deletions | additions       diff --git a/MonodisperseCharges/results.aux b/MonodisperseCharges/results.aux  new file mode 100644  index 0000000..4cb2944  --- /dev/null  +++ b/MonodisperseCharges/results.aux 
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\relax   \@writefile{toc}{\contentsline {section}{\numberline {3}Results}{13}}  \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Overview}{13}}  \newlabel{eq:r1}{{21}{13}}  \newlabel{eq:r2}{{22}{13}}  \@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Tribocharging Rate}{14}}  \@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Snapshot taken at $1.8 \hskip 1em\relax \mathrm {s}$ of eight different fluidization cases. Cases (A)-(D) have superficial velocity of $0.2V_t$ while cases (E)-(H) have superficial velocity of $0.3V_t$. The background is colored by the solids volume fraction, and particles are colored based on the vertical velocity. Every $20$:th particle is shown in the figure from total of $36410$ particles.}}{15}}  \newlabel{fig:c0}{{4}{15}}  \@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Charging rate of the fluidized bed with various rations of electrostatic forces to gravity.}}{16}}  \newlabel{fig:c1}{{5}{16}}  \@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Charging rate of the fluidized bed with various two ratios of electrostatic forces to gravity, and varying superficial velocity.}}{16}}  \newlabel{fig:cc1}{{6}{16}}  \@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Probability distribution of charge.}}{17}}  \newlabel{fig:cc2}{{7}{17}}  \@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Probability distribution of charge respect to walls and interior.}}{17}}  \newlabel{fig:cc3}{{8}{17}}  \@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Particle Volume and Charge Distribution}{17}}  \@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Radial particle distribution.}}{18}}  \newlabel{fig:c2}{{9}{18}}  \@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Particle Velocity Distribution}{18}}  \@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Particle fraction at the wall.}}{19}}  \newlabel{fig:w2}{{10}{19}}  \@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces Radial average particle charge distribution.}}{19}}  \newlabel{fig:c3}{{11}{19}}  \citation{hassani_numerical_2013}  \@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Time averaged vertical velocity distribution at different distances from the center of the bed. Various work function values and superficial velocities are shown. }}{20}}  \newlabel{fig:c5}{{12}{20}}  \@writefile{toc}{\contentsline {subsection}{\numberline {3.5}Effects on Bed Height and to Pressure Loss}{20}}  \@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Figure showing instantenous bed heights that contain $95\%$ of the particles. }}{21}}  \newlabel{fig:c7}{{13}{21}}  \@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces Time averaged pressure curves from bed bottom to the outlet with varying electrostatic force. }}{22}}  \newlabel{fig:c6}{{14}{22}}  \@setckpt{results}{  \setcounter{page}{23}  \setcounter{equation}{22}  \setcounter{enumi}{0}  \setcounter{enumii}{0}  \setcounter{enumiii}{0}  \setcounter{enumiv}{0}  \setcounter{footnote}{0}  \setcounter{mpfootnote}{0}  \setcounter{part}{0}  \setcounter{section}{3}  \setcounter{subsection}{5}  \setcounter{subsubsection}{0}  \setcounter{paragraph}{0}  \setcounter{subparagraph}{0}  \setcounter{figure}{14}  \setcounter{table}{0}  \setcounter{parentequation}{0}  \setcounter{NAT@ctr}{0}  }