Gaussian Surface Research Articles

Propagation properties of finite Airy beams on curved surfaces.

Airy beams have provided exciting inspiration in the field of optical communication, particle manipulation, and imaging. We investigate the propagation properties of the exponential truncation Airy beams (ETABs) on constant Gaussian curvature surfaces (CGCSs) in this paper. The analytical expression of the electric field of ETABs propagating on the CGCSs is derived. It shows that the equivalent periodical accelerations of the trajectories of ETABs on the curved surface are always larger than the constant one on the flat surface because the CGCSs have a strong focusing ability. For the same reason, the non-diffraction propagation of ETABs is found when the focusing ability of the CGCSs is strong enough. Moreover, we investigate the self-healing length of ETABs on CGCSs and explore that the ability of self-healing is related to the geometry of CGCSs besides the width of the block and the size of the beam. The self-healing length gets larger with the increase of radius of CGCSs and finally consists with that on the flat surface. These propagation characteristics are different from those in the flat space and are useful for the future applications of ETABs in particle manipulation on waveguides, light-sheet fluorescence microscopy, curved nanophotonics, and so on.

An evolving ensemble model of multi-stream convolutional neural networks for human action recognition in still images

Still image human action recognition (HAR) is a challenging problem owing to limited sources of information and large intra-class and small inter-class variations which requires highly discriminative features. Transfer learning offers the necessary capabilities in producing such features by preserving prior knowledge while learning new representations. However, optimally identifying dynamic numbers of re-trainable layers in the transfer learning process poses a challenge. In this study, we aim to automate the process of optimal configuration identification. Specifically, we propose a novel particle swarm optimisation (PSO) variant, denoted as EnvPSO, for optimal hyper-parameter selection in the transfer learning process with respect to HAR tasks with still images. It incorporates Gaussian fitness surface prediction and exponential search coefficients to overcome stagnation. It optimises the learning rate, batch size, and number of re-trained layers of a pre-trained convolutional neural network (CNN). To overcome bias of single optimised networks, an ensemble model with three optimised CNN streams is introduced. The first and second streams employ raw images and segmentation masks yielded by mask R-CNN as inputs, while the third stream fuses a pair of networks with raw image and saliency maps as inputs, respectively. The final prediction results are obtained by computing the average of class predictions from all three streams. By leveraging differences between learned representations within optimised streams, our ensemble model outperforms counterparts devised by PSO and other state-of-the-art methods for HAR. In addition, evaluated using diverse artificial landscape functions, EnvPSO performs better than other search methods with statistically significant difference in performance.

Scattering of partially coherent vortex beam by rough surface in atmospheric turbulence.

A double-passage propagation model of partially coherent Laguerre-Gaussian (LG) vortex beams with orbital angular momentum (OAM) modes in turbulent atmosphere after scattering from Gaussian rough surfaces was formulated. Rough surface scattering had a weak effect on the spreading of a vortex beam in turbulent atmosphere. However, it severely influenced the phase on this beam, rapidly reducing the original OAM mode's relative intensity. The OAM spectrum information is more useful than the intensity information for rough surface object remote sensing. Additionally, by comparing the scattering intensity in monostatic and bistatic systems, the enhanced backscatter of vortex beams from Gaussian rough surfaces was verified.

Threshold speed of short journal bearings considering the non-Gaussian longitudinal surface roughness

During the actual machining process of journal surface, such as milling and fine turning, the surface roughness has strong non-Gaussianity. Thus, the effect of non-Gaussian longitudinal roughness on threshold speed of short journal bearings is investigated in this study. Introducing the parameters of kurtosis and skewness, the model of non-Gaussian surface roughness is established by modifying the Gaussian distribution. It is found that the non-Gaussianity of surface roughness cannot be neglected especially for the journal rotating with a larger eccentricity ratio, the error of Gaussian distribution surface reaches 19.33% when the eccentricity ratio equal 0.7. The increasing of kurtosis would reduce the threshold speed, while the increasing of skewness would enhance the threshold speed. For a larger eccentricity ratio, the effect of kurtosis and skewness on threshold speed is more distinctly.

