Aperture Angle Research Articles

Numerical modelling of unilateral point-focusing electromagnetic acoustic transducer with experimental validation

Electromagnetic ultrasonic testing, based on the propagation characteristics of the ultrasonic wave in the medium, is an effective technique for defect detection. The structural of the electromagnetic acoustic transducer (EMAT) determines the detection effect, which should be reasonably designed. We propose an improved unilateral point-focusing EMAT structure with curved coils in this manuscript. The 3D model of the designed EMAT is numerically simulated utilizing the finite element method, and the bilateral point-focusing EMAT is also studied for comparison. The simulation results of the magnetic field intensity and the distributions of the displacement are shown in the manuscript, which prove the effectiveness of the improved unilateral point-focusing EMAT. Five impact parameters such as aperture angle, focal position, excitation current, lift-off distance, and coil winding number are investigated in detail. We verify the calculation results of the aperture angle and excitation current by the experiments. The conclusion shows that the focusing intensity of the improved unilateral point-focusing EMAT is relatively higher, and other factors also have a significant effect on the focal intensity.

Analysis of light extraction in light pipes by linear and elliptical grooves using different source aperture angles

An analytical and numerical analysis of light extraction from light pipes using total internal reflection grooves with linear and elliptical profiles is presented. We performed the study considering light sources with different aperture angles, such as sunlight delivered by optical fibers and LEDs. With this analysis, we propose an analytical model based on the edge ray concept that allows selecting the most convenient profile, size, and orientation of the groove to extract light with a desired illumination area according to the source aperture angle employed in the light pipe system. We also have numerically found that for sources with high aperture angles, the light extracted by the linear and elliptical grooves produces similar irradiance and angular distributions, whereas for sources with low aperture angles, the elliptical groove focuses the extracted light and produces a higher angular distribution in comparison to this obtained with the linear groove. Our results are scalable to different light pipe dimensions and provide a systematic way to obtain preliminary designs of grooves for lighting systems that employ optical sources with different aperture angles.

Hydraulic Conductivity Behaviors of Karst Aquifer With Conduit-Fissure Geomaterials

This study uses laboratory analog and numerical experiments to simulate groundwater flow in karst aquifer and investigate the dimension-dependent hydraulic conductivity for groundwater flow in conduit-fissure medium. A coupled Darcy-Navier-Stokes mathematical model were developed to simulate groundwater flow transmitting process in karst aquifer. The Darcy law was used to model the flow in the fissure and the Navier-Stokes equations were used for the flow in the conduit. A laboratory analog which simulate the conduit-fissure domains of a karst aquifer was used to provide verification of proposed mathematical models and the calibration of numerical simulations. Numerical simulations were adopted to solved the coupled Darcy-Navier-Stokes mathematical model. The numerical simulation results for flow match well with laboratory experimental results. Furthermore, the hydraulic conductivity for fully developed flow was identified as four control factors (conduit diameter, fracture aperture, hydraulic pressure and strata dip angle) by the numerical simulations. A new empirical equation was proposed to derive the hydraulic conductivity. The significance of each factor on the hydraulic conductivity was evaluated by statistical analysis. The evidence shows that the conduit diameter and fracture aperture have the most influence on the hydraulic conductivity.

Suppression of the Higher-Order Azimuthal Mode Competition in an ${X}$ -Band Triaxial Klystron Amplifier With a Slotted Coaxial Waveguide

