Lecture Syllabus - PHY401 (Spring
'13)
Chapter
1: Introduction to Progamming and Numerical Solutions (Jan 15+17)
- 1.Order differential equations
(DEQs) and Euler method; nuclear decay
- Code
design and construction
- Code
debugging+checking; numerical parameters and accuracy
- Runge-Kutta Method
Chapter 2: Drag Forces in 1- and 2-D Motion (Jan 22+24)
- 1-D:
car/bicycle with velocity-dependent force
- 2-D: smooth cannon shell
- Effects of turbulence, wind
spinning
Chapter 3: Oscillatory Motion and Chaos (Jan 29+31, Feb 05)
- 2.Order
DEQ: Simple Harmonic Motion, Euler-Cromer method
- Driven Harmonic Motion,
transition to Chaos, Lyapunov exponent
- Bifurcation, Logistic Map
- Billard
problem
Chapter 4: The Solar System (Feb 07, 12, 14)
- Kepler's laws in cartesian
coordinates
- Elliptic orbits and stability of the
inverse-square force law
- Correction to 1/r2-orbits: general relativity, 3-body;
least-square fit
- 3-Body problem, Kirkwood Gaps
Chapter 5: Potentials and Fields (Feb 19, 21, 26)
- Partial differential equations
(PDEs): Laplace equation and relaxation algorithm
- Inclusion of charges: Poisson
equation
- Magnetic fields (wire, solenoid),
numerical integration
Chapter 6: Waves and Spectral Analysis (Feb 28, Mar 05+07)
- Ideal wave equation (in
space-time, DEQ), stability
- Frequency spectra, (fast) Fourier analysis, power
spectrum
- Realistic string: stiffness and friction
- Spectral methods
---- Midterm Exam: Mar 19 in class
----
Chapter 7: Random Systems (Mar 21, 26, 28, Apr 02)
- Random
number generators
- Random Walk, Self-Avoiding Walk, Flory Exponent
- Diffusion equation, entropy
- Cluster growth
- Fractal dimensions
- Percolation and 2. order phase transition
Chapter 8: Statistical Mechanics, Ising Model and Phase
Transitions (Apr 04, 09, 11)
- Ising Model, Mean-Field Theory
- Monte-Carlo method
- Ising model and 2.order phase transition, critical exponents,
correlation function
- External magnetic field, 1.order phase tranition
Chapter
9: Molecular Dynamics (Apr 16+18)
- Dilute gas, equations of motion,
Verlet method
- Boundary conditions and initialization
- Equilibrium and equipartition theorem
- Solidification and melting transition
Chapter 10: Quantum Mechanics (Apr 23+25)
- Time-independent Schroedinger
equation (SEQ)
- Numerical solutions (shooting+matching method)
- Matrix methods
- Energy minimization and variational approach