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Name: jay
Title:
speed of sound
Question:
c       Programme for speed of sound in SCQGP
c       Bannur
implicit real*8(a-h,o-z)
pi=4.d0*datan(1.d0)
tempc=0.275d0           !for nf=0
c
do 300 ii=1,201
tilde=1.d0 0.1d0*dfloat(ii-1)
temp=tilde*tempc
tcd=temp/tempc
anf=0.d0
anc=3.d0        !no of colors
c       alambda=0.037d0       !n_f=3
c       alambda=0.0805d0       !n_f=2
alambda=0.1375d0       !n_f=0
af=(16.d0 (21.d0*anf/2.d0))*pi**2/90.d0
ent1=entemp(temp,tempc,anf,anc,alambda,tcd)
ent=ent1*3.d0*af*temp**4
ent4=ent/temp**4
ptem=ptemp(temp,tempc,anf,anc,alambda,tcd)
pt4=ptem/temp**4
write(*,*)tilde,pt4
300      continue
stop
end
c       subprograme for energy density e(T)
function entemp(temp,tempc,anf,anc,alambda,tcd)
implicit real*8(a-h,o-z)
Dimension pl(10000),pl1(10000)
pi=4.d0*datan(1.d0)
fac1=(6.d0*pi)
fac2=(33.d0-2.d0*anf)*dlog(temp/alambda)
fac3=3.d0*(153.d0-19.d0*anf)/((33.d0-2.d0*anf)**2)
fac4=dlog(2.d0*dlog(temp/alambda))/dlog(temp/alambda)
alpha=(fac1/fac2)*(1.d0-fac3*fac4)
c       alpha=fac1/(fac2*(1.d0 fac3*fac4))
gsq=4.d0*pi*alpha       !g^2_s
den1=(16.d0 (21.d0*anf/2))*(pi**2/90.d0)
den=1.1d0*den1*temp**3                 !n
rav=(3.d0/(4.d0*pi*den))**0.33333333333d0
fact=(anc/3.d0) (anf/6.d0)
amdLO=dsqrt(fact*gsq)*temp
c          debye=amdLO
c        Debye Mass(SU(3)_c)
n=100
am=0.890052d0
bm=1.29752d0
cm=-2.42922d0
dm=3.60965d0
ax=tilde              !T/T_c
az=am*dexp(-(bm/tcd**2)-(cm/tcd**4)-(dm/tcd**6))
do 20 k=1,n
pl(k)=az**k/k**2
pl1(k)=(-az)**k/k**2
20        continue
sum=0.d0
sum2=0.d0
do 30 k=1,n
sum=sum pl(k)
sum2=sum2 pl1(k)
30        continue
c         write(*,*)sum
sum1=sum
sum3=sum2
sigma=0.184d0                !string tension(GeV^2)
c
potn2=alpha
potn3=potn1-potn2
potn4=potn3*dexp(-debrt)/rav
potnf=(potn4-potn5 potn6-potn7)
gammaf=potnf/temp
tau=abs(gammaf)
enertau1=(1.d0/2.7d0)*(dsqrt(3.d0)/2.d0)
enertau=1.d0-enertau1*tau**(3.d0/2.d0)
entemp=enertau
return
end
c
c       subprograme in pressure
function ptemp(temp,tempc,anf,anc,alambda,tcd)
implicit real*8(a-h,o-z)
dimension funtemp(1901)
Dimension pl(10000),pl1(10000)
pi=4.d0*atan(1.d0)
af=(16.d0 (21.d0*anf/2.d0))*pi**2/90.d0
alower=tempc
aupper=temp
numb=101
dtau=(aupper-alower)/dfloat(numb-1)
c       Generation of integrand
do 88 i=1,numb
temp=alower dtau*dfloat(i-1)
fac1=(6.d0*pi)
fac2=(33.d0-2.d0*anf)*dlog(temp/alambda)
fac3=3.d0*(153.d0-19.d0*anf)/((33.d0-2.d0*anf)**2)
fac4=dlog(2.d0*dlog(temp/alambda))/dlog(temp/alambda)
alpha=(fac1/fac2)*(1.d0-fac3*fac4)
c       alpha=fac1/(fac2*(1.d0 fac3*fac4))
gsq=4.d0*pi*alpha       !g^2_s
den1=(16.d0 (21.d0*anf/2))*(pi**2/90.d0)
den=1.1d0*den1*temp**3                 !n
rav=(3.d0/(4.d0*pi*den))**0.33333333333d0
fact=(anc/3.d0) (anf/6.d0)
c        amdLO=dsqrt(fact*gsq)*temp
c          debye=amdLO
c        Debye Mass(SU(3)_c)
n=100
am=0.890052d0
bm=1.29752d0
cm=-2.42922d0
dm=3.60965d0
ax=tilde              !T/T_c
az=am*dexp(-(bm/tcd**2)-(cm/tcd**4)-(dm/tcd**6))
do 20 k=1,n
pl(k)=az**k/k**2
pl1(k)=(-az)**k/k**2
20        continue
sum=0.d0
sum2=0.d0
do 30 k=1,n
sum=sum pl(k)
sum2=sum2 pl1(k)
30        continue
c         write(*,*)sum
sum1=sum
sum3=sum2
sigma=0.184d0                !string tension(GeV^2)
c
potn2=alpha
potn3=potn1-potn2
potn4=potn3*dexp(-debrt)/rav
potnf=(potn4-potn5 potn6-potn7)
gammaf=potnf/temp
tau=abs(gammaf)
etau1=(1.d0/2.7d0)*(dsqrt(3.d0)/2.d0)
enertau=1.d0-etau1*tau**(3.d0/2.d0)
funtemp(i)=temp**2*enertau
88      continue
call simson(alower,aupper,numb,funtemp,rr)
plus=rr*3.d0*af*aupper
ptauc=0.0707d0*(tempc**3)*aupper
ptemp=plus ptauc
return
end
c
subroutine simson(a,b,nmx,func,r)
implicit real*8(a-h,o-z)
dimension func(1901)
cnum=nmx
h=(b-a)/(cnum-1.d0)
odd=0.d0
even=0.d0
index=0
do 11 m=1,nmx
if (index)3,3,4
3       odd=odd func(m)
index=1
go to 11
4       even=even func(m)
index=0
11      continue
tot=2.d0*odd 4.d0*even-func(1)-func(nmx)
r=h*tot/3.d0
return
end

Name: спт
var a,b,t,M,R: integer;
Function F(x:integer): integer;
begin
F := x*x   2*x   10
end;
begin
a := -10; b := 10;
M := a; R := F(a);
for t := a to b do begin
if (F(t) < R) then begin
M := t;
R := F(t)
end
end;
write(M)
end.