# Plot 3D doesn't show anything

Good Evening,

I defined a function which is composed of other several functions. Mathematica compiles well but I can't get a plot and I do not understand way.

Can anyone help me with the code and explaining me why nothing is showed on the plot?

f1 = 0.0;
f2 = 0.0;
f3 = -9.0; (*fN*)
T = 300;(*K*)
ν = 1.002; (*(fN*s )/μm^2*)

Subscript[r, 0] = 0.5;(*μm*)
Subscript[r, 2] = 0.8;(*μm*)

Subscript[r, 1] = 0.2;(*μm*)

Subscript[γ, 0] = 6 π ν Subscript[r, 0];
Subscript[γ, 2] = 6 π ν Subscript[r, 2]
Subscript[γ, 1] = 6 π ν Subscript[r, 1]
(* 15.1098 *)
(* 3.77745 *)

ϕ1 = π/3;
ϕ2 = π/4;

V1[Tkin_] := (1/Subscript[γ, 1])[
f2 - f3 (((Tkin - T)/T) Cos[θ] Sin[θ])/(
Subscript[γ, 1]/Subscript[γ,
0] + ((Tkin - T)/T) (Sin[θ])^2)];
V2[Tkin_] := (1/Subscript[γ, 2])[
f2 - f3 (((Tkin - T)/T) Cos[θ] Sin[θ])/(
Subscript[γ, 2]/Subscript[γ,
0] + ((Tkin - T)/T) (Sin[θ])^2)];

V11 = V1[Tkin1]; (* Velocity of the 1st particle in protocol 1*)
V21 =
V2[Tkin1]; (* Velocity of the 2nd particle in protocol 1*)

V12 = V1[Tkin2]; (* Velocity of the 1st particle in protocol 2*)

V22 = V2[Tkin2]; (* Velocity of the 2nd particle in protocol 2*)

VA[Tkin1_,
Tkin2_, ϕ1_, ϕ2_] := {{V11 Sin[ϕ1] -
V12 Sin[ϕ2], V11 Cos[ϕ1] + V12 Cos[ϕ2]}};
VB[Tkin1_,
Tkin2_, ϕ1_, ϕ2_] := {{V21 Sin[ϕ1] -
V22 Sin[ϕ2], V21 Cos[ϕ1] - V22 Cos[ϕ2]}};

VAA = VA[Tkin1, Tkin2, ϕ1, ϕ2];
VBB = VB[Tkin1, Tkin2, ϕ1, ϕ2];

delta[Tkin1_, Tkin2_] =
ArcCos[VAA.Transpose[VBB]/(Norm[VAA] Norm[VBB])];
Plot3D[delta, {Tkin1, 300, 1000}, {Tkin2, 300, 1000},
AxesLabel -> {"Tkin1", "Tkin2", "γ"},
ColorFunction -> "BrownCyanTones", PlotRange -> Automatic]

• You should avoid using Subscript while defining symbols (variables). Subscript[x, 1] is not a symbol, but a compound expression where Subscript is an operator without built-in meaning. You expect to do $x_1=2$ but you are actually doing Set[Subscript[x, 1], 2] which is to assign a Downvalue to the oprator Subscript and not an Ownvalue to an indexed x as you may intend. Read how to properly define indexed variables here May 25, 2017 at 17:44
• There are many errors in your code. You should start by testing something simpler first. if delta is a function, then it should be called with parameters. [theta] is not defined May 25, 2017 at 17:49
• To expand on rherman's comment. Mathematica is a front end for a programming language. You shouldn't be trying to make everything pretty when you don't know how to do it safely. γ1 is just as useful as Subscript[γ, 1] May 25, 2017 at 17:50

The code does not run properly due many simple issues. First, we cannot use brackets and braces in the function definitions because Mathematica will comprehend differently from conventional math. Secondly, the functions V11,V12,V21 and V22 can be neglected and just use V1 and V2 with the proper Tkin variable. The functions VAA and VBB can be erased because VA and VB have the same definition. Ultimately, the angle $\theta$ needs a value.

f1 = 0.0;
f2 = 0.0;
f3 = -9.0;       (*fN*)
T = 300;         (*K*)
\[Nu] = 1.002;   (*(fN*s)/\[Mu]m^2*)

r = 0.5;      (*\[Mu]m*)
r = 0.2;      (*\[Mu]m*)
r = 0.8;      (*\[Mu]m*)

\[Gamma] = 6 \[Pi] \[Nu] r;
\[Gamma] = 6 \[Pi] \[Nu] r;
\[Gamma] = 6 \[Pi] \[Nu] r;

(*15.1098*)
(*3.77745*)

\[Theta] = 3.14;

V1[x_] := (1/\[Gamma]) (f2 -
f3 (((x - T)/T) Cos[\[Theta]] Sin[\[Theta]])/(\[Gamma][
1]/\[Gamma] + ((x - T)/T) (Sin[\[Theta]])^2));
V2[y_] := (1/\[Gamma]) (f2 -
f3 (((y - T)/T) Cos[\[Theta]] Sin[\[Theta]])/(\[Gamma][
2]/\[Gamma] + ((y - T)/T) (Sin[\[Theta]])^2));

VA[Tkin1_,
Tkin2_, \[Phi]1_, \[Phi]2_] := {{V1[Tkin1] Sin[\[Phi]1] -
V1 [Tkin2] Sin[\[Phi]2],
V1[Tkin1] Cos[\[Phi]1] + V1[Tkin2] Cos[\[Phi]2]}};
VB[Tkin1_,
Tkin2_, \[Phi]1_, \[Phi]2_] := {{V2[Tkin1] Sin[\[Phi]1] -
V2[Tkin2] Sin[\[Phi]2],
V2[Tkin1] Cos[\[Phi]1] - V2[Tkin2] Cos[\[Phi]2]}};

delta[Tkin1_, Tkin2_, \[Phi]1_, \[Phi]2_] :=
ArcCos[(VA[Tkin1, Tkin2, \[Phi]1, \[Phi]2].Transpose[
VB[Tkin1, Tkin2, \[Phi]1, \[Phi]2]])/(Norm[
VA[Tkin1, Tkin2, \[Phi]1, \[Phi]2]] Norm[
VB[Tkin1, Tkin2, \[Phi]1, \[Phi]2]])];

\[Phi]1 = \[Pi]/3;
\[Phi]2 = \[Pi]/4;

Plot3D[delta[Tkin1, Tkin2, \[Phi]1, \[Phi]2], {Tkin1, 300,
1000}, {Tkin2, 300, 1000},
AxesLabel -> {"Tkin1", "Tkin2", "\[Gamma]"},
ColorFunction -> "BrownCyanTones", PlotRange -> Automatic]


The plot of the angle $\Delta$ will be Surely this code can be improved in order to get a more elegant and fine working algorithm.