Shallow-water equations and low-order shallow-water moment models use vertically coarse representations and therefore cannot, in general, resolve the thin wall-affected region produced by a no-slip bottom. Enforcing the pointwise wall value on a low-order global polynomial reconstruction can introduce stiff relaxation and distort the resolved interior velocity profile. Starting from the incompressible Navier–Stokes equations with Navier bottom friction, we derive a bottom-to-mean relation in a distinguished regular-friction regime and use it to define an endpoint-consistent effective wall-traction closure for the shallow-water equations and the hyperbolic shallow-water moment equations. The closure represents the momentum effect of unresolved near-wall dynamics; it neither resolves the physical boundary layer nor imposes the pointwise no-slip trace on the reconstructed polynomial. It recovers the perfect-slip wall contribution when the friction coefficient vanishes. Because only source terms are changed, the homogeneous principal matrices and their established two-dimensional hyperbolicity classification remain unchanged. We compare the standard and modified reduced models with two-phase incompressible Navier–Stokes computations in OpenFOAM for wet-bed dam-break and three-dimensional collapse tests. In the cases considered, the modified closure reduces the excessive damping of the classical low-order wall source and improves agreement in depth-averaged and resolved-interior velocity diagnostics, but it does not uniformly improve front-propagation speed. The regular-friction asymptotic remainder is not uniform in the large-friction numerical regime; there the effective coefficient is used as a wall-model continuation and assessed empirically.
Suppose that f (x) E 1[8[x1, ... , xn] and g(x) E 1[8[x1, ... , xn] are two real polynomials of degree d in n variables. If the polynomials f and g are the same up to orthogonal symmetry, a natural question is then what element of the orthogonal group induces the orthogonal symmetry; i.e. to find the element R E O(n) such that f (R inverted perpendicular x) = g(x). One may directly solve this problem by constructing a nonlinear system of equations induced by the relation f (R inverted perpendicular x) = g(x) along with the identities of the orthogonal group. However, this approach becomes quite computationally expensive for larger values of nand d. To give an alternative and significantly more scalable solution to this problem, we introduce the concept of Polynomial-Weighted Principal Component Analys is (PW-PCA). We in particular show how PW-PCA can be effectively computed and how these techniques can be used to obtain a certificate of orthogonal equivalence, that is we find the R E O(n) such that f (R inverted perpendicular x) = g(x). (c) 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
The normalized distance Laplacian matrix $\mathcal{D}^{\mathcal{L}}(G)$ of a graph $G$ is a natural generalization of the normalized Laplacian matrix, arising from the matrix of pairwise distances between vertices rather than the adjacency matrix. Following the motif that this matrix behaves quite differently to the normalized Laplacian matrix, we show that both the spectral gap and Cheeger constant of $\mathcal{D}^{\mathcal{L}}(G)$ are bounded away from $0$ independently of the graph $G$. The spectral result holds more generally for finite metric spaces.
Bio-oil obtained from biomass pyrolysis needs further hydrodeoxygenation (HDO) for its suitability in fuel applications. However, catalysts studied to date suffer from coke formation and low yields. In this study, Cu-based catalysts, prepared using the wet impregnation method, were characterized, and their performance in the twostep HDO (mild stabilization followed by severe treatment in a batch reactor) was investigated. HDO in the presence of a Cu/Al2O3 catalyst achieved a maximum 50.5 wt.% treated oil yield and 67.6% carbon conversion compared to Co-Mo/Al2O3 and Co/Al2O3 catalysts. The measured coke formation was less than 3% for the Cubased catalyst, which was attributed to controlled deoxygenation and hydrogenation. The high heating value of the treated bio-oil ranged from 31.4 to 34.6 MJ kg-1. Additionally, gas chromatography-mass spectrometry showed that the treated bio-oils were rich in alkyl phenols and hydrocarbons, with the concentration ranging from 4.6 to 55.3 and 15.9 to 32.0 wt.% of total, respectively. Direct deoxygenation, hydrogenation, and demethoxylation were the significant reactions leading to the formation of hydrocarbons. Based on the findings, Cu-based catalysts can be used for HDO of pyrolysis bio-oil to obtain valuable chemicals and fuels.
Abstract This study presents results from large-scale wave flume experiments investigating pore water pressure response under solitary wave impact for both free-field (without structure) and soil–foundation (with structure) conditions. Tests were conducted under varying wave heights and foundation embedment depths. Pore pressure sensors were embedded in sandy soil at varying depths and lateral locations. The study evaluates the evolution of excess pore pressure and seepage gradients relative to established seepage and liquefaction criteria. Under both testing conditions, neither excess pore pressure nor vertical seepage pressures exceeded the critical threshold. When testing the soil–foundation case, increasing wave height at constant embedment depth caused downward seepage at shallower depths, but resulted in upward seepage at deeper layers. Increasing embedment depth further reduced upward-directed seepage pressures, particularly beneath the foundation, while location-dependent responses persisted elsewhere. In the free-field condition, wave impact generated positive excess pore pressure peaks followed by accumulation due to rundown effects. Higher wave heights led to greater excess pore pressure and seepage pressure amplitudes, with responses attenuating with depth. Although liquefaction was not observed dominantly, structural instability was likely influenced by a combination of high wave loading and the development of upward-directed seepage beneath the foundation. These findings provide mechanistic insight into the wave–soil–structure interaction and offer a large-scale experimental benchmark for future numerical modeling.
