Rough Boundary Research Articles

Terahertz Emission Modeling of Lunar Regolith

We investigate the terahertz (THz) scattering and emission properties of lunar regolith by modeling it as a random medium with rough top and bottom boundaries and a host medium situated beneath. The total scattering and emission arise from three sources: the rough boundaries, the volume, and the interactions between the boundaries and the volume. To account for these sources, we model their respective phase matrices and apply the matrix doubling approach to couple these phase matrices to compute the total emission. The model is then used to explore insights into lunar regolith scattering and emission processes. The simulations reveal that surface roughness is the primary contributor to total scattering, while dielectric contrasts between the volume and the boundaries dominate total emission. The THz emissivity is highly sensitive to the regolith dielectric constant, particularly its imaginary part, making it a promising alternative for identifying previously undetected water ice in the lunar polar regions. The THz emissivity model developed in this study can be readily applied to invert the surface parameters of lunar regolith using THz observations.

Effects of asymmetric rough boundaries on turbulent Rayleigh–Bénard convection

We report on an experimental study of turbulent Rayleigh–Bénard convection with asymmetric top and bottom plates. The plates are covered with pyramid-shaped roughness elements whose aspect ratios are $\lambda =1$ or $\lambda =4$ . In the low-Rayleigh-number regime ( $Ra<1.9\times 10^9$ ), the heat transport efficiencies in the asymmetric cells, characterized by the Nusselt number, are smaller than those measured in a symmetric $\lambda = 1$ cell and are greater than those for a symmetric $\lambda = 4$ cell, whereas in the high-Rayleigh-number regime ( $Ra>1.9\times 10^9$ ), the Nusselt numbers of the asymmetric cells are, in turn, greater than those for the symmetric cell with $\lambda = 1$ and smaller than those for the symmetric cell with $\lambda = 4$ . In addition, the heat transports of individual plates are studied based on the temperature drops across both halves of the cell. In the low- $Ra$ regime, the $\lambda =1$ plate shows higher heat transfer than the $\lambda =4$ plate, while for the high- $Ra$ regime, the $\lambda =4$ plate shows a higher heat transport ability. In both regimes, the individual Nusselt number of the plate with lower heat transfer is insensitive to the topology of the other plate. Besides, it is found that the symmetry of the centre temperature distribution is robust to the symmetry breaking of boundary topographies. For the $Ra$ range explored, a weak temperature inversion is observed in the bulk of asymmetric rough cells. Finally, we remark that the temperature fluctuation at the cell centre and the Reynolds number associated with the large-scale circulation show universal power laws in terms of the flux Rayleigh number as $\sigma _{T_{c}}\sim Ra_F^{0.68}$ and $Re_{LSC}\sim Ra_F^{0.36}$ , respectively.

Existence and Regularity of Random Attractors for Stochastic Evolution Equations Driven by Rough Noise

AbstractThis work establishes the existence and regularity of random pullback attractors for parabolic partial differential equations with rough nonlinear multiplicative noise under natural assumptions on the coefficients. To this aim, we combine tools from rough path theory and random dynamical systems. An application is given by partial differential equations with rough boundary noise, for which flow transformations are not available.

Interaction of a UWB impulse with a layer of sandy soil, having a rough upper boundary

ABSTRACT In this paper, the changes in the character of time shapes, amplitudes, frequency spectra, and time delay of ultra-wideband (UWB) impulses (duration of 0.33 ns) reflected from the layer of wet sand with a rough upper boundary were investigated. It was shown that the attenuation of UWB impulse amplitude, which is reflected from the upper rough boundary of the sand layer, can be described by the model of Fresnel reflection coefficient for a smooth surface using the Gaussian correction factor (FRGC). At this root-mean-square (RMS), height of soil surface roughness was in the range of ~0–21 mm, but the determination coefficient and RMS error (RMSE) were found to be equal to 0.94 and 0.02, respectively. An experiment close to linear increase/decrease in the propagation time of impulses reflected from the upper/lower boundary of the layer, respectively, was found with increasing the RMS heights of upper boundary. It is shown that the propagation time of such impulses can be described by the modified FRGC model with an error from RMSE = 0.09 ns to RMSE = 0.15 ns. The results of these findings are of practical importance for the interpretation of remote sensing data for precise soil moisture measurements from unmanned aerial vehicle platforms using UWB impulses.

