01TEPRT

A.A. 2018/19

Course Language

Inglese

Course degree

Doctorate Research in Matematica Pura E Applicata - Torino

Course structure

Teaching | Hours |
---|---|

Lezioni | 25 |

Teachers

Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut | Years teaching |
---|---|---|---|---|---|---|---|

Chiado' Piat Valeria | Professore Ordinario | MAT/05 | 2 | 0 | 0 | 0 | 1 |

Teaching assistant

Context

SSD | CFU | Activities | Area context |
---|---|---|---|

*** N/A *** |

2018/19

PERIOD: FEBRUARY
The course is based on the courses given for the master and Ph.D. students in 2015‐2018
at Skoltech (Moscow), University of Chile (Santiago), University of Lyon (University Jean
Monnet). The course introduces main mathematical models describing mechanical
behavior at microscopic level of heterogeneous media and for blood flow in network of
vessels. The homogenization technique is applied for multiscale analysis of
heterogeneous media. For the network of vessels the asymptotic methods (matching,
boundary layers) is presented. The method of asymptotic partial decomposition of the
domain defines hybrid dimension models combining one‐dimensional description
obtained by the dimension reduction with three‐dimensional zooms. It justifies the
special exponentially precise junction conditions at the interface of 1D and 3D parts. It
can be applied to model the blood flow in vessels with trombs or stents.
(more

PERIOD: FEBRUARY
The course is based on the courses given for the master and Ph.D. students in 2015‐2018
at Skoltech (Moscow), University of Chile (Santiago), University of Lyon (University Jean
Monnet). The course introduces main mathematical models describing mechanical
behavior at microscopic level of heterogeneous media and for blood flow in network of
vessels. The homogenization technique is applied for multiscale analysis of
heterogeneous media. For the network of vessels the asymptotic methods (matching,
boundary layers) is presented. The method of asymptotic partial decomposition of the
domain defines hybrid dimension models combining one‐dimensional description
obtained by the dimension reduction with three‐dimensional zooms. It justifies the
special exponentially precise junction conditions at the interface of 1D and 3D parts. It
can be applied to model the blood flow in vessels with trombs or stents.
(more

"Multiscale mathematical modeling in engineering, biology and medicine"
by Grigory Panasenko (CMM and University of Lyon)
1) Introduction to the main equations of mathematical physics used in the
mathematical modeling and boundary and initial conditions.
Diffusion‐convection equation
Viscous flows equations (Navier‐Stokes equations, Stokes equations, nonnewtonian
flows)
Elasticity equations, visco‐elasticity equations
Dirichlet's, Neumann's, Robin's and periodic boundary conditions; number of
initial conditions; periodic in time problems
Derivation from physic laws (ideas) and notion of mathematical analysis (weak
formulation, existence, uniqueness and stability of the solution, i.e. wellposedness).
2) Modeling of composite materials and meta‐materials. Homogenization technique
in mechanics of solids: passage from microscopic scale to the macroscopic scale.
3) Models of flows. Thin tube structures and multi‐structures. Asymptotic analysis.
Method of partial asymptotic decomposition of the domain for flows in a tube
structure with rigid walls. Elastic and viscoelastic walls of the flows: special
boundary conditions for the fluid.

"Multiscale mathematical modeling in engineering, biology and medicine"
by Grigory Panasenko (CMM and University of Lyon)
1) Introduction to the main equations of mathematical physics used in the
mathematical modeling and boundary and initial conditions.
Diffusion‐convection equation
Viscous flows equations (Navier‐Stokes equations, Stokes equations, nonnewtonian
flows)
Elasticity equations, visco‐elasticity equations
Dirichlet's, Neumann's, Robin's and periodic boundary conditions; number of
initial conditions; periodic in time problems
Derivation from physic laws (ideas) and notion of mathematical analysis (weak
formulation, existence, uniqueness and stability of the solution, i.e. wellposedness).
2) Modeling of composite materials and meta‐materials. Homogenization technique
in mechanics of solids: passage from microscopic scale to the macroscopic scale.
3) Models of flows. Thin tube structures and multi‐structures. Asymptotic analysis.
Method of partial asymptotic decomposition of the domain for flows in a tube
structure with rigid walls. Elastic and viscoelastic walls of the flows: special
boundary conditions for the fluid.

Schedule:
Mon 18 room 7D, 10‐12 + 14‐16
Tue 19 room 1D, 10‐12 + 14‐16
Wed 20 room Buzano (DISMA) 10‐13
Thu 21 room Buzano, 10‐13 14‐16
Fri 22 room Buzano, 10‐12 + 14‐16
Mon 25 room Buzano, 10‐12 + 14‐16

Schedule:
Mon 18 room 7D, 10‐12 + 14‐16
Tue 19 room 1D, 10‐12 + 14‐16
Wed 20 room Buzano (DISMA) 10‐13
Thu 21 room Buzano, 10‐13 14‐16
Fri 22 room Buzano, 10‐12 + 14‐16
Mon 25 room Buzano, 10‐12 + 14‐16

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.

© Politecnico di Torino

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY