# Tag Info

2

To plot the solution for a range of delc, make these changes to your code: (1) Remove delc = 1; Leave delc undefined. It will be your parameter. (2) Keep the ParametricDSolveValue command and its first argument, but change the other arguments to get s = ParametricNDSolveValue[ ... , {1/2*(V11[t] + V22[t] - 2*V12[t])^(-1)}, {t, 0, 100}, delc]; ...

2

The output of Solve (stored in sol) gives more than one solution (actually, there are 9 possible solutions): sol = Solve[((I*(del + gamma*Abs[a1]^2) - k/2) a1 - (ke/2) a2 + Sqrt[ke] s == 0) && ((I*(del + gamma*Abs[a2]^2) - k/2) a2 - (ke/2) a1 + Sqrt[ke] s == 0), {a1, a2}]; Length@% 9 You can plot them individually: n = 1; ...

1

Here is method for examining the relationship between P, T and G as functions of r. First we find the functions. Clear[P, T, G] {P[r_], T[r_], G[r_]} = Solve[ {P == T/r - 1/(2 π r^2) + 2/(π r^4), T == 1/(4 π r) + 2 P r - 1/(4 π r^3), G == r/4 - (2 Pi P r^3)/3 + 3/(4 r)}, {P, T, G}][[1, All, 2]] Then we make an interactive plot of the ...

0

ClearAll[T, P, G, t, p, g] t = 1/(4 Pi r) + 2 P r - 1/(4 Pi r^3); p = T/r - 1/(2 Pi r^2) + 2/(Pi r^4); g = r/4 - (2 Pi P r^3)/3 + 3/(4 r); func = {G, p, T} /. Solve[Eliminate[{T == t, P == p, G == g}, P], {G, T}, Reals][[1]]; {(23 + r^2)/(12 r), 2/(π r^4) - 1/(2 π r^2) + (-15 + 3 r^2)/( 4 π r^4), (-15 + 3 r^2)/(4 π r^3)} Quiet @ ...

1

ParametricPlot3D[{{s, 0, Sin[s]}, {0, s, Sin[s]}, {s, s, Sin[s]}}, {s, 0, 4 Pi}, PlotStyle -> Tube[.07], ImageSize -> Large]

0

axes[x_, y_, z_, f_, a_] := Graphics3D[ Join[{Red, Arrowheads[a]}, Arrow[Tube[{{0, 0, 0}, #}]] & /@ {{x, 0, 0}, {0, y, 0}, {0, 0, z}}, {Text[ Style["x", FontSize -> Scaled[f]], {0.9*x, 0.1*y, 0.1*z}], Text[Style["y", FontSize -> Scaled[f]], {0.1 x, 0.9*y, 0.1*z}], Text[Style["z", FontSize -> Scaled[f]], {0.1*x, 0.1*...

4

With little modifications it seems to wotk: s = ParametricNDSolveValue[{Derivative[2][y][x] + (a + b*(2 + (2/Pi)*ArcTan[x]))*y[x] == 0, y[-10] == Exp[I*10*Sqrt[a + b]], Derivative[1][y][-10] == (-I)*Sqrt[a + b]*Exp[I*10*Sqrt[a + b]]}, y, {x, -10, 10}, {a, b}] u = ParametricNDSolveValue[{Derivative[2][z][x] + (a + b*(2 + (2/Pi)*ArcTan[x]))*z[x] == 0, z[...

2

Let me give a little example. Since i am working with MMa version 8.0, where ParametricNDSolve is not jet implemented, here a little workaround. Please adapt it to ParametricNDSolve. I add intial conditions and look for minimum, not maximum, here. eqs = {alpha* Derivative[2, 0, 0][x][t, alpha, beta] + y[t, alpha, beta]*Derivative[1, 0, 0][x][t, alpha, ...

3

I think you're going about this in such a way as to make this harder than it is. Polygon represents a closed curve where the final point will connect to the first by default so we can just use that here. No need to add a line or anything. The way this will work is as such, first get a tabular set of your noisy data. I'll do this in a slow way (with lots of ...

3

To expand a little on MarcoB's answer, if you want the plot to extend to the point {0., -1.99877}, you must tweak the plot options appropriately. Like so: With[{γ = 0.172969}, ParametricPlot[{hR[Tan[α], γ], Areac[Tan[α], γ]}, {α, FBc[γ], FAc[γ] - 0.001}, PlotRange -> {{0, 1.2}, {-10, -1}}, PlotRangePadding -> {{.1, Automatic}, Automatic}, ...

4

The point you want corresponds to the very first lowest value of $\alpha$; playing around with the values of your expression shows that very small changes in the value of $\alpha$ in this region translate to huge changes in the abscissa of the parametric points you want plotted. In other words, it is extremely easy for the adaptive internal plotting routines ...

2

This is just to fill out what I already said in a comment to the question. You have made a simple typing mistake. You are omitting two commas from the last two segments that you added in 2nd example. You need commas before 0.41 < t <= 0.49 and 0.49 < t <= 0.53 Here is how plot looks when those commas are inserted: ParametricPlot[ Piecewise[ ...

7

Use Cases to extract the GraphicsComplex from the plot: c1 = RevolutionPlot3D[{t, -1*2 t}, {t, 0, 1}]; gc = Cases[c1, _GraphicsComplex, Infinity]; Now use GeometricTransformation to apply different transformation functions onto the graphics: Graphics3D[ { gc, GeometricTransformation[gc /. _RGBColor :> Red, ReflectionTransform @ {0, ...

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