Smooth Regions Research Articles

A new third-order EXP-WENO scheme for Hamilton–Jacobi equations

The authors of this research paper have introduced a new method for solving Hamilton–Jacobi (HJ) equations called third-order weighted essentially nonoscillatory (WENO) method. This method uses exponential polynomials to construct numerical fluxes and smoothness indicators, which helps distinguish between singular and smooth regions more efficiently. The smoothness indicators are created using a finite difference operator that eliminates exponential polynomials. The numerical flux is constructed using an interpolation method based on exponential polynomials, which results in better outcomes around steep gradients. The new method maintains a high level of accuracy (i.e. three) in smooth regions, even near critical points. The authors have presented some numerical results to demonstrate the effectiveness of the new method and compared it with other WENO methods.

Evaluation of a high-order central-difference solver for highly compressible flows out of thermochemical equilibrium

A high-order shock-capturing central finite-difference scheme is evaluated for numerical simulations of hypersonic high-enthalpy flows out of thermochemical equilibrium. The scheme is an extension to thermochemical out-of-equilibrium flows of the technique presented in Sciacovelli et al. (2021) for high-speed flows in chemical nonequilibrium. It relies on a standard tenth-order accurate central-difference approximation of the inviscid fluxes, supplemented with a high-order accurate nonlinear artificial dissipation term of ninth-order accuracy in smooth flow regions. Close to flow discontinuities, a shock-capturing low-order term is activated based on a highly selective shock sensor. To enable robust and non oscillatory solutions in regions of strong discontinuities of the thermodynamic variables, including the vibrational temperature, a shock detector consisting of a combination of a pressure-based term and Ducros’ vorticity/dilatation sensor is applied to all conservation equations except that of vibrational energy. For the latter, a shock sensor based on the vibrational temperature itself is adopted instead, to account for the loose coupling between vibrational energy and pressure. The accuracy and robustness of the proposed approach is demonstrated for a variety of thermochemical non-equilibrium configurations, ranging from one-dimensional benchmarks to three-dimensional turbulent flows, for which the ILES capabilities of the selective high-order numerical dissipation are also showcased.

A class of smooth, possibly data-adaptive nonparametric copula estimators containing the empirical beta copula

A broad class of smooth, possibly data-adaptive nonparametric copula estimators that contains empirical Bernstein copulas introduced by Sancetta and Satchell (and thus the empirical beta copula proposed by Segers, Sibuya and Tsukahara) is studied. Within this class, a subclass of estimators that depend on a scalar parameter determining the amount of marginal smoothing and a functional parameter controlling the shape of the smoothing region is specifically considered. Empirical investigations of the influence of these parameters suggest to focus on two particular data-adaptive smooth copula estimators that were found to be uniformly better than the empirical beta copula in all of the considered Monte Carlo experiments. Finally, with future applications to change-point detection in mind, conditions under which related sequential empirical copula processes converge weakly are provided.

Fractionation and antioxidation activities of polysaccharides from Zanthoxylum bungeanum Maxim

Zanthoxylum bungeanum has a lengthy history of widespread use as a food ingredient in China. However, the composition of Zanthoxylum bungeanum polysaccharide remains ambiguous, and the antioxidant effect has received limited attention. This study aimed to extract water-soluble polysaccharide from the dried pericarp of Zanthoxylum bungeanum, referred to as WZBP, which was fractionated into a neutral component (WZBP-N) and three pectic components (WZBP-A-I, WZBP-A-II, WZBP-A-III). The findings indicated that WZBP-A-III is a pectic polysaccharide “smooth region” without many side chains. All components of WZBP exhibited a notable capacity for scavenging free radicals, with WZBP-A-III demonstrating the most potent antioxidation activity, and WZBP-A-III also observed to effectively extend the lifespan of Drosophila melanogaster and enhanced the activity of antioxidant enzymes. These results provide valuable insight and direction for future research on Zanthoxylum bungeanum polysaccharide as an antioxidant agent.

