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exercise:mm_uzh:h2o_diff [2014/05/13 11:54] – talirzexercises:2014_uzh_molsim:h2o_diff [2020/08/21 10:15] (current) – external edit 127.0.0.1
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 When simulating liquids or solids under periodic boundary conditions, we are making two fundamental approximations: When simulating liquids or solids under periodic boundary conditions, we are making two fundamental approximations:
-  - We simulate an infinite system, thus neglecting the fact that any real-world system has surfaces. This approximation becomes problematic, when the real-world system to be studied consists only of a few simulation cells.+  - We simulate an infinite system, thus neglecting the fact that any real-world system is finite. This approximation becomes problematic, when the real-world system to be studied consists only of a few simulation cells.
   - We impose the condition that the properties of the system under study repeat //exactly// from one simulation cell to the next. The quality of this approximation depends on the system under study and the quantity of interest.   - We impose the condition that the properties of the system under study repeat //exactly// from one simulation cell to the next. The quality of this approximation depends on the system under study and the quantity of interest.
  
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   - We want to simulate diffusion at room temperature. Why aren't we using the $NVT$ ensemble? //Hint:// Think about how thermostats work.   - We want to simulate diffusion at room temperature. Why aren't we using the $NVT$ ensemble? //Hint:// Think about how thermostats work.
   - Use the provided script ''./get_t_sigma file.ener'' to calculate the standard deviation of the temperature for your simulation as well as for the provided simulations of larger cells containing 64, 128 and 256 water molecules.   - Use the provided script ''./get_t_sigma file.ener'' to calculate the standard deviation of the temperature for your simulation as well as for the provided simulations of larger cells containing 64, 128 and 256 water molecules.
-  - How are temperature fluctuations expected to depend on system size? Use gnuplot's fitting functionality to check whether they follow the corresponding law. (2P)+  - How are temperature fluctuations expected to depend on system size? Use gnuplot's fitting functionality to check whether they follow the corresponding law. //Hint:// See e.g. [[http://books.google.ch/books?id=5qTzldS9ROIC|"Understanding Molecular Simulations"]] by Frenkel and Smit, sections 4.1 and 6.2. (2P)
 </note> </note>
  
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   - Plot $D_{PBC}$ as a function of $1/L$, where $L$ is the length of the edge of the simulation box.   - Plot $D_{PBC}$ as a function of $1/L$, where $L$ is the length of the edge of the simulation box.
   - Perform a linear fit of this curve to obtain the diffusion constant $D=D_{pbc}(L=\infty)$   - Perform a linear fit of this curve to obtain the diffusion constant $D=D_{pbc}(L=\infty)$
-  - Use equation (12) in the article to calculate the viscosity.+  - Use equation (12) in the article to calculate the viscosity $\eta$ from the slope of $D_{PBC}(1/L)$.
   - Compare the results to the data in the paper.   - Compare the results to the data in the paper.
 </note> </note>
exercises/2014_uzh_molsim/h2o_diff.1399982072.txt.gz · Last modified: 2020/08/21 10:14 (external edit)