Generalized cluster states from Hopf algebras: non-invertible symmetry and Hopf tensor network representation

Cluster states are crucial resources for measurement-based quantum computation (MBQC). It exhibits symmetry-protected topological (SPT) order, thus also playing a crucial role in studying topological phases. We present the construction of cluster states based on Hopf algebras. By generalizing the finite group valued qudit to a Hopf algebra valued qudit and introducing the generalized Pauli-X operator based on the regular action of the Hopf algebra, as well as the generalized Pauli-Z operator based on the irreducible representation action on the Hopf algebra, we develop a comprehensive theory of Hopf qudits. We demonstrate that non-invertible symmetry naturally emerges for Hopf qudits. Subsequently, for a bipartite graph termed the cluster graph, we assign the identity state and trivial representation state to even and odd vertices, respectively. Introducing the edge entangler as controlled regular action, we provide a general construction of Hopf cluster states. To ensure the commutativity of the edge entangler, we propose a method to construct a cluster lattice for any triangulable manifold. We use the 1d cluster state as an example to illustrate our construction. As this serves as a promising candidate for SPT phases, we construct the gapped Hamiltonian for this scenario and provide a detailed discussion of its non-invertible symmetries. We demonstrate that the 1d cluster state model is equivalent to the quasi-1d Hopf quantum double model with one rough boundary and one smooth boundary. We also discuss the generalization of the Hopf cluster state model to the Hopf ladder model through symmetry topological field theory. Furthermore, we introduce the Hopf tensor network representation of Hopf cluster states by integrating the tensor representation of structure constants with the string diagrams of the Hopf algebra, which can be used to solve the Hopf cluster state model.

Strong barriers for weighted quasilinear equations

In potential theory, use of barriers is one of the most important techniques. We construct strong barriers for weighted quasilinear elliptic operators. There are two applications: (i) solvability of Poisson-type equations with boundary singular data, and (ii) a geometric version of Hardy inequality. Our construction method can be applied to a general class of divergence form elliptic operators on domains with rough boundary.

Cartographic Generalization of Islands Using Remote Sensing Images for Multiscale Representation

The multi-scale representation of remote sensing images provides various levels of image information crucial for decision-making in GIS applications and plays a significant role in information processing, data analysis, and geographic modeling. Traditional methods for multi-scale representation of remote sensing images often struggle to simplify local details of individual targets while preserving the overall characteristics of target groups. These methods also encounter issues such as transitional texture distortion and rough final boundaries. This paper proposes a novel multi-scale representation method for remote sensing images based on computer vision techniques, which effectively maintains the overall characteristics of target groups. Initially, the K-means algorithm is employed to distinguish between islands and oceans. Subsequently, a superpixel segmentation algorithm is used to aggregate island groups and simplify the generated boundaries. Finally, texture synthesis and transfer are applied based on the original image to produce the aggregated island images. Evaluation metrics demonstrate that this method can generate multi-scale aggregated images of islands, effectively eliminate redundant information, and produce smooth boundaries.

Uniqueness, regularity, continuity, and stability of solutions of integral equations in irregular domains

This study explores the uniqueness, regularity, continuity, and stability of solutions to integral equations related to elliptical boundary value problems in irregular domains. Traditional methods usually consider soft boundaries, but this work extends these results to include domains with rough boundaries. By employing Sobolev spaces, especially fractional Sobolev spaces, we develop a comprehensive theoretical framework. Under appropriate conditions, the studied integral equation has a unique solution in fractional Sobolev spaces, maintaining the regularity properties of the input function. Two new theorems are introduced to strengthen the findings. The first theorem establishes that solutions are continuous with respect to perturbations in the input data. This means small changes in the input do not cause significant deviations in the solution, ensuring robustness in practical applications. The second theorem demonstrates the stability of the solutions when the domain geometry undergoes small changes. This stability is crucial for real-world scenarios where the exact shapes of domains may not be perfectly known or may vary slightly. These results significantly improve the mathematical understanding of boundary value problems in non-smooth domains. The proposed extended framework allows for more generalized applications, addressing challenges in various fields of physics and engineering. The ability to handle irregular domains with rough boundaries opens up new possibilities for modeling and solving complex problems where traditional soft boundary assumptions are not valid. This research provides a robust basis for future studies and applications, highlighting the importance of considering fractional Sobolev spaces in the analysis of integral equations.

