Models to detect scientific creativity: Why something simpler than Fréchet Metric Manifolds?

We claim that the models needed to describe scientific creativity (and, in particular, suitable to effectively detect it) have to be very sophisticated. Indeed, the process of creating original and predictive scientific theories is manifestly the most complex ever investigated by the human mind (There are also some paradoxical aspects in the action of a mind that is investigating its own way of functioning, but we are confident that it will be possible to avoid them). In mathematical physics one of the most complex state space structures is given by Frechet Metric Manifolds. We conjecture that they will be needed to model the state of complexity of the mind of a scientist (However, we will not be surprised if an even more complex structure could be needed). The obtained models have a very important application: they are essential to design and rule the selection process that assigns a university chair (or a research grant). Recently some algorithms have been introduced to calculate some bibliometric indices. We claim that it is not reasonable to use them to evaluate the scientific quality of researchers, chair or grant holders, departments or whole universities. Instead, the only presently viable process must involve carefully designed procedures, similar to those used for forming juries. These procedures must be enforced to rule the formation and functioning of ad hoc peer committees entrusted to evaluate academic institutions and nominate professors, chairs or research grant holders. Bibliometrics and Scientometrics are too young as disciplines and therefore it is not possible yet, by means of the theoretical insight gained thanks to them, to design a more effective evaluation process. Only when game and artificial intelligence theories become sufficiently advanced will it become possible to efficiently replace selection peers committees (i.e. academic juries)

Vibration control in plates by uniformly distributed PZT actuators interconnected via electric networks

In this paper a novel device aimed at controlling the mechanical vibrations of plates by means of a set of electrically-interconnected piezoelectric actuators is described. The actuators are embedded uniformly in the plate wherein they connect every node of an electric network to ground, thus playing the two-fold role of capacitive element in the electric network and of couple suppliers. A mathematical model is introduced to describe the propagation of electro-mechanical waves in the device; its validity is restricted to the case of wave-forms with wave-length greater than the dimension of the piezoelectric actuators used. A self-resonance criterion is established which assures the possibility of electro-mechanical energy exchange. Finally the problem of vibration control in simply supported and clamped plates is addressed; the optimal net-impedance is determined. The results indicate that the proposed device can improve the performances of piezoelectric actuationComment: 22 page

Optimal piezo-electro-mechanical coupling to control plate vibrations

A new way of coupling electrical and mechanical waves, using piezoelectric effect, is presented here. Since the energy exchange between two systems supporting wave propagation is maximum when their evolution is governed by similar equations, hence, an optimal electromechanical coupling is obtained by designing an electric network which is "analog" to the mechanical structure to be controlled. In this paper, we exploit this idea to enhance the coupling, between a Kirchhoff-Love plate and one possible synthesis of its circuital analog, as obtained by means of a set of piezoelectric actuators uniformly distributed upon the plate. It is shown how this approach allows for an optimal energy exchange between the mechanic and the electric forms independent of the modal evolution of the structure. Moreover, we show how an efficient electric dissipation of the mechanical energy can be obtained adding dissipative elements in the electric network.Comment: 9 page

King post truss as a motif for internal structure of (meta)material with controlled elastic properties

One of the most interesting challenges in the modern theory of materials consists in the determination of those microstructures which produce, at the macro-level, a class of metamaterials whose elastic range is many orders of magnitude wider than the one exhibited by ‘standard’ materials. In Dell’Isola et al. (2015 Zeitschrift für angewandte Mathematik und Physik 66, 3473- 3498. (doi: 10.1007/s00033-015-0556-4)), it was proved that, with a pantographic microstructure constituted by ‘long’ microbeams it is possible to obtainmetamaterials whose elastic range spans up to an elongation exceeding 30%. In this paper, we demonstrate that the same behaviour can be obtained bymeans of an internal microstructure based on a king post motif. This solution shows many advantages: it involves only microbeams; all constituting beams are undergoing only extension or compression; all internal constraints are terminal pivots. While the elastic deformation energy can be determined as easily as in the case of long-beam microstructure, the proposed design seems to have obvious remarkable advantages: it seems to be more damage resistant and therefore to be able to have a wider elastic range; it can be realized with the same three-dimensional printing technology; it seems to be less subject to compression buckling. The analysis which we present here includes: (i) the determination of Hencky-type discrete models for king post trusses, (ii) the application of an effective integration scheme to a class of relevant deformation tests for the proposed metamaterial and (iii) the numerical determination of an equivalent second gradient continuum model. The numerical tools which we have developed and which are presented here can be readily used to develop an extensive measurement campaign for the proposed metamaterial

Macroscopic description of microscopically strongly inhomogenous systems: A mathematical basis for the synthesis of higher gradients metamaterials

We consider the time evolution of a one dimensional $n$-gradient continuum. Our aim is to construct and analyze discrete approximations in terms of physically realizable mechanical systems, called microscopic because they are living on a smaller space scale. We validate our construction by proving a convergence theorem of the microscopic system to the given continuum, as the scale parameter goes to zero.Comment: 20 page