Quadratic Theory Research Articles

Quantum-chemistry study of the ground and excited state absorption of distyrylbenzene: Multi vs single reference methods.

State-of-the-art complete active space self-consistent field/complete active space second order perturbation theory (CASPT2) calculations are used to investigate the role of double excitations on the ground state absorption (GSA) and excited state absorption (ESA) spectra of distyrylbenzene, an important prototype medium-sized π-conjugated organic compound for optoelectronics. The multi-reference results are compared with linear and quadratic response time-dependent density functional theory (DFT) results, revealing an incomplete description of the electronic transitions in the latter. Careful selection of the active space and basis set in the CASPT2 approach allows for a reliable description of the GSA and ESA features; cost-effective DFT-based geometries can be utilized without a significant loss of accuracy. Double excitations are shown to play a pivotal role already for higher excited states in the GSA spectrum, however, without a relevant impact on the discernible spectral features. In the ESA, which shows a much more complex electronic situation, the crucial importance of double (and higher) excitations in all relevant electronic transitions, indeed, mandates a multiconfigurational treatment as done in the present benchmark study.

Cosmology of quadratic metric-affine gravity

We investigate the cosmological aspects of the most general parity preserving Metric-Affine Gravity theory quadratic in torsion and non-metricity in the presence of a cosmological hyperfluid. The equations of motion are obtained by varying the action with respect to the metric and the independent affine connection. Subsequently, considering a Friedmann-Lema\^itre-Robertson-Walker background, we derive the most general form of the modified Friedmann equations for the full quadratic theory. We then focus on a characteristic sub-case involving only two quadratic contributions given in terms of torsion and non-metricity vectors. In this setup, studying the modified Friedmann equations along with the conservation laws of the perfect cosmological hyperfluid, we provide exact solutions both for purely dilation and for purely spin hypermomentum sources. We then discuss the physical consequences of our model and the prominent role of torsion and non-metricity in this cosmological setup.

Research on automobile four-wheel steering control system based on yaw angular velocity and centroid cornering angle

In order to improve the handling stability of four-wheel steering (4WS) cars, a two-degree-of-freedom 4WS vehicle dynamics model is constructed here, and the motion differential equation of the system model is established. Based on the quadratic optimal control theory, the optimal control of 4WS system is proposed in this paper. When running at low speed and high speed, through yaw rate feedback control, state feedback control, and optimal control, the 4WS cars are controlled based on yaw rate and centroid cornering angle with MATLAB/Simulink simulation. The result indicates that 4WS control based on the optimal control can improve the displacement of the cars. And, the optimal control of 4WS proposed in this paper can eliminate centroid cornering angle completely compared with other two traditional optimal control methods. Besides, the optimal control enjoys faster response speed and no overshoot happens. In conclusion, the optimal control method proposed in the paper represents better stability, moving track and stability, thereby further enhancing the handling property of cars.

Misalignment algorithm of a wide-field survey telescope based on third-order quadratic nodal aberration theory

Off-axis three-mirror anastigmatic (TMA) telescopes with designed decenters and tilts, have many misalignment degrees of freedom and strong coupling between each misalignment degree of freedom. Therefore, it is difficult to establish misalignment equations only using A222 and A131 in nodal aberration theory (NAT). In addition, for off-axis TMA optical systems with designed decenters and tilts, the robustness of the existing fifth-order NAT misalignment calculation algorithm based on high-order Zernike coefficients and boresight errors decreases, so it is difficult to realize its engineering application. To solve the issue of insufficient practicality of the existing misalignment algorithm based on fifth-order NAT, a third-order NAT calculation algorithm based on quadratic aberration field decenter vectors is derived and established. Two concepts of inherent aberration field decenter vector and misalignment aberration field decenter vector are proposed. Taking an off-axis TMA optical system with 6-m focal length as the research object, simulations, and alignment verification experiments were carried out. Compared with the existing fifth-order NAT misalignment algorithm, the results show that when measurement noise is not considered, the two methods can both obtain convergent calculation results, and the average RMS wavefront errors (WFE) of the optical system are both corrected to be below 0.0574 waves. When different levels of measurement noise are introduced, the robustness of the fifth-order NAT misalignment algorithm decreases, and there are even cases where the optical system completely fails to be corrected. However, the algorithm based on quadratic aberration field decenter vectors shows better robustness. Under different levels of measurement noise, this algorithm could correct the average RMS WFE of the optical system to around 0.0574 waves.

