Incremental Integration of Computational Physics into Traditional Undergraduate Courses Kelly R. Roos, Department of Physics, Bradley University Peoria, IL 61625, 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