On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and discontinuous shocks

We study the generalization of the dispersionless Kadomtsev - Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one dimensional waves in the absence of dispersion and dissipation, and arising in several physical contexts, like acoustics, plasma physics, hydrodynamics and nonlinear optics. In 2+1 dimensions and with quadratic nonlinearity, this equation is integrable through a novel IST, and it has been recently shown to be a prototype model equation in the description of the two dimensional wave breaking of localized initial data. In higher dimensions and with higher nonlinearity, the generalized dKP equations are not integrable, but their invariance under motions on the paraboloid allows one to construct in this paper a family of exact solutions describing waves constant on their paraboloidal wave front and breaking simultaneously in all points of it, developing after breaking either multivaluedness or single valued discontinuous shocks. Then such exact solutions are used to build the longtime behavior of the solutions of the Cauchy problem, for small and localized initial data, showing that wave breaking of small initial data takes place in the longtime regime if and only if $m(n-1)\le 2$. At last, the analytic aspects of such a wave breaking are investigated in detail in terms of the small initial data, in both cases in which the solution becomes multivalued after breaking or it develops a discontinuous shock. These results, contained in the 2012 master thesis of one of the authors (FS), generalize those obtained by one of the authors (PMS) and S.V.Manakov for the dKP equation in n+1 dimensions with quadratic nonlinearity, and are obtained following the same strategy.Comment: 31 pages, 11 figure

A local field emission study of partially aligned carbon-nanotubes by AFM probe

We report on the application of Atomic Force Microscopy (AFM) for studying the Field Emission (FE) properties of a dense array of long and vertically quasi-aligned multi-walled carbon nanotubes grown by catalytic Chemical Vapor Deposition on a silicon substrate. The use of nanometric probes enables local field emission measurements allowing investigation of effects non detectable with a conventional parallel plate setup, where the emission current is averaged on a large sample area. The micrometric inter-electrode distance let achieve high electric fields with a modest voltage source. Those features allowed us to characterize field emission for macroscopic electric fields up to 250 V/$\mu$m and attain current densities larger than 10$^5$ A/cm$^2$. FE behaviour is analyzed in the framework of the Fowler-Nordheim theory. A field enhancement factor $\gamma \approx$ 40-50 and a turn-on field $E_{turn-on} \sim$15 V/$\mu$m at an inter-electrode distance of 1 $\mu$m are estimated. Current saturation observed at high voltages in the I-V characteristics is explained in terms of a series resistance of the order of M$\Omega$. Additional effects as electrical conditioning, CNT degradation, response to laser irradiation and time stability are investigated and discussed

Field emission from single multi-wall carbon nanotubes

Electron field emission characteristics of individual multiwalled carbon nanotubes have been investigated by a piezoelectric nanomanipulation system operating inside a scanning electron microscopy chamber. The experimental setup ensures a high control capability on the geometric parameters of the field emission system (CNT length, diameter and anode-cathode distance). For several multiwalled carbon nanotubes, reproducible and quite stable emission current behaviour has been obtained with a dependence on the applied voltage well described by a series resistance modified Fowler-Nordheim model. A turn-on field of about 30 V/um and a field enhancement factor of around 100 at a cathode-anode distance of the order of 1 um have been evaluated. Finally, the effect of selective electron beam irradiation on the nanotube field emission capabilities has been extensively investigated.Comment: 16 pages, 5 figure

Fracture Surfaces as Multiscaling Graphs

Fracture paths in quasi-two-dimenisonal (2D) media (e.g thin layers of materials, paper) are analyzed as self-affine graphs $h(x)$ of height $h$ as a function of length $x$. We show that these are multiscaling, in the sense that $n^{th}$ order moments of the height fluctuations across any distance $\ell$ scale with a characteristic exponent that depends nonlinearly on the order of the moment. Having demonstrated this, one rules out a widely held conjecture that fracture in 2D belongs to the universality class of directed polymers in random media. In fact, 2D fracture does not belong to any of the known kinetic roughening models. The presence of multiscaling offers a stringent test for any theoretical model; we show that a recently introduced model of quasi-static fracture passes this test.Comment: 4 pages, 5 figure

