# 1.5.1.3. 2017-10 Group Meeting¶

## 1.5.1.3.1. 2017-10-05¶

Bipolar model with matter effect. (link)

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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