State Propagation Research Articles

Second-Order State Propagation for Continuous-Thrust Relative Motion in $J_{2}$-Perturbed Elliptic Orbits

The second-order analytical state propagation under an arbitrary continuous thrust is proposed for relative motion in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$J_{2}$</tex-math></inline-formula> -perturbed elliptic chief orbits. The mean relative orbital elements are used to describe the relative motion. The second-order relative motion equations are obtained by performing the Taylor expansion of the nonlinear relative motion equations about the chief orbit. The original thrust acceleration is approximated by a truncated Fourier series in terms of eccentric anomaly of the chief orbit. Based on the first-order state propagation and the thrust acceleration Fourier-series expansion, the second-order propagation of the mean relative orbital elements is obtained. Numerical simulations show that the state propagation errors of the second-order solution are reduced by 1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> 2 orders of magnitude when compared with the first-order solution.

Characterization of elastic topological states using dynamic mode decomposition

Elastic topological states have been receiving increased attention in numerous scientific and engineering fields due to their defect-immune nature, resulting in applications of vibration control and information processing. Here, we present the data-driven discovery of elastic topological states using dynamic mode decomposition (DMD). The DMD spectrum and DMD modes are retrieved from the propagation of the relevant states along the topological boundary, where their nature is learned by DMD. Applications such as classification and synthesis of wave propagation can be achieved by the underlying characteristics from DMD. We demonstrate the classification between topological and traditional metamaterials using DMD modes. Moreover, the model enabled by the DMD modes realizes the synthesis of topological state propagation along the given interface. Our approach to characterizing topological states using DMD can pave the way towards data-driven discovery of topological phenomena in material physics and more broadly lattice systems.

Dynamics of the fractional quantum Hall edge probed by stroboscope measurements of trions

By using observations from pump-probe stroboscopic confocal microscopy and spectroscopy, we demonstrate the dynamics of trions and the fractional quantum Hall edge on the order of ∼1 ps. The propagation of the quantum Hall edge state excited by a voltage pulse is detected as a temporal change in reflectance in the downstream edge probed by optical pulses synchronized with the voltage pulse. The temporal resolution of such stroboscopic pump-probe measurements is as fast as the duration time of the probe pulse (∼1 ps). This ultra-fast stroboscope measurement enables us to distinguish between the normal mode of edge excitation, known as the edge magneto-plasmon or charge density wave, and other high-energy non-linear excitations. This is the only experimental method available to study the ultra-fast dynamics of quantum Hall edges and makes it possible to derive the metric tensor gμν of the (1+1)=2-dimensional curved spacetime in quantum universe and black hole analogs implemented in the quantum Hall edge.

Quantum propagator for a general time-dependent quadratic Hamiltonian: Application to interacting oscillators in external fields

In this paper, we find the quantum propagator for a general time-dependent quadratic Hamiltonian. The method is based on the properties of the propagator and the fact that the quantum propagator fulfills two independent partial differential equations originating from Heisenberg equations for positions and momenta. As an application of the method, we find the quantum propagator for a linear chain of interacting oscillators for both periodic and Dirichlet boundary conditions. The state and excitation propagation along the harmonic chain in the absence and presence of an external classical source is studied and discussed. The location of the first maxima of the probability amplitude P(n, τ) is a straight line in the (n, τ)-plane, indicating a constant speed of excitation propagation along the chain.

Moment-Based Model Predictive Control of Autonomous Systems

Great efforts have been devoted to the intelligent control of autonomous systems. Yet, most of existing methods fail to effectively handle the uncertainty of their environment and models. Uncertain locations of dynamic obstacles pose a major challenge for their optimal control and safety, while their linearization or simplified system models reduce their actual performance. To address them, this paper presents a new model predictive control framework with finite samples and a Gaussian model, resulting in a chance-constrained program. Its nominal model is combined with a Gaussian process. Its residual model uncertainty is learned. The resulting method addresses an efficiently solvable approximate formulation of a stochastic optimal control problem by using approximations for efficient computation. There is no perfect distribution knowledge of a dynamic obstacle's location uncertainty. Only finite samples from sensors or past data are available for moment estimation. We use the uncertainty propagation of a system's state and obstacles' locations to derive a general collision avoidance condition under tight concentration bounds on the error of the estimated moments. Thus, this condition is suitable for different obstacles, e.g., bounding box and ellipsoid obstacles. We provide proved guarantees on the satisfaction of the chance-constraints corresponding to the nominal yet unknown moments. Simulation examples of a vehicle's control are used to show that the proposed method can well realize autonomous control and obstacle avoidance of a vehicle, when it operates in an uncertain environment with moving obstacles. It outperforms the existing moment methods in both performance and computational time.