Improving the quality of gluten-free plant-based meat analogs based on soy protein isolate with insoluble soy fibers and low acyl gellan gum

This study describes the effects of incorporating insoluble soy fiber and low acyl gellan gum as an alternative for wheat gluten in plant-based meat analogs made from soy protein isolate (SPI). The formulations containing insoluble soy fiber (ranging from 0 to 3%) and low acyl gellan gum (0–2%) were processed in a high-temperature shear cell (HTSC) and then analyzed in terms of macrostructure, microstructure, rheological properties, tensile strength, and water absorption capacity (WAC). Macrostructural analysis revealed that the control product containing SPI without insoluble soy fiber and low acyl gellan gum exhibited a dense and gel-like structure, devoid of visible fibers. The addition of 1, 2, and 3 wt.% of insoluble soy fiber increased the formation of visually elongated fibers in both macro- and microscopic levels in the shear direction, resulting in anisotropic plant-based meat analogs with improved tensile strength and elasticity. The use of 1 and 2 wt.% low acyl gellan gum led to the formation of short and thin filaments that were less oriented in the shear direction, resulting in decreased tensile strength. When combined with low acyl gellan gum, insoluble soy fiber failed to produce lengthy and elongated fibers, resulting in short and thin fibrils. These findings suggest that the interaction between insoluble soy fiber and low acyl gellan gum under the processing conditions may hinder fiber formation and mechanical anisotropy. Microscopic examination reveals smoother regions in products enriched with insoluble soy fiber and rougher surfaces in those containing low acyl gellan gum. Moreover, X-ray microtomography confirms that insoluble soy fiber enhanced air retention, contributing to enhanced structural integrity. In contrast, low acyl gellan gum introduces irregularly shaped air bubbles, compromising structural improvement. In summary, this study underscores the potential of insoluble soy fiber to enhance the structural and the textural properties of plant-based meat analogs. However, it also highlights the challenges posed by low acyl gellan gum, which, despite improving water retention, may hinder fiber formation and mechanical anisotropy. These findings offer insights for advancing the quality of plant-based meat products.

Adaptive symmetric flux limiters with long computation times for hyperbolic conservation laws

The construction of the limiter is a critical factor in the traditional Total Variation Diminishing (TVD) scheme. Among the classical limiters, superbee has the lowest numerical dissipation, but it can lead to over-compression in smooth regions and excessive artificial steepening at discontinuities and critical points if the computation time is prolonged. Classical limiters like Minmod, van Leer, van Albada, and MC fail to distinguish between different wave types, and they can even cause numerical oscillations for multi-critical value problems with prolonged computation times. A class of adaptive limiters has been created by combining classical limiters with superbee. This adaptive limiter can achieve second-order accuracy in smoothed regions and effectively reduce over-compression and excessive artificial steepening for long computation times. Analytical and numerical results show that the MUSCL scheme with an adaptive limiter is efficient.

A new type of non-polynomial based TENO scheme for hyperbolic conservation laws

For classical WENO/TENO reconstructions, the high-order polynomial interpolation is one of the main building-blocks for constructing the numerical fluxes. However, due to the inherent characteristics of polynomials, the polynomial interpolation is not suitable to represent the flow scale with sharp transitions such as high-wavenumber fluctuations or discontinuities. In this work, based on a new candidate stencil arrangement with explicit detection of non-smooth regions, a new shock-capturing framework is proposed by combining the infinitely differentiable non-polynomial RBF-based reconstruction in smooth regions with the jump-like non-polynomial interpolation for genuine discontinuities. The resulting scheme not only achieves the desired high-order accuracy for smooth flow scales but also resolves the genuine discontinuities with a sub-cell resolution. Moreover, with the observation that the built-in parameter has a significant impact on the basic shape of the Gaussian RBF kernel function, a nonlinear adaptation strategy for the shape parameter is proposed to incorporate the local features of the flow field and further minimize the numerical dissipation errors for smooth flow scales. In order to demonstrate the robust shock-capturing and high wave-resolution properties of the proposed non-polynomial based scheme, a set of challenging benchmark cases with a wide range of Mach numbers is simulated without the necessity of parameter tuning case by case.