Suppression of the higher-order azimuthal mode competition is significant in the design of an X-band triaxial klystron amplifier (TKA), since coaxial waveguide cannot cut off the low-order coaxial TE modes. In this article, the generation mechanism of the higher-order azimuthal mode competition is analyzed, and a slotted coaxial waveguide is specially designed to suppress the coaxial TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">81</sub> mode leakage. The results show that the reflection coefficient of the slotted coaxial waveguide can be optimized over 99%, and the reflection coefficient is sensitive to the variation of the slot length rather than the aperture angle or the thickness of the inner conductor. The combination of two identical slotted coaxial waveguides staggered azimuthally can effectively reflect the arbitrary polarized coaxial TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">81</sub> mode. Together with the reflectors specially designed to suppress the coaxial TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">61</sub> mode leakage, all of the asymmetric TE modes' competitions are restrained in this device. In the 3-D particle-in-cell simulation, the pulse-shortening resulting from the coaxial TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">81</sub> mode leakage is successfully suppressed with the slotted coaxial waveguide. The output power of the TKA achieves 1.28 GW, and the efficiency and gain are 34.5% and 41.5 dB, respectively. The slotted coaxial waveguide together with the reflectors eliminates the utilization of attenuation materials.

Three-dimensional isotropic STED microscopy generated by 4[formula omitted] focusing of a radially polarized vortex Laguerre–Gaussian beam

In this study, a method is proposed to generate a three-dimensional (3D) isotropic super-resolution spot using stimulated emission depletion (STED) microscopy. A focused radially polarized Laguerre–Gaussian (LG01) beam is used as the pump beam. A focused depletion spot is produced by a radially polarized vortex Laguerre–Gaussian beam in a 4π focusing system. The influences of the topological charge, the order of LG, the maximum aperture angle, and the ratio of the pupil radius to the beam waist (β) on the spherical symmetry of the fluorescent spot are analyzed in detail. With the optimization parameters, an isotropic fluorescent spot is realized. The full widths at half maximum (FWHM) value of the isotropic fluorescent spot are 0.0348λ in both the r and z directions in a saturated case. The proposed model can provide a useful and simple guideline to obtain the spherical spot in 3D microscopy, which is very useful for trapping specific pathological ultra-structures of spherical shaped molecules and related medical applications.

Experimental and numerical investigation on nonlinear flow behaviour through three dimensional fracture intersections and fracture networks

Abstract Fluid flow tests were conducted on four kinds of fracture intersections, namely straight fracture intersection, buckling fracture intersection, crossing fracture intersection and furcating fracture intersection. Corresponding numerical simulations were performed by solving the Navier-Stokes equations. The resultant flow force perpendicular to fracture walls were derived. The results show that at high hydraulic gradients the increased normal resultant force perpendicular to fracture walls will change the original flow direction and consequently cause the formation of eddies which triggers flow nonlinearity. Greater buckling angle and smaller crossing angle would result in the onset of nonlinear flow at a higher critical hydraulic gradient for the cases of buckling and crossing fracture intersections. The critical hydraulic gradient for the case of furcating fracture intersection depends on the absolute angle between furcating flow and the original flow direction. Based on the analyses, three nonlinear models for coefficient B in the Forchheimer law corresponding to three cases of fracture intersections are proposed, which are related to the fracture intersection angle and hydraulic aperture. These models are further validated using flow experimental data from a real fracture network created in a rock specimen with the corresponding fracture model constructed using the computed tomography (CT) method.

Correction of 2D-telecentric scan systems with freeform surfaces.

For scanning systems the resolution, distortion as well as the telecentricity are important performance criteria. For two-dimensional scanning systems, scan mirrors deflecting in only one transverse direction are not allowing for telecentricity in x and y simultaneously in case of an axisymmetric system. It is possible to achieve two-dimensional telecentricity by splitting the pupils in x- and y-direction and shifting the principal planes in one dimension by changing the focal power using an anamorphic setup. However, for higher specifications concerning a large aperture and wide scanning angle, using cylindrical lenses are not enough to achieve a good system quality. It has been proved in many researches that freeform surfaces are effective to improve the resolution of systems without rotational symmetry. In this work, a systematic case study is presented to investigate the potential of freeform surfaces to improve the resolution, telecentricity, and distortion simultaneously. It is shown as a result that freeform surfaces offer large correction ability in all the three aspects concerning high specifications of 2D-telecentric anamorphic scan systems. This contribution provides the insight into the application of freeform surfaces in non-rotationally symmetric optical systems with refractive components.