A procedure for numerically model surface of the corroded specimen

ABSTRACT The paper presents a procedure for numerically modelling the surface of corroded specimens. A 3D laser scan is utilised to derive surface morphology and corrosion pit depth distribution. This corrosion depth is analyzed with a probability model to assess the morphology difference and the characteristic of the corrosion pit depth at a particular volumetric change. Furthermore, the goodness fit test statistic is carried out to observe the propensity of corrosion depth to a specific distribution, i.e. the Gaussian and non-Gaussian. The corroded specimens that conform to Gaussian distribution are numerically modelled with ANSYS APDL to generate a Gaussian surface. Furthermore, the non-Gaussian surface model is simplified as a single corrosion pit with various geometrical shapes. The mesh convergence is carried out to provide accurate stress distribution . The procedure is adjustable and applicable to the other surface morphology.

Radar Imaging Statistics of Non-Gaussian Rough Surface: A Physics-Based Simulation Study

This paper investigates the radar image statistics of rough surfaces by simulating the scattered signal’s dependence on the surface roughness. Statistically, the roughness characteristics include the height probability density (HPD) and, to the second-order, the power spectral density (PSD). We simulated the radar backscattered signal by computing the far-field scattered field from the rough surface within the antenna beam volume in the context of synthetic aperture radar (SAR) imaging. To account for the non-Gaussian height distribution, we consider microscopic details of the roughness on comparable radar wavelength scales to include specularly, singly, and multiply scatterers. We introduce surface roughness index (RSI) to distinguish the statistical characteristics of rough surfaces with different height distributions. Results suggest that increasing the RMS height does not impact the Gaussian HPD surface but significantly affects the Weibull surface. The results confirm that as the radar frequency increases, or reaches a relatively larger roughness, the surface’s HPD causes significant changes in incoherent scattering due to more frequent multiple scattering contributions. As a result, the speckle move further away from the Rayleigh model. By examining individual RSI, we see that the Gaussian HPD surface is much less sensitive to RMS height than the Weibull HPD surface. We demonstrate that to retrieve the surface parameters (both dielectric and roughness) from the estimated RCS, less accuracy is expected for the non-Gaussian surface than the Gaussian surface under the same conditions. Therefore, results drawn from this study are helpful for system performance evaluations, parameters estimation, and target detection for SAR imaging of a rough surface.

Numerical analysis of the correlation between the pitting severity and surface roughness of corroded specimens

ABSTRACT Repeated wet–dry cycle exposure to seawater during ballasting processes hastens the surface corrosion rate. Moreover, the larger volumetric changes of corroded ballast tanks generate lower pitting severity. This paper models the pitting severity of corroded ballast tanks of varying roughness and volumes. Seven rectangular finite elements models with Gaussian rough surfaces are examined. The surface roughness modelling is analyzed with correlation among corrosion-statistical parameters at various corroded specimen volume changes. Additionally, the paper elaborates the severity of pitting corrosion characteristics using the pitting factor and the relationship between the maximum and average pit depth. The pitting severity – volumetric changes scenario investigates the model’s stress distribution, showing that the greater change in volume and lower pitting severity tend to have a lower stress distribution, which is randomly concentrated on the larger area. Comparison of the theoretical results with physical test data using 3D laser scans indicates a close match.

Deep Learning for the Detection and Phase Unwrapping of Mining-Induced Deformation in Large-Scale Interferograms

This article proposes deep convolutional neural networks to detect and map localized, rapid subsidence caused by mining activities using time-series Sentinel-1 synthetic aperture radar (SAR) images. A deformation detection network (DDNet) is developed to automatically identify rapidly subsiding areas from wrapped interferograms, and a phase unwrapping network (PUNet) is designed to unwrap the cropped interferogram patches centered on the detected subsiding locations. To train the two networks, interferogram simulation strategies are developed to generate various training samples using the distorted 2-D Gaussian surface and fractal Perlin noises. The performance of the DDNet is verified by simulations on a synthetic dataset with 13 large interferograms, while the PUNet is evaluated by simulations using synthetic datasets with different levels of deformation gradients and noises. Compared with the traditional and deep-learning methods, the PUNet exhibits excellent performance and efficiency in unwrapping interferograms with rapid mining-induced deformation. The proposed networks are further verified by applying them to Shanxi province, China, which is characterized by serious ground subsidence hazards caused by long-term coal mining activities. The time-series deformations of 1344 detected subsidence areas are calculated with the vertical velocities ranging from −19.7 to −254.8 cm/year. The results are validated using the ascending and descending Sentinel-1 Interferograms and an L-band ALOS-2 interferogram covering the same area within the acquisition period, showing highly consistent vertical deformation rates. The proposed strategy and methods introduce deep learning to the time-series interferometric SAR (InSAR) processing chain and may have profound implications on the detection and monitoring of localized mining-induced deformation using InSAR.