Modeling and flapping vibration suppression of a novel tailless flapping wing micro air vehicle

This paper establishes and analyzes a high-fidelity nonlinear time-periodic dynamic model and the corresponding state observer for flapping vibration suppression of a novel tailless Flapping Wing Micro Air Vehicle (FWMAV), named NPU-Tinybird. Firstly, a complete modeling of NPU-Tinybird is determined, including the aerodynamic model based on the quasi-steady method, the kinematic and dynamic model about the mechanism of flapping and attitude control, combined with the single rigid body dynamic model. Based on this, a linearized longitudinal pitch dynamic cycle-averaged model is obtained and analyzed through the methods of neural network fitting and system identification, preparing for the design of flapping vibration suppression observer. Flapping vibration is an inherent property of the tailless FWMAV, which arises from the influence of time-periodic aerodynamic forces and moments. It can be captured by attitude and position sensors on the plane, which impairs the flight performance and efficiency of flight controller and actuators. To deal with this problem, a novel state observer for flapping vibration suppression is designed. A robust optimal controller based on the linear quadratic theory is also designed to stabilize the closed-loop system. Simulation results are given to verify the performance of the observer, including the closed loop responses combined with robust optimal controller, the comparison of different parameters of observer and the comparison with several classic methods, such as Kalman filter, H-infinity filter and low-pass filter, which prove that the novel observer owns a fairly good suppression effect on flapping vibration and benefits for the improvement of flight performance and control efficiency.

Nonlinear Hamiltonian analysis of new quadratic torsion theories: Cases with curvature-free constraints

It was recently found that, when linearised in the absence of matter, 58 cases of the general gravitational theory with quadratic curvature and torsion are (i) free from ghosts and tachyons and (ii) power-counting renormalisable. We inspect the nonlinear Hamiltonian structure of the eight cases whose primary constraints do not depend on the curvature tensor. We confirm the particle spectra and unitarity of all these theories in the linear regime. We uncover qualitative dynamical changes in the nonlinear regimes of all eight cases, suggesting at least a broken gauge symmetry, and possibly the activation of negative kinetic energy spin-parity sectors and acausal behaviour. Two of the cases propagate a pair of massless modes at the linear level, and were interesting as candidate theories of gravity. However, we identify these modes with vector excitations, rather than the tensor polarisations of the graviton. Moreover, we show that these theories do not support a viable cosmological background.

Constraints on high-order gravitational theories from weak cosmic censorship

Weak cosmic censorship conjecture (WCCC) is a basic principle that guarantees the predictability of spacetime and should be valid in any classical theories. One critical scientific question is whether the WCCC can serve as a constraint to the gravitational theories. To explore this question, we perform the first-order Sorce-Wald's gedanken experiments to test the WCCC in the higher-order gravitational theories and find that there exists a destruction condition $S_\text{ext}'(r_h)<0$ for the extremal black holes. To show the power of this condition, we evaluate the constraints given by WCCC in the quadratic and cubic gravitational theories. Our investigation makes an essential step toward applying WCCC to constrain the modified gravitational theories, and opens a new avenue to judge which theory is reasonable.

