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Computational Statistical Mechanics
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Lauree triennali, magistrali, a ciclo unico
Scienze matematiche, fisiche e naturali
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Lauree Magistrali
Computational Statistical Mechanics
Written material with audiocomments
Lesson 23: Harmonic Oscillator
Open course index
Lesson 23: Harmonic Oscillator
Click
Langevin-HarmonicOscillator.pdf
link to view the file.
◄ An example of a stochastic equation Audio
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Syllabus
Lessons: topics and bibliography (2018)
Lesson 1:Microcanonical ensemble
Microcanonical Ensemble - Audio
Lesson 1: Canonical Ensemble
Canonical Ensemble Audio
Lesson 1: Isobaric-isothermal ensemble
Isobaric ensemble Audio
Lesson 2: Grandcanonical ensemble
GrandCanonical Ensemble Audio
Lesson 2: Diatomic molecules (I)
Diatomic Molecules (I) Audio
Lesson 2: Diatomic molecules (II)
Diatomic Molecules (II) Audio
Lesson 3: Virial Pressure
Virial pressure Audio 1
Virial pressure Audio 2
Lesson 3: Distribution functions (I)
Distribution function (I) Audio
Lesson 3: Distribution functions (II)
Distribution Function (II) Audio
Lesson 4: Numerical Distributions
Numerical Distributions Audio
Lesson 4: Gaussian Random Numbers
Random Gaussian Numbers Audio
Lesson 4: Errors and Bias
Errors and Bias Audio 1
Errors and bias Audio 2
Lesson 4: Estimation of the variance
Estimation of the variance Audio
Lesson 5: Error Propagation Formula
Error Propagation Formula Audio
Lesson 5: Errors and Bias on Ratios
Errors and Bias on Ratios Audio 1
Errors and Bias on Ratios Audio 2
Errors and Bias on Ratios Audio 3
Lesson 6: The Jackknife Method (with corrections)
The Jackknife Method Audio 1
The Jackknife Method Audio 2
Lesson 6: The Binning Method
The Binning Method Audio
Lesson 6: Introduction to dynamic MC methods
Introduction to dynamic Monte Carlo Methods Audio
Lesson 7: Markov chains
Markov Chains Audio (I)
Markov Chain Audio (II)
Markov Chain Audio (III)
Lesson 7: Dynamic Monte Carlo
Dynamic Monte Carlo Audio
Lesson 7: The Metropolis Algorithm
The Metropolis Algorithm Audio
Lesson 8: Metropolis. Examples (I)
Metropolis. Examples (I) Audio 1
Metropolis. Examples (I) Audio 2
Lesson 8: Metropolis. Examples (II)
Metropolis. Examples (II) Audio
Lesson 8: Computation of the bias
Computation of the bias Audio
Lesson 8: Supplementary material on the bias
Lesson 9: Errors for Correlated Data
Errors For Correlated Data Audio 1
Errors for Correlated Data Audio 2
Lesson 9: Supplementary Material on the Autocorrelation Function
Lesson 9: Autocorrelation time
Autocorrelation time Audio
Lesson 9: The Blocking Method
The Blocking Method Audio
Homework 1: an example of a report
Homework 1 Audio
Lesson10: Improved Blocking Method
Improved Blocking Method Audio
Lesson10: Metropolis in the Canonical Ensemble
Metropolis in the Canonical Ensemble Audio
Lesson 10: Metropolis in the Isobaric Ensemble
Metropolis in the Isobaric Ensemble Audio
Lesson 11: Chemical Potential in the Canonical Ensemble
Chemical Potential in the Canonical Ensemble Audio
Lesson 11: Metropolis in the GrandCanonical Ensemble
Metropolis in the GrandCanonical Ensemble Audio
Lesson 11: Heat Bath Algorithm
Heat Bath Algorithm Audio
Lesson 12: Truncations
Truncations Audio
Lesson 12: Boundary Conditions
Boundary Conditions Audio
Lesson 12: Reduced Units
Reduced Units Audio
Lesson 13: Computation of the pair distribution function
Computation of the Pair Distribution Function Audio
Lesson 13: Fluctuation Relations
Fluctuation Relations Audio
Lesson 13: Energy Distribution
Energy Distribution Audio
Lesson 14: Reweighting Data
Reweighting Data Audio 1
Reweighting Data Audio 2
Lesson 14: Weighted Average
Weighted Average Audio
Lesson 15: The Multihistogram Method
Multihistogram Method Audio 1
Multihistogram Method Audio 2
Multihistogram Method Audio 3
Lesson 15: Umbrella Sampling
Umbrella Sampling Audio
Lesson 16: Optimizing the Umbrella Distribution
Optimizing the Umbrella Distribution Audio
Lesson 16: Simulated Tempering
Simulated Tempering Audio 1
Simulated Tempering Audio 2
Lesson 17: Parallel Tempering
Parallel Tempering Audio
Lesson 17: Molecular Dynamics
Molecular Dynamics Audio
Lesson 18: Verlet algorithm
Verlet Algorithm Audio 1
Verlet Algorithm Audio 2
Verlet Algorithm Audio 3
Verlet Algorithm Audio 4
Lesson 18: TIme reversal
Time Reversal Audio
Lesson 18: Momentum conservation
Momentum Conservation Audio
Received Homeworks 2: CHECK!
