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This study aims to analyse the non-linear losses of a porous media (stack) composed by parallel plates and inserted in a resonator tube in oscillatory flows by proposing numerical correlations between pressure gradient and velocity.

The numerical correlations origin from computational fluid dynamics simulations, conducted at the microscopic scale, in which three fluid channels representing the porous media are taken into account. More specifically, for a specific frequency and stack porosity, the oscillating pressure input is varied, and the velocity and the pressure-drop are post-processed in the frequency domain (Fast Fourier Transform analysis).

It emerges that the viscous component of pressure drop follows a quadratic trend with respect to velocity inside the stack, while the inertial component is linear also at high-velocity regimes. Furthermore, the non-linear coefficient b of the correlation ax + bx² (related to the Forchheimer coefficient) is discovered to be dependent on frequency. The largest value of the b is found at low frequencies as the fluid particle displacement is comparable to the stack length. Furthermore, the lower the porosity the higher the Forchheimer term because the velocity gradients at the stack geometrical discontinuities are more pronounced.

The main novelty of this work is that, for the first time, non-linear losses of a parallel plate stack are investigated from a macroscopic point of view and summarised into a non-linear correlation, similar to the steady-state and well-known Darcy–Forchheimer law. The main difference is that it considers the frequency dependence of both Darcy and Forchheimer terms. The results can be used to enhance the analysis and design of thermoacoustic devices, which use the kind of stacks studied in the present work.

The purpose of this paper is to show how the EStra-Many method works on optimization problems characterized by high-dimensionality of the objective space. Moreover, a comparison with a more classical approach (a constrained bi-objective problem solved by means of NSGA-II) is done.

The six reactances of a compensation network (CN) for a wireless power transfer system (WPTS) are synthesized by means of an automated optimal design. In particular, an evolutionary algorithm EStra-Many coupled with a sorting strategy has been applied to an optimization problem with four objective functions (OFs). To assess the obtained results, a classical genetic algorithm NSGA-II has been run on a bi-objective problem, constrained by two functions, and the solutions have been analyzed and compared with the ones obtained by EStra-Many.

The proposed EStra-Many method identified a solution (CN synthesis) that enhances the WPTS, considering all the four OFs. In particular, to assess the synthesized CN, the Bode diagram of the frequency response and a circuital simulation were evaluated a posteriori; they showed good performance of the CN, with smooth response and without unwanted oscillations when fed by a square wave signal with offset. The EStra-Many method has been able to find a good solution among all the feasible solutions, showing potentiality also for other fields of research, in fact, a solution nondominated with respect to the starting point has been identified. From the methodological viewpoint, the main finding is a new formulation of the many-objective optimization problem based on the concept of degree of conflict, which gives rise to an implementation free from hierarchical weights.

The new approach EStra-Many used in this paper showed to properly find an optimal solution, trading-off multiple objectives. The compensation network so synthesized by the proposed method showed good properties in terms of frequency response and robustness. The proposed method, able to deal effectively with four OFs, could be applied to solve problems with a higher number of OFs in a variety of applications because of its generality.

Background: Geostatistics focuses on spatial or spatiotemporal datasets. Geostatistics was initially developed to generate probability distribution predictions of ore grade in the mining industry; however, it has been successfully applied in diverse scientific disciplines. This technique includes univariate, multivariate, and simulations. Kriging geostatistical methods, simple, ordinary, and universal Kriging, are not multivariate models in the usual statistical function. Notwithstanding, simple, ordinary, and universal kriging techniques utilize random function models that include unlimited random variables while modeling one attribute. The coKriging technique is a multivariate estimation method that simultaneously models two or more attributes defined with the same domains as coregionalization.

Objective: This study investigates the impact of populations on traffic volumes as a variable. The additional variable determines the strength or accuracy obtained when data integration is adopted. In addition, this is to help improve the estimation of annual average daily traffic (AADT).

Methods procedures, process: The investigation adopts the coKriging technique with AADT data from 2009 to 2016 from Montana, Minnesota, and Washington as primary attributes and population as a controlling factor (second variable). CK is implemented for this study after reviewing the literature and work completed by comparing it with other geostatistical methods.

Results, observations, and conclusions: The Investigation employed two variables. The data integration methods employed in CK yield more reliable models because their strength is drawn from multiple variables. The cross-validation results of the model types explored with the CK technique successfully evaluate the interpolation technique's performance and help select optimal models for each state. The results from Montana and Minnesota models accurately represent the states' traffic and population density. The Washington model had a few exceptions. However, the secondary attribute helped yield an accurate interpretation. Consequently, the impact of tourism, shopping, recreation centers, and possible transiting patterns throughout the state is worth exploring.