Quantum interference in external gravitational fields beyond General Relativity

In this paper, we study the phenomenon of quantum interference in the presence of external gravitational fields described by alternative theories of gravity. We analyze both non-relativistic and relativistic effects induced by the underlying curved background on a superposed quantum system. In the non-relativistic regime, it is possible to come across a gravitational counterpart of the Bohm–Aharonov effect, which results in a phase shift proportional to the derivative of the modified Newtonian potential. On the other hand, beyond the Newtonian approximation, the relativistic nature of gravity plays a crucial rôle. Indeed, the existence of a gravitational time dilation between the two arms of the interferometer causes a loss of coherence that is in principle observable in quantum interference patterns. We work in the context of generalized quadratic theories of gravity to compare their physical predictions with the analogous outcomes in general relativity. In so doing, we show that the decoherence rate strongly depends on the gravitational model under investigation, which means that this approach turns out to be a promising test bench to probe and discriminate among all the extensions of Einstein’s theory in future experiments.

Dynamic Optimal Mean-Variance Investment with Mispricing in the Family of 4/2 Stochastic Volatility Models

This paper considers an optimal investment problem with mispricing in the family of 4/2 stochastic volatility models under mean–variance criterion. The financial market consists of a risk-free asset, a market index and a pair of mispriced stocks. By applying the linear–quadratic stochastic control theory and solving the corresponding Hamilton–Jacobi–Bellman equation, explicit expressions for the statically optimal (pre-commitment) strategy and the corresponding optimal value function are derived. Moreover, a necessary verification theorem was provided based on an assumption of the model parameters with the investment horizon. Due to the time-inconsistency under mean–variance criterion, we give a dynamic formulation of the problem and obtain the closed-form expression of the dynamically optimal (time-consistent) strategy. This strategy is shown to keep the wealth process strictly below the target (expected terminal wealth) before the terminal time. Results on the special case without mispricing are included. Finally, some numerical examples are given to illustrate the effects of model parameters on the efficient frontier and the difference between static and dynamic optimality.

Boson stars in Palatini gravity

We explore equilibrium solutions of spherically symmetric boson stars in the Palatini formulation of gravity. We account for the modifications introduced in the gravitational sector by using a recently established correspondence between modified gravity with scalar matter and general relativity with modified scalar matter. We focus on the quadratic theory and compare its solutions with those found in general relativity, exploring both positive and negative values of the coupling parameter ξ. As matter source, a complex, massive scalar field with and without self-interaction terms is considered. Our results show that the existence curves of boson stars in Palatini gravity are fairly similar to those found in general relativity. Major differences are observed for negative values of the coupling parameter which results in a repulsive gravitational component for high enough scalar field density distributions. Adding self-interactions makes the degeneracy between and general relativity even more pronounced, leaving very little room for observational discrimination between the two theories.

Evaluation of the collapse mode of isolated structures subjected to multi-directional dynamic coupling excitation based on reliability theory

The identification of the structural collapse mode is an important foundation of structural anti-collapse design and safety evaluation. The collapse mode evaluation method based on probability reliability is widely used in theoretical research and engineering applications. However, studies on the collapse mode of isolated structures have rarely been reported. For the initial damage, the main control excitation and the remaining system constraints of isolated structures all being different from that of traditional fixed-base structures, the collapse mode and the collapse mechanical behaviors of the isolated structure are disparate from the traditional fixed-base structures. The most likely collapse mode of isolated structures subjected to multi-directional dynamic coupling excitation is evaluated based on reliability theory in the presented research work. First, multi-directional dynamic coupling analysis on the isolated structure is performed. Then, a reliability analysis method suitable for isolated structures is proposed, which takes the damage index as the state parameter, and calculates the failure probability based on the quadratic fourth-order moment theory method. The structural collapse probabilities under different collapse modes are calculated, in order to evaluate the most likely collapse mode of the isolated structure. Finally, the identification method is applied to one prototype isolated structure designed in accordance with the Chinese design code. The results indicate that the identification method based on cumulative damage and reliability theory could effectively be used for evaluation of the most likely collapse mode of the isolated structure.

