Geometric Field Research Articles

Morphological diversity in the sensory system of phyllostomid bats: Implications for acoustic and dietary ecology

Abstract Sensory systems perform fitness‐relevant functions, and specialized sensory structures allow organisms to accomplish challenging tasks. However, broad comparative analyses of sensory morphologies and their performance are lacking for diverse mammalian radiations. Neotropical leaf‐nosed bats (Phyllostomidae) are one of the most ecologically diverse mammal groups; including a wide range of diets and foraging behaviours, and extreme morphological variation in external sensory structures used in echolocation (nose leaf and pinnae). We coupled 3D geometric morphometrics and acoustic field recordings under a phylogenetic framework to investigate the mechanisms underlying the diversification of external sensory morphologies in phyllostomids, and explored the potential implications of sensory morphological diversity to functional outputs and dietary ecology. We found that the nose leaf consists of two evolutionary modules—spear and horseshoe—suggesting that modularity enabled morphological and functional diversification of this structure. We found a significant association between some aspects of nose leaf shape and maximum frequency and bandwidth of echolocation calls, but not between pinnae shape and echolocation call parameters. This may be explained by the use of multiple sensory modes across phyllostomids and plasticity of some echolocation call parameters. Species with different diets significantly differed in nose leaf shape, specifically in spear breadth, presence of a midrib, and cupping and anterior rotation of the horseshoe. This may relate to different levels of prey type specificity within each diet. Pinnae shape significantly differed between species that consume non‐mobile, non‐evasive prey (broad rounded, cupped pinnae) and mobile, evasive prey (flattened pinnae with a sharp tapering apex). This may reflect the use of different sound cues to detect prey. Our results give insight into the morphological evolution of external sensory structures in bats, and highlight new links between morphological diversity and ecology. A free Plain Language Summary can be found within the Supporting Information of this article.

A Novel Set of Geometric Verification Test Fields with Application to Distance Measures

Abstract As part of the second phase of the spatial forecast verification intercomparison project (ICP), dubbed the Mesoscale Verification Intercomparison in Complex Terrain (MesoVICT) project, a new set of idealized test fields is prepared. This paper describes these new fields and their rationale and uses them to analyze a number of summary measures associated with distance and geometric-based approaches. The results provide guidance about how they inform about performance under various scenarios. The new case comparisons are grouped into four categories: (i) pathological situations such as when a variable is zero valued at all grid points; (ii) circular events aimed at evaluating how different methods handle contrived situations, such as equal but opposite translations, the presence of multiple events of same/different size, boundary effects, and the influence of the positioning of events in the domain; (iii) elliptical events representing simplified scenarios that mimic commonly encountered weather phenomena in complex terrain; and (iv) cases aimed at analyzing how the verification methods handle small-scale scattered events, very large events with holes (e.g., a small portion of clear sky on a cloudy overcast day), and the presence of noise in one or both fields. Results show that all analyzed measures perform poorly in the pathological setting. They are either not able to provide a result at all or they instigate a special rule to prescribe a value resulting in erratic results. The analysis also showed that methods provide similar information in many situations, but that each has its positive properties along with certain unique limitations.

Maxwell equations in curved space-time: non-vanishing magnetic field in pure electrostatic systems

Solutions of the Maxwell equations for electrostatic systems with manifestly vanishing electric currents in the curved space-time for stationary metrics are shown to exhibit a non-vanishing magnetic field of pure geometric origin. In contrast to the conventional magnetic field of the Earth it can not be screened away by a magnetic shielding. As an example of practical significance we treat electrostatic systems at rest on the rotating Earth and derive the relevant geometric magnetic field. We comment on its impact on the ultimate precision searches of the electric dipole moments of ultracold neutrons and of protons in all electric storage rings.

Mechanical and microstructural testing of wire and arc additively manufactured sheet material

Wire and arc additive manufacturing (WAAM) is a method of 3D printing that enables large elements to be built, with reasonable printing times and costs. There are, however, uncertainties relating to the structural performance of WAAM material, including the basic mechanical properties, the degree of anisotropy, the influence of the as-built geometry and the variability in response. Towards addressing this knowledge gap, a comprehensive series of tensile tests on WAAM stainless steel was conducted; the results are presented herein. As-built and machined coupons were tested to investigate the influence of the geometrical irregularity on the stress-strain characteristics, while material anisotropy was explored by testing coupons produced at different angles to the printing orientation. Non-contact measurement techniques were employed to determine the geometric properties and deformation fields of the specimens, while sophisticated analysis methods were used for post processing the test data. The material response revealed a significant degree of anisotropy, explained by the existence of a strong crystallographic texture, uncovered by means of electron backscatter diffraction. Finally, the effective mechanical properties of the as-built material were shown to be strongly dependent on the geometric variability; simple geometric measures were therefore developed to characterise the key aspects of the observed behaviour.

