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Re: [Phys-L] Ex: Re: Spontaneous Symmetry Breaking in Unexpected Places: A Looped Double Catenary & A Block/Plank Balanced on a Cylinder (very long)



Just a quick note to say that, while I haven’t gone through David’s work in ANY detail, its simple beauty is immediately obvious. Moreover, the results are not only reasonable, but, I might suggest, almost intuitively “obvious.”

I REALLY hope he considers writing it up for publication in AJP because it is exactly the kind of paper there should be a LOT more of—readily understood and accessible scenarios that nicely illustrate advanced concepts and methods.

John Mallinckrodt

On Jun 29, 2022, at 4:00 PM, David Bowman <David_Bowman@georgetowncollege.edu> wrote:

Regarding:

It might be amusing to plot this and to work
out the critical exponent.

I've worked that out. The 'order parameter' critical exponent has
classical mean-field value of 1/2. In particular, if we let
Δ_0 = 0.257736456168094 be the critical mean relative excess slack, then
just above the critical point the asymmetry parameter has the form,
σ ≈ A*( Δ - Δ_0 )^(1/2).

The above referenced graph and nine others related to the looped double catenary system are now available at
https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fimgur.com%2Fa%2FXl2c9Az&amp;data=05%7C01%7Cajm%40cpp.edu%7Cb7335653dcd74075ec9808da5a232c11%7C164ba61e39ec4f5d89ffaa1f00a521b4%7C0%7C0%7C637921405487166316%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&amp;sdata=pyOuan%2B3ixJccRg7H54nkM6VpmunIHn7RV6mmNaqoto%3D&amp;reserved=0 .

David Bowman

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