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.
Abstract This study investigates the mechanical performance of slag placed over subgrade soil, with a focus on the reinforcing role of woven geotextiles under cyclic loading. To achieve this, two complementary experimental approaches were employed: large-scale box tests simulating repeated traffic loads with a peak load of 20 kN applied over 100,000 cycles and resilient modulus ( M R ) tests conducted in accordance with AASHTO T 307. Results showed that the inclusion of a woven geotextile layer substantially enhanced both the permanent deformation and resilient behavior of the combined slag–subgrade system. In the large-scale tests, geotextile reinforcement reduced permanent deformation beneath the loading plate by 70.5%, compared to the unreinforced case. Similar improvements were observed around the loading plate, indicating enhanced lateral confinement. Stress–strain responses confirmed stabilized behavior in the reinforced sections, free from peak stress surges and instability. Furthermore, resilient modulus results demonstrated a consistent increase in M R values across all stress stages, confirming improved recoverability and stiffness under repeated loading. Overall, the combined findings reveal that the utilized geotextile reinforcement effectively suppresses plastic deformation while improving the resilient performance of granular layers, underscoring its potential as a structurally reliable solution for pavement base systems incorporating slag.
In the current series of research papers, we study the global dynamics of a two-species model that combines mixed-type chemotaxis sensitivities together with Lotka-Volterra competitive kinetics, { u(t) = Delta u - chi(1)del & sdot; ( u/w del w) + u(a(1) - b(1)u - c,v), x is an element of Omega, v(t) = Delta v - chi(2)del & sdot; (v del z) + v(a(2) - b(2)v - c(2 )u), x is an element of Omega, 0 = Delta w - lambda(1)w + mu(1)v, x is an element of Omega, 0 = Delta z - lambda(2)z + mu(2)u, x is an element of Omega, (0.1) under no-flux boundary conditions in a smoothly bounded domain Omega subset of & Ropf;(n) with n >= 2, where the parameters chi(i) , lambda(i) , mu(i) , a(i) , b(i) , c(i) > 0 for i = 1, 2 are positive constants. We first wanted to emphasize that the system described by Eq. (0.1) marks the first comprehensive analysis of a mixed-type chemotaxis competition framework. This model involves two species and two stimuli, integrating both regular and singular sensitivities along with the competitive dynamics characterized by the Lotka-Volterra equations. The key novelty of this work lies in its incorporation of both sensitivity types within a single framework, allowing for a direct comparison and discussion of these two distinct mechanisms within a unified setting. This first installment of the series investigates the L-p -boundedness and global existence of classical solutions to system (0.1). Under suitable parameter conditions, it is shown that any globally defined positive solution is L-p -bounded for some p > 1. Moreover, for all sufficiently smooth and positive initial data, system (0.1) admits a unique global classical solution in the two-dimensional case, without imposing any additional assumptions on the model parameters. For dimensions n >= 3, the existence of global classical solutions to system (0.1) is established under appropriate parameter restrictions. In addition, we present several numerical simulations in one, two, and three spatial dimensions to explore the dynamics of classical solutions. The computational simulations are fully consistent with the analytical results on global existence and further provide insight into the global dynamics of classical solutions such as boundedness (global and uniform sense), persistence (mass and pointwise sense), and stability (coexistence and extinction sense), which will be discussed in the second and third installment of the series
Food-waste reduction platforms allow restaurants to redistribute surplus food, but their branding implications remain unclear. Drawing on signaling theory, we conceptualize restaurant presence on these platforms as a hybrid sustainability signal that embeds sustainability and commercial meanings within the same marketplace cue. Across three experiments, we examine whether this hybrid signal enhances restaurant brand equity through green brand image and whether consumer residence and restaurant type condition its effects. Study 1 shows that platform presence enhances brand equity, partially through green brand image. Study 2 replicates the main effect and provides directional evidence that the premium of platform presence may be stronger among urban than rural consumers. Study 3 shows that this effect depends jointly on consumer residence and restaurant type, and that mediation through green brand image is evident primarily for full-service restaurants. These findings identify platform presence as a hybrid, context-dependent sustainability signal with branding implications.
qcombo is a Python package for the symbolic evaluation of commutators between general quantum many-body operators expressed in normal-ordered form using the generalized Wick theorem. The package provides an automated and systematic framework for generating the corresponding algebraic expressions, significantly reducing the risk of human error in lengthy and complex analytical derivations. It is designed to assist the development and implementation of modern many-body methods in nuclear physics, quantum chemistry, and related fields. The functionality and workflow of the package are demonstrated through an application to the in-medium similarity renormalization group (IMSRG) method, which has been widely used for nuclear ab initio calculations. As a representative example, qcombo is employed to automatically generate the complete set of multi-reference IMSRG flow equations with operators truncated at the normal-ordered three-body level. PROGRAM SUMMARY Program Title: qcomboCPC Library link to program files: (to be added by Technical Editor)Developer’s repository link: https://github.com/chenlh73/qcombo.gitLicensing provisions: MITProgramming language: Python (Requires-Python >=3.12)Required additional packages: SymPySupplementary material: https://pypi.org/project/qcombo/Nature of problem:Many modern quantum many-body methods require the evaluation of commutators between general many-body operators expressed in normal-ordered form. The derivation of these commutators involves repeated applications of the generalized Wick theorem and typically generates a large number of algebraic terms with complicated index structures. Carrying out these derivations manually is therefore extremely labor-intensive and prone to human error, especially when higher-body operators or multi-reference states are considered.Solution method: The program implements a symbolic framework based on the generalized Wick theorem to automatically evaluate commutators between normal-ordered many-body operators. It systematically generates all operator contractions and constructs the resulting expressions, which are then simplified using symmetry properties of operators and by transforming to the natural-orbital basis. The final results are provided in symbolic form for further analytical or numerical use.Additional comments including restrictions and unusual features: None.
