Geometric Field Research Articles

Optimization of linear and planar array geometries for unmanned underwater vehicle acoustic imaging techniques

Unmanned underwater vehicles (UUVs) are becoming more prevalent in industrial and scientific applications. A wide range of designs is available and many platforms are highly configurable, resulting in an ever-changing acoustic profile. Changes in the UUV’s noise may affect onboard sensors and potentially disturb the environment. An acoustic source imaging process is under development to provide a detailed analysis of the UUV noise in a rapid-turnaround environment. Measurements from a hydrophone array in the geometric near field of a UUV may be input to an acoustic inverse method [e.g., generalized inverse beamforming (GINV) or statistically optimized near-field acoustical holography (SONAH)] to spatially separate noise components and ascertain their levels. However, source resolution and accuracy are highly dependent on array design. Results of a recent numerical case study are presented towards the optimization of linear and planar array geometries. The array geometry is iterated and tuned based on the resultant beamwidth, sidelobe levels, and source localization accuracy for a range of octave frequency bands and source locations. The optimization results provide insight into the critical design factors for acoustical imaging techniques, as well as a suitable array geometry for improved UUV acoustic imaging.

Global Texture Mapping for Dynamic Objects

AbstractWe propose a novel framework to generate a global texture atlas for a deforming geometry. Our approach distinguishes from prior arts in two aspects. First, instead of generating a texture map for each timestamp to color a dynamic scene, our framework reconstructs a global texture atlas that can be consistently mapped to a deforming object. Second, our approach is based on a single RGB‐D camera, without the need of a multiple‐camera setup surrounding a scene. In our framework, the input is a 3D template model with an RGB‐D image sequence, and geometric warping fields are found using a state‐of‐the‐art non‐rigid registration method [GXW*15] to align the template mesh to noisy and incomplete input depth images. With these warping fields, our multi‐scale approach for texture coordinate optimization generates a sharp and clear texture atlas that is consistent with multiple color observations over time. Our approach is accelerated by graphical hardware and provides a handy configuration to capture a dynamic geometry along with a clean texture atlas. We demonstrate our approach with practical scenarios, particularly human performance capture. We also show that our approach is resilient on misalignment issues caused by imperfect estimation of warping fields and inaccurate camera parameters.

Development of low voltage gas ionization tunneling sensor based on p-type ZnO nanostructures

In this article, we report design, fabrication, and characterization of a gas field ionization-tunneling sensor (GFITS) based on zinc oxide (ZnO) nanowires. The device that operates at very low voltages is made up of two parallel plates separated by a narrow gap. ZnO nanowires are grown on one of the plates and used as the anode of this capacitive device. The nanowires that were synthesized using electrochemical technique on silicon or gold substrates, amplify the electric field between the two plates and reduce the ionization voltage of the gas molecules. Electrons from the gas atoms tunnel through the potential barrier of the gas atoms into the tips of nanowires. The generated tunneling current can be used to identify unknown gases. Nanowires with different aspect ratios and various morphologies were used to assemble the device, which was then tested for several gases. Distinct I–V characteristics for gases like Ar, He, and N2 at low pressures were achieved. Our observations show that nanowires grown on gold substrates do not have vertically parallel structures, rather they grow in the form of flower shapes and the devices made of those samples operate at much lower voltages compared to those made of parallel nanowires grown on semiconductor substrates. To investigate the effect of geometrical field enhancement on the operating voltage of the sensor, the electric field enhancement of nanowires has been simulated using COMSOL Multiphysics. The results show that the enhancement factor of flower-like nanostructures of ZnO is much higher than those of freestanding nanowires.

Growth of Wafer-Scale ReS2 with "Tunable" Geometry toward Electron Field-Emission Application.

Despite high potential, the promise of 2D materials has not been realized practically because of limits of tiny grown size and difficult manipulation of the active spot. The utilization of 2D layers is the ultimate approach, which should be supported by large-scale production. In this very first report, we demonstrate the wafer-scale production of ReS2 using the conventional sputtering method. The controllability of ReS2 geometry has been investigated to form typical thin films or vertically aligned layers that are further applied for field emission. The vertically aligned ReS2 layers exhibit ultralow turn-on electric field (0.6 V μm-1) with the current density (0.6 mA cm-2) and significantly low threshold electric field (0.8 V μm-1), respectively, along with outstanding emission stability. The results are attributed to weakly coupled ReS2 layers and the high geometrical field enhancement factor (∼1.08 × 105). Further, Kelvin probe force microscopy measurements confirm that lowering the work function is not solely responsible to achieve the ultralow operative field. Moreover, finite element simulation suggests that not only the length, width, and separation of the nanostructures but also the local slope plays an important role in suppressing screening effects.

