Vector Perturbations Research Articles

Automatic Landing Control for Fixed-Wing UAV in Longitudinal Channel Based on Deep Reinforcement Learning

The objective is to address the control problem associated with the landing process of unmanned aerial vehicles (UAVs), with a particular focus on fixed-wing UAVs. The Proportional–Integral–Derivative (PID) controller is a widely used control method, which requires the tuning of its parameters to account for the specific characteristics of the landing environment and the potential for external disturbances. In contrast, neural networks can be modeled to operate under given inputs, allowing for a more precise control strategy. In light of these considerations, a control system based on reinforcement learning is put forth, which is integrated with the conventional PID guidance law to facilitate the autonomous landing of fixed-wing UAVs and the automated tuning of PID parameters through the use of a Deep Q-learning Network (DQN). A traditional PID control system is constructed based on a fixed-wing UAV dynamics model, with the flight state being discretized. The landing problem is transformed into a Markov Decision Process (MDP), and the reward function is designed in accordance with the landing conditions and the UAV’s attitude, respectively. The state vectors are fed into the neural network framework, and the optimized PID parameters are output by the reinforcement learning algorithm. The optimal policy is obtained through the training of the network, which enables the automatic adjustment of parameters and the optimization of the traditional PID control system. Furthermore, the efficacy of the control algorithms in actual scenarios is validated through the simulation of UAV state vector perturbations and ideal gliding curves. The results demonstrate that the controller modified by the DQN network exhibits a markedly superior convergence effect and maneuverability compared to the unmodified traditional controller.

A novel iterative algorithm for nonlinear inelastic dynamic analysis of truss structures; MCB-Spline+Sp time integration method

The focus of this work is on the development of a novel algorithm for the nonlinear dynamic analysis of structures. In the sake of a general and easy-to-implement solution method, the tangential stiffness matrix is calculated by combining the Cauchy-Riemann equations derived from the differentiation of complex functions and using the nodal displacement perturbation vector. An implicit direct time integration method based on a cubic B-Spline is integrated with the incremental-iterative method using a quadrature rule based on the interpolation of spline functions, which is referred to as the MCB-Spline+Sp time integration method. A step-by-step algorithm for developing a computer code to implement this method is provided. The effectiveness of the proposed approach is evaluated through several nonlinear time history analyses, which demonstrate its accuracy and efficiency by observing less computational efforts and fast convergence rate. Moreover, a comparison is made between the developed method and well-established techniques such as the Newmark and Standard-Bathe time integration methods in combination with the iterative Newton-Raphson method.

Perturbation Transmit Beamformer Based Fast Constant Modulus MIMO Radar Waveform Design

In this paper, a fast method to generate a constant-modulus (CM) waveform for a multiple-input, multiple-output, (MIMO) radar is proposed. To simplify the optimization process, the design of the transmit waveform is decoupled from the design of transmit beamformers (TBs) and subpulses. To further improve the computational efficiency, the TBs’ optimization is conducted in parallel, and a linear programming model is proposed to match the desired beampattern. Additionally, we incorporate the perturbation vectors into the TBs’ optimization so that the TBs can be adjusted to satisfy the CM constraint. To quickly generate the CM subpulses with the desired range-compression (RC) performance, the classical linear frequency modulation (LFM) signal and non-LFM (NLFM) are adopted as subpulses. Meanwhile, to guarantee the RC performance of the final angular waveform, the selection of LFM signal parameters is analyzed to achieve a low cross-correlation between subpulses. Numerical simulations verify the transmit beampattern performance, RC performance, and computational efficiency of the proposed method.

Even- and odd-parity stabilities of black holes in Einstein-Aether gravity

In Einstein-Aether theories with a timelike unit vector field, we study the linear stability of static and spherically symmetric black holes against both even- and odd-parity perturbations.For this purpose, we formulate a gauge-invariant black hole perturbation theory in the background Aether-orthogonal frame where the spacelike property of hypersurfaces orthogonal to the timelike Aether field is always maintained even inside the metric horizon. Using a short-wavelength approximation with large radial and angular momenta, we show that, in general, there are three dynamical degreesof freedom arising from the even-parity sector besides two propagating degrees of freedom present in the odd-parity sector. The propagation speeds of even-parity perturbations and their no-ghost conditions coincide with those of tensor, vector, and scalar perturbations on the Minkowski background, while the odd sector contains tensor and vector modes with the same propagation speeds as those in the even-parity sector (and hence as those on the Minkowski background).Thus, the consistent study of black hole perturbations in the Aether-orthogonal frame on static and spherically symmetric backgrounds does not add new small-scale stability conditions to those known for the Minkowski background in the literature.