Thermodynamic behaviour of solid–liquid grain boundary grooves

ABSTRACT Grain boundary grooves (GBGs) are local features that develop along polycrystalline solid–liquid interfaces. Interest in GBGs lies in their ability to form interface defects during crystallization that promote, in fact, dominate, morphological instability and affect microstructure formation in cast alloys. Recently, we reported on unobserved subtle aspects of the thermodynamic behaviour of GBG microstructures by combining sharp-interface field theory with diffuse-interface phase-field simulations. A surprising feature revealed about steady-state GBGs is that despite their stationarity they nonetheless support persistent capillary-mediated energy fluxes with divergences that continuously cool their interfaces and increase local curvatures. We now analyse the energetic behaviour of GBGs as ‘open’ thermodynamic systems, and report further details of their formation free energy that show how geometric constraints and capillary-mediated thermodynamic fields self-interact and influence the steady-state shapes of GBGs.

Lie symmetry analysis, symmetry reductions with exact solutions, and conservation laws of (2+1)‐dimensional Bogoyavlenskii‐Schieff equation of higher order in plasma physics

In this article, similarity reductions of the (2 1)‐dimensional Bogoyavlenskii‐Schieff equation of higher order have been done by Lie group method. We have determine the geometric vector field, infinitesimal generators, symmetric groups, and commutator table of Lie algebra with the help of Lie symmetry analysis. The new close form solutions and similarity solutions of the (2 1)‐dimensional Bogoyavlenskii‐Schieff equation of higher order have been determined from the reduction equations. Also, the conservation laws have been derived by invoking the new conservation theorem proposed by Ibragimov.

The FIREBIRD-II CubeSat mission: Focused investigations of relativistic electron burst intensity, range, and dynamics.

FIREBIRD-II is a National Science Foundation funded CubeSat mission designed to study the scale size and energy spectrum of relativistic electron microbursts. The mission consists of two identical 1.5 U CubeSats in a low earth polar orbit, each with two solid state detectors that differ only in the size of their geometric factors and fields of view. Having two spacecraft in close orbit allows the scale size of microbursts to be investigated through the intra-spacecraft separation when microbursts are observed simultaneously on each unit. Each detector returns high cadence (10 s of ms) measurements of the electron population from 200 keV to >1 MeV across six energy channels. The energy channels were selected to fill a gap in the observations of the Heavy Ion Large Telescope instrument on the Solar, Anomalous, and Magnetospheric Particle Explorer. FIREBIRD-II has been in orbit for 5 years and continues to return high quality data. After the first month in orbit, the spacecraft had separated beyond the expected scale size of microbursts, so the focus has shifted toward conjunctions with other magnetospheric missions. FIREBIRD-II has addressed all of its primary science objectives, and its long lifetime and focus on conjunctions has enabled additional science beyond the scope of the original mission. This paper presents a brief history of the FIREBIRD mission's science goals, followed by a description of the instrument and spacecraft. The data products are then discussed along with some caveats necessary for proper use of the data.

Development of singularities of the Skyrme model

The Skyrme model is a geometric field theory and a quasilinear modification of the Nonlinear Sigma Model (Wave Maps). In this paper, we study the development of singularities for the equivariant Skyrme Model, in the strong-field limit, where the restoration of scale invariance allows us to look for self-similar blow-up behavior. After introducing the Skyrme Model and reviewing what’s known about formation of singularities in equivariant Wave Maps, we prove the existence of smooth self-similar solutions to the [Formula: see text]-dimensional Skyrme Model in the strong-field limit, and use that to conclude that the solution to the corresponding Cauchy problem blows-up in finite time, starting from a particular class of everywhere smooth initial data.

Design of Misalignment-Insensitive Inductive Power Transfer via Interoperable Coil Module and Dynamic Power Control

This article proposes a misalignment-insensitive inductive power transfer (IPT) via interoperable tricoil module and dynamic power control. Since the misaligned coils is known to affect the power transmission efficiency and coupling performance, the article is devoted to the design of an interoperable tricoil module along with power modulation technique in the anticipation of reaching the misalignment-insensitive IPT. In this circuit design, three half-bridge inverters are deployed to drive three transmitting coils. Both geometric structure and magnetic field of coil modules are assessed. A dynamic power control strategy is implemented to adjust the amount of transferable power following the determination of the direction of movement of receiving coils, ensuring a higher efficiency of power transfer and coupling balance at the time of misalignment. To validate the practicality of this approach, the hardware prototype of tricoil module with IPT capability of 3.2-kW is realized with a 7% improvement of efficiency at a misalignment of 100 mm. These results support the feasibility of the proposed approach, serving as beneficial references for automatic guided vehicle applications.

