Return to Answer

deleted 377 characters in body

Source Link

edited Mar 1, 2018 at 18:19

10.9k
1
19
40

ClearAll["Global`*"]
 
\[CapitalLambda] Λ = -30;
u[\[Eta]_]u[η_] := (2*\[Eta]2*η - 2*\[Eta]^32*η^3 + \[Eta]^4η^4) + \[CapitalLambda]Λ/
     6*(\[Eta]η - 3*\[Eta]^23*η^2 + 3*\[Eta]^33*η^3 - \[Eta]^4η^4);
\[Theta]θ = Integrate[u[\[Eta]]*Integrate[u[η]*(1 - u[\[Eta]]u[η]), {\[Eta]η, 0, 1}] // N;
\[Delta]δ = 1/\[Theta];θ;
u[y_] := Piecewise[{{1, 
    y > \[Delta]δ}, {(2*y/\[Delta]δ - 
       2*(y/\[Delta]δ)^3 + (y/\[Delta]δ)^4) + \[CapitalLambda]Λ/
       6*((y/\[Delta]δ) - 3*(y/\[Delta]δ)^2 + 
        3*(y/\[Delta]δ)^3 - (y/\[Delta]δ)^4), True}}]
Assuming[yd \[Element]∈ Reals, 
 FindRoot[Integrate[u[y], {y, 0, yd}], {yd, 1}]]

{yd -> 6.20224*10^-9}

\[CapitalLambda]Λ = -30;
u[\[Eta]_]u[η_] := (2*\[Eta]2*η - 2*\[Eta]^32*η^3 + \[Eta]^4η^4) + \[CapitalLambda]Λ/
     6*(\[Eta]η - 3*\[Eta]^23*η^2 + 3*\[Eta]^33*η^3 - \[Eta]^4η^4);
\[Theta]θ = Integrate[u[\[Eta]]*Integrate[u[η]*(1 - u[\[Eta]]u[η]), {\[Eta]η, 0, 1}] // N;
\[Delta]δ = 1/\[Theta];θ;
u[y_] := Piecewise[{{1, 
    y > \[Delta]δ}, {(2*y/\[Delta]δ - 
       2*(y/\[Delta]δ)^3 + (y/\[Delta]δ)^4) + \[CapitalLambda]Λ/
       6*((y/\[Delta]δ) - 3*(y/\[Delta]δ)^2 + 
        3*(y/\[Delta]δ)^3 - (y/\[Delta]δ)^4), True}}]
Assuming[yd \[Element]∈ Reals, NSolve[Integrate[u[y], {y, 0, yd}], yd]]

{{yd -> 0}, {yd -> 9.01341}}

ClearAll["Global`*"]
 
\[CapitalLambda] = -30;
u[\[Eta]_] := (2*\[Eta] - 2*\[Eta]^3 + \[Eta]^4) + \[CapitalLambda]/
     6*(\[Eta] - 3*\[Eta]^2 + 3*\[Eta]^3 - \[Eta]^4);
\[Theta] = Integrate[u[\[Eta]]*(1 - u[\[Eta]]), {\[Eta], 0, 1}] // N;
\[Delta] = 1/\[Theta];
u[y_] := Piecewise[{{1, 
    y > \[Delta]}, {(2*y/\[Delta] - 
       2*(y/\[Delta])^3 + (y/\[Delta])^4) + \[CapitalLambda]/
       6*((y/\[Delta]) - 3*(y/\[Delta])^2 + 
        3*(y/\[Delta])^3 - (y/\[Delta])^4), True}}]
Assuming[yd \[Element] Reals, 
 FindRoot[Integrate[u[y], {y, 0, yd}], {yd, 1}]]

{yd -> 6.20224*10^-9}

\[CapitalLambda] = -30;
u[\[Eta]_] := (2*\[Eta] - 2*\[Eta]^3 + \[Eta]^4) + \[CapitalLambda]/
     6*(\[Eta] - 3*\[Eta]^2 + 3*\[Eta]^3 - \[Eta]^4);
\[Theta] = Integrate[u[\[Eta]]*(1 - u[\[Eta]]), {\[Eta], 0, 1}] // N;
\[Delta] = 1/\[Theta];
u[y_] := Piecewise[{{1, 
    y > \[Delta]}, {(2*y/\[Delta] - 
       2*(y/\[Delta])^3 + (y/\[Delta])^4) + \[CapitalLambda]/
       6*((y/\[Delta]) - 3*(y/\[Delta])^2 + 
        3*(y/\[Delta])^3 - (y/\[Delta])^4), True}}]
Assuming[yd \[Element] Reals, NSolve[Integrate[u[y], {y, 0, yd}], yd]]