Density-Based Isogeometric Topology Optimization of Shell Structures

Shell structures with high stiffness-to-weight ratios are desirable in various engineering applications. Topology optimization serves as a popular and effective tool for generating optimal shell structures. The solid isotropic material with penalization (SIMP) method is often chosen because of its simplicity and convenience. However, SIMP method is typically integrated with conventional Finite Element Analysis (FEA) which has limitations in computational accuracy. Achieving high accuracy with FEA necessitates a substantial number of elements, leading to computational burdens. In addition, the discrete representation of the material distribution function may result in rough boundaries. Owing to these limitations, this paper proposes an Isogeometric Analysis (IGA) based SIMP method for optimizing the topology of shell structures based on Reissner–Mindlin theory. This method uses Non-Uniform Rational B-Splines (NURBS) to represent both the shell structure and the material distribution function with the same basis functions, allowing for higher accuracy and smoother boundaries. The optimization model takes compliance as the objective function with a volume fraction constraint and the coefficients of the density function as design variables, resulting in an optimized shell structure defined by the material distribution function. To obtain fairing boundaries of the holes in the optimized shell structure, further process is conducted by fitting the boundaries with fair B-spline curves automatically. Furthermore, the proposed IGA-SIMP framework is applied to generate porous shell structures by imposing different local volume fraction constraints. Numerical examples are provided to demonstrate the feasibility and efficiency of the IGA-SIMP method, showing that it outperforms the FEA-SIMP method and produces smoother boundaries.

Realizing the High Efficiency of Type‐II Superlattice Infrared Sensors Integrated Wire‐Grid Polarizer via Femtosecond Laser Polishing

AbstractA comprehensive strategy to enhance the polarization performance of mid‐wave infrared photodetectors (PDs) is developed and implemented by integrating wire‐grid polarizers (WGPs) using nanoimprint lithography and femtosecond laser (FSL) polishing. This combined approach offers significant advantages, including large‐area fabrication capabilities, practical device integration, and improved polarization characteristics. By addressing optical losses, the primary factor contributing to polarization degradation through the thermal effects of FSL polishing, substantial improvements are achieved in surface roughness and grain boundary reduction on the WGP, resulting in remarkable performance enhancements. As a result, the extinction ratio of the integrated WGP InAs/GaSb type‐II superlattice PD achieves an impressive value of up to 1044. This approach holds promising potential for advancing polarization‐based imaging and measurement systems to new heights.

Boundary effect on the soil strength estimation from T-bar penetration tests

The T-bar penetration tests have gained widespread use in assessing the undrained shear strength of marine clays. However, when dealing with model tests or sampled soil with a small diameter of the tube, the reliability of T-bar test results is influenced by both the boundary effect and the soil flow mechanism around the T-bar. In this paper, a comprehensive investigation into the boundary effect on T-bar penetration resistance was conducted by using the large deformation finite element (LDFE) method in conjunction with laboratory tests. The study reveals that the boundary conditions significantly impact the T-bar resistance when the lateral boundary dimension is smaller than 12D. Specifically, the T-bar penetration resistance is underestimated for smooth boundaries and overestimated for rough boundaries. For soils with higher strength, a larger boundary size is required. The bottom boundary also affects the T-bar resistance until the full-flow mechanism is established. However, once the full-flow mechanism is achieved, the boundary effect on T-bar penetration resistance diminishes, even for small lateral boundary sizes (2D). Considering the fact that it is challenging to attain the full-flow mechanism, especially for higher strength soils, a simple algorithm is proposed to estimate soil strength based on a shallow penetration depth (2D). This algorithm is validated through laboratory tests. To address the difficulty in achieving the full-flow mechanism, by applying the overburden pressure during the T-bar test, a novel T-bar test method is suggested. This innovative approach promises to resolve the issue effectively.

