Gaussian Cross Section Research Articles

Driving Risk Field and Control Strategies for Autonomous Vehicles at a Signalized Intersection

Driving pattern has been increasingly researched to improve driving safety and develop autonomous vehicles. Oriented towards the complex infrastructures at signalized intersections, this research digs into the risk sources brought by different kinds of road elements, including road lane markings, road curbs, median separators, signal timing, and neighboring vehicles around the ego car. Referring to vehicle speed both in the longitudinal and latitudinal dimensions, risk scope and distribution are quantified with the vehicle position of a torus with a Gaussian cross-section. Then, the risk is summed over all the road elements across all the points involved by the ego car, the level of which should be controlled within the threshold value when the ego vehicle explores to minimize trip delay. Thus, autonomous driving strategies are developed with respect to vehicle speed and steering angle. The proposed model is validated with NGSIM data, where a signalized intersection on Peachtree Street is selected and vehicles moving in different directions are analyzed. It is found that the proposed model manages to control vehicles with risk at the accepted level and to enhance the speed level as well as reduce acceleration fluctuations. This research contributes to improving autonomous driving against complex driving conditions for driving safety and efficiency.

Models of bars − II. Exponential profiles

ABSTRACT We present a new model for galactic bars with exponentially falling major axis luminosity profiles and Gaussian cross-sections. This is based on the linear superposition of Gaussian potential–density pairs with an exponential weight function, using an extension of the method originally introduced by Long & Murali. We compute the density, potential, and forces, using Gaussian quadrature. These quantities are given as explicit functions of position. There are three independent scaled bar parameters that can be varied continuously to produce bespoke bars of a given mass and shape. We categorize the effective potential by splitting a reduced parameter space into six regions. Unusually, we find bars with three stable Lagrange points on the major axis are possible. Our model reveals a variety of unexpected orbital structure, including a bifurcating x1 orbit coexisting with a stable x4 orbit. Propeller orbits are found to play a dominant role in the orbital structure, and we find striking similarities between our bar configuration and the model of Kaufmann & Contopoulos. We find a candidate orbital family, sired from the propeller orbits, that may be responsible for the observed high-velocity peaks in the Milky Way’s bar. As a cross-check, we inspect, for the first time, the proper motions of stars in the high-velocity peaks, which also match our suggested orbital family well. This work adds to the increasing body of evidence that real galactic bars may be supported at least partly by propeller orbits rather than solely by elliptical-like orbits of the x1 family.

Nanomechanics of Pectin-Linked β-Lactoglobulin Nanofibril Bundles.

Nanofibrils of β-lactoglobulin can be assembled into bundles by site-specific noncovalent cross-linking with high-methoxyl pectin (Hettiarachchi et al. Soft Matter 2016, 12, 756). Here we characterized the nanomechanical properties of bundles using atomic force microscopy and force spectroscopy. Bundles had Gaussian cross sections and a mean height of 17.4 ± 1.4 nm. Persistence lengths were calculated using image analysis with the mean-squared end-to-end model. The relationship between the persistence length and the thickness had exponents of 1.69-2.30, which is consistent with previous reports for other fibril types. In force spectroscopy experiments, the bundles stretched in a qualitatively different manner to fibrils, and some of the force curves were consistent with peeling fibrils away from bundles. The flexibility of pectin-linked nanofibril bundles is likely to be tunable by modulating the stiffness and length of fibrils and the ratio of pectin to fibrils, giving rise to a wide range of structures and functionalities.

Phase-only shaping algorithm for Gaussian-apodized Bessel beams

Gaussian-apodized Bessel beams can be used to create a Bessel-like axial line focus at a distance from the focusing lens. For many applications it is desirable to create an axial intensity profile that is uniform along the Bessel zone. In this article, we show that this can be accomplished through phase-only shaping of the wavefront in the far field where the beam has an annular ring structure with a Gaussian cross section. We use a one-dimensional transform to map the radial input field to the axial Bessel field and then optimized the axial intensity with a Gerchberg-Saxton algorithm. By separating out the quadratic portion of the shaping phase the algorithm converges more rapidly.

