PARADISCYL:Scale-Rule - Revision history

Cweinber at 17:03, 27 October 2008

2008-10-27T17:03:23Z

← Older revision		Revision as of 17:03, 27 October 2008
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	<DIV>		<DIV>

	This document describes the extension of the ParaDiS program that implements the cylindrical free surface boundary condition. This extension is based on Weinberger and Cai, J. Mech. Phys. Solids, 55, 2027 (2007)([http://micro.stanford.edu/~caiwei/papers/Weinberger07jmps-image.pdf PDF]). The code is written by Chris Weinberger. It is ~~owned by Chris~~ and is not included in the standard distribution of ParaDiS. Keonwook Kang wrote the first draft of this document, which was later revised by Chris Weinberger and Wei Cai. Questions on this document should be addressed to [[Chris Weinberger]]. Please read the manual of ParaDiS before reading this document.		This document describes the extension of the ParaDiS program that implements the cylindrical free surface boundary condition. This extension is based on Weinberger and Cai, J. Mech. Phys. Solids, 55, 2027 (2007)([http://micro.stanford.edu/~caiwei/papers/Weinberger07jmps-image.pdf PDF]). The code is written by Chris Weinberger and Wei Cai and is not included in the standard distribution of ParaDiS. Keonwook Kang wrote the first draft of this document, which was later revised by Chris Weinberger and Wei Cai. Questions on this document should be addressed to [[Chris Weinberger]]. Please read the manual of ParaDiS before reading this document.

	== Motivation ==		== Motivation ==

Caiwei at 08:51, 25 October 2008

2008-10-25T08:51:00Z

← Older revision		Revision as of 08:51, 25 October 2008
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	<DIV>		<DIV>

	This document describes the extension of the ParaDiS program that implements the cylindrical free surface boundary condition. This extension is based on Weinberger and Cai, J. Mech. Phys. Solids, 55, 2027 (2007)([http://micro.stanford.edu/~caiwei/papers/Weinberger07jmps-image.pdf PDF]). The code is written by Chris Weinberger. It is owned by Chris and is not included in the standard distribution of ParaDiS. Keonwook Kang wrote the first draft of this document, which was later revised by Chris Weinberger and Wei Cai. Please read the manual of ParaDiS before reading this document.		This document describes the extension of the ParaDiS program that implements the cylindrical free surface boundary condition. This extension is based on Weinberger and Cai, J. Mech. Phys. Solids, 55, 2027 (2007)([http://micro.stanford.edu/~caiwei/papers/Weinberger07jmps-image.pdf PDF]). The code is written by Chris Weinberger. It is owned by Chris and is not included in the standard distribution of ParaDiS. Keonwook Kang wrote the first draft of this document, which was later revised by Chris Weinberger and Wei Cai. Questions on this document should be addressed to [[Chris Weinberger]]. Please read the manual of ParaDiS before reading this document.

	== Motivation ==		== Motivation ==

Caiwei at 08:24, 25 October 2008

2008-10-25T08:24:59Z

← Older revision		Revision as of 08:24, 25 October 2008
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	This document describes the extension of the ParaDiS program that implements the cylindrical free surface boundary condition. This extension is based on Weinberger and Cai, J. Mech. Phys. Solids, 55, 2027 (2007)([http://micro.stanford.edu/~caiwei/papers/Weinberger07jmps-image.pdf PDF]). The code is written by Chris Weinberger. It is owned by Chris and is not included in the standard distribution of ParaDiS. Keonwook Kang wrote the first draft of this document, which was later revised by Chris Weinberger and Wei Cai. Please read the manual of ParaDiS before reading this document.		This document describes the extension of the ParaDiS program that implements the cylindrical free surface boundary condition. This extension is based on Weinberger and Cai, J. Mech. Phys. Solids, 55, 2027 (2007)([http://micro.stanford.edu/~caiwei/papers/Weinberger07jmps-image.pdf PDF]). The code is written by Chris Weinberger. It is owned by Chris and is not included in the standard distribution of ParaDiS. Keonwook Kang wrote the first draft of this document, which was later revised by Chris Weinberger and Wei Cai. Please read the manual of ParaDiS before reading this document.

