In this paper, we present new fixed point results for multivalued maps on extension spaces with respect to a map.

Classical and multiscale non-equilibrium thermodynamics have dif- ferent histories and different objectives. In this Note we explain the differences and review some topics in which the multiscale viewpoint of mesoscopic time evolution of macroscopic systems helped to advance the classical non-equilibrium thermodynamics. Eventually, we illustrate the Braun-Le Chatelier principie in dissipative thermodynamics.

In this paper, we consider an extension of the two-fluid model for superfluid helium. Over the years, two kinds of models have been pro- posed to describe the observations on helium II: the two-fluid model, in which the specific entropy of the superfluid is assumed to be zero, and the extended one-fluid model, derived from extended thermodynamics. Since the statement that the entropy of the superfluid fraction vanishes has not been demonstrated theoretically, in this paper we generalize the standard (Landau and Tisza) two-fluid model allowing that a small amount of entropy is carried by the superfluid component.

This work presents an energy management system for stand-alone direct current microgrids, based on a fuzzy controller that employs a bracket operator. The system takes as input the net power and the state of charge of the storage unit, processed through a structure in- spired by proportional-integral-derivative regulators. The control logic effectively governs the activation of the fuel cell, optimizing resource usage while maintaining operational stability. The performance of the system, validated on both simulated and real data, shows a high degree of consistency in the two contexts, confirming the reliability of the ap- proach and the potential of simulation as a support tool for designing real-world systems with a low error margin.

The problem of stabilization of dynamical systems is very impor­tant, as part of the control systems field. The theory of positive polynomials in control has the seeds in the 1980’s, based on the work of Naum Zuselevich. They can be used to solve a variety of problems in robust control, non-linear control and also in non-convex optimization. The present paper approaches the problem of finding a stabilizing feedback for homogeneous polynomial systems in the plane. It is known that the polynomial systems in the plane have a lot of special properties which can be easier approached thanks to the dimension 2. The case of systems arising from excitable media is taken into account, and the results will be used to deduce properties for further detailed analysis.

In this paper we propose a reduction procedure for determining generalized traveling waves for first order quasilinear hyperbolic non-homogeneous systems. The basic idea is to look for solutions of the governing model that satisfy a further set of differential constraints. Some applications are given for a barotropic fluid with a source term.

In a previous paper, a linear theory for magnetic relaxation phe- nomena in reacting anisotropic fluid mixtures was developed, within the framework of the irreversible processes thermodynamics with internal variables. In that model, the total magnetization was split into two irreversible contributions, introducing one of them as an internal variable. In this paper, the same approach is applied to isotropic and perfect isotropic magnetizable reacting fluid mixtures. In the latter case, it is shown that in the phenomenological equations no cross effects arise between magnetic relaxation and other irreversible phenomena, since fluxes and thermodynamic forces of different tensorial character do not couple (Curie’s principle). For perfect isotropic mixtures, we also derive the equations of state and the magnetic relaxation equa- tion, which, unlike in the anisotropic case, do not contain contributions from temperature, concentrations, and their time derivatives. Special cases are treated. The results have applications in nuclear resonance, biology, medicine, and other fields.

A toy model is proposed for the Cosmic Dipole consisting in the Shapley attractor and the so-called Dipole repeller, whose action is assimilated to an anti-gravitational force. According to this model, the local group will collapse in finite time with the Shapley attractor and, by using the available figures for distances and masses, it is shown that it will happen in less than 100 billion years. To obtain a more precise estimate, more knowledge will be necessary on the equivalent negative mass of the repeller.

A set of field equations for a multi-temperature gas mixture in spherical symmetry is considered within the framework of Rational Extended Thermodynamics. The invariance with respect to stretching group of transformations is investigated and the associated canonical variables are introduced. This makes it possible to write the system in autonomous form. Special similarity solutions are determined and the propagation of weak discontinuities in a non-constant state of the original system is studied. Finally, the evolution of the discontinuity is illustrated for a mixture of Helium and Argon.