In this contribution, we study scalar nonlocal conservation laws with the p-norm. Here, "nonlocal" means that the velocity of the conservation law depends on an integral term in space. Typically, the nonlocal term is an L1-type weighted average of the solution whereas here we study the case when the solution is integrated in the Lp-norm. We also consider the case of the Lp-quasi-norm when p is an element of (0, 1) and establish, for an initial datum which is uniformly bounded away from zero, the existence and uniqueness of weak solutions. We then demonstrate that weak solutions also exist for initial data that may vanish under more restrictive assumptions. Furthermore, we investigate the singular limit, i.e., what happens when the nonlocal kernel converges to a Dirac distribution. Indeed, for the one-sided exponential kernel, we recover the (entropy) solution of the corresponding local conservation law for all p is an element of (0, infinity) with further restrictions for p is an element of (0, 1). This generalizes the celebrated singular limit result for nonlocal conservation laws for p = 1 significantly and showcases the robustness of the approximation of local conservation laws by nonlocal ones. We also investigate the monotonicity of the solution when assuming that the initial datum is monotone. Finally, we prove the convergence of solutions for p -> 0, resulting in a different kind of nonlocal conservation law. The paper concludes with numerical studies illustrating the effect of p on singular-limit convergence and related phenomena. (c) 2026 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Large language models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks, yet their potential as optimization engines for engineering design remains largely unexplored. This study introduces an iterative optimization framework in which an LLM serves as the primary optimizer for reliability–redundancy allocation problems (RRAP), a class of challenging NP-hard problems with nonlinear constraints and mixed-integer decision variables. The framework leverages in-context learning and carefully designed prompts to generate progressively improved candidate solutions based on problem formulation, resource constraints, and quantitative feedback from previous iterations. Two variants are developed and evaluated, a Pure LLM configuration and a Hybrid variant that incorporates coordinate descent local search. The proposed approach is benchmarked against ten well-established problems from the literature, covering series, series–parallel, complex bridge, and large-scale system configurations, and is compared against a random search baseline and six recent metaheuristics under matched evaluation budgets. Results show that the LLM-based framework achieves competitive or optimal solutions across most cases while requiring one to three orders of magnitude fewer function evaluations than conventional metaheuristics, and it returns a feasible solution in every run of every problem. Performance is particularly strong on integer-only redundancy allocation problems, where the framework remains fully feasible even where undirected search fails, while its gap to the reference widens on high-dimensional and tightly constrained mixed-integer problems. This study establishes LLMs as a sample-efficient and interpretable alternative to population-based metaheuristics in reliability engineering, most advantageous when each evaluation is computationally expensive. A dedicated test on anonymized, perturbed problems further indicates that the framework performs genuine structure-driven search rather than reproducing memorized solutions.
The development of hierarchical SAPO-11 catalysts typically relies on expensive synthetic mesoporogens or post-synthetic treatment that compromise structural integrity. Herein, we present a novel, cost-effective mesoporogen-free strategy for synthesizing hierarchical SAPO-11 by exploiting halloysite nanotubes (HNTs) as a dual-function precursor, serving simultaneously as a source of silicon and aluminum and as a template for secondary porosity. Hydrothermal synthesis conditions (180-200 degrees C, 48-72 h) were optimized to leverage HNTs' inherent mesoporosity and chemical composition, yielding SAPO-11 with high crystallinity, moderate acidity and enhanced textural properties. Characterization by XRD, SEM, TEM, nitrogen sorption, Py-IR and NH3-TPD confirmed the hierarchical porosity (mesopore volume up to 54 %) and controlled acidity, attributed to pseudomorphic transformation of HNTs during synthesis. Pt-loaded catalyst supported on hierarchical SAPO-11 demonstrated higher platinum dispersion and catalytic efficiency, achieving a C16-isomers yield of 80 % under optimized conditions (380 degrees C, 3.5 MPa H2, LHSV 4 h-1, H2/feedstock volume ratio 500 nL & times; L-1), outperforming conventional SAPO-11 and other hierarchical counterparts. The hierarchical structure facilitated diffusion of multi-branched isomers, reducing cracking byproducts (cracking/isomerization ratio of 0.29 vs. 0.43 for conventional SAPO-11). Furthermore, stability tests over 500 h on stream confirmed the catalyst's resistance to deactivation, attributed to its hierarchical porosity, mild acidity, and optimal metal-acid balance. This mesoporogen-free approach offers a scalable, eco-friendly route to high-performance catalysts that provide activity, selectivity, and stability while leveraging abundant natural resources.
Liquid organic hydrogen carriers (LOHCs) based on alpha,w-alkanediol/lactone systems offer significantly lower dehydrogenation enthalpies than conventional aromatic carriers. This study investigates how the chain length and branching of alkyl substituents on the lactone ring influence the thermodynamic equilibrium of reversible hydrogen storage. Using a hybrid approach combining experimental thermochemistry and high-level quantum-chemical calculations (G3MP2), the reaction enthalpies, entropies, and Gibbs energies for both liquid and gas phases have been determined. Results reveal that extending the chain and increasing the branching of the alkyl group substantially reduce the Gibbs reaction energy. For instance, 2-tert-butyl-gamma-butyrolactone exhibits a negative Gibbs reaction energy (-5.3 kJ & sdot;mol-1 at 298.15 K), indicating that thermodynamically spontaneous hydrogen release is possible at room temperature, provided suitable catalysts are available. However, while highly branched substituents greatly facilitate hydrogen release, they reduce volumetric hydrogen storage density and make the reverse hydrogenation step more challenging. Ultimately, a structure-property analysis demonstrates that tuning the size and branching of alkyl substituents provides a versatile strategy to balance the competing thermodynamic demands of hydrogen storage and release, enabling the rational design of tailored diol/lactone LOHCs.
The current research aims to evaluate the photocatalytic activity of (TiO2) with various loading ratios (5%-60%) supported on mesoporous aluminosilicate (zeolite type) called Siral, with aluminum content ranging from 20% to 70%, to enhance the performance of degradation of ibuprofen (IBP) as a pharmaceutical pollutant. The batch reactor is furnished with solarium light to simulate sunlight UV for efficient degradation. The supported substance (Siral) exhibits elevated surface area and a regular mesoporous structure; hence, it might be regarded as an efficient photocatalyst support. The characterizations and effectiveness of the prepared catalyst were achieved by X-ray diffraction (XRD), Brunauer-Emmett-Teller (BET), scanning electron microscopy (SEM) and UV-visible spectroscopy. The results exhibit the highest photo-degradation ratio (90%) for (60% TiO2/Siral40) after 4 hours. The highest surface area is 448.3685 m²/g for 15% TiO₂/Siral40. The photodegradation efficiency increases as the weight percentage of TiO2 particles rises from 5 to 60 %. TiO2/Siral NCs photocatalysts demonstrate remarkable photostability and reusability, especially in organic molecule degradation.
