Surface Shape Research Articles

Liquid vortex surface deformation probed by light reflection

Abstract We propose a method that combines an optical system with image processing techniques to scrutinize the dependence of liquid vortex deformation on varying angular velocity based on light reflection on liquid surfaces due to dynamic wettability. In our experiment, a broadened and collimated laser beam is directed onto curved surfaces, providing information on the vortex parameters through the analysis of the reflected beam profile. Additionally, the physical model of the liquid surface in a rotating cylinder before dewetting is examined. We investigate the liquid vortex forms of a saline solution and propylene glycol across various angular velocities, comparing them to the ideal parabolic vortex surface shape. The results show that, under the same experimental conditions, the vortex profiles of both solutions are equivalent. The vortex surface shape at certain angular velocity values, as determined by fitting plots, closely resembles a parabola, with R2 > 99%. The proposed method introduces a new approach for characterizing the dynamics of liquids as well as monitoring natural phenomena.

Pendent steady rivulets and droplets: from lubrication to bifurcation

Abstract We consider the shape of the free surface of steady pendent rivulets (or equivalently, two-dimensional droplets) beneath a planar substrate. We formulate the governing equations in terms of two closely related dynamical systems and use classical phase-plane techniques, in particular time maps, to analyse the bifurcation structure of the problem. Our results explain why lubrication theory is unable to capture this bifurcation structure for pendent rivulets, although it is successful in the related problem of sessile rivulets.

Development of Laminated Egg-Shaped Tsunami Shelter Structure Made of Steel-Cushioning-Steel

When a tsunami is caused by an earthquake or other event, spherical shelters are developed to protect people from the tsunami. This study proposes a new egg-shaped laminated tsunami shelter with a buffer layer to improve the functionality of traditional spherical shelters. The inner and outer shells of this shelter are made from thin-walled stainless steel, using the integral hydro bulge forming (IHBF) process. The space between these two layers was filled with urethane foam, providing an elastic buffer. This resulted in a laminated egg-shaped structure designed for tsunami protection. To verify the proposed laminated egg-shaped tsunami shelter and its processing method, an egg-shaped shell with an external shape (length 660 mm, width 493 mm) was fabricated using a 1.0 mm thick stainless plate, and a laminated egg-shaped tsunami shelter with a 25 mm thick intermediate layer made of urethane foam was fabricated. The shape accuracy of the processed egg-shaped laminated tsunami shelter structure was measured, and the maximum error between the surface shape of the molded egg-shaped shell and the true egg shape was -4.13 mm, and the relative error to the maximum radius of the egg shape of 246.5 mm was -1.68%. In addition, to assess the buffering effect under external impact loads, acceleration sensors were attached to both the inner and outer layers of the fabricated egg-shaped laminated tsunami shelters. A hammer was used to apply an impact load to the outer layer, and the response acceleration values recorded by the sensors on both layers were compared. It was found that the response acceleration of the inner layer was 15.81% lower than that of the outer layer.

Hybrid Refractive and Diffractive Testing Method for Free-Form Convex Mirror in High-Resolution Remote-Sensing Cameras

The development of high-resolution and large field of view remote-sensing cameras is inextricably linked to the application of free-form mirrors. The free-form mirror offers higher design of freedom and is more effective at correcting aberrations in optical systems. The surface shape error of a free-form mirror directly affects the imaging quality of remote-sensing cameras. Consequently, a high-precision free-form mirror detection method is of paramount importance. For the convex free-form surface mirror with a large aperture, a hybrid refractive and diffractive testing method combining computer-generated holography (CGH) and spherical mirrors for high-precision null test is proposed in this paper. When comparing the effect of error and the detection sensitivity of different designs, the results showed that the influence of the system error is reduced by about 42% and the sensitivity is increased by more than 2.6 times. The proposed method can achieve higher testing accuracy and represents an effective and feasible approach for the surface shape detection method.