DETERMINATION OF THE DENSITY VALUE SPECIFICALLY AT THE FOCAL POINT OF THE MIRROR CONCENTRATING SYSTEM

When designing mirror concentrating systems, it is necessary to determine in advance the optical-geometric and optical-energy characteristics of the installation. One is required to choose the mirrors with a reflection coefficient to satisfy the expected energy distribution in the focal area and to pay attention to the accuracy of the reflective surfaces of the mirrors, to the accuracy of the tracking system of the heliostats to the trajectory of the apparent motion of the Sun, to the partial shading to the reflective surfaces, etc. Based on these data, it is necessary to calculate the irradiance distribution in the focal zone of the installation. During installation and utilization of the equipment it is necessary to measure and monitor these parameters and, if necessary, to recalculate the energy distribution taking into account the new parameters.The methods for calculating the density distribution of the radiant flux in the focal zone of mirror-concentrating systems have been developed in parallel with the requirements of exploitation. They do not always correctly reflect the true picture formed in the focus of the heliostat. In this paper, the analysis presents the existing methods for calculating paraboloid concentrators based on the Gaussian distribution of energy in the focal plane. Developing the method of fallen and reflected elementary cone beam and on the basis of generated scattered optical images of the Sun and of the visible angular size (2γо = 32 angle of minutes) of the Sun, which shows non-Gaussian nature of the resulting distribution in the focal plane due to the influence of aberration of the optical paraboloidal surface depending on the change of the aperture angle 2U, we obtained an analytical calculation formula to determine the value of the concentrated radiant flux specifically at the focal point of a paraboloid mirror concentrating system.

Design of Wide Angle and Large Aperture Optical System with Inner Focus for Compact System Camera Applications

Conventionally, a bright, very wide-angle optical system is designed as a floating type optical system that moves two or more lens groups composed of multiple lens in order to focus accurately. These have been widely used as phase detection auto focus (AF) methods within conventional digital single-lens reflex (DSLR) cameras. However, a phase detection AF optical system cannot be used when recording motion pictures. In contrast, a compact system camera (CSC) performs AF by the contrast method, where a stepper motor is used as the driving source for moving the optical lens. Nonetheless, to ensure that the focusing lens is lighter, these stepper motors should not have high torque and AF must be possible by moving only one lens. Yet, when focusing is performed with only one lens, aberration change due to focusing lens movement is magnified. Therefore, a very wide-angle optical system comprised of a half-angle of view more than 40 degrees and F of 1/4 has not been developed. Here, a very wide-angle optical system was designed with high resolving power that enables high speed AF, even in contrast mode, by moving only one lens while minimizing aberration change.

Zernike like functions on spherical cap: principle and applications in optical surface fitting and graphics rendering

Zernike circular polynomials (ZCP) are widely used in optical testing, fabrication and adaptive optics. However, their ability to characterize information on spherical cap is often limited by aperture angle, with highly curved surface being particularly challenging. In this study, we propose a simple and systematic process to derive Zernike like functions that are applicable to all types of spherical cap. The analytical expressions of three function sets are calculated using Gram-Schmidt algorithm. They are hemispherical harmonics (HSH), Zernike spherical function (ZSF) and longitudinal spherical function (LSF). HSH satisfies Laplacian equation and composes a subset of spherical harmonics (SH). ZSF and LSF can be applied to arbitrary spherical cap and their orthogonality is invariant to aperture. The achieved functions, with their complete and orthogonal performance, can serve as essential tools for surface characterization required for a wide range of applications like large-angle lenses description in illumination design, aberration analysis in high aperture systems, human cornea measurement fitting, geomagnetic field modelling, etc. Moreover, they are important for graphics rendering in virtual reality and games by solving the reflectance equation efficiently.

