[HYKE Intensive Lecture] HYKE Intensive Lectures on Symmetric Hyperbolic Systems of Balance Laws and State

There will be an HYKE Intensive Lectures.

Title: HYKE Intensive Lectures on Symmetric Hyperbolic Systems of Balance Laws and State
Lecturers: Prof. Tommaso Ruggeri (Univ. of Bologna)
                   Prof. Masaru Sugiyama (Nagoya Institute of Technology)

Time: 2019 December 3rd, 9:00am~1:00pm
           2019 December 6th, 9:00am~5:00pm
           2019 December 11th, 9:00am~11:00am

Place: 27-116 (3rd), 27-220 (6th, 11th)
Lecture Topics:
Prof. Ruggeri:
Lecture 1,2: Balance Laws, Hyperbolic Systems, Symmetric Systems. Main field and theorem of symmetrization. Examples of Euler fluids, non-linear elasticity, MHD, Born-Infeld nonlinear electrodynamics, relativistic fluids.
Lecture 3,4: Compatibility between Galilean invariance and Entropy Principle. Qualitative analysis, K -condition and global existence of smooth solutions. Principal subsystems and nesting theories with examples. The mixture of gas and connection with Cucker-Smale models.
Lecture 5,6: Shock wave and growth of entropy across the shock, shock structure and sub-shocks formation. Problematic of Rational Extended Thermodynamics in mono and polyatomic gas.
Prof. Sugiyama:
0. Preliminary Discussion
1. Introduction
  1.1 How to describe macroscopic phenomena?
  1.2 Three levels of description of macroscopic systems
2. Equilibrium Statistical Mechanics
  2.1 Distribution function and the Liouville equation
  2.2 Gibbs ensembles
     2.2.1 Microcanonical ensemble, and its application to ideal gas
     2.2.2 Canonical ensemble, and its applications to ideal gas and a system of harmonic oscillators
     2.2.3 Grandcanonical ensemble, and its application to ideal gas
  2.3 Remarks
     2.3.1 Gibbs entropy and information entropy
     2.3.2 Fluctuation
     2.3.3 Validity range of classical statistical mechanics
3. Some Topics I
  3.1 Phase transition
     3.1.1 Virial expansion and the van der Waals equation of state
     3.1.2 Yang and Lee theory of phase transition
     3.1.3 Ising model
     3.1.4 Critical phenomena: Renormalization group approach
  3.2 Fermi statistics and Bose statistics
4. Non-Equilibrium Statistical Mechanics
  4.1 BBGKY hierarchy of the distribution functions
  4.2 Boltzmann equation and the system of moment equations
5. Some Topics II
  5.1 Extended thermodynamics – A new non-equilibrium thermodynamics –
  5.2 Linear response theory
  5.3 Stochastic processes
6. Concluding Remarks and Outlook

[Invited talk]Hyper-elastic Ricci Flow

There will be an invited talk.

Title: Hyper-elastic Ricci Flow
Speaker: Prof. Marshall Slemrod (University of Wisconsin-Madison)
Time: 2019 November 5th, 11:00am~12:00pm
Place: 27-220
In this talk, I will introduce the concept of hyper-elastic Ricci flow. The equation of hyper-elastic Ricci flow amends the classical Ricci flow by the addition of Cauchy stress tensor which itself is derived from the free energy. The main implication of the theory is a uniformization of material behavior which follows from application of a parabolic minimum principle.