	== ~~Rule of Scale~~ ==		== Motivation ==

	For simplicity, the ParaDiS Cylinder program requires the radius of the cylinder to be 1. Because elasticity model does not have an intrinsic length scale, we can model a cylinder with arbitrary radius by appropriately scaling all lengths in the problem. Accordingly, other parameters, such as stress may also change. In this manual, we will describe how all quantities scale with the cylinder radius ''R''. ~~In our test case '''concentric_loop_test.ctrl''' in [[Test-Run#Examples\|M02 Test Run]], we can find the following lines.~~		For simplicity, the ParaDiS Cylinder program requires the radius of the cylinder to be 1. Because elasticity model does not have an intrinsic length scale, we can model a cylinder with arbitrary radius by appropriately scaling all lengths in the problem. Accordingly, other parameters, such as stress may also change. In this manual, we will describe how all quantities scale with the cylinder radius ''R''.

			== Rule of Scale ==
			In our test case '''concentric_loop_test.ctrl''' in [[Test-Run#Examples\|M02 Test Run]], we can find the following lines.

	<pre>		<pre>

Caiwei at 08:22, 25 October 2008

2008-10-25T08:22:32Z

← Older revision		Revision as of 08:22, 25 October 2008
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	How Units Are Scaled</H1>		How Units Are Scaled</H1>
	<DIV>		<DIV>

			This document describes the extension of the ParaDiS program that implements the cylindrical free surface boundary condition. This extension is based on Weinberger and Cai, J. Mech. Phys. Solids, 55, 2027 (2007)([http://micro.stanford.edu/~caiwei/papers/Weinberger07jmps-image.pdf PDF]). The code is written by Chris Weinberger. It is owned by Chris and is not included in the standard distribution of ParaDiS. Keonwook Kang wrote the first draft of this document, which was later revised by Chris Weinberger and Wei Cai. Please read the manual of ParaDiS before reading this document.

	== Rule of Scale ==		== Rule of Scale ==

Caiwei: /* Rule of Scale */

2008-10-25T08:20:36Z

Rule of Scale

← Older revision		Revision as of 08:20, 25 October 2008
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	\|-		\|-
	! Physical quantity		! Physical quantity
	! Multiplication factor ~~(or reference value)~~		! Multiplication factor
	! ''e.g.''		! ''e.g.''
	\|-		\|-

Caiwei: /* Rule of Scale */

2008-10-25T07:59:49Z

Rule of Scale

← Older revision		Revision as of 07:59, 25 October 2008
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	== Rule of Scale ==		== Rule of Scale ==

	For simplicity, the ParaDiS Cylinder program requires the radius of the cylinder to be 1. Because elasticity model does not have an intrinsic length scale, we can model a cylinder with arbitrary radius by appropriately scaling all lengths of the problem. In our test case '''concentric_loop_test.ctrl''' in [[Test-Run#Examples\|M02 Test Run]], we can find the following lines.		For simplicity, the ParaDiS Cylinder program requires the radius of the cylinder to be 1. Because elasticity model does not have an intrinsic length scale, we can model a cylinder with arbitrary radius by appropriately scaling all lengths in the problem. Accordingly, other parameters, such as stress may also change. In this manual, we will describe how all quantities scale with the cylinder radius ''R''. In our test case '''concentric_loop_test.ctrl''' in [[Test-Run#Examples\|M02 Test Run]], we can find the following lines.

	<pre>		<pre>
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	</pre>		</pre>

	Let's find out what each line means in real physical units, if we want to model to represent a cylinder with a radius that is not 1.		Let's find out what each line means in real physical units, if we want to model to represent a cylinder with a radius ''R'' that is not 1.

	Non-dimensional quantity will be notified with the asterisk (). For example, the dimensionless radius is expressed as <math> R^ = R/R_c </math> and is fixed to be 1 in ParaDiS Cylinder codes, which means all the length units are scaled by the cylinder radius (''R'') since <math> R_c = R </math>. The cut-off radius '''rc''' in the script is the scaled cut-off radius (''r''<sub>c</sub><sup>*</sup>) and is .375 nm in real unit if the cylinder radius is given as 375 nm, because		Non-dimensional quantity will be notified with the asterisk (). For example, the dimensionless radius is expressed as <math> R^ = R/R_c </math> and is fixed to be 1 in ParaDiS Cylinder codes, which means all the length units are scaled by the cylinder radius (''R'') since <math> R_c = R </math>. The cut-off radius '''rc''' in the script is the scaled cut-off radius (''r''<sub>c</sub><sup>*</sup>) and is .375 nm in real unit if the cylinder radius is given as 375 nm, because