Seismic behaviour of geotechnical structures

This paper deals with some fundamental considerations regarding the behaviour of geotechnical structures under seismic loading. First a complete definition of the earthquake disaster risk is provided, followed by the importance of performing site-specific hazard analysis. Then some suggestions are provided in regard to adequate assessment of soil parameters, a crucial point to properly analyze the seismic behaviour of geotechnical structures. The core of the paper is centered on a critical review of the analysis methods available for studying geotechnical structures under seismic loadings. All of the available methods can be classified into three main classes, including the pseudo-static, pseudo-dynamic and dynamic approaches, each of which is reviewed for applicability. A more advanced analysis procedure, suitable for a so-called performance-based design approach, is also described in the paper. Finally, the seismic behaviour of the El Infiernillo Dam was investigated. It was shown that coupled elastoplastic dynamic analyses disclose some of the important features of dam behaviour under seismic loading, confirmed by comparing analytical computation and experimental measurements on the dam body during and after a past earthquake

Handover procedures in integrated satellite and terrestrial mobile systems

The integration of satellite and terrestrial mobile systems is investigated in terms of the strategies for handover across the integrated cellular coverage. The handover procedure is subdivided into an initialization phase, where the need for issuing a handover request must be identified, and an execution phase, where the request must be satisfied, if possible, according to a certain channel assignment strategy. A modeling approach that allows the design of the parameters that influence the performance of the overall handover procedure is presented, along with a few numerical results

Parametric cost modelling of components for turbomachines: Preliminary study

The ever-increasing competitiveness, due to the market globalisation, has forced the industries to modify their design and production strategies. Hence, it is crucial to estimate and optimise costs as early as possible since any following changes will negatively impact the redesign effort and lead time. This paper aims to compare different parametric cost estimation methods that can be used for analysing mechanical components. The current work presents a cost estimation methodology which uses non-historical data for the database population. The database is settled using should cost data obtained from analytical cost models implemented in a cost estimation software. Then, the paper compares different parametric cost modelling techniques (artificial neural networks, deep learning, random forest and linear regression) to define the best one for industrial components. Such methods have been tested on 9 axial compressor discs, different in dimensions. Then, by considering other materials and batch sizes, it was possible to reach a training dataset of 90 records. From the analysis carried out in this work, it is possible to conclude that the machine learning techniques are a valid alternative to the traditional linear regression ones

Cardiolipin drives cytochrome c proapoptotic and antiapoptotic actions

""\\"Cytochrome c (cytc) is pivotal in mitochondrial respiration and apoptosis. The heme-Fe-atom of native hexacoordinated horse heart cytc (hhcytc) displays a very low reactivity toward ligands and does not exhibit catalytic properties. However, on interaction with cardiolipin (CL), hhcytc changes its tertiary structure disrupting the heme-Fe-Met80 distal bond. The CL-hhcytc complex displays a very low midpoint potential, out of the range required for its physiological role, binds CO and NO with high affinity, facilitates peroxynitrite isomerization to NO(3)(-), and displays peroxidase activity. As a whole, the CL-hhcytc complex could play either proapoptotic effects, catalyzing lipid peroxidation and the subsequent hhcytc release into the cytoplasm, or antiapoptotic actions, such as scavenging peroxynitrite (i.e., protecting the mitochondrion from reactive nitrogen and oxygen species), and binding of CO and NO (i.e., inhibiting lipid peroxidation and hhcytc traslocation). Here, the CL-driven allosteric modulation of hhcytc properties is reviewed, highlighting proapoptotic and antiapoptotic actions. (C) 2011 IUBMB IUBMB Life, 63(3): 160-165, 2011\\""