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 Seminars Apr. 16, 2010 A new lower bound for the Linear Arrangement of a graph Prof. Juan-José Salazar-González, Department of Statistics, Operational Research and Computation, University of "La Laguna" (Spain) Abstract: Minimum Linear Arrangement is a classical basic combinatorial optimization problem from the 1960s, which turns out to be extremely challenging in practice. In particular, for most of its benchmark instances, even the order of magnitude of the optimal solution value is unknown, as testified by the surveys on the problem that contain tables in which the best known solution value often has one more digit than the best known lower bound value. In this talk, we propose a linear-programming based approach to compute lower bounds on the optimum. This allows us, for the first time, to show that the best known solutions are indeed not far from optimal for most of the benchmark instances. This is a join work with Alberto Caprara (Bologna, Italia) and Adam Letchford (Lancaster, U.K.). Dec. 15, 2009 A relation between compatibility and hysteresis and its role in the search for new active materials Prof. Richard James, Department of Aerospace Engineering and Mechanics, University of Minnesota (U.S.A) Abstract: We present some recent measurements of hysteresis, in materials undergoing big first order phase transformations, that resulted from a systematic program of tuning of the lattice parameters by changing composition. The lattice parameters were tuned so that a certain non generic condition of compatibility between phases was satisfied. An exceptionally sharp drop of size of the hysteresis of the transformation was observed at the special lattice parameters. The data has some fascinating features, including an apparent singularity. We re-examine the origins of hysteresis in light of these measurements, commenting also on the role of defects and pinning, and the use of this kind of tuning to discover "unlikely" new materials. These thoughts lead us to consider hysteresis as arising from an elastic energy barrier associated with the failure of certain conditions of compatibility. We calculate this barrier based on methods of Gamma-convergence, where the small parameter is related to the near satisfaction of this non-generic condition of compatibility. A recent study suggest suggests a tantalizing relation between the emerging alloys with minimum hysteresis and stability of the transformation under cycling. Joint work with Stefan Mueller, Nick Schryvers and Jerry Zhang. Dec. 17, 2008 On the motion of a rigid body in a Navier-Stokes liquid under the influence of a time- periodic driving mechanism Prof. Giovanni P. Galdi, Department of Mechanical Engineering, University of Pittsburgh (U.S.A) Abstract: This talk is devoted to the mathematical investigation of the motion of a rigid body in an infinite Navier-Sokes liquid,under the action of a time-periodic driving mechanism.This latter can be,for example, a time periodic force acting along a given constant direction, or time periodic boundary data. The main objective is to find conditions under which the body is propelled by the driving mechanism, namely, conditions that ensure that the body can cover a given trajectory in a finite time interval. This research is in collaboration with Ana L. Silvestre (IST Lisbon,Portugal). Jun. 10, 2008 Gamma-convergence for conservation laws Dr. Matteo Novaga, Department of Mathematics, University of Pisa (Italy) Abstract: We considered a control problem for the viscous approximation of a scalar conservation law. We study the Gamma-convergence of its cost functional in the case where the viscosity coefficient tends to zero. In this case, we are able to characterize the entropic solutions as the locus of the Gamma-limit zeros. Mag. 14, 2008 Modelli matematici per incendi nei tunnel stradali Prof. Ingo Gasser, Schwerpunkt Differentialgleichungen und Dynamische Systeme, University of Hamburg (Germany) Abstract: The following topics will be covered: We discuss various approaches for modelling tunnel fires. We derive a new model and analyse it. Finally, we present numerical simulation on real situations. Apr. 16, 2008 GRID and distributed computing Prof. Federico Calzolari, Scuola Normale Superiore, University of Pisa (Italy) Abstract: The following topics will be covered: What is a Grid? Grid for science and engineering applications Why and how to use Grid How to have 1 Million free CPU, or store 1 PB of data GOOGLE hacking: How to exploit Google: some idea Benefits of hacking Google Apr. 15-24, 2008 Ph.D. course on Linear and Nonlinear Optimization Organizer: Dr. Gaetano Zanghirati, Department of Mathematics and Math4Tech Center, University of Ferrara Apr. 7, 14, 21, 28, 2008 Ph.D. course on Mathematical Models for Traffic Flows Organizer: Prof. Andrea