List of Symbols

${A}$	area
${A}_{\text{ref}}$	reference area
${\vec{b}}_{\text{max}}$	maximum index vector of a rectangular axis aligned box
${\vec{b}}_{\text{min}}$	minimum index vector of a rectangular axis aligned box
${\mathcal{B}}$	rectangular axis aligned box
${C_\text{CFL}}$	CFL number
${d}$	diameter
${D}$	number of dimensions
${D}^{-}_i$	backward difference operator
${D}^0_i$	central difference operator
${D}^{+}_i$	forward difference operator
${\mathcal{D}}$	tangential disk
${e}$	elementary charge $=\SI{1.602e-19}{\coulomb}$
${\vec{e}}_i$	unit vector in ${x}_i$ -direction
${E}$	energy
${F}$	flux on surface ${\mathcal {S}}$
${F}^{\text{src}}$	flux on source plane ${\mathcal {P}}$
${F}^{\text{tot}}$	total flux through source plane ${\mathcal {P}}$
${\vec{g}}^{\text{max}}$	maximum index vector of grid
${\vec{g}}^{\text{min}}$	minimum index vector of grid
${G}$	reemission probability function
${\mathcal{G}}$	set of all grid point index vectors, ${\mathcal{G}}\subseteq\mathbb{Z}^{D}$
${H}$	Hamiltonian
${\hat{H}}$	numerical approximation to the Hamiltonian
${I}$	electric current
${k_B}$	Boltzmann constant $=\SI{1.381e-23}{\joule\per\kelvin}$
${\mathcal{L}}$	layer of grid points, ${\mathcal{L}}\subseteq{\mathcal{G}}$
${m}$	mass
${M}$	number of different material regions
${\mathcal{M}}$	material region
${\vec{n}}$	normal unit vector on ${\mathcal {S}}$ , ${\vec{n}}=\left({n}_1,\ldots,{n}_{D}\right)$
${\vec{n}}_{\mathcal{P}}$	normal unit vector on ${\mathcal {P}}$ pointing towards ${\mathcal {S}}$
${{N}_{\text{B}}}$	number of boxes of the spatial subdivision
${{N}_\text{CPU}}$	number of CPUs
${{N}_\text{D}}$	number of defined grid points
${{N}_\text{E}}$	number of edges in a graph
${{N}_\text{R}}$	number of surface rates
${{N}_\text{P}}$	number of simulated particles
${{N}_\text{V}}$	number of vertices in a graph
${\mathcal{O}}$	big O notation
${\vec{p}}$	grid point indices, ${\vec{p}}=\left({p}_1,\ldots,{p}_{D}\right)\in\mathbb{Z}^{D}$
${P}$	pressure
${\mathcal {P}}$	source plane
${q}$	particle species
${Q}$	number of process relevant particle species
${r}$	radius
${R}$	surface rate
${s}$	sticking probability
${\mathcal {S}}$	surface
${t}$	time
${T}$	temperature
${\bar{{v}}}$	mean particle velocity
${V}$	surface velocity (field)
${w}$	particle weight factor
${\vec{x}}$	point in space, ${\vec{x}}=\left({x}_1,\ldots,{x}_{D}\right)\in\mathbb{R}^{D}$
${\vec{x}}_{\text{cp}}$	closest point on surface
${Y}$	yield function
${Y}^{\text{tot}}$	total sputter rate
${\Gamma}$	arrival flux distribution on surface ${\mathcal {S}}$
${\Gamma}_{\text{re}}$	reemitted flux distribution on surface ${\mathcal {S}}$
${\Gamma}_{\text{src}}$	arrival flux distribution on source plane ${\mathcal {P}}$
$\delta$	Dirac/Kronecker delta function
$\Delta{t}$	time increment
${\Delta x}$	grid spacing
${\eta }$	surface reaction order
${\theta}$	polar angle
${\Theta}$	surface coverage
${\kappa}$	mean curvature
${\bar{\lambda}}$	mean free path
${\nu}$	exponent in power cosine distribution
${\rho}$	bulk density
${\sigma}$	standard deviation
${\phi}$	azimuthal angle
${\chi}$	weight factor for SAH
${\vec{\omega}}$	direction unit vector
${\Omega}$	solid angle