Multi-Branch Attention Fusion Network for Cloud and Cloud Shadow Segmentation

In remote sensing image processing, the segmentation of clouds and their shadows is a fundamental and vital task. For cloud images, traditional deep learning methods often have weak generalization capabilities and are prone to interference from ground objects and noise, which not only results in poor boundary segmentation but also causes false and missed detections of small targets. To address these issues, we proposed a multi-branch attention fusion network (MAFNet). In the encoder section, the dual branches of ResNet50 and the Swin transformer extract features together. A multi-branch attention fusion module (MAFM) uses positional encoding to add position information. Additionally, multi-branch aggregation attention (MAA) in the MAFM fully fuses the same level of deep features extracted by ResNet50 and the Swin transformer, which enhances the boundary segmentation ability and small target detection capability. To address the challenge of detecting small cloud and shadow targets, an information deep aggregation module (IDAM) was introduced to perform multi-scale deep feature aggregation, which supplements high semantic information, improving small target detection. For the problem of rough segmentation boundaries, a recovery guided module (RGM) was designed in the decoder section, which enables the model to effectively allocate attention to complex boundary information, enhancing the network’s focus on boundary information. Experimental results on the Cloud and Cloud Shadow dataset, HRC-WHU dataset, and SPARCS dataset indicate that MAFNet surpasses existing advanced semantic segmentation techniques.

P‐196: Control of the Molecular Orientation in EML Using Substrate Temperature for Improving the Electro‐Optical Characteristics and Lifetime

In this paper, we controlled the molecular alignment property of the EML layer in horizontal direction by changing the substrate temperature (Tsub) during deposition at ‐4, 20, and 40 °C and observed the effect of molecular orientation characteristics of the EML on the electro‐optical characteristics and the lifetime of OLED devices. The color property of the devices fabricated in different Tsub show same properties, but the optical performance of the cells fabricated at ‐4 °C was better than those fabricated at high temperatures as we expected due to the horizontal component of the molecular orientation. In particular, as for the lifetime of the cell, we observed over 4 times longer lifetime of the cell fabricated at ‐4 °C than the cell fabricated at 40 °C. To analyze the cause of the increase in lifetime, we also observed the surface roughness and grain boundary of the EML fabricated in each Tsub conditions. In addition, more detail data including binding energies between the molecule and deformation data using major molecule weight are also presented either. As a result, we confirm that the Tsub during deposition strongly affects to the molecular anisotropy factor and we can improve the electro‐optical and lifetime performance of the OLED cell through low Tsub.

Elucidating optimal nanohole structures for suppressing phonon transport in nanomeshes

Nanomeshes, often referred to as phononic crystals, have been extensively explored for their unique properties, including phonon coherence and ultralow thermal conductivity (κ). However, experimental demonstrations of phonon coherence are rare and indirect, often relying on comparison with numerical modeling. Notably, a significant aspect of phonon coherence, namely the disorder-induced reduction in κ observed in superlattices, has yet to be experimentally demonstrated. In this study, through atomistic modeling and spectral analysis, we systematically investigate and compare phonon transport behaviors in graphene nanomeshes, characterized by 1D line-like hole boundaries, and silicon nanomeshes, featuring 2D surface-like hole boundaries, while considering various forms of hole boundary roughness. Our findings highlight that to demonstrate a disorder-induced reduction in κ of nanomeshes, optimal conditions include low temperature, smooth and planar hole boundaries, and the utilization of thick films composed of 3D materials.

