Projection Of Vector Research Articles

Primordial black holes from confinement

A mechanism for the formation of primordial black holes is proposed. Here, heavy quarks of a confining gauge theory produced by de Sitter fluctuations are pushed apart by inflation and get confined after horizon re-entry. The large amount of energy stored in the colour flux tubes connecting the quark pair leads to black-hole formation. These are much lighter and can be of higher spin than those produced by standard collapse of horizon-size inflationary overdensities. Other difficulties exhibited by such mechanisms are also avoided. Phenomenological features of the new mechanism are discussed as well as accounting for both the entirety of the dark matter and the supermassive black holes in the galactic centres. Under proper conditions, the mechanism can be realised in a generic confinement theory, including ordinary QCD. We discuss a possible string-theoretic realisation via $D$-branes. Interestingly, for conservative values of the string scale, the produced gravity waves are within the range of recent NANOGrav data. Simple generalisations of the mechanism allow for the existence of a significant scalar component of gravity waves with distinct observational signatures.

Statistics of interferograms in three-level systems

We report on the high-frequency (HF) regime of a microwave (MW) pulse consisting of a superimposition of N harmonics acting transversally on a three-level system (ThLS) simultaneously driven in the longitudinal direction by a radio-frequency (RF) signal and in the presence of a zero-energy splitting term D(Sz)2 where D denotes the uniaxial anisotropy and Sz the projection of the spin-1 vector along the quantization direction. We carry out the study by numerical simulations of the Bloch equation (in the absence of relaxation) and present the associated interference patterns for various combinations of the system's parameters. We have established that at high frequencies, the MW opens 2N windows for replication of the action of the RF on the interferograms. The ThLS exhibits multiple (N successive) coherent destruction of tunneling (CDT) when the RF drives it to avoided level crossings where it undergoes Landau-Zener-Stückelberg-Majorana (LZSM) transitions. These CDT are centered at resonance points where D matches the characteristic frequencies of the counter-rotating and rotating terms in the MW pulse. The effects observed are explained by invoking the rotating wave approximation and the Floquet theory. Our analytical results are found in satisfactory agreement with numerics. We have equally observed an infinite multiplication of interferograms for a bichromatic RF pulse when the characteristic amplitude and frequency of the additional signal are large even in the absence of a periodic MW pulse.

Supervised dimensionality reduction technology of generalized discriminant component analysis and its kernelization forms

Supervised subspace projection technology is a major method for dimensionality reduction in pattern recognition. At present, most supervised subspace projection algorithms are derived from the multi-dimensional extended version of Fisher linear discriminant analysis (FDA), also known as Multi-dimensional Fisher discriminant analysis (MD-FDA). However, MD-FDA needs to be improved further because the projection vectors in the noise-subspace cannot be sorted and the ill-condition of the within-class scatter matrix may cause severe numerical instabilities. Generalized discriminant component analysis (GDCA), the generalization of MD-FDA, together with its kernelization forms are proposed and correspondingly rigorous mathematical proofs are detailed in this paper. By virtue of 5 validation data sets derived from UCI Machine Learning Repository and our laboratory, the theoretical validity and technical advantages of GDCA as well as its kernelization forms are verified, and the effectiveness of the newly proposed method is demonstrated in comparison with 36 kinds of state-of-the-art dimensionality reduction algorithms.

Measuring the spins of heavy binary black holes

An accurate and precise measurement of the spins of individual merging black holes is required to understand their origin. While previous studies have indicated that most of the spin information comes from the inspiral part of the signal, the informative spin measurement of the heavy binary black hole system GW190521 suggests that the merger and ringdown can contribute significantly to the spin constraints for such massive systems. We perform a systematic study into the measurability of the spin parameters of individual heavy binary black hole mergers using a numerical relativity surrogate waveform model including the effects of both spin-induced precession and higher-order modes. We find that the spin measurements are driven by the merger and ringdown parts of the signal for GW190521-like systems, but the uncertainty in the measurement increases with the total mass of the system. We are able to place meaningful constraints on the spin parameters even for systems observed at moderate signal-to-noise ratios, but the measurability depends on the exact six-dimensional spin configuration of the system. Finally, we find that the azimuthal angle between the in-plane projections of the component spin vectors at a given reference frequency cannot be well-measured for most of our simulated configurations even for signals observed with high signal-to-noise ratios.

