This work is focused on polymorphic uncertainties in the framework of constitutive modeling for transversely isotropic materials.To this end, we propose a hybrid fuzzy-stochastic model, where the stochastic part accounting for aleatory uncertainties of material parameters is expanded with the multivariate polynomial chaos expansion.In order to account for epistemic uncertainties, polynomial chaos coefficients are treated as fuzzy variables.The underlying minimum and maximum optimization problem for the fuzzy analysis is approximated by α-level discretization, resulting in a separation of minimum and maximum problems.To become more universal, so-called quantities of interest are employed, which allow a general formulation for the target problem.Numerical examples with fuzzy, fuzzy-stochastic, and hybrid fuzzy-stochastic input demonstrate the versatility of the proposed formulation.

In order to model the flow of liquids with internal rotational degrees of freedom the theory of micropolar fluids according to Eringen is applied.The essentials of the theory are outlined and then specialized to Couette flow.The profiles for linear and angular velocities will be computed, and in particular, we shall also study the rise in temperature due to viscous dissipation, which is frequently ignored by mechanicians.Closed-form solutions for all three fields are derived for different boundary conditions.The question as to how the boundary conditions are realized physically will be discussed.

We prove the -convergence of a pantographic microstructured sheet with inextensible fibers to a 2D generalized continuum model.Large deformations considered as geometrical nonlinearities are taken into account, and the -convergence argument is developed in terms of convergence of measure functionals.We also prove a relative compactness property for the sequence of discrete energy functionals.

To assess the degree (i.e., isotropy, transverse isotropy, or orthotropy) and the directions of anisotropy of a three-dimensional structure, information about its mesostructure is necessary. Usually, a topological analysis of computed tomography or microcomputed tomography images is performed and requires an interpretation of the constitutive elements of the three-dimensional structure, which may lead to a simplistic description of the geometry. In this paper we propose an alternative technique based on a geometric tensor and we use it to analyze 38 representative elementary volumes extracted from 24 specimens of cortical bone in a human femur whose geometries have been reconstructed via microcomputed tomography images.

The paper summarizes and discusses the main theses exposed in a previous book (L' America dimenticata, Mondadori Universita, 2013 [in Italian]) in light of more recent results. Specifically, the work addresses the problem of explaining the origin of the systematic error on longitudes in Ptolemy's Geographia and its logical relation with the reduced estimate for the dimension of the Earth there given. The thesis is sustained that, conversely to a frequently advanced conjecture, the shrinking of the dimension of the Earth is a consequence of the scale error on the longitudes, which, in turn, was originated by a misidentification of the Islands of the Blessed. The location of the Islands of the Blessed according the source of Ptolemy is identified in the Caribbean. The analysis of a passage by Pliny provides an independent and quantitative confirmation of the proposed identification, which sheds new light on possible contact among civilizations.

We prove that, for a suitable choice of real numbers $a, b$, every operator from $\ell_2$ to $X_{a,b}$ and from $X_{a,b}$ to $\ell_2$ must be compact, where $X_{a,b}$ is the Bourgain- Delbaen's space.

This paper focuses on the relation between Gibbs and Markov random fields, one instance of the close relation between abstract and applied mathematics so often stressed by Lucio Russo in his scientific work.We start by proving a more explicit version, based on spin products, of the Hammersley-Clifford theorem, a classic result which identifies Gibbs and Markov fields under finite energy.Then we argue that the celebrated counterexample of Moussouris, intended to show that there is no complete coincidence between Markov and Gibbs random fields in the presence of hard-core constraints, is not really such.In fact, the notion of a constrained Gibbs random field used in the example and in the subsequent literature makes the unnatural assumption that the constraints are infinite energy Gibbs interactions on the same graph.Here we consider the more natural extended version of the equivalence problem, in which constraints are more generally based on a possibly larger graph, and solve it.The bearing of the more natural approach is shown by considering identifiability of discrete random fields from support, conditional independencies and corresponding moments.In fact, by means of our previous results, we show identifiability for a large class of problems, and also examples with no identifiability.Various open questions surface along the way.

The contributions of Lucio Russo to the mathematics of percolation and disordered systems are outlined. The context of his work is explained, and its ongoing impact on current work is described and amplified.

We study a system of two coupled oscillators linked by a linear elastic spring and positioned vertically in a uniform gravity field.It is demonstrated that the system has different equilibrium configurations below and above the oscillators' suspension centers.We obtained the relations of the string stiffness and the distance between the suspension centers identifying the stability region of the oscillators.

In this paper, a method to analyze the electromagnetic scattering of an elliptically polarized plane wave through a stratified lossy medium is presented. The interaction of the electromagnetic radiation with the stratified material is taken into account by means of the transfer-matrix approach: in this way, we can consider the stratified medium as an effective single interface. To do that, it was necessary to represent the complex plane-wave propagation vector with two different formulations: the phase and attenuation vectors and the complex angle. Thanks to these two formalisms, it is possible to describe the behaviors of this canonical phenomenon in an elegant way in all the cases of presence of a stratified lossy medium. A numerical code has been implemented to compute the field over the whole space. Finally, to validate the presented model, comparisons with the results presented in the literature have been provided.