Determination of Biconical Cavity Eigenfrequencies Using Method of Partial Intersecting Regions and Approximation by Rational Fractions

The paper considers the problem of determining the eigenfrequencies of biconical cavity making it possible to simplify the eigenfrequency-based design of devices. We used the solving of the excitation problem for biconical cavity using the method of partial intersecting regions in combination with the collocation method. Based on the concept of the search of quasisolution for determining eigenfrequencies, it was proposed to apply the fractionally rational approximation of cavity response obtained as a result of solving the problem of resonator excitation. The efficiency of finding eigenfrequencies of biconical cavity was substantiated by using the fractionally rational approximation based on the chain fraction interpolation of cavity response calculated only at collocation points. Using the above approach, we have obtained the relationship of eigenfrequencies of azimuth-symmetric oscillations of biconical cavity as a function of the aperture angle, and the typing of lower azimuth-symmetric transverse electric modes of biconical cavity has been performed.

Simulation-based design and characterization of a microwave applicator for MR-guided hyperthermia experimental studies in small animals

Purpose: The objective of this study was to design and characterize a 2.45 GHz microwave hyperthermia applicator for delivering hyperthermia in experimental small animals to 2–4 mm diameter targets located 1–3 mm from the skin surface, with minimal heating of the surrounding tissue, under 14.1 T MRI real-time monitoring and feedback control. Materials and methods: An experimentally validated 3D computational model was employed to design and characterize a non-invasive directional water-cooled microwave hyperthermia applicator. We assessed the effects of: reflector geometry, monopole shape, cooling water temperature, and flow rate on spatial-temperature profiles. The system was integrated with real-time MR thermometry and feedback control to monitor and maintain temperature elevations in the range of 4 °C–5 °C at 1–3 mm from the applicator surface. The quality of heating was quantified by determining the fraction of the target volume heated to the desired temperature, and the extent of heating in non-targeted regions. Results: Model-predicted hyperthermic profiles were in good agreement with experimental measurements (Dice Similarity Coefficient of 0.95–0.99). Among the four considered criteria, a reflector aperture angle of 120°, S-shaped monopole antenna with 0.6 mm displacement, and coolant flow rate of 150 ml min−1 were selected as the end result of the applicator design. The temperature of circulating water and input power were identified as free variables, allowing considerable flexibility in heating target sizes within varying distances from the applicator surface. 2–4 mm diameter targets positioned 1–3 mm from the applicator surface were heated to hyperthermic temperatures, with target coverage ratio ranging between 76%–93% and 11%–26% of non-targeted tissue heated. Conclusion: We have designed an experimental platform for MR-guided hyperthermia, incorporating a microwave applicator integrated with temperature-based feedback control to heat deep-seated targets for experimental studies in small animals.

Geometric and mechanical properties of a shear-formed fracture occurring in a rock bridge between discontinuous joints

Rock bridges are commonly encountered in rock engineering practices and play a significant role in the stabilization of rock masses. Under shear loading, they are supposed to provide resistance not only at before-failure stages, but also at after-failure stages, and this is not fully understood yet by now. To promote the solving of this problem, the present study tried to discover the geometric and mechanical properties of a shear-formed fracture occurring in a rock bridge between discontinuous open joints through laboratory experiments. After careful preparation of sandstone specimens containing discontinuous open joints, a series of direct shear tests were carried out under constant normal load (CNL) conditions. Once the rock bridge failed, another two sets of cyclic loading were subsequently applied to the specimen to examine the after-failure properties. The geometric properties of the newly formed fracture in rock bridge area, including undulating angle, fracture roughness, and fracture aperture, were systematically examined and analyzed with respect to the applied normal stress and joint persistence. Furthermore, the failure mode was dependent on the normal stress and joint persistence and also influenced the properties of the shear-formed fracture. Accordingly, different fracture types occurring to the rock bridges were summarized and described in terms of geometric morphology. The findings in present study would enhance our understanding of the influence of rock bridges, especially at after-failure stages, on engineering practices such as rock slopes.

