1.5.1.3. 2017-10 Group Meeting

1.5.1.3.1. 2017-10-05

Bipolar model with matter effect. (link)

../../../_images/matter-bipolar-alpha-1-lambda-c2t-range-300.png

Fig. 1.211 With \(\alpha=1\), \(\lambda=\cos 2\theta_v\), \(\mu=3\omega\), where everything is in unit of \(\omega\). Range of calculation is \([0,300]\).

The frequencies are 1.95547, 3.39437, 5.25602.

The plots obviously show that the NFIS’s going through three fourier modes,

\[A_1 \cos( \gamma_1 t ) + A_2 \cos( \gamma_2 t ) + A_3 \cos( \gamma_3 t ).\]

Guess

It should be

\[\mathbf P = \sum_{i=1}^3 \mathbf P_{f,i} \cos(\gamma_i t).\]

Before we work out the data fitting, it would be nice if I can find the relation between the parameters and coefficients and frequencies.

I should work out \(\alpha=0.5,0.8,1,1.2,1.5\), \(\mu=0.5,1,2,3\), as well as some change in \(\lambda\).

Observations

Generally speaking, small \(\alpha\) enhances the first frequency.

Frist we calculate \(\lambda=\cos 2\theta_v\) and \(\mu=3\)

For \(\alpha=1\)

  1. frequencies: {1.95547, 3.39437, 5.25602}
  2. A: {0.111267, 0.0282127, 0.021448}
  3. Abar: {0.0397217, 0.0496267, 0.0205751}

For \(\alpha=0.8\)

  1. frequencies: {1.50333, 3.4475, 4.96213}
  2. A: {0.146606, 0.0257919, 0.0199095}
  3. Abar: {0.0434389, 0.038914, 0.0167421}

For \(\alpha=0.6\)

  1. {1.16424, 3.59444, 4.72477}
  2. {0.189593, 0.021267, 0.0167421}
  3. {0.0459276, 0.0316742, 0.0153846}

For \(\alpha=0.5\)

  1. frequencies: {1.03651, 3.58314, 4.6279}
  2. A: {0.225792, 0.0217194, 0.0134389}
  3. Abar: {0.0459276, 0.0255656, 0.0104072}

So the amplitude for neutrinos seems to be changing linearly as a function of \(\alpha\).

Keep \(\alpha=1\) and \(\lambda=\cos 2\theta_v\), while change \(\mu\).

For \(\mu=2\).

  1. Frequencies: {1.46942, 2.91624, 4.38567}
  2. A: {0.122172, 0.0303167, 0.0217195}
  3. Abar: {0.0312217, 0.0533937, 0.0190045}

I consider the amplitudes unchanged but the frequencies are shifted to lower values.


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