Corli, Department of Mathematics and Math4Tech Center, University of Ferrara Mar. 10, 2008 On nonlinear stability of linear pinch Prof. Maria Rosaria Padula, Department of Mathematics, University of Ferrara Abstract:  Everyday one encounters plasmas: the flash of a lightning bolt, the soft glow of Aurora Borealis, the conducting gas inside a fluorescent tube or neon sign. Furthermore, applications of plasma Physics, where only classical laws of Physics are needed, include gas discharges, controlled thermonuclear fusion, etc.. Several equilibrium configurations of plasmas in the vacuum have been studied, and stability of such configurations has been carried out. Surprisingly enough, despite the wide range of applications, the models used frequently differ each other, and Mathematics appears in most of the papers not clear, and frequently uncorrect. We start from a criticism of the earlier results, and show how the boundary conditions usually adopted are uncorrect. To simplify the problem, we limit ourselves to study the linear pinch. In this case, we give a correct definition of perturbations for the magnetic and electrical fields. After that we provide a global in time estimate for the L2 norm of perturbations by using Dirichlet-Lyapunov method. In absence of surface currents we may prove stability for large perturbations at initial time. The result is rigorously nonlinear. The most interesting result is provided by the effect of surface currents that cause necking, or sausage instability, as it is well known. The next step is to study nonlinear instability. Jan. 8, 2008 Numerical algorithms for free boundary flows with strong interfacial effects [pdf 4.0MB] Prof. Giovanna Guidoboni, Department of Mathematics, University of Houston Abstract: Free boundary flows involve the motion of a fluid in a region of space which is not fixed but it evolves in time depending on the fluid flow itself. Free boundary flows involve deformable interfaces, such as gas-liquid, liquid-liquid or solid-liquid interfaces. Two are the main reasons why the numerical solution of free boundary flows is more complicated than the numerical solution of fluid flows in fixed domains: (1) In free boundary flows one has to solve not only for the fluid velocity and pressure, but simultaneously also for the location of the interface and its evolution in time. (2) The deformation of the interface is coupled to the fluid flow both kinematically (continuity of the velocities) and dynamically (balance of stresses), and the coupling is nonlinear. These interfacial nonlinearities summate to the nonlinearities already present in the fluid (and/or solid) equations and they oftentimes lead to undesired numerical instabilities. Because of the large amount of variables and nonlinearities involved in the problem, partitioned algorithms seem to be a natural choice for the numerical solution of free boundary flows. Partitioned algorithms are based on the idea of splitting the original problem in a sequence of simpler sub-problems which involve only a sub-set of the unknowns and the equations of the original full problem. Unfortunately, to date, partitioned schemes available in literature are unstable when applied to free boundary flows where the interfacial coupling is highly nonlinear. This is the case in blood flow simulations and in coating flows. In this talk, we will present some new ideas on the development of efficient numerical solvers for free boundary flows with strong interfacial effects. Our objective is to obtain numerical schemes which combine good stability properties with affordable memory requirement, low computational costs and minimal implementation time. To reach this goal, we use the operator splitting technique to discretize in time the full coupled problem. The choice for the time-discretization is driven by the mathematical features of the interfacial nonlinearities arising through the conditions of continuity of stresses and velocities at the deformable interfaces. Numerical results will be discussed. Mar. 16, 2007 Plasticità policristallina: effetti scala e modellazione "strain gradient" Dr. Ing. Lorenzo Bardella, Department of Civil Engineering (DICATA), University of Brescia (Italy) Abstract: Si presenta una teoria per la modellazione della plasticità dei metalli che tiene conto della struttura cristallografica degli stessi. Al fine di descrivere gli effetti scala esibiti dai componenti metallici nel range dimensionale che va da pochi decimi a poche decine di micron, la teoria classica può essere estesa aggiungendo, costitutivamente, opportune dipendenze dal gradiente di alcune misure di deformazione plastica. Ciò è fatto nel contesto di una teoria non-standard ("strain gradient" di tipo "high-order") in cui, quindi, vengono definite nuove misure di sforzo e condizioni al contorno, capaci di descrivere a livello