Nonlinear Buckling and Postbuckling of a FGM Toroidal Shell Segment Under a Torsional Load in a Thermal Environment Within Reddy’s Third-Order Shear Deformation Shell Theory

The nonlinear buckling and postbuckling of FGM toroidal shell segments surrounded by elastic foundations in a thermal environment and subjected to a torsional load are investigated by an analytical method. Based on Reddy’s third-order shear deformation shell theory (TSDT) with geometrical nonlinearity in the von Karman sense, the governing equations are derived. Using the Galerkin method and a stress function, closed-form expressions for determining the critical torsional load and postbuckling load–deflection curves are obtained. Effects of the geometrical shape, material properties, temperature field, and foundation parameters on the stability of the shells are examined in detail.

Stringy (Galilei) Newton-Hooke Chern-Simons gravities

We construct Chern-Simons gravities in (2 + 1)-dimensional space-time considering the Stringy Galilei algebra both with and without non-central extensions. In the first case, there is an invariant and non-degenerate bilinear form, however the field equations do not allow to express the spin connections in terms of the dreibeins. In the second case there is no invariant non-degenerate bilinear form. Therefore, in both cases we do not have an ordinary gravity theory. Instead, if we consider the stringy Newton-Hooke algebra with extensions as gauge group we have an invariant non-degenerate metric and from the field equations we express the spin connections in terms of the geometric fields.

Proposal of 28 GHz In Vitro Exposure System Based on Field Uniformity for Three-Dimensional Cell Culture Experiments.

This paper proposes a novel in vitro exposure system operating at millimeter-wave (mmWave) 28 GHz, one of the frequency bands under consideration for fifth generation (5G) communication. We employed the field uniformity concept along cross-sectional observation planes at shorter distances from the radiation antenna for better efficiency and a small-size system. A choke-ring antenna was designed for this purpose in consideration of a wider beamwidth (BW) and a symmetric far-field pattern across three principal planes. The permittivity of Dulbecco's modified Eagle's medium solution was measured to examine the specific absorption rate (SAR) of the skin cell layer inside a Petri dish model for a three-dimensional (3D) cell culture in vitro experiment. The best deployment of Petri dishes, taking into account a geometrical field symmetry, was proposed. Local SAR values within the cell layer among the Petri dishes were determined with different polarization angles. It was determined that this polarization effect should be considered when the actual exposure and deployment were conducted. We finally proposed an in vitro exposure system based on the field uniformity including downward exposure from an antenna for 3D cell culture experiments. A small-size chamber system was obtained, and the size was estimated using the planar near-field chamber design rule. Bioelectromagnetics. 2019;40:445-457. © 2019 Bioelectromagnetics Society.

Blow-ups and class field theory for curves

We propose another proof of the geometric class field theory for curves by considering blow-ups of symmetric products of curves.

On the ramified class field theory of relative curves

We generalize Deligne's approach to tame geometric class field theory to the case of a relative curve, with arbitrary ramification.

Some features of the nonlocal correlation and geometric phase of the quantum system in two-mode nondegenerate entangled states

We propose a quantum two-level system interacting with a two-mode nondegenerate entangled states (TMNESs). The dynamical properties of entropy squeezing component is investigated based on atomic density matrix in the absence and presence of classical field effect. Moreover, the dynamical properties of the nonlocal correlation between the atom and TMNESs are studied and compared with geometric phase. We examine the influence of the initial interaction conditions and classical field on the evolution of nonlocal correlation, linear entropy and geometric phase. Furthermore, we discuss the link between the geometric phase, field purity and nonlocal correlation during the time dynamics. Finally, the results clarified that a geometric phase and entanglement are strongly affected by the classical field and detuning parameter.

Field Optimization and Electrostatic Stress Reduction of Proposed Conductor Scheme for Pliable Gas-Insulated Transmission Lines

The implementation of stranded conductors in flexible gas-insulated transmission lines (FGILs) requires field intensity minimization as well as field irregularity suppression in order to avoid dielectric breakdown. Moreover, the interdependence of enclosure and conductor sizes of FGILs regarding electrostatic aspects necessitate critical consideration of their dimensional specifications. In this research, geometric and electrostatic field optimization for FGILs regarding stranded conductors is performed. In addition, the effect of conductor irregularity on field dispersion is analyzed, and a semiconducting film (SCF)-coated stranded conductor is proposed as a potential candidate for FGILs. Considering the performed optimized design, an 11 kV scaled-down model of a 132-kV FGIL was also fabricated in order to practically analyze its electrostatic and dielectric performances regarding simple and SCF-coated stranded conductors. Simulation and experimental investigations revealed that the SCF-coated stranded conductor significantly minimized the field irregularity of the FGIL along with improving in its dielectric breakdown characteristics.