Nonlinear 2D C1 Quadratic Spline Quasi-Interpolants on Triangulations for the Approximation of Piecewise Smooth Functions

The aim of this paper is to present and study nonlinear bivariate C1 quadratic spline quasi-interpolants on uniform criss-cross triangulations for the approximation of piecewise smooth functions. Indeed, by using classical spline quasi-interpolants, the Gibbs phenomenon appears when approximating near discontinuities. Here, we use weighted essentially non-oscillatory techniques to modify classical quasi-interpolants in order to avoid oscillations near discontinuities and maintain high-order accuracy in smooth regions. We study the convergence properties of the proposed quasi-interpolants and we provide some numerical and graphical tests confirming the theoretical results.

Explicit strong stability preserving second derivative multistep methods for the Euler and Navier–Stokes equations

In this paper, we develop the explicit second derivative multistep methods (SDMMs) for the Euler and Navier–Stokes equations. The SDMMs use the calculated results from the previous steps, which can improve computational efficiency. The third-order and fourth-order SDMMs temporal discretization methods are constructed based on the order conditions. Additionally, the strong stability preserving (SSP) condition for the SDMMs is proposed, which provides the corresponding parameters for optimal SSP SDMMs. For numerical experiments, the SDMMs can achieve the order of accuracy as designed on the smooth regions, and the optimal SSP coefficient for the SDMMs is shown to be roughly the same in theory as in the numerical results. Moreover, the SDMMs have approximately twice the computational efficiency compared with the third-order and fourth-order two-derivative Runge–Kutta methods, and the SDMMs are also more efficient than the classical three-stage third-order SSP Runge–Kutta method.

Advancing high-speed flow simulations: SAUSM – an innovative hybrid numerical scheme for shock stability and accuracy

This paper introduces a novel hybrid numerical method, SAUSM, designed for accurate and robust simulation of compressible flows governed by the Euler equations. While the AUSM[Formula: see text] scheme provides proper resolution of smooth flow features, it is susceptible to anomalies, particularly the carbuncle phenomenon near strong shock discontinuities. Conversely, the AUFS scheme offers inherent stability in capturing shocks; however, it lacks the accuracy of AUSM[Formula: see text] in smooth regions. The proposed SAUSM method combines AUSM[Formula: see text] and AUFS through an adaptive weighting function, facilitating a seamless transition between the schemes. This approach preserves the accuracy of AUSM[Formula: see text] in smooth regions while ensuring robust shock-capturing capabilities near discontinuities. The effectiveness of the SAUSM method is rigorously demonstrated through a comprehensive suite of progressively complex test cases. Numerical experiments demonstrate SAUSM’s proficiency in resolving intense shock patterns and discontinuities without introducing anomalies. In the selected test cases, SAUSM agrees with reference solutions and effectively mitigates anomalies observed in AUSM[Formula: see text], including kinked Mach stems. In the challenging test case involving hypersonic blunt body flow over a cylinder, SAUSM adapts dissipation effectively by utilizing its adaptive weighting function to generate smooth pressure distributions, thereby eliminating the carbuncle instability linked to AUSM[Formula: see text] when applied to a high aspect ratio grid. The consistent formulation of flux splitting and the adaptive weighting in SAUSM prevent excessive dissipation away from discontinuities, thus preserving accuracy comparable to that of exact Riemann solvers. Consequently, SAUSM emerges as a promising and innovative approach to accurately and robustly simulate a wide range of compressible Euler flows. The comprehensive results obtained from the validation tests firmly establish SAUSM as a highly effective general-purpose technique for computational fluid dynamics in academic research.