continuo alcune delle peculiarità del comportamento delle dislocazioni, principali responsabili della plasticità nei metalli. In particolare, si fa uso del tensore di Nye per tenere conto delle cosiddette dislocazioni geometricamente necessarie (DGN), di cui esso misura la densità. Tale grandezza cinematica va a incrementare l'energia libera tramite l'energia dei difetti (Gurtin, 2002) e permette di modellare, al diminuire delle dimensioni, sia l'aumento della pendenza del ramo incrudente che la variazione dell'ampiezza della "zona di processo" dove le DGN contribuiscono all'effetto scala osservato; macroscopicamente, tale prescrizione costitutiva risulta anche influenzare l'incrudimento cinematico (associato all'effetto Bauschinger). Inoltre, si mostra come un'ulteriore dipendenza non-standard dal gradiente del vettore contenente gli scorrimenti plastici, questa volta "dissipativa" in quanto introdotta nelle equazioni che governano l'evoluzione dell'incrudimento isotropo dovuto al moto di tutte le dislocazioni statisticamente immagazzinate, permetta la descrizione qualitativa dell'aumento di sforzo di snervamento apparente al diminuire delle dimensioni. Infine, si discute la natura delle condizioni al contorno non-standard in relazione alla possibilità di modellare costitutivamente i bordi di grano interni nei policristalli. Ciò, per esempio, appare importante per stabilire il campo di validità del ben noto effetto scala di Hall-Petch. La modellazione è sviluppata in ambito olonomo ("deformation theory"), pur facendo sempre riferimento alla più appropriata controparte incrementale. Ciò permette di usufruire di notevoli vantaggi computazionali e, insieme, di ottenere risultati analitici importanti per gli sviluppi teorici. Mar. 14, 2007 On Some Mathematical models for Liquid-Vapour Flow with Phase Transition Prof. Christian Rhode, Universität Stuttgart, Institut für Angewandte Analysis und Numerische Simulation Abstract:  Mathematical models that describe the dynamics of compressible liquid-vapour flow with phase transitions are usually either sharp-interface models or diffuse-interface models. In the first case the phase boundary is represented as a discontinuous function, in the second case as a steep but smooth function. In the talk models for both approaches will be discussed starting from the equilibrium situation: isentropic Euler equations and Navier-Stokes-Korteweg equations. Main analytical results will be addressed but the focus will be on the numerical treatment of the above mentioned models. For the sharp interface ansatz we will present a ghostfluid-type algorithm which leads by construction to a sharp resolution of all phase boundaries. To solve the Navier-Stokes-Korteweg equations the discontinuous-Galerkin method will be used. Finally we present some numerical approximations on bubble dynamics. The talk relies on joint work with Christian Merkle, Dennis Diehl and Frederic Coquel. Feb. 21, 2007 Probabilistic encryption, part 2 Prof. Mohan Nair, Department of Mathematics, University of Glasgow (UK) Feb. 20, 2007 Probabilistic encryption, part 1 Prof. Mohan Nair, Department of Mathematics, University of Glasgow (UK) Abstract:  Probabilistic encryption will be introduced and how it differs from deterministic systems, such as the R.S.A., will be briefly described. Two applications will be described: the El Gamal cryptosystem and the Blum-Goldwasser cryptosystem, both illustrated with MAPLE programs. This will appeal to a general audience. Jan. 15, 2007 Ground states in complex bodies - Minimi di energia in corpi complessi Prof. Paolo M. Mariano, Department of Civil Engineering, University of Florence, Italy Abstract: Conditions in which appropriate weak diffeomorphisms and Sobolev maps are minimizers of the energy of non-linear elastic complex bodies are discussed. The approach makes use of classical semicontinuity results and of Cartesian currents. General substructures are considered: their morphology is represented by elements of some differentiable manifold. In this way the results apply to a variety of special classes of complex materials. At the end I would like to introduce a few remarks about the variational formulation of quasi-static crack growth in complex bodies (an issue that suggests the need to analyze the possibility of finding minimizers in appropriate SBV spaces). Jan. 11, 2007 Deformation mechanisms of regular open-cell cellular structures Dr. Eng. Matej Vesenjak, Faculty of Mechanical Engineering, University of Maribor, Maribor, Slovenia. Abstract: Open-cell cellular specimens made of aluminium alloy and polymer were experimentally tested with aim to determine their behaviour under mechanical loading. The quasi-static and dynamic compressive loading has been applied to the cellular structures in order to evaluate the failure conditions and the strain rate