Introduction to hydrodynamics

An Introduction to Relativistic Hydrodynamics

This lecture provides some introduction to perfect fluid dynamics within the framework of general relativity. The presentation is based on the Carter-Lichnerowicz approach. It has the advantage over the more traditional approach of leading very straightforwardly to important conservation laws, such as the relativistic generalizations of Bernoulli’s theorem or Kelvin’s circulation theorem. It al...

Boulder Summer School Lecture: Introduction to Hydrodynamics

The last lecture has been more words than equations. Today we are going to do some paradigmatic calculations. We’ll start with -one at high Reynolds number and one at low Reynolds number –which represent critical ideas for the subject of fluid mechanics. The first calculation is arguably the most important applied-mathematical idea of the twentieth century (at least I would argue it), and it is...

Smoothed Particle Hydrodynamics 3.1 Introduction

X iv :a st ro -p h/ 05 07 47 2v 1 2 0 Ju l 2 00 5 “I went on to test the program in every way I could devise. I strained it to expose its weaknesses. I ran it for high-mass stars and low-mass stars, for stars born exceedingly hot and those born relatively cold. I ran it assuming the superfluid currents beneath the crust to be absent – not because I wanted to know the answer, but because I had d...

An Introduction to Sociolinguistics

Introduction to circular data

In many diverse scientific fields, the measurements are directions. For instance, a biologist may be measuring the direction of flight of a bird or the orientation of an animal. A series of such observations is called ”directional data”. Since a direction has no magnitude, these can be conveniently represented as points on the circumference of a unit circle centered at the origin or as unit ...