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

---

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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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