sensitivity. Additionally, the specimens with viscous fillers have been tested to determine the increase of the energy absorption. The tests have shown that brittle behaviour of the cellular structure due to sudden rupture of intercellular walls observed in quasi-static and dynamic tests is reduced by introduction of viscous filler, while at the same time the energy absorption is increased. Furthermore, computational models were developed, considering the fully coupled interaction between the base material and the pore filler. The explicit nonlinear finite element code LS-DYNA was used for computational simulations. The results of parametric computational simulations were used to determine the influence of fluid filler on cellular material deformation under impact loading. Different failure criteria were evaluated to simulate the collapsing of intercellular walls and the failure mechanism of cellular structures in general. The developed models contribute to more realistic and reliable simulations of different cellular materials behaviour under impact conditions. Dec. 19, 2006 Biomechanics of the initiation and growth of intracranial aneurysms Prof. Anne M. Robertson, Department of Mechanical Engineering, University of Pittsburgh (USA) Abstract: Intracranial aneurysms (ICA) are abnormal saccular dilations of cerebral arteries, commonly found at apices of arterial bifurcations and curved segments of arteries at the base of the brain. If untreated, an ICA can continue to expand until rupture, resulting in hemorrhage which is followed by death or severe disability in the majority of patients. Screening and preventative treatment strategies are notably absent in the clinical handling of this disease. This is in stark contrast to other diseases such as atherosclerosis, in which detailed knowledge of the pathobiology is instrumental in establishing screening procedures and developing effective pharmaceutical treatments such as statins. ICA are only identified prior to rupture in approximately 10% of the cases. As a result, little information is known about the initiation and growth process. In the first part of this talk, we discuss several theories regarding the initiation process and evidence to support or dispute these theories. Previous biomechanical modeling of aneurysm behavior focused on deformations of a preformed aneurysm. In these studies, the aneurysm tissue was treated as a different entity than the arterial tissue from which it developed. The size, shape, thickness, anisotropy and inhomogeneity of the undeformed reference configuration are specified. In the second part of this talk, we discuss a new constitutive equation for cerebral arterial walls that employs multiple reference configurations to model the structural changes that occur during early stages in the formation process [1]. This constitutive equation is motivated by mechanical and histological tests on cerebral arterial tissue that suggest the development of cerebral aneurysms is tied to the recruitment of collagen fibers and breakage of elastin and collagen in the original arterial wall [2,3]. Recently this model has been extended to include the dependence of arterial wall properties on mechanical loading. We have used this constitutive equation to model the development of an early stage aneurysm, or bleb. Results from this study are consistent with clinically observed characteristics of aneurysm development. References [1] Wulandana R. and Robertson A.M., An Inelastic Multi-Mechanism Constitutive Equation for Cerebral Arterial Tissue, Biomech. Model. Mechanobiol. 4(4), pp. 235-248, 2005. [2] Scott S., Ferguson G., and Roach M.R., Comparison of the elastic properties of human intracranial arteries and aneurysms, Can. J. Physiol. Pharm. 50, pp. 328-332, 1972. [3] Hazama F., Kataoka H., Yamada E., Kayembe K., Hashimoto N., Kojima M., Kim C., Early changes of experimentally induced cerebral aneurysms in rats. Light-microscopic study. Am. J. Pathol. 124, pp. 399–404, 1986. Dec. 18, 2006 Navier-Stokes Equations: The Beauty and the Beast Prof. Giovanni P. Galdi, Department of Mechanical Engineering, University of Pittsburgh (USA) Abstract: As it is well-known, the Navier-Stokes equations are at the foundations of many branches of applied sciences, including Meteorology, Oceanography, Oil Industry, Airplane, Ship and Car Industries, etc. In each of the above areas, these equations have collected many undisputed successes, which definitely place them among the most accurate, simple and beautiful models of mathematical physics. However, in spite of these successes, to date, a number of unresolved basic questions –mostly, for the physically relevant case of three-dimentional (3D) motions– remain open. Among them, certainly, the most famous is that of proving or disproving existence of 3D regular solutions for all times and for data of