Automatic detection of modal spacing (Yellott's ring) in adaptive optics scanning light ophthalmoscope images

Purpose An impediment for the clinical utilisation of ophthalmic adaptive optics imaging systems is the automated assessment of photoreceptor mosaic integrity. Here we propose a fully automated algorithm for estimating photoreceptor density based on the radius of Yellott's ring.Methods The discrete Fourier transform (DFT) was used to obtain the power spectrum for a series of images of the human photoreceptor mosaic. Cell spacing is estimated by least-square fitting an annular pattern with a Gaussian cross section to the power spectrum; the radius of the resulting annulus provides an estimate of the modal spacing of the photoreceptors in the retinal image. The intrasession repeatability of the cone density estimates from the algorithm was evaluated, and the accuracy of the algorithm was validated against direct count estimates from a previous study. Accuracy in the presence of multiple cell types and disruptions in the mosaic was examined using images from four patients with retinal pathology and perifoveal images from two subjects with normal vision.Results Intrasession repeatability of the power spectrum method was comparable to a fully automated direct counting algorithm, but worse than that for the manually adjusted direct count values. In images of the normal parafoveal cone mosaic, we find good agreement between the power-spectrum derived density and that from the direct counting algorithm. In diseased eyes, the power spectrum method is insensitive to photoreceptor loss, with cone density estimates overestimating the density determined with direct counting. The automated power spectrum method also produced unreliable estimates of rod and cone density in perifoveal images of the photoreceptor mosaic, though manual correction of the initial algorithm output results in density estimates in better agreement with direct count values.Conclusions We developed and validated an automated algorithm based on the power spectrum for extracting estimates of cone spacing, from which estimates of density can be derived. This approach may be used to estimate cone density in images where not every single cone is visible, though caution is needed, as this robustness becomes a weakness when dealing with images from patients with some retinal diseases. This study represents an important first step in carefully assessing the relative utility of metrics for analysing the photoreceptor mosaic, and similar analyses of other metrics/algorithms are needed.

Back-reflection Second-harmonic Generation of (111)Si: Theory and Experiment

We consider second-harmonic generation (SHG) from a (111) surface of a tetrahedrally bonded semiconductor illuminated at normal incidence by a focused pump beam of Gaussian cross section as a model of SHG by focused beams. Calculations are done in the anisotropic bond model (ABM) and the results are applied to Si. The unit-cell configuration is simple enough for the calculations to be done analytically, so the results can be compared directly to similar calculations done for amorphous material. Although the differences in unit-cell symmetry occur on the atomic scale, they lead to large differences in the spatial distribution of the emerging radiation. Lateral focusing, which might be expected to increase the bulk contribution to SHG by increasing the lateral field gradient, has little effect; the spatial-dispersion contribution remains dominated by the phase term. Focusing does not inhibit backscattered SHG from the bulk, although our data on the oxidation of H-terminated (111)Si clearly show that in some cases the interface contribution dominates by a wide margin.

Investigation into the optimum beam shape and fluence for selective ablation of dental calculus at λ = 400 nm

A frequency-doubled Ti:sapphire laser is shown to selectively ablate dental calculus. The optimal transverse shape of the laser beam, including its variability under water-cooling, is determined for selective ablation of dental calculus. Intensity profiles under various water-cooling conditions were optically observed. The 400-nm laser was coupled into a multimode optical fiber using an f = 2.5-cm lens and light-shaping diffuser. Water-cooling was supplied coaxially around the fiber. Five human tooth samples (four with calculus and one pristine) were irradiated perpendicular to the tooth surface while the tooth was moved back and forth at 0.3 mm/second, varying between 20 and 180 iterations. The teeth were imaged before and after irradiation using light microscopy with a flashing blue light-emitting diode (LED). An environmental scanning electron microscope imaged each tooth after irradiation. High-order super-Gaussian intensity profiles are observed at the output of a fiber coiled around a 4-in. diameter drum. Super-Gaussian beams have a more-homogenous fluence distribution than Gaussian beams and have a higher energy efficiency for selective ablation. Coaxial water-cooling does not noticeably distort the intensity distribution within 1 mm from the optical fiber. In contrast, lasers focused to a Gaussian cross section (< or =50-microm diameter) without fiber propagation and cooled by a water spray are heavily distorted and may lead to variable ablation. Calculus is preferentially ablated at high fluences (> or =2 J/cm(2)); below this fluence, stalling occurs because of photo-bleaching of the calculus. Healthy dental hard tissue is not removed at fluences < or =3 J/cm(2). Supplying laser light to a tooth using an optical fiber with coaxial water-cooling is determined to be the most appropriate method when selectively removing calculus with a frequency-doubled Ti:sapphire laser. Fluences over 2 J/cm(2) are required to remove calculus efficiently since photo-bleaching stalls calculus removal below that value.