Toward a green economy: Lignin-based hybrid materials as functional additives in flame-retardant polymer coatings

This study describes the combination of unique properties of lignin with TiO2 as an innovative and effective preparation method for high-performance flame-retardant additives that may be utilized as polymer coatings. The use of lignin resulted in numerous advantages including an increased number of functional groups, satisfactory biocompatibility, low toxicity, and high carbon content. The major benefit of lignin is associated with the reduced carbon footprint of the manufactured product. Lignin can be classified as a natural flame-retardant agent owing to the high amount of char formed during combustion. In turn, TiO2 exhibits high chemical stability and low operating costs and is considered a non-toxic and environmentally friendly material. During the experiments, commercial TiO2 in anatase crystallographic form, TiO2 synthesized from titanyl sulfate hydrate, and kraft lignin as well as organic–inorganic hybrid materials composed of these materials were evaluated as functional additives in epoxy-resin-based polymer coatings (Epidian 601) and their properties were investigated in detail. The cone colorimetry test confirmed that the obtained hybrids are effective flame-retardant additives for polymer coatings, with a notable fire hazard reduction observed for samples containing a synergistic system of titanium oxide and lignin. The coating with lignin was the most effective in fire suppression processes. The conducted thermal and mechanical investigations confirmed good performance properties of the coatings indicating thermal resistance up to 360 °C and Shore D hardness in a range of 80.36–86.28°Sh, accordingly. Optical profilometry investigations show that the lignin/TiO2 hybrids exhibit a stable topological surface shape as well as good dispersion and uniformity in the polymer matrix. All the conducted tests allowed confirmation that the presence of functional additives in polymer coatings in the form of lignin and TiO2 can be a promising alternative to non-biodegradable synthetic materials which improve flame-retardant properties.

Advances in predicting surface shape changes of mirror blanks through elliptical nozzle gas jet forming

To facilitate the formation of bifocal aspheric optical surfaces, we present an approach for predicting the surface profile of bifocal aspheric surfaces formed by the gas-liquid interface when an elliptical nozzle gas jet is employed. Through an analysis of the gas flow field morphology emanating from the elliptical nozzle, we inferred the impact of gas jet parameters on the gas-liquid interface surface shape within the core region of the gas jet. By analyzing the variation in the gas flow field morphology emitted from an elliptical nozzle, we deduced the influence patterns of gas jet parameters on the gas-liquid interface surface shape within the gas jet's core region. Theoretical analysis is substantiated by numerical simulations, confirming regular changes in the vertex curvature and conic constant of mirror blanks concerning variations in jet initial velocity and nozzle aspect ratio. A comparison between experimental data and numerical simulation results reveals an average prediction deviation of 0.0083 mm−1 for the vertex curvature and a prediction deviation of 10.7 % for the conic constant, challenging to rectify within numerical simulations. Hence, an empirical model, incorporating jet parameters, is developed based on experimental data to predict the vertex curvature and conic constant of mirror blanks. This model demonstrates an average prediction error of 2.901 × 10−3 mm−1 for the vertex curvature and 7.64 % for the conic constant, surpassing the predictive accuracy of the numerical simulation model.

FEM Investigation of the Roughness and Residual Stress of Diamond Burnished Surface

Characterization of surface integrity is possible with three critical metrics: microstructure, surface roughness, and residual stress. The latter two are discussed in this paper for low-alloyed aluminum material quality. Ball burnishing is a regularly used finishing procedure to improve surface roughness, shape accuracy, and fatigue life, taking advantage of the fact that it can favorably influence the variation in stress conditions in the material. The effect of burnishing is investigated using finite element simulation with DEFORM 2D software using the real surface roughness of the workpiece. The FEM model of the process is validated with experimental tests, the surface roughness is measured using an AltiSurf520 measuring device, and the residual stress is analyzed with a Stresstech Xstress 3000 G3R X-ray diffraction system (Stresstech, Vaajakoski, Finland). The results indicate that the burnishing process improves the surface roughness and stress conditions of AlCu6BiPb low-alloyed aluminum, and the study shows that there is good agreement between the FE and experimental results, further revealing the effect of the process parameters on the distribution of the compressive residual stress.

