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Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2019/2020
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Insegnamento 097660 - METHODS AND MODELS FOR STATISTICAL MECHANICS
Docente Lorenzani Silvia
Cfu 8.00 Tipo insegnamento Monodisciplinare

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento
Ing Ind - Inf (Mag.)(ord. 270) - MI (487) MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA*AZZZZ097660 - METHODS AND MODELS FOR STATISTICAL MECHANICS

Obiettivi dell'insegnamento

           Aims and scope

 

The course aims to derive the macroscopic properties of gaseous systems starting from

their microscopic (molecular dynamics) analysis.

In this perspective, analytical and numerical methods for the solution of the Boltzmann equation

are introduced and the influence of rarefied gas properties in micro-nano-technologies is

highlighted.

 


Risultati di apprendimento attesi

               Knowledge and understanding

 

At  the end of the course the students are expected to:

-know the basic mathematical properties of the Boltzmann equation

-be able to solve the Boltzmann equation both analytically and numerically

-be able to model various problems arising in the micro-technology environment

 by using the Boltzmann equation.


Argomenti trattati

                       Program

 

1-Introduction to Statistical Mechanics

-The postulate of classical statistical mechanics.

-Microcanonical Ensemble.

-Canonical Ensemble.

-Grand Canonical Ensemble.

2-Thermodynamics and Kinetic Theory

-The laws of Thermodynamics.

-Entropy.

-The problem of Kinetic Theory.

3-The Boltzmann equation 

-Derivation (Lanford Theorem). Existence of solutions (Diperna-Lions Theorem).

-The BBGKY Hierarchy.

-Elementary properties of the collision operator.

-Boundary conditions and the gas-surface interaction.

-The H-Theorem and the problem of irreversibility.

-Kinetic Models.

4-Methods of solution of the Boltzmann equation

-Variational Methods.

-Transformation into Integral Equations.

-The method of Elementary Solutions.

-Numerical methods.

5-Application of the Boltzmann equation to Microfluidics

-Analytical and numerical investigation of microchannel flows (Poiseuille, Couette and

 Thermal-Creep problems; sound waves propagation).

-Slip boundary conditions for the Navier-Stokes equations.

-Kinetic modeling of gas mixtures.

6-Mathematical Models and Methods in Micro-Nano-Technologies

-Characterization of Micro-Electro-Mechanical Systems (MEMS) devices.

-Analysis of damping forces in low-frequency and radio-frequency MEMS devices.

7-Boltzmann-type equations in Socio-Economic applications

 


Prerequisiti

                  Preconditions

 

First level courses concerning Mathematical Analysis, Numerical Analysis

and Probability.


Modalità di valutazione

                  Examination

 

The final exam consists either in an oral discussion on the whole program,

or in a written project in which one of the topics, dealt with during the course,

is investigated thoroughly.


Bibliografia
Risorsa bibliografica facoltativaKerson Huang, Statistical Mechanics, Editore: John Wiley & Sons, Anno edizione: 1987, ISBN: 978-0-471-81518-1
Risorsa bibliografica facoltativaCarlo Cercignani, The Boltzmann Equation and Its Applications, Editore: Springer-Verlag, Anno edizione: 1988, ISBN: 3-540-96637-4
Risorsa bibliografica facoltativaCarlo Cercignani, Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations, Editore: Cambridge University Press, Anno edizione: 2000, ISBN: 0-521-65992-2

Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
(hh:mm)
Ore di studio autonome
(hh:mm)
Lezione
52:00
78:00
Esercitazione
28:00
42:00
Laboratorio Informatico
0:00
0:00
Laboratorio Sperimentale
0:00
0:00
Laboratorio Di Progetto
0:00
0:00
Totale 80:00 120:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese
schedaincarico v. 1.6.1 / 1.6.1
Area Servizi ICT
06/04/2020