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2015

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Vol 6, No 2: [Theme issue] Fractional Calculus, Probability and Non-local Operators: Applications and Recent Developments, Part 2


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M-Wright/Mainardi function. A wide variety of processes in engineering and applied science exhibit behaviour that cannot be modelled by classical methods, motivating and inspiring research on extended mathematical tools. Recently, the study of fractional calculus (integrals and derivatives of non-integer order) has led to new fundamental results. This approach has been successful in describing anomalous behaviour including fractional diffusion-wave equations. From a mathematical point of view, diffusion and wave equations are known to be governed by partial differential equations of order 1 and 2 in time. The introduction of time-fractional derivatives of real order beta ranging from 0 to 2 leads to fractional partial differential equations that well describe the desired anomalous behaviours. The cover image presents plots of the so-called M-Wright/Mainardi function M_nu(|x|) for different values of parameter nu that is associated to the order of derivation in time by the formula beta=2 nu. The M-Wright/Mainardi function embodies the Green function of the time-fractional diffusion-wave equation whose special cases are the Gaussian function, for pure diffusive processes nu=0.5, and the Dirac delta function, for pure wave motion nu=1. More details can be found in G. Pagnini, E. Scalas, Commun. Appl. Ind. Math., Vol 6 (1), e-496 (2015), doi:10.1685/journal.caim.496

Cover Page

Vol 6, No 1: [Theme Issue] Fractional Calculus, Probability and Non-local Operators: Applications and Recent Developments, Part 1


ABOUT COVER IMAGE

M-Wright/Mainardi function. A wide variety of processes in engineering and applied science exhibit behaviour that cannot be modelled by classical methods, motivating and inspiring research on extended mathematical tools. Recently, the study of fractional calculus (integrals and derivatives of non-integer order) has led to new fundamental results. This approach has been successful in describing anomalous behaviour including fractional diffusion-wave equations. From a mathematical point of view, diffusion and wave equations are known to be governed by partial differential equations of order 1 and 2 in time. The introduction of time-fractional derivatives of real order beta ranging from 0 to 2 leads to fractional partial differential equations that well describe the desired anomalous behaviours. The cover image presents plots of the so-called M-Wright/Mainardi function M_nu(|x|) for different values of parameter nu that is associated to the order of derivation in time by the formula beta=2 nu. The M-Wright/Mainardi function embodies the Green function of the time-fractional diffusion-wave equation whose special cases are the Gaussian function, for pure diffusive processes nu=0.5, and the Dirac delta function, for pure wave motion nu=1. More details can be found in G. Pagnini, E. Scalas, Commun. Appl. Ind. Math., Vol 6 (1), e-496 (2015), doi:10.1685/journal.caim.496



2013

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Vol 4 (2013)


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Fast approximate (LP-relaxed) solution to a 3D-packing optimization problem. The maximization of the loaded cargo is a very demanding task, frequently arising in space engineering, when dealing with cargo accommodation of modules and vehicles. Complex rules are supposed to be taken into account, in compliance with strict balancing conditions and very tight operational restrictions. The International Space Station (ISS) project, with its logistic support necessity, has paved the way to a relevant research and development activity. The dedicated in-house packing software CAST (Cargo Accommodation Support Tool), funded by the European Space Agency (ESA), has been conceived by Thales Alenia Space for this purpose. Extensively utilized to carry out the whole loading of the Automated Transfer Vehicle (ATV, ESA), it has been further adapted to an ad hoc version, tailored to support the Columbus (ISS attached laboratory) on-board stowage. Mixed integer linear (MIP) and non-linear formulations have been thought up to tackle complex non-standard packing problems. A specific non-linear approach is aimed at improving initial approximate LP-relaxed solutions, whose graphical representation is provided by the cover image (where overlapping between items is allowed). More details can be found in G. Fasano, A. Castellazzo, Commun. Appl. Ind. Math., Vol 4, e-449 (2013), doi:10.1685/journal.caim.449

Image Credit: Giorgio Fasano, Alessandro Castellazzo, Thales Alenia Space Italia S.p.A., Turin, Italy



2012

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Vol 3, No 2 (2012)


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Observed errors in numerically preserving the Hamiltonian of the simple pendulum by multivalue integrators Geometric numerical integration of Hamiltonian problems is devoted to accurately and efficiently maintaining along the numerical solution the invariants preserved along the exact one. Runge-Kutta methods exhibit some fundamental conservation properties if they are symplectic. Even if multivalue methods cannot be symplectic, it is possible to enforce a nearly canonical behavior: this is made possible if the numerical method generates bounded parasitic components over long intervals. This aspect is discussed in R. D’Ambrosio, G. De Martino, B. Paternoster, CAIM Vol 3, No 2, 2012 doi: 10.1685/journal.caim.412 The figures, reported in the mentioned paper, show the errors observed in conserving the Hamiltonian of the simple pendulum by three different multivalue integrators: the top picture regards a method whose parasitic components are non-bounded, while the others are originated by applying two new multivalue methods with bounded parasitic components, both derived in the above paper. The numerical evidence confirms that, if parasitism is controlled, the Hamiltonian of the mechanical system is accurately preserved over long time intervals.

