3 deleted 14 characters in body
source | link
vpw = 3.3; 
Mp = 80; 
rp = 0.014*Mp; 
b0 = 26.31016273 - 1.7168*(10^3/t) - 3.5519*Log[t]; 
b1 = 24.65681838 - 1.547*(10^3/t) - 3.4314*Log[t]; 
b2 = 9.080370819 - 6.9445*(10^2/t) - 1.2222*Log[t]; 
g = b0 + b1*phip + b2*phip^2; 
dg = b1 + 2*b2*phip; 
ddg = 2*b2; 
dddg = 0; 

S1 = 1/(phip*rp*vpw) + 1/(1 - phip) - (2*g - 2*(1 - 2*phip)*dg - 
     phip*(1 - phip)*ddg); 
S2 = -(1/(phip^2*rp*vpw)) + 1/(1 - phip)^2 - 
    (6*dg - 3*(1 - 2*phip)*ddg - phip*(1 - phip)*dddg); 

   p = Apply[{phip, t} /. FindRoot[{S1 == 0, S2 == 0}, {phip, #1}, 
      {t, #2}] & , 
   {{-2, 400}, {3-0.05, 800}20}, {1}]

{{-1.2873402582429673, 414.62463948474493800}}, 
  {2.6101985365488636, 820.8522532621079}1}
 ]

{{-1.28734, 414.625}, {-0.0436006, 23.3922}, {2.6102, 820.852}}

ContourPlot[{S1 == 0, S2 == 0}, {phip, -2, 3}, {t, 0, 1000}, 
  PlotTheme -> "Detailed", PlotPoints -> 100, 
  Epilog -> {Red, PointSize[Large], Point[p]}]

Contourplot1

In the range near zero there is no crossing. Verify:Contourplot3

   ContourPlot[{S1 == 0, S2 == 0}, {phip, -0.2, 0.3}, {t, 0, 20100}, 
  PlotTheme -> "Detailed", PlotPoints -> 100]100, 
  Epilog -> {Red, PointSize[Large], Point[p]}]

Contourplot2Contourplot4

A question, how can I insert plots here?

vpw = 3.3; 
Mp = 80; 
rp = 0.014*Mp; 
b0 = 26.31016273 - 1.7168*(10^3/t) - 3.5519*Log[t]; 
b1 = 24.65681838 - 1.547*(10^3/t) - 3.4314*Log[t]; 
b2 = 9.080370819 - 6.9445*(10^2/t) - 1.2222*Log[t]; 
g = b0 + b1*phip + b2*phip^2; 
dg = b1 + 2*b2*phip; 
ddg = 2*b2; 
dddg = 0; 

S1 = 1/(phip*rp*vpw) + 1/(1 - phip) - (2*g - 2*(1 - 2*phip)*dg - 
     phip*(1 - phip)*ddg); 
S2 = -(1/(phip^2*rp*vpw)) + 1/(1 - phip)^2 - 
    (6*dg - 3*(1 - 2*phip)*ddg - phip*(1 - phip)*dddg); 

p = Apply[{phip, t} /. FindRoot[{S1 == 0, S2 == 0}, {phip, #1}, 
      {t, #2}] & , {{-2, 400}, {3, 800}}, {1}]

{{-1.287340258242967, 414.62463948474493}, 
  {2.6101985365488636, 820.8522532621079}}
 
ContourPlot[{S1 == 0, S2 == 0}, {phip, -2, 3}, {t, 0, 1000}, 
  PlotTheme -> "Detailed", PlotPoints -> 100, 
  Epilog -> {Red, PointSize[Large], Point[p]}]

Contourplot1

In the range near zero there is no crossing. Verify:

ContourPlot[{S1 == 0, S2 == 0}, {phip, -0.2, 0.3}, {t, 0, 20}, 
  PlotTheme -> "Detailed", PlotPoints -> 100]

Contourplot2

A question, how can I insert plots here?

vpw = 3.3; 
Mp = 80; 
rp = 0.014*Mp; 
b0 = 26.31016273 - 1.7168*(10^3/t) - 3.5519*Log[t]; 
b1 = 24.65681838 - 1.547*(10^3/t) - 3.4314*Log[t]; 
b2 = 9.080370819 - 6.9445*(10^2/t) - 1.2222*Log[t]; 
g = b0 + b1*phip + b2*phip^2; 
dg = b1 + 2*b2*phip; 
ddg = 2*b2; 
dddg = 0; 