Dependence of Optimum Thickness of Ultrathin Diamond-like Carbon Coatings over Carbon Nanotubes on Geometric Field Enhancement Factor

The generation of a field emission (FE) cathode electron source has attracted wide attention for its miniaturization, high-frequency operability, and low energy consumption. However, the FE performance of cold cathodes is limited by poor current stabilities of carbon nanotube (CNT) emitters. Coating CNTs with sp3-bonded carbon coatings is considered as a successful approach to stabilize the FE currents. High-quality ultrathin diamond-like carbon (DLC) films, which serve as sp3 carbon coatings, are deposited uniformly on CNTs by filtered cathodic vacuum arc evaporation in this research. The thicknesses of DLC coatings and the field enhancement factors of pristine CNTs affect to a large extent the FE properties. An optimum coating thickness of DLC layers corresponding to the lowest threshold field exists due to space-charge-induced band bending, at which the depletion region of the DLC layer in equilibrium is maximized. The optimum coating thickness increases with the geometric field enhancement factor of p...

Sensitive colorimetric detection of Pb2+ by geometric field amplification and surface plasmon resonance visualization

Pb2+ is one of the major environmental pollutants, which can be visually detected by surface plasmon resonance of nanoparticles. Paper based analytical device, as a newly developed microfluidic detection platform, is featured in cost-effective and suitable for on-site analysis. In this paper, a sensitive and portable detection method for Pb2+ was proposed, in which Pb2+ was electrokinetically stacked on the paper fluidic channel by geometric field amplification effect and visualized online by glutathione-modified silver nanoparticles. Colorimetric quantification of the visualized stacking band was conducted by smart phone camera. To avoid unfavorable influence from pH change on the surface plasmon resonance visualization, field amplification effect was introduced by geometric design of the paper fluidic channel. The enriched Pb2+ was clearly visible on the paper substrate, and the stacking band intensity was about four orders of magnitude enhanced, comparing to the intensity without stacking. A linear response to Pb2+ was observed in the range of 0.3–7.0 μM (R2 = 0.997) with a limit of detection of 86 nM and a limit of quantity of 0.28 μM. The established method was used in the detection of Pb2+ from river and lake water samples, and the results were confirmed by atomic absorption spectroscopy method.

A Comprehensive Survey on Geometric Deep Learning

Deep learning methods have achieved great success in analyzing traditional data such as texts, sounds, images and videos. More and more research works are carrying out to extend standard deep learning technologies to geometric data such as point cloud or voxel grid of 3D objects, real life networks such as social and citation network. Many methods have been proposed in the research area. In this work, we aim to provide a comprehensive survey of geometric deep learning and related methods. First, we introduce the relevant knowledge and history of geometric deep learning field as well as the theoretical background. In the method part, we review different graph network models for graphs and manifold data. Besides, practical applications of these methods, datasets currently available in different research area and the problems and challenges are also summarized.

A Sufficient Convexity Condition for Parametric Bézier Surface over Rectangle

Surface convexity is a key issue in computer aided geometric design, which is widely applied in geometric modeling field, such as physical models, industrial design, automatic manufacturing, etc. In this paper, a sufficient convexity condition of the parametric Bezier surface over rectangles is proposed, which is firstly considered as a sufficient convexity condition for the Bezier control grid. The condition is proved by De Casteljau surface subdivision arithmetic, in which the recursive expressions elaborate that the control grid eventually converges to the surface. At last, two examples for the modeling of interpolation-type surface are discussed, one of which is a general surface and the other is a degenerate surface.

