June 1-12, 2015

Yukawa Institute for Theoretical Physics, Kyoto University

## Scope:

Vlasov-Poisson equations govern the dynamics of dark matter in the Universe as well as stars in galaxies. Traditionally, these equations are solved numerically by relying on a N-body approach where the phase-space distribution function is represented by a set of Dirac functions, that is an ensemble of particles. The discrete nature of this representation induces many defects in the simulations due, in particular, to N-body relaxation and to the shot noise of the particles. The goal of this workshop is to discuss and to work on state of the art methods to resolve numerically Vlasov-Poisson equations without resorting to particles. Semi-Lagrangian methods, widely developed in plasma physics, where the phase-space distribution function is represented on a grid, will be discussed and their application to the gravitational case will be studied. The cold case, particularly relevant to dark matter in the Universe, where the distribution function is supported by a smooth three-dimensional sheet evolving in 6-dimensional phase-space however deserves a special treatment, that will be discussed and studied as well. To best serve the purpose of this workshop, in the first two days of the workshop, a number of talks will be given by specialists on the subjects discussed just above, both in astrophysics and in plasma physics. In the remaining time of the workshop, current state of the art of the methods will be discussed and studied through ongoing and new collaborations.

## Organizing committee:

Nicolas Besse, Stéphane Colombi, Yves Elskens, Isabelle Guillerme, Thierry Sousbie, Yasushi Suto, Atsushi Taruya

**Contact address** -> mailto:vlasov-poisson [snail] yukawa [period] kyoto-u [period] ac [period] jp

## List of participants (and the *title of their talk*)

- Tom Abel (Kavli Institute for Particle Astrophysics and Cosmology, Stanford University):
*Dark Matter Dynamics*
- Raul Angulo (Centro de Estudios de Física del Cosmos de Aragón, Teruel):
*Cosmological structure formation in the continuous limit*
- Joshua Barnes (Institute for Astronomy, Hawaii):
*N-body methods: review and topics*
- Nicolas Besse (Institut Jean Lamour, CNRS & Université de Lorraine):
*A non exhaustive review of semi-Lagrangian methods for the Vlasov equation*
- Stéphane Colombi (Institut d'Astrophysique de Paris, CNRS & UPMC)
- Erwan Deriaz (Institut Jean Lamour, CNRS & Université de Lorraine):
*A high-order finite differences adaptive scheme applied to high-dimensional Vlasov-Poisson simulation*
- Yohan Dubois (Institut d'Astrophysique de Paris, CNRS & UPMC):
*Shaping the dark matter distribution with baryons*
- Yves Elskens (Aix-Marseille University):
*Direct path from N-body dynamics in plasmas to Debye shielding, and uniform derivation of Coulomb collisional transport*
- Takao Fujiwara (Kyoto City University of Arts):
*The Vlasov-Poisson approach to stellar systems in 1980s*
- Oliver Hahn (Université de Nice):
*An adaptively refined phase-space element method for cosmological simulations and collisionless dynamics*
- Anaelle Hallé (Institut d'Astrophysique de Paris, CNRS & UPMC):
*Fine structure of dark-matter haloes from Vlasov-Poisson or N-body simulations*
- Shunsuke Hozumi (Faculty of Education, Shiga University):
*Reproduction of Phase Space with a Self-Consistent Field Method*
- Eric Madaule (Institut Jean Lamour, CNRS & Université de Lorraine):
*Adaptive semi-Lagrangian scheme for Vlasov-Poisson*
- Takashi Minoshima (Japan Agency for Marine-Earth Science and Technology):
*Multi-moment advection scheme for Vlasov simulations of magnetized plasma*
- Takahiro Nishimichi (Kavli Institute for the Physics and Mathematics of the Universe, the University of Tokyo):
*Response function of the large-scale structure of the universe to the small scale inhomogeneities*
- Sébastien Peirani (Institut d'Astrophysique de Paris, CNRS & UPMC):
*On the inner density profile of dark matter haloes and galaxies: effect of AGN feedback*
- Thierry Sousbie (Institut d'Astrophysique de Paris, CNRS & UPMC and RESCEU, School of Science, The University of Tokyo):
*A phase space Vlasov-Poisson solver for CDM*
- Kohsuke Sumiyoshi (Numazu College of Technology):
*Numerical challenges in modeling supernova explosions by 6D Boltzmann equations*
- Yasushi Suto (RESCEU, School of Science, The University of Tokyo):
*Beyond the spherical dust collapse model*
- Atsushi Taruya (Yukawa Institute for Theoretical Physics, Kyoto University):
*Describing cosmological neutrinos with and without Vlasov-Poisson equation*
- Jihad Touma (American University of Beirut):
*Dynamics of phase-space curves*
- Yoshiyuki Yamaguchi (Laboratory of Theory and Applications of Dynamical Systems, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University):
*Dynamics around stable stationary states in Vlasov systems*
- Kohji Yoshikawa (Center for Computational Sciences, University of Tsukuba):
*6D Vlasov-Poisson simulation of self-gravitating systems and its application to the dynamics of cosmic neutrinos*

## Program

**June 1**

Auditorium of Yukawa Hall

9:30-9:50 : Welcome and registration

9:50-10:00 : Introduction

10:00-10:45 : Barnes

10:45-11:00 : Coffee break

11:00-11:30 : Fujiwara

11:30-12:00 : Elskens

12:00-14:00 : Lunch break

14:00-14:45 : Besse

14:45-15:15 : Hozumi

15:15-15:45 : Minoshima

15:45-16:15 : Madaule

16:15-16:30 : Coffee break

16:30-17:15 : Yoshikawa

17:15-17:45 : Sumiyoshi

17:45-18:15 : Deriaz

19:00 : *Banquet*

**June 2**

Auditorium of Yukawa Hall

9:45-10:15 : Abel

10:15-11:00 : Dubois

11:00-11:15 : Coffee break

11:15-11:45 : Peirani

11:45-12:15 : Nishimichi

12:15-14:00 : Lunch break

14:00-14:30 : Suto

14:30-15:00 : Touma

15:00-15:30 : Hallé

15:30-15:45 : Coffee break

15:45-16:15 : Angulo

16:15-16:45 : Hahn

16:45-17:15 : Sousbie

17:15-17:25 : Concluding words

**June 3 - 12**

Research building, rooms K102 and K202

Discussions, collaborations, informal seminars

June 4 :

15h30-16h30 : Informal discussion: Taruya (room K202)

June 5 :

14h00-15h00 : Yamaguchi (room K202)

June 10 :

14h00-15h00 : Informal discussion about Vlasov equations and galactic dynamics : Barnes & Touma (room K202)

June 11 :

14h30-15h30 : Colombi (room K202): post-collapse perturbation theory

## Access to YITP

Details can be found here

The first 2 days of the workshop will take place in the auditorium of Yukawa Hall, while the remaining will be held in rooms K202 and K102 of the research building:

From Palace Side Hotel:

## Sponsors

This workshop is sponsored by Yukawa Institute for Theoretical Physics through an International molecule-type workshop grant, by Agence Nationale de la Recherche through VLASIX project grant ANR-13-MONU-0003 and by Institut Lagrange de Paris.