Темная материя - начало

Last modified by Alexey Popov on 2019/06/05 16:56

$B_x = \frac{G}{c^2}M ( v_y (r_z - r_{z1}) - v_z (r_y - r_{y1}) ) \frac{1}{|r - r_{1}|^3}$

$B_y = \frac{G}{c^2}M ( v_z (r_x - r_{x1}) - v_x (r_z - r_{z1}) ) \frac{1}{|r - r_{1}|^3}$

$B_z = \frac{G}{c^2}M ( v_x (r_y - r_{y1}) - v_y (r_x - r_{x1}) ) \frac{1}{|r - r_{1}|^3}$

$|r - r_{1}| = \sqrt{(r_x - r_{x1})^2 + (r_y - r_{y1})^2 +(r_z - r_{z1})^2 }$

$A_x = \frac{G}{c^2}M v_x \frac{1}{|r - r_{1}|}$

$A_y = \frac{G}{c^2}M v_y \frac{1}{|r - r_{1}|}$

$A_z = \frac{G}{c^2}M v_z \frac{1}{|r - r_{1}|}$

$\mathbf E = \mathbf A \times \mathbf B$

$E_x = A_y B_z - A_z B_y = \frac{G^2}{c^4}M^2 \frac{1}{|r - r_{1}|^4}\left (v_y ( v_x (r_y - r_{y1}) - v_y (r_x - r_{x1}) ) - v_z ( v_z (r_x - r_{x1}) - v_x (r_z - r_{z1}) ) \right )$

$E_x = - (A_x A_x +A_y A_y+A_z A_z) \frac{r_x - r_{x1}}{|r - r_{1}|^2}$

$E_y = - (A_x A_x +A_y A_y+A_z A_z)\frac{r_y - r_{y1}}{|r - r_{1}|^2}$

$E_z = - (A_x A_x +A_y A_y+A_z A_z) \frac{r_z - r_{z1}}{|r - r_{1}|^2}$

$J_x = - \frac{1}{2}(E_x E_x +E_y E_y+E_z E_z) \frac{v_x - v_{x1}}{|v - v_{1}|^2}$

$\mathbf E = \int \mathbf J dt$

Диффузия

$\mathbf E = -D \Delta \mathbf A = -D\mu_0 \mathbf J$

$\Delta \varphi = \frac{1}{4 \pi \epsilon_0}\rho$

$\Delta \mathbf A = \frac{1}{4 \pi \epsilon_0}\rho \mathbf v$

$\varphi = \frac{1}{4 \pi \epsilon_0}\int \rho dV \frac{1}{\mathbf r}$

$\mathbf A = \frac{1}{4 \pi \epsilon_0}\int \rho \mathbf v dV \frac{1}{\mathbf r}$

$\mathbf E = - D \frac{1}{4 \pi \epsilon_0}\rho \mathbf v$

$\mathbf a = - D \frac{G}{c^2}\rho \mathbf v$

$\mathbf J = \rho \mathbf v = M\frac{3}{4\pi r^3}\mathbf v$

$\mathbf a = - D \frac{G}{c^2}M\frac{3}{4\pi r^3}\mathbf v$

$\mathbf a = - D \frac{G^2}{c^4}M^2\frac{3}{4\pi r^4}\mathbf v$

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Created by Alexey Popov on 2019/06/05 10:02

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