subroutine gradt * * solution of the cubic equation characteristic of the mixing length * theory (u is essentially the ratio of radiative to convective * conductivities) Bohm-Vitense version (ML1) * implicit double precision(a-h,o-z) common/c/az(3),z(3),taux,ts,ps,sm,rs,err,te,gs,rho,ol1x,rl1x,el1x 1 ,atgx,rtgx,tl,pl,xmass,acu,am,bk,an0,pi common/grad/ drdtp(400),cp(400),ttg(400),drdtpx,cpx,pecx,ttgx, 1 deptx,dpdr,dtdr,dmdr,dr,xr,xt,cv,drdptx u=pecx if ( u .lt. 1.e-10 ) then ttgx=atgx return elseif ( u .gt. 1.e+10 ) then ttgx=rtgx return endif q=368./729.*u**2 r=4672./19683.*u**3+4./9.*u*(rtgx-atgx) s1=(r+(q**3+r**2)**0.5)**0.3333333 s2=-q/s1 if ( u .le. 1. ) then super=(s1+s2+19./27.*u)**2-u**2 if ( super .le. 0. ) super=0. ttgx=atgx+super return else super=9.*(s1+s2-8./27.*u)**3/u/8. if ( super .le. 0. ) super=0. ttgx=rtgx-super return endif end ************************************************************************