High performance lunar constellation for navigation services to Moon orbiting users

In order to assist the ever growing number of missions planned to visit the Moon, an international effort is being made to design and commission a communication and navigation lunar constellation of satellites. To this purpose, the goal of this study is to provide first a strategy to help the design of a small-sized lunar constellation, entailing different objectives and users to assist. Then, various optimised constellations are tested including the orbital users’ filtering architectures, extracting insights on the state estimation achievable and its capability to support critical GNC tasks.Given the early stage design phase in which this study is carried out, the constellation design does not entail strong and clearly defined requirements yet. For such reason, a multi-objective optimisation (MOO) has been employed, which proved to be extremely beneficial, ensuring a correct amount of versatility to provide a large set of Pareto-optimal solutions. Different objectives associated to both various services and users have been put in place, exploring a search space based on classical Keplerian elements of the constellation servicers.To compare the resulting constellations and validate correctly the performance from a navigation perspective the users navigation scheme has been considered to be based on a GNSS/INS tightly coupled formulation. The GNSS receiver measurements are fused with accelerometer outputs through a navigation filter, providing thus a strategy where the absence of GNSS observables is partially covered by an inertial propagation of the on-board state. Attention is here focused on polar orbiters operational in Low Lunar Orbit (LLO) environment and the obtained results showed navigation capabilities good enough to enable correct execution of missions in the low lunar orbital region.

Propagation of well-prepared states along Martinet singular geodesics

We prove that for the Martinet wave equation with “flat” metric, which is a subelliptic wave equation, singularities can propagate at any speed between 0 and 1 along any singular geodesic. This is in strong contrast with the usual propagation of singularities at speed 1 for wave equations with elliptic Laplacian.

Unidirectional propagation of helical edge states via exciting pseudospin d states in two-dimensional photonic crystals

Helical edge states (HESs) in two-dimensional topological spin photonic crystals can be used to realize pseudospin-locked unidirectional propagation of waves. In general, the excitation of HESs is by taking light sources carrying orbital angular momentum of order 1 to stimulate the pseudospin p states in spin photonic crystals. In this paper, we think of the HESs as combinations of the pseudospin p states and the pseudospin d states, which corresponding to the pseudospin modes carrying orbital angular momentum of order 1 and the pseudospin modes carrying orbital angular momentum of order 2, respectively, with their chirality related to the unidirectional propagations of the HESs. By analyzing the field distributions of HESs and via exciting the pseudospin d states with light sources carrying orbital angular momentum of order 2, we demonstrate the unidirectional propagation of the HESs in spin photonic crystals and verify their robustness by checking the unidirectional performance as they propagate along a Z-shape interface containing sharp corners, cavity defect, and disorders. Our study deepens understanding of the nature of HESs and expands methods to excitation and regulation of HESs in topological spin photonics.

Uncertainty-Aware Variational Inference for Target Tracking

In the low Earth orbit, target tracking with ground based assets in the context of situational awareness is particularly difficult. Because of the nonlinear state propagation between the moments of measurement arrivals, the inevitably accumulated errors will make the target state prediction and the measurement likelihood inaccurate and uncertain. In this article, optimizable models with learned parameters are constructed to model the state and measurement prediction uncertainties. A closed-loop variational iterative framework is proposed to jointly achieve parameter inference and state estimation, which comprises an uncertainty-aware variational filter (UnAVF). The theoretical expression of the evidence lower bound and the maximization of the variational lower bound are derived without the need for the true states, which reflect the awareness and reduction of uncertainties. The evidence lower bound can also evaluate the estimation performance of other Gaussian density filters, not only the UnAVF. Moreover, two rules, estimation consistency and lower bound consistency, are proposed to conduct the initialization of hyperparameters. Finally, the superior performance of UnAVF is demonstrated over an orbit state estimation problem.

Optimizing the propagation of mesoscopic twin-beam states for novel quantum communication protocols

Nowadays, optical Quantum Communication has reached a mature level, especially in free space and through optical fibers. Experimental implementations usually involve single-photon states or weak coherent states detected by single-photon detectors. In contrast to these standard configurations, in our work we consider mesoscopic twin-beam (TWB) states revealed by photon-number-resolving detectors. By properly acting on the natural divergence of the generated beams, we show that they remain nonclassical even at a moderate distance from the nonlinear crystal in which they are produced. We also consider the case where one of the two parties of TWB is partially transmitted through water, and show that the nonclassicality of the states is preserved. This result suggests that mesoscopic TWB states can be considered for the new and growing scenario of underwater Quantum Communication.