High-order implicit shock tracking boundary conditions for flows with parametrized shocks

High-order implicit shock tracking (fitting) is a class of high-order, optimization-based numerical methods to approximate solutions of conservation laws with non-smooth features by aligning elements of the computational mesh with non-smooth features. This ensures the non-smooth features are perfectly represented by inter-element jumps and high-order basis functions approximate smooth regions of the solution without nonlinear stabilization, which leads to accurate approximations on traditionally coarse meshes. In this work, we introduce a robust implicit shock tracking framework specialized for problems with parameter-dependent lead shocks (i.e., shocks separating a farfield condition from the downstream flow), which commonly arise in high-speed aerodynamics and astrophysics applications. After a shock-aligned mesh is produced at one parameter configuration, all elements upstream of the lead shock are removed and the nodes on the lead shock are positioned for new parameter configurations using the implicit shock tracking solver. The proposed framework can be used for most many-query applications involving parametrized lead shocks such as optimization, uncertainty quantification, parameter sweeps, “what-if” scenarios, or parameter-based continuation. We demonstrate the robustness and flexibility of the framework using a one-dimensional space-time Riemann problem, and two- and three-dimensional supersonic and hypersonic benchmark problems.

3D Printed Voronoi Structures Inspired by Paracentrotus lividus Shells

The present paper investigates the mechanical behavior of a biomimetic Voronoi structure, inspired by the microstructure of the shell of the sea urchin Paracentrotus lividus, with its characteristic topological attributes constituting the technical evaluation stage of a novel biomimetic design strategy. A parametric design algorithm was used as a basis to generate design permutations with gradually increasing rod thickness, node count, and model smoothness, geometric parameters that define a Voronoi structure and increase its relative density as they are enhanced. Physical PLA specimens were manufactured with a fused filament fabrication (FFF) printer and subjected to quasi-static loading. Finite element analysis (FEA) was conducted in order to verify the experimental results. A minor discrepancy between the relative density of the designed and printed models was calculated. The tests revealed that the compressive behavior of the structure consists of an elastic region followed by a smooth plateau region and, finally, by the densification zone. The yield strength, compressive modulus, and plateau stress of the structure are improved as the specific geometric parameters are enhanced. The same trend is observed in the energy absorption capabilities of the structure while a reverse one characterizes the densification strain of the specimens. A second-degree polynomial relation is also identified between the modulus, plateau stress, and energy capacity when plotted against the relative density of the specimens. Distinct Voronoi morphologies can be acquired with similar mechanical characteristics, depending on the design requirements and application. Potential applications include lightweight structural materials and protective gear and accessories.

Fast CU Partition Algorithm for Intra Frame Coding Based on Joint Texture Classification and CNN.

High-efficiency video coding (HEVC/H.265) is one of the most widely used video coding standards. HEVC introduces a quad-tree coding unit (CU) partition structure to improve video compression efficiency. The determination of the optimal CU partition is achieved through the brute-force search rate-distortion optimization method, which may result in high encoding complexity and hardware implementation challenges. To address this problem, this paper proposes a method that combines convolutional neural networks (CNN) with joint texture recognition to reduce encoding complexity. First, a classification decision method based on the global and local texture features of the CU is proposed, efficiently dividing the CU into smooth and complex texture regions. Second, for the CUs in smooth texture regions, the partition is determined by terminating early. For the CUs in complex texture regions, a proposed CNN is used for predictive partitioning, thus avoiding the traditional recursive approach. Finally, combined with texture classification, the proposed CNN achieves a good balance between the coding complexity and the coding performance. The experimental results demonstrate that the proposed algorithm reduces computational complexity by 61.23%, while only increasing BD-BR by 1.86% and decreasing BD-PSNR by just 0.09 dB.

WENO smoothness indicator based troubled‐cell indicator for hyperbolic conservation laws

