Questions about dimensionless parameters in PRISMS-PF and derivatives of variational total energy.

[Xuesong Gao]

Hi guys, 

1. I think it's cool PRISMS-PF uses dimensionless parameters, e.g., the domain size, mobility, etc. However, I am confused when applying this code to realistic applications where all variables have a dimension. For example, my domain size is 40 mm and mobility is 20 m^2/s. How can i convert these values to dimensionless ones? Or I just need to select a consistent unit system, like UI? 

2. How to get the derivative of total energy integration. I know the math is variational, such as F = integration [f(x,y,y')]. The derivatives I find is dF/dy, but here what we use is dF/dx (x is the order parameter, y is the free energy)? Can you offer some materials on the mathematical background?  

Thanks, 

Xuesong 

[David Montiel]

Hello, Xuesong

Please see my inline replies below.

On Mon, Oct 14, 2024 at 10:27 AM Xuesong Gao <gaoxue...@gmail.com> wrote:

Hi guys, 

1. I think it's cool PRISMS-PF uses dimensionless parameters, e.g., the domain size, mobility, etc. However, I am confused when applying this code to realistic applications where all variables have a dimension. For example, my domain size is 40 mm and mobility is 20 m^2/s. How can i convert these values to dimensionless ones? Or I just need to select a consistent unit system, like UI? 

Just to clarify, PRISMS-PF does not necessarily use dimensionless parameters. You can input parameters that have units, and should get the expected results as long as the units are consistent (example, all SI). In other words, PRISMS-PF only solves the governing equations, and it is up to you to provide the parameters, with or without units.

2. How to get the derivative of total energy integration. I know the math is variational, such as F = integration [f(x,y,y')]. The derivatives I find is dF/dy, but here what we use is dF/dx (x is the order parameter, y is the free energy)? Can you offer some materials on the mathematical background?  

Yes, you can have a look at the following lecture by Prof. Peter Voorhees (especially the section on variational calculus):

https://www.youtube.com/embed/W02PH1fZJgw 

Personally, I also like the variational calculus section of Arfken's book

https://www.sciencedirect.com/book/9780123846549/mathematical-methods-for-physicists

Finally, I would check out the Best Practices Guide pages (still under development) from the PFHub community. 

I hope this helps, 

Best,

David

 

Thanks, 

Xuesong 

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