arbitrary "size", no matter how smooth. This notorious question has challenged several generations of mathematicians since the beginning of the 20th century who, yet, have not been able two furnish a complete answer. The problem has become so obsessive and intriguing that mathematicians have decided to put a generous bounty on it. In fact, properly formulated, it is listed as the third of the seven $1M Millennium Prize Problems of the Clay Mathematical Institute. It should be observed that the analogous question in the two-dimensional (2D) case received a positive answer about half a century ago. In this talk I shall present the main known results of existence, uniqueness and regularity of solutions to the corresponding initial-boundary value problem in a way that should be accessible also to non-specialists. Moreover, I will furnish a number of significant open questions and explain why the current mathematical approaches fail to answer them. In some cases, I shall also point out possible strategies of resolution. Nov. 24, 2006 On the modeling of contact mechanics [rar 3MB] Prof. Frédéric Lebon, Laboratoire de Mécanique et d'Acoustique, Université de Provence, France. Abstract: The first part of the talk will show experimental and numerical tests for the modeling of brick-walls interfaces and the main difficulties in the modeling processes will be highlighted. In the second part of the talk a formulation of the tensions for contact will be discussed. Both theoretical and numerical results will then be shown. The talk is based on recent works with F. Fouchal and F. Kuss. Jun. 30, 2006 Analisi asintotica di un funzionale non locale legato ad una transizione guscio-membrana Prof. Andrea Braides, Department of Mathematics, University of Rome "Tor Vergata", Italy Abstract: Si studia un modello variazionale di guscio sottile quando il suo spessore tende a zero. Matematicamente, il problema può essere tradotto come lo studio di una famiglia di funzionali non-locali con una perturbazione singolare. Si trovano due scale caratteristiche delle energie (in termini dello spessore) che corrispondono rispettivamente a soluzioni finemente oscillanti e a soluzioni con un numero finito di transizioni tra la configurazione "a riposo" e quella "eversa". La novità maggiore in questo tipo di energie è la presenza di un integrale (doppio) di una densita' di energia che cambia segno, e che quindi porta a dei fenomeni di "compensazione", in particolare un fenomeno di Gibbs. Lavoro in collaborazione con N. Ansini (Roma 1) e V. Valente (IAC). Jun. 15, 2006 From Griffith to Paris via Barenblatt: a variational approach to fatigue Prof. J. J. Marigo, Laboratoire des Propriétés Mécaniques et Thermodynamiques des Matériaux (LPMTM), Université de Paris XIII, France. Abstract: Il seminario ha per oggetto la teoria della frattura dei corpi elastici. Nella formulazione di G. Francfort e J.J. Marigo [1], il problema della frattura è ridotto al problema di minimo di un funzionale energia costituito da due termini: un’energia a densità volumetrica, dipendente dal gradiente della deformazione, e un’energia a densità superficiale, proporzionale all’area della superficie di frattura. Seguendo l’evoluzione della deformazione al variare di un parametro di carico, è possibile sia predire la formazione della frattura che seguirne la propagazione. Ciò è possibile grazie alla tecnica risolutiva messa a punto in [2], basata sull’approssimazione del funzionale energia, che è definito sulle funzioni a variazione limitata, mediante una famiglia di funzionali più regolari, definiti sugli ordinari spazi di Sobolev. La convergenza dei funzionali approssimanti è assicurata nel senso della Gamma-convergenza. Il modello di minimizzazione adottato in [1] è in linea con il tradizionale approccio di Griffith (1920). Alcuni difetti del modello di Griffith, ad esempio, l’incapacità di predire la formazione della frattura nel caso monodimensionale, possono essere corretti adottando un’energia regolarizzata “alla Barenblatt” (1959). In questo spirito, e ricorrendo alla scelta di un’opportuna “metrica” della dissipazione, diventa possibile estendere il modello al problema della fatica. Nel seminario verrà fatto cenno di quest’ultimo risultato, recentemente ottenuto in [3]. Riferimenti [1] Francfort G.A., J.J. Marigo, "Revisiting brittle fracture as an energy minimization problem", J. Mech. Phys. Solids, 46, 1998, pp. 1319-1342. [2] Ambrosio L., V.M. Tortorelli, "Approximation of functionals depending on jumps by elliptic functionals via Gamma-convergence", Comm. Pure Appl. Math., 43, 1990, pp. 999-1036. [3] Jaubert A., J.J. Marigo, "Justification of Paris-type fatigue laws ....", in stampa su Cont. Mech. Termodynamics. Jun. 9, 2006 Alcuni argomenti attuali di ricerca sulla stabilità elastica, sulla frattura e sul comportamento dei materiali Prof. Gianpietro