In-bucket Garbage Shape Estimation based on Time-varying Gaussian Process Implicit Surface using Proximity Sensor

In-bucket Garbage Shape Estimation based on Time-varying Gaussian Process Implicit Surface using Proximity Sensor

Average Infrared Brightness Temperature of Lunar Rough Surface in Field of View of High-Resolution Infrared Radiation Sounder and Application to Calibration

The Moon’s surface shows long-term stability and may be a suitable candidate of thermal calibration source. When the field of view (FOV) of an Earth radiometer, e.g., the high-resolution infrared radiation sounder (HIRS), occasionally scans across the Moon, it measures the average brightness temperature (TB) of the entire nearside of the Moon. The lunar surface roughness causes changes in the surface emissivity and anisothermality. Analysis of the infrared TB (IR TB) of the lunar surface from the nadir observations of the Diviner IR radiometer showed that the IR TB difference (TB-D) between the Diviner channels is largest near sunrise and sunset, when the anisothermality is most significant. In this article, the nearside of the lunar surface is divided into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$30\times 30$ </tex-math></inline-formula> subregions, where a rough surface is constructed using small triangular meshes. The ray-tracing method is used to determine the shaded meshes. Heat conduction equations are solved for the temperatures of all meshes. The simulated IR TB and TB-D are compared with the Diviner data. The thermal emissions of Gaussian rough surfaces with different height variances, the cratered surface with digital elevation model, and two-scale rough surface are simulated to discuss the influence of topographies. Under nonnadir observation conditions, the ray-tracing method is used to determine the visibility of each mesh in the detector’s FOV. The IR TB characteristics are asymmetric with respect to the emission angle. The average IR TB of the nearside of the Moon at the wavelength of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$14~\mu \text{m}$ </tex-math></inline-formula> is obtained and compared with the IR TB derived from HIRS data. The rough surface model can more feasibly describe the average IR TB data than flat surface model and is favorable for HIRS calibration/validation.

3D Finite-Element Forward Modeling of Airborne EM Systems in Frequency-Domain Using Octree Meshes

The 3-D airborne electromagnetic (AEM) inversions have been restricted by the modeling efficiency resulting from the complex geology in exploration areas and massive amount of data collected by AEM systems. In order to improve the modeling efficiency, we develop an algorithm that combines the hexahedral vector finite element (FE) with octree meshes, in which the boundary conditions are imposed via an algebraic constraint to ensure the continuity of the FE solution. This makes the division with hexahedral meshes more flexible for complex geology such as rugged topography or underground structures so that we can reduce the number of elements while maintaining the accuracy. After formulating the forward problem, we check the accuracy of our algorithm by taking a homogeneous half-space model and comparing the results of our octree method with the semianalytical solutions. Furthermore, we demonstrate the efficiency of our octree method by comparing with the traditional FE method using tetrahedral meshes. Finally, we subdivide a complex topography constructed using the 2-D Gaussian rough surface and calculate the EM responses with and without anomaly embedded. The results show that the EM responses are overwhelmed by the Earth topography. We carry out the topographic correction by taking a method based on the ratio of EM responses with and without anomaly. The experiments show that after topographic correction to AEM data, the response of anomaly becomes more distinguishable so that the anomaly can be clearly identified. Furthermore, we also calculate the EM response for a realistic model&#x2014;the Ovoid Zone ore body located at Voisey&#x2019;s Bay, Labrador, Canada, to verify the flexibility and practicality of our algorithm.

Topological defects and nanoholes in graphene oxide/hexagonal boron nitride heterostructures: stress buildup and accumulation.

