Equation J(kS,zeta)

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