Impact of Conduit Geometry on the Performance of Typical Particulate Microchip Packings

This work investigates the impact of conduit geometry on the chromatographic performance of typical particulate microchip packings. For this purpose, high-performance liquid chromatography (HPLC)/UV-microchips with separation channels of quadratic, trapezoidal, or Gaussian cross section were fabricated by direct laser ablation and lamination of multiple polyimide layers and then slurry-packed with either 3 or 5 microm spherical porous C8-silica particles under optimized packing conditions. Experimentally determined plate height curves for the empty microchannels are compared with dispersion coefficients from theoretical calculations. Packing densities and plate height curves for the various microchip packings are presented and conclusively explained. The 3 microm packings display a high packing density irrespective of their conduit geometries, and their performance reflects the dispersion behavior of the empty channels. Dispersion in 5 microm packings correlates with the achieved packing densities, which are limited by the number and accessibility of corners in a given conduit shape.

Tsunami Generation by Submarine Mass Failure. I: Modeling, Experimental Validation, and Sensitivity Analyses

Numerical simulations are performed with a two-dimensional (2D) fully nonlinear potential flow (FNPF) model for tsunami generation by two idealized types of submarine mass failure (SMF): underwater slides and slumps. These simulations feature rigid or deforming SMFs with a Gaussian cross section, translating down a plane slope. In each case, the SMF center of mass motion is expressed as a function of geometric, hydrodynamic, and material parameters, following a simple wavemaker formalism, and prescribed as a boundary condition in the FNPF model. Tsunami amplitudes and runup are obtained from computed free surface elevations. Model results are experimentally validated for a rigid 2D slide. Sensitivity studies are performed to estimate the effects of SMF-shape, type, and initial submergence depth—on the generated tsunamis. A strong SMF deformation during motion is shown to significantly enhance tsunami generation, particularly in the far-field. Typical slumps are shown to generate smaller tsunamis than corresponding slides. Both tsunami amplitude and runup are shown to depend strongly on initial SMF submergence depth. For the selected SMF idealized geometry, this dependence is simply expressed by power laws. Other sensitivity analyses are presented in a companion paper, and results from numerical simulations are converted into empirical curve fits predicting characteristic tsunami amplitudes as functions of nondimensional governing parameters. It should be stressed that these empirical formulas are only valid in the vicinity of the tsunami sources and, because of the complexity of the problem, many simplifications were necessary. It is further shown in the companion paper how 2D results can be modified to account for three-dimensional tsunami generation and used for quickly estimating tsunami hazard or for performing simple case studies.

Flat-topped light beams with non-circular cross-sections

A set of flat-topped light beams with non-circular cross-sections is introduced. This set includes beams with rectangular, elliptical, pyramidal and one-dimensional Gaussian cross-sections. The one-dimensional Gaussian denotes a beam with Gaussian distribution in one direction and a long flattened distribution in the perpendicular direction. Field distributions of this set of beams can be expressed as sums of the lowest order Gaussian modes (TEM00) having different parameters. The main features of the beam are investigated throughout the space without using the orthogonal polynomials.

Ultrashort pulsed Gaussian light beams

We find a family of solutions of the paraxial wave equation that represents ultrashort pulsed light beams propagating in free space. These pulsed beams have an arbitrary temporal form and a nearly Gaussian cross section, while modeling for the pulses emitted by mode-locked lasers with stable two-mirror resonators. We also study the effects arising from their spatiotemporal coupled behavior, such as pulse time delay, distortion, and a frequency shift toward the beam periphery. Time-varying diffraction (with diffraction reduction at the first instants of arrival of the pulsed beam at a given distance) and the dependence of the spatial distribution of energy on the pulse form are also described. These effects become important for pulsed beams with a few optical oscillations within the pulse envelope.