Influence of bottom supporting columns and cooling rate on the surface shape characteristics of sapphire substrates

The manufacturing process of sapphire substrates involves several key steps, including epitaxy, annealing, cutting, and processing. Among these, epitaxy and annealing are particularly crucial. The temperature variances along both the longitudinal and transverse axes within the furnace during the crystallization process play a significant role in determining the crystallization rate and internal structure of sapphire crystals. Furthermore, annealing sapphire serves to alleviate internal stress, enhance crystal structure, optimize physical properties, improve optoelectronic characteristics, enhance surface quality, and increase overall yield. This step is paramount in enhancing the performance and application value of sapphire materials. In order to investigate and optimize the effects of different thermal conductivities of support columns at the base and various annealing procedures on the surface characteristics of sapphire substrates, thereby improving product quality, this study conducted research by utilizing support columns made of different materials and carefully controlling the cooling rate parameters for sapphire. The findings revealed that using graphite as the base support column for the crystal furnace can reduce both the longitudinal and transverse temperature gradients within the furnace, consequently promoting crystal growth and enhancing the quality of sapphire ingots. Additionally, sapphire chips annealed using the rapid one-step annealing program exhibited the highest average warpage and bending rate variation, reaching 2.0 μm, and the average dislocation density was half that of conventionally produced chips, at 108.89 pits/cm2.

Noncircular Slip Surface Search on Slopes Based on Minimum Potential Energy Method and Improved SA Algorithm

ABSTRACTThe limit equilibrium method has been widely used in the study of searching the slip surface of slopes. However, the method ignores the deformation characteristics of the rock mass and assumes that the shape of the slip surface is circular, which is quite different from the actual situation of the slope. For this reason, this paper proposes a fast search method for noncircular slip surface considering the deformation characteristics of the rock mass. The method is able to calculate the compression and shear deformation energies stored in the slip surface, as well as the virtual displacement generated by the slide mass when the slope is in a critical equilibrium state. The direction of motion of the slide mass is further calculated from the magnitude of the virtual displacement. In addition, this paper improves the generation of new solutions in the simulated annealing (SA) algorithm for the structural characteristics of the slip surface of the slope, thus achieving a fast search of the slip surface. Finally, the method of this paper is compared with the test question of ACADS and the simulation results of the finite difference method (FDM) to verify the effectiveness of the method of this paper.

Analysis of corneal surface shape following overnight orthokeratology with different optical zone diameters.

This study analyzed the corneal surface shape following overnight orthokeratology with different optical zone diameters. A total of 82 eyes belonging to 41 myopic children who completed 1 month of the orthokeratology (ortho-k) lens wear at the Eye Hospital of Wenzhou Medical University from January 2022 to January 2023 were retrospectively analyzed. According to the size of the base curve (BC) of ortho-k lens, patients were divided into BC 5.0 and BC 6.0 groups. The changes in decentration distance and corneal refraction of the two groups after the ortho-k lens wear were analyzed. Independent sample t-tests were used to compare these two outcome measures between the two groups. The decentration distance of BC 5.0 group (0.37 ± 0.19 mm) was significantly lower than that of BC 6.0 group (0.49 ± 0.25 mm, t = -2.330, p = 0.022). In the BC 5.0 group, the direction of decentration was superonasal in 3 cases, inferonasal in 2 cases, inferotemporal in 21 cases, and superotemporal in 6 cases. In the BC 6.0 group, the direction of decentration was superonasal in 2 cases, inferonasal in 2 cases, inferotemporal in 27 cases, and superotemporal in 19 cases. The optical zone area (8.19 ± 2.96 mm2) and reverse curve zone area (30.05 ± 6.74 mm2) in the BC 5.0 group were significantly lower than in the BC 6.0 group (10.42 ± 2.03 mm2, t = -4.043, p < 0.001; 38.21 ± 4.77 mm2, t = -6.422, p < 0.001). The change in the rate of refraction in the horizontal direction in BC 5.0 group were significant higher than in BC 6.0 group. Base curve 5.0 mm ortho-k lens is better positioned than BC 6.0 mm lens. A small BC ortho-k forms a smaller optical zone and reverse curve area, which might get a greater aiameter of alignment curve to facilitate positioning better than the traditional BC lens. In addition, a small BC lens increases positive refraction in the peripheral area, resulting in a greater negative pressure than the traditional BC lens.