Impact of the geometric field of view on drivers’ speed perception and lateral position in driving simulators

Abstract Driving simulators have become an effective tool in road safety research. In recent years, the validity of simulators raised debates concerning the extant to which driving in the simulator resembles driving in the reality. Different types of driving simulators with different characteristics have been developed to study driver behavior, however, the fidelity and reliability of such systems are questionable if no proper validation is conducted. Regarding the visual aspect, the fidelity of the simulators can be assessed based on the field of view of the simulator screens. Drivers’ speed perception and lateral position were compared for two different geometric field of view (GFOV) angles (i.e., 60 and 135 degrees). Results from the ANOVA tests showed that drivers highly underestimate their driving speed while driving for the condition with 60 degrees of GFOV compared to the condition with 135 degrees of GFOV. Furthermore, drivers drove closer to the real-world situations in the condition with 135 degree of GFOV compared to the condition with 60 degree. Results of this study suggest that, using incorrect GFOV for any simulator would generate biased results in speed and lateral position. Therefore, a proper calibration criterion of the GFOV for the simulators is essential. This study recommends using a scale factor (GFOV/FOV) of 1.00 for virtual environment offered by the simulation scenarios such as GFOV of 135 degree for simulators having three screens with 135 degree of field of view (FOV).

Some geometric vector fields on 5-dimensional 2-step homogeneous nilmanifolds

In this paper, we examine some geometric vector fields on 2-step nilmanifolds of dimension 5. We show that there is not any invariant concurrent vector field on such spaces. Our results show that in these manifolds each invariant conformal vector field is Killing and every invariant projective field is affine. Also, the space of some other invariant geometric fields such as affine, Killing, and harmonic vector fields on the manifolds are determined.

Biodiesel oil pool fire under air crossflow conditions: Burning rate, flame geometric parameters and temperatures

The replacement of fossil fuels with renewable ones is an irreversible worldwide trend. More specifically, biodiesel made either from animal fat residue or vegetable oil is being increasingly used. Biodiesel storage tanks are as prone to hazardous fires as other fuel tanks. In this article we present the results of an experimental investigation of biodiesel B100 pool fires in reduced scale submitted to an air crossflow. Regular and infrared images were used to obtain flame geometric parameters and temperature fields for conditions ranging from quiescent air to crossflow velocities of up to 4.0 m/s. Mass burning rates were also obtained for the same air flow conditions. Results were compared with a previous study of regular diesel pool fires conducted with the same experimental apparatus and correlations from literature. It was shown that, compared to diesel fires, biodiesel fires presented longer flames and higher temperatures both in the flame and plume regions as well as downstream of the pool. This indicates that biodiesel storage devices are likely more prone to dangerous fire events than diesel ones.

Accelerating universe with decreasing gravitational constant

We study the cosmology of dark energy in an extended theory of gravity in Lyra’s geometry. By analyzing a possible phenomenological interaction between the matter field with a constant equation-of-state parameter ωm (0≤ωm<1) and the geometric displacement field in Lyra’s geometry, we find that the displacement vector field engenders an effective time-dependent gravitational constant Geff constrained in the region 0<Geff(t)≤G. We show that the effective equation-of-state parameter ωeff(t) evolves in the same way as the effective time-dependent gravitational constant which, by decreasing with time, can give rise to the late-time cosmic acceleration with ω=-1 crossing in a flat Robertson-Walker background without adding dynamical ghost mode.

Generalized Jacobians and explicit descents

We develop a cohomological description of various explicit descents in terms of generalized Jacobians, generalizing the known description for hyperelliptic curves. Specifically, given an integer $n$ dividing the degree of some reduced effective divisor $\mathfrak{m}$ on a curve $C$, we show that multiplication by $n$ on the generalized Jacobian $J_\frak{m}$ factors through an isogeny $\varphi:A_{\mathfrak{m}} \rightarrow J_{\mathfrak{m}}$ whose kernel is naturally the dual of the Galois module $(\operatorname{Pic}(C_{\overline{k}})/\mathfrak{m})[n]$. By geometric class field theory, this corresponds to an abelian covering of $C_{\overline{k}} := C \times_{\operatorname{Spec}{k}} \operatorname{Spec}(\overline{k})$ of exponent $n$ unramified outside $\mathfrak{m}$. The $n$-coverings of $C$ parameterized by explicit descents are the maximal unramified subcoverings of the $k$-forms of this ramified covering. We present applications of this to the computation of Mordell-Weil groups of Jacobians.

Modeling Vector Fields in Space of Affine Connection

The authors have been constructed the splitting of the basic geometric images vector field (points, straights, hyperplanes and hyperguadrics) in transition from n-dimensional affine space to the space of affine connection. All invectigations have been fulfilled in the moving coordinate system of zero order.

Arithmetic summable sequence space over non-Newtonian field

In this article, we introduce the sequence spaces AS(G) and AC(G) of arithmetic summable and arithmetic convergent sequences, respectively, suggested by the geometric sum as k ranges over the divisors of m. We further obtain an analogous of Mobius inversion formula in the sense of geometric calculus and give interesting results in the geometric field.