Coordinate Space Research Articles

Nonminimal non-Abelian quantum vector fields in curved spacetime

The quantum effective action of non-minimal vector fields with Abelian or non-Abelian gauge degrees of freedom in curved spacetime is studied. The Proca or Yang-Mills fields are coupled to a local mass-like term acting in both coordinate and gauge spaces. Pathologies due to gauge invariance in the ultraviolet are avoided through the introduction of a non-Abelian version of the Stueckelberg field. It is found that the breaking of gauge invariance induced by the mass term affects only the tree level part of the effective action. The ultraviolet divergent part of the effective action to one loop is obtained using the method of covariant symbols and dimensional regularization. Formulas are given valid for any spacetime dimension and explicit results are shown for the two-dimensional case. As already happened for a single vector field, the ultraviolet divergences are local but not of polynomial type.

Analysis of the current induced by the motion of a magnet pendulum with a large initial angle

In this study, formulae for the waveform of an induced current, generated when a magnet traverses along a rectangular coil with a narrow width were theoretically obtained considering the relative motion of the magnet and coil. Consequently, an experiment was performed under experimental conditions that matched the formulas, and the results obtained were compared with the theoretical predictions. The dependence of on the initial angle of the magnet pendulum and the width of the rectangular coil was found to be consistent with the theoretical prediction. Thus, the formulae obtained in this study are expected to be useful in addressing temporal variations in the waveform of the induced current produced by a magnet moving in a polar coordinate space.

Geometrical digital twins of masonry structures for documentation and structural assessment using machine learning

The generation of numerical models for masonry structures is a timely and costly procedure since it requires the discretization of a large quantity of smaller particles. Similarly, traditional visual inspection involves the cautious consideration of each element on a masonry construction. In both cases, each brick element needs to be considered individually. The work presented in this document aims to alleviate the issues arising from documenting individual masonry units and cracks on a structure using computer vision and convolutional neural networks (CNN). In particular, for the first time a dynamic workflow has been developed in which masonry units and cracks in masonry structures are automatically detected and used for the development of a complete geometric digital twin. The outcome is a collection of space coordinates and geometrical objects that represent the masonry fabric entity and allow the comprehension of the object for documentation and structural assessment. This interoperability between architectural, structural, and structural analysis models paves the way to use engineering to create a smarter, safer, and more sustainable future for our existing infrastructures.

Calculations of the np→dγ reaction in chiral effective field theory

We present a calculation of the radiative capture cross section $p(n,\gamma )d$ in the low-energy range, where the $M1$ reaction channel dominates. Employing the LENPIC nucleon-nucleon interaction up to the fifth order (N4LO) that is regularized by the semi-local coordinate space regulators, we obtain the initial and final state wave functions, and evaluate the phase shifts of the scattering state and deuteron properties. We derive the transition operator from the chiral effective field theory up to the next-to-next-to leading order (N2LO), where we also regularize the transition operator using regulators consistent with those of the interactions. We compute the capture cross sections and the results show a converging pattern with the chiral-order expansion of the nucleon-nucleon interaction, where the regulator dependence of the results is weak when higher-order nucleon-nucleon interactions are employed. We quantify the uncertainties of the cross-section results due to the chiral-order truncation. The chirally complete and consistent cross-section results are performed up to N2LO and they compare well with the experiments and other theoretical predictions.

Open quantum dynamics of strongly coupled oscillators with multi-configuration time-dependent Hartree propagation and Markovian quantum jumps.

Modeling the non-equilibrium dissipative dynamics of strongly interacting quantized degrees of freedom is a fundamental problem in several branches of physics and chemistry. We implement a quantum state trajectory scheme for solving Lindblad quantum master equations that describe coherent and dissipative processes for a set of strongly coupled quantized oscillators. The scheme involves a sequence of stochastic quantum jumps with transition probabilities determined by the system state and the system-reservoir dynamics. Between consecutive jumps, the wave function is propagated in a coordinate space using the multi-configuration time-dependent Hartree method. We compare this hybrid propagation methodology with exact Liouville space solutions for physical systems of interest in cavity quantum electrodynamics, demonstrating accurate results for experimentally relevant observables using a tractable number of quantum trajectories. We show the potential for solving the dissipative dynamics of finite size arrays of strongly interacting quantized oscillators with high excitation densities, a scenario that is challenging for conventional density matrix propagators due to the large dimensionality of the underlying Hilbert space.

Color Recurrence Plots for Bearing Fault Diagnosis.