Gauge symmetries and conserved currents in AdS/BCFT

In this paper, we study massless/massive vector and p-form field perturbations in AdS spacetime with an end-of-the-world brane. By imposing Υ(1) preserving Neumann boundary condition on the end-of-the-world brane, we study their spectrum and discuss their implications for dual BCFT operators. When the perturbation is massless, the dual BCFT operator is a conserved current and we show that such an operator indeed satisfies the Υ(1) preserving conformal boundary condition. On the other hand, when the perturbation is massive, in general there exists non-vanishing perpendicular components of the dual BCFT operator, even in the massless limit. We explain this difference between massless and massive perturbations from the point of view of the bulk gauge symmetry, or equivalently from different structure of equations of motion. We also find several brane-tension-independent modes in massless perturbations, and these are understood as boundary-condition-independent modes from the dual BCFT point of view.

Research on uncertainties in fuel centrifugal pump based on prediction and reconstruction of internal flow field

Geometric machining errors in the blade profile and variable operating conditions in the extreme operating environment are primary factors leading to the uncertainties in pump performance. This paper presents an analysis of uncertainties of fuel centrifugal pumps by modeling the geometry uncertainty in blade machining based on the Karhunen–Loève (KL) expansion and using a polynomial chaos expansion (PCE) model. First, the geometric uncertainty in the blade machining is described by the KL expansion in three sections and a stochastic simulation of the blade geometry is performed. Then, a PCE surrogate model is trained based on the least angle regression method and validated by the bootstrap method to quantify the uncertainties of performance indices. Finally, the influence mechanism and relative importance of each input uncertainty parameter are investigated using a quasi-Monte Carlo simulation method. The results show that the KL expansion of the blade profile uses the random vector perturbation superposition of three stream surface, achieving the dimensional reduction in the blade machining error. The PCE surrogate model, trained with a dataset of 3 × 106 sample points, exhibits excellent fit, and the R-squared and adjusted R-squared for head coefficient and efficiency are both above 80%. The variance of parameter control points of the reconstructed flow field is less than 0.002. The uncertainties in both operating conditions and parameters have an influence on the distribution of the global flow field, while the influence of the uncertainty in machining error on the global flow field mainly concentrates on the power-generating positions of the blade.

General perturbations in D+1 standard and brane cosmology revisited

In this work, we generalize the theory of perturbations in a ([Formula: see text])-dimensional space–time with cosmological constant, studying scalar, vector and tensor perturbations, as well as its structure in Newtonian and Synchronous gauge. We also show the theory of perturbations in the context of brane cosmology, where branes are embedded in a set of D-spatial dimensions, a temporal dimension, and an additional spatial dimension. In both standard and brane cosmology, an unperturbed space–time is provided with a Friedmann–Lemaitre–Robertson–Walker metric and arbitrary sectional curvature, the matter content has the shape of a perfect fluid. In addition, we consider the arbitrary sectional curvature, obtaining the respective equations in the Newtonian and Synchronous gauge. We highlight that the results presented in this paper can be used to treat brane cosmology with two concentric branes or tackle the [Formula: see text] tension with a braneworld approach. Finally, as an example of the utility of all the technology presented in this paper, we show an application to the energy flux and the repercussions in the framework of the braneworlds.

Matrix model correlators from non-Abelian T-dual of AdS5 × S5

We study various perturbations and their holographic interpretation for non-Abelian T-dual of AdS5 × S5 where the T-duality is applied along the SU(2) of AdS5. This paper focuses on two types of perturbations, namely the scalar and the vector fields on NATD of AdS5 × S5. For scalar perturbations, the corresponding solutions could be categorised into two classes. For one of these classes of solutions, we build up the associated holographic dictionary where the asymptotic radial mode sources scalar operators for the (0 + 1)d matrix model. These scalar operators correspond to either a marginal or an irrelevant deformation of the dual matrix model at strong coupling. We calculate the two point correlation between these scalar operators and explore their high as well as low frequency behaviour. We also discuss the completion of these geometries by setting an upper cut-off along the holographic axis and discuss the corresponding corrections to the scalar correlators in the dual matrix model. Finally, we extend our results for vector perturbations where we obtain asymptotic solutions for a particular class of modes. These are further used to calculate the boundary charge density at finite chemical potential.

