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3 added 823 characters in body
source | link

Use ContourPlot.

fs[kappa_] := (1 + 32 kappa^2)/(1 - 
     kappa^2) - (3 kappa^2 ArcTanh[Sqrt[1 - kappa^2]])/(1 - 
      kappa^2)^(3/2)

zero[kappa_, edd_, lambda_] = 
  3 kappa edd (((lambda^2/2) + 1) fs[kappa]/(1 - kappa^2) + (edd - 
  1) + (edd - 1) (kappa^2 - lambda^2);

Show[{ContourPlot[
 Evaluate@Table[zero[kappaEvaluate@
Table[zero[kappa, edd, lambda] == 0, {lambda, 40, 2, 1/3}], {edd, 
0, 1.8}, {kappa, 0, 2}, FrameLabel -> Automatic, 
AspectRatio -> 6/10], 
ContourPlot[edd + 1, {edd, 0, 1.58}, {kappa, 0, 2}, 
FrameLabel -> Automatic, AspectRatio -> 6/10, 
RegionFunction -> Function[{x, y, z}, 1 < x < 2], 
ContourStyle -> {Directive[Lighter[Red, 0.8], Dashed]}, 
Contours -> 100, ContourShading -> None], 
ContourPlot[edd + 1, {edd, 0, 1.8}, {kappa, 0, 2}, 
FrameLabel -> Automatic, AspectRatio -> 6/10, 
RegionFunction -> Function[{x, y, z}, (x - 2)^2 + (y)^2 < 1], 
ContourStyle -> {Directive[Lighter[Blue, 0.7], Dashed]}, 
Contours -> 100, ContourShading -> None]}, 
Epilog -> {Text[unstable, {1.4, 0.5}], Text[metastable, {1.4, 1.5}], 
Text[stable, {0.6, 1.8}]}]

enter image description here

Use ContourPlot.

fs[kappa_] := (1 + 3 kappa^2)/(1 - 
     kappa^2) - (3 kappa^2 ArcTanh[Sqrt[1 - kappa^2]])/(1 - 
      kappa^2)^(3/2)

zero[kappa_, edd_, lambda_] = 
  3 kappa edd ((lambda^2/2) + 1) fs[kappa]/(1 - kappa^2) + (edd - 
      1) (kappa^2 - lambda^2);

ContourPlot[
 Evaluate@Table[zero[kappa, edd, lambda] == 0, {lambda, 4}], {edd, 0, 
  1.5}, {kappa, 0, 2}]

Use ContourPlot.

fs[kappa_] := (1 + 2 kappa^2)/(1 - 
 kappa^2) - (3 kappa^2 ArcTanh[Sqrt[1 - kappa^2]])/(1 - 
  kappa^2)^(3/2)

zero[kappa_, edd_, lambda_] = 
3 kappa edd (((lambda^2/2) + 1) fs[kappa]/(1 - kappa^2) - 
  1) + (edd - 1) (kappa^2 - lambda^2);

Show[{ContourPlot[
Evaluate@
Table[zero[kappa, edd, lambda] == 0, {lambda, 0, 2, 1/3}], {edd, 
0, 1.8}, {kappa, 0, 2}, FrameLabel -> Automatic, 
AspectRatio -> 6/10], 
ContourPlot[edd + 1, {edd, 0, 1.8}, {kappa, 0, 2}, 
FrameLabel -> Automatic, AspectRatio -> 6/10, 
RegionFunction -> Function[{x, y, z}, 1 < x < 2], 
ContourStyle -> {Directive[Lighter[Red, 0.8], Dashed]}, 
Contours -> 100, ContourShading -> None], 
ContourPlot[edd + 1, {edd, 0, 1.8}, {kappa, 0, 2}, 
FrameLabel -> Automatic, AspectRatio -> 6/10, 
RegionFunction -> Function[{x, y, z}, (x - 2)^2 + (y)^2 < 1], 
ContourStyle -> {Directive[Lighter[Blue, 0.7], Dashed]}, 
Contours -> 100, ContourShading -> None]}, 
Epilog -> {Text[unstable, {1.4, 0.5}], Text[metastable, {1.4, 1.5}], 
Text[stable, {0.6, 1.8}]}]

enter image description here

2 deleted 114 characters in body
source | link

Use ContourPlot. That does not reproduce your plot, probably because as you explain, it does not correspond to the same problem.

fs[kappa_] := (1 + 3 kappa^2)/(1 - 
     kappa^2) - (3 kappa^2 ArcTanh[Sqrt[1 - kappa^2]])/(1 - 
      kappa^2)^(3/2)

zero[kappa_, edd_, lambda_] = 
  3 kappa^2kappa edd ((lambda^2/2) + 1) fs[kappa]/(1 - kappa^2) + (edd - 
      1) (kappa^2 - lambda^2);

ContourPlot[
 Evaluate@Table[zero[kappa, edd, lambda] == 0, {lambda, 54}], {edd, 0, 
  1.5}, {kappa, 0, 2}]

Use ContourPlot. That does not reproduce your plot, probably because as you explain, it does not correspond to the same problem.

fs[kappa_] := (1 + 3 kappa^2)/(1 - 
     kappa^2) - (3 kappa^2 ArcTanh[Sqrt[1 - kappa^2]])/(1 - 
      kappa^2)^(3/2)

zero[kappa_, edd_, lambda_] = 
  3 kappa^2 edd ((lambda^2/2) + 1) fs[kappa]/(1 - kappa^2) + (edd - 
      1) (kappa^2 - lambda^2);

ContourPlot[
 Evaluate@Table[zero[kappa, edd, lambda] == 0, {lambda, 5}], {edd, 0, 
  1.5}, {kappa, 0, 2}]

Use ContourPlot.

fs[kappa_] := (1 + 3 kappa^2)/(1 - 
     kappa^2) - (3 kappa^2 ArcTanh[Sqrt[1 - kappa^2]])/(1 - 
      kappa^2)^(3/2)

zero[kappa_, edd_, lambda_] = 
  3 kappa edd ((lambda^2/2) + 1) fs[kappa]/(1 - kappa^2) + (edd - 
      1) (kappa^2 - lambda^2);

ContourPlot[
 Evaluate@Table[zero[kappa, edd, lambda] == 0, {lambda, 4}], {edd, 0, 
  1.5}, {kappa, 0, 2}]
1
source | link

Use ContourPlot. That does not reproduce your plot, probably because as you explain, it does not correspond to the same problem.

fs[kappa_] := (1 + 3 kappa^2)/(1 - 
     kappa^2) - (3 kappa^2 ArcTanh[Sqrt[1 - kappa^2]])/(1 - 
      kappa^2)^(3/2)

zero[kappa_, edd_, lambda_] = 
  3 kappa^2 edd ((lambda^2/2) + 1) fs[kappa]/(1 - kappa^2) + (edd - 
      1) (kappa^2 - lambda^2);

ContourPlot[
 Evaluate@Table[zero[kappa, edd, lambda] == 0, {lambda, 5}], {edd, 0, 
  1.5}, {kappa, 0, 2}]