Del Piero, Department of Engineering, University of Ferrara, Italy Abstract: Verranno illustrati alcuni argomenti di ricerca sui quali è concentrata attualmente l’attività scientifica del relatore. Il primo riguarda la ricerca di condizioni sufficienti di stabilità per un solido elastico, comprimibile o incomprimibile, in regime di grandi deformazioni. Mentre la formulazione di condizioni necessarie è relativamente semplice e ben conosciuta, non vi è molto, in letteratura, sulle condizioni sufficienti, le quali, per contro, sono quelle di maggior interesse applicativo. Su questo tema verrà data una rassegna dei risultati esistenti, e verranno accennati alcuni dei progressi ottenuti. Per il problema modello del cilindro caricato assialmente, verrà dato un confronto con i risultati esistenti in letteratura. Nel campo della frattura verrà brevemente illustrata la tecnica risolutiva introdotta da G. Francfort e da J.J. Marigo, basata sulla minimizzazione dell’energia di una famiglia di funzionali regolari, e cioè definiti sugli ordinari spazi di Sobolev. Per essi è assicurata la convergenza, nel senso della Gamma-convergenza, all’energia del solido fratturato, definita su un particolare insieme di funzioni a variazione limitata. Verranno illustrati, in particolare, alcuni problemi che insorgono nel passaggio dall’elasticità lineare all’elasticità finita, e verranno mostrate le differenze ottenute nella risposta di una struttura bidimensionale. Infine, per quanto riguarda il comportamento dei materiali, verrà discusso il modello del solido elastico con energia coesiva. Mediante la minimizzazione di un funzionale energia formato da una parte elastica e una parte coesiva, a seconda della forma scelta per la parte coesiva, il modello consente di riprodurre le curve di risposta tensione-deformazione incontrate nei problemi di frattura, di plasticità, e di danneggiamento. May 12, 2006 Accoppiamento di equazioni differenziali e algebrico-differenziali in modellistica microelettronica [pdf 1.5KB] Prof. Giuseppe Alì, IAC-CNR Napoli, Italy Abstract: Per descrivere adeguatamente nuovi tipi di dispositivi elettronici, le cui dimensioni sono sempre più ridotte, occorre prendere in considerazione effetti di accoppiamento tra dispositivi e circuiti elettrici, che in precedenza venivano trattati come effetti secondari trascurabili. Si propone un semplice modello in cui i dispositivi sono descritti a livello microscopico mediante sistemi di PDE (Partial-Differential Equations); a loro volta, i dati al contorno di queste PDE sono parte delle variabili usate per descrivere macroscopicamente il circuito a cui i dispositivi sono collegati; infine, il circuito è descritto mediante un sistema di DAE (Differential-Algebraic Equations). Si discutono i primi risultati generali su questa classe di modelli, riguardanti la buona posizione, l'esistenza e l'unicità di soluzioni. May 10, 2006 Il paradigma dei sistemi dinamici nella previsione meteorologica e negli studi climatici Prof. Antonio Speranza, Department of Mathematics and Computer Science, University of Camerino, Italy Abstract: A partire dai primi anni ottanta lo sviluppo della meteorologia operativa su scala globale - soprattutto presso lo ECMWF (European Centre for Numerical Weather Forecasts) e l’allora NMC (National Metorological Center) statunitense, attualmente NCEP (National Center for Environmental Prediction) – ha avuto come supporto euristico base la teoria dei sistemi dinamici. Questa aveva ricevuto alla fine degli anni settanta uno straordinario impulso dalla "riscoperta" (soprattutto ad opera di Ruelle e Takens) del celebrato(*) lavoro di Lorenz (1963) sulla struttura dell’attrattore strano delle equazioni di Saltzmann (1962) per la convezione. Parte di questo ruolo centrale della teoria dei sistemi dinamici è dovuta al fatto che Ed Lorenz (così come Barry Saltzmann) era già al tempo un importantissimo studioso della Meteorologia oltre che valente matematico. Ma va anche considerato che la modellistica numerica affrontava in quel momento una "crisi di visione" dovuta all’aumentare continuo e straordinariamente rapido del numero di informazioni da gestire conoscitivamente prodotte in ogni "run" modellistico. Fatto sta che, per poter gestire sinteticamente milioni e milioni di numeri, molti aspetti, esistenti ma negletti, della teoria qualitativa delle equazioni differenziali (il lavoro di Arnold, per esempio) vennero in quegli anni riscoperti ed utilizzati anche nella pratica operativa quotidiana. Da quei tempi il ruolo del paradigma sistemi dinamici si è consolidato giorno dopo giorno fino a divenire parte integrante della "professionalità" dei modellisti numerici operativi. Una specie di "bibbia" del settore è attualmente costituita dal recente libro di Eugenia Kalnay (ex allieva di Lorenz nei corsi di Meteorologia presso MIT) nel quale, per