Error State Extended Kalman Filter Localization for Underground Mining Environments

The article addresses the issue of mobile robotic platform positioning in GNSS-denied environments in real-time. The proposed system relies on fusing data from an Inertial Measurement Unit (IMU), magnetometer, and encoders. To get symmetrical error gauss distribution for the measurement model and achieve better performance, the Error-state Extended Kalman Filter (ES EKF) is chosen. There are two stages of vector state determination: vector state propagation based on accelerometer and gyroscope data and correction by measurements from additional sensors. The error state vector is composed of the velocities along the x and y axes generated by combining encoder data and the orientation of the magnetometer around the axis z. The orientation angle is obtained from the magnetometer directly. The key feature of the algorithm is the IMU measurements’ isolation from additional sensor data, with its further summation in the correction step. Validation is performed by a simulation in the ROS (Robot Operating System) and the Gazebo environment on the grounds of the developed mathematical model. Trajectories for the ES EKF, Extended Kalman Filter (EKF), and Unscented Kalman Filter (UKF) algorithms are obtained. Absolute position errors for all trajectories are calculated with an EVO package. It is shown that using the simplified version of IMU’s error equations allows for the achievement of comparable position errors for the proposed algorithm, EKF and UKF.

Floquet generation of a magnonic NOON state

We propose a concise and deterministic protocol to generate NOON states in a hybrid system consisting of a superconducting qubit, a circuit resonator mode, and two magnonic modes, based on Floquet engineering. In particular, we construct a time-reversal-symmetry broken Hamiltonian for chiral state propagation of the three continuous-variable modes depending on qubit state, by the time modulation over qubit-resonator interaction and magnon frequency. Then an arbitrary magnonic NOON state can be generated by a typical preparing-and-measurement procedure. We analyze the robustness of our protocol against the systematic errors in the qubit-magnon coupling strength, the Floquet-driving intensity, the frequency mismatch of the magnons, and the counter-rotating interactions. We can obtain a high-fidelity NOON state in the presence of the quantum dissipation on all components.

Quasiperiodic photonic crystal fiber [Invited

In the fields of light manipulation and localization, quasiperiodic photonic crystals, or photonic quasicrystals (PQs), are causing an upsurge in research because of their rotational symmetry and long-range orientation of transverse lattice arrays, as they lack translational symmetry. It allows for the optimization of well-established light propagation properties and has introduced new guiding features. Therefore, as a class, quasiperiodic photonic crystal fibers, or photonic quasicrystal fibers (PQFs), are considered to add flexibility and richness to the optical properties of fibers and are expected to offer significant potential applications to optical fiber fields. In this review, the fundamental concept, working mechanisms, and invention history of PQFs are explained. Recent progress in optical property improvement and its novel applications in fields such as dispersion control, polarization-maintenance, supercontinuum generation, orbital angular momentum transmission, plasmon-based sensors and filters, and high nonlinearity and topological mode transmission, are then reviewed in detail. Bandgap-type air-guiding PQFs supporting low attenuation propagation and regulation of photonic density states of quasiperiodic cladding and in which light guidance is achieved by coherent Bragg scattering are also summarized. Finally, current challenges encountered in the guiding mechanisms and practical preparation techniques, as well as the prospects and research trends of PQFs, are also presented.

Optimal Multi-impulse Linear Rendezvous via Reinforcement Learning

A reinforcement learning-based approach is proposed to design the multi-impulse rendezvous trajectories in linear relative motions. For the relative motion in elliptical orbits, the relative state propagation is obtained directly from the state transition matrix. This rendezvous problem is constructed as a Markov decision process that reflects the fuel consumption, the transfer time, the relative state, and the dynamical model. An actor–critic algorithm is used to train policy for generating rendezvous maneuvers. The results of the numerical optimization (e.g., differential evolution) are adopted as the expert data set to accelerate the training process. By deploying a policy network, the multi-impulse rendezvous trajectories can be obtained on board. Moreover, the proposed approach is also applied to generate a feasible solution for many impulses (e.g., 20 impulses), which can be used as an initial value for further optimization. The numerical examples with random initial states show that the proposed method is much faster and has slightly worse performance indexes when compared with the evolutionary algorithm.

Mapping the photochemistry of cyclopentadiene: from theory to ultrafast X-ray scattering.

The photoinduced ring-conversion reaction when cyclopentadiene (CP) is excited at 5.10 eV is simulated using surface-hopping semiclassical trajectories with XMS(3)-CASPT2(4,4)/cc-pVDZ electronic structure theory. In addition, PBE0/def2-SV(P) is employed for ground state propagation of the trajectories. The dynamics is propagated for 10 ps, mapping both the nonadiabatic short-time dynamics (<300 fs) and the increasingly statistical dynamics on the electronic ground state. The short-time dynamics yields a mixture of hot CP and bicyclo[2.1.0]pentene (BP), with the two products reached via different regions of the same conical intersection seam. On the ground state, we observe slow conversion from BP to CP which is modelled by RRKM theory with a transition state determined using PBE0/def2-TZVP. The CP products are furthermore associated with ground state hydrogen shifts and some H-atom dissociation. Finally, the prospects for detailed experimental mapping using novel ultrafast X-ray scattering experiments are discussed and observables for such experiments are predicted. In particular, we assess the possibility of retrieving electronic states and their populations alongside the structural dynamics.

