A discrete Boltzmann model (DBM) is developed to investigate the hydrodynamic and thermodynamic non-equilibrium (TNE) effects in phase separation processes. The interparticle force drives changes and the gradient force, induced by gradients of macroscopic quantities, opposes them. In this paper, we investigate the interplay between them by providing a detailed inspection of various non-equilibrium observables. Based on the TNE features, we define TNE strength which roughly estimates the deviation amplitude from the thermodynamic equilibrium. The time evolution of the TNE intensity provides a convenient and efficient physical criterion to discriminate the stages of the spinodal decomposition and domain growth. Via the DBM simulation and this criterion, we quantitatively study the effects of latent heat and surface tension on phase separation. It is found that the TNE strength attains its maximum at the end of the spinodal decomposition stage, and it decreases when the latent heat increases from zero. The surface tension effects are threefold, prolong the duration of the spinodal decomposition stage, decrease the maximum TNE intensity, and accelerate the speed of the domain growth stage.

This paper deals with the issue of forecasting energy production of a Photo-Voltaic (PV) plant, needed by the Distribution System Operator (DSO) for grid planning. As the energy production of a PV plant is strongly dependent on the environmental conditions, the DSO has difficulties to manage an electrical system with stochastic generation. This implies the need to have a reliable forecasting of the irradiance level for the next day in order to setup the whole distribution network. To this aim, this paper proposes the use of transfer function models. The assessment of quality and accuracy of the proposed method has been conducted on a set of scenarios based on real data.

Nowadays, Magnetic Resonance Spectroscopy (MRS) represents a powerful nuclear magnetic resonance (NMR) technique in oncology since it provides information on the biochemical profile of tissues, thereby allowing clinicians and radiologists to identify in a non-invasive way the different tissue types characterising the sample under investigation. The main purpose of the pre-sent chapter is to provide a review of the most recent and significant applica-tions of non-negative matrix factorization (NMF) to MRS data in the field of tissue typing methods for tumour diagnosis. Specifically, NMF-based methods for the recovery of constituent spectra in ex vivo and in vivo brain MRS data, for brain tissue pattern differentiation using Magnetic Resonance Spectro-scopic Imaging (MRSI) data, and for automatic detection and visualisation of prostate tumours will be described. Furthermore, since several NMF imple-mentations are available in the literature, a comparison in terms of pattern de-tection accuracy of some NMF algorithms will be reported and discussed, and the NMF performance for MRS data analysis will be compared with that of other blind source separation (BSS) techniques.

In this work, we find and test a new approximated formula (based on the thin plate approximation), for recovering small, unknown damages on the inaccessible surface of a thin conducting (aluminium) plate. We solve this inverse problem from a controlled heat flux and a sequence of temperature maps on the accessible front boundary of our sample. We heat the front boundary by means of a sinusoidal flux. In the meanwhile, we take a sequence of temperature maps of the same side by means of an infrared camera. This procedure is called active infrared thermography. The solution of the heat equation on the accessible boundary of the damaged sample simulates the collection of data. We use domain derivative to linearize the boundary value problem for heat equation. Then, Fourier analysis on the periodic component of solutions leads us to an elliptic BVP. Finally, we apply perturbation theory in order to find out an approximation of the damage. Numerical tests obtained with synthetic data are encouraging. The solution of the heat equation on the accessible boundary of the damaged sample simulates the collection of data by means of the infrared camera. We use domain derivative to linearize the BVP for heat equation. Then, Fourier analysis on the periodic component of solutions leads us to an elliptic BVP. Finally, we apply the perturbation theory in (Formula presented.) (a is the thickness of our sample) in order to find out an approximation of the damage. Numerical tests obtained with synthetic data are encouraging.

We address the problem of supply chain management for a set of fresh and highly perishable products. Our activity mainly concerns forecasting sales. The study involves 19 retailers (small and medium size stores) and a set of 156 different fresh products. The available data is made of three year sales for each store from 2011 to 2013. The forecasting activity started from a pre-processing analysis to identify seasonality, cycle and trend components, and data filtering to remove noise. Moreover, we performed a statistical analysis to estimate the impact of prices and promotions on sales and customers' behaviour. The filtered data is used as input for a forecasting algorithm which is designed to be interactive for the user. The latter is asked to specify ID store, items, training set and planning horizon, and the algorithm provides sales forecasting. We used ARIMA, ARIMAX and transfer function models in which the value of parameters ranges in predefined intervals. The best setting of these parameters is chosen via a two-step analysis, the first based on well-known indicators of information entropy and parsimony, and the second based on standard statistical indicators. The exogenous components of the forecasting models take the impact of prices into account. Quality and accuracy of forecasting are evaluated and compared on a set of real data and some examples are reported.

