We quantify, with guaranteed two-sided bounds, the finite-thickness error of the classical thin-walled rules for the torsion constant J(t), the warping constant C-w, the shear centre and the restrained-member warping stress. The method combines a kinematically admissible warping field with a statically admissible shear-flow field; the energy mismatch between these two physical descriptions is a computable certificate for the exact continuum solution and propagates to guaranteed intervals for the quantities used in member checks. All finite-dimensional certificates are evaluated in exact arithmetic; the few transcendental response terms are enclosed by directed interval evaluation with explicit remainder bounds. Three results follow. A closed parametric sandwich C-w,0(-)(a, b) <= C-w <= C-w,0(+)(a, b) holds for every rectangle, proving the classical root strip formula as the thin limit with two-sided rate 1 +/- 4 root 2(b/a)/pi+O((b/a)(2)), and |omega| <= |xy|; closed parametric certificates are also obtained for the torsion constant and shear-centre position of a uniform-thickness T-section family. The equal-and unequal-flange I-sections, the channel, the angle and the closed box are certified only at the stated reference geometries, with only the explicitly identified quantities certified for the angle. An adjoint certificate reduces the relative half-widths of the shear-centre intervals to 0.14%-0.93%. Exact singular enrichment at 3 pi/2 re-entrant corners preserves exact arithmetic, reduces the duality gap by 54.7%-70.5%, and certifies five independent leading corner coefficients. For stubby reference sections, twelve classical section values and two rectangle peak-response values are rigorously excluded with signed errors; the T-section junction rule misplaces the shear centre by 24.8%-27.3%, with a certified thickness sweep consistent with quadratic decay. Analytical and parametric certificates are digit-reproducible from the paper; fixed-geometry intervals are independently verifiable.
Mitochondria are multifaceted organelles having their own genome, although most of the mitochondrial proteins are encoded by the nuclear genome and then imported into mitochondria. Beyond the classical function in generating ATP, mitochondria regulate plenty of eukaryotic cell functions including cell death, redox status, proliferation, and differentiation. Participating in a variety of signaling pathways, a tight crosstalk between mitochondria and the rest of the cell is required. As a predictable consequence, mitochondrial dysfunctions account for countless pathological conditions such as inflammation, cancer, and metabolic diseases. Therefore deepening the mitochondrial knowledge represents an important contribution to the management of many diseases. This chapter will focus on several traits of mitochondrial physiology among which metabolism, dynamics, redox, and cell death signaling, thus opening new ways in understanding mitochondrial biology.
Municipal wastewater treatment plants face increasing pressure to improve energy recovery while reducing sludge volumes and operational costs. In this context, low-input process intensification strategies are of growing interest. This study evaluated a continuous side-stream magnetization strategy applied during 44 days of mesophilic anaerobic digestion (37 +/- 2 degrees C) of sewage sludge, where digesting sludge was continuously recirculated through a tubular rare-earth-material magnetic polarizer generating a low-intensity static magnetic field (20 mT). The experimental results revealed a substantial increase in AD performance, with the SMF-exposed reactor achieving a 48.3% increase in specific biomethane production and a 15% higher reduction in volatile solids compared to the control reactor. Additionally, the digestate exposed to the SMF showed an improved dewaterability, evidenced by a 26.8% reduction in capillary suction time compared to the non-magnetized digestate. Microbial community analysis at the end of the AD process indicated that continuous exposure to SMF significantly enhanced the abundance of key methanogens, including Methanosarcina and Methanobacterium, which contributed to the higher biomethane production observed during AD. These findings indicate that continuous SMF exposure during AD can significantly enhance biomethane production and can be regarded as a promising approach to improve energy recovery from sewage sludge.
In this work we present a novel discrete collocation method for the numerical solution of Fredholm integral equations of the second kind in the space of continuous functions equipped with the uniform norm. The method is based on a rational interpolation scheme recently developed within the general framework of reproducing kernel Hilbert spaces. This rational approximation has no real poles, interpolates the target function at arbitrary Jacobi nodes and exhibits uniformly bounded Lebesgue constants. Moreover, it converges uniformly for all continuous functions at a rate at least equal to that of the best uniform polynomial approximation. These interesting properties are inherited by the resulting numerical method, for which stability, convergence and good conditioning are established under minimal assumptions on the integral kernel. A series of numerical experiments confirm the theoretical findings and indicate that, in the presence of particularly challenging kernels, the proposed approach provides a robust and effective alternative to Nyström-type methods.
Surface texturing has emerged as a promising approach to improve lubrication performance and reduce energy losses in mechanical systems. However, the influence of dimple size and density on the frictional behavior of lubricated nonconformal contacts remains insufficiently explored, especially using cost-effective mechanical methods. This study aims to address this gap by investigating the effect of microindented textures, produced via Vickers microhardness indentation, on the lubricated tribological response of 100Cr6 steel spherical surfaces. Two load levels were used (0.5 N and 5 N), thus allowing us to investigate two dimple sizes (diagonal dimension of 10 and 30 & micro;m) and two void ratios (VR) (5% and 17%). The tribological performance was evaluated under various sliding speeds using a ball-on-disk setup and two lubricants with different viscosities (CADT-605 and Lubro Lam) to capture the full Stribeck curve. Results reveal that fine dimples with the highest VR (VR = 17%) significantly reduce the coefficient of friction (COF), by up to 40%, across all lubrication regimes, due to enhanced secondary lubrication. Conversely, large dimples increased the COF due to pile-up formation and lubricant vortex generation. These findings provide new insights into the role of texture geometry in optimizing lubrication performance and pave the way for scalable and economic surface functionalization techniques in tribological applications.
