Category: v – EU Meetups

Juan Calsiano
to Jim, David

Hi again,

Well, you haven’t forward all your exchanges with Don so I may be missing something, but I’ll answer with what I have.

Your email is titled “If alpha is function of j, does it not fall off as j decrease?”. In any relatively meaningful way, and in terms of a mathematical yet physical approach, I agree with Don that alpha is not a function of j. His paper and equations are all about mapping the magnetic field (and the current density) as a function of r. All B, j and r are physical variables, while alpha is just a scalar that appears in the quantitative relationship of the physical variables. So in that sense, it is quite meaningless or even wrong to say that alpha is a function of the current density (even if you can rearrange the symbols to try to make your point).

That said, Don seems to be well aware that he has been assuming alpha to be constant, and he is not dismissing the possibility that alpha may be not constant but a function of r.

In his answer, he said: “we have to choose what alpha will be. If we can find a reasonable function of r for it, that’s good.” In his paper, he says: “The step-wise Euler method described here can also be used in the event the state-equations are nonlinear due to choosing an arbitrary α = α (r).”

Also, in his paper he says: “Allowing α = α(r) would distort the radial axis used to plot Bz(r) and Bθ(r)”

That is related to what you want. So, if you choose the adequate α = α(r), then yes, the current density j may fall off more strongly with r (which is not the same as saying that alpha is a function of j). Even more, with the adequate α = α(r) you may get a more convincing argument for the Titius Bode observation to replace the one made by Don in 2015, in which he used a constant alpha of 19.5, seemingly leaving lots of unused possible orbits between real orbits.

Cheers,

Juan

On 2 December 2017 at 02:04, Jim Weninger <jwen1@yahoo.com> wrote:

Juan and David,

     Read especially section 3 and the derivation of equation (14):

http://www.ptep-online.com/2015/PP-41-13.PDF

then tell me where Don or I made a mistake.  Alpha does to me seem to be a function of j, and then would be the key to fitting the Bessel function to the solar system.  I’m always willing to accept that I’ve made an error, but here I don’t even understand the objection.  Perhaps Either of you can help?

—– Forwarded Message —–

From: Donald Scott <dascott3@cox.net>

To: Jim Weninger <jwen1@yahoo.com>

Sent: Friday, December 1, 2017, 12:15:10 PM MST

Subject: Re: If alpha is function of j, does it not fall off as j decrease?

Alpha is not a function of j.

Alpha is a scale factor between the dimensionless independent Bessel function variable, x, and the real-world variable, r.

An Example: The first zero of Bessel function of J0(x) is at x = 2.4048. That’s the radius where the central lobe of j and B ends – where the z component stops and the encircling wrap-around component is maximum. It’s where the “first orbit” is. So, if we want to use “astronomical units” (Earth-Sun distance) as our real-world radius unit, the orbit of Mercury is at about r = 0.3. That means: alpha = x/r = 2.4048 / 0.3 = 8.016. That is a constant, not a variable that depends on r or j  or anything else. The next realistic orbit would (IMO) be at x = 8.6537, or r  = 8.6537/ 8.016 ~ 1. (I don’t know what happened to Venus??)

The point is, we have to choose what alpha will be. If we can find a reasonable function of r for it, that’s good.

Feel free to disagree, but I want to make sure you understand where I am coming from on this.

Don

 

to Juan, Jim

This keeps ringing for me – The spatial frequency of the bessel function as a function of r:

​

On Fri, Dec 1, 2017 at 9:34 PM, Juan Calsiano <juancalsiano@gmail.com> wrote:

Don is right in that alpha is not strictly a function of j, and you are probably right in that alpha is not a constant along all the filament but a function of r, thus making j a more complex non-linear function than what is simplistically assumed in Don’s paper. He even says: “If we can find a reasonable function of r for it, that’s good.”

I’ll expand later.

On 2 December 2017 at 02:04, Jim Weninger <jwen1@yahoo.com> wrote:

Juan and David,

     Read especially section 3 and the derivation of equation (14):

http://www.ptep-online.com/2015/PP-41-13.PDF

then tell me where Don or I made a mistake.  Alpha does to me seem to be a function of j, and then would be the key to fitting the Bessel function to the solar system.  I’m always willing to accept that I’ve made an error, but here I don’t even understand the objection.  Perhaps Either of you can help?

—– Forwarded Message —–

From: Donald Scott <dascott3@cox.net>

To: Jim Weninger <jwen1@yahoo.com>

Sent: Friday, December 1, 2017, 12:15:10 PM MST

Subject: Re: If alpha is function of j, does it not fall off as j decrease?

Alpha is not a function of j.

Alpha is a scale factor between the dimensionless independent Bessel function variable, x, and the real-world variable, r.

An Example: The first zero of Bessel function of J0(x) is at x = 2.4048. That’s the radius where the central lobe of j and B ends – where the z component stops and the encircling wrap-around component is maximum. It’s where the “first orbit” is. So, if we want to use “astronomical units” (Earth-Sun distance) as our real-world radius unit, the orbit of Mercury is at about r = 0.3. That means: alpha = x/r = 2.4048 / 0.3 = 8.016. That is a constant, not a variable that depends on r or j  or anything else. The next realistic orbit would (IMO) be at x = 8.6537, or r  = 8.6537/ 8.016 ~ 1. (I don’t know what happened to Venus??)

The point is, we have to choose what alpha will be. If we can find a reasonable function of r for it, that’s good.

Feel free to disagree, but I want to make sure you understand where I am coming from on this.

Don

 

 

On Dec 1, 2017, at 9:50 AM, Donald Scott <dascott3@cox.net> wrote:

Jim,
Here are my reactions to your last email.
D
<ForJim2.docx>

Platonic solids/The Structure Atom Model (SAM) by Edwin Kaal from Science to Sage on Vimeo.

at:

Netherlands   7:00 pm

UTC-3            3:00pm

EST:               1:00pm

MST:              11:00am

PST               10:00am

​
​

​

 

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“Without doubt, therefore, there is a definite intention to teach young people upside-down methods of working with which they have to miss-earn their daily bread. That is to say, instead of moving forwards, they go backwards all the more rapidly in step with the improvements in the contrary methods of motion. For only thus can today’s teaching principles flourish.”

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