l’appunto, il supporto euristico della visione sistemi dinamici e continuo ed esplicito. Come avviene spesso (per non dire sempre!) in questo tipo di processi di "istituzionalizzazione" scientifico-tecnico-culturale, man mano che la visione inizialmente pionieristica diviene scolastica e di "common consensus", le barriere difensive di consapevolezza e criticit` si abbassano fino al punto di prendere per scontate cose che, matematicamente e fisicamente, non lo sono affatto. Le possibili conseguenze, scientifiche ma anche pratiche, sono facilmente immaginabili. Nel seminario in questione il relatore, che è stato diretto testimone negli anni settanta ed ottanta (per lo più presso MIT) degli sviluppi menzionati sopra, cercherà brevemente di riassumere le principali criticità (sia scientifiche che pratiche) dell’attuale "visione sistemi dinamici in supporto della modellistica numerica operativa", concentrandosi poi su un tema specifico di grande importanza potenziale: la potenziale singolarità delle linearizzazioni locali nello spazio delle fasi che sono di uso corrente nelle pratiche di inzializzazione-assimilazione dei modelli numerici di uso operativo. __________________________________ (*) Celebrato adesso, ma ignorato in tutti i secondi anni sessanta e primi settanta! Mar. 28, 2006 Linnik's method for the functional equation of Dirichlet L-functions Prof. Alberto Perelli, DIPTEM, Department of Production Engineering, Thermoenergetics and Mathematical Models, Section of Mathematical Methods and Models, University of Genova, Italy Abstract: There are several ways of proving the functional equation of Dirichlet L-functions$L(s,\chi)$, the standard one being via the Poisson summation formula. Linnik (1947) proposed another approach, based on a direct use of the Riemann zeta function$\zeta(s)$. His method starts with an integral expression of$L(s,\chi)$in terms of$\zeta(s)$, obtained by the Mellin transform. Then, using the functional equation of$\zeta(s)$and its Dirichlet series expansion, one is faced with a series involving a certain special function of hypergeometric type. Thanks to the special form of such a function, the series can be summed, giving the asymmetric form of the functional equation of$L(s,\chi)\$. Some nice applications of Linnik's method to the distribution of the zeros, obtained by Sprindzuk, are also discussed. Mar. 24, 2006 3D object recognition with local features [pdf 2.1MB] Dr. Francesca Odone, DISI, Department of Computer and Information Sciences, University of Genova, Italy Abstract: Many classification tasks based on visual cues can be successfully addressed by first extracting meaningful information from images, then finding descriptions based on this information, and finally designing classification algorithms able to discriminate between the classes of interest. The image descriptions should maximize the interclass distance and minimize the intraclass variability. On this respect, in the last years a huge amount of work on finding image keypoints robust to environment and viewpoint variations have been carried out. In this talk I will address 3D object recognition, proposing a method based on image description with scale invariant local keypoints, and recognition with a collection of Kernel-based classifiers. One of the main challenges of this approach is due to the variable-length descriptions obtained from local keypoints. I will describe a "bag of keypoints" approach to this problem, reporting promising recognition results. I will also discuss the connections between this approach and very recent works on kernel engineering for local features, highlighting the pros and cons of the two choices. (Joint work with E. Arnaud, E. Delponte, A. Verri) Mar. 22, 2006 Mathematical Analysis of Some Problems Related to Liquid-Particle Flow [pdf 900KB] Prof. Giovanni P. Galdi, Department of Mechanical Engineering, University of Pittsburgh (USA) Abstract: Over the last 40 years the study of the motion of small particles in a viscous liquid has become one of the main focuses of engineering research, including the manufacturing of short-fiber composites, separation of macromolecules by electrophoresis, flow-induced microstructures, and also blood flow problems. The presence of the particles affects the flow of the liquid, and this, in turn, affects the motion of the particles, so that the problem of determining the flow characteristics is highly coupled. It is just this latter feature that makes any fundamental mathematical problem related to liquid-particle interaction a particularly challenging one. Interestingly enough, even though the mathematical theory of the motion of rigid particles in a liquid is one of the oldest and most classical problems in fluid mechanics, owed to the seminal contributions of Stokes, Kirchhoff, and Lord Kelvin, only very recently have mathematicians