Experimental study on EHD effects on wetting characteristics of liquid in open rectangular microgrooves

Liquid wetting characteristics under EHD (Electrohydrodynamic) effects as a function of heat flux, voltages, microgroove inclination and dimensions in open rectangular microgrooves have been experimentally investigated. Two planar electrodes were used to generate electric fields. Wetting length was captured by a camera and it was determined according to the locations of marking lines that were measured by a caliper. The uncertainties of the heat loss and wetting length are 11.11% and 7.46%, respectively. Results indicate that higher heat flux can be achieved by electric fields effects. Wetting length increases notably by EHD pumping at a lower inclination. It is observed that microgrooves with smaller depth/width ratio perform a more pronounced increase of wetting length in the presence of electric fields. In addition, theoretical analyses show that the wetting length under electric field effects increases with the increasing groove depth while decreases as the groove width increases. Besides, both the threshold and optimal voltage are smaller for microgrooves with larger depth/width ratio. Moreover, the threshold voltage decreases with the increase of the depth/width ratio linearly. The findings are useful for the design of the EHD augmented grooved microfluidic devices with considering the fair geometrical dimensions and electric field voltages.

On the Lie 2-algebra of sections of an [formula omitted]-groupoid

In this work we introduce the category of multiplicative sections of an LA-groupoid. We prove that this category carries a natural strict Lie 2-algebra structure, which is Morita invariant. As applications, we study the algebraic structure underlying multiplicative vector fields on a Lie groupoid and in particular vector fields on differentiable stacks. We also introduce the notion of geometric vector field on the quotient stack of a Lie groupoid, showing that the space of such vector fields is a Lie algebra. We describe the Lie algebra of geometric vector fields in several cases, including classifying stacks, quotient stacks of regular Lie groupoids and in particular orbifolds, and foliation groupoids.

Conformal wave equations for the Einstein-tracefree matter system

Inspired by a similar analysis for the vacuum conformal Einstein field equations by Paetz (Ann Henri Poincaré 16:2059, 2015), in this article we show how to construct a system of quasilinear wave equations for the geometric fields associated to the conformal Einstein field equations coupled to matter models whose energy-momentum tensor has vanishing trace. In this case, the equation of conservation for the energy-momentum tensor is conformally invariant. Our analysis includes the construction of a subsidiary evolution which allows to prove the propagation of the constraints. We discuss how the underlying structure behind these systems of equations is the set of integrability conditions satisfied by the conformal field equations. The main result of our analysis is that both the evolution and subsidiary equations for the geometric part of the conformal Einstein-tracefree matter field equations close without the need of any further assumption on the matter models other that the vanishing of the trace of the energy-momentum tensor. Our work is supplemented by an analysis of the evolution and subsidiary equations associated to three basic tracefree matter models: the conformally invariant scalar field, the Maxwell field and the Yang–Mills field. As an application we provide a global existence and stability result for de Sitter-like spacetimes. In particular, the result for the conformally invariant scalar field is new in the literature.

Diffraction of waves by a perfect electromagnetic conductor half-plane between isorefractive media

In this study, diffraction of waves by a perfectly electromagnetic conductor half-plane which is lying at the boundary of isorefractive media is investigated. The diffracted field expressions are constructed by using the relation between scattered geometrical optics fields and the transition boundaries. The high frequency asymptotic expressions of diffracted fields reach infinite magnitude values at the transition boundaries. The uniform expressions of fields are obtained by using the uniform theory of diffraction method in order to obtain the finite magnitude values at the transition boundaries and the results are analyzed numerically for different set of parameters.

