Illinois MatSE485/Phys466/CSE485 - Atomic-Scale Simulation

By David M. Ceperley

University of Illinois at Urbana-Champaign



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THE OBJECTIVE is to learn and apply fundamental techniques used in (primarily classical) simulations in order to help understand and predict properties of microscopic systems in materials science, physics, chemistry, and biology.

  • THE EMPHASIS will be on connections between the simulation results and real properties of materials (structural or thermodynamic quantities), as well as numerical algorithms and systematic and statistical error estimations
  • FOR WHOM? This class is oriented for the first-year graduate or advanced undergraduate. It connects atomistics to observable, rather than investigates, e.g., cellular automata type approaches, and introduces all necessary concepts. A course project is required, rather than a final exam (see Teams and Projects in navigator bar).
  • Methods and Applications:
  • Molecular Dynamics: integration algorithms, static and dynamic correlations functions and their connection to order and transport
  • Monte Carlo and Random Walks: variance reduction, Metropolis algorithms, Kinetic Monte Carlo, heat diffusion, Brownian motion, etc
  • Phase Transitions: melting-freezing, calculating free energies
  • Polymers: growth and equilibrium structure
  • Quantum Simulation: zero temperature and finite temperature methods
  • Optimization techniques such as simulated annealing

Cite this work

Researchers should cite this work as follows:

  • David M. Ceperley (2009), "Illinois MatSE485/Phys466/CSE485 - Atomic-Scale Simulation,"

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Lecture Number/Topic Online Lecture Video Lecture Notes Supplemental Material Suggested Exercises
Illinois PHYS 466, Lecture 1: Introduction View Flash
Introduction to Simulation Content: Why do simulations? Moore's law Two Simulation Modes Dirac, 1929 Challenges of Simulation: Physical and mathematical underpinnings ...

Illinois PHYS 466, Lecture 3: Basics of Statistical Mechanics View Flash
Basics of Statistical Mechanics Review of ensembles Microcanonical, canonical, Maxwell-Boltzmann Constant pressure, temperature, volume,… Thermodynamic limit Ergodicity ...

Illinois PHYS 466, Lecture 4: Molecular Dynamics View Flash
Molecular Dynamics What to choose in an integrator The Verlet algorithm Boundary Conditions in Space and time Reading assignment: Frenkel and Smit Chapter 4 Content: ...

Illinois PHYS 466, Lecture 5: Interatomic Potentials View Flash
Interatomic Potentials Before we can start a simulation, we need the model! Interaction between atoms and molecules is determined by quantum mechanics But we don’t know...

Illinois PHYS 466, Lecture 6: Scalar Properties and Static Correlations View Flash
Scalar Properties, Static Correlations and Order Parameters What do we get out of a simulation? Static properties: pressure, specific heat, etc. Density Pair correlations in real space and...

Illinois PHYS 466, Lecture 7: Dynamical Correlations & Transport Coefficients View Flash
Dynamical correlations and transport coefficients Dynamics is why we do molecular dynamics! Perturbation theory Linear-response theory Diffusion constants, velocity-velocity auto...

Illinois PHYS 466, Lecture 8: Temperature and Pressure Controls View Flash
Temperature and Pressure Controls Content: Constant Temperature MD Quench method Brownian dynamics/Anderson thermostat Nose-Hoover thermostat (FS 6.1.2) Nose-Hoover thermodynamics ...

Illinois PHYS 466, Lecture 9: Probability tools & Random number generators View Flash
Random Number Generation (RNG) read “Numerical Recipes” on random numbers and chi-squared test Today we discuss how to generate and test random numbers. What is a random number? A single...

Illinois PHYS 466, Lecture 10: Sampling View Flash
Fundamentals of Monte Carlo What is Monte Carlo? Named at Los Alamos in 1940’s after the casino. Any method which uses (pseudo)random numbers> as an essential part of the algorithm. ...

Illinois PHYS 466, Lecture 11: Importance Sampling View Flash
Importance sampling Today We will talk about the third option: Importance sampling and correlated sampling Content: Importance Sampling Finding Optimal p*(x) for Sampling Example of...

Illinois PHYS 466, Lecture 12: Random Walks View Flash
Random Walks Today we will discuss Markov chains (random walks), detailed balance and transition rules. These methods were introduced by Metropolis et al. in 1953 who applied it to a...

Illinois PHYS 466, Lecture 13: Brownian Dynamics View Flash
Brownian Dynamics Let’s explore the connection between Brownian motion and Metropolis Monte Carlo. Why? Connection with smart MC Introduce the idea of kinetic Monte Carlo Get rid of...

Illinois PHYS 466, Lecture 14: Neighbor Tables, Long-Range Potentials, Ewald Sums View Flash
Illinois PHYS 466, Lecture 15: Constraints View Flash
Illinois PHYS 466, Lecture 16: Free Energies from Simulations View Flash
Illinois PHYS 466, Lecture 17: Simulation of Polymers View Flash
Illinois PHYS 466, Lecture 18: Kinetic Monte Carlo (KMC) View Flash
Illinois PHYS 466, Lecture 19: The Ising Model View Flash