Illinois PHYS 466, Lecture 1: Introduction |
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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 |
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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 |
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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 |
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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 |
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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...
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Illinois PHYS 466, Lecture 7: Dynamical Correlations & Transport Coefficients |
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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 |
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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 |
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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...
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Illinois PHYS 466, Lecture 10: Sampling |
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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 |
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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 |
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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 |
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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 |
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Illinois PHYS 466, Lecture 15: Constraints |
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Illinois PHYS 466, Lecture 16: Free Energies from Simulations |
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Illinois PHYS 466, Lecture 17: Simulation of Polymers |
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Illinois PHYS 466, Lecture 18: Kinetic Monte Carlo (KMC) |
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Illinois PHYS 466, Lecture 19: The Ising Model |
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