In this paper we study an overdetermined problem which is directly related to the well known torsion problem studied by J. Serrin. A perturbed version of the latter is tackled by using asymptotic series as well as tools borrowed from the celebrated Nekhoroshev Theorem. In a similar fashion to this class of results, we establish the existence of infinitely many approximants for the perturbed problem’s solution, whose approximation error is so small which can be regarded as negligible for practical applications. The approach is fully constructive and this feature is demonstrated via an example in a final section.
Activated carbon (AC) is a renewable carbon material with tunable surface properties that make it a promising support for enzyme immobilization. In this study, bamboo-derived activated carbon (BAC) produced at 300, 400, 500, and 600 degrees C were evaluated as supports for the immobilization of Candida antarctica lipase B (CaLB) and applied to the enzymatic polycondensation of dimethyl adipate and 1,8-octanediol. The effect of pyrolysis temperature on BAC properties was investigated by elemental analysis, infrared spectroscopy, and Brunauer-Emmett-Teller (BET) surface area analysis. Increasing the pyrolysis temperature promoted carbonization, aromatization, and pore development, leading to a marked increase in surface area and CaLB immobilization efficiency. However, higher enzyme loading did not result in better catalytic performance. The BAC produced at 400 degrees C (B400) showed the best overall performance, producing the highest polyester number-average molecular weight (Mn approximate to 11 kDa) while achieving approximately 97% monomer conversion. In addition, B400 exhibited the highest operational stability over five consecutive reaction cycles. The improved performance was attributed to its balanced combination of surface chemistry, accessible porosity, and enzyme-support interactions, which favored enzyme immobilization while preserving catalytic accessibility. This work highlights that tailoring BAC properties through controlled pyrolysis provides an effective strategy for developing renewable and low-cost alternatives to conventional petroleum-derived supports for enzymatic polymerization.
The transition towards low-carbon energy systems is increasing the importance of efficient and controllable heating and cooling technologies in buildings. Ground source heat pump (GSHP) systems represent a mature solution for building thermal energy supply, while advances in system configurations, ground heat exchanger (GHE) technologies, modelling, control, and thermal energy storage (TES) integration are expanding their operational capabilities. This review provides a comprehensive overview of GSHP systems in building applications, progressing from their technological foundations and system configurations to modelling and control approaches, TES integration, demand-side management (DSM), and their emerging potential to provide energy flexibility. The review first examines GSHP and GHE configurations, followed by modelling approaches and control strategies for predicting and managing system operation. The role of TES is then discussed, with particular attention to its ability to decouple thermal demand from electricity consumption and enhance load-shifting capabilities. Building on these technological and operational foundations, the review examines DSM and demand response strategies and discusses how GSHP systems can contribute to peak-demand reduction, load shifting, and flexible building-grid interaction. Current barriers include system complexity, high upfront costs, limitations in available data and standardised assessment methods, and challenges associated with control and system integration.
Over the last decades, the schlieren technique has evolved from a qualitative thermal/flow visualization tool into a quantitative optical diagnostic method capable of measuring temperature gradients and local convective heat transfer coefficients in transparent fluids. This paper reviews the development and systematic application of focal-filament quantitative schlieren methodology at the University of Genoa since the early 1990s. The theoretical relationship between optical deflection and temperature gradient is revisited, and the corresponding implementation using a large-mirror Z-type configuration is described. The work is positioned within the broader international evolution of schlieren diagnostics, including colour schlieren, synthetic schlieren, Background-Oriented Schlieren (BOS), and schlieren-based tomographic techniques. Applications to buoyancy-driven heat transfer in air and water, smooth and rib-roughened surfaces (both isolated and in channels), as well as three-dimensional free-convective fields, are discussed. The analysis demonstrates that classical mirror-based quantitative schlieren remains highly effective for weak-gradient natural convection, complementing modern digital approaches.