The built-in distorted stress field of graphene (Gr) and its derivatives in defective state will induce local geometrical buckling due to the geometry of monatomic layer. The random distribution and types of functional groups (FGOs) and defects will have a significant impact on the stress accumulation and geometrical deformation of two-dimensional (2D) materials. By using molecular dynamics (MD), structure design and nonlinear mechanics theory, a new model (combining both planar 2D heterostructures and graphene oxide (GO)) was established to study geometrical effects, stress accumulation, bonding energies and mechanical properties of 2D interface (key point) at stress distortion field and accumulated stress field. The results show that grain boundaries (GBs), nanoholes and FGOs have different effects on the mechanical properties and out-of-plane deformation of 2D materials. By using Von-mises stresses and statistical mechanics, the geometrical effects, built-in distortion stress transfer and attenuation appeared in the each domain of 2D materials during the order-disorder transition processes. Moreover, there are two opposite aspects of stress accumulation, transmission, attenuation and geometrical effects of grain boundary (GBs), FGOs and nanoholes with distance. The ratio of strain energy (bond length and angle) is very sensitive to each domain of 2D materials. Finally, the 2D planar configuration gradually changes to a negative Gaussian surface, and the softening and weakening effects induced by GBs, nanoholes and FGOs are gradually enhanced. It is hoped that the current results can be used as a guide to adjust the geometry and stress accumulation of 2D materials in the new growth point.

A new technique for modelling phonon scattering processes at rough interfaces and free boundaries of solids

Scattering processes at interfaces and free boundaries of solids strongly affect heat transfer in micro- and nanostructures such as integrated circuits, periodic nanostructures, multilayer thin films, and other nanomaterials. Among many influencing factors, surface roughness due to atomic disorder plays a significant role in the rate of thermal transport. Existing approaches have been developed only for the limiting cases of smooth or completely diffuse surfaces. We have developed a new effective and simple method based on a direct consideration of the scattering of elastic waves from a statistically random profile (using a normal Gaussian surface as an example). This approach, first, allows to generalize common methods for determining the thermal properties of a real random rough surface using simple modifications, and, second, provides a tool for calculating the Kapitza conductance and the effective longitudinal thermal conductivity and studying the influence of roughness on heat transfer.

End-exclusion zones in strongly stretched, molten polymer brushes of arbitrary shape.

Theories of strongly stretched polymer brushes, particularly the parabolic brush theory, are valuable for providing analytically tractable predictions for the thermodynamic behavior of surface-grafted polymers in a wide range of settings. However, the parabolic brush limit fails to describe polymers grafted to convex curved substrates, such as the surfaces of spherical nanoparticles or the interfaces of strongly segregated block copolymers. It has previously been shown that strongly stretched curved brushes require a boundary layer devoid of free chain ends, requiring modifications of the theoretical analysis. While this "end-exclusion zone" has been successfully incorporated into the descriptions of brushes grafted onto the outer surfaces of cylinders and spheres, the behavior of brushes on surfaces of arbitrary curvature has not yet been studied. We present a formulation of the strong-stretching theory for molten brushes on the surfaces of arbitrary curvature and identify four distinct regimes of interest for which brushes are predicted to possess end-exclusion zones, notably including regimes of positive mean curvature but negative Gaussian curvature. Through numerical solutions of the strong-stretching brush equations, we report predicted scaling of the size of the end-exclusion zone, the chain end distribution, the chain polarization, and the free energy of stretching with mean and Gaussian surface curvatures. Through these results, we present a comprehensive picture of how the brush geometry influences the end-exclusion zones and exact strong-stretching free energies, which can be applied, for example, to model the full spectrum of brush geometries encountered in block copolymer melt assembly.

