### Seminari

### Prossimi Seminari

**Dealing with unreliable computing platforms at extreme scale**

Luc Giraud, INRIA (Inria Bordeaux – Sud-Ouest)

mercoledì 23 gennaio 2019 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Poroelasticity: Discretizations and fast solvers based on geometric multigrid methods**

Francisco José Gaspar Lorenz, Department of Applied Mathematics -Zaragoza University – Spain

giovedì 31 gennaio 2019 alle ore 14:00, Sala Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Application of Polyconvexity and multivariable convexity of energy potentials in nonlinear solid mechanics**

Javier Bonet, University of Greenwich

giovedì 14 febbraio 2019 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

### Seminari Passati

**Simulazione della circolazione feto-placentare: una possibile applicazione di modelli multiscala?**

Caterina Guiot, Dip Neuroscienze-Sez Fisiologia-Lab Fisica medica

martedì 16 settembre 2003 alle ore 15:00, Aula Seminari MOX – 6° piano dip. di matematicaABSTRACTAn increased interest towards the feto-placental venous circulation has

been recently devoted by clinicians, mainly regarding the umbilical

cord (morphological structure and feasibility of quantitative

measurements of the venous blood flow with Doppler US), the Ductus

Venosus and the inferior vena cava.

To investigate the haemodynamic changes leading to pathologies we

have developed a lumped mathematical model (implemented using SIMULINK ™)

simulating the feto-placental circulation from the inlet of

the umbilical artery (where the pressure waveform is assumed to be

known) across the placenta, the intraamniotic and intrahepatic umbilical

vein, the ductus venosus and the inferior vena cava until the fetal

atrium, where again a pressure waveform is assumed.

The main original assumptions of the lumped model are that the

umbilical vein behaves as a collapsible tube subject to an external

pressure exerted by the arteries which are coiled together inside the

cord and that the ductus venosus can dilate and, being in parallel with

the portal-hepatic system, can actively modify the outlet resistance

for the umbilical vein. All these features, however, could be described

with greater detail provided more sophisticated mathematical and numerical

treatments are properly included in the basic model.

The potential for model improvements due to a multiscale approach will

be discussed and evaluated.

**Blow-up for Nonlinear Hyperbolic Problems**

Stanislav I. Pohozaev, Steklov Institute of Mathematics, Mosca (Russia)

lunedì 15 settembre 2003 alle ore 17:00, Dipartimento di Matematica – Università degli Studi di Milano – Via Saldini 50 – Milano – Sala di RappresentanzaABSTRACT“By using the concept of nonlinear capacity we suggest the general approach to the blow-up phenomena in nonlinear problems. This approach does not use the maximum principle arguments and properties of the fundamental solutions of related differential operators. That fact gives the possibility to consider a wide classes of nonlinear problems and obtain the sharp results for blow-up problems including the estimates for the “”blow-up time””. Finally we construct the “”Mendeleev table”” for nolinear problems. I am going to demonstrate this approach for nonlinear (multidimensional) hyperbolic problems. The results are obtained jointly with E.Mitidieri, L.Veron and A.Tesei.”**On a class of nonvariational elliptic problems**

Djairo De Figueiredo, UNICAMP, Campinas (Brasile)

giovedì 28 agosto 2003 alle ore 17:00, Dipartimento di Matematica – Università degli Studi di Milano – Via Saldini 50 – Milano – Sala di RappresentanzaABSTRACTA priori bounds for positive solutions of a class of nonvariational elliptic systems is obtained by the blow-up method. Some Liouville type results are discussed.**Dynamics of the Discretized FitzHugh-Nagumo Equation**

Yakov Pesin, Penn State University, PA (U.S.A.)

martedì 1 luglio 2003 alle ore 17:00, Dipartimento di Matematica – Università degli Studi di Milano – Via Saldini 50 – Milano – Sala di RappresentanzaABSTRACTI will consider the FitzHugh-Nagumo PDE. It is well-known in neuroscience and is used to describe the propagation of voltage impulse through a nurve axion. Its discrete version provides a competing model that I discuss in the talk. I present some results on the dynamics of the evolution operator on the space of traveling wave solutions and in particular, show that this dynamics changes from Morse-Smale type to a chaotic attractor to a horseshoe as a leading parameter (corresponding to the Reynolds number) of the system varies.**Problemi di unicità in tomografia geometrica.**

Paolo Dulio, Politecnico di Milano

venerdì 27 giugno 2003 alle ore 11:00, Dipartimento di Matematica – Politecnico di Milano**Introduzione alla trattazione numerica di equazioni differenziali ordinarie stocastiche**

Raffaella Pavani, Dipartimento di Matematica – Politecnico di Milano

giovedì 26 giugno 2003 alle ore 00:00, Auletta del V Piano – Dipartimento di MatematicaABSTRACTThe aim of this talk is tho provide a practical introduction to numerical

methods for the stochastic ordinary differential equations. To this purpose,

only the simplest numerical methods are considered, so the concepts of

convergence and linear stability are studied in a simple way. It is shown

that such concepts are generalized from analogous concepts for deterministic

ordinary differential equations. Differences and similarities between the

deterministic case and the stochastic one are enlightened.

**Mathematical aspects of the theory of guided waves in nonlinear optical fibres**

Charles A. Stuart, Ecole Polytechnique Fédérale, Losanna (Svizzera)

giovedì 12 giugno 2003 alle ore 15:00, Dipartimento di Matematica – Università degli Studi di Milano – Via Saldini 50 – Milano – Sala di RappresentanzaABSTRACTGuided waves in nonlinear optical fibres are modelled as special solutions of Maxwell’s equations in an axi-symmetric dielectric medium whose refractive index depends on the intensity of the electric field. I shall present some situations in which the problem can be reduced to a nonlinear eigenvalue problem and then I shall summarise some of the rigorous results that have been obtained and how they relate to the underlying physical problem.**ENERGY, HELICITY AND CROSSING NUMBER RELATIONS FOR COMPLEX FLOWS**

Renzo L. Ricca, Dip. di Mat.Univ. College London & Milano-Bicocca

giovedì 5 giugno 2003 alle ore 16:00, Aula Seminari MOX – 6° piano dip. mat.ABSTRACTAlgebraic and topological measures based on crossing number relations

provide bounds on energy and helicity of ideal fluid flows and can be

used to quantify morphological complexity of complex tangles of vortex

filaments [1,2]. Recent work [3], based on simulation of superfluid

vortex tangles, demonstrates that structural complexity can indeed be

identified with crossing number measurements, and provides evidence for

possible new relations between complexity and energy of structured flows.

These results find useful applications, from diagnostics of turbulent

flows (superfluid and classical) to energy estimates of

complex coherent structures.

[1] Ricca, R.L. 2002 Energy, helicity and crossing number relations

for complex flows. In Tubes, Sheets and Singularities in Fluid

Dynamics (ed. K. Bajer & H.K. Moffatt), pp. 225-230.

NATO ASI Series II, to appear, Kluwer.

[2] Ricca, R.L. 2001 Geometric and topological aspects of vortex

motion. In An Introduction to the Geometry and Topology of Fluid

Flows (ed. R.L. Ricca), pp. 203-228. NATO ASI Series II, vol. 47,

Kluwer.

[3] Barenghi, C.F., Ricca, R.L. & Samuels, D.C. 2001 How tangled is a

tangle? Physica D vol. 157, 197-206.