Image Credit: Raffaele D'Ambrosio, Giuseppe De Martino, Beatrice Paternoster, Dipartimento di Matematica, Facoltà di Scienze MM.FF.NN., Università degli Studi di Salerno, Italy


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Vol 3, No 1 (2012)


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Asymmetric scattering of electrons on graphene The level of miniaturization reached by modern semiconductor technology has brought electronic devices on the border of (and in many cases inside) the quantum realm. The macroscopic behavior of such devices is determined by the microscopic, and often non-intuitive, quantum dynamics of many carriers. Applied mathematics has, therefore, the difficult task of providing electronic industry with models that combine an accurate description of such behavior with the "handiness" of a classical picture. The theory of Quantum Fluid Dynamics (QFD) is expected to furnish an ideal tool to reach such a compromise. The cover image is taken from a numerical simulation that exploits QFD techniques: an electron wave packet moves on a graphene sheet and is scattered by an asymmetric potential barrier. The complete figure is reported in L. Barletti, CAIM Vol 3, No 1, 2012 doi: 10.1685/journal.caim.417 where methods and results of QFD are presented. The paper is focused on peculiar quantum effects arising from the statistics of identical particles and from spin-like degrees of freedom. The latter is the case of electrons in graphene, where they acquire a "pseudospin" which strongly affects the scattering properties.

Image Credit: L. Barletti Dipartimento di Matematica “Ulisse Dini” Università di Firenze, Italy


2011

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Vol 2, No 2 (2011)


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Functional data analysis of three-dimensional cerebral vascular geometries. The widespread diffusion in science and medicine of sophisticated technological instruments, capable of recording high dimensional signals, calls for new methods of data analysis. In particular, some data exhibit a functional nature, i.e., they may be represented via suitable curves and surfaces. The analysis of this type of data poses new and fascinating problems to modern statistics. An instance of functional data, obtained from three-dimensional cerebral angiographic images, was analyzed within the AneuRisk Project. This scientific endeavor aimed at investigating the role of vessel morphology and hemodynamics on the pathogenesis of cerebral aneurysms. The cover image is a detail of a figure displaying the estimated first derivatives of Internal Carotid Arteries centerlines of 65 patients; for complete figure see Sangalli, Secchi, Vantini and Vitelli, CAIM, vol 1., n. 1., doi: 10.1685/2010CAIM486. The paper presented a technique for efficiently classifying multidimensional curves, even in presence of curve misalignment. Data misalignment, apparent in the image, is a peculiar issue to functional data, and specifically to data coming from medical imaging corresponding to different patients.

Image Credit: L.M. Sangalli, P. Secchi, S. Vantini; Politecnico di Milano and V. Vitelli; Ecole Centrale Paris e Supélec.
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Vol 2, No 1 (2011): Selected Contributions from SIMAI 2010 (II)


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SIMAI 2010 visual identity (detail). The first issue of the second year of Communications in Applied and Industrial Mathematics concludes the selection of papers presented at SIMAI 2010. The cover of this issue contains a detail of the official hallmark of the Conference; hopefully, this will remember to all participants the high quality of the scientific program, the friendly atmosphere, and the beauty of Cagliari. For the complete image see the conference website.

Image Credit: Stefano Asili, Cagliari

2010

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Vol 1, No 2 (2010): Selected Contributions from SIMAI 2010 (I)


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SIMAI 2010 visual identity (detail). The second issue of Communications in Applied and Industrial Mathematics is dedicated to several papers presented at SIMAI 2010, the 10th Congress of SIMAI recently held in Cagliari, Italy from June 21 to June 25, 2010. Contemporary, yet largely inspired by various examples of ancient Sardinian art, this image in its sheer simplicity is highly representative of the spirit of the conference. For the complete image see the conference website.

Image Credit: Stefano Asili, Cagliari
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Vol 1, No 1 (2010): Inaugural Issue: Perspectives on Industrial and Applied Mathematics in Italy


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Electric current density imaging. Imaging techniques represent a powerful instrument in the localization of current sources in a conductor starting from the measurements of its external magnetic field. This determines the necessity to deal with magnetic inverse problems which are ill-posed and ill-conditioned, thus regularization techniques are needed. This visualization refers to the localization of sparse electric current densities of groups of current dipoles via classical Tikhonov regularization. The unequally space distribution due to the sparsity of current sources and the ill-conditioning caused by the high noise affecting the magnetic data make the reconstruction quite difficult and require the use of new methods privileging sparsity, as showed in the study of Bretti et al., doi:10.1685/2010CAIM493 . The xy plane is discretized with 128x128 pixels; the number of magnetometers used for measurements is 256 and the current density vector is decomposed in the basis of Daubechies orthonormal wavelets with four vanishing moments.

Image Credit: Gabriella Bretti, Università Campus Biomedico di Roma

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Communications in Applied and Industrial Mathematics
ISSN: 2038-0909