In this work, we present a new technique for the decomposition of multivariate data, which we call Multivariate Fast Iterative Filtering (MvFIF) algorithm. We study its properties, proving rigorously that it converges in finite time when applied to the decomposition of any kind of multivariate signal. We test MvFIF performance using a wide variety of artificial and real multivariate signals, showing its ability to: separate multivariate modulated oscillations; align frequencies along different channels; produce a quasi–dyadic filterbank when decomposing white Gaussian noise; decompose the signal in a quasi–orthogonal set of components; being robust to noise perturbation, even when the number of channels is increased considerably. Finally, we compare it and its performance with the main methods developed so far in the literature, proving that MvFIF produces, without any a priori assumption on the signal under investigation and in a fast and reliable manner, a uniquely defined decomposition of any multivariate signal.

Differential problems with the Riesz derivative in space are widely used to model anomalous diffusion. Although the Riesz–Caputo derivative is more suitable for modeling real phenomena, there are few examples in literature where numerical methods are used to solve such differential problems. In this paper, we propose to approximate the Riesz–Caputo derivative of a given function with a cubic spline. As far as we are aware, this is the first time that cubic splines have been used in the context of the Riesz–Caputo derivative. To show the effectiveness of the proposed numerical method, we present numerical tests in which we compare the analytical solution of several boundary differential problems which have the Riesz–Caputo derivative in space with the numerical solution we obtain by a spline collocation method. The numerical results show that the proposed method is efficient and accurate.

In order to integrate mole balances (partial differential equations) of an Axial Dispersion Plug Flow Reactor (ADPFR) model, the overall superficial velocity is usually considered constant, a hypothesis which fits well only null or negligible variations of volumetric flow rate, e.g. feeding flow strongly diluted by inert species. This work proposes a numerical-integration approach (based on the method of lines) for ADPFR dynamic modelling, applied to simulate the CO₂ capture in an isothermal-isobaric packed bed, made of purposely synthesized and experimentally characterized CaO-mayenite sorbent particles. This approach proved to be suitable for both constant and variable superficial velocity with respect to time and space. With the latter option, velocity profiles agreed with simulated reactive phenomena, while discrepancies between solutions from the two options became increasingly evident as dilution of inlet CO₂ decreased. N₂ flow rate and CO₂ mole balances obtained from numerical-integrations with variable superficial velocity appeared as the most physicochemically reasonable.

This paper proposes a numerical solution of the nonlinear equations that describes the hysteretic behavior of ferromagnetic materials. From the proper definition and solution of these equations, an equivalent circuit model for a ferromagnetic core is developed and proposed. The results obtained from the equivalent circuit are compared with those obtained by a rigorous numerical solution.