A comparative study for selecting and using simulation methods of Gaussian random surfaces

Conventional methods for generating Gaussian random surfaces, including the moving average (MA) time series model with nonlinear conjugate gradient method (NCGM), two-dimensional (2-D) digital filter method, and spectral representation method (SRM), are implemented with a wide range of autocorrelation length and truncation length values of the autocorrelation function (ACF). The ACF, power spectral density function (PSDF), and essential roughness parameters of the simulated surfaces are calculated and compared. Based on the simulation results, the mechanism of the truncation length of ACF affecting the simulated surfaces can be summarized as that the step formed by truncating ACF is not sufficiently small, thus resulting in non-negligible errors in the corresponding PSDF. Such errors will be propagated to the simulated surfaces. A conservative criterion is proposed to avoid the adverse effects of truncating ACF: make the autocorrelation length less than 8% of the surface dimensions and the truncation length at least seven times autocorrelation length. The results show that the MA model with NCGM overestimates the PSDF values of simulated surfaces in the high-frequency region, meaning significant high-frequency noise in the simulated surfaces. The 2-D digital filter method and the SRM have almost the same performance, and both methods are better than the MA model with NCGM when the criterion of truncating ACF is fulfilled. The SRM generates rough surfaces with the smallest standard deviation in terms of the roughness parameters, ACF, and PSDF in most cases, meaning that it can generate accurate surfaces at every single simulation and is more stable and efficient. Therefore, the SRM is the most recommended method among the three methods studied.

Isotherm penetration depth under a moving Gaussian surface heat source on a thick substrate

This paper presents novel explicit exDEFAULTpressions for the penetration depth of an isotherm induced by a moving heat Gaussian source on a semi-infinite solid. This work is novel in its methodology of dimensional analysis, asymptotics, and blending of more than one parameter, and provides closed form expressions of high accuracy compared to the exact solution. The solutions obtained are based on the governing equations, not on empirical fittings, and are valid for any material and heat source that are captured by the original governing differential equations. Previous scaling laws for penetration depth of temperature due to moving heat sources were based on point heat sources, and predicted a finite penetration under all conditions, which is against observations that penetration becomes zero for heat sources that are too weak, too distributed, or too fast. This discrepancy is especially relevant for modern processes such as laser heat treatment, laser cladding, and additive manufacturing of metals using lasers; the analysis and expressions presented here account for all those effects. The dimensionless maximum isotherm penetration depth depends on two dimensionless groups: the heat source distribution parameter and the Rykalin number associated with the velocity of the heat source. Previous work on blending involved a single parameter, and a novel extension of the blending technique is presented here to tackle the increased complexity. Maximum isotherm penetration depth is determined for the first time with explicit closed-form expressions over a wide range of heat distributions and Rykalin numbers with an error below 9.7% against the exact solution. The proposed equations are validated against experiments reported in the literature. The expressions developed can be evaluated using a handheld calculator or a spreadsheet and are suitable for practitioners in industry to optimize process parameters and for researchers to validate numerical models.

Spectral analysis of the topography parameters for isotropic Gaussian rough surfaces applied to gold coating

In the fabrication of microelectronic devices, sputtering of thin films leads to isotropic rough surfaces described by (i) a Gaussian height distribution and (ii) a constant power spectral density (PSD) up to a roll-off frequency of q0 from which it decays as a power law. This paper introduces a robust approach to estimate the topography parameters such as the density, the mean radius of curvature and the height distribution of summits for isotropic Gaussian rough micro-surfaces. The proposed approach consists of computing the PSD function from the atomic force microscopy measurements, approximating the value of q0 and the magnitude P0 of the plateau by curve fitting algorithms, and analytically deriving the topography parameters using the random process theory. The robustness of the proposed methodology is assessed on a sputtered gold micro-surface. The investigations show that the proposed PSD-based approach reduces the dependence of the topography parameters on the sampling length compared to the deterministic method. Moreover, the PSD-based estimated density of summits is in a good agreement with scanning electron microscopy analysis, in contrast to both deterministic and autocorrelation-based methods. The proposed approach is therefore more suitable to extract topography parameters from measurements of micro-surfaces for the development of contact asperity-based models.

