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Overlay of two functions leaves gaps
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$begingroup$
I have a function defined as:
$rho_{m}left(epsilon,mright)=left[-2epsilon rpmleft(4epsilon^{2}r^{2}+mlambda r^{3}right)^{frac{1}{2}}right]^{frac{1}{2}}$
I want to plot it for some $min mathbb{Z}$, so I wrote this code:
Clear[r,[Lambda]];
[Lambda]=685*10^-9;
r=25*10^-3;
[Rho]1[[Epsilon]_,m_]=(-2*[Epsilon]*r+(4*[Epsilon]^2*r^2+m*[Lambda]*r^3)^(1/2))^(1/2);
[Rho]2[[Epsilon]_,m_]=(-2*[Epsilon]*r-(4*[Epsilon]^2*r^2+m*[Lambda]*r^3)^(1/2))^(1/2);
M=Range[-5,5,1];
p1=Show[Plot[[Rho]1[[Epsilon]*10^-3,#]*10^3, {[Epsilon],-0.5,0.5}, PlotRange -> {{-0.5,0.5},{0, 5}},AxesOrigin->{-0.5,0},PlotTheme->"Monochrome"] & /@ M];
p2=Show[Plot[[Rho]2[[Epsilon]*10^-3,#]*10^3, {[Epsilon],-0.5,0.5}, PlotRange -> {{-0.5,0.5},{0, 5}},AxesOrigin->{-0.5,0},PlotTheme->"Monochrome"] & /@ M];
Show[{p1,p2}]
Which outputs:
However, there are some tiny gaps where the two functiosn meet, but I was expecting them to be continuous. How can I fix that?
plotting graphics
asked 1 hour ago
RodrigoRodrigo
1056
$endgroup$
add a comment |
$begingroup$
I have a function defined as:
$rho_{m}left(epsilon,mright)=left[-2epsilon rpmleft(4epsilon^{2}r^{2}+mlambda r^{3}right)^{frac{1}{2}}right]^{frac{1}{2}}$
I want to plot it for some $min mathbb{Z}$, so I wrote this code:
Clear[r,[Lambda]];
[Lambda]=685*10^-9;
r=25*10^-3;
[Rho]1[[Epsilon]_,m_]=(-2*[Epsilon]*r+(4*[Epsilon]^2*r^2+m*[Lambda]*r^3)^(1/2))^(1/2);
[Rho]2[[Epsilon]_,m_]=(-2*[Epsilon]*r-(4*[Epsilon]^2*r^2+m*[Lambda]*r^3)^(1/2))^(1/2);
M=Range[-5,5,1];
p1=Show[Plot[[Rho]1[[Epsilon]*10^-3,#]*10^3, {[Epsilon],-0.5,0.5}, PlotRange -> {{-0.5,0.5},{0, 5}},AxesOrigin->{-0.5,0},PlotTheme->"Monochrome"] & /@ M];
p2=Show[Plot[[Rho]2[[Epsilon]*10^-3,#]*10^3, {[Epsilon],-0.5,0.5}, PlotRange -> {{-0.5,0.5},{0, 5}},AxesOrigin->{-0.5,0},PlotTheme->"Monochrome"] & /@ M];
Show[{p1,p2}]
Which outputs:
However, there are some tiny gaps where the two functiosn meet, but I was expecting them to be continuous. How can I fix that?
plotting graphics
asked 1 hour ago
RodrigoRodrigo
1056
$endgroup$
$begingroup$
Adding the option PlotPoints->1000 to both your Plots will make those gaps much less visible.
$endgroup$
– Bill
1 hour ago
$begingroup$
I think that the problem may be that the functions become imaginary at $epsilon = 0$.Plotdoesn't plot anything at all when the value is imaginary. When it happens precisely at the point where they're supposed to meet I guess it becomes a numerical issue, hence whyPlotPointsmay help.
$endgroup$
– C. E.