This paper presents bearing fault diagnosis using the image classification of different fault patterns. Feature extraction for image classification is carried out using a novel approach of Color recurrence plots, which is presented for the first time. Color recurrence plots are created using non-linear embedding of the vibration signals into delay coordinate space with variable time lags. Deep learning-based image classification is then performed by building the database of the extracted features of the bearing vibration signals in the form of Color recurrence plots. A Series of computational experiments are performed to compare the accuracy of bearing fault classification using Color recurrence plots. The standard bearing vibration dataset of Case Western Reserve University is used for those purposes. The paper demonstrates the efficacy and the accuracy of a new and unique approach of scalar time series extraction into two-dimensional Color recurrence plots for bearing fault diagnosis.

Model reduction of convection-dominated partial differential equations via optimization-based implicit feature tracking

This work introduces a new approach to reduce the computational cost of solving partial differential equations (PDEs) with convection-dominated solutions: model reduction with implicit feature tracking. Traditional model reduction techniques use an affine subspace to reduce the dimensionality of the solution manifold and, as a result, yield limited reduction and require extensive training due to the slowly decaying Kolmogorov n-width of convection-dominated problems. The proposed approach circumvents the slowly decaying n-width limitation by using a nonlinear approximation manifold systematically defined by composing a low-dimensional affine space with a space of bijections of the underlying domain. Central to the implicit feature tracking approach is a residual minimization problem over the reduced nonlinear manifold that simultaneously determines the reduced coordinates in the affine space and the domain mapping that minimize the residual of the unreduced PDE discretization. This is analogous to standard minimum-residual reduced-order models, except instead of only minimizing the residual over the affine subspace of PDE states, our method enriches the optimization space to also include admissible domain mappings. The nonlinear trial manifold is constructed by using the proposed residual minimization formulation to determine domain mappings that cause parametrized features to align in a reference domain for a set of training parameters. Because the feature is stationary in the reference domain, i.e., the convective nature of solution removed, the snapshots are effectively compressed to define an affine subspace. The space of domain mappings, originally constructed using high-order finite elements, is also compressed in a way that ensures the boundaries of the original domain are maintained. Several numerical experiments are provided, including transonic and supersonic, inviscid, compressible flows, to demonstrate the potential of the method to yield accurate approximations to convection-dominated problems with limited training.

Localization in Two-Dimensional Quasicrystalline Lattices.

We investigate the emergence of localization in a weakly interacting Bose gas confined in quasicrystalline lattices with three different rotational symmetries: five, eight, and twelve. The analysis, performed at a mean field level and from which localization is detected, relies on the study of two observables: the inverse participation ratio (IPR) and the Shannon entropy in the coordinate space. Those physical quantities were determined from a robust statistical study for the stationary density profiles of the interacting condensate. Localization was identified for each lattice type as a function of the potential depth. Our analysis revealed a range of the potential depths for which the condensate density becomes localized, from partially at random lattice sites to fully in a single site. We found that localization in the case of five-fold rotational symmetry appears for (6ER,9ER), while it occurs in the interval (12ER,15ER) for octagonal and dodecagonal symmetries.

A Novel Localization System in SAR-Demining Applications Using Invariant Radar Channel Fingerprints.

In this paper, we present a novel two dimensional (2D) frequency-modulated continuous-wave (FMCW) localization method for handheld systems based on the extraction of distinguishable subchannel fingerprints. Compared with other concepts, only one subdivided radar source channel is needed in order to instantly map a one-dimensional measurement to higher-dimensional space coordinates. The additional information of the detected target is implemented with low-cost hardware component features, which exhibit distinguishable space-dependent fingerprint codes. Using the given a priori information of the hardware thus leads to a universally applicable extension for low-cost synthetic aperture radar (SAR)-demining purposes. In addition to the description of the system concept and its requirements, the signal processing steps and the hardware components are presented. Furthermore, the 2D localization accuracy of the system and the classification accuracy of the frequency-coded fingerprints are described in a defined test environment to proof the operational reliability of the realized setup, reaching a classification accuracy of 94.7% and an averaged localization error of 4.9 mm.

Special Relativity in Six Dimensions

In the four-dimensional spacetime theory of special relativity, the space coordinate is time contracted along the motion, while perpendicular coordinates are invariant and time varies with position. This leads to a velocity transformation valid at speed of light and used in showing invariance electric and magnetic fields which are invariant along x-axis but change occur along y, and z-axes, contrary to the classical electrodynamics. In this work we introduce a new six-dimensional spacetime theory which allows time (position) change of position (time) in three coordinate axes and still satisfy the Lorentz invariance conditions of metric and Maxwell’s wave equations between two frames. We derive a new velocity transformation rule which is valid at any relative speed of massive frames moving with respect to each other. We derived expressions for relativistic mass, energy, Doppler shift, time dilation, length contraction, photon rest mass, and used the conservation of relativistic power to prove that the electric and magnetic fields and consequently, Maxwell wave equations are Lorentz invariant between two massive frames with and without nonzero photon mass in vacuum and materials medium. Calculated photon mass is in excellent agreement with the measured and observed upper bounds of 1.24x10-54 kg and1.75x 10-53 kg, respectively.