Synthesis of a measurement procedure for estimating the orientation of a small unmanned aerial vehicle under conditions of changing status of measurement results

The problem of processing measurement information with changing status of measurement results of micromechanical sensors of an intelligent on-board measuring system of a small unmanned aerial vehicle is considered. While vehicle is in the air, the measurement results status changes from confirmed to orienting, for example, due to sensor defects, degradation of the measuring channel, the appearance of false measurement output signals of micromechanical sensors due to vibrations and shocks caused by the movement of air masses. As a result, the probability of stability loss of a small unmanned aerial vehicle increases and it is necessary to raise the accuracy of estimating its orientation in conditions of changing status of measurement results. The measuring procedure of the Kalman structure is considered, the equations of which are determined with accuracy to the parameters of the transition and noise matrices of the state, as well as the perturbation vector, characterizing the measuring process. The parameter values are determined by a mathematical model for converting measuring information based on a dynamic mathematical model, which distinguishes the developed measuring procedure from a measuring procedure with a classical transition matrix. A neural network is used to find unknown parameters. A multilayer perceptron was selected as the basis of a neural network, for which an error back propagation algorithm is used to train. Based on the results of mathematical modeling and measurement experiment, it was found that the accuracy of the synthesized measuring procedure based on a dynamic mathematical model is higher than the accuracy of the measuring procedure of the Kalman structure with a classical transition matrix. The results of the study will be useful in the development of intelligent measurement procedures for on-board measurement systems operating under conditions of changing status of measurement results

Sphaleron damping and effects on normal and anomalous charge transport in high-temperature QCD plasmas

We modify the hydrodynamic equations of a relativistic chiral plasma to account for dissipative effects due to QCD sphaleron transitions. By analyzing the linearized hydrodynamic equations, we show that sphaleron transitions lead to nontrivial effects on vector and axial charge transport phenomena in the presence of a magnetic field. Notably, dissipative effects of sphaleron transitions lead to the emergence of a wavenumber threshold that characterizes the onset of Chiral Magnetic Waves. Sphaleron damping also significantly impacts the time evolution of both vector and axial charge perturbations in the presence of a magnetic field. We further investigate the dependence of charge separation on the rate of sphaleron transitions, which may have implications for the experimental search for the Chiral Magnetic Effect in heavy ion collisions.

An adaptive differential evolution with opposition-learning based diversity enhancement

Differential Evolution (DE), as a powerful population-based stochastic optimization algorithm, has attracted the attention of researchers from various fields due to its advantages such as simple operation, strong robustness, and few control parameters. However, many existing DE variants often suffer from drawbacks such as premature convergence and stagnation when solving complicated optimization problems. In view of the aforementioned issues, this paper proposes an adaptive DE with opposition learning-based diversity enhancement (OLBADE). The main contributions can be summarized as follows: Firstly, a new adaptive parameter control is proposed with a non-linear weighting strategy incorporating into the framework of parameter adaptation. Secondly, a donor vector perturbation strategy is introduced to complement existing strategy for increasing population diversity. Thirdly, a novel stagnation indicator is proposed, and then opposition learning strategy is employed to renew stagnated individuals in the population when stagnation occurs. OLBADE is compared with five excellent DE variants under a large test-bed containing CEC2013, CEC2014, CEC2017 and CEC2022 test suites to verify its effectiveness. In addition, OLBADE is applied in parameter identification problem of photovoltaic model to verify its feasibility. Experimental results demonstrate that OLBADE achieves higher solution accuracy, faster convergence speed and better stability.

A braneworld model in a massive gravity

A Randall–Sundrum-like braneworld scenario is constructed in a 5D extension of the Lorentz-violating massive gravity. The gauge hierarchy problem is solved in current model. The linear perturbations are calculated, and it is found that the tensor and vector perturbations are robust and free from the ghost and tachyonic instabilities, however, the scalar perturbation is a ghost filed. After Kaluza–Klein reduction, all the tensor, vector and scalar modes are massive and possess the mass splitting of order of TeV in their respective mass spectra. The massive ground states of tensor and scalar modes propagate only along the brane, however, the vector ground state is absent in the mass spectrum. By introducing the Goldberger-Wise mechanism to stabilize the extra dimension, the 4D effective theory on the brane includes a nearly massless graviton plus three towers of very massive spin-2, spin-1 and ghost spin-0 particles.