Astigmatic thermal lensing due to surface bulging in Yb:KYW laser crystals

One of the sources of thermal lensing in crystals is surface bulging that results from an inhomogeneous temperature distribution. We investigate a thermal lens caused by surface bulging in an end-pumped Yb:KYW crystal, which serves as a gain medium in lasers and optical amplifiers. The surface profile of the pumped crystal is measured using a Fizeau-type interferometer and compared with a numerical simulation using a finite element method. The study reveals that due to anisotropic thermal expansion, the surface shape of the Yb:KYW crystal is anisotropic and the profile of the expansion is transversely displaced with respect to the pump beam profile which generates the temperature distribution. The observed surface bulging gives rise to aberrations and deflection of the transmitted beam. It was found that the surface bulging introduces astigmatism that is significantly larger than previously estimated [Appl. Opt. 56, 3857 (2017)10.1364/AO.56.003857]. Our results allow the evaluation of the bulging contribution with improved accuracy. We show that these effects can be significant in certain designs of amplifiers and lasers.

Phase imaging through a single multimode fiber.

Phase imaging techniques are pivotal for achieving high-contrast visualization of unstained biological specimens in vitro, which is typically not applicable in narrow spaces. Recently, multimode fiber (MMF) has shown promise in enabling high-resolution in vivo endoscopy in biological research. Herein, we introduce a novel, to the best of our knowledge, phase imaging microscopy technique employing a single multimode fiber, showcasing remarkable capabilities in high-contrast imaging and quantitative shape reconstruction through frequency-domain modulation. Our method, validated through comparisons with reflection and phase-contrast results, demonstrates exceptional ability in imaging diverse samples, including microspheres, semiconductor chips, and oral epithelial cells. Notably, the quantitative reconstruction of surface shape achieves a sensitivity of less than 100 nm, enabling the extraction of three-dimensional information from single focal plane images. Moreover, our technique excels in contrast enhancement and defocused background suppression, presenting a promising avenue for minimally invasive, high-contrast, label-free in vivo phase imaging.

Experimental Study on the Combustion Characteristics of Ultralow-Concentration Methane in Divergent Porous Media Burner

ABSTRACT To improve the stable combustion characteristics of ultralow-concentration methane (Concentration of 3.5%-5.0%), a series of combustion experiments were carried out by filling alumina spheres with different particle sizes (i.e. 5 mm, 10 mm and 15 mm) in a divergent burner, and the effects of divergent angle (i.e. 10°, 20° and 30°) and pore distribution on the flame propagation and stable combustion characteristics of ultralow-concentration methane were revealed. The results show that larger particle sizes and methane flow rates lead to the double flame surface phenomenon, and increasing angle and decreasing particle size can help to improve the preheating efficiency of the burner. Moreover, the inlet flow rates corresponding to the steady combustion of ultra-low concentrations methane are between 0.225 m/s and 0.308 m/s, the increase in inlet velocity, particle size, and angle will reduce the stability of the flame and make the shape of the flame surface developed in the order of “V→W→∧.” The burner with 10 mm particles and 30° angle has a wider stable combustion range, and the burner filled with smaller pore distribution help to improve the utilization of the lower concentration methane premixed.