Unified theory of spin and charge in a ferromagnet

We derive a unified theory of spin and charge degrees of freedom in a ferromagnet. The spin-transfer torque and spin electromotive force are examined from the coarse-grained perspective of collective coordinates. The resulting equations of motion reflect a balance of conservative, gyroscopic (Berry-phase), and dissipative forces. We then expand the space of collective coordinates by adding the electric charge. The adiabatic spin-transfer torque and spin electromotive force (emf) turn out to be a gyroscopic force; their nonadiabatic counterparts are a dissipative force.

Physically motivated ansatz for the Kerr spacetime

Despite some 60 years of work on the subject of the Kerr rotating black hole there is as yet no widely accepted physically based and pedagogically viable ansatz suitable for deriving the Kerr solution without significant computational effort. (Typically involving computer-aided symbolic algebra.) Perhaps the closest one gets in this regard is the Newman–Janis trick; a trick which requires several physically unmotivated choices in order to work. Herein we shall try to make some progress on this issue by using a non-ortho-normal tetrad based on oblate spheroidal coordinates to absorb as much of the messy angular dependence as possible, leaving one to deal with a relatively simple angle-independent tetrad-component metric. That is, we shall write seeking to keep both the tetrad-component metric g AB and the non-ortho-normal co-tetrad relatively simple but non-trivial. We shall see that it is possible to put all the mass dependence into g AB , while the non-ortho-normal co-tetrad can be chosen to be a mass-independent representation of flat Minkowski space in oblate spheroidal coordinates: . This procedure separates out, to the greatest extent possible, the mass dependence from the rotational dependence, and makes the Kerr solution perhaps a little less mysterious.

An Uncertainty Weighted Non-Cooperative Target Pose Estimation Algorithm, Based on Intersecting Vectors

Aiming at the relative pose estimation of non-cooperative targets in space traffic management tasks, a two-step pose estimation method, based on spatially intersecting straight lines, is proposed, which mainly includes three aspects: (1) Use binocular vision to reconstruct the straight space line, and based on the direction vector of the straight line and the intersection of the straight line, solve the pose of the measured target in the measurement coordinate system, and obtain the initial value of the pose estimation. (2) Analyze the uncertainty of the spatial straight-line imaging, construct the uncertainty description matrix of the line, and filter the line features, accordingly. (3) Analyze the problems existing in the current linear distance measurement, construct the spatial linear back-projection error in the parametric coordinate space, and use the linear imaging uncertainty to weigh the projection error term to establish the optimization objective function of the pose estimation. Finally, the nonlinear optimization algorithm is used to iteratively solve the above optimization problem, to obtain high-precision pose estimation results. The experimental results show that the two-step pose estimation algorithm, proposed in this paper, can effectively achieve a high-precision and robust pose estimation for non-cooperative spatial targets. When the measurement distance is 10 m, the position accuracy can reach 10 mm, and the attitude measurement accuracy can reach 1°, which meets the pose estimation accuracy requirements of space traffic management.

Ground motion around a semi-cylindrical canyon in saturated soil: P wave incidence

Based on Biot wave theory in saturated two-phase medium, the analytical solution of plane P-wave scattering by semi-circular canyon in half space in saturated two-phase medium is given by using complex function method and Hankel function integral transformation method. Firstly, a semi-circular depression model in saturated half space is constructed, the wave field potential function in the medium is solved, and its general solution form is obtained. Secondly, the unknown coefficient value in the potential function is obtained by substituting the corresponding stress boundary conditions. With the help of Hankel function integral transformation method, the wave potential function in complex coordinates is transformed to meet the horizontal boundary conditions of half space in rectangular coordinates. Finally, the surface displacement amplitude at the semi-circular depression and the surrounding horizontal boundary is obtained through the total wave field potential function, and the variation law of surface displacement amplitude under the influence of different parameters is analyzed.

Predictive value of magnetoencephalography in guiding the intracranial implant strategy for intractable epilepsy.