Design and Validation of Low-Power Secure and Dependable Elliptic Curve Cryptosystem

The elliptic curve cryptosystem (ECC) has been proven to be vulnerable to non-invasive side-channel analysis attacks, such as timing, power, visible light, electromagnetic emanation, and acoustic analysis attacks. In ECC, the scalar multiplication component is considered to be highly susceptible to side-channel attacks (SCAs) because it consumes the most power and leaks the most information. In this work, we design a robust asynchronous circuit for scalar multiplication that is resistant to state-of-the-art timing, power, and fault analysis attacks. We leverage the genetic algorithm with multi-objective fitness function to generate a standard Boolean logic-based combinational circuit for scalar multiplication. We transform this circuit into a multi-threshold dual-spacer dual-rail delay-insensitive logic (MTD3L) circuit. We then design point-addition and point-doubling circuits using the same procedure. Finally, we integrate these components together into a complete secure and dependable ECC processor. We design and validate the ECC processor using Xilinx ISE 14.7 and implement it in a Xilinx Kintex-7 field-programmable gate array (FPGA).

Focusing a vortex laser beam and converting linear to circular polarization

We show that when strongly focusing a linearly polarized optical vortex with the topological charge 2, in the near-focus region, there occurs not only a reverse energy flow (where the projection of the Pointing vector is negative) but the right-handed circular polarization of light as well. Notably, thanks to spin–orbital conversion the on-axis polarization vector handedness is the same as that of the transverse energy flow, i.e. anticlockwise. An absorbing spherical microparticle centered on the optical axis placed in the focus may be expected to rotate anticlockwise around its axis and its center of masses. Theoretical predictions are corroborated by the numerical simulation.

Focusing a Vortex Laser Beam with Polarization Conversion

We show that when strongly focusing a linearly polarized optical vortex with the topological charge 2 (or −2) in the near-focus region, there occurs not only a reverse energy flow (where the projection of the Poynting vector is negative) but the right- (or left-) handed circular polarization of light as well. Notably, thanks to spin–orbital conversion, the on-axis polarization vector handedness is the same as that of the transverse energy flow, i.e., anticlockwise (clockwise). An absorbing spherical microparticle centered on the optical axis placed in the focus may be expected to rotate anticlockwise (clockwise) around its axis and its center of masses. We also show that in the case of sharp focusing of light with linear polarization (without an optical vortex) before and after focus, the light has an even number of local regions with left- and right-handed circular (elliptical) polarizations. Theoretical predictions are corroborated by the numerical simulation.

Determining reaction pathways at low temperatures by isotopic substitution: the case of BeD + + H2O

Trapped Be+ ions are a leading platform for quantum information science (Gaebler et al 2016 Phys. Rev. Lett. 117 060505), but reactions with background gas species, such as H2 and H2O, result in qubit loss. Our experiment reveals that the BeOH+ ion is the final trapped ion species when both H2 and H2O exist in a vacuum system with cold, trapped Be+. The BeH+ product in the Be+ + H2 reaction further reacts with H2O to form BeOH+. To understand the loss mechanism, low-temperature reactions between sympathetically cooled BeD+ ions and H2O molecules have been investigated using an integrated, laser-cooled Be+ ion trap and high-resolution time-of-flight mass spectrometer (Schneider et al 2014 Phys. Rev. Appl. 2 034013). Among all the possible products, BeH2O+, H2DO+, BeOD+, and BeOH+, only the BeOH+ molecular ion was observed experimentally, with the assumed co-product of HD. Theoretical analyses based on explicitly correlated restricted coupled cluster singles, doubles, and perturbative triples (RCCSD(T)-F12) method with the augmented correlation-consistent polarized triple zeta (AVTZ) basis set reveal that two intuitive direct abstraction product channels, Be + H2DO+ and D + BeH2O+, are not energetically accessible at the present reaction temperature (∼150 K). Instead, a double displacement BeOH+ + HD product channel is accessible due to a large exothermicity of 1.885 eV through a submerged barrier in the reaction pathway. While the BeOD+ + H2 product channel has a similar exothermicity, the reaction pathway is dynamically unfavourable, as suggested by a sudden vector projection analysis. This work sheds light on the origin of the loss and contaminations of the laser-cooled Be+ ions in quantum-information experiments.