S1 = 1/(phip*rp*vpw) + 1/(1 - phip) - (2*g - 2*(1 - 2*phip)*dg - 
     phip*(1 - phip)*ddg); 
S2 = -(1/(phip^2*rp*vpw)) + 1/(1 - phip)^2 - 
    (6*dg - 3*(1 - 2*phip)*ddg - phip*(1 - phip)*dddg); 

   p = Apply[{phip, t} /. FindRoot[{S1 == 0, S2 == 0}, {phip, #1}, {t, #2}] & , 
   {{-2, 400}, {-0.05, 20}, {3, 800}}, {1}]

{{-1.28734, 414.625}, {-0.0436006, 23.3922}, {2.6102, 820.852}}

ContourPlot[{S1 == 0, S2 == 0}, {phip, -2, 3}, {t, 0, 1000}, 
  PlotTheme -> "Detailed", PlotPoints -> 100, 
  Epilog -> {Red, PointSize[Large], Point[p]}]

Contourplot3

   ContourPlot[{S1 == 0, S2 == 0}, {phip, -0.2, 0.3}, {t, 0, 100}, 
  PlotTheme -> "Detailed", PlotPoints -> 100, 
  Epilog -> {Red, PointSize[Large], Point[p]}]

Contourplot4

A question, how can I insert plots here?

2 added 144 characters in body
source | link
vpw = 3.3; 
Mp = 80; 
rp = 0.014*Mp; 
b0 = 26.31016273 - 1.7168*(10^3/t) - 3.5519*Log[t]; 
b1 = 24.65681838 - 1.547*(10^3/t) - 3.4314*Log[t]; 
b2 = 9.080370819 - 6.9445*(10^2/t) - 1.2222*Log[t]; 
g = b0 + b1*phip + b2*phip^2; 
dg = b1 + 2*b2*phip; 
ddg = 2*b2; 
dddg = 0; 

S1 = 1/(phip*rp*vpw) + 1/(1 - phip) - (2*g - 2*(1 - 2*phip)*dg - 
     phip*(1 - phip)*ddg); 
S2 = -(1/(phip^2*rp*vpw)) + 1/(1 - phip)^2 - 
    (6*dg - 3*(1 - 2*phip)*ddg - phip*(1 - phip)*dddg); 

p = Apply[{phip, t} /. FindRoot[{S1 == 0, S2 == 0}, {phip, #1}, 
      {t, #2}] & , {{-2, 400}, {3, 800}}, {1}]

{{-1.287340258242967, 414.62463948474493}, 
  {2.6101985365488636, 820.8522532621079}}

ContourPlot[{S1 == 0, S2 == 0}, {phip, -2, 3}, {t, 0, 1000}, 
  PlotTheme -> "Detailed", PlotPoints -> 100, 
  Epilog -> {Red, PointSize[Large], Point[p]}]

Contourplot1

In the range near zero there is no crossing. Verify:

ContourPlot[{S1 == 0, S2 == 0}, {phip, -0.2, 0.3}, {t, 0, 20}, 
  PlotTheme -> "Detailed", PlotPoints -> 100]

Contourplot2

A question, how can I insert plots here?

vpw = 3.3; 
Mp = 80; 
rp = 0.014*Mp; 
b0 = 26.31016273 - 1.7168*(10^3/t) - 3.5519*Log[t]; 
b1 = 24.65681838 - 1.547*(10^3/t) - 3.4314*Log[t]; 
b2 = 9.080370819 - 6.9445*(10^2/t) - 1.2222*Log[t]; 
g = b0 + b1*phip + b2*phip^2; 
dg = b1 + 2*b2*phip; 
ddg = 2*b2; 
dddg = 0; 

S1 = 1/(phip*rp*vpw) + 1/(1 - phip) - (2*g - 2*(1 - 2*phip)*dg - 
     phip*(1 - phip)*ddg); 
S2 = -(1/(phip^2*rp*vpw)) + 1/(1 - phip)^2 - 
    (6*dg - 3*(1 - 2*phip)*ddg - phip*(1 - phip)*dddg); 

p = Apply[{phip, t} /. FindRoot[{S1 == 0, S2 == 0}, {phip, #1}, 
      {t, #2}] & , {{-2, 400}, {3, 800}}, {1}]

