PARADISCYL:Scale-Rule

Manual 03 for ParaDiS Cylinder Codes
How Units Are Scaled

Keonwook Kang, Chris Weinberger and Wei Cai

Original date : Oct 23 , 2008

Latest update on Oct 23 , 2008

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Rule of Scale

ParaDiS Cylinder program is hard-coded such that the radius of a cylinder be 1. Accordingly, the input numbers such as cut-off radius need to be scaled appropriately. In the test script concentric_loop_test.ctrl in M02 Test Run, you see

 
 burgMag = 1.0e0

 #Elastic constants 
 shearModulus = 1.0e+0
 pois = 3.050000e-01

 #Core cut-off radius
 rc = 1.0e-3

Let's figure out what each line means in real physical unit.

Non-dimensional quantity is notified with the asterisk (*). For example, the dimensionless radius is expressed as $R^{*}=R/R_{c}$ and is fixed to be 1, which means all the length units are scaled by the cylinder radius (R) since $R_{c}=R$. The cut-off radius rc in the script is the scaled cut-off radius (r_c) and is .375 nm in real unit if the cylinder radius is given as 375 nm, because

$r_{c}=r_{c}^{*}\times R.$

Table of Scale

key physical quantities	scale parameter	e.x.
Shear Modulus, μ	α	23e9 Pa
Burgers vector magnitude, b	β	3e-10 meter
Cylinder radius, R	γ	.35e-6 meter
Bobility, m	δ	1 /(Pa*sec)

physical quantities	scale parameter	e.x.
σint	αβ/γ	105e6 Pa