Using airborne vector magnetic data to calculate the projection of the magnetic anomaly vector onto a normal geomagnetic field

The total-field magnetic anomaly [Formula: see text] is an approximation of the projection [Formula: see text] of the magnetic anomaly vector [Formula: see text] onto the normal geomagnetic field [Formula: see text]. However, for highly magnetic sources, the approximation error of [Formula: see text] cannot be ignored. To reduce the error, we have developed a method for calculating [Formula: see text] by using airborne vector magnetic data based on the vector relationship of geomagnetic field [Formula: see text]. The calculation uses the magnitude of the vectors [Formula: see text], [Formula: see text], and [Formula: see text] through a simple approach. To ensure that each magnitude has the same level, we normalize the magnitude of [Formula: see text] using the total-field magnetic data measured by the scalar magnetic sensor. The method is applied to the measured airborne vector magnetic data at the Qixin area of the East Tianshan Mountains in China. The results indicate that the calculated [Formula: see text] has high precision and can distinguish the approximation error of approximately 0.1 nT. We also analyze the characteristics of the approximation error that are caused by the effects of different total magnetization inclinations. These error characteristics are used to predict the total magnetization inclination of a 2D magnetic source based on the measured airborne vector magnetic data.

SOME VECTORS FIELDS ON THE TANGENT BUNDLE WITH A SEMI-SYMMETRIC METRIC CONNECTION

Let $M$ is a (pseudo-)Riemannian manifold and $TM$ be its tangent bundlewith the semi-symmetric metric connection $\overline{\nabla }$. In thispaper, we examine some special vector fields, such as incompressible vectorfields, harmonic vector fields, concurrent vector fields, conformal vectorfields and projective vector fields on $TM$ with respect to thesemi-symmetric metric connection $\overline{\nabla }$ and obtain someproperties related to them.

Development a model of robot movement with five degrees of freedom for a warehouse

The object of research is a mathematical model describing the movement of a robot with five degrees of freedom for a warehouse. The work was aimed at analyzing the kinematic structure of the manipulator, on the basis of which the base and local coordinate systems were selected, as well as further formalized recording of the kinematic equations in matrix form. It is noted that one of the most problematic places is that the algorithms for controlling the robot most often contain local rules for the interaction of robots between themselves and the external environment, and emergent behavior is manifested as a result of the application of these rules, which does not have a formal description. Therefore, it is important to modernize the models describing the motion of a robot with five degrees of freedom for a warehouse. Using the matrix method, the sequence of constructing coordinate systems is described and its mathematical description is given, which will make it possible to eliminate this drawback in the future. The computer implementation of the developed algorithms was carried out using methods for processing matrix data structures. The principle of constructing a kinematic model of a robot is presented, with the help of which the main coordinate transformation matrices are obtained for robot with five degrees of freedom, and the possibility of taking into account the size of the gaps in the joints is shown. The resulting model is obtained, which is proposed for use in building control algorithms for a robot with an automatic gap selection, as well as in robot calibration. This is due to the fact that the proposed model has a number of features, in particular, the basic coordinate system and the coordinate system of each link of robot with five degrees of freedom are taken into account. This makes it possible to obtain the values of the indicators for the projection of the robot position vector in the initial state, in the rotation of the fourth link at a well-defined angle and in the case of a vertically straightened manipulator. Compared to similar known studies, this provides advantages such as minimizing errors in position, speed and motion accuracy. The object of research is a mathematical model describing the movement of a robot with five degrees of freedom for a warehouse. The work was aimed at analyzing the kinematic structure of the manipulator, on the basis of which the base and local coordinate systems were selected, as well as further formalized recording of the kinematic equations in matrix form. It is noted that one of the most problematic places is that the algorithms for controlling the robot most often contain local rules for the interaction of robots between themselves and the external environment, and emergent behavior is manifested as a result of the application of these rules, which does not have a formal description. Therefore, it is important to modernize the models describing the motion of a robot with five degrees of freedom for a warehouse. Using the matrix method, the sequence of constructing coordinate systems is described and its mathematical description is given, which will make it possible to eliminate this drawback in the future. The computer implementation of the developed algorithms was carried out using methods for processing matrix data structures. The principle of constructing a kinematic model of a robot is presented, with the help of which the main coordinate transformation matrices are obtained for robot with five degrees of freedom, and the possibility of taking into account the size of the gaps in the joints is shown. The resulting model is obtained, which is proposed for use in building control algorithms for a robot with an automatic gap selection, as well as in robot calibration. This is due to the fact that the proposed model has a number of features, in particular, the basic coordinate system and the coordinate system of each link of robot with five degrees of freedom are taken into account. This makes it possible to obtain the values of the indicators for the projection of the robot position vector in the initial state, in the rotation of the fourth link at a well-defined angle and in the case of a vertically straightened manipulator. Compared to similar known studies, this provides advantages such as minimizing errors in position, speed and motion accuracy.