{{-1.287340258242967, 414.62463948474493}, 
  {2.6101985365488636, 820.8522532621079}}

ContourPlot[{S1 == 0, S2 == 0}, {phip, -2, 3}, {t, 0, 1000}, 
  PlotTheme -> "Detailed", PlotPoints -> 100, 
  Epilog -> {Red, PointSize[Large], Point[p]}]

In the range near zero there is no crossing. Verify:

ContourPlot[{S1 == 0, S2 == 0}, {phip, -0.2, 0.3}, {t, 0, 20}, 
  PlotTheme -> "Detailed", PlotPoints -> 100]

A question, how can I insert plots here?

vpw = 3.3; 
Mp = 80; 
rp = 0.014*Mp; 
b0 = 26.31016273 - 1.7168*(10^3/t) - 3.5519*Log[t]; 
b1 = 24.65681838 - 1.547*(10^3/t) - 3.4314*Log[t]; 
b2 = 9.080370819 - 6.9445*(10^2/t) - 1.2222*Log[t]; 
g = b0 + b1*phip + b2*phip^2; 
dg = b1 + 2*b2*phip; 
ddg = 2*b2; 
dddg = 0; 

S1 = 1/(phip*rp*vpw) + 1/(1 - phip) - (2*g - 2*(1 - 2*phip)*dg - 
     phip*(1 - phip)*ddg); 
S2 = -(1/(phip^2*rp*vpw)) + 1/(1 - phip)^2 - 
    (6*dg - 3*(1 - 2*phip)*ddg - phip*(1 - phip)*dddg); 

p = Apply[{phip, t} /. FindRoot[{S1 == 0, S2 == 0}, {phip, #1}, 
      {t, #2}] & , {{-2, 400}, {3, 800}}, {1}]

{{-1.287340258242967, 414.62463948474493}, 
  {2.6101985365488636, 820.8522532621079}}

ContourPlot[{S1 == 0, S2 == 0}, {phip, -2, 3}, {t, 0, 1000}, 
  PlotTheme -> "Detailed", PlotPoints -> 100, 
  Epilog -> {Red, PointSize[Large], Point[p]}]

Contourplot1

In the range near zero there is no crossing. Verify:

ContourPlot[{S1 == 0, S2 == 0}, {phip, -0.2, 0.3}, {t, 0, 20}, 
  PlotTheme -> "Detailed", PlotPoints -> 100]

Contourplot2

A question, how can I insert plots here?

1
source | link

vpw = 3.3; 
Mp = 80; 
rp = 0.014*Mp; 
b0 = 26.31016273 - 1.7168*(10^3/t) - 3.5519*Log[t]; 
b1 = 24.65681838 - 1.547*(10^3/t) - 3.4314*Log[t]; 
b2 = 9.080370819 - 6.9445*(10^2/t) - 1.2222*Log[t]; 
g = b0 + b1*phip + b2*phip^2; 
dg = b1 + 2*b2*phip; 
ddg = 2*b2; 
dddg = 0; 

S1 = 1/(phip*rp*vpw) + 1/(1 - phip) - (2*g - 2*(1 - 2*phip)*dg - 
     phip*(1 - phip)*ddg); 
S2 = -(1/(phip^2*rp*vpw)) + 1/(1 - phip)^2 - 
    (6*dg - 3*(1 - 2*phip)*ddg - phip*(1 - phip)*dddg); 

p = Apply[{phip, t} /. FindRoot[{S1 == 0, S2 == 0}, {phip, #1}, 
      {t, #2}] & , {{-2, 400}, {3, 800}}, {1}]

{{-1.287340258242967, 414.62463948474493}, 
  {2.6101985365488636, 820.8522532621079}}

ContourPlot[{S1 == 0, S2 == 0}, {phip, -2, 3}, {t, 0, 1000}, 
  PlotTheme -> "Detailed", PlotPoints -> 100, 
  Epilog -> {Red, PointSize[Large], Point[p]}]

In the range near zero there is no crossing. Verify:

ContourPlot[{S1 == 0, S2 == 0}, {phip, -0.2, 0.3}, {t, 0, 20}, 
  PlotTheme -> "Detailed", PlotPoints -> 100]

A question, how can I insert plots here?