Complex dynamics of the passive biped robot with flat feet: Gait bifurcation, intermittency and crisis

During the past decades, the walking dynamics of different types of passive biped robots have garnered significant attention. This paper investigates the complex dynamics of a passive flat-footed robot, encompassing both the local bifurcation of limit cycles and global bifurcation, resulting in significant changes in the system’s walking pattern. To identify the robot’s dynamic behavior, the Lyapunov Exponents (LEs) are calculated using the small orthogonal perturbation vectors method. The obtained LEs diagram also unveils several subtle periodic windows scattered within the chaotic region, where interior crisis and intermittency occur. Moreover, two new kinds of gaits that coexist with the traditional period-1 ones are found. Of particular significance is the discovery of the double boundary crisis that caused by the critical period-3 unstable periodic orbit, and this crisis serves as the fundamental reason to the falling down on slopes of the flat-footed robots. By gaining a better understanding of the nature of passive dynamic walking, it becomes possible to design more efficient controllers that impose less stringent torque requirements on biped walking robots.

Cosmological perturbations in the teleparallel analog of Horndeski gravity

In this work we study the cosmological perturbations in Bahamonde-Dialektopoulos-Levi Said (BDLS) theory, i.e. the teleparallel analog of Horndeski gravity. In order to understand the evolution of structure in a cosmological model, it is necessary to study its cosmology not only in the background but also perturbatively. Both Horndeski and its teleparallel analog have been analyzed a lot in the literature, but in order to study them quantitatively, we need to know their cosmological perturbations. That is why, we study here the scalar-vector-tensor decomposition of the theory and we also express the so-called alpha parameters in terms of the arbitrary functions of the theory, that designate the deviation from the ΛCDM model. We have explored tensor, vector and scalar perturbation of the action up to second order, which drastically opens up new possibilities on searches in the parameter space of scalar-tensor theories in the context of observations.

Evolution of perturbations in a universe with exotic solid-like matter

We study cosmological perturbations in a universe with only one matter component described by a triplet of fields. Configuration of these fields is the same as for body coordinates of a solid, and they enter the matter Lagrangian only through the kinetic term. We restrict ourselves only to cases with constant pressure to energy density ratio w. Superhorizon perturbations have no constant modes with scalar vector and tensor perturbations decaying or growing at different rates, and in cases with pressure to energy density ratio w>(19−87)/3=̇−0.722 perturbations propagate with superluminal sound speed. Regarding our universe, these results illustrate possible challenges with comparing the observational data to models similar to solid inflation, if the inflation is followed by a period during which the studied model is a sufficiently good approximation.

Decomposition of Acoustic and Entropy Modes in a Non-Isothermal Gas Affected by a Mass Force

Diagnostics and decomposition of atmospheric disturbances in a planar flow are considered in this work. The study examines a situation in which the stationary equilibrium temperature of a gas may depend on the vertical coordinate due to external forces. The relations connecting perturbations are analytically established. These perturbations specify acoustic and entropy modes in an arbitrary stratified gas affected by a constant mass force. The diagnostic relations link acoustic and entropy modes, and are independent of time. Hence, they provide an ability to decompose the total vector of perturbations into acoustic and non-acoustic (entropy) parts, and to establish the distribution of energy between the sound and entropy modes, uniquely at any instant. The total energy of a flow is hence determined in its parts which are connected with acoustic and entropy modes. The examples presented in this work consider the equilibrium temperature of a gas, which linearly depends on the vertical coordinate. Individual profiles of acoustic and entropy parts for some impulses are illustrated with plots.

Shadow and stability of quantum-corrected black holes

Recently the quantum Oppenheimer–Snyder gravitational collapse model has been proposed in loop quantum gravity, providing quantum-corrected Schwarzschild spacetimes as the exterior of the collapsing dust ball. In this paper, the quantum gravity effects on the black hole shadows in this model are studied, and the stability of the quantum-corrected black holes is also analyzed by calculating the quasinormal modes. It turns out that the quantum correction always shrinks the radius of shadows, and the quantum-corrected black holes are stable against the scalar and vector perturbations.