High-resolution feature pyramid attention network for high spatial resolution images land-cover classification in arid oasis zones

ABSTRACT Land-cover classification based on remote sensing technology has been adopted for decision-making concerning agricultural development, urban planning, and ecosystem protection in arid oasis zones. The semantic segmentation method based on deep learning, as a new paradigm, can effectively overcome the limitations of traditional pixel-based and object-based methods and obtain good classification results from high spatial resolution (HSR) remote sensing images. However, how to extract the exact category boundary and realize the high precision mapping is still a problem. This paper proposes a novel high-resolution feature pyramid attention network (HRFPANet) for land-cover classification. It effectively integrates the advantages of multi-scale feature extraction, attention mechanism, and feature fusion and alleviates boundary inconsistency, roughness, and category fragmentation associated with previous semantic segmentation models. The experimental results show that the mIoU score of HRFPANet is 79.5%, which is 11.5% and 2.6% higher than that of PSPNet and UPerNet, respectively. It proves the proposed model can be used for qualified land-cover mapping in arid oasis zones. Our source code is available at https://github.com/HPU-CPD/HRFPANet.git.

Turbulent kinetic energy budget of sediment-laden open-channel flows: bedload-induced wall-roughness similarity

New experiments in highly turbulent, steady, subcritical and uniform water open-channel flows have been carried out to measure the mean turbulent kinetic energy (TKE) budget of sediment-laden boundary layer flows with two sizes (dp = 3 mm and 1 mm) of Plexiglas particles $({\rm relative\ density}\ = 1.192)$ . The experiments covered energetic sediment transport conditions (Shields number of $0.35 < \theta < 1.2$ ) ranging from non-capacity to full-capacity flows in bedload-to-suspension-dominated transport modes (suspension number of $0.5 < {w_s}/{u_\ast } < 1.3$ where ${w_s}$ is the settling velocity and $u_*$ is the friction velocity) and for weakly to highly inertial, finite size turbulence-particle conditions (Stokes number of 0.1 < St < 3.5 and dp/η > 10 where $\eta$ is the Kolmogorov length scale). It was shown that the effects of sediments on the TKE budget are very pronounced in all large particle experiments for which a bedload layer of several grain diameter thickness is developed above the channel bed. When compared with the corresponding reference clear-water flows, the TKE shear-production rate for the 3 mm particle flows is strongly reduced in the wall region corresponding to the bedload layer. This turbulence damping is seen to increase with sediment load until full capacity for flows with constant Shields value, as well as with Shields number value. Inside this damped TKE shear-production zone, a distinct peak of maximal turbulence production appears to coincide with the upper edge of the bedload layer delimited by a sharp gradient in mean sediment concentration. This vertically upshifted peak of TKE production is accompanied by an enhanced net downward oriented TKE flux when compared with the reference clear-water flows. The downward diffused TKE is found to act in the bedload layer as a local energy source in reasonable balance with the sediment transport term. The mechanism behind this downward TKE transport was further analysed on the basis of coherent flow structure dynamics controlled by ejection- and sweep-type events. The agreement between the height of downward directed mean TKE flux and the height below which sweep-type events dominate the Reynolds shear-stress contribution over ejections, revealed the leading role played by sweeps in mean TKE transport. This agreement holds for all reference clear-water flows supporting the well-known wall-roughness-induced dominance of the sweep contribution in turbulent, rough clear-water boundary layer flows. Furthermore, for all 3 mm particle flows, the two referred to transition levels were significantly and similarly upshifted to the upper edge of the bedload layer. Only for these sediment-laden flows, the bedload layer thickness is seen to exceed the wall-roughness sublayer of the reference clear-water flows. This supports a strong analogy between wall-roughness effects in clear-water flows and bedload layer effects in sediment-laden flows, on the mean TKE budget induced by a similarly modified coherent flow structure dynamics. The bedload layer-controlled wall roughness is finally confirmed by the good prediction of the wall-roughness parameter ks of the logarithmic velocity distribution. An empirical formulation fitting the presented measurements is presented, valid over the range of Shields number values covered herein.

