Global Warming and Fourier Transforms
Atmospheric Carbon Dioxide
Situated at 11,135 ft on the north ank of the Mauna Loa volcano on the Big Island of Hawaii, the
National Oceanic and Atmospheric Administrations Mauna Loa Observatory http:/www.mlo.noaa.gov
Solar System: Planets Asteroids Comets
The Solar System
Our Sun is an average star which moves around the center of our Milky Way galaxy with a speed of
220 km/s once every 200 million years. It drags along with it numerous captive objects, 8 planets, 5 d
Homework Assignment 10
Due: Tuesday December 8, 11:59 pm, UBlearns Digitial Dropbox
PHY 410: choose any two problems.
PHY 505: work all three problems
1. Run the percolation codes to convince yourself that there is a phase transition at pc = 0.5. Compare
Supernova Cosmology and Chi-square Fitting
Type Ia Supernovae as Standard Candles
A white dwarf is a star that has exhausted its supply of hydrogen fuel, blows o its outer envelope, and
collapses into a dense core of free electrons and nuclei that is supp
Diusion-Limited Aggregration
Kinetic Growth Phenomena
Many structures in nature are formed by random addition of particles. Starting with a seed particle, the
structure can capture freely moving (kinetic) particles that happen to collide with it. This gro
Monte Carlo Particle Transport
Particle Transport
Many important problems in physics and practical applications in technology involve the motion of
particles through an object or a medium.
One of the rst such applications to use a digital computer was the
Metropolis Monte Carlo
Nonuniform Sampling
The simplest Monte Carlo applications make use of uniformly distributed random sequences. Random
number generator algorithms normally produce sequences of integers from a nite set chosen with equal
probabilities.
Random Walks and Diusion
Monte Carlo Simulation
To simulate is to mimic or imitate. A simulation is especially useful when it is simpler or easier to control
than the system being imitated. A computer simulation is the execution of a computer program that
Random Number Generators
Random Sequences
There is no such thing as a random number! A random sequence is a sequence of values x0 , x1 , . . . chosen
from a set cfw_s1 , s2 , . . . , sM of size M with a given probability distribution p1 , p2 , . . . , pM
Self-Avoiding Walks and Polymers
Polymers in Solvent
A polymer is a chain molecule with a large number n + 1 of monomers joined by n strong covalent bonds.
Protein molecules [1] are polymer chains made from 20 types of amino acid.
In a solvent, the polyme
The CMB and General Linear Least Squares
The Cosmic Microwave Background
The Universe is bathed in a homogenous and isotropic sea of photons left over from the Big Bang that has
a nearly perfect black body spectrum with temperature T = 2.725 0.001 K shown
Homework Assignment 8
Due: Tuesday November 17, 11:59 pm, UBlearns Digitial Dropbox
PHY 410: choose any two problems.
PHY 505: work all three problems
1. Add code to infwell.cpp to compute the eigenfunction n (x) after it has found an eigenvalue En .
Make
Earthquakes and Nonlinear Model Fitting
Earthquakes
The Earths crust is made up of large tectonic plates that move relative to one another. This motion causes
cracks or faults in the crust between sections of plates that move relative to one another. When
Homework Assignment 1
Due: Sunday September 13, 11:59 pm, UBlearns Digitial Dropbox
PHY 410: choose any two problems.
PHY 505: work all three problems
1. Modify the Hubble program to make a least-squares t to the 9 open circles in Fig. [1] and compare
the
Homework Assignment 2
Due: Monday September 21, 11:59 pm, UBlearns Digitial Dropbox
PHY 410: choose any two problems.
PHY 505: work all three problems
1. Download http:/nssdc.gsfc.nasa.gov/planetary/factsheet/cometfact.html (NASAs Comet
Fact Sheet on 20 s
Hubbles Law and Least Squares Fitting
Computational Physics
Physics is a natural science which attempts to describe the Universe in terms of a few basic concepts such
as time, space, mass, and electric charge. These quantities can be assigned numerical va
Homework Assignment 3
Due: Thursday October 1, 11:59 pm, UBlearns Digitial Dropbox
PHY 410: choose any two problems.
PHY 505: work all three problems
1. Modify the program pi.cpp to compute the volume of a sphere of radius R = 1 in three dimensions.
Plot
Homework Assignment 5
Due: Sunday October 18, 11:59 pm, UBlearns Digitial Dropbox
PHY 410: choose any two problems.
PHY 505: work all three problems
1. Modify the program halley.cpp to measure the period of the orbit. Compare this with the prediction
from
Homework Assignment 4
Due: Sunday October 11, 11:59 pm, UBlearns Digitial Dropbox
PHY 410: choose any two problems.
PHY 505: work all three problems
1. Use http:/www.physics.buffalo.edu/phy410-505/topic2/dla.cpp to measure the fractal
dimension of DLA clu
Homework Assignment 6
Due: Sunday November 1, 11:59 pm, UBlearns Digitial Dropbox
PHY 410: choose any two problems.
PHY 505: work all three problems
1. Use the Lyapunov program to make a plot of the exponent as a function of the parameter r in the
period
Homework Assignment 7
Due: Tuesday November 10, 11:59 pm, UBlearns Digitial Dropbox
PHY 410: choose any two problems.
PHY 505: work all three problems
1. Explore the dynamics of the pendulum and describe 5 types of motion that you nd most interesting,
pro
Newtons Laws and Kepler Orbits
Dynamics of Solar System Objects
The orbits around the Sun of solar system bodies[1] are determined by Newtons Law of Universal
Gravitation, and Newtons equations of motion. These are systems of ordinary dierential equations
Runge-Kutta Methods for ODE Systems
Ordinary dierential equations
An ordinary dierential equation (ODE) has one independent variable x, and one or more dependent
variables y(x), . . .
Physicists are usually interested in a particular solution of a dierent
Black Holes and Schwarzschild Orbits
Precession of the Perihelion of Mercury
If two bodies interaction potential energy of two bodies depends only on the magnitude of their relative
separation, then angular momentum is conserved. The orbit lies in a plane
Harmonic Oscillator: Numerov Algorithm
Linear equations and the Sturm-Liouville problem
Many important dierential equations in physics are second order and linear in the solution u(x) of the
form
du
d2 u
+ d(x)
+ q(x)u = s(x) ,
(1)
dx2
dx
where d(x), q(x)
Chaos in the Three Body Problem
Restricted Planar Circular Three-Body Problem
The gravitational three-body problem is not integrable. Trajectories may be chaotic, depending on the
masses of the three bodies and the initial conditions. To simplify the prob
The Percolation Phase Transition
Statistical Mechanics
If a system consists of a very small number of particles, we can attempt to predict its properties in
complete detail using classical or quantum mechanics. If the system consists of a very large numbe
Energy Bands and Gaps in Periodic Solids
The Kronig Penney Model
The Kronig-Penney model is a simple one-dimensional model that illustrates the formation of energy bands
and gaps.
Lattice periodicity
Consider a simple one-dimensional model of a crystal. N
The Hopeld Neural Network Model
Neural Networks and the Brain
There are many computational tasks for which digital computers are vastly more ecient than human
beings, especially if such tasks can be done using deterministic numerical algorithms.
On other
Critical Slowing Down and Cluster
Algorithms
Reducing critical slowing down
The Metropolis Monte Carlo method works very well in simulating the properties of the 2-D Ising model.
However, close to the Curie temperature Tc , the simulations suer from criti