{{yd -> 0}, {yd -> 9.01341}}

ClearAll["Global`*"]
 Λ = -30;
u[η_] := (2*η - 2*η^3 + η^4) + Λ/
     6*(η - 3*η^2 + 3*η^3 - η^4);
θ = Integrate[u[η]*(1 - u[η]), {η, 0, 1}] // N;
δ = 1/θ;
u[y_] := Piecewise[{{1, 
    y > δ}, {(2*y/δ - 
       2*(y/δ)^3 + (y/δ)^4) + Λ/
       6*((y/δ) - 3*(y/δ)^2 + 
        3*(y/δ)^3 - (y/δ)^4), True}}]
Assuming[yd ∈ Reals, 
 FindRoot[Integrate[u[y], {y, 0, yd}], {yd, 1}]]

{yd -> 6.20224*10^-9}

Λ = -30;
u[η_] := (2*η - 2*η^3 + η^4) + Λ/
     6*(η - 3*η^2 + 3*η^3 - η^4);
θ = Integrate[u[η]*(1 - u[η]), {η, 0, 1}] // N;
δ = 1/θ;
u[y_] := Piecewise[{{1, 
    y > δ}, {(2*y/δ - 
       2*(y/δ)^3 + (y/δ)^4) + Λ/
       6*((y/δ) - 3*(y/δ)^2 + 
        3*(y/δ)^3 - (y/δ)^4), True}}]
Assuming[yd ∈ Reals, NSolve[Integrate[u[y], {y, 0, yd}], yd]]

{{yd -> 0}, {yd -> 9.01341}}

Source Link

created Mar 1, 2018 at 18:11

OkkesDulgerci

10.9k
1
19
40

ClearAll["Global`*"]

\[CapitalLambda] = -30;
u[\[Eta]_] := (2*\[Eta] - 2*\[Eta]^3 + \[Eta]^4) + \[CapitalLambda]/
     6*(\[Eta] - 3*\[Eta]^2 + 3*\[Eta]^3 - \[Eta]^4);
\[Theta] = Integrate[u[\[Eta]]*(1 - u[\[Eta]]), {\[Eta], 0, 1}] // N;
\[Delta] = 1/\[Theta];
u[y_] := Piecewise[{{1, 
    y > \[Delta]}, {(2*y/\[Delta] - 
       2*(y/\[Delta])^3 + (y/\[Delta])^4) + \[CapitalLambda]/
       6*((y/\[Delta]) - 3*(y/\[Delta])^2 + 
        3*(y/\[Delta])^3 - (y/\[Delta])^4), True}}]
Assuming[yd \[Element] Reals, 
 FindRoot[Integrate[u[y], {y, 0, yd}], {yd, 1}]]

{yd -> 6.20224*10^-9}

\[CapitalLambda] = -30;
u[\[Eta]_] := (2*\[Eta] - 2*\[Eta]^3 + \[Eta]^4) + \[CapitalLambda]/
     6*(\[Eta] - 3*\[Eta]^2 + 3*\[Eta]^3 - \[Eta]^4);
\[Theta] = Integrate[u[\[Eta]]*(1 - u[\[Eta]]), {\[Eta], 0, 1}] // N;
\[Delta] = 1/\[Theta];
u[y_] := Piecewise[{{1, 
    y > \[Delta]}, {(2*y/\[Delta] - 
       2*(y/\[Delta])^3 + (y/\[Delta])^4) + \[CapitalLambda]/
       6*((y/\[Delta]) - 3*(y/\[Delta])^2 + 
        3*(y/\[Delta])^3 - (y/\[Delta])^4), True}}]
Assuming[yd \[Element] Reals, NSolve[Integrate[u[y], {y, 0, yd}], yd]]

{{yd -> 0}, {yd -> 9.01341}}