Functions for noise reduction in acoustic standards: evaluating reverberation time, mean absorption coefficient, and a novel approach

Contemporary European acoustic standards utilize dimensioning functions based on either reverberation time or mean absorption coefficient. For spaces with the primary goal of noise reduction, achieving consistent overall sound pressure level (SPL) reduction, regardless of room sizes and shapes is evidently desirable. The conditions under which reverberation time and mean absorption coefficient approaches align with the objective of consistent SPL reduction are analyzed. Generally, both approaches fall short of achieving consistency in case of varying ground surface or room shape, i.e. length, width and height relations. Additionally, in large rooms, constant or room height-dependent reverberation time functions may lead to extensive absorption areas, complicating the installation of acoustical treatments and degrading their economic efficiency. A novel dimensioning function, providing consistent SPL reduction independently of room size and shape, is derived based on diffuse field theory. The novel function is multiplied by a linear function of room height and length, to alleviate accuracy limitations of diffuse field theory in case of varying room shapes. Finally, simulations systematically varying room sizes and shapes demonstrate that the novel dimensioning function significantly outperforms existing approaches in achieving consistent SPL reduction.

Reconstruction of the shape of a flaw in ferromagnetic plate by solving inverse problem of magnetostatics and series of direct problems

The article presents a verification technique for solving the inverse geometric problem of magnetostatics in a soft magnetic ferromagnet plate. The technique involves solving a number of direct problems, in which the shape of the defect obtained by solving the inverse geometric problem of magnetostatics is used as a first approximation, and then increasing or decreasing the depth of the defect without changing the shape of the boundary surface — comparing the topographies of the magnetic field components obtained during measurements above the plate surface and calculated (as a result of solving the direct problem) at the same points of the components of the magnetic stray field from the reconstructed three-dimensional defect. As a result of applying the technique, the geometric parameters of the defect under study can also be refined. Obtaining the initial conditions for solving the inverse problem and solving direct problems of magnetostatics is carried out using the finite element method in the ELMER program. The technique works with one-sided access to any surface of the plate (a defect-free surface or a surface with a defect).

Zonal shape reconstruction for Shack-Hartmann sensors and deflectometry

Some metrological means, such as Shack-Hartmann, deflectometry sensors or fringe projection profilometry, measure the shape of an optical surface indirectly from slope measurements. Zonal shape reconstruction, a method to reconstruct shape with a high number of degrees of freedom, is used for all of these applications. It has risen in interest with the use of deflectometers for the acquisition of high resolution slope data for optical manufacturing, especially because shape reconstruction is limiting in terms of shape estimation error.Zonal reconstruction methods all rely on the choice of a data formation model, a basis on which the shape will be decomposed, and an estimator. In this paper, we first study the canonical Fried and Southwell models of the literature and analyze their limitations. We show that modeling the slope measurement by a point-wise derivative as they both do can induce a bias on the shape estimation, and that the bases on which the shape is decomposed are imposed because of this assumption.In the second part of this paper, we propose to build an unbiased model of the data formation, without constraints on the choice of the decomposition basis. We then compare these models to the canonical models of Fried and Southwell.Lastly, we perform a regularized MAP reconstruction, and compare the performance in terms of total shape error of this method to the state of the art for the Southwell and Fried models, first by simulation, then on experimental data. We demonstrate that the suggested method outperforms the canonical models in terms of total shape reconstruction error on a deflectometry measurement of the high-frequency content of a freeform mirror.