Polarization as a signature of local parity violation in hot QCD matter

We show that local parity violation due to chirality imbalance in relativistic nuclear collisions can be revealed by measuring the projection of the polarization vector onto the momentum, i.e. the helicity, of final state baryons. The proposed method does not require a coupling to the electromagnetic field, like in the Chiral Magnetic Effect. By using linear response theory, we show that, in the presence of a chiral imbalance, the spin 1/2 baryons and anti-baryons receive an additional contribution to the polarization along their momentum and proportional to the axial chemical potential. The additional, parity-breaking, contribution to helicity can be detected by studying helicity-helicity azimuthal angular correlation.

The MRI posterior drawer test to assess posterior cruciate ligament functionality and knee joint laxity

Clinical Magnetic Resonance Imaging (MRI) of joints is limited to mere morphologic evaluation and fails to directly visualize joint or ligament function. In this controlled laboratory study, we show that knee joint functionality may be quantified in situ and as a function of graded posterior cruciate ligament (PCL)-deficiency by combining MRI and standardized loading. 11 human knee joints underwent MRI under standardized posterior loading in the unloaded and loaded (147 N) configurations and in the intact, partially, and completely PCL-injured conditions. For each specimen, configuration, and condition, 3D joint models were implemented to analyse joint kinematics based on 3D Euclidean vectors and their projections on the Cartesian planes. Manual 2D measurements served as reference. With increasing PCL deficiency, vector projections increased significantly in the anteroposterior dimension under loading and manual measurements demonstrated similar patterns of change. Consequently, if combined with advanced image post-processing, stress MRI is a powerful diagnostic adjunct to evaluate ligament functionality and joint laxity in multiple dimensions and may have a role in differentiating PCL injury patterns, therapeutic decision-making, and treatment monitoring.

Shape Sensing Using Two Outer Cores of Multicore Fiber and Optical Frequency Domain Reflectometer

A method, i.e., vector projections, using two outer cores of multicore fiber without calibration and OFDR was proposed to realize three-dimensional (3D) shape sensing. A complement for apparent curvature vector method using three outer cores of multicore fiber was also proposed to determine the viable fiber cores arrangement for shape sensing. Compared with apparent curvature vector method, the vector projections method based on two outer cores of multicore fiber decreased the number of fiber cores, which eliminating the requirement for fiber cores arrangement. Based on these methods, a reconstructed shape with a higher accuracy was obtained based on integrating all fiber shape from all cores combinations. The maximum root-mean-square errors (RMSEs) of end position for the vector projections and apparent curvature vector method were 13.1 and 12.4 mm, while a higher accuracy, i.e., maximum RMSEs of 11.9 and 12.1 mm, was obtained based on the integrated fiber shapes.

Some measured frequency domain characteristics of the underwater vector and scalar acoustic field components with applications to communication receivers

Vector and scalar components of the underwater acoustic field can be used for multichannel signal demodulation [A. Abdi, et al., “A new vector sensor receiver for underwater acoustic communication,” in Proceedings of the Oceans (2007), pp. 1–10; A. Abdi and H. Guo, “A new compact multichannel receiver for underwater wireless communication networks,” IEEE Trans. Wireless Commun. 8, 3326–3329 (2009)]. In frequency domain-based communication methods such as orthogonal frequency division multiplexing (OFDM) using multiple collected signals, understanding the behavior of the channels in frequency domain is important for proper system design. In this paper, we examine the experimental data obtained by transmitting pilot tones for channel estimation, to estimate various channel frequency responses. More specifically, channel frequency responses of the X, Y and Z components of the underwater acoustic vector field are estimated, in addition to the scalar field component channel frequency response. Analysis of the measured frequency responses reveals differences in parameters such as condition numbers and eigenvalues of measured channel matrices. Knowledge of these parameters is needed for designing communication receivers that utilize the vector and scalar components of the acoustic field in frequency domain. [The work is supported in part by NSF, Grant IIP-1500123.]

Vector Detection Network: An Application Study on Robots Reading Analog Meters in the Wild

Analog meters equipped with one or multiple pointers are wildly utilized to monitor vital devices’ status in industrial sites for safety concerns. Reading these legacy meters <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">autonomously</i> remains an open problem since estimating pointer origin and direction under imaging damping factors imposed in the wild could be challenging. Nevertheless, high accuracy, flexibility, and real-time performance are demanded. In this work, we propose the vector detection network (VDN) to detect analog meters’ pointers given their images, eliminating the barriers for autonomously reading such meters using intelligent agents like robots. We tackled the pointer as a 2-D vector, whose initial point coincides with the tip, and the direction is along tail-to-tip. The network estimates a confidence map, wherein the peak pixels are treated as vectors’ initial points, along with a two-layer scalar map, whose pixel values at each peak form the scalar components in the directions of the coordinate axes. We established the Pointer-10 K dataset composing of real-world analog meter images to evaluate our approach due to no similar dataset is available for now. Experiments on the dataset demonstrated that our methods generalize well to various meters, robust to harsh imaging factors, and run in real-time.

