## Illinois MatSE485/Phys466/CSE485 - Atomic-Scale Simulation

Lecture Number/Topic | Online Lecture | Video | Lecture Notes | Supplemental Material | Suggested Exercises |
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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
... |
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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 ... |
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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:
... |
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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... |
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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... |
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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... |
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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
... |
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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... |
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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.
... |
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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... |
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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... |
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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... |
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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 |