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Computer Program Detail Page

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HS-WCA-LJ Monte Carlo Model
written by Fernando Silva Fernandes
The HS-WCA-LJ Monte Carlo Model performs simultaneous canonical Monte Carlo (MC) simulations of 108, 256 or 500 particles interacting through the hard sphere (HS), the Weeks, Chandler and Andersen (WCA) and the Lennard-Jones (LJ) pair potentials. It was inspired by the review of Chandler, Weeks and Anderson on WCA theory, illustrating that "the attractive interactions help fix the volume of the system, but the arrangements and motions of molecules within that volume are determined primarily by the local packing and steric effects produced by the repulsive forces". The radial distribution functions for the three systems are plotted after every MC cycle, at densities and temperatures chosen by the user, and the data Tables display thermodynamic results from the LJ and WCA potentials. The thermodynamics of the HS system was addressed to another application cataloged at Open Source Physics.
The objective of this application is: (i) to illustrate the canonical MC method with three different systems;(ii) to probe the densities and temperatures at which the HS and WCA potentials approach the structure(defined by the radial distribution functions) of the LJ system, regarding their use in perturbation theory.

The HS-WCA-LJ Monte Carlo Model was developed using the Easy Java Simulations (EJS) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.   Double clicking the jar file will run the program if Java is installed.  You can modify this simulation if you have EJS installed by right-clicking within the map and selecting "Open Ejs Model" from the pop-up menu item.

Please note that this resource requires at least version 1.6 of Java (JRE).
1 supplemental document is available
Subjects Levels Resource Types
Mathematical Tools
- Statistics
Thermo & Stat Mech
- First Law
= Equations of State
- Models
= Ideal Gas
= Lennard-Jones Potential
- Phase Transitions
- Graduate/Professional
- Upper Undergraduate
- Instructional Material
= Model
= Simulation
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- Educators
- Learners
- Researchers
- application/java
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Access Rights:
Free access
This material is released under a GNU General Public License Version 3 license.
Rights Holder:
Fernando M.S. Silva Fernandes
Record Cloner:
Metadata instance created March 12, 2013 by Wolfgang Christian
Record Updated:
July 4, 2014 by Wolfgang Christian
Last Update
when Cataloged:
March 12, 2013

Radial disctibution jump

Author: Wolfgang
Posted: June 19, 2014 at 7:57AM

While using the program with 500 particles, reduced density of 0.3, reduced temperature of 0.5, and maximum movement for LJ particles of 0.2, there is a jump in the radial distribution plot around 300 cycles and the first peak never stops.  I was wondering if this was supposed to happen or if there was a problem with the program.

» reply

Re: Radial disctibution jump

Author: Wolfgang

Dear Anthony,

The code seems OK.
Please note that the sate you mention (density=0.3; temperature=0.5) is under the vapor-solid (below LJ triple point) coexistence line (please see the LJ phase-diagram at the Theory&Remarks page). Therefore, it is an unstable state that will try to separate into two phases at equilibrium. However, on the one side NVT simulations preclude volume fluctuations and on the other side only one simulation box is used turning the simulation of phase equilibrium almost impossible. In such cases we have to resort to other simulation techniques.
This application is intended to homogeneous fluid phases. We have not stressed this, but a new version is in progress where your interesting question will be referred to. I will let you know when it is finished. In that version we can see the 3D structure of the fluid trying to separate into two phases.
Mind you, your point is also observed with 108 or 256 particles. Please note, for that state the pressure comes out negative which is by itself indicative of unstable or metastable states. Finally, the jump you mention at 300 cycles is the end of the equilibration run (nCy=300 by default) when all the accumulators for averages are put to zero.

Is this explanation satisfactory?

Best regards,


» reply

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Record Link
AIP Format
F. Fernandes, Computer Program HS-WCA-LJ MONTE CARLO MODEL (2013), WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12657&DocID=3234).
F. Fernandes, Computer Program HS-WCA-LJ MONTE CARLO MODEL (2013), <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12657&DocID=3234>.
APA Format
Fernandes, F. (2013). HS-WCA-LJ Monte Carlo Model [Computer software]. Retrieved July 19, 2024, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12657&DocID=3234
Chicago Format
Fernandes, Fernando Silva. "HS-WCA-LJ Monte Carlo Model." https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12657&DocID=3234 (accessed 19 July 2024).
MLA Format
Fernandes, Fernando Silva. HS-WCA-LJ Monte Carlo Model. Computer software. 2013. Java (JRE) 1.6. 19 July 2024 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12657&DocID=3234>.
BibTeX Export Format
@misc{ Author = "Fernando Silva Fernandes", Title = {HS-WCA-LJ Monte Carlo Model}, Month = {March}, Year = {2013} }
Refer Export Format

%A Fernando Silva Fernandes %T HS-WCA-LJ Monte Carlo Model %D March 12, 2013 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12657&DocID=3234 %O application/java

EndNote Export Format

%0 Computer Program %A Fernandes, Fernando Silva %D March 12, 2013 %T HS-WCA-LJ Monte Carlo Model %8 March 12, 2013 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12657&DocID=3234

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HS-WCA-LJ Monte Carlo Model:

Is Based On Easy Java Simulations Modeling and Authoring Tool

The Easy Java Simulations Modeling and Authoring Tool is needed to explore the computational model used in the HS-WCA-LJ Monte Carlo Model.

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