2D CVM Free Energy Minimization Applied to a Large Scale Free-Like Pattern:

New experimental results show that a scale free-like pattern undergoing 2D CVM-type free energy minimization undergoes substantial topology changes; this is the first time that free energy has been used to influence a 2D topography. While specific topographies would differ, depending on the both starting pattern as well as the (random) selection of flipped-nodes (for free energy reduction), the resulting topographies will likely have similar patterns for given h-values (interaction enthalpy parameters).

Here’s Pattern 6, which is four times the size of my typical patterns. It was created by juxtaposing four instances of my basic scale free-like pattern, to create a 32×32 node grid.

Here’s the result after free energy minimization is applied, with the h-value set as h=1.165.

If you’re interested in the details, the slidedeck listed below in the section for The 2D CVM – Code, Documentation, V&V Documents, and Experimental Results tells it all. LOTS of detail.

That’s all for now, folks. It’s been a long day.

 

 

Live free or die, my friend –

AJ Maren

Live free or die: Death is not the worst of evils.
Attr. to Gen. John Stark, American Revolutionary War

 

 

Key References

 

Cluster Variation Method – Essential Papers

• Kikuchi, R. (1951). A theory of cooperative phenomena. Phys. Rev. 81, 988-1003, pdf, accessed 2018/09/17.
• Kikuchi, R., & Brush, S.G. (1967), “Improvement of the Cluster‐Variation Method,” J. Chem. Phys. 47, 195; online as: online – for purchase through American Inst. Physics. Costs $30.00 for non-members.
• Maren, A.J. (2016). The Cluster Variation Method: A Primer for Neuroscientists. Brain Sci. 6(4), 44, https://doi.org/10.3390/brainsci6040044; online access, pdf; accessed 2018/09/19.

 

The 2D CVM – Code, Documentation, V&V Documents, and Experimental Results (Including Slidedecks)

• GitHub for 2-D CVM Cluster Variation Method (Public Repository)
• Documentation / Experimental results for free energy minimization applied to Pattern 6: Pattern-6_Before-and-After-FEM_2019-03-21.pptx (The NEW PPT with experimental results, giving more detail about what’s in today’s blog).
• Documentation / Experimental results showing computation versus analytic: 2D-CVM_Expts-vary-eps0-and-eps1_computational_2019-01-19.pptx (PREVIOUS new PPT with experimental results).

NOTE: I’m not making my code for this available just yet. I HAVE put a copy my PPT slidedeck up on my public GitHub repository; the one listed above. It’s got all kinds of juicy things; we’ll discuss over the next few weeks. But not the code. Not just yet.

Let me get a paper or two published, and then we’ll see.

At over 4,400 lines … not trivial.

 

Previous Related Posts

• Filling Out the Phase Space Boundaries
• Obvious, But Useful (Getting the Epsilon0 Value when the Interaction Enthalpy Is Zero)
• An Interesting Little Thing about the CVM Entropy (With Code)
• Expressing Total Microstates (Omega) for the 1-D and 2-D CVM (Part 2)
• Expressing Total Microstates (Omega) for the 1-D Cluster Variation Method – Part 1
• Wrapping Our Heads around Entropy
• Figuring Out the Puzzle (in a 2-D CVM Grid).
• 2-D Cluster Variation Method: Code Verification and Validation
• The Big, Bad, Scary Free Energy Equation (and New Experimental Results)