Monte Carlo Simulation and Microcanonical Ensemble
Budget: £10 – £20 GBP
This project invites those with a strong understanding of Monte Carlo simulation and the Gibbs microcanonical ensemble, capable of creating clear and effective flowcharts, deriving equations, and performing calculations.
Key tasks would be:
- Explain the Gibbs microcanonical ensemble concept.
- Derive related mathematical equations.
- Create flowcharts for a Monte Carlo simulation using any software. Although I have no specific preferences for the design, it should be clear and easy to understand.
- Conduct relevant calculations.
Ideal candidates should have expertise in statistical physics, particularly in the area of Monte Carlo simulations and the Gibbs microcanonical ensemble. Also, proficiency in using flowchart creation tools like Microsoft Visio, Lucidchart, or draw.io is ideal. A knack for conveying complex ideas in a simple, precise manner would also be beneficial.
A full list of tasks:
1) Design two flowcharts: one for a Monte Carlo simulation and one molecular dynamics simulation. Explain/indicate how new microstates are generated in Monte Carlo and molecular dynamics simulation, and how thermodynamic properties are obtained from these configurations.
2) Explain and discuss the Gibbs microcanonical ensemble and the types of equilibrium. Use the concepts of macrostates, microstates, fluctuations and the phase space
3) Explain and derive an expression for the mean energy of a molecule in terms of the molecular partition function, using the Boltzmann distribution.
4) A molecule has a degenerate excited state 400 cm-1 above the non degenerate ground state. Calculate the temperature at which 15% of the molecules will be in the upper level for the following cases: the excited state is single, double, triple and quadruple degenerate. Plot the temperature as a function of the degeneracy. Explain/comment each step
5) Calculate and plot the vibrational partition function of CSe2 between 500K and 1000K (with a step of 100K) given the wavenumbers 313 cm-1 (bend two modes), 369 cm-1 (symmetric stretch ) and 1302 cm-1 (asymmetric stretch) assuming that each vibrational mode can be treated as a simple harmonic oscillator. Explain and discuss each step
6) Explain the main idea of the Lagrange multiplier method in the context of statistical mechanics
A week to complete tasks
Key tasks would be:
- Explain the Gibbs microcanonical ensemble concept.
- Derive related mathematical equations.
- Create flowcharts for a Monte Carlo simulation using any software. Although I have no specific preferences for the design, it should be clear and easy to understand.
- Conduct relevant calculations.
Ideal candidates should have expertise in statistical physics, particularly in the area of Monte Carlo simulations and the Gibbs microcanonical ensemble. Also, proficiency in using flowchart creation tools like Microsoft Visio, Lucidchart, or draw.io is ideal. A knack for conveying complex ideas in a simple, precise manner would also be beneficial.
A full list of tasks:
1) Design two flowcharts: one for a Monte Carlo simulation and one molecular dynamics simulation. Explain/indicate how new microstates are generated in Monte Carlo and molecular dynamics simulation, and how thermodynamic properties are obtained from these configurations.
2) Explain and discuss the Gibbs microcanonical ensemble and the types of equilibrium. Use the concepts of macrostates, microstates, fluctuations and the phase space
3) Explain and derive an expression for the mean energy of a molecule in terms of the molecular partition function, using the Boltzmann distribution.
4) A molecule has a degenerate excited state 400 cm-1 above the non degenerate ground state. Calculate the temperature at which 15% of the molecules will be in the upper level for the following cases: the excited state is single, double, triple and quadruple degenerate. Plot the temperature as a function of the degeneracy. Explain/comment each step
5) Calculate and plot the vibrational partition function of CSe2 between 500K and 1000K (with a step of 100K) given the wavenumbers 313 cm-1 (bend two modes), 369 cm-1 (symmetric stretch ) and 1302 cm-1 (asymmetric stretch) assuming that each vibrational mode can be treated as a simple harmonic oscillator. Explain and discuss each step
6) Explain the main idea of the Lagrange multiplier method in the context of statistical mechanics
A week to complete tasks