Effect of boundary roughness on the attenuation of specular phonon reflection in graphene

Effect of boundary roughness on the attenuation of specular phonon reflection in graphene

Efficiency Evaluation of Surface Water Collection Infrastructure during Floods: Information Analysis and Zoning Management

Objective: Flood events, occurring as natural and unexpected phenomena, have become increasingly prevalent in recent decades. Assessing the probability of flood risk and creating flood zoning maps in vulnerable areas, particularly urban regions, are crucial for mitigating flood damages and managing such events. This research aims to determine the flood-prone zones along the Darakeh River, located in Tehran, the capital city of Iran, by integrating the hydraulic model HEC-RAS with Geographic Information System (GIS). Methods: After establishing the physiographic characteristics of the watershed, including area, perimeter, elevation, slope, and time of concentration, influential factors on flood occurrences such as permeability, hydrological soil groups, runoff potential, curve number, land use, and vegetation cover were identified. This information, along with other hydraulic data and flow specifications such as boundary conditions, roughness coefficients, and design discharge, was incorporated into the HEC-RAS model. The model was executed for different return periods of 2, 5, 10, 25, 50, and 100 years. Subsequently, the hydraulic model outputs were transferred to the GIS model to obtain the flood-prone zones along the Darakeh River for the aforementioned return periods. Results: As observed, in the middle section of the Khoshke Channel, which has a lower gradient, the floodplain exhibits a wider extent. Furthermore, along the course of the river and after passing through a stretch of the Khoshke Channel with a reduced gradient, the floodplain's area increases up to the location of the western flood channel. Conclusion: It is concluded that areas with lower river slopes exhibited larger flood-prone zones, highlighting the necessity of increased attention to prevent significant damages in urban areas during flood events.

Vibration-assisted vat photopolymerization for pixelated-aliasing-free surface fabrication

Mask image projection-based vat photopolymerization (MIP-VPP) offers advantages like low cost, high resolution, and a wide material range, making it popular in industry and education. Recently, MIP-VPP employing liquid crystal displays (LCDs) has gained traction, increasingly replacing digital micromirror devices, particularly among hobbyists and in educational settings, and is now beginning to be used in industrial environments. However, LCD-based MIP-VPP suffers from pronounced pixelated aliasing arising from LCD’s discrete image pixels and its direct-contact configuration in MIP-VPP machines, leading to rough surfaces on the 3D-printed parts. Here, we propose a vibration-assisted MIP-VPP method that utilizes a microscale vibration to uniformize the light intensity distribution of the LCD-based mask image on VPP’s building platform. By maintaining the same fabrication speed, our technique generates a smoother, non-pixelated mask image, reducing the roughness on flat surfaces and boundary segments of 3D-printed parts. Through light intensity modeling and simulation, we derived an optimal vibration pattern for LCD mask images, subsequently validated by experiments. We assessed the surface texture, boundary integrity, and dimensional accuracy of components produced using the vibration-assisted approach. The notably smoother surfaces and improved boundary roughness enhance the printing quality of MIP-VPP, enabling its promising applications in sectors like the production of 3D-printed optical devices and others.

Quantitative coarse graining of laminar fluid flow penetration in rough boundaries

The interaction between a fluid and a wall is described with a certain boundary condition for the fluid velocity at the wall. To understand how fluids behave near a rough wall in a completely laminar flow regime, the fluid velocity at every point on the rough surface may be provided. This approach requires detailed knowledge of, and likely depends strongly on the roughness. Another approach of modelling the boundary conditions of a rough wall is to coarse grain and extract a penetration depth over which on average the fluid penetrates into the roughness. In this work, we examine the impact of well-defined patterned surfaces on the fluid flow behaviour. We considered two extreme cases: one with horizontal ridges and another with vertical ridges on the wall and an intermediate case with ridges at an angle on the wall. We show that for a broad range of periodic roughness patterns and relative flow velocities, a universal penetration depth function can be obtained. We obtain these results with experiments and complementary numerical simulations. We evaluate how this penetration depth depends on the various roughness parameters such as ridge depth, ridge spacing and ridge angle. Our results present a novel approach to investigating wall roughness boundary conditions by considering the penetration depth δ that captures the spatially averaged behaviour of the decaying velocity profile between the asperities. We find that this penetration depth δ can be rescaled into a simple exponential master curve δ = δ∞(1 − e−kD/S) for horizontal ridges with varying depth D and spacing S. A similar variation of δ with D and S is observed for vertical ridges, but with a smaller magnitude δ∞, while for ridges at an angle, the penetration depth lies between the two extreme cases.