A stochastic model for describing the firing activity of a couple of interacting neurons subject to time-dependent stimuli is proposed. Two stochastic differential equations suitably coupled and including periodic terms to represent stimuli imposed to one or both neurons are considered to describe the problem. We investigate the first passage time densities through specified firing thresholds for the involved time non-homogeneous Gauss-Markov processes. We provide simulation results and numerical approximations of the firing densities. Asymptotic behaviors of the first passage times are also given.

In this work, we exploit the integration of an advanced synthetic aperture radar (SAR) interferometry technique and the application of the finite-element method for the assessment and the interpretation of a localized subsidence phenomenon that took place within a specific area of Lisbon, Portugal. SAR images over the Lisbon city, covering different time intervals in the period of 1995-2010, were acquired and processed by means of the persistent scatterers (PSs) technique. Results clearly reveals a localized subsidence, limited to an area 2 km × 1.5 km wide, which has been confirmed by the leveling performed in 1976, 1996, and 2010. A physical interpretation of the observed ground deformations is provided based on the results of a finite-element model using stratigraphic data, \textit{in situ} piezometric measurements, and geotechnical properties of the involved soils. The ground subsidence is interpreted as the consequence of a consolidation process affecting the central fine-grained soil layer, which in turn has been driven by water withdrawal from the existing aquifers. The change of the hydraulic boundary conditions was generated by the excavation works for the construction of underground lines and also by the reduction of rainfall water infiltration as an effect of the increase in ground surface impermeable areas due to urbanization. The consequent consolidation process of the compressible fine-grained soil layer is supposed to provide a reasonable explanation of the observed time series of ground displacement in the examined area.

The work mainly discusses the use of the Ground-Based Synthetic Aperture Radar (GBSAR) interferometry technique to observe and control the behavior of earthfill or rockfill embankments for dam impoundments. This non-invasive technique provides overall displacements patterns measured with a sub-millimeter accuracy. The need of reliable monitoring of old embankment dams is rapidly increasing since a large number of these structures are still equipped with old monitoring devices, usually installed some decades ago, which can give only information on localized areas of the embankment. A case study regarding the monitoring of an earthfill dam embankment in Southern Italy by means of GBSAR interferometry is presented.

Solutions to the n-Laplace equation with a right-hand side f are considered. We exhibit the largest rearrangement-invariant space to which f has to belong for every local weak solution to be continuous. Moreover, we find the optimal modulus of continuity of solutions when f ranges in classes of rearrangement-invariant spaces, including Lorentz, Lorentz-Zygmund and various standard Orlicz spaces.

We formulate a smoothed-particle hydrodynamics numerical method, traditionally used for the Euler equations for fluid dynamics in the context of astrophysical simulations, to solve the nonlinear Schrodinger equation in the Madelung formulation. The probability density of the wave function is discretized into moving particles, whose properties are smoothed by a kernel function. The traditional fluid pressure is replaced by a quantum pressure tensor, for which a robust discretization is found. We demonstrate our numerical method on a variety of numerical test problems involving the simple harmonic oscillator, soliton-soliton collision, Bose-Einstein condensates, collapsing singularities, and dark matter halos governed by the Gross-Pitaevskii-Poisson equation. Our method is conservative, applicable to unbounded domains, and is automatically adaptive in its resolution, making it well suited to study problems with collapsing solutions.

Numerical simulations were conducted to determine the effects of flat-edge and curved-edge channel wall obstacles on the vortex entrapment of uniform-size particles in a microchannel with a T-shape divergent flow zone at different flow Reynolds numbers (Re). Two-particle simulations with a non-pulsating flow indicated that although particles were consistently entrapped in a vortex zone in a microchannel with flat-edge wall obstacles at all Re studied, vortex zone entrapment of particles occurred only at the lowest Re in a microchannel with curved-edge wall obstacles. In a microchannel with flat-edge obstacles, small particles avoided entrapment in vortices in a non-pulsating flow where large particles got trapped. Interparticle and particle-wall repulsive interaction potentials prevented vortex entrapment of particles in a microchannel with flat-edge wall obstacles only at high flow Re, revealing the existence of a threshold inertial force for particle liberation, if combined inertial and repulsive forces are considered in non-pulsating flow simulations. Pulsating flow enhanced the chance for liberation of particles that were otherwise trapped in vortices, but did not always ensure the particle liberation. Simulations with larger particle concentrations demonstrated that the location of particle-trapping vortices varied with changes in particle concentration. Simulation results further demonstrated the significance of particle retaining capabilities of vortices in a T-shape divergent zone within a microchannel.

We present a new approach to find accurate solutions to the Poisson equation, as obtained from the steady-state limit of a diffusion equation with strong source terms. For this purpose, we start from Boltzmann's kinetic theory and investigate the influence of higher-order terms on the resulting macroscopic equations. By performing an appropriate expansion of the equilibrium distribution, we provide a method to remove the unnecessary terms up to a desired order and show that it is possible to find, with high level of accuracy, the steady-state solution of the diffusion equation for sizeable Knudsen numbers. In order to test our kinetic approach, we discretize the Boltzmann equation and solve the Poisson equation, spending up to six order of magnitude less computational time for a given precision than standard lattice Boltzmann methods (LBMs).

