Equation J(kS,zeta)

Supplementary material to the contribution <b>"Spatially dependent friction - a way of adjusting bottleneck flow in cellular models"</b> to <i>Traffic and Granular Flow 2019</i>.<br>The file <b>Eq_JkSzeta.mat</b> contains all neceassary variables to reproduce the <b>Equation (3)</b> in the contribution: <b><i>J = J</i>(<i>kS, zeta</i>)</b>. The formula is contained in the symbolical variable <b>'J'</b>, which is symbolic expression in variables <b>'p'</b> and <b>'z'</b>, where<i>p</i> = exp{<i>kS</i>} in [1, +<i>Infty</i>),<i>z</i> = <i>zeta</i> in [0, 1].<br>The workspace is primarily designed for MATLAB software, however, it can be imported to other mathematical softwares as well.In MATLAB use<b>load('Eq_JkSzeta.mat')</b><br>The value of the flow can be reached by substitution<b>j = subs(J, {'p', 'z'}, [pval, zval]);</b><br><b>Example:</b> to get stationary flow for <i>kS</i> = 3 and <i>zeta</i> = 0.55 do<b>load('Eq_JkSzeta.mat')</b> % load variables to workspace<b>j = subs(J, {'p', 'z'}, [exp(3), 0.55]);</b> % substitute values to the formula<b>j = double(j);</b> % convert symbolical expresion to double