That is why one needs, in my view, at least charge-separated or polar material in multi-axis hydro-dynamic shear and optimally with resonance. This allows the kink instabilities and magnetic re-connection to ultimately produce fractal arrangements in a way that is similar to that described, but not fully elucidated, by Dijkhuis, G. C. (1999) - see reference 3:
"Loops moving over a surface are twisted by friction torques on their leading and trailing sections. Opposing torques deform an unbroken loop into two halves with opposite helicity as seen in the contorsions of a rubber band sheared by a ruler moving over a table. To achieve scaling vortex deformation let helical vortex lines break and reconnect when twisted beyond the lowest eigenvalue for domain and pitch in a specific lattice type. For compact scaling let each mesh refinement step increase torsion until (i) each untwisted vortex ring splits into a smaller replica and a loop with dipolar helicity, (ii) each dipolar loop splits into two monopolar loops with opposite helicity, and (iii) each monopolar loop splits into a smaller replica and an untwisted ring. This torsion cycle distributes vorticity and helicity evenly over a lattice with arbitrary mesh refinement.
Starting from a single initial vortex ring the number and total length of monopolar loops G, increases recursively according to: [equation] with even terms keeping right- and left-handed helicity in balance. The series converges towards exponential growth of chiral monopole abundance with growth factor g=2.
Neither physicist, nor mathematician, but the calcs. or rather the torus reminds me of "The Cosmic Wheel", eternally spiralling and as we are thrown out to the edges of it we must make our way to the central axis about which is said;
"The axle at the centre of the wheel is the innermost core of consciousness which cannot be expressed in language."
Never stops anyone from trying... sounds like a challenge tbh.
They say the closer one moves to the centre of the wheel, the less suffering one feels. At the very centre, there is absolute stillness and no motion. The conscious experience of time is related to how rapidly the wheel spins, or how far away from the centre one’s mind is focused.
Pretty specific philosophical framework. Not saying it can't be done. But yes, good luck.
Again, before we get to what is happening in toroids, look at Don's model for a straight line filament (a toroid is just a circular version of that).
How Don's Bessel function model allows for superconductivity first:
With our ideas of current flowing along a wire, with a magnetic field wrapped around the wire, then all charge flowing along the wire must "cross" the magnetic field. The beauty of Don's bessel function idea, is that if the magnetic field is axial anywhere (current can flow WITHOUT crossing magnetic field "lines", then once you get a current flowing, axially, there is NO resistance? That is how you get superconductivity.
I am familiar with the Scott/Lundquist field aligned model. Infact, I just submitted a paper to Monthly Notices of Royal Astronomy Society which is based upon that model.
Noble effort - this kind of stability considerations sounds a lot like John Wheeler's (1911-2008) comments on GEONs.
https://youtu.be/LarJgZOOL_U?si=gZDCpjbAvoosSzO5
yes, the instability does "ring" similar.
makes me think of
https://arxiv.org/abs/2102.03636
https://pmc.ncbi.nlm.nih.gov/articles/PMC8501108/
Yes, however, all pulsed-only systems suffer from stability breakdown
https://remoteview.substack.com/p/the-real-challenge-of-emerging-science
That is why one needs, in my view, at least charge-separated or polar material in multi-axis hydro-dynamic shear and optimally with resonance. This allows the kink instabilities and magnetic re-connection to ultimately produce fractal arrangements in a way that is similar to that described, but not fully elucidated, by Dijkhuis, G. C. (1999) - see reference 3:
https://remoteview.substack.com/p/the-new-fire-are-we-there-yet
"Loops moving over a surface are twisted by friction torques on their leading and trailing sections. Opposing torques deform an unbroken loop into two halves with opposite helicity as seen in the contorsions of a rubber band sheared by a ruler moving over a table. To achieve scaling vortex deformation let helical vortex lines break and reconnect when twisted beyond the lowest eigenvalue for domain and pitch in a specific lattice type. For compact scaling let each mesh refinement step increase torsion until (i) each untwisted vortex ring splits into a smaller replica and a loop with dipolar helicity, (ii) each dipolar loop splits into two monopolar loops with opposite helicity, and (iii) each monopolar loop splits into a smaller replica and an untwisted ring. This torsion cycle distributes vorticity and helicity evenly over a lattice with arbitrary mesh refinement.
Starting from a single initial vortex ring the number and total length of monopolar loops G, increases recursively according to: [equation] with even terms keeping right- and left-handed helicity in balance. The series converges towards exponential growth of chiral monopole abundance with growth factor g=2.
ha. Too much specialized vocabulary in all that for me to make much understanding of. Maybe later :)
Neither physicist, nor mathematician, but the calcs. or rather the torus reminds me of "The Cosmic Wheel", eternally spiralling and as we are thrown out to the edges of it we must make our way to the central axis about which is said;
"The axle at the centre of the wheel is the innermost core of consciousness which cannot be expressed in language."
Never stops anyone from trying... sounds like a challenge tbh.
They say the closer one moves to the centre of the wheel, the less suffering one feels. At the very centre, there is absolute stillness and no motion. The conscious experience of time is related to how rapidly the wheel spins, or how far away from the centre one’s mind is focused.
Pretty specific philosophical framework. Not saying it can't be done. But yes, good luck.
Michael,
Again, before we get to what is happening in toroids, look at Don's model for a straight line filament (a toroid is just a circular version of that).
How Don's Bessel function model allows for superconductivity first:
With our ideas of current flowing along a wire, with a magnetic field wrapped around the wire, then all charge flowing along the wire must "cross" the magnetic field. The beauty of Don's bessel function idea, is that if the magnetic field is axial anywhere (current can flow WITHOUT crossing magnetic field "lines", then once you get a current flowing, axially, there is NO resistance? That is how you get superconductivity.
I am familiar with the Scott/Lundquist field aligned model. Infact, I just submitted a paper to Monthly Notices of Royal Astronomy Society which is based upon that model.
I'm glad you have this, and yet another important idea isn't falling through the cracks