Talk:DWBA

From GISAXS
Revision as of 17:02, 6 March 2018 by KevinYager (talk | contribs)
Jump to: navigation, search

Using the notation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_i = T(\alpha_i)} for compactness, the DWBA equation can be written as:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} I_d(q_{z}) & = | T_i T_f F(+Q_{z1}) + T_i R_f F(-Q_{z2}) + R_i T_f F(+Q_{z2}) + R_i R_f F(-Q_{z1}) | ^{2} \\ & \begin{align} = \,\, & T_i^2 T_f^2 | F(+Q_{z1}) |^2 && + T_i^2 T_f R_f F(+Q_{z1})F(-Q_{z2}) \\ & && + T_i R_i T_f R_f F(+Q_{z1})F(+Q_{z2}) + T_i R_i T_f R_f F(+Q_{z1}) F(-Q_{z1}) \\ & + T_i^2 R_f^2 | F(-Q_{z2}) |^2 && + T_i^2T_fR_f F(+Q_{z1}) F(-Q_{z2}) \\ & && + T_i R_i T_f R_f F(+Q_{z2})F(-Q_{z2}) + T_i R_i R_f^2 F(-Q_{z1}) F(-Q_{z2}) \\ & + R_i^2 T_f^2 | F(+Q_{z2}) |^2 && + T_i R_i T_f^2 F(+Q_{z1}) F(+Q_{z2}) \\ & && + T_i R_i T_f R_f F(+Q_{z2})F(-Q_{z2}) + R_i^2 T_f R_f F(-Q_{z1}) F(+Q_{z2}) \\ & + R_i^2 R_f^2 | F(-Q_{z1}) |^2 && + T_i R_i T_f R_f F(+Q_{z1}) F(-Q_{z1}) \\ & && + T_i R_i R_f^2 F(-Q_{z1})F(-Q_{z2}) + R_i^2 T_f R_f F(-Q_{z1}) F(+Q_{z2}) \\ \end{align} \\ \end{align} } The DWBA equation is: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I_d(q_{z}) = T_i^2 T_f^2 | F(+Q_{z1}) |^2 + T_i^2 R_f^2 | F(-Q_{z2}) |^2 + R_i^2 T_f^2 | F(+Q_{z2}) |^2 + R_i^2 R_f^2 | F(-Q_{z1}) |^2 }

Taking advantage of the fact that Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |F(Q)|^2 = I(Q)} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I(+Q)=I(-Q)} , we can rearrange to:


Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}I_{d}(q_{z})=\,\,&T_{i}^{2}T_{f}^{2}|F(+Q_{z1})|^{2}+T_{i}^{2}R_{f}^{2}|F(-Q_{z2})|^{2}+R_{i}^{2}T_{f}^{2}|F(+Q_{z2})|^{2}+R_{i}^{2}R_{f}^{2}|F(-Q_{z1})|^{2}\\&+T_{i}^{2}T_{f}R_{f}F(+Q_{z1})F(-Q_{z2})\\&+T_{i}R_{i}T_{f}R_{f}F(+Q_{z1})F(+Q_{z2})+T_{i}R_{i}T_{f}R_{f}F(+Q_{z1})F(-Q_{z1})\\&+T_{i}^{2}T_{f}R_{f}F(+Q_{z1})F(-Q_{z2})\\&+T_{i}R_{i}T_{f}R_{f}F(+Q_{z2})F(-Q_{z2})+T_{i}R_{i}R_{f}^{2}F(-Q_{z1})F(-Q_{z2})\\&+T_{i}R_{i}T_{f}^{2}F(+Q_{z1})F(+Q_{z2})\\&+T_{i}R_{i}T_{f}R_{f}F(+Q_{z2})F(-Q_{z2})+R_{i}^{2}T_{f}R_{f}F(-Q_{z1})F(+Q_{z2})\\&+T_{i}R_{i}T_{f}R_{f}F(+Q_{z1})F(-Q_{z1})\\&+T_{i}R_{i}R_{f}^{2}F(-Q_{z1})F(-Q_{z2})+R_{i}^{2}T_{f}R_{f}F(-Q_{z1})F(+Q_{z2})\\=\,\,&T_{i}^{2}T_{f}^{2}|F(+Q_{z1})|^{2}+T_{i}^{2}R_{f}^{2}|F(-Q_{z2})|^{2}+R_{i}^{2}T_{f}^{2}|F(+Q_{z2})|^{2}+R_{i}^{2}R_{f}^{2}|F(-Q_{z1})|^{2}\\&+2\times T_{i}^{2}T_{f}R_{f}F(+Q_{z1})F(-Q_{z2})\\&+T_{i}R_{i}T_{f}R_{f}[2F(+Q_{z1})F(-Q_{z1})+F(+Q_{z1})F(+Q_{z2})+2F(+Q_{z2})F(-Q_{z2})]\\&+2\times T_{i}R_{i}R_{f}^{2}F(-Q_{z1})F(-Q_{z2})\\&+T_{i}R_{i}T_{f}^{2}F(+Q_{z1})F(+Q_{z2})\\&+2\times R_{i}^{2}T_{f}R_{f}F(-Q_{z1})F(+Q_{z2})\\\end{aligned}}}

Retrieved from "http://gisaxs.com/index.php?title=Talk:DWBA&oldid=5847"