Spatial and Temporal Analysis of Surface Urban Heat Island and Thermal Comfort Using Landsat Satellite Images between 1989 and 2019: A Case Study in Tehran

Mapping and monitoring the spatio-temporal variations of the Surface Urban Heat Island (SUHI) and thermal comfort of metropolitan areas are vital to obtaining the necessary information about the environmental conditions and promoting sustainable cities. As the most populated city of Iran, Tehran has experienced considerable population growth and Land Cover/Land Use (LULC) changes in the last decades, which resulted in several adverse environmental issues. In this study, 68 Landsat-5 and Landsat-8 images, collected from the Google Earth Engine (GEE), were employed to map and monitor the spatio-temporal variations of LULC, SUHI, and thermal comfort of Tehran between 1989 and 2019. In this regard, planar fitting and Gaussian Surface Model (GSM) approaches were employed to map SUHIs and derive the relevant statistical values. Likewise, the thermal comfort of the city was investigated by the Urban Thermal Field Variance Index (UTFVI). The results indicated that the SUHI intensities have generally increased throughout the city by an average value of about 2.02 °C in the past three decades. The most common reasons for this unfavorable increase were the loss of vegetation cover (i.e., 34.72%) and massive urban expansions (i.e., 53.33%). Additionally, the intra-annual investigations in 2019 revealed that summer and winter, with respectively 8.28 °C and 4.37 °C, had the highest and lowest SUHI magnitudes. Furthermore, the decadal UTFVI maps revealed notable thermal comfort degradation of Tehran, by which in 2019, approximately 52.35% of the city was identified as the region with the worst environmental condition, of which 59.94% was related to human residents. Additionally, the relationships between various air pollutants and SUHI intensities were appraised, suggesting positive relationships (i.e., ranging between 0.23 and 0.43) that can be used for establishing possible two-way mitigations strategies. This study provided analyses of spatio-temporal monitoring of SUHI and UTFVI throughout Tehran that urban managers and policymakers can consider for adaption and sustainable development.

Morphological principles of neuronal mitochondria.

In the highly dynamic metabolic landscape of a neuron, mitochondrial membrane architectures can provide critical insight into the unique energy balance of the cell. Current theoretical calculations of functional outputs like adenosine triphosphate and heat often represent mitochondria as idealized geometries, and therefore, can miscalculate the metabolic fluxes. To analyze mitochondrial morphology in neurons of mouse cerebellum neuropil, 3D tracings of complete synaptic and axonal mitochondria were constructed using a database of serial transmission electron microscopy (TEM) tomography images and converted to watertight meshes with minimal distortion of the original microscopy volumes with a granularity of 1.64 nanometer isotropic voxels. The resulting in-silico representations were subsequently quantified by differential geometry methods in terms of the mean and Gaussian curvatures, surface areas, volumes, and membrane motifs, all of which can alter the metabolic output of the organelle. Finally, we identify structural motifs present across this population of mitochondria, which may contribute to future modeling studies of mitochondrial physiology and metabolism in neurons.

Influence of hexadecylphosphocholine (Miltefosine) in phytantriol-based cubosomes: A structural investigation

Miltefosine (hexadecylphosphocholine, HePC) is a broad spectrum antimicrobial, anti-leishmanial drug, originally developed as anti-cancer agent. Because of its toxic side effects, several nanotechnology-based formulations have been considered as carriers for HePC. It is clear that the loading efficiency and bioavailability are strongly correlated to structural properties of the considered nanocarries. Therefore, the interplay between the structure stability and the entrapped compounds is worthy of investigation. In the present study, we evaluated the structural properties of phytantriol (PHY) cubosomes prepared in full hydrated conditions in the presence of increasing HePC concentrations. Dynamic Light scattering (DLS), cryogenic transmission electron microscopy (cryo-TEM) and small angle X-ray scattering (SAXS) were used. According to our data, HePC did not influence the nanoparticle average size at least up to 10 mol% HePC/PHY, even if the nanoparticle polydispersity index (PDI) increased by two-fold. On the other side, the nanoparticle inner structure shows a strong drug concentration dependence. Up to 3.5 mol%, the nanoparticles show a bicontinuous Pn3m Cubic internal structure, the lattice parameter of which increases as far as HePC is added to the system. The calculated structural data suggest that the HePC mixing with phytantriol induces a larger hydration capacity of the lipid polar surfaces. For HePC concentrations higher than 7.0 mol%, the internal structure of cubosomes is characterized by the coexistence of Pn3m and Im3m bicontinuous cubic phases, indicating that the swelling of the Pn3m phase arrived at saturation. The calculated number of water molecules per lipid in the cubic unit cell confirms such an indication. The structural parameters derived for the two cubic phases also indicate that HePC influence modify the negative Gaussian surface of the cubosomes.