Poloidal magnetic field reconstruction by laser-driven ion-beam trace probe in spherical tokamak

The poloidal magnetic field ( plays a critical role in plasma equilibrium, confinement and transport of magnetic confinement devices. Multiple diagnostic methods are needed to complement each other to obtain a more accurate profile. Recently, the laser-driven ion-beam trace probe (LITP) has been proposed as a promising tool for diagnosing and radial electric field ( ) profiles in tokamaks [Yang X Y et al 2014 Rev. Sci. Instrum. 85 11E429]. The spherical tokamak (ST) is a promising compact device with high plasma beta and naturally large elongation. However, when applying LITP to diagnosing in STs, the larger invalidates the linear reconstruction relationship for conventional tokamaks, necessitating the development of a nonlinear reconstruction principle tailored to STs. This novel approach employs an iterative reconstruction method based on Newton’s method to solve the nonlinear equation. Subsequently, a simulation model to reconstruct the profile of STs is developed and the experimental setup of LITP is designed for EXL-50, a middle-sized ST. Simulation results of the reconstruction show that the relative errors of reconstruction are mostly below 5%. Moreover, even with 5 mm measurement error on beam traces or 1 cm flux surface shape error, the average relative error of reconstruction remains below 15%, initially demonstrating the robustness of LITP in diagnosing profiles in STs.

Thrust Model and Trajectory Design of an Interplanetary CubeSat with a Hybrid Propulsion System

This paper analyzes the performance of an interplanetary CubeSat equipped with a hybrid propulsion system (HPS), which combines two different types of thrusters in the same deep space vehicle, in a heliocentric transfer between two assigned (Keplerian) orbits. More precisely, the propulsion system of the CubeSat considered in this work consists of a combination of a (low-performance) photonic solar sail and a more conventional solar electric thruster. In particular, the characteristics of the solar electric thruster are modeled using a recent mathematical approach that describes the performance of the miniaturized engine that will be installed on board the proposed ESA’s M-ARGO CubeSat. The latter will hopefully be the first interplanetary CubeSat to complete a heliocentric transfer towards a near-Earth asteroid using its own propulsion system. In order to simplify the design of the CubeSat attitude control subsystem, we assume that the orientation of the photonic solar sail is kept Sun-facing, i.e., the sail reference plane is perpendicular to the Sun-CubeSat line. That specific condition can be obtained, passively, by using an appropriate design of the shape of the sail reflective surface. The performance of an HPS-based CubeSat is analyzed by optimizing the transfer trajectory in a three-dimensional heliocentric transfer between two closed orbits of given characteristics. In particular, the CubeSat transfer towards the near-Earth asteroid 99942 Apophis is studied in detail.

Weak overcomes strong in sensory integration: shading warps the disparity field

Human perception is often based on the integration of multiple sensory cues, where more statistically reliable cues are considered to have stronger influence on the percept. For example, in three-dimensional shape perception, binocular disparity is considered the most reliable cue at close distances, while pictorial cues like shading are considered less reliable. In three within-subject experiments, we instead show that shading can override disparity, a result that cannot be explained by its measured reliability, cue vetoing or cue promotion. Observers judged the shape of a disparity surface that was combined with different shading patterns. In all tests, shading altered the perceived shape specified by a strong disparity signal in a way that could not be predicted by standard accounts of three-dimensional perception. We find an example of unaccounted for cue cooperation, where shading becomes strong when it interacts with disparity.

Comparison of stability analysis methods for safe design of volcanic rock slope

The performance of the stability chart (SC), limit equilibrium (LE), and finite element (FE) methods for stability analysis of weathered volcanic rock slopes under static and earthquake loads is not fully understood. This research aimed to evaluate the performance of the SC, LE, and FE methods for slope stability analyses by studying a case of a weathered volcanic rock slope at the Leuwikeris Dam diversion tunnel in Indonesia. Site characterisations were carried out to obtain the input parameters for the static and pseudostatic slope stability analyses. The results showed that using various search methods of failure surface and the suggested optimum number of finite elements, multiple non-circular failure surfaces were predicted from the LE and FE methods that were not anticipated in the initial slope design based on the SC method. The location and shape of the failure surfaces from the LE method agreed with those from the FE method. The difference between the Fs values from the static LE analysis and those from the static FE analyses was less than 14%, but the discrepancy increased up to 78% in the pseudostatic analyses. This study highlights the importance of validating the results from one method with the other methods to prevent slope failures.