Verifications of Schottky's Conjecture

Schottky's Conjecture posits that the geometric field enhancement produced by a hybrid shape formed from a small perturbation on a larger base is the product of the individual field enhancement factors of the base and perturbation in isolation. This is a powerful concept with practical applications to understanding field emitter design and operation, as actual field emitters have complicated surface shapes with structure and, therefore, contributions to field enhancement, occurring simultaneously on many length scales. Recent studies of the Conjecture imply that the degree to which it accurately predicts a hybrid structure's total field enhancement depends on the degree of self-similarity between the base and perturbation shapes. To explore these aspects of the Conjecture, we have used the zero-potential surface produced by simple charge distributions to produce compound shapes with small perturbations on larger base structures. In the limit of small perturbation strength, these simple models adequately approximate idealized compound shapes, such a hemisphere-on-hemisphere geometry. Changing the base shape and the location of the perturbation allows us to selectively degrade the self-similarity present in the problem geometry. Proofs of the Schottky Conjecture in the limit of small perturbation strength will be provided, using these techniques, for hemisphere-on-hemisphere and half-cylinder-on-half-cylinder systems—the latter being the geometry considered by Schottky and for which the Conjecture was first proposed, but not proven.

Václav Hlavatý on intuition in Riemannian space

We present a historical commentary together with an English translation of a mathematical-philosophical paper by the Czech differential geometer and later proponent of a geometrized unified field theory Václav Hlavatý (1894–1969). The paper was published in 1924 at the height of interpretational debates about recent advancements in differential geometry triggered by the advent of Einstein's general theory of relativity. In the paper he argued against a naive generalization of analogical reasoning valid for curves and surfaces in three-dimensional Euclidean space to the case of higher-dimensional curved Riemannian spaces. Instead, he claimed, the only secure ground to arrive at results is analytical calculation. We briefly discuss the biographical circumstances of the composition of the paper and characterize its publication venue the journal Ruch filosofický. We also give a discussion of the mathematical background for Hlavatý's argument.

A 1.2 T canted cosθ dipole magnet using high-temperature superconducting CORC® wires

REBa2Cu3Ox (REBCO, RE = rare earth elements) coated conductors can carry high current in high background fields, in principle enabling dipole magnetic fields beyond 20 T. Although model accelerator magnets wound with single REBCO tapes have been successfully demonstrated, magnet technology based on high-current REBCO cables for high-field accelerator magnet applications has yet to be established. We developed a two-layer canted cosθ dipole magnet with an aperture of 70 mm using 30 m long commercial Conductor on Round Core (CORC®) wires. The 3.1 mm diameter CORC® wire contained 16 commercial REBCO tapes with a 30 μm thick substrate. The magnet was tested at 77 and 4.2 K. It generated a peak dipole field of 1.2 T with 4.8 kA at 4.2 K with neither thermal runaway nor training. Reasonable geometric field quality and strong magnetization-current effects with multipole decay were observed. Our work demonstrated a feasible high-temperature superconducting magnet technology as a first step toward a new accelerator magnet paradigm that will enable high-field inserts for next-generation circular colliders and stand-alone magnets that can operate over a wide temperature range for a broad range of applications.

Resonance Variations of the Microwave Refractive Index in YIG Plates

The influence of microwave resonance phenomena on complex refractive index in YIG plates has been theoretically and experimentally studied in the frequency range 26–38 GHz. It has been shown that a change in the magnetic field causes severe resonance-type changes in transmission and reflection factors. These changes are due both to effective interaction between millimeter electromagnetic waves and YIG plates (specifically, under ferromagnetic resonance conditions) and to the fulfillment of geometrical resonance conditions (when an integer number of half-waves or an integer odd number of quarter-waves are accommodated on the thickness of the plate). An algorithm to calculate complex refractive index with regard to the tensor-type magnetic permeability of YIG is suggested. The field and frequency dependences of complex refractive index have been analyzed. Geometrical resonance fields have been compared with extrema in the field dependences of the transmission and reflection factor moduli.

Inductive localization accuracy of a passive 3-D coil in an Industry 4.0 environment

Abstract. In this paper a localization system of a passive 3-D coil is proposed and signal uncertainties due to the 3-D coil's arbitrary orientation are analyzed. The 3-D coil is excited by an alternating primary magnetic field. Geometrically distributed pick-up coils measure the 3-D coil's secondary field. By means of a simulated look-up table that assigns expected voltages from the pick-up coils to the positions of the 3-D coil, the position of the 3-D coil is deduced by a least-squares approach. A basic assumption is that the secondary field is invariant to the orientation of the 3-D coil. This allows a reduction of the computational effort for the look-up table generation and the table search during the localization phase since for each position the field distribution for only one orientation has to be calculated. However, the assumption of invariance to rotation is only valid for a dipole model. In this paper we investigate the localization error introduced by this assumption when using 3-D coils with a geometric extent in an inhomogeneous primary field. Optimized localization methods that decrease the statistical error are proposed. The theoretical results are verified with measurements conducted on a laboratory system.