Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Collisionless Boltzmann Equation

In course

PHYS-401: Astrophysics IV : stellar and galactic dynamics

The aim of this course is to acquire the basic knowledge on specific dynamical phenomena related to the origin, equilibrium, and evolution of star clusters, galaxies, and galaxy clusters. ...

Description

This lecture covers the Collisionless Boltzmann Equation, Jeans theorems, equilibria of collisionless systems, and connections between barotropic fluids and ergodic stellar systems. It explains the distribution function, velocity dispersions, and various coordinates systems used in the study of collisionless systems.

Instructor

Yves Revaz

Yves Revaz is a scientist at LASTRO/EPFL. After successful studies in physics at EPFL, he accomplished his PhD entitled: "Dynamics of external regions of spiral galaxies and constraints on the dark matter", at the Geneva Observatory in the galactic dynamics group of Prof. D. Pfenniger. He then moved to the Paris Observatory to work at the LERMA (Laboratory for Studies of Radiation and Matter in Astrophysics) under the supervision of Prof. F. Combes on the understanding of cooling flows in galaxy clusters. He joined LASTRO at EPFL in 2007, where, in collaboration with Pascale Jablonka, he developed a new TreePM/SPH chemo-dynamical code called GEAR, designed to study the chemical evolution of galaxies. His current main research focus on the evolution of dwarf spheroidal galaxies and their link with the cosmology. Yves Revaz is also the author of pNbody, a parallelized python toolbox designed to manipulate large N-body systems.

Official source

Related concepts (32)

Cumulative distribution function

In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable , or just distribution function of , evaluated at , is the probability that will take a value less than or equal to . Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by a right-continuous monotone increasing function (a càdlàg function) satisfying and .

Spherical coordinate system

In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin; its polar angle measured from a fixed polar axis or zenith direction; and the azimuthal angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the fixed axis, measured from another fixed reference direction on that plane.

Probability density function

In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample.

Quantile function

In probability and statistics, the quantile function outputs the value of a random variable such that its probability is less than or equal to an input probability value. Intuitively, the quantile function associates with a range at and below a probability input the likelihood that a random variable is realized in that range for some probability distribution. It is also called the percentile function (after the percentile), percent-point function or inverse cumulative distribution function (after the cumulative distribution function).

Empirical distribution function

In statistics, an empirical distribution function (commonly also called an empirical cumulative distribution function, eCDF) is the distribution function associated with the empirical measure of a sample. This cumulative distribution function is a step function that jumps up by 1/n at each of the n data points. Its value at any specified value of the measured variable is the fraction of observations of the measured variable that are less than or equal to the specified value.

Related lectures (34)

Continuous Random Variables

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.

Collisionless Boltzmann Equation

Explores the Collisionless Boltzmann equation, distribution functions, Jeans theorems, resonances, chaotic orbits, and equilibria in stellar systems.

Normal Distribution: Properties and Calculations

Covers properties and calculations related to the normal distribution, including probabilities and quantiles.

Probability and Statistics: Discrete Random Variables

Explores discrete random variables, mass functions, and distribution functions in probability and statistics.

Discrete Random Variables