Integer weighing matrices (IW-matrices for short) are integer valued orthogonal square matrices. One usecase of these is to create classical weighing matrices with various block structures. In this paper we study and classify the space IW (n,k) of the integer weighing matrices of small size n & times; nand weight k. Our classification includes a full list of all inequivalent matrices up to Hadamard equivalence and automorphism groups [14]. We then continue to a secondary classification of the symmetric and anti-symmetric IW up to symmetric Hadamard equivalence. We apply this to the case of projective space weighing matrices. Next we use the classification to count the cardinality of the spaces of all IW (n, k) as well as the symmetric and anti-symmetric subspace. We supply practical algorithms and implement them in Sagemath [11]. Finding an (anti-)symmetric IWmatrix in a given Hadamard class can be done for significantly higher orders. In particular we solve some open cases: Symmetric W (23, 16), W (28, 25) and W (30, 17), and an anti-symmetric W (28, 25). We conclude by showing a detailed classification of IW (7, 25). We have also improved the NSOKS [30] algorithm to find all possible representations of an integer k as a sum of n integer squares. (c) 2026 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
The development of firing technologies like flash sintering and ultrafast high-temperature sintering has renewed interest in how heating rates influence microstructural evolution during sintering. Herein, we observe an exceptional heating-rate effect during conventional consolidation of 3YSZ nanopowder (20 nm). Increasing the heating rate from 2.5 to 50 degrees C min(-1) accelerates sintering by a factor of similar to 1000, reversing the positions of the sintering curves in dilatometric analysis: the material sinters at a lower temperature when heated faster. We attribute this behavior to "microstructural separation" in which high-density regions of the green body draw mass from lower-density ones via surface-mediated transport, causing the formation of pores significantly larger than the grain size. This observation highlights the importance of the green shaping procedure: sintering of more homogeneous green bodies is less sensitive to the heating rate because the driving force for surface transport between differently packed regions is reduced.
Functionally graded materials (FGMs) are advanced composite materials characterized by a gradual variation in composition and continuously changing material properties, typically along the thickness direction. This paper focuses on the geometrically nonlinear analysis of thin FGM structures by means of a solid-shell element based on the Cosserat point theory. Within the Cosserat point framework, the response of the element is governed by a strain energy function decomposed into homogeneous and inhomogeneous contributions. The homogeneous component is expressed in terms of an average deformation measure, whereas the inhomogeneous component depends quadratically on the inhomogeneous strain measures. An additional coupling term is introduced to account for the interaction between the homogeneous and inhomogeneous deformation modes induced by the material gradation of the FGM. The locking pathologies commonly encountered in the finite element analysis of thin structures are eliminated through the Assumed Natural Inhomogeneous Strain (ANIS) approach, which selectively modifies only the inhomogeneous component of the point-wise Green-Lagrange strain tensor, in combination with an appropriate determination of the constitutive coefficients governing the inhomogeneous strain energy function. The performance of the proposed solid-shell element is demonstrated through a set of benchmark tests that confirm its accuracy, robustness, and locking-free response in modeling thin FGM structures under finite deformations.
The global transition to low-carbon energy systems drives the need for continuous efficiency improvements in fossil-fuel-based power generation. Combined cycle power plants (CCPPs) represent the state-of-the-art in commercial thermal power generation, yet further efficiency gains through conventional methods face diminishing returns. This paper presents a comprehensive thermodynamic analysis of a combined cycle power plant integrated with a chemically recuperated gas turbine (CCPP-CRGT) based on a modern high-temperature gas turbine with turbine inlet temperature of 1600 degrees C. Unlike conventional recuperation that transfers sensible heat, thermochemical recuperation utilizes exhaust heat to drive endothermic steam methane reforming, converting exhaust heat into chemical energy stored in hydrogen-rich syngas. The performance of the CCPP-CRGT is benchmarked against a conventional CCPP across a range of steam-to-methane molar ratios (S/C = 1.0-3.0). The results demonstrate that thermochemical recuperation shifts the power generation from the steam turbine cycle towards the more efficient gas turbine cycle, increasing the gas turbine net work from 465 MW in the conventional case to 598 MW at S/C = 3.0, while reducing condenser heat rejection from 327 MW to only 117 MW. The overall combined cycle efficiency improves from 62.49% to 65.42%, representing a gain of 2.93 percentage points. The temperature-heat transfer profiles reveal that the reformer consumes up to 28% of the available exhaust heat, displacing the superheater section of the heat recovery steam generator. The material balance shows a progressive reduction in air mass flow rate from 2680 t/h to 2463 t/h as S/C increases, while the syngas flow grows correspondingly to 323.3 t/h. These findings confirm that the CCPP-CRGT configuration offers a viable pathway to surpass the efficiency ceiling of conventional CCPPs by leveraging the high-temperature end of the exhaust heat cascade for thermochemical recuperation rather than for steam generation, thereby reducing the heat rejected in the bottoming cycle by redirecting a portion of the exhaust heat.
A novel autoignition-assisted, high-temperature High-Pressure Well-Stirred Turbulent Combustor (HP-WSTC) has been developed for detailed kinetic studies of fuels under gas-turbine conditions that were difficult to obtain with conventional reactors and flame chemistry facilities. It is designed for operations at 1-20 atm, 1200-2200 K, and residence times of 1-100 ms, enabling treatment as a zero-dimensional premixed-combustion system. Methane combustion experiments at 1-10 atm were compared with 0D simulations, showing good agreement for major species across a wide equivalence-ratio range, demonstrating the reliability of the HP-WSTC. Although methane combustion kinetics are well established, NO predictions still show large discrepancies, even at atmospheric pressure. Sensitivity analyses identify CH-pool reactions, including CH2 + O2 = CH2O + O and CH + CO2 = HCO + CO, as key uncertain reactions. The developed HP-WSTC provides a new platform for fuel kinetic investigations and bridges the gap between reactor and flame facilities for high-temperature kinetic studies under gas-turbine conditions.
