systems that are initially described by a general linear combination of different states, which can include the ground state, and show how with a special set of time-dependent cluster operators such propagations are performed. Our theory shows strong consistency with numerically exact results for the determination of quantum mechanical observables, probabilities, and coherences. We discuss unperturbed non-stationary states within second response theory and their ability to predict matrix elements that agree with those found in linear and quadratic response theories. This work also discusses an approximate regularized methodology to treat systems with potential instabilities in their ground-state cluster amplitudes, and compares such approximations with respect to reference results from standard unitary theory.

Efficient Protocol for Computing MCD Spectra in a Broad Frequency Range Combining Resonant and Damped CC2 Quadratic Response Theory.

Coupled cluster response theory offers a path to high-accuracy calculations of spectroscopic properties, such as magnetic circular dichroism (MCD). However, divergence or slow convergence issues are often encountered for electronic transitions in high-energy regions with a high density of states. This is here addressed for MCD by an implementation of damped quadratic response theory for resolution-of-identity coupled cluster singles-and-approximate-doubles (RI-CC2), along with an implementation of the MCD term from resonant response theory. Combined, damped and resonant response theory calculations provide an efficient strategy to obtain MCD spectra over a broad frequency range and for systems that include highly symmetric molecules with degenerate excited states. The protocol is illustrated by application to zinc tetrabenzoporphyrin in the energy region of 2-8 eV and comparison to experimental data. Timings are reported for the resonant and damped approaches, showing that a greater part of the calculation time is consumed by the construction of the building blocks for the final MCD ellipticity. A recommendation on how to use the procedure is outlined.

Numerical and Experimental Analysis to Predict the Compressive Strength of Pristine Composite Laminates

In this work, the numerical and experimental work has been carried out to verify the compressive strength of pristine composite laminates. Theoretical computations have been carried out using MATLAB to compute the strength and buckling load. Finite Element Analysis has been carried out for the composite laminate using two and three dimensional elements. PATRAN as the Pre and Post processing package and NASTRAN as the solver have been used in this work. The various failure theories considered in this article are Tsai-Wu, Hill, Hoffman, Maximum Stress and Quadratic failure theory (YSFT). All the first four failure theories are available as a standard criterion in the PATRAN package. The fifth quadratic failure criterion has been implemented using PATRAN Command Language. Static analysis along with failure theories has been carried out to compute the strength of the laminate. Static and buckling analysis has been presented for both in two-and three-dimensional models. Experiments have been carried out on number of pristine laminates and the strain values obtained from FEA have been compared with the experimental values. The theoretical computation provides a load value which is about the elastic limit of the specimen. It is generally observed that quadratic failure theory (YSFT) provides least failure indices and may be employed for conservative design.

An Exact Model of a Gravitational Wave in the Bianchi III Universe Based on Shapovalov II Wave Spacetime and the Quadratic Theory of Gravity

Exact models of primordial gravitational waves in the Bianchi type-III universe were constructed on the basis of the quadratic theory of gravity with a scalar field and pure radiation in Shapovalov wave spacetimes of type II (subtype 2). Exact solutions of the field equations and scalar equation were obtained. The characteristics of pure radiation were determined. An explicit form of the scalar field functions included in the Lagrangian of the considered quadratic theory of gravity was found. The trajectories of the propagation of light rays in the considered gravitational wave models were obtained.