SummaryHybrid algorithms are an efficient and popular choice for computing the solutions of hyperbolic conservation laws. In general, hybrid algorithms involve low‐cost high‐order accurate schemes in smooth regions and non‐oscillatory shock‐capturing schemes in the vicinity of discontinuities. Troubled‐cell indicators which measure the smoothness of the solution play a significant role in the efficiency of hybrid algorithms. This article proposes a new troubled‐cell indicator utilising the smoothness indicators of WENO schemes for hyperbolic conservation laws. The proposed troubled‐cell indicators are simple, efficient, effective, and are used to construct three new adaptive WENO algorithms of high‐order accuracy. The hybrid algorithms developed are independent of the order and type of the WENO reconstruction. For demonstration, we have considered the fifth and seventh order WENO‐Z reconstruction. The first two algorithms have comparable accuracy and resolution of the solution across discontinuities to that of the WENO‐Z scheme but at a less computational cost. The third algorithm ensures the convergence of the proposed scheme to the correct entropy solution when applied to a hyperbolic conservation law with non‐convex flux for which the WENO schemes fail. We have performed several 1D and 2D numerical experiments to demonstrate the efficiency of the proposed algorithms and their performance compared with the WENO‐Z schemes. The proposed algorithms are efficient and take 30%–75% less computational time than the WENO‐Z schemes while retaining the advantages of WENO‐Z schemes.

A new mixed node-based solid-like finite element method (MNS-FEM) for laminated shell structures

A new solid-shell finite element formulation is investigated in this paper. Departing from the S-FEM concept of node-based stress smoothing scheme, a new pattern that introduces new stress variables linked with an extra smoothing region inside the element is proposed. This finding preserves all the advantageous features of the standard NS-FEM but it makes approximate solutions much more accurate. The assumed natural strain (ANS) and the Discrete shear gap (DSG) techniques are employed to alleviate trapezoidal and shear locking. The simple assumptions made allow the analytical computation of the discrete operators based on the node-based backgrounds making the model particularly efficient. Popular benchmark tests are successfully solved for structured and unstructured triangular meshes in linear and buckling analysis. Numerical results show that the proposed method avoids cross-diagonal meshes, which reduces the generality of three-node degenerated shell elements proposed in the literature. This aspect makes the present formulation much more appealing than the published methods available in the literature. Moreover, in the context of the S-FEMs it is the first time in which geometric nonlinear contributions are presented.

Robust Texture-Aware Local Adaptive Image Watermarking With Perceptual Guarantee

Watermarking involves embedding a watermark in an image and later extracting it to prove the image’s copyright. In most cases, a complete image contains both smooth and textured regions. As a rule of thumb, the visual quality of an image with a watermark embedded in its textured regions is better than that of the same image with a watermark in smooth regions. This paper, by taking advantage of the fact, proposes a texture-aware local adaptive watermarking algorithm to maximize the watermark’s robustness while maintaining its imperceptibility. To identify textured regions in an image, we introduce the texture value, an efficient and proper metric of the richness of image texture. It combines the texture correlation of the AC coefficients, the luminance masking of the DC coefficient, and the distribution of image texture. A watermark is embedded adaptively into multiple non-overlapping textured regions of an image under the specified SSIM condition. Its adaptiveness comes from a novel texture-aware adaptive parameter model derived by multivariate regression analysis. Correct extraction of watermarks from multiple textured regions can be done by the cooperation of embedding and extraction strategies, with the assistance of RS-based watermark coding model. They allow for greater robustness, faster extraction, and adjustable watermark capacity. The simulation experiments on 100 images demonstrate that our proposed algorithm outperforms state-of-the-art algorithms with respect to imperceptibility, robustness, and adaptability.

A new type of increasingly higher order finite difference and finite volume MR-WENO schemes with adaptive linear weights for hyperbolic conservation laws

In this paper, the new fifth-order, seventh-order, and ninth-order finite difference and finite volume multi-resolution weighted essentially non-oscillatory (MR-WENO) schemes with adaptive linear weights are presented for hyperbolic conservation laws on structured meshes. They are termed as high-order finite difference and finite volume ALW-WENO schemes. These ALW-WENO schemes only apply one small stencil and one large stencil in reconstruction processes, which could achieve the desired accuracy in the region of smoothness and non-oscillatory properties in the region of containing strong shocks. The linear weights that sum to one can be automatically adjusted to any positive numbers. This is the first time that arbitrary high-order finite difference and finite volume WENO schemes are designed by using only two unequal-sized central spatial stencils. The structure of these novel WENO schemes is simple, so it is easier for obtaining high-order accuracy and solving multi-dimensional problems in large scale engineering applications. Compared to traditional MR-WENO schemes with same order, the computational efficiency can be further improved. Some benchmark tests indicate that these new ALW-WENO schemes have good robustness and performance.

