HYKE members gathered and had a Farewell Party on December 6th, 2019.

# [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**

# HYKE seminar – Invited talk by Dr. Min-Jun Choi

A seminar, titled , spoken by Dr. Min-Jun Choi, was held on November 6th, 2019, at Seoul National University.

# HYKE Seminar – Invited Talk by Prof. Marshall Slemrod

# [Invited talk]A condition for blow-up solutions to discrete semilinear wave equations on networks

# [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**

Abstract:

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.