Spatially fractionated radiotherapy: tumor response modelling including immunomodulation

A mathematical tumor response model has been developed, encompassing the interplay between immune cells and cancer cells initiated by either partial or full tumor irradiation. The iterative four-compartment model employs the linear–quadratic radiation response theory for four cell types: active and inactive cytotoxic T lymphocytes (immune cells, CD8+ T cells in particular), viable cancer cells (undamaged and reparable cells) and doomed cells (irreparably damaged cells). The cell compartment interactions are calculated per day, with total tumor volume (TV) as the main quantity of interest. The model was fitted to previously published data on syngeneic xenografts (67NR breast carcinoma and Lewis lung carcinoma; (Markovsky et al 2019 Int. J. Radiat. Oncol. Biol. Phys. 103 697–708)) subjected to single doses of 10 or 15 Gy by 50% (partial) or 100% (full) TV irradiation. The experimental data included effects from anti-CD8+ antibodies and immunosuppressive drugs. Using a new optimization method, promising fits were obtained where the lowest and highest root-mean-squared error values were observed for anti-CD8+ treatment and unirradiated control data, respectively, for both cell types. Additionally, predictive capabilities of the model were tested by using the estimated model parameters to predict scenarios for higher doses and different TV irradiation fractions. Here, mean relative deviations in the range of 19%–34% from experimental data were found. However, more validation data is needed to conclude on the model’s predictive capabilities. In conclusion, the model was found useful in evaluating the impact from partial and full TV irradiation on the immune response and subsequent tumor growth. The model shows potential to support and guide spatially fractionated radiotherapy in future pre-clinical and clinical studies.

Pentacene-Bridge Interactions in an Axially Chiral Binaphthyl Pentacene Dimer.

Molecular chirality can be exploited as a sensitive reporter of the nature of intra- and interchromophore interactions in π-conjugated systems. In this report, we designed an intramolecular singlet fission (iSF)-based pentacene dimer with an axially chiral binaphthyl bridge (2,2'-(2,2'-dimethoxy-[1,1'-binaphthalene]-3,3'-diyl) n-octyl-di-isopropyl silylethynyl dipentacene, BNBP) to utilize its chiroptical response as a marker of iSF chromophore-bridge-chromophore (SFC-β-SFC) interactions. The axial chirality of the bridge enforces significant one-handed excitonic coupling of the pentacene monomer units; as such, BNBP exhibits significant chiroptical response in the ground and excited states. We analyzed the chiroptical response of BNBP using the exciton coupling method and quadratic response density functional theory calculations to reveal that higher energy singlet transitions in BNBP involve significant delocalization of the electronic density on the bridging binaphthyl group. Our results highlight the promising application of chiroptical techniques to investigate the nature of SFC-β-SFC interactions that impact singlet fission dynamics.

Linear stability of Einstein and de Sitter universes in the quadratic theory of modified gravity

We consider the Einstein static and the de Sitter universe solutions and examine their instabilities in a subclass of quadratic modified theories for gravity. This modification proposed by Nash is an attempt to generalize general relativity. Interestingly, we discover that the Einstein static universe is unstable in the context of the modified gravity. In contrast to Einstein static universe, the de Sitter universe remains stable under metric perturbation up to the second order.

Incomplete Information Pursuit-Evasion Game Control for a Space Non-Cooperative Target

Aiming to solve the optimal control problem for the pursuit-evasion game with a space non-cooperative target under the condition of incomplete information, a new method degenerating the game into a strong tracking problem is proposed, where the unknown target maneuver is processed as colored noise. First, the relative motion is modeled in the rotating local vertical local horizontal (LVLH) frame originated at a virtual Chief based on the Hill-Clohessy-Wiltshire relative dynamics, while the measurement models for three different sensor schemes (i.e., single LOS (line-of-sight) sensor, LOS range sensor and double LOS sensor) are established and an extended Kalman Filter (EKF) is used to obtain the relative state of target. Next, under the assumption that the unknown maneuver of the target is colored noise, the game control law of chaser is derived based on the linear quadratic differential game theory. Furthermore, the optimal control law considering the thrust limitation is obtained. After that, the observability of the relative orbit state is analyzed, where the relative orbit is weakly observable in a short period of time in the case of only LOS angle measurements, fully observable in the cases of LOS range and double LOS measurement schemes. Finally, numerical simulations are conducted to verify the proposed method. The results show that by using the single LOS scheme, the chaser would firstly approach the target but then would lose the game because of the existence of the target’s unknown maneuver. Conversely, the chaser can successfully win the game in the cases of LOS range and double LOS sensor schemes.

