37°35′17″N 77°30′50″W / 37.58806°N 77.51389°W / 37.58806; -77.51389

User:UBX/Commendation Medal

I live in Richmond, Virginia in the United States of America and I like nuclear engineering, mathematics, computers, and guns.

Grandma

Willard Wright Hubbard III (1915-1987)

Mom

Dad

Uncle John

My brother Bill

Me!

My brother Jim

My brother Greg

• http://en.wikipedia.org/key/Omicron_Delta_Kappa
• http://en.wikipedia.org/key/United_States_Naval_Academy
• http://en.wikipedia.org/key/University_of_Virginia
• http://en.wikipedia.org/key/Yodle,_Inc
• http://en.wikipedia.org/key/ReachLocal

I am a former Senior Manager of Software Development at Amazon, where I managed the development of the amazon.com content selection and delivery software (i.e. Amabot). I also invented, designed, and developed the engineering of Amazon.com's behaviorial-targeted third-party display advertising product.

${\displaystyle \left({\frac {1}{v(E)}}{\frac {\partial }{\partial t}}+\mathbf {\hat {\Omega }} \cdot \nabla +\Sigma _{t}(\mathbf {r} ,E,t)\right)\psi (\mathbf {r} ,E,\mathbf {\hat {\Omega }} ,t)=\quad }$

${\displaystyle \quad {\frac {\chi _{p}\left(E\right)}{4\pi }}\int _{0}^{\infty }dE^{\prime }\nu _{p}\left(E^{\prime }\right)\Sigma _{f}\left(\mathbf {r} ,E^{\prime },t\right)\phi \left(\mathbf {r} ,E^{\prime },t\right)+\sum _{i=1}^{N}{\frac {\chi _{di}\left(E\right)}{4\pi }}\lambda _{i}C_{i}\left(\mathbf {r} ,t\right)+\quad }$

${\displaystyle \quad \int _{4\pi }d\Omega ^{\prime }\int _{0}^{\infty }dE^{\prime }\,\Sigma _{s}(\mathbf {r} ,E^{\prime }\rightarrow E,\mathbf {\hat {\Omega }} ^{\prime }\rightarrow \mathbf {\hat {\Omega }} ,t)\psi (\mathbf {r} ,E^{\prime },\mathbf {{\hat {\Omega }}^{\prime }} ,t)+s(\mathbf {r} ,E,\mathbf {\hat {\Omega }} ,t)}$

Where:

Symbol	Meaning	Comments
${\displaystyle \mathbf {r} }$	Position vector (i.e. x,y,z)
${\displaystyle E}$	Energy
${\displaystyle \mathbf {\hat {\Omega }} ={\frac {\mathbf {v} (E)}{|\mathbf {v} (E)|}}={\frac {\mathbf {v} (E)}{v(E)}}}$	Unit vector (solid angle) in direction of motion
${\displaystyle t}$	Time
${\displaystyle \mathbf {v} (E)}$	Neutron velocity vector
${\displaystyle \psi (\mathbf {r} ,E,\mathbf {\hat {\Omega }} ,t)dr\,dE\,d\Omega }$	Angular neutron flux Amount of neutron track length in a differential volume ${\displaystyle dr}$ about ${\displaystyle r}$, associated with particles of a differential energy in ${\displaystyle dE}$ about ${\displaystyle E}$, moving in a differential solid angle in ${\displaystyle d\Omega }$ about ${\displaystyle \mathbf {\hat {\Omega }} }$, at time ${\displaystyle t}$.	Note integrating over all angles yields scalar neutron flux ${\displaystyle \phi \ =\ \int _{4\pi }d\Omega \psi }$
${\displaystyle \phi (\mathbf {r} ,E,t)dr\,dE}$	Scalar neutron flux Amount of neutron track length in a differential volume ${\displaystyle dr}$ about ${\displaystyle r}$, associated with particles of a differential energy in ${\displaystyle dE}$ about ${\displaystyle E}$, at time ${\displaystyle t}$.
${\displaystyle \nu _{p}}$	Average number of neutrons produced per fission (e.g., 2.43 for U-235).
${\displaystyle \chi _{p}(E)}$	Probability density function for neutrons of exit energy ${\displaystyle E}$ from all neutrons produced by fission
${\displaystyle \chi _{di}(E)}$	Probability density function for neutrons of exit energy ${\displaystyle E}$ from all neutrons produced by delayed neutron precursors
${\displaystyle \Sigma _{t}(\mathbf {r} ,E,t)}$	Macroscopic total cross section, which includes all possible interactions
${\displaystyle \Sigma _{f}(\mathbf {r} ,E^{\prime },t)}$	Macroscopic fission cross section, which includes all fission interactions in ${\displaystyle dE^{\prime }}$ about ${\displaystyle E^{\prime }}$
${\displaystyle \Sigma _{s}(\mathbf {r} ,E'\rightarrow E,\mathbf {\hat {\Omega }} '\rightarrow \mathbf {\hat {\Omega }} ,t)dE^{\prime }d\Omega ^{\prime }}$	Double differential scattering cross section Characterizes scattering of a neutron from an incident energy ${\displaystyle E^{\prime }}$ in ${\displaystyle dE^{\prime }}$ and direction ${\displaystyle \mathbf {\hat {\Omega ^{\prime }}} }$ in ${\displaystyle d\Omega ^{\prime }}$ to a final energy ${\displaystyle E}$ and direction ${\displaystyle \mathbf {\hat {\Omega }} }$.
${\displaystyle N}$	Number of delayed neutron precursors
${\displaystyle \lambda _{i}}$	Decay constant for precursor i
${\displaystyle C_{i}\left(\mathbf {r} ,t\right)}$	Total number of precursor i in ${\displaystyle \mathbf {r} }$ at time ${\displaystyle t}$
${\displaystyle s(\mathbf {r} ,E,\mathbf {\hat {\Omega }} ,t)}$	Source term

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