Homework 1: Revisions.
Lesson 19: Conservation of Phase Space Volume
Conservation of Phase Space Volume Audio
Lesson 19: Harmonic Oscillator
Harmonic Oscillator Audio
Lesson 19: Liouvillian
Liouvillian Audio
Lesson 20: Verlet again (I)
Verlet again (I) Audio
Lesson 20: Verlet again (II)
Verlet again (II) Audio 1
Verlet again (II) Audio 2
Lesson 20: Leap-Frog Algorithm
Leap-Frog Algorithm Audio
Homework 3: Text
Homework 3: Comments Audio
Homework 1: Final results
Homework 2: FIrst results
Lesson 21: General results on Exponentials
General results on Exponentials Audio
Lesson 21: Verlet conserved Hamiltonian
Verlet conserved Hamiltonian Audio
Lesson 21: Verlet Hamiltonian Examples
Verlet Hamiltonian Examples Audio
Lesson 21: Verlet again (III)
Verlet again (III) Audio
Lesson 22: Multiple time-step algorithms
Multiple Time-Step Algorithms Audio
Lesson 22: Dynamics with Constraints
Dynamics with Constraints Audio
Lesson 22: Hybrid MC Algorithms
Hybrid MC Algorithms Audio
Lezione 22: Gaussian Noise
Gaussian Noise Audio
Lesson 23: A new derivation of the Verlet algorithm
A new derivation of the Verlet algorithm Audio
Lezione 23: An example of a stochastic equation
An example of a stochastic equation Audio
Harmonic Oscillator Audio 1
Harmonic Oscillator Audio 2
Lesson 24: General results on the noise
General results on the noise Audio 1
General results on the noise Audio 2
Lesson 24: Langevin Equation
Langevin Equation Audio
Lesson 25: Nose'-Hoover Ensemble
Nose'-Hoover Ensemble Audio 1
Nose'-Hoover Ensemble Audio 2
Lesson 25: Nose'-Hoover dynamics
Nose'-Hoover dynamics Audio
Exam program
Homework 3: results
Homework 2: revisions
Homework results: summary (06/18/2020)
Useful notes to compute autocorrelation functions and ratios
Example: Camerin (2017)
Example: Verdel Aranda (2017)
data1.txt (2021)
data2.txt (2021)
Homework 1 (2021)
Homework 2: Some comments
Homework 2: Some comments Audio
Homework2 Audio
Homework 2: An example [Grimmel (2017)]
Homework 2 (2021)
Homework 3: Starting Configuration
Starting Configuration Audio
Homework 3 2021
Notes
Error analysis for independent sampling
Dynamic Monte Carlo
data1.txt (2020)
data2.txt (2020)
Homework 1 (2020)
data1.txt (2019)
data2.txt (2019)
homework 1 (2019)
data1.txt 2018
data2.txt 2018
Homework 1 2018
data1.txt 2017
data2.txt 2017
Homework 2017
data3.txt 2016
data2.txt 2016
data1.txt 2016
datablocked.txt 2016
Homework 2016
Homework 2015
Homework 2 (2020)
Homework 2 (2019)
Homework 2 (2018)
Homework 2 2017
Homework 2 2016
Homework2 2015
Homework 3 2019
Homework 3 2018
Homework 3 2017
Homework 3 2016
Homework 3 2015
Harmonic Oscillator Audio 1 ►
