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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
Monte Carlo Methods
Error analysis for independent sampling
Open course index
Error analysis for independent sampling
Error analysis for independent sampling
Click
seminarI.pdf
link to view the file.
◄ Notes
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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
Lesson 23: Harmonic Oscillator
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
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
Dynamic Monte Carlo ►