Caiwei at 07:57, 25 October 2008

2008-10-25T07:57:52Z

← Older revision		Revision as of 07:57, 25 October 2008
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	<H1 ALIGN="CENTER"><FONT SIZE="-1">Manual 03 for ParaDiS Cylinder Codes</FONT>		<H1 ALIGN="CENTER"><FONT SIZE="-1">Manual 03 for ParaDiS Cylinder Codes</FONT>
	<BR>		<br><br>
	How Units Are Scaled</H1>		How Units Are Scaled</H1>
	<DIV>		<DIV>

	<P ALIGN="CENTER"><STRONG>Keonwook Kang, Chris Weinberger and Wei Cai</STRONG></P>
	</DIV>
	<P ALIGN="CENTER">Original date : [[ Oct 23 ]], [[2008]]</P>
	<P ALIGN="CENTER">Latest update on [[ Oct 23 ]], [[2008]]</P>
	<P>
	<BR><HR>
	<!--Table of Child-Links-->

	== Rule of Scale ==		== 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 [[Test-Run#Examples\|M02 Test Run]], ~~you~~ ~~see~~		For simplicity, the ParaDiS Cylinder program requires the radius of the cylinder to be 1. Because elasticity model does not have an intrinsic length scale, we can model a cylinder with arbitrary radius by appropriately scaling all lengths of the problem. In our test case '''concentric_loop_test.ctrl''' in [[Test-Run#Examples\|M02 Test Run]], we can find the following lines.

	<pre>		<pre>
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	#Applied stress in Pa (xx,yy,zz,yz,zx,xy)		#Applied stress in Pa (xx,yy,zz,yz,zx,xy)
	#appliedStress = [ 0. 0. -9e+0 0. 0. 0. ]
	#appliedStress = [ 0 0 0 0 -3e0 0 ]
	appliedStress = [ 0 0 0 0 0 0 ]		appliedStress = [ 0 0 0 0 0 0 ]
	</pre>		</pre>

	Let's ~~figure~~ out what each line means in real physical ~~unit~~.Pa		Let's find out what each line means in real physical units, if we want to model to represent a cylinder with a radius that is not 1.

	Non-dimensional quantity will be notified with the asterisk (). For example, the dimensionless radius is expressed as <math> R^ = R/R_c </math> and is fixed to be 1 in ParaDiS Cylinder codes, which means all the length units are scaled by the cylinder radius (''R'') since <math> R_c = R </math>. The cut-off radius '''rc''' in the script is the scaled cut-off radius (''r''<sub>c</sub><sup>*</sup>) and is .375 nm in real unit if the cylinder radius is given as 375 nm, because		Non-dimensional quantity will be notified with the asterisk (). For example, the dimensionless radius is expressed as <math> R^ = R/R_c </math> and is fixed to be 1 in ParaDiS Cylinder codes, which means all the length units are scaled by the cylinder radius (''R'') since <math> R_c = R </math>. The cut-off radius '''rc''' in the script is the scaled cut-off radius (''r''<sub>c</sub><sup>*</sup>) and is .375 nm in real unit if the cylinder radius is given as 375 nm, because

Caiwei: Scale-Rule moved to PARADISCYL:Scale-Rule

2008-10-25T07:09:10Z

Scale-Rule moved to PARADISCYL:Scale-Rule

← Older revision	Revision as of 07:09, 25 October 2008
(No difference)

Kwkang: /* Rule of Scale */

2008-10-24T07:29:13Z

Rule of Scale

← Older revision		Revision as of 07:29, 24 October 2008
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	{\|border="0" align="center"		{\|border="0" align="center"
	\|<math> r_c = r_c^* \times R_c = r_c^* \times R. </math>		\|<math> r_c = r_c^* \times R_c = r_c^* \times R. </math>
			\|}

			In addition, according to the script ('''burgMag = 1.0e0''' and '''shearModulus = 1.0e+0'''), both shear modulus and Bergers vector magnitude are scaled to be 1 or ''μ''<sup></sup> = 1 and ''b''<sup></sup> = 1. In other words,

			{\|border="0" align="center"
			\| ''μ''<sub>c</sub> = ''μ'' and ''b''<sub>c</sub> = ''b''.
	\|}		\|}

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	{\|border="0" align="center"		{\|border="0" align="center"
	\|<math> \sigma_c = \frac{\mu b}{ R} </math>		\|<math> \sigma_c = \frac{\mu_c b_c}{ R_c} = \frac{\mu b}{ R} </math>
	\|}		\|}

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	\| 6.7935e-5 (sec)		\| 6.7935e-5 (sec)
	\|}		\|}

			The Poisson number '''pois''' is already dimensionless and it doesn't need to be scaled additionaly.

