Towards the Formalization of Fractional Calculus in Higher-Order Logic

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to analyze a wide class of physical systems in various fields of science and engineering. In this paper, we describe an ongoing project which aims at formalizing the basic theories of fractional calculus in the HOL Light theorem prover. Mainly, we present the motivation and application of such formalization efforts, a roadmap to achieve our goals, current status of the project and future milestones.Comment: 9 page

Piezo-electromechanical smart materials with distributed arrays of piezoelectric transducers: Current and upcoming applications

This review paper intends to gather and organize a series of works which discuss the possibility of exploiting the mechanical properties of distributed arrays of piezoelectric transducers. The concept can be described as follows: on every structural member one can uniformly distribute an array of piezoelectric transducers whose electric terminals are to be connected to a suitably optimized electric waveguide. If the aim of such a modification is identified to be the suppression of mechanical vibrations then the optimal electric waveguide is identified to be the 'electric analog' of the considered structural member. The obtained electromechanical systems were called PEM (PiezoElectroMechanical) structures. The authors especially focus on the role played by Lagrange methods in the design of these analog circuits and in the study of PEM structures and we suggest some possible research developments in the conception of new devices, in their study and in their technological application. Other potential uses of PEMs, such as Structural Health Monitoring and Energy Harvesting, are described as well. PEM structures can be regarded as a particular kind of smart materials, i.e. materials especially designed and engineered to show a specific andwell-defined response to external excitations: for this reason, the authors try to find connection between PEM beams and plates and some micromorphic materials whose properties as carriers of waves have been studied recently. Finally, this paper aims to establish some links among some concepts which are used in different cultural groups, as smart structure, metamaterial and functional structural modifications, showing how appropriate would be to avoid the use of different names for similar concepts. © 2015 - IOS Press and the authors

Kirchhoff's Law Can Be Exact

Kirchhoff's current law is thought to describe the translational movement of charged particles through resistors. But Kirchhoff's law is widely used to describe movements of current through resistors in high speed devices. Current at high frequencies/short times involves much more than the translation of particles. Transients abound. Augmentation of the resistors with ad hoc 'stray' capacitances is often used to introduce transients into models like those in real resistors. But augmentation hides the underlying problem, rather than solves it: the location, value and dielectric properties of the stray capacitances are not well determined. Here, we suggest a more general approach, that is well determined. If current is redefined as in Maxwell's equations, independent of the properties of dielectrics, Kirchhoff's law is exact and transients arise automatically without ambiguity. The transients in a particular real circuit-a high density integrated circuit for example-can then be described by measured constitutive equations together with Maxwell's equations without the introduction of arbitrary circuit elements.Comment: Version 3: Expanded treatment of continuity equatio

Computing parametrized solutions for plasmonic nanogap structures

The interaction of electromagnetic waves with metallic nanostructures generates resonant oscillations of the conduction-band electrons at the metal surface. These resonances can lead to large enhancements of the incident field and to the confinement of light to small regions, typically several orders of magnitude smaller than the incident wavelength. The accurate prediction of these resonances entails several challenges. Small geometric variations in the plasmonic structure may lead to large variations in the electromagnetic field responses. Furthermore, the material parameters that characterize the optical behavior of metals at the nanoscale need to be determined experimentally and are consequently subject to measurement errors. It then becomes essential that any predictive tool for the simulation and design of plasmonic structures accounts for fabrication tolerances and measurement uncertainties. In this paper, we develop a reduced order modeling framework that is capable of real-time accurate electromagnetic responses of plasmonic nanogap structures for a wide range of geometry and material parameters. The main ingredients of the proposed method are: (i) the hybridizable discontinuous Galerkin method to numerically solve the equations governing electromagnetic wave propagation in dielectric and metallic media, (ii) a reference domain formulation of the time-harmonic Maxwell's equations to account for geometry variations; and (iii) proper orthogonal decomposition and empirical interpolation techniques to construct an efficient reduced model. To demonstrate effectiveness of the models developed, we analyze geometry sensitivities and explore optimal designs of a 3D periodic annular nanogap structure.Comment: 28 pages, 9 figures, 4 tables, 2 appendice

Reply to ‘Comment on “Dependence of shear wave seismoelectrics on soil textures: a numerical study in the vadose zone by F.I. Zyserman, L.B. Monachesi and L. Jouniaux” by Revil, A.’

In this paper we reply to a the comment made by Revil (2017) on our paper (2017, Geophys. J. Int., 208), where we describe seismoelectric phenomena in the vadose zone based on the theory of Pride empirically extended for unsaturated conditions. We analyse and answer each one of the enumerated critics, and reaffirm the conclusions of our work. In particular, we prove that using the conductivity model suggested by Revil (2017) does not change our predictions significantly, contrary to what was argued in the comment. Further, in the light of previous and new theoretical and experimental results existing in the literature, we confirm the reasonability of having tested a non-monotonic saturation dependent streaming potential coefficient model besides the monotonic one, and discuss the suitability of assuming a linear relation between the permeability and the excess charge.Fil: Zyserman, Fabio Ivan. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas. Departamento de Geofísica Aplicada; ArgentinaFil: Monachesi, Leonardo Bruno. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Río Negro. Sede Alto Valle. Instituto de Investigaciones en Paleobiología y Geología; ArgentinaFil: Jouniaux, L.. Centre National de la Recherche Scientifique; Franci

Engineering handbook

1999 handbook for the faculty of Engineerin

Engineering handbook

2006 handbook for the faculty of Engineerin