Mixed boundary-value problem for periodic baffles in acoustic medium is solved with help of the method developed earlier in electrostatics. The nice feature of the method is that the resulting matrices are relatively easy for computations and that the results satisfy exactly the energy conservation law. Illustrative numerical examples present the wave-beam steering (in the far-field) in a baffle system that may be considered as a model of one-dimensional ultrasonic transducer array.

This study focuses on the complex dynamics of heat dissipation within diaphragm walls during concrete hydration, crucial in construction engineering. Experimental measurements from three sites in Poland, featuring diaphragm walls of varying thicknesses, ranging from 1 to 1.5 meters, were compared to a numerical model. The model, using a Finite Difference Method, incorporated stages of execution of adjacent panels and their thermal influence. The results closely mirrored the measured temperatures, validating the accuracy of its predictions. Despite minor discrepancies, mostly within ±3°C, the method effectively approximated real-life scenarios. Suggestions for model enhancements include incorporating the effect of concrete admixtures and refining the modeling of sequential panel execution. The thermal soil parameters, their possible range, and their impact on hydration heat dissipation in deep foundations emerged as crucial insights. This research serves as a foundation for deeper investigations into early-age behavior in deep foundations, aiming to extend the analysis to stress and strain domains to unravel characteristic cracking patterns observed in diaphragm walls.