Servizi per la didattica

PORTALE DELLA DIDATTICA

01TEPRT

A.A. 2018/19

Course Language

English

Course degree

Doctorate Research in Pure And Applied Mathematics - 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

© Politecnico di Torino

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY