Interplay between bending and stretching in carbon nanoribbons

We investigate the bending properties of carbon nanoribbons by combining continuum elasticity theory and tight-binding atomistic simulations. First, we develop a complete analysis of a given bended configuration through continuum mechanics. Then, we provide by tight-binding calculations the value of the bending rigidity in good agreement with recent literature. We discuss the emergence of a stretching field induced by the full atomic-scale relaxation of the nanoribbon architecture. We further prove that such an in-plane strain field can be decomposed into a first contribution due to the actual bending of the sheet and a second one due to edge effects.Comment: 5 pages, 6 figure

A novel CMB polarization likelihood package for large angular scales built from combined WMAP and Planck LFI legacy maps

We present a CMB large-scale polarization dataset obtained by combining WMAP Ka, Q and V with Planck 70 GHz maps. We employ the legacy frequency maps released by the WMAP and Planck collaborations and perform our own Galactic foreground mitigation technique, which relies on Planck 353 GHz for polarized dust and on Planck 30 GHz and WMAP K for polarized synchrotron. We derive a single, optimally-noise-weighted, low-residual-foreground map and the accompanying noise covariance matrix. These are shown, through $\chi^2$ analysis, to be robust over an ample collection of Galactic masks. We use this dataset, along with the Planck legacy Commander temperature solution, to build a pixel-based low-resolution CMB likelihood package, whose robustness we test extensively with the aid of simulations, finding excellent consistency. Using this likelihood package alone, we constrain the optical depth to reionazation $\tau=0.069^{+0.011}_{-0.012}$ at $68\%$ C.L., on 54\% of the sky. Adding the Planck high-$\ell$ temperature and polarization legacy likelihood, the Planck lensing likelihood and BAO observations we find $\tau=0.0714_{-0.0096}^{+0.0087}$ in a full $\Lambda$CDM exploration. The latter bounds are slightly less constraining than those obtained employing \Planck\ HFI CMB data for large angle polarization, that only include EE correlations. Our bounds are based on a largely independent dataset that does include also TE correlations. They are generally well compatible with Planck HFI preferring slightly higher values of $\tau$. We make the low-resolution Planck and WMAP joint dataset publicly available along with the accompanying likelihood code.Comment: The WMAP+LFI likelihood module is available on \http://www.fe.infn.it/u/pagano/low_ell_datasets/wmap_lfi_legacy

Nanofriction behavior of cluster-assembled carbon films

We have characterized the frictional properties of nanostructured (ns) carbon films grown by Supersonic Cluster Beam Deposition (SCBD) via an Atomic Force-Friction Force Microscope (AFM-FFM). The experimental data are discussed on the basis of a modified Amonton's law for friction, stating a linear dependence of friction on load plus an adhesive offset accounting for a finite friction force in the limit of null total applied load. Molecular Dynamics simulations of the interaction of the AFM tip with the nanostructured carbon confirm the validity of the friction model used for this system. Experimental results show that the friction coefficient is not influenced by the nanostructure of the films nor by the relative humidity. On the other hand the adhesion coefficient depends on these parameters.Comment: 22 pages, 6 figures, RevTex

Schur functions and their realizations in the slice hyperholomorphic setting

we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable resolvent, the so called S-resolvent operator and to extend several results that hold in the complex case to the quaternionic case. We discuss reproducing kernels, positive definite functions in this setting and we show how they can be obtained in our setting using the extension operator and the slice regular product. We define Schur multipliers, and find their co-isometric realization in terms of the associated de Branges-Rovnyak space

Orbital dynamics of "smart dust" devices with solar radiation pressure and drag

This paper investigates how perturbations due to asymmetric solar radiation pressure, in the presence of Earth shadow, and atmospheric drag can be balanced to obtain long-lived Earth centred orbits for swarms of micro-scale 'smart dust' devices, without the use of active control. The secular variation of Keplerian elements is expressed analytically through an averaging technique. Families of solutions are then identified where Sun-synchronous apse-line precession is achieved passively to maintain asymmetric solar radiation pressure. The long-term orbit evolution is characterized by librational motion, progressively decaying due to the non-conservative effect of atmospheric drag. Long-lived orbits can then be designed through the interaction of energy gain from asymmetric solar radiation pressure and energy dissipation due to drag. In this way, the usual short drag lifetime of such high area-to-mass spacecraft can be greatly extended (and indeed selected). In addition, the effect of atmospheric drag can be exploited to ensure the rapid end-of-life decay of such devices, thus preventing long-lived orbit debris

Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem

We answer a question left open in [4] and [3], by proving that the blow-up of minimizers u of the lower dimensional obstacle problem is unique at generic point of the free boundary

The phenomenology of depression

The phenomenological method, characterized by the suspension of judgment (epoché), has helped analyzing the subjective experience of patients affected by mental disorders. Psychiatry, dealing with the human being itself in its complexity and unicity, is placed between the biological positivistic attempt, for which the symptoms of mental illness are a mere consequence of brain dysfunctions and the phenomenological-existential approach, inclined to consider the symptoms as meaningful phenomena of the person’s subjective experience. Eugène Minkowski, Ludwig Binswanger, Arthur Tatossian, Kimura Bin, Henri Maldiney and Hubertus Tellenbach are fundamental authors in the phenomenological psychopathology of depression; they described the alterations of the lived time, space, body and others experienced by the depressed. Starting from the main theoretical contributions of the authors, we will focus on the psychopathology and discuss the key themes of clinical depression: guilt, poverty and hypochondriasis. Finally we will focus on the typus melancholicus construct

Analysis of an Inverse Problem Arising in Photolithography

We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship between the target shape and the unknown is modeled through diffractive optics. We develop a variational formulation that is well-posed and propose an approximation that can be shown to have convergence properties. The approximate problem can serve as a foundation to numerical methods.Comment: 28 pages, 1 figur

Semi-autonomous Intersection Collision Avoidance through Job-shop Scheduling

In this paper, we design a supervisor to prevent vehicle collisions at intersections. An intersection is modeled as an area containing multiple conflict points where vehicle paths cross in the future. At every time step, the supervisor determines whether there will be more than one vehicle in the vicinity of a conflict point at the same time. If there is, then an impending collision is detected, and the supervisor overrides the drivers to avoid collision. A major challenge in the design of a supervisor as opposed to an autonomous vehicle controller is to verify whether future collisions will occur based on the current drivers choices. This verification problem is particularly hard due to the large number of vehicles often involved in intersection collision, to the multitude of conflict points, and to the vehicles dynamics. In order to solve the verification problem, we translate the problem to a job-shop scheduling problem that yields equivalent answers. The job-shop scheduling problem can, in turn, be transformed into a mixed-integer linear program when the vehicle dynamics are first-order dynamics, and can thus be solved by using a commercial solver.Comment: Submitted to Hybrid Systems: Computation and Control (HSCC) 201