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Course, academic year 2019/2020
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Classical Problems of Continuum Mechanics - NMMO432
Title in English: Klasické úlohy mechaniky kontinua
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2014
Semester: summer
E-Credits: 4
Hours per week, examination: summer s.:2/1 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: Mgr. Vít Průša, Ph.D.
Class: M Mgr. MOD
M Mgr. MOD > Povinně volitelné
Classification: Mathematics > Mathematical Modeling in Physics
Annotation -
Last update: Mgr. Vít Průša, Ph.D. (11.09.2013)
The aim of the subject is to introduce some classical problems in continuum mechanics, and discuss their physical background and related mathematical techniques that have been developed in order to solve these problems. The spectrum of the problems studied during the lecture is deliberately very broad and the lecture should provide a summary of some major achievements in the field.
Course completion requirements -
Last update: Mgr. Vít Průša, Ph.D. (01.03.2018)

Pass the exam and get credits for the tutorials.

Conditions for getting the credit for the tutorials:

1) Attendance.

2) Solving homework problems.

You can enroll for the exam only if you already got credits for the tutorials.

Literature -
Last update: Mgr. Vít Průša, Ph.D. (11.09.2013)

M. Brdička, L. Samek and B. Sopko: Mechanika kontinua, Academia, Praha, 2000.

S. Chandrasekhar: Hydrodynamic and hydromagnetic stability, Clarendon Press, Oxford, 1961.

C. C. Lin: The Theory of Hydrodynamic Stability, Cambridge University Press, Cambridge, 1955.

H. Schlichting and K. Gersten: Boundary layer theory, Springer, Berlin, 8th edition, 2000.

L. M. Milne-Thomson: Theoretical hydrodynamics, Macmillan, New York, 2nd edition, 1950.

H. Lamb: Hydrodynamics, Cambridge University Press, Cambridge, 6th edition, 1993.

A. S. Saada: Elasticity theory and applications, Krieger Publishing, Malabar, 2nd edition, 1993.

P. G. Drazin and N. Riley: The Navier-Stokes equations: a classication of flows and exact solutions, Cambridge University Press, Cambridge, 2006.

P. Villaggio: Mathematical models for elastic structures, Cambridge University Press, Cambridge, 1997.

S. S. Antman: Nonlinear problems of elasticity, Springer, New York, 2nd edition, 2005.

R. Berker: Integration des equations du mouvement d'un fluide visqueus incompressible. In S. Flüge, editor, Handbuch der Physik , volume VIII, 1-384. Springer, 1963.

N. I. Muskhelishvili: Some basic problems of the mathematical theory of elasticit, Noordhoff, Leiden, 1977.

R. W. Ogden: Nonlinear elastic deformations, Ellis Horwood, Chichester, 1984.

Requirements to the exam -
Last update: Mgr. Vít Průša, Ph.D. (01.03.2018)

You can enroll for the exam only if you already got credits for the tutorials.

The exam is an oral exam, and it consists of three parts:

1) Proof of a simple theorem. The theorem will be specified at the end of the semester. Typically, you will be asked to prove a theorem that has been formulated during the lecture without a proof. (The proof can be usually found in standard textbooks.) In presenting the proof, you can use your own notes.

2) Presentation of a solution to a problem discussed in a scientific paper. The objective is to show that you know what is the paper about, and what are the used methods and conclusions. The paper will be specified at the end of semester. Typically there will be a list of papers from which you can choose the paper that is most readable/conveninent/interesting for you. In discussing the problem, you can use your own notes!

3) During our conversation we will definitely encounter some notions from the field of continuum mechanics. You will be asked to explain some of the notions. Detailed list of the definitions/theorems and concepts you are expected to know will be specified at the end of the semester.

More information is available on the lecture's webpage.

Syllabus -
Last update: Mgr. Vít Průša, Ph.D. (11.09.2013)

1. Some examples of analytical solutions to the Navier--Stokes equations. Viscometric flows.

2. Some examples of analytical solutions in the linearized theory of elasticity. Elastic potentials, stress concentration factors. Waves in elastic materials.

3. Stability of fluid flows. Energy method, linearized stability theory and its limits, Orr-Sommerfeld equation, self sustaining processes.

4. Oberbeck-Boussinesq aproximation, Rayleigh-Bénard problem. Finite amplitude disturbances. Lorentz equations.

5. Flow past bodies, drag and lift. Prandtl boundary layer theory.

Entry requirements -
Last update: Mgr. Vít Průša, Ph.D. (18.05.2018)

Elementary continuum mechanics (for example within the scope of lecture Continuum mechanics, NMMO401). Fundamentals of linear algebra, multivariable calculus.

 
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