The gravitational field of a star in quadratic gravity

The characterization of the gravitational field of isolated objects is still an open question in quadratic theories of gravity.We study static equilibrium solutions for a self-gravitating fluid in extensions of General Relativity includingterms quadratic in the Weyl tensor C μνρσ and in the Ricci scalar R, as suggested by one-loop corrections to classical gravity. By the means of a shooting method procedure we link the total gravitational mass and the strength of the Yukawa corrections associated with the quadratic terms with the fluid properties at the center.It is shown that the inclusion of the C μνρσ μνρσ coupling in the lagrangian has a much strongerimpact than the R 2 correction in the determination of the radius and of the maximum mass of a compact object.We also suggest that the ambiguity in the definition of mass in quadratic gravity theories can convenientlybe exploited to detect deviations from standard General Relativity.

Open effective theory of scalar field in rotating plasma

We study the effective dynamics of an open scalar field interacting with a strongly-coupled two-dimensional rotating CFT plasma. The effective theory is determined by the real-time correlation functions of the thermal plasma. We employ holographic Schwinger-Keldysh path integral techniques to compute the effective theory. The quadratic effective theory computed using holography leads to the linear Langevin dynamics with rotation. The noise and dissipation terms in this equation get related by the fluctuation-dissipation relation in presence of chemical potential due to angular momentum. We further compute higher order terms in the effective theory of the open scalar field. At quartic order, we explicitly compute the coefficient functions that appear in front of various terms in the effective action in the limit when the background plasma is slowly rotating. The higher order effective theory has a description in terms of the non-linear Langevin equation with non-Gaussianity in the thermal noise.

The cosmology of quadratic torsionful gravity

We study the cosmology of a quadratic metric-compatible torsionful gravity theory in the presence of a perfect hyperfluid. The gravitational action is an extension of the Einstein–Cartan theory given by the usual Einstein–Hilbert contribution plus all the admitted quadratic parity even torsion scalars and the matter action also exhibits a dependence on the connection. The equations of motion are obtained by regarding the metric and the metric-compatible torsionful connection as independent variables. We then consider a Friedmann–Lemaître–Robertson–Walker background, analyze the conservation laws, and derive the torsion modified Friedmann equations for our theory. Remarkably, we are able to provide exact analytic solutions for the torsionful cosmology.

Theoretical study of linear and non-linear optical activity in dithienylethene-based photo-switch and its derivatives

In this contribution, our aim is to study the linear and non-linear optical activity and their variation with the addition/removal of electron withdrawing and electron donating groups in hexafluorinated dithienylethenes (HFDTE). By varying the terminal groups in the parent HFDTE, we have considered 16 closed-open pairs of substituted HFDTE and studied their electronic structures, one and two-photon absorption spectra and static first hyperpolarizability. All the calculations have been performed using the state-of-the-art linear and quadratic response theory within the framework of TD-DFT methods. RI-CC2 method is used as a reference to validate the applicability of TD-DFT method.

Formula omitted]-dominant switched linear systems

This paper studies the asymptotic behavior of switched linear systems, beyond classical stability. We focus on systems having a low-dimensional asymptotic behavior, that is, systems whose trajectories converge to a common time-varying low-dimensional subspace. We introduce the concept of path-complete p-dominance for switched linear systems, which generalizes the approach of quadratic Lyapunov theory by replacing the contracting ellipsoids by families of quadratic cones whose contraction properties are dictated by an automaton. We show that path-complete p-dominant switched linear systems are exactly the ones that have a p-dimensional asymptotic behavior. Then, we describe an algorithm for the computation of the cones involved in the property of p-dominance. This allows us to provide an algorithmic framework for the analysis of switched linear systems with a low-dimensional asymptotic behavior.