Uncertainty growth and forecast reliability during extratropical cyclogenesis

Abstract. In global numerical weather prediction, the strongest contribution to ensemble variance growth over the first few days is at synoptic scales. Hence it is particularly important to ensure that this synoptic-scale variance is reliable. Here we focus on wintertime synoptic-scale growth in the North Atlantic storm track. In the 12 h background forecasts of the Ensemble of Data Assimilations (EDA) from the European Centre for Medium-Range Weather Forecasts (ECMWF), we find that initial variance growth at synoptic scales tends to be organized in particular flow situations, such as during the deepening of cyclones (cyclogenesis). Both baroclinic and diabatic aspects may be involved in the overall growth rate. However, evaluation of reliability through use of an extended error–spread equation indicates that the ECMWF ensemble forecast, which is initialized from the EDA but with additional singular vector perturbations, appears to have too much variance at a lead time of 2 d and that this over-spread is associated with cyclogenesis situations. Comparison of variance growth rates and reliability with other forecast systems within The International Grand Global Ensemble (TIGGE) archive indicates some sensitivity to the model or its initialization. For the ECMWF ensemble forecast, sensitivity experiments suggest that a large part of the total day-2 spread in cyclogenesis cases is associated with the growth of EDA uncertainty, but up to 25 % can be associated with the additional singular vector perturbations to the initial conditions and up to 25 % with the representation of model uncertainty. The sensitivities of spread to resolution, the explicit representation of convection, and the assimilation of local observations are also considered. The study raises the question of whether the EDA now successfully represents initial uncertainty (and the enhanced growth rates associated with cyclogenesis) to the extent that singular vector perturbations could be reduced in magnitude to improve storm track reliability. This would leave a more seamless forecast system, allowing short-range diagnostics to better help improve the model and model-uncertainty representation, which could be beneficial throughout the forecast range.

Upper Mantle Structure Beneath the Contiguous US Resolved With Array Observations of SKS Multipathing and Slowness Vector Perturbations

AbstractContinent‐scale observations of seismic phenomena have provided multi‐scale constraints of the Earth's interior. Of those analyzed, array‐based observations of slowness vector properties (backazimuth and horizontal slowness) and multipathing have yet to be made on a continental scale. Slowness vector measurements give inferences on mantle heterogeneity properties such as velocity perturbation and velocity gradient strength and quantify their effect on the wavefield. Multipathing is a consequence of waves interacting with strong velocity gradients resulting in two arrivals with different slowness vector properties and times. The mantle structure beneath the contiguous Unites States has been thoroughly analyzed by previous seismic studies and is data‐rich, making it an excellent testing ground to both analyze mantle structure with our approach and compare with other imaging techniques. We apply an automated array‐analysis technique to an SKS data set to create the first continent‐scale data set of multipathing and slowness vector measurements. We analyze the divergence of the slowness vector deviation field to highlight seismically slow and fast regions. Our results resolve several slow mantle anomalies beneath Yellowstone, the Appalachian mountains and fast anomalies throughout the mantle. Many of the anomalies cause multipathing in frequency bands 0.15–0.30 and 0.20–0.40 Hz which suggests velocity transitions over at most 500 km exist. Comparing our observations to synthetics created from tomography models, we find model NA13 (Bedle et al., 2021, https://doi.org/10.1029/2021GC009674) fits our data best but differences still remain. We therefore suggest slowness vector measurements should be used as an additional constraint in tomographic inversions and will lead to better resolved models of the mantle.

Detecting vector charge with extreme mass ratio inspirals onto Kerr black holes

Extreme mass ratio inspirals (EMRIs) are excellent sources for space-based observatories to explore the properties of black holes and test no-hair theorems. We consider EMRIs with a charged compact object inspiralling onto a Kerr black hole in quasi-circular orbits. Using the Teukolsky and generalized Sasaki-Nakamura formalisms for the gravitational and vector perturbations about a Kerr black hole, we numerically calculate the energy fluxes for both gravitational and vector perturbations induced by a charged particle moving in equatorial circular orbits. With one-year observations of EMRIs, we apply the Fisher information matrix method to estimate the charge uncertainty detected by space-based gravitational wave detectors such as the Laser Interferometer Space Antenna, TianQin, and Taiji, and we find that it is possible to detect vector charges as small as q ∼ 0.0049. The results show that EMRIs composed of a Kerr black hole with a higher spin a and lighter mass M, and a secondary charged object with more vector charge give smaller relative error on the charge, thus constrain the charge better. The positive spin of the Kerr black hole can decrease the charge uncertainty by about one or two orders of magnitude.