1. Incremental Integration of Computational Physics into Traditional Undergraduate Courses Kelly R. Roos, Department of Physics, Bradley University Peoria, IL 61625, rooster@bradley.edu Course TopicComputational AssignmentComputational Method and Skills Acquired Projectile MotionRealistic projectile motion with air resistance - Simulating a model - Euler method - programming and debugging fundamentals - necessity of error control Linear oscillationsSimple harmonic oscillator- artifact identification - Basic Runge-Kutta method - increased programming skills - function plotting - phase space plots Nonlinear oscillations- Simple pendulum - Damped driven pendulum - Higher order Runge-Kutta methods - introduction to Verlet and Gear algorithms - chaos identification - Poincaré sections - Lyapunov exponents - period doubling and transition to chaos Lagrangian dynamics- Double pendulum - Numerical integration of other dynamical systems more sophisticated programming Classical gravitation and central force motion - Verify Kepler’s laws - 2-body problem - 3-body problem Rotational reference frames- Projectile motion with Coriolis deflection 3D trajectory visualization Precis:In a department wherein the creation of specific computation physics courses has not been possible, I have devised a mode of computational physics instruction wherein I incrementally integrate computational physics instruction into the traditional format of two upper-level undergraduate course I have taught for many years. Summary of computational topics covered and skills acquired: Classical MechanicsStatistical Mechanics and Thermodynamics Course TopicComputational AssignmentComputational Method and Skills Acquired MappingLinear Congruential Generatorrandom number sequence generation Methods of statistical analysis- Random occupation of a square lattice - 2D random walk - application of random number generator - simulation of a stochastic model - stochastic vs. deterministic models - calculate probability distributions - importance of concept of ensemble - computational realization of large ensemble Ideal and non-ideal Gases- Hard sphere simulation of ideal gas - Non-ideal gas model with Lennard-Jones potentials - Molecular Dynamics (MD) method - importance of material boundaries and appropriate boundary conditions - visualization of connection between macroscopic observables and microscopic states - utilization of Verlet and/or Gear algorithms MagnetismIsing Model- Monte Carlo (MC) method and the Metropolis algorithm - ferromagnetic phase transition in 2D system Non-equilibrium physics- Diffusion-limited aggregation (DLA) - Kinetic MC simulation of initial stages of thin film growth - Numerical Integration of nonlinear stochastic microscopic rate equations - kinetic MC method - box counting method for determining fractal dimension of DLA structures - application of periodic boundaries - finite simulation size effects - realistic model of non-equilibrium atomistic processes at surfaces - complicated programming - verification of analytic theory with simulation results Examples of student calculations from Statistical Mechanics: 2D Random Walk on a square lattice Equal probability in each of four directions Probability distribution Modeling Sub-Monatomic Layer Epitaxial Growth Stochastic rate equations Random Occupation of sites on a square lattice Ave. site occupation = 4 40,000 depositions on a 100x100 lattice Poisson Distribution Effect of increasing temperature Kinetic Monte Carlo Simulations 100 x 100 lattice (periodic boundaries) Effect of increasing Edge diffusion Diffusion Limited Aggregation Hausdorff dimension N = r D D ≈ 1.6 High binding energy between atoms Low binding energy between atoms