Magnetoencephalography (MEG) is a useful component of the presurgical evaluation of patients with epilepsy. Due to its high spatiotemporal resolution, MEG often provides additional information to the clinician when forming hypotheses about the epileptogenic zone (EZ). Because of the increasing utilization of stereo-electroencephalography (sEEG), MEG clusters are used to guide sEEG electrode targeting with increasing frequency. However, there are no predefined features of an MEG cluster that predict ictal activity. This study aims to determine which MEG cluster characteristics are predictive of the EZ. The authors retrospectively analyzed all patients who had an MEG study (2017-2021) and underwent subsequent sEEG evaluation. MEG dipoles and sEEG electrodes were reconstructed in the same coordinate space to calculate overlap among individual contacts on electrodes and MEG clusters. MEG cluster features-including number of dipoles, proximity, angle, density, magnitude, confidence parameters, and brain region-were used to predict ictal activity in sEEG. Logistic regression was used to identify important cluster features and to train a binary classifier to predict ictal activity. Across 40 included patients, 196 electrodes (42.2%) sampled MEG clusters. Electrodes that sampled MEG clusters had higher rates of ictal and interictal activity than those that did not sample MEG clusters (ictal 68.4% vs 39.8%, p < 0.001; interictal 71.9% vs 44.6%, p < 0.001). Logistic regression revealed that the number of dipoles (odds ratio [OR] 1.09, 95% confidence interval [CI] 1.04-1.14, t = 3.43) and confidence volume (OR 0.02, 95% CI 0.00-0.86, t = -2.032) were predictive of ictal activity. This model was predictive of ictal activity with 77.3% accuracy (sensitivity = 80%, specificity = 74%, C-statistic = 0.81). Using only the number of dipoles had a predictive accuracy of 75%, whereas a threshold between 14 and 17 dipoles in a cluster detected ictal activity with 75.9%-85.2% sensitivity. MEG clusters with approximately 14 or more dipoles are strong predictors of ictal activity and may be useful in the preoperative planning of sEEG implantation.

A Time-Optimal Trajectory Planning Strategy for an Aircraft With a Suspended Payload via Optimization and Learning Approaches

In this article, a real-time interactive time-optimal trajectory planning (TOTP) strategy is proposed for aircraft slung-load systems, in which the practical performance is guaranteed by taking advantage of convex optimization and reinforcement learning (RL) techniques. To the best of our knowledge, it is the first TOTP solution for an aircraft suspension system subject to path, velocity, acceleration, and cable tension constraints, where a practice-oriented RL policy is designed to interact with the system online. Specifically, by exploring the differential flatness property of the system, the states are projected into path coordinate space, where all the physical constraints are formulated in the TOTP with convex forms. Then, the TOTP is transformed into a large sparse optimization problem after discretization, which can be efficiently solved using convex solvers. Subsequently, a deep RL network is designed to optimize the TOTP results, where efficient learning is achieved in the solution space, thereby guaranteeing practical reliability and strong robustness via online interaction in applications. In addition, by incorporating convex optimization and learning techniques, the gap between simulation and experiment is successfully bridged, where the physical feasibility and efficient learning are ensured in the framework. Finally, comparative simulations and experimental results are included to show the effectiveness of the proposed strategy.

Monocular Robust 3D Human Localization by Global and Body-Parts Depth Awareness

Learning the human depth localization in camera coordinate space plays a crucial role in understanding the behavior and activities of multi-person in 3D scenes. However, existing monocular-based methods rarely combine the global image features and the human body-parts features effectively, resulting in a large gap from the actual location in some cases, e.g., the special body-sized persons and mutual occlusion between humans in the image. This paper presents a novel Robust 3D Human Localization (R3HL) network consisting of two stages: global depth awareness and body-parts depth awareness, to significantly improve the robustness and accuracy of the 3D location. In the first stage, the front-back and far-near relationship estimation module based on multi-person are proposed to make the network extract depth features from the global perspective. In the second stage, the network focuses on the target human. We propose a Pose-guided Multi-person Repulsion (PMR) module to enhance the target human’s features and reduce the interference features produced by the background and other people. In addition, an Adaptive Body-parts Attention (ABA) module is designed to assign different feature weights to each joint. Finally, the human’s absolute depth is obtained through global pooling and fully connected layers. The experimental results show that the attention from the whole image to a single person helps find the absolute location of different body-sized and poses people from diverse scenes. Our method can achieve better performance than other state-of-the-art methods on both indoor and outdoor 3D multi-person datasets.

