> restart:

Standard Worksheet SSSPF

M-W I = F-S

Physical quatities are defined in the initialization file

> grts();

Created definition for G(up,dn) 

Created definition for rho

Created definition for Iso

Created definition for p

Created definition for gthetatheta

Created definition for R(dn,dn,up,up) 

Created definition for mass

> qload(mwfs);

Physical parameters

> grcalc(Iso,rho,p,mass):

> gralter(_,6,7):

Component simplification of a GRTensorII object:

Applying routine expand to object Iso

Applying routine expand to object rho

Applying routine expand to object p

Applying routine expand to object mass

Applying routine factor to object Iso

Applying routine factor to object rho

Applying routine factor to object p

Applying routine factor to object mass

> grdisplay(_);

Juncion conditions

> Y1:=1/((-2+alpha));

> P1:=(2*cos(alpha^(1/2)/(-2+alpha)^(1/2))*sin(alpha^(1/2)/(-2+alpha)^(1/2))*alpha-2*cos(alpha^(1/2)/(-2+alpha)^(1/2))*sin(alpha^(1/2)/(-2+alpha)^(1/2))-sqrt((-2+alpha)*alpha))/(2-2*cos(alpha^(1/2)/(-2+alpha)^(1/2))^2-alpha+2*cos(alpha^(1/2)/(-2+alpha)^(1/2))^2*alpha);

Perssure plots

> pj:=subs(Y=Y1,P=P1,grcomponent(p,[])):

> p1:=subs(R=1,alpha=6,pj):

> p2:=subs(R=1,alpha=5,pj):

> p3:=subs(R=1,alpha=4,pj):

> p4:=subs(R=1,alpha=3,pj):

> plot([p1,p2,p3,p4],xi=0..1,color=[red,green,blue,black],title="Pressure M-W I = F-S");

Energy density plots

> rhoj:=subs(Y=Y1,P=P1,grcomponent(rho,[])):

> rho1:=subs(R=1,alpha=6,rhoj):

> rho2:=subs(R=1,alpha=5,rhoj):

> rho3:=subs(R=1,alpha=4,rhoj):

> rho4:=subs(R=1,alpha=3,rhoj):

> plot([rho1,rho2,rho3,rho4],xi=0..1,color=[red,green,blue,black],title="Energy Density M-W I = F-S");

Mass plots

> mj:=subs(Y=Y1,P=P1,grcomponent(mass,[])):

> mj1:=subs(R=1,alpha=6,mj):

> mj2:=subs(R=1,alpha=5,mj):

> mj3:=subs(R=1,alpha=4,mj):

> mj4:=subs(R=1,alpha=3,mj):

> plot([mj1,mj2,mj3,mj4],xi=0..1,color=[red,green,blue,black],title="Mass M-W I = F-S");

Trapping

Potential impac parameter

> B:=sqrt(grcomponent(g(dn,dn),[theta,theta]))/sqrt(-grcomponent(g(dn,dn),[t,t])):

> Bj:=subs(Y=Y1,P=P1,B):

> B1:=subs(R=1,alpha=3.00,Bj):

> B2:=subs(R=1,alpha=2.9,Bj):

> B3:=subs(R=1,alpha=2.8,Bj):

> B4:=subs(R=1,alpha=2.7,Bj):

> plot([B1,B2,B3,B4],xi=0..1,color=[red,green,blue,black],title="Trapping M-W I = F-S");

w - modes

Potential

> V:=1/((Bj^2))*(6+4*Pi*xi^2*R^2*(grcomponent(rho,[])-grcomponent(p,[]))-6*grcomponent(mass,[])/(xi*R)):

> Vj:=subs(Y=Y1,P=P1,V):

> V1:=subs(R=1,alpha=3.0,Vj):

> V2:=subs(R=1,alpha=2.93,Vj):

> V3:=subs(R=1,alpha=2.85,Vj):

> V4:=subs(R=1,alpha=2.8,Vj):

> plot([V1,V2,V3,V4],xi=0.4..1.0,color=[red,green,blue,black],title="w - modes M-W I = F-S");

V:=sqrt(dp/dr/drho/dr)

> vs:=sqrt(diff(grcomponent(p,[]),xi)/(diff(grcomponent(rho,[]),xi))):

> vsj:=subs(Y=Y1,P=P1,vs):

> vs1:=subs(R=1,alpha=6,vsj):

> vs2:=subs(R=1,alpha=5,vsj):

> vs3:=subs(R=1,alpha=4,vsj):

> vs4:=subs(R=1,alpha=3.5,vsj):

> plot([vs1,vs2,vs3,vs4],xi=0..1,color=[red,green,blue,black],title="V M-W I = F-S");

>