Sparse Bayesian Learning With Weakly Informative Hyperprior and Extended Predictive Information Criterion.

This article considers the regression problem with sparse Bayesian learning (SBL) when the number of weights P is larger than the data size N, i.e., P》 N. The situation induces overfitting and makes regression tasks, such as prediction and basis selection, challenging. We show a strategy to address this problem. Our strategy consists of two steps. The first is to apply an inverse gamma hyperprior with a shape parameter close to zero over the noise precision of automatic relevance determination (ARD) prior. This hyperprior is associated with the concept of a weakly informative prior in terms of enhancing sparsity. The model sparsity can be controlled by adjusting a scale parameter of inverse gamma hyperprior, leading to the prevention of overfitting. The second is to select an optimal scale parameter. We develop an extended predictive information criterion (EPIC) for optimal selection. We investigate the strategy through relevance vector machine (RVM) with a multiple-kernel scheme dealing with highly nonlinear data, including smooth and less smooth regions. This setting is one form of the regression task with SBL in the P》 N situation. As an empirical evaluation, regression analyses on four artificial datasets and eight real datasets are performed. We see that the overfitting is prevented, while predictive performance may be not drastically superior to comparative methods. Our methods allow us to select a small number of nonzero weights while keeping the model sparse. Thus, the methods are expected to be useful for basis and variable selection.

Direct joining of quartz glass and copper by nanosecond laser

In present study, quartz glass and copper, which are with a large difference of coefficient of thermal expansion by 38 times, were successfully welded without any interlayer by nanosecond (ns) laser under non-optical contact for the first time. By reasonably tuning the welding parameters, well-formed quartz glass/copper joints without any defects such as microcracks or voids can be achieved. The welded seam includes laser-unirradiated smooth region and laser-irradiated spindle melted region and both the region are composed of “Cu2O″-SiO2 system (Cu–O–Si system) and CuO. The formation of such a particular microstructure feature is attributed to the recoil pressure from ns laser ablation and the Marangoni convection at the interface. The parameters of ns laser welding including laser power, scanning velocity and the number of scans influence the laser energy input and thermal accumulation greatly during welding, thus affecting the interfacial feature and the mechanical property of the resultant joints. The shear strength of the joint can reach 33.4 MPa, which is about 80% of quartz glass shear strength. The metallurgical bonding from interfacial reaction and mechanical interlocking from physical spindle structures are the main reasons for achieving a high shear strength of the joint. We expect this study could provide a new idea for joining materials with large differences in thermophysical properties.

A dependence of binary and planetary system destruction on subtle variations in the substructure in young star-forming regions

ABSTRACT Simulations of the effects of stellar fly-bys on planetary systems in star-forming regions show a strong dependence on subtle variations in the initial spatial and kinematic substructure of the regions. For similar stellar densities, the more substructured star-forming regions disrupt up to a factor of 2 more planetary systems. We extend this work to look at the effects of substructure on stellar binary populations. We present N-body simulations of substructured, and non-substructured (smooth) star-forming regions in which we place different populations of stellar binaries. We find that for binary populations that are dominated by close (<100 au) systems, a higher proportion are destroyed in substructured regions. However, for wider systems (>100 au), a higher proportion are destroyed in smooth regions. The difference is likely due to the hard–soft or fast–slow boundary for binary destruction. Hard (fast/close) binaries are more likely to be destroyed in environments with a small velocity dispersion (kinematically substructured regions), whereas soft (slow/wide) binaries are more likely to be destroyed in environments with higher velocity dispersions (non-kinematically substructured regions). Due to the vast range of stellar binary semimajor axes in star-forming regions (10−2 to 104 au), these differences are small and hence unlikely to be observable. However, planetary systems have a much smaller initial semimajor axis range (likely ∼1–100 au for gas giants) and here the difference in the fraction of companions due to substructure could be observed if the star-forming regions that disrupt planetary systems formed with similar stellar densities.