become interested in a systematic study of the basic problems related to liquid-particle interaction. In this talk we focus on the mathematical analysis of two problems related to the motion of a sphere in a channel. Specifically, in the first problem a sphere is moving under the gradient of shear generated by a unidirectional two-dimensional Poiseuille flow of a viscoelastic liquid in a horizontal channel. In the second problem a sphere is sedimenting in a vertical channel under the action of gravity. In both problems the setting is two-dimensional and the viscoelastic liquid is taken to be a second-order liquid model. Our main goal is to evaluate, at first order in a suitable Reynolds number and in the Weissenberg number, the equilibrium position of the sphere with respect to one of the walls, and its translational and angular velocities. Moreover, we investigate the attainability and the stability of the equilibria and their dependence on the (effective) mass of the sphere and on the physical properties of the liquid. Feb. 14, 2006 Logic Programs and Annotated Disjunctions [pdf 490KB] Dr. Fabrizio Riguzzi, Engineering Department, University of Ferrara, Italy Abstract: I programmi logici con disgiunzione annotata sono un formalismo che combina la logica con la probabilità. Questi programmi possono essere usati per esprimere reti bayesiane in generale una distribuzione di probabilità su interpretazioni e su formule logiche. Una dimostrazione procedure è disponibile per questi programmi che, data una formula logica, ne ritorna la probabilità. È disponibile anche un algoritmo per apprenderli partendo da un insieme di interpretazioni di Herbrand annotate con una probabilità. Nel corso della presentazione verranno presentati vari problemi aperti: dare una semantica a questi programmi quando sono presenti simboli di funzione; valutare l'efficienza della procedura di prova in confronto a quella di algoritmi per il ragionamento con reti bayesiane; migliorare l'efficienza dell'algoritmo di apprendimento, in particolare sfruttando algoritmi per apprendere reti bayesiane Dec. 16, 2005 Functional Imaging in Medicine: Information Extraction and Elaboration [pdf 38.3MB, in Italian] Prof. Melchiore Giganti, Dept. of Surgical and Radiological Sciences, Nuclear Medicine Section, University of Ferrara, Italy Abstract: Unavailable. Dec. 16, 2005 Molecular Imaging [pdf 5.9MB] Prof. Adriano Duatti, Dept. of Surgical and Radiological Sciences, Nuclear Medicine Section, University of Ferrara, Italy Abstract: Unavailable. Nov. 29, 2005 A Statistical Approach to Caos with Applications to Information Engineering [pdf 4.9MB] Prof. Gianluca Setti, Engineering Department, University of Ferrara, Italy Abstract: In this lecture we will introduce a statistical framework to tackle the complex (chaotic) behavior that characterize even very simple, discrete-time dynamical systems (i.e. maps). More specifically, we will have a look on how such maps can be considered as stochastic processes generators with tunable statistical features. We will then apply such an approach to some hot topics in Information Technology, namely: Spreading sequence design for DS-CDMA EMI (Electro-Magnetic Interference) reduction High Troughput Random Number generation More details follow on each sub-topic. 1) DS-CDMA We will show that the substitution of spreading sequences generated by a suitable chaotic map for for classical Gold or m-sequences in a standard DS-CDMA systems allows to increase by 15% the number of allocable users with the same link quality. Non-average performance can be optimized to obtain peak of more than 60% increase in capacity. 2) EMI We will show that the use of chaos-based frequency modulated timing signal allows to reduce the power spectrum peak of EMI in power converters or digital systems boards by approximately 9dB with respect to other know and patented methodologies for spread spectrum clocking generation. 3) High Throughput TRNG We will here consider a methodology, based on chaotic maps, for implementing TRNGs which, in terms of implementation easiness, has features similar to widely employed pseudo-RNGs. More specifically, they can be practically realized out of pipeline analog-to-digital converters (ADC) parts so that one can easily reuse design expertise and even analog Intellectual-Property blocks to quickly embed true random sources in SOCs and specialized apparatuses. A chaos-based TRNG based on this approach has been designed in AMS 0.35um CMOS technology. Measurement results showed that the designed chaos-based TRNG: operates at a throughput of approximately 20Mbits/s, i.e. faster than current state-of-the-art TRNG; behaves in a completely satisfactory way when validated against two standard randomness test suites proposed by NIST (FIPS 140.2 and SP800-22)
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