Kwkang: /* Rule of Scale */

2008-10-24T07:06:32Z

Rule of Scale

← Older revision		Revision as of 07:06, 24 October 2008
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	</pre>		</pre>

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

	Non-dimensional quantity will be notified with the asterisk (). For example, the dimensionless radius is expressed as <math> R^ = R/R_c </math> and is fixed to be 1 in ParaDiS Cylinder codes, which means all the length units are scaled by the cylinder radius (''R'') since <math> R_c = R </math>. The cut-off radius '''rc''' in the script is the scaled cut-off radius (''r''<sub>c</sub><sup>*</sup>) and is .375 nm in real unit if the cylinder radius is given as 375 nm, because		Non-dimensional quantity will be notified with the asterisk (). For example, the dimensionless radius is expressed as <math> R^ = R/R_c </math> and is fixed to be 1 in ParaDiS Cylinder codes, which means all the length units are scaled by the cylinder radius (''R'') since <math> R_c = R </math>. The cut-off radius '''rc''' in the script is the scaled cut-off radius (''r''<sub>c</sub><sup>*</sup>) and is .375 nm in real unit if the cylinder radius is given as 375 nm, because
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	In the table below, listed are four key physical quantities which will be used to scale other physical quantity.		In the table below, listed are four key physical quantities which will be used to scale other physical quantity.

	{\| ~~class~~="~~wikitable~~" align="center"		{\|border="0" align="center"
			\|
			{\| class="wikitable"
	\|-		\|-
	! Scaling Parameters		! Scaling Parameters
	! ''e.x.''		! ''e.g.''
	\|-		\|-
	\| Shear Modulus, ''μ''		\| Shear Modulus, ''μ''
	\| 23e9 Pa		\| 23e9 (Pa)
	\|-		\|-
	\| Burgers vector magnitude, ''b''		\| Burgers vector magnitude, ''b''
	\| 3e-10 meter		\| 3e-10 (meter)
	\|-		\|-
	\| Cylinder radius, ''R''		\| Cylinder radius, ''R''
	\| .~~35e~~-6 meter		\| .375e-6 (meter)
	\|-		\|-
	\| ~~Bobility~~, ''m''		\| Mobility, ''m''
	\| 1 /(Pa*sec)		\| 1 /(Pa*sec)
			\|}
	\|}		\|}

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	\|}		\|}

	You would understand the choice of reference stress considering that the stress is proportional to		You would understand the choice of reference stress considering that the stress due to a dislocation is proportional to

	{\|border="0" align="center"		{\|border="0" align="center"
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	\|}		\|}

	where ''L'' is in the unit of distance, according to the elasticity solution.		where ''L'' is in the unit of distance, according to the elasticity solution. Thus, one of the stress components -3 in the script, though commented out, becomes 55.2 (MPa) in compression in real unit if you multiply ''μb/R'' (=18.4 MPa when μ = 23e9Pa, b = 3Å and R = 375 nm )

			Energy stored per unit length ''E''' in the elastic media due to a dislocation is proportional to μb<sup>2</sup>, which is natural reference choice for energy per unit length. (or effectively force.)

			The next table lists multiplcation factors to convert the scaled quantity to the real one.

	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
			! Physical quantity
	! physical quantities
			! Multiplication factor (or reference value)
	! scale parameter
	! ''e.x.''		! ''e.g.''
			\|-
			\| Length, ''L''
			\| R
			\| .375e-6 (meter)
			\|-
			\| Stress, σ
			\| μb/R
			\| 18.4e6 (Pa)
			\|-
			\| Energy per length, ''E''' (effectively, force)
			\| μb<sup>2</sup>
			\| 2.07e-9 (Newton or Pa<math>\cdot</math>meter<sup>2</sup>)
			\|-
			\| Force per length, ''F'''
			\| μb<sup>2</sup>/R
			\| 5.52e-3 (Newton/meter or Pa<math>\cdot</math>meter)
			\|-
			\| Velocity, ''v''
			\| μb<sup>2</sup>m/R
			\| 5.52e-3 (meter/sec)
			\|-
			\| Strain rate, <math>\dot\epsilon</math>
			\| μb<sup>2</sup>m/R<sup>2</sup>
			\| 1.472e+4 (1/sec)
	\|-		\|-
	\| ~~Stress~~, ~~σ~~		\| Time, ''t''
			\| (μb<sup>2</sup>m/R<sup>2</sup>)<sup>-1</sup>
	\| αβ/γ
			\| 6.7935e-5 (sec)
	\| 105e6 Pa
	\|}		\|}