Sorption and desorption of Sr onto a rough single fractured granite

To investigate the migration behavior of Sr (strontium) in granite, a rough-walled single fracture of granite was prepared with the self-built rock splitting apparatus. Surface roughness angle and hydraulic aperture of the fracture were measured by 3D laser scanning and fluid flow experiment, respectively. The sorption and desorption breakthrough experiments of Sr in the single fracture were conducted at different flow rates and initial concentrates of Sr, and the important transport parameters were derived by fitting the BTCs and DPCs. The results suggested that the sorption of Sr onto the fracture surface was a linear and reversible ion-exchange process, unaffected by the variation of flow rate and initial concentrate of Sr.

The Influence of Micro-Fractures on the Flow in Tight Oil Reservoirs Based on Pore-Network Models

In this paper, the influence of micro-fractures on the flow of tight reservoirs is studied on the microscopic scale. Three-dimensional digital cores of fractured tight sandstone with varying fracture apertures, lengths, and dip angles are constructed using computed tomography (CT) scans. Pore-network models are built using the three-dimensional digital cores to simulate the flow in tight oil reservoirs. The effects of the micro-fracture aperture, length and dip angle on the pore-throat structure, single-phase flow, and two-phase flow for fracture surfaces with/without roughness are studied. The study demonstrates different influences of micro-fracture characteristics on the flow, and the fracture aperture has the most critical effect. Meanwhile, the roughness of the micro-fracture makes a difference in addition to the three factors of micro-fractures. This paper provides a theoretical basis for the effective development of tight sandstone reservoirs.

Dynamics of an ultrasound contrast agent microbubble near spherical boundary in ultrasound field**Project supported by the National Natural Science Foundation of China (Grant Nos. 11774088 and 11474090), the Hunan-Provincial Natural Science Foundation of China (Grant No. 13JJ3076), and the Science Research Program of Education Department of Hunan Province of China (Grant No. 14A127).

The goal of this article is to establish the conditions of excitation where one has to deal with ultrasound contrast agent (UCA) microbubbles pulsating near biological tissues with spherical boundary in ultrasound field for targeted drug delivery and cavitation-enhanced thrombolysis, etc., and contributes to understanding of mechanisms at play in such an interaction. A modified model is presented for describing microbubble dynamics near a spherical boundary (including convex boundary and concave boundary) with an arbitrary-sized aperture angle. The novelty of the model is such that an oscillating microbubble is influenced by an additional pressure produced by the sound reflection from the boundary wall. It is found that the amplitude of microbubble oscillation is positively correlated to the curve radius of the wall and negatively correlated to the aperture angle of the wall and the sound reflection coefficient. Moreover, the natural frequency of the microbubble oscillation for such a compliable wall increases with the wall compliance, but decreases with the reduction of the wall size, indicating distinct increase of the natural frequency compared to a common rigid wall. The proposed model may allow obtaining accurate information on the radiation force and signals that may be used to advantage in related as drug delivery and contrast agent imaging.

Study on EEBS for linewidth imaging by a Monte Carlo method

A systematic analysis about the influences of electron beam focusing on scanning electron microscope (SEM) imaging for silicon (Si) trapezoidal lines was performed based on a sophisticated Monte Carlo (MC) simulation program. It was found that the focus position and the aperture angle highly affect the final quality of SEM imaging. The effective electron beam shape (EEBS) is hence suggested as the broadening function to overcome this issue for theoretical analysis, rather than the widely-used Gaussian profile. However, EEBS is hardly acquired due to it strongly depends on both the sample topography and the electron beam focusing condition, which make it is impossible to be applied in practical analysis. An approach is proposed to find a best-fit traditional Gaussian profile, which can optimally replace the EEBS in the case of the same sample structure and experimental condition for establishing a database of the parameter in traditional Gaussian profile. Experimenters will benefit from this database to obtain true line-scan profiles for accurate gate linewidth measurement. This investigated result could greatly improve the accuracy of linewidth measurement.