3D Interconnected Magnetic Nanowire Networks as Potential Integrated Multistate Memristors.

Interconnected magnetic nanowire (NW) networks offer a promising platform for three-dimensional (3D) information storage and integrated neuromorphic computing. Here we report discrete propagation of magnetic states in interconnected Co nanowire networks driven by magnetic field and current, manifested in distinct magnetoresistance (MR) features. In these networks, when only a few interconnected NWs were measured, multiple MR kinks and local minima were observed, including a significant minimum at a positive field during the descending field sweep. Micromagnetic simulations showed that this unusual feature was due to domain wall (DW) pinning at the NW intersections, which was confirmed by off-axis electron holography imaging. In a complex network with many intersections, sequential switching of nanowire sections separated by interconnects was observed, along with stochastic characteristics. The pinning/depinning of the DWs can be further controlled by the driving current density. These results illustrate the promise of such interconnected networks as integrated multistate memristors.

Reservoir computing with nonlinear optical media

Reservoir computing is a versatile approach for implementing physically Recurrent Neural networks which take advantage of a reservoir, consisting of a set of interconnected neurons with temporal dynamics, whose weights and biases are fixed and do not need to be optimized. Instead, the training takes place only at the output layer towards a specific task. One important requirement for these systems to work is nonlinearity, which in optical setups is usually obtained via the saturation of the detection device. In this work, we explore a distinct approach using a photorefractive crystal as the source of the nonlinearity in the reservoir. Furthermore, by leveraging on the time response of the photorefractive media, one can also have the temporal interaction required for such architecture. If we space out in time the propagation of different states, the temporal interaction is lost, and the system can work as an extreme learning machine. This corresponds to a physical implementation of a Feed-Forward Neural Network with a single hidden layer and fixed random weights and biases. Some preliminary results are presented and discussed.

Quasi-steady state propagation in the davydov-type model with linear on-site interactions

The problem of electron transportation along a discrete deformable medium with linear on-site interactions in the Davydov approach is considered. It is found that the quasi-stationary state of the full equations of motion leads to a discrete nonlocal nonlinear Schrödinger (DNNLS) equation whose nonlocality is of the exponential type and depending on the on-site parameter. We use the variational approach to approximate discrete traveling wave solutions in the DNNLS equation. We find that the discrete solutions continued from the discrete nonlinear Schrödinger equation, corresponding to the vanishing of the on-site parameter, bifurcates in a critical on-site value. Additionally, a threshold in the velocity of propagation of the discrete structures is found.

Excited-state response theory within the context of the coupled-cluster formalism

Time-dependent response theories are foundational to the development of algorithms that determine quantum properties of electronic excited states of molecules and periodic systems. They are employed in wave-function, density-functional, and semiempirical methods, and are applied in an incremental order: linear, quadratic, cubic, etc. Linear response theory is known to produce electronic transitions from ground to excited state, and vice versa. In this work, a linear-response approach, within the context of the coupled cluster formalism, is developed to offer transition elements between different excited states (including permanent elements), and related properties. Our formalism, second linear response theory, is consistent with quadratic response theory, and can serve as an alternative to develop and study excited-state theoretical methods, including pathways for algorithmic acceleration. This work also formulates an extension of our theory for general propagations under non-linear external perturbations, where the observables are given by linked expressions which can predict their time-evolution under arbitrary initial states and could serve as a means of constructing general state propagators. A connection with the physics of wavefunction theory is developed as well, in which dynamical cluster operator amplitudes are related to wavefunction linear superposition coefficients.

A Stochastic Dynamic Traffic Assignment Model for Emergency Evacuations That Considers Background Traffic

In this work, we present a stochastic dynamic traffic assignment model for emergency evacuations that considers background traffic. First, the equilibrium functions of the entry time and path choice are formulated based on the logit model. The constraints of this formulation include the state equation, propagation function, and conservation. The proposed equilibrium functions are formulated as a variational inequality problem, which is solved by the dynamic traffic network demand loading iterative method. Based on a case study in Wenling, China, we verify the proposed model on the basis of iterative evolution, path assignment, and model comparison. In addition, we perform sensitivity analysis of four relevant parameters, namely, the length of the time interval, total number of evacuation vehicles, perception error parameters of the total travel cost, and path travel cost. The results make it evident that the proposed model assists evacuation planners to effectively understand real-time dynamic changes of evacuation vehicles and the influence of background vehicles and to generate optimal emergency plans.