Kinetic and non-equilibrium conservation laws

MATH-532 / 5 credits

Teacher: Gorji Mohammadhossein

Language: English

Summary

Study of kinetic models and non-equilibrium conservation laws, linking particle interactions to macroscopic behavior. Covers analysis, simulation, and modeling across scales and media using kinetic theory, reduced-order models, and particle methods.

Content

  • Interacting Particle Systems: Markov processes, Langevin Dynamics
  • Fundamental Kinetic Equations: Boltzmann, Vlasov, and Fokker-Planck Equations
  • Moment Hierarchy & Hydrodynamic Limit
  • Fluctuation-Dissipation Theorem & Mori-Zwanzig Formalism
  • Numerical Methods for Kinetic Equations and Particle Simulations

 

Keywords

Kinetic Theory, Langevin Dynamics, Particle Methods

Learning Prerequisites

Required courses

Background in PDEs, stochastic processes, and basic numerical methods is required.

Teaching methods

Lectures: Delivered using both blackboard and slides. Lecture notes will be provided.

Exercise Sessions: Weekly sessions combining problem-solving exercises with seminar-style discussions.

 

 

Assessment methods

Oral

 

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Resources

Moodle Link

In the programs

  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Kinetic and non-equilibrium conservation laws
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Kinetic and non-equilibrium conservation laws
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Kinetic and non-equilibrium conservation laws
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Kinetic and non-equilibrium conservation laws
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Kinetic and non-equilibrium conservation laws
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Kinetic and non-equilibrium conservation laws
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional

Reference week

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