Ray tracing study of whistlers guided by a field-aligned depression of electron density in the magnetosphere

The properties of VLF waves guided by a field-aligned depression of electron density in different models of the magnetosphere are studied. Ray tracing calculations show that the guidance of VLF waves from one hemisphere to the other is made possible by the existence of Gaussian cross-section trough. The guidance of VLF waves occurs only at the inner side of the trough, when it is located at L ⩽ 2.2 and L ⩾ 4.0 for the winter night model and at L ⩾ 1.5 for the summer day model of the magnetosphere. All analyzed troughs are modelled with the same electron density depression of 15% and with the effective width of 215 km in the equatorial plane. Initial latitude ranges for various wave normal directions, from which rays are successfully guided, are moved equatorward from the trough centre. For one trough the initial latitude ranges are defined so that corresponding rays reach 300 km altitude in the conjugate hemisphere with a final wave normal angle inside the ionospheric transmission cone. The guidance of VLF waves by a trough is possible in a para-longitudinal mode or a gradient trapping mode, depending on initial positions. Changing these positions, there is a continuous transition from one ray path to the other. The main difference in the characteristics of rays guided in a para-longitudinal mode and a gradient trapping mode is the behaviour of the wave normal angle to the geomagnetic field. A para-longitudinal mode has lower value of this parameter than a gradient trapping mode. A ray guided in a gradient trapping mode deeply enters a trough. A slight difference of latitudinal gradients of the geomagnetic field and electron density in the lower altitude magnetosphere is responsible for determining a type of mode for guiding whistlers by a trough. These whistlers are characterized by an upper cut-off frequency which is almost 0.5 ƒBmin.

Large‐eddy simulation of aircraft exhaust plumes in the free atmosphere: Effective diffusivities and cross‐sections

The effective diffusion of aircraft emissions in the free stably stratified atmosphere is investigated by means of large‐eddy simulation in a domain of size 4.3 × 1.1 × 1.1 km³. On that scale, the atmosphere is represented by a weakly turbulent flow under uniformly stratified and shearless conditions. It is assumed that aircraft induced turbulence has ceased. The exhaust plumes of aircraft are represented by line sources with Gaussian cross‐sections. The stratification has been varied between 0.006 s−1 and 0.03 s−1. The computed effective horizontal diffusion coefficient lies between 11±2 m²s−1 and 21±4 m²s−1, depending on the level of stratification. Likewise the vertical diffusivity ranges from 2.3±0.6 m²s−1 to 0.37±0.04 m²s−1 in the beginning of the diffusion process, and amounts almost independently of the stratification to about 0.15±0.01 m²s−1 later on. The plume cross‐sections increase with time and stratification. The scattering of the results for a given stratification reflects the action of decaying, anisotropic, and homogeneous turbulence. The results confirm very well data from recent in‐situ flight measurements in the North‐Atlantic flight corridor in the tropopause region.

Optically induced quasiparticle density profiles in superconducting thin films.

We present numerical solutions of the coupled phonon-quasiparticle rate equations, with quasiparticle (qp) and phonon diffusion included, for a superconducting thin film illuminated by a temporally pulsed and spatially inhomogeneous optical intensity pattern. We consider optical intensities in the form of both a finite circular spot with a Gaussian cross section and a sinusoidal interference pattern. Thereby we demonstrate that spatially well-defined qp density profiles, including a qp grating, can be optically induced on nanosecond time scales. For the qp grating we use the ${\mathit{T}}^{\mathrm{*}}$ formalism to calculate the resulting conductivity grating in the film, and then calculate the grating diffraction peaks for incident microwaves.

The upper cut-off frequency of nose whistlers and implications for duct structure

The upper cut-off frequency of whistlers for ducted propagation in a field-aligned enhancement of electron density is determined (i) theoretically not accounting for ambient plasma gradients and (ii) with the effect of ambient gradients for L-values around 3–4. using both ray tracing in a realistic plasmaspheric model and also by using formulae previously derived by other workers. It is found that the minimum enhancement required for a given duct width to guide whistler-mode rays from low altitude (∼ 1000 km) in one hemisphere to a similar altitude in the conjugate hemisphere (corresponding to whistler paths) is significantly larger than previously determined for frequencies close to half the minimum electron gyrofrequency along the path. Three different effects are shown to be important; that is, (i) the finite ratio of plasma frequency to gyrofrequency, (ii) the magnetic field and ambient electron density gradient across the duct in the region of the equatorial plane and along the length of the duct and (iii) the curvature of the field lines. From ray-tracing calculations in uniform enhancement Gaussian cross-section ducts, it is found that for normal whistlers at L ∼ 4, a much wider range for the ratio of upper cut-off frequency to equatorial electron gyrofrequency would be expected than is experimentally observed. Possible reasons for this are discussed and it is concluded that either there is an amplitude threshhold or df dt limit for whistler amplification or ducts have a more complicated morphology; an increasing enhancement along the field line or superimposed fine structure. Mechanisms for whistler cut-offs above half the electron gyrofrequency are also discussed, with particular reference to the occurrence of super-whistlers.