Erosion of an exoplanetary atmosphere caused by stellar winds

Aims.We present a formalism for a first-order estimation of the magnetosphere radius of exoplanets orbiting stars in the range from 0.08 to 1.3M⊙. With this radius, we estimate the atmospheric surface that is not protected from stellar winds. We have analyzed this unprotected surface for the most extreme environment for exoplanets: GKM-type and very low-mass stars at the two limits of the habitable zone. The estimated unprotected surface makes it possible to define a likelihood for an exoplanet to retain its atmosphere. This function can be incorporated into the new habitability index SEPHI.Methods.Using different formulations in the literature in addition to stellar and exoplanet physical characteristics, we estimated the stellar magnetic induction, the main characteristics of the stellar wind, and the different star-planet interaction regions (sub- and super-Alfvénic, sub- and supersonic). With this information, we can estimate the radius of the exoplanet magnetopause and thus the exoplanet unprotected surface.Results.We have conducted a study of the auroral aperture angles for Earth-like exoplanets orbiting the habitable zone of its star, and found different behaviors depending on whether the star is in rotational saturated or unsaturated regimes, with angles of aperture of the auroral ring above or below 36°, respectively, and with different slopes for the linear relation between the auroral aperture angle at the inner edge of the habitable zone versus the difference between auroral aperture angles at the two boundaries of the habitable zone. When the planet is tidally locked, the unprotected angle increases dramatically to values higher than 40° with a low likelihood of keeping its atmosphere. When the impact of stellar wind is produced in the sub-Alfvénic regime, the likelihood of keeping the atmosphere is almost zero for exoplanets orbiting very close to their star, regardless of whether they are saturated or not.

Coarse to Fine Audio-Visual Size Correspondences Develop During Primary School Age.

Developmental studies have shown that children can associate visual size with non-visual and apparently unrelated stimuli, such as pure tone frequencies. Most research to date has focused on audio-visual size associations by showing that children can associate low pure tone frequencies with large objects, and high pure tone frequencies with small objects. Researchers relate these findings to coarser association, i.e., less precise associations for which binary categories of stimuli are used such as in the case of low versus high frequencies and large versus small visual stimuli. This study investigates how finer, more precise, crossmodal audio-visual associations develop during primary school age (from 6 to 11 years old). To unveil such patterns, we took advantage of a range of auditory pure tones and tested how primary school children match sounds with visually presented shapes. We tested 66 children (6–11 years old) in an audio-visual matching task involving a range of pure tone frequencies. Visual stimuli were circles or angles of different sizes. We asked participants to indicate the shape matching the sound. All children associated large objects/angles with low pitch, and small objects/angles with high pitch sounds. Interestingly, older children made greater use of intermediate visual sizes to provide their responses. Indeed, audio-visual associations for finer differences between stimulus features such as size and pure tone frequencies, may develop later depending on the maturation of supramodal size perception processes. Considering our results, we suggest that audio-visual size correspondences can be used for educational purposes by aiding the discrimination of sizes, including angles of different aperture. Moreover, their use should be shaped according to children’s specific developmental stage.

Rupture of a Liquid Bridge between a Cone and a Plane.

In this work, a systematic experimental study of the rupture of an axially symmetric liquid bridge between a cone and a plane was performed, with focus on the volume distribution after break up. A model based on the Young-Laplace equation is presented, and its solutions are compared to experimental data. Cones and conical cavities with different aperture angles were used in our experiments. We found that this aperture influences the potential pinning of the contact line, the meniscus shape, and therefore the liquid transfer. For half aperture angles α < 70°, where no pinning was observed, the liquid bridge slips off from the cone and almost no transfer to the cone is observed. However, at α > 70°, contact line pinning on the cone induces a net liquid transfer to the cone at rupture. In the case of conical cavities, a maximum of liquid transfer is observed for at α = 110°. The distance at which the rupture of the liquid bridge occurs is also discussed. The model can fairly predict the transfer ratio and the rupture height of the liquid bridge.