Based on the past twenty-five years of lattice Boltzmann research, we venture into a far-flung prediction for the next twenty-five, with past and future privileged over the present state of affairs. Copyright (C) EPLA, 2015

Gaussian quadrature has been extensively studied in literature and several error estimates have been proved under dierent smoothness assumptions of the integrand function. In this talk we are going to state a general error estimate for Gauss-Jacobi quadrature, based on the weighted moduli of smoothness introduced by Z. Ditzian and V. Totik in [1]. Such estimate improves a previous result in [1, Theorem 7.4.1] and it includes several error bounds from literature as particular cases. Its proof has been achieved by using certain delayed means of the Fourier projections (de la Vallee Poussin means), which approximation properties will be also discussed. References [1] Z.Ditzian, V.Totik, Moduli of smoothness, SCMG Springer{Verlag, New York, 1987.

One of the most popular discrete approximating polynomials is the Lagrange interpolation polynomial and the Jacobi zeros provide a particularly convenient choice of the interpolation knots on [?1, 1]. However, it is well known that there is no point system such that the associate sequence of Lagrange polynomials, interpolating an arbitrary function f, would converge to f w.r.t. any weighted uniform or L1 norm. To overcome this problem, some discrete approximating polynomials have been originated from certain delayed arithmetic means of the Fourier-Jacobi partial sums (de la Vallee Poussin means) by approximating the Fourier coefficients with a Gaussian quadrature rule. The uniform convergence of these polynomials in suitable spaces of continuous functions has been recently proved. In this talk we complete the study by analyzing the approximation error w.r.t. the weighted L1 norm. In the main estimate we state, we use Ditzian-Totik moduli of smoothness.

We show that causality violation in a Kerr naked singularity spacetime is constrained by the existence of (radial) potential barriers. We extend to the class of vortical non-equatorial null geodesics confined to $$\theta $$? $$=$$= constant hyperboloids (boreal orbits) previous results concerning timelike ones (Calvani et al. in Gen Rel Gravit 9:155, 1978), showing that within this class of orbits, the causality principle is rigorously satisfied.

We study the motion of test particles in the metric of a localized and slowly rotating astronomical source, within the framework of linear gravitoelectromagnetism, grounded on a Post-Minkowskian approximation of general relativity. Special attention is paid to gravitational inductive effects due to time-varying gravitomagnetic fields. We show that, within the limits of the approximation mentioned above, there are cumulative effects on the orbit of the particles either for planetary sources or for binary systems. They turn out to be negligible.

We study the behavior of massless Dirac particles in the vacuum C-metric spacetime, representing the nonlinear superposition of the Schwarzschild black hole solution and the Rindler flat spacetime associated with uniformly accelerated observers. Under certain conditions, the C-metric can be considered as a unique laboratory to test the coupling between intrinsic properties of particles and fields with the background acceleration in the full (exact) strong-field regime. The Dirac equation is separable by using, e.g., a spherical-like coordinate system, reducing the problem to one-dimensional radial and angular parts. Both radial and angular equations can be solved exactly in terms of general Heun functions. We also provide perturbative solutions to first order in a suitably defined acceleration parameter, and compute the acceleration-induced corrections to the particle absorption rate as well as to the angle-averaged cross section of the associated scattering problem in the low-frequency limit. Furthermore, we show that the angular eigenvalue problem can be put in one-to-one correspondence with the analogous problem for a Kerr spacetime, by identifying a map between these 'acceleration' harmonics and Kerr spheroidal harmonics. Finally, in this respect we discuss the nature of the coupling between intrinsic spin and spacetime acceleration in comparison with the well known Kerr spin-rotation coupling.

The features of equatorial motion of an extended body in Kerr spacetime are investigated in the framework of the Mathisson-Papapetrou-Dixon model. The body is assumed to stay at quasiequilibrium and respond instantly to external perturbations. Besides the mass, it is completely determined by its spin, the multipolar expansion being truncated at the quadrupole order, with a spin-induced quadrupole tensor. The study of the radial effective potential allows us to analytically determine the innermost stable circular orbit shift due to spin and the associated frequency of the last circular orbit.

A general framework is developed to investigate the properties of useful choices of stationary spacelike slicings of stationary spacetimes whose congruences of timelike orthogonal trajectories are interpreted as the world lines of an associated family of observers, the kinematical properties of which in turn may be used to geometrically characterize the original slicings. On the other hand, properties of the slicings themselves can directly characterize their utility motivated instead by other considerations like the initial value and evolution problems in the 3-plus-1 approach to general relativity. An attempt is made to categorize the various slicing conditions or "time gauges" used in the literature for the most familiar stationary spacetimes: black holes and their flat spacetime limit.