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In any membrane filtration, the prediction of permeate flux is critical to calculate the membrane surface required, which is an essential parameter for scaling-up, equipment sizing, and cost determination. For this reason, several models based on phenomenological or theoretical derivation (such as gel-polarization, osmotic pressure, resistance-in-series, and fouling models) and non-phenomenological models have been developed and widely used to describe the limiting phenomena as well as to predict the permeate flux. In general, the development of models or their modifications is done for a particular synthetic model solution and membrane system that shows a good capacity of prediction. However, in more complex matrices, such as fruit juices, those models might not have the same performance. In this context, the present work shows a review of different phenomenological and non-phenomenological models for permeate flux prediction in UF, and a comparison, between selected models, of the permeate flux predictive capacity. Selected models were tested with data from our previous work reported for three fruit juices (bergamot, kiwi, and pomegranate) processed in a cross-flow system for 10 h. The validation of each selected model’s capacity of prediction was performed through a robust statistical examination, including a residual analysis. The results obtained, within the statistically validated models, showed that phenomenological models present a high variability of prediction (values of R-square in the range of 75.91–99.78%), Mean Absolute Percentage Error (MAPE) in the range of 3.14–51.69, and Root Mean Square Error (RMSE) in the range of 0.22–2.01 among the investigated juices. The non-phenomenological models showed a great capacity to predict permeate flux with R-squares higher than 97% and lower MAPE (0.25–2.03) and RMSE (3.74–28.91). Even though the estimated parameters have no physical meaning and do not shed light into the fundamental mechanistic principles that govern these processes, these results suggest that non-phenomenological models are a useful tool from a practical point of view to predict the permeate flux, under defined operating conditions, in membrane separation processes. However, the phenomenological models are still a proper tool for scaling-up and for an understanding the UF process.

Abstract Nowadays High Energy Physics experiments can accumulate unprecedented statistics of heavy flavour decays that allows to apply new methods, based on the study of very rare phenomena, which used to be just desperate. In this paper we propose a new method to measure composition of K 0- K ¯$$ \\overline{K} $$0, produced in a decay of heavy hadrons. This composition contains important information, in particular about weak and strong phases between amplitudes of the produced K 0 and K ¯$$ \\overline{K} $$0. We consider possibility to measure these parameters with time-dependent K 0 → π + π − analysis. Due to C P -violation in kaon mixing time-dependent decay rates of K 0 and K ¯$$ \\overline{K} $$0 differ, and the initial amplitudes revealed in the CP-violating decay pattern. We perform phenomenological study of K 0 decay evolution initially produced as a combination a K 0 t + b K ¯ 0 t$$ a\\left.|{K}^0(t)\\right\\rangle +b\\left.|{\\overline{K}}^0(t)\\right\\rangle $$, where a and b, complex amplitudes, could also be dependent on decay time of heavy mother particle. In particular we consider cases of charmed hadrons decays: D + → K 0 π +, D s +$$ {D}_s^{+} $$→ K 0 K +, Λ → pK 0 and with some assumptions D 0 → K 0 π 0. This can be used to test the sum rule for charmed mesons and to obtain input for the full constraint of the two body amplitudes of D-mesons.

Abstract We investigate the new contributions to the parameters g L and g R of the Zb b ¯ Zbb̅ vertex in a multi-Higgs-doublet model (MHDM). We emphasize that those contributions generally worsen the fit of those parameters to the experimental data. We propose a solution to this problem, wherein g R has the opposite sign from the one predicted by the Standard Model; this solution, though, necessitates light scalars and large Yukawa couplings in the MHDM.