Page History

Q^{\downarrow}_{AQ}= B \cdot \int_0^t W_{eD} \left( \frac{(t-\tau)\chi}{r_e^2}, \frac{r_a}{r_e}  \right) \dot p(\tau) d\tau

W_{eD}(t) = \int_0^{t} \frac{\partial p_1}{\partial r_D} \bigg|_{r_D = 1} dt_D 

q^{\downarrow}_{AQ}(t)= \frac{dQ^{\downarrow}_{AQ}}{dt}

p_1 = p_1(t_D, r_D)

\frac{\partial p_1}{\partial t_D} =  \frac{\partial^2 p_1}{\partial r_D^2} + \frac{1}{r_D}\cdot \frac{\partial p_1}{\partial r_D}

p_1(t_D = 0, r_D)= 0

p_1(t_D, r_D=1) = 1

\frac{\partial p_1(t_D, r_D)}{\partial r_D} 
\Bigg|_{r_D=r_{aD}} = 0

 p_1(t_D, r_D = \infty) = 0

Q^{\downarrow}_{AQ}(t)= B \cdot \sum_\alpha W_{eD} 
\left( \frac{ (t-\tau_\alpha) \chi}{r_e^2}, \frac{r_a}{r_e}  \right)\Delta p_\alpha 


= B \cdot W_{eD} 
\left( \frac{ (t-\tau_1) \chi}{r_e^2}, \frac{r_a}{r_e}  \right)\Delta p_1 +
 B \cdot W_{eD} 
\left( \frac{ (t-\tau_2) \chi}{r_e^2}, \frac{r_a}{r_e}  \right)\Delta p_2
+ ... + B \cdot W_{eD} 
\left( \frac{ (t-\tau_N) \chi}{r_e^2}, \frac{r_a}{r_e}  \right)\Delta p_N