Courses

In 2024:


Course "Hidden symmetries in fluid dynamics" (with Simon Thalabard, U. Nice)

Wed & Fri, 10/1-2/2 at 15:00-17:00 in room 232.

VIDEOS on IMPA's YouTube Channel:

Lecture 1: Navier-Stokes (NS) and Euler equations. Symmetries. Conservation of energy.

Lecture 2: NS turbulence, Gaussian HIT, Gaussian vs. NS, viscous effects.

Lecture 3: Scaling  anomaly, Random-h model, Multifractal theory.

Lecture 4: Solvable intermittent model of turbulence.

Lecture 5: Hidden scaling symmetry in shell models. Anomalous scaling laws.

Lecture 6: Kolmogorov multipliers. Rescaled NS equations.

Lecture 7: Hidden symmetries in NS turbulence.

Lecture 8: Group theory approach to hidden scaling symmetries.

Lecture 9: Group theory approach to quasi-Lagrangian formalism. Perspectives.

Notes: Simon (lecture_1, lecture_2, lecture_3, lecture_6_7) & Alexei (lecture_4_5_6, lecture_8_9)


In 2023:


Análise Complexa (Complex Analysis)

Classes: Monday and Wednesday at 15:30, room 224 (March 13 - June 30)

Monitor: Gabriel Santos Barbosa (gabriel.barbosa@impa.br).

Lists of exercises: List 1, List 2, List 3, List 4, List 5, List 6List 7: Ch.VII.1: Ex.4,7; Ch.VII.2: Ex.7,9; Ch.VII.3: Ex.4,7.


Introduction to the Theory of Oscillations and Waves

Classes: January-February, Monday/Tuesday/Wednesday, 10:00-12:00. Room 232. Videos of classes on Youtube

Material: 

Exercises: 

Solutions can be delivered to me or to the monitor at the class.

You can also send them scanned or photographed by e-mail to the monitor (antoine.barlet@impa.br) and me (alexei@impa.br)

Monitor of the course: Antoine Barlet, e-mail: antoine.barlet@impa.br, sala 108 (laboratory of Fluid Dynamics)


In 2022:


Numerical Analysis (March-June 2022):

Wednesday and Friday 13:30-15:00. IMPA, Auditorium 1. 


IMPA Summer School course (January-February 2021): 

Topics in Mathematics of Turbulence

January-February, Wednesday/Thursday/Friday, 15:00-17:00. IMPA, Auditorium 1.


In 2021:

Linear Algebra and Applications

March-June: Thursday at 10:30, Friday at 9:30. 

12/03 (video, notes), 18/03 (video, notes), 19/03 (video, notes), 25/03 (video, notes), 1/04 (video, notes), 08/04 (video, notes), 09/04 (video, notes), 

15/04 (video, notes), 16/04 (video, notes), 22/04 (video, notes), 23/04 (video, notes), 29/04 (video, notes), 30/04 (video, notes), 06/05 (video, notes),

07/05 (video, notes), 13/05 (video, notes), 14/05 (video, notes), 20/05 (video, notes), 21/05 (video, notes), 27/05 (video, notes),

28/05 (video1, video2, notes), 4/06 (video, notes), 10/06 (video, notes), 11/06 (video, notes), 17/06 (video, notes), 18/06 (video, notes)

  • List 1 for April 1. 
  • List 2 for April 22. 
  • List 3 for May 6. 
  • List 4 for May 20. 
  • List 5 for June 8.
  • List 6 for June 18. Please send to Julia (monitor) with a copy to me. 

Monitor: Julia Domingues, e-mail: juliahdomingues@hotmail.com 

Time for monitoria: please select HERE

Link for online class: it will be sent by email to all registered students, and you can ask me for this link by email.


Introduction to the Theory of Oscillations and Waves

January-February, Wednesday/Thursday/Friday, 10:00-12:00.

Online: feel free to ask me for the link by email.

  • Lecture notes: Part 1 [PDF in Portuguese], Part 2.2 [PDF in English], Part 3 [PDF in Portuguese, PDF in English]
  • Old videos on YouTube (in Portuguese): full collection at "Cursos do IMPA" 

 


In 2020:


Álgebra Linear e Aplicações March-June, Tue & Wed 15:30-17:00


Thermal and Statistical Aspects of Fluid Dynamics (together with Simon Thalabard

January-February, Tue, Wed, Fri 15:00-17:00, room 224 (starting on January 7)

Description

LECTURE NOTES: 

Section 1 (by Alexei Mailybaev)

  • Part 1 (classical mechanics)
  • Part 2 (basic statistical properties)
  • Part 3 (thermodynamic potentials)
  • Part 4 (Gibbs distribution and ideal gas)
  • Part 5 (phases and reactions)
  • Part 6 (ideal fluid dynamics)
  • Part 7 (thermal aspects of fluid flows)
  • Part 8 (multicomponent and multi-phase flows)
  • Questions   7/fev, 9:00, room 224

Section 2 (by Simon Thalabard)


In 2019:

August 1: Mini-course on Parametric Resonance 

At the São Paulo School of Advanced Sciences on NONLINEAR DYNAMICS

LECTURE NOTES

COURSE VIDEO

Temporary links: youtube1, youtube2, youtube3, youtube4


March-June: Fluid Dynamics

Tue, Wed 13:30-15:00, room 333

  1. Exercises (for Tue - April 2): see page 23 of Part1

Recommended literature: 

ACHESON, D. J. – Elementary Fluid Dynamics, Oxford University Press, 1990.
BATCHELOR, G. – An Introduction to Fluid Dynamics, Cambridge University Press, 1967.
CHORIN, A. J., MARSDEN, J. E. – A Mathematical Introduction to Fluid Mechanics, second edition, Springer-Verlag, 1990.
COURANT, R., FRIEDRICHS, K. O. – Supersonic Flow and Shock Waves, Springer-Verlag, 1976.
LANDAU L.D., LIFSHITZ, E.M. Fluid Mechanics. (Course of T.P., Vol.6).
WHITHAM, G. – Linear and Nonlinear Waves. New York, John Wiley, 1974.


January-FebruaryIntroduction to the Theory of Oscillations and Waves

  • Lecture notes: Part 1 [PDF in Portuguese], Part 2.2 [PDF in English], Part 3 [PDF in Portuguese, PDF in English]
  • Videos on YouTube (in Portuguese): full collection at "Cursos do IMPA" 
  1. Exercises (for Fri - 18/01),
  2. Exercises (for Wed - 30/01) - pages 54-55 in PDF of Part1.
  3. Exercises (for Wed - 6/02)
  4. Exercises (for Thu - 14/02)
  5. Exercises (for Fri - 22/02)

Some rather old notes

Exam questions with literature references 


Earlier:

Ordinary Differential Equations

Hydrodynamic Turbulence (reading course)

Spontaneous Stochasticity  (mini-course)

Bifurcations in ordinary differential equations

Fluid Dynamics

Introduction to the Theory of Oscillations and Waves

  • Lecture notes: Part 1 [PDF in Portuguese], Part 3 [PDF in Portuguese, PDF in English]
  • Videos on YouTube (in Portuguese): full collection at "Cursos do IMPA" 

Lectures on Boundaries of Stability Domains (mini-course)

Partial Differential Equations

Measure and Integration

Thermal Flow of Fluids

Stability and Catastrophes in Mechanical Systems

Introduction to the Lattice Boltzmann method for fluid dynamics (reading course)