Determination of etching characteristics of a vacuum generators AG21 argon-ion gun by interference colour and ellipsometric assessment of craters etched in tantalum oxide films

Interference-coloured tantalum oxide films were used in a qualitative and quantitative assessment of crater shapes formed by a Vacuum Generators AG21 argon-ion gun. Changes in interference colours, as a result of argon etching, clearly showed the elliptical shape of the craters formed and, under suitable circumstances, the elliptical contours of constant thickness around the crater walls. Quantitative assessment by scanning ellipsometry established that craters have approximately Gaussian cross-sections. However, in certain areas of the crater the cross-section is modified as a result of the influence of a small diameter beam of neutrals atom within the ion beam. Deviations from the Gaussian cross-sections also occur after prolonged etching.

Dust distribution in the inner coma of comet Halley: Comparison with models

The images of the inner coma of comet Halley that were taken with the Giotto camera have been evaluated to obtain information on the near-nucleus dust distribution and its relationship to the nuclear source regions. Over two-thirds of the dust in the inner coma can be modeled remarkably well with only three source regions, each emitting dust into broad jets with opening half-angles of 30 to 50°. The dust in the jets is not sharply bounded but disperses with a Gaussian cross section, consistent with a model in which both gas and dust emissions are confined to finite source regions. Departures from the simple R −1 relationship for the radial distribution of dust near the nucleus are reproduced by a model that considers the source region as a composite of adjacent subareas, each emitting dust into cones with opening half-angles of about 10°. Comparison of the azimuthal and radial dust distributions with model predictions gives information on the coma dust, the dust-gas interaction, and the properties of the emitting regions.

Remote measurement of in-plane diffusivity components in plates

A method of determining thermal diffusivity in thin plates is presented. The method, using infrared images of evolving thermal patterns previously injected with a laser, is noncontacting, one-sided, and remote. It does not require independent estimates of either the emissivity of the sample or the sample thickness. With a line-segment pattern for thermal input, it yields the in-plane components of the diffusivity tensor in anisotropic materials and also the rate of heat loss to the environment of the plate. Two methods of data analysis are presented, one corresponding to a heating line of general cross section and the other considering a Gaussian cross section, thereby saving considerable computer time. Both methods produce a statistical evaluation of measurement quality as well as estimates of diffusivity and loss rate. Results are shown for plates of metals and graphite-epoxy composite materials. Principal components and orientation for the diffusivity tensor are obtained in the anisotropic graphite-epoxy sample.

Free-space propagation of ultrashort light pulses

A boundary-value problem for Maxwell’s equations is formulated whose solutions represent ultrashort pulses of electromagnetic energy that travel along an axis. A paraxial approximation to the solution is introduced that, in the case of Gaussian boundary data, is expressed as a single integral over frequency. Calculations are presented for a pulse of Gaussian cross section and Gaussian time profile. A careful study is made of the error introduced by the paraxial approximation, and an error bound is derived.

Three-dimensional small-signal analysis of a free-electron laser.

We present a three-dimensional formulation of the cw free-electron laser amplifier in the small-signal domain. The formalism is used to calculate expressions for the power gain in both small-gain and large-gain situations, and differences from the corresponding formulas of the one-dimensional theory are studied in detail for an input optical beam of Gaussian cross section. In the small-gain case, the maximum of the gain profile is shifted from that of the one-dimensional theory, in accord with previous results. In the large-gain case, we show that the primary effect of diffraction of the fields is conveniently expressed in terms of radially dependent shifts in the resonance frequency and the overall phase. This leads to the result that an optical beam, as it amplifies in the electron-wiggler system, undergoes a smaller diffractive spreading than what it would have in free space.