Q_s 1[W/m^3] "Steady heat release"
u_s 1[m/s] "Steady fluid flow"
tau_u 1e-4[s] "Time lag"
n 5 "Scale parameter"
delta_f 0.001[m] "Width of flame region"
P_s 1[atm] "Steady pressure"
L 0.5[m] "Length"
c1 347.19[m/s] "Sound speed, cold area"
Gamma 0.5 "Gamma factor"
freq_lin 200[Hz] "Linearization frequency for the solver"
omega10 4*c1/L*acos(sqrt(1/4*(Gamma-1)/(Gamma+1)+3/4)) "First mode, inactive flame"
omega1Res 4*c1/L*acos(sqrt(1/4*(Gamma*(1+n*exp(-i*tau_u*omega10))-1)/(Gamma*(1+n*exp(-i*tau_u*omega10))+1)+3/4)) "First mode, active flame 1st iteration"
omega1Res2 4*c1/L*acos(sqrt(1/4*(Gamma*(1+n*exp(-i*tau_u*omega1Res))-1)/(Gamma*(1+n*exp(-i*tau_u*omega1Res))+1)+3/4)) "First mode, active flame 2nd iteration"
omega1Res3 4*c1/L*acos(sqrt(1/4*(Gamma*(1+n*exp(-i*tau_u*omega1Res2))-1)/(Gamma*(1+n*exp(-i*tau_u*omega1Res2))+1)+3/4)) "First mode, active flame 3rd iteration"
omega30 4*c1/L*acos(-sqrt(1/4*(Gamma-1)/(Gamma+1)+3/4)) "Third mode, inactive flame"
omega3Res 4*c1/L*acos(-sqrt(1/4*(Gamma*(1+n*exp(-i*tau_u*omega30))-1)/(Gamma*(1+n*exp(-i*tau_u*omega30))+1)+3/4)) "Third mode, active flame 1st iteration"
omega3Res2 4*c1/L*acos(-sqrt(1/4*(Gamma*(1+n*exp(-i*tau_u*omega3Res))-1)/(Gamma*(1+n*exp(-i*tau_u*omega3Res))+1)+3/4)) "Third mode, active flame 2nd iteration"
omega3Res3 4*c1/L*acos(-sqrt(1/4*(Gamma*(1+n*exp(-i*tau_u*omega3Res2))-1)/(Gamma*(1+n*exp(-i*tau_u*omega3Res2))+1)+3/4)) "Third mode, active flame 3rd iteration"
omega40 4*c1/L*(-acos(-sqrt(1/4*(Gamma-1)/(Gamma+1)+3/4))+2*pi) "Fourth mode, inactive flame"
omega4Res 4*c1/L*(-acos(-sqrt(1/4*(Gamma*(1+n*exp(-i*tau_u*omega40))-1)/(Gamma*(1+n*exp(-i*tau_u*omega40))+1)+3/4))+2*pi) "Fourth mode, active flame 1st iteration"
omega4Res2 4*c1/L*(-acos(-sqrt(1/4*(Gamma*(1+n*exp(-i*tau_u*omega4Res))-1)/(Gamma*(1+n*exp(-i*tau_u*omega4Res))+1)+3/4))+2*pi) "Fourth mode, active flame 2nd iteration"
omega4Res3 4*c1/L*(-acos(-sqrt(1/4*(Gamma*(1+n*exp(-i*tau_u*omega4Res2))-1)/(Gamma*(1+n*exp(-i*tau_u*omega4Res2))+1)+3/4))+2*pi) "Fourth mode, active flame 3rd iteration"