One Ligand Fits All: Formation and Stabilization of a Single‐Ligand Arenethiolato Cobalt(II) Complex via Metal‐π Coordination from a Bulky Acylamino Group

AbstractMetalloproteins activate inert molecules under mild conditions by exploiting the low‐coordinated metal centers formed in protein pockets. The creation of biomimetic metal centers using bulky ligands is an attractive strategy in bioinorganic chemistry. Herein, we report a highly bulky arenethiolato ligand containing acylamino groups that forms a neutral single‐ligand Co(II) complex. X‐ray analysis revealed that the amide NH group of the ligand was deprotonated to form an S,N‐chelate, and the cobalt center was stabilized by strong π coordination. The cobalt center exhibited a quasi‐square‐planar geometry inducing a low‐spin configuration in the solid state and in toluene, which was revealed by SQUID and ESR measurements. By contrast, Co(II)‐π coordination could be reversibly replaced by THF molecule, resulting in a high‐spin state. The novel structure was induced by the local coordination space, wherein the binding atoms were appropriately positioned, as in the hydrophobic pockets of proteins.

An Optimal Solution Study on a Non-Invasive Stereotactic Radiosurgery Instrument Optimizer for Stereotactic Radiosurgery of Single Brain Metastasis

<h3>Purpose/Objective(s)</h3> This study looks at a fast inverse planning (FIP) optimizer that enables more efficient and less planner dependent stereotactic radiosurgery (SRS) treatment planning. FIP generates a plan using multiple user-inputted variables that affect plan quality metrics, such as target coverage (TC), maximum dose to the target and organs-at-risk, low dose (LD), and beam-on time (BOT). The objective of this study is to systematically characterize each of these variables and determine which combination leads to the best SRS plan quality metrics. <h3>Materials/Methods</h3> Thirty patients with a single brain metastasis who were previously treated with SRS were evaluated. Each lesion was planned using FIP by varying the LD and BOT variables in 0.1 increments from 0.0 to 1.0 (i.e., plan #1 [0.0, 0.0], plan #2 [0.0, 0.1], ..., plan #120 [1.0, 0.9] and plan #121 [1.0, 1.0]). All plans were generated with the same prescription dose (24 Gy/1 fraction), TC (100%), maximum allowed dose (43.2 Gy), and Gamma angle (90°). The following metrics were recorded for each plan to evaluate plan quality: Paddick conformity index (PCI), gradient index (GI), and BOT. Heat maps for each of the above metrics as a function of LD and BOT penalties were analyzed. An objective score matrix was calculated for each plan using a linear weighted combination of scaled and normalized GI, PCI, and BOT. An optimal solution space containing the 5 lowest values of the score matrix per patient was extracted. A frequency histogram was subsequently created in the LD-BOT coordinate space. <h3>Results</h3> The target volumes in the study ranged from 1.0 cc to 2.5 cc. For every patient, 121 plans were generated across the range of LD and BOT penalties, resulting in 3630 plans included in this analysis. The range of PCI, GI, and BOT across all plans were 0.71 to 0.95, 2.5 to 2.9, and 17.2 to 221 minutes, respectively. The variation of the LD/BOT penalties had a much larger impact resulting in a higher deviation about the mean for BOT (169%), followed by PCI (28%). Heat map analysis revealed that the plans that maximized PCI and minimized GI values occupied the upper triangular matrix of the LD/BOT penalty space, while plans that minimized BOT occupied the lower triangular space. The optimal solutions frequently occupied the diagonal space in between these zones. Specifically, the histogram analysis showed that 4 highest frequencies occurred at the user-inputted settings (LD, BOT) of (0.6, 0.5), (0.8, 0.6), (0.7, 0.5), and (0.7, 0.6), in order of plan quality. <h3>Conclusion</h3> In this study, the user-inputted variables (LD and BOT) were systematically varied to determine the optimal solutions to simultaneously maximize PCI while minimizing GI and BOT. The results of this study may permit SRS planners to generate single brain metastasis plans more efficiently using the study-defined optimal settings of LD and BOT.

The eccentricity distribution of wide binaries

ABSTRACT Future Gaia and Legacy Survey of Space and Time data releases, together with wide area spectroscopic surveys, will deliver large samples of resolved binary stars with phase space coordinates, albeit with low-cadence. Given an eccentricity law f(ϵ), we derive properties of (i) the velocity distribution $v/\sqrt{G M/r}$ normalized by the value for a circular orbit at the measured separation r; (ii) the astrometric acceleration distributions a/(GM/r2) again normalized to the circular orbit value. Our formulation yields analytic predictions for the full statistical distribution for some commonly used eccentricity laws, if the time-scale of data sampling is comparable to or exceeds the binary period. In particular, the velocity distribution for the linear eccentricity law is surprisingly simple. With Bayesian analysis, we suggest a method to infer the eccentricity distribution based on the measured velocity distribution.