Topic 7
Fluid Dynamics
Lecture 1
Fluid Dynamics in Astrophysics and Cosmology
Large systems of particles are approximated in Fluid dynamics by continuous media which obey
partial dierential equations. Computational uid dynamics is important in astrophysic
Topic 7
Fluid Dynamics
Lecture 1
Fluid Dynamics in Astrophysics and Cosmology
Large systems of particles are approximated in Fluid dynamics by continuous media which obey partial
dierential equations. Computational uid dynamics is important in astrophysic
Topic 7
Fluid Dynamics
Lecture 4
Equations of State and Solving the TOV Equation
A white dwarf or neutron star in equilibrium has exhausted all its nuclear fuel. Gravitational collapse is
prevented by fermion degeneracy pressure. The thermal energy per fe
Topic 7
Fluid Dynamics
Lecture 5
General-Relativistic Gravitational Collapse
One of rst detailed numerical calculations of the collapse of a spherically symmetric massive star was done
by M.M. May and R.H. White, Phys. Rev. 141, 1232-1241 (1966).
PHY 411-
Topic 7
Fluid Dynamics
Lecture 6
Cosmological Evolution and Structure Formation
New Simulation Published This Week!
M. Vogelsberger et al., Properties of galaxies reproduced by a hydrodynamic simulation, Nature 509,
177-182 (2014)
Our simulation code, ARE
Topic 7
Fluid Dynamics
Lecture 3
Equilibrium of White Dwarfs and Neutron Stars
These are stars that have exhausted their nuclear fuel. They can be modeled as balls of ideal Fermi gases
at temperature T = 0 with fermion degeneracy (Pauli exclusion) pressur
Topic 1
Molecular Dynamics
Lecture 3
Gravity Waves and Solitons
A Scottish engineer in the mid nineteenth century John Scott Russell built a 30 wave tank in his backyard.
Dropping a weight at one end of the channel produced a solitary gravity wave with sp
Topic 2
Monte Carlo Methods
Lecture 3
The Ising Model of Ferromagnetism
Magnetism in matter is caused by charged particles moving in closed orbits or spinning around their axes.
Recall that a current loop creates a magnetic eld according to Amp`res law. A
Topic 7
Fluid Dynamics
Lecture 2
The Riemann Problem and Shock Tube Problem
A simple one dimensional model of a gas was introduced by G.A. Sod, J. Computational Physics 27, 1
(1978), to test various algorithms for solving uid dynamics problems with shock
Topic 5
Quantum Monte Carlo
Lecture 5
The Path Integral Monte Carlo Method
The Path Integral formulation of quantum mechanics was suggested by Dirac Rev. Mod. Phys. 17, 195199 (1945), and extensively developed by Feynman, Rev. Mod. Phys. 20, 367-387 (1948
Topic 6
Quantum Field Theory
Lecture 3
Hadron Collisions and Parton Distribution Functions
The Cross Section for Z Boson Production at the LHC
S. Chatrchyan et al., CMS Collaboration, Measurement of the Drell-Yan cross section in pp collisions
at s = 7 Te
Topic 7
Fluid Dynamics
Lecture 2
The Riemann Problem and Shock Tube Problem
Sods Shock Tube Problem
A simple one dimensional model of a gas was introduced by G.A. Sod, J. Computational Physics 27,
1 (1978), to test the ability of various algorithms in sol
Topic 7
Fluid Dynamics
Lecture 6
Cosmological Evolution and Structure Formation
The Millenium Simulation
The Millennium Simulation is the largest N-Body Simulation ever carried out, containing over 10
billion particles. The simulation was carried out by t
Topic 6
Quantum Field Theory
Lecture 5
Abelian Lattice Gauge Theories
The article by M. Creutz, L. Jacobs, C. Rebbi, Monte Carlo study of Abelian lattice gauge theories,
Phys. Rev. D20, 1915-1922 (1979) describes simulations of lattice QED that illustrate
Topic 7
Fluid Dynamics
Lecture 4
Equations of State and Solving the TOV Equation
The Ground State of Nuclear Matter
A white dwarf or neutron star in equilibrium has exhausted all its nuclear fuel. Gravitational collpase
is prevented by fermion degeneracy
Topic 7
Fluid Dynamics
Lecture 3
Equilibrium of White Dwarfs and Neutron Stars
Basic Physics of White Dwarfs and Neutron Stars
These are stars that have exhausted their nuclear fuel. They can be modeled as balls of ideal Fermi
gases at temperature T = 0 w
Topic 6
Quantum Field Theory
Lecture 1
Monte Carlo Quadrature in Quantum Field Theory
Applications of relativistic quantum eld theories like the Standard Model of elementary particles
generally use perturbative Feynman diagram methods to compute cross sec
Topic 7
Fluid Dynamics
Lecture 5
General-Relativistic Gravitational Collapse
Spherically Symmetric Hydrodynamic Collapse
One of rst detailed numerical calculations was done by M.M. May and R.H. White
Phys. Rev. 141, 1232-1241 (1966).
411-506 Computational
Topic 6
Quantum Field Theory
Lecture 6
Lattice Quantumchromodynamics
Perturbation theory in the QCD coupling s (Q) can be used only at high energies Q
1 GeV.
Predictions for low energy properties, such as the spectrum of mesons and baryons, the decays of
Topic 5
Quantum Monte Carlo
Lecture 1
Variational Monte Carlo (VMC) for the Harmonic Oscillator
In this topic, we will study simple quantum mechanical systems of particles which have bound states.
The simplest such system is the quantum harmonic oscillato
Topic 5
Quantum Monte Carlo
Lecture 4
The Diusion Monte Carlo (DMC) Method
In this approach, the ground state of the system is found by modeling a diusion process.
Diusion and random walks
Consider a random walk on a lattice with spacing a in one dimensio
Topic 5
Quantum Monte Carlo
Lecture 2
Variational Monte Carlo for Hydrogen and Helium
The Hydrogen Atom
The Hydrogen atom is a system with two particles, electron and proton. The conguration space in
which the system moves is therefore six dimensional. By
Topic 6
Quantum Field Theory
Lecture 4
Lattice Gauge Theories
Lattice Quantumchromodynamics
Unlike the QED ne structure constant , the QCD coupling parameter s (Q) depends strongly
on the energy (inverse distance) scale at which the strong interaction tak