Signal detection in time spreading underwater environments using vector and scalar sensors

In this paper, we aim to examine the effects of the time-spreading signal distortion caused by multipath propagation in underwater environments, using experimental data. We use the Replica Correlation Integration detector [B. Friedlander and A. Zeira, “Detection of broadband signals in frequency and time dispersive channels,” IEEE Trans. Signal Process. 44(7), 1613–1622 (1996)], which is designed to take the multiple echoes of the transmitted signal into consideration. We apply this detector to measured data collected by underwater acoustic sensors. We use two types of sensors. The first sensor is a hydrophone that measures only the scalar component of the acoustic field, i.e., the acoustic pressure. The second sensor is a vector sensor that simultaneously measures the scalar and the three vector components of the acoustic field, i.e., the three acoustic particle velocity x, y, and z components. This sensor can perform as a multi-channel detector. Analysis of the measured data provides insights into the signal detection capabilities of the vector field components in time-spreading underwater environments. [The work is supported in part by NSF, Grant IIP-1500123, and ONR.]

Simultaneous measurement of pole figure and residual stress for polycrystalline thin films: ω–φ′ compensated grazing-incidence diffraction in side-inclination mode

A new grazing-incidence diffraction (GID) measurement geometry between in plane and out of plane is proposed. It is improved from the previous ω–φ compensated GID in side-inclination mode for measurement of residual stress in polycrystalline thin films [Wang &amp; van Riessen (2017). Powder Diffr. 32, S9–S15]. Instead of keeping a constant azimuthal direction of the incident beam on the thin film sample, the current proposed variation maintains a constant azimuthal direction of the scattering vector projection on the thin film sample. The variation is named `ω–φ′ compensated GID in side-inclination mode' and enables d-spacing measurements along the same azimuthal direction. An Excel spreadsheet is included for readers to plan the measurement and to calculate the residual stress for the planned sample azimuthal direction. Anisotropic residual stresses of a polycrystalline NiFe thin film on an Si 001 substrate are measured by combining this method with phi rotations. Highly automated data analysis templates are developed using DIFFRAC.TOPAS v7 launch mode to calculate residual stress for all planned azimuthal directions sequentially. A pole figure file in simple text format is also generated from the same data set using DIFFRAC.TOPAS v7 launch mode, and can be directly imported into DIFFRAC.TEXTURE v4.1 for further texture analysis. Corrections for the incident-beam refraction have been implemented in both data analysis models.

Global Convection Characteristics of Conical Taylor‐Couette Flow with Shear‐Thinning Fluids

AbstractA method to intensify the mixing process of scalar components within shear‐thinning fluids is proposed. A conical Taylor‐Couette flow enabled fluid elements to circulate in the entire fluid column owing to the global circulation flow (i.e., meridional flow) for keeping good local mixing within Taylor cells. The global convection and mixing characteristics were numerically investigated. The meridional flow was found to be enhanced with increasing shear‐thinning. In addition, the mixing performance was evaluated using a passive tracer. Global mixing with shear‐thinning fluids was promoted by the enhanced meridional flow compared with that of Newtonian fluids. Therefore, the conical Taylor‐Couette apparatus could be used for intensifying mixing processes in shear‐thinning fluid systems.

Vibrational mode-specificity in the dynamics of the Cl + C2H6 → HCl + C2H5 reaction.

We report a detailed dynamics study on the mode-specificity of the Cl + C2H6 → HCl + C2H5 H-abstraction reaction. We perform quasi-classical trajectory simulations using a recently developed high-level ab initio full-dimensional potential energy surface by exciting five different vibrational modes of ethane at four collision energies. We find that all the studied vibrational excitations, except that of the CC-stretching mode, clearly promote the title reaction, and the vibrational enhancements are consistent with the predictions of the Sudden Vector Projection (SVP) model, with the largest effect caused by the CH-stretching excitations. Intramolecular vibrational redistribution is also monitored for the differently excited ethane molecule. Our results indicate that the mechanism of the reaction changes with increasing collision energy, with no mode-specificity at high energies. The initial translational energy mostly converts into product recoil, while a significant part of the excess vibrational energy remains in the ethyl radical. An interesting competition between translational and vibrational energies is observed for the HCl vibrational distribution: the effect of exciting the low-frequency ethane modes, having small SVP values, is suppressed by translational excitation, whereas a part of the excess vibrational energy pumped into the CH-stretching modes (larger SVP values) efficiently flows into the HCl vibration.