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FrogPad
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Ok, I'm trying to recreate some results from a paper, and I am really lacking in understanding. I'm getting extremely frustrated.
I'll try to create a similar problem that replicates the original problem. The original problem, is three coupled non-linear differential equations that must be solved numerically. The new problem that I am writing here will just be one differential equation.
If I have the following function:
[tex] \alpha \frac{d \phi}{d\theta} = A_{23} + B_{23} \sin \phi [/tex]
Now they say they have normalized [itex] A_{23}, \,\, B_{23} [/itex], and later they say that [itex] \frac{d \phi}{d \theta} [/itex] is a normlized voltage.
So now should I believe that [itex] \frac{d \phi}{d\theta} [/itex] has no units, and that [itex] A_{23} + B_{23} \sin \phi [/itex] has no units? This would make sense correct?
Now, they define [itex] \alpha [/itex] as:
[tex] \alpha = \frac{h \omega}{2 e I_C R_n} [/tex] and
[tex] \theta = \omega t [/tex]
Now, h is Planck's constant, omega is angular frequency, e is the fundamental quantity of charge (coulombs), and I_C*R_n would have the units of volts. Specifically, [itex] \alpha \sim 10^{-12} seconds [/itex] (with the given I_C*R_n = 0.45mV) -- This is also assuming that I can simply change [itex] d\theta = \omega dt [/itex] and cancel the [itex] \omega [/itex] in teh [itex] \alpha [/itex] term.
Now here is my question (assuming everything else I did was ok). If I use MATLAB's ODE45 solver, with the tspan of [a, b]. What units is this even in? Is this seconds? Nanoseconds... how do I know? Also, why would they put [tex] \alpha [/tex] out there like that?
I hope I have made myself clear. I'm struggling on this one.
I'll try to create a similar problem that replicates the original problem. The original problem, is three coupled non-linear differential equations that must be solved numerically. The new problem that I am writing here will just be one differential equation.
If I have the following function:
[tex] \alpha \frac{d \phi}{d\theta} = A_{23} + B_{23} \sin \phi [/tex]
Now they say they have normalized [itex] A_{23}, \,\, B_{23} [/itex], and later they say that [itex] \frac{d \phi}{d \theta} [/itex] is a normlized voltage.
So now should I believe that [itex] \frac{d \phi}{d\theta} [/itex] has no units, and that [itex] A_{23} + B_{23} \sin \phi [/itex] has no units? This would make sense correct?
Now, they define [itex] \alpha [/itex] as:
[tex] \alpha = \frac{h \omega}{2 e I_C R_n} [/tex] and
[tex] \theta = \omega t [/tex]
Now, h is Planck's constant, omega is angular frequency, e is the fundamental quantity of charge (coulombs), and I_C*R_n would have the units of volts. Specifically, [itex] \alpha \sim 10^{-12} seconds [/itex] (with the given I_C*R_n = 0.45mV) -- This is also assuming that I can simply change [itex] d\theta = \omega dt [/itex] and cancel the [itex] \omega [/itex] in teh [itex] \alpha [/itex] term.
Now here is my question (assuming everything else I did was ok). If I use MATLAB's ODE45 solver, with the tspan of [a, b]. What units is this even in? Is this seconds? Nanoseconds... how do I know? Also, why would they put [tex] \alpha [/tex] out there like that?
I hope I have made myself clear. I'm struggling on this one.
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