57 mins ago
add a comment |
$begingroup$
I have a function defined as:
$rho_{m}left(epsilon,mright)=left[-2epsilon rpmleft(4epsilon^{2}r^{2}+mlambda r^{3}right)^{frac{1}{2}}right]^{frac{1}{2}}$
I want to plot it for some $min mathbb{Z}$, so I wrote this code:
Clear[r,[Lambda]];
[Lambda]=685*10^-9;
r=25*10^-3;
[Rho]1[[Epsilon]_,m_]=(-2*[Epsilon]*r+(4*[Epsilon]^2*r^2+m*[Lambda]*r^3)^(1/2))^(1/2);
[Rho]2[[Epsilon]_,m_]=(-2*[Epsilon]*r-(4*[Epsilon]^2*r^2+m*[Lambda]*r^3)^(1/2))^(1/2);
M=Range[-5,5,1];
p1=Show[Plot[[Rho]1[[Epsilon]*10^-3,#]*10^3, {[Epsilon],-0.5,0.5}, PlotRange -> {{-0.5,0.5},{0, 5}},AxesOrigin->{-0.5,0},PlotTheme->"Monochrome"] & /@ M];
p2=Show[Plot[[Rho]2[[Epsilon]*10^-3,#]*10^3, {[Epsilon],-0.5,0.5}, PlotRange -> {{-0.5,0.5},{0, 5}},AxesOrigin->{-0.5,0},PlotTheme->"Monochrome"] & /@ M];
Show[{p1,p2}]
Which outputs:
However, there are some tiny gaps where the two functiosn meet, but I was expecting them to be continuous. How can I fix that?
plotting graphics
asked 1 hour ago
RodrigoRodrigo
1056
$endgroup$
I have a function defined as:
$rho_{m}left(epsilon,mright)=left[-2epsilon rpmleft(4epsilon^{2}r^{2}+mlambda r^{3}right)^{frac{1}{2}}right]^{frac{1}{2}}$
I want to plot it for some $min mathbb{Z}$, so I wrote this code:
Clear[r,[Lambda]];
[Lambda]=685*10^-9;
r=25*10^-3;
[Rho]1[[Epsilon]_,m_]=(-2*[Epsilon]*r+(4*[Epsilon]^2*r^2+m*[Lambda]*r^3)^(1/2))^(1/2);
[Rho]2[[Epsilon]_,m_]=(-2*[Epsilon]*r-(4*[Epsilon]^2*r^2+m*[Lambda]*r^3)^(1/2))^(1/2);
M=Range[-5,5,1];
p1=Show[Plot[[Rho]1[[Epsilon]*10^-3,#]*10^3, {[Epsilon],-0.5,0.5}, PlotRange -> {{-0.5,0.5},{0, 5}},AxesOrigin->{-0.5,0},PlotTheme->"Monochrome"] & /@ M];
p2=Show[Plot[[Rho]2[[Epsilon]*10^-3,#]*10^3, {[Epsilon],-0.5,0.5}, PlotRange -> {{-0.5,0.5},{0, 5}},AxesOrigin->{-0.5,0},PlotTheme->"Monochrome"] & /@ M];
Show[{p1,p2}]
Which outputs:
However, there are some tiny gaps where the two functiosn meet, but I was expecting them to be continuous. How can I fix that?
plotting graphics
plotting graphics
asked 1 hour ago
RodrigoRodrigo
1056
asked 1 hour ago
RodrigoRodrigo
1056
asked 1 hour ago
RodrigoRodrigo
1056
asked 1 hour ago
RodrigoRodrigo
1056
asked 1 hour ago
RodrigoRodrigo
1056
1056
$begingroup$
Adding the option PlotPoints->1000 to both your Plots will make those gaps much less visible.
$endgroup$
– Bill
1 hour ago
$begingroup$
I think that the problem may be that the functions become imaginary at $epsilon = 0$.Plotdoesn't plot anything at all when the value is imaginary. When it happens precisely at the point where they're supposed to meet I guess it becomes a numerical issue, hence whyPlotPointsmay help.
$endgroup$
– C. E.
57 mins ago
add a comment |
$begingroup$
Adding the option PlotPoints->1000 to both your Plots will make those gaps much less visible.
$endgroup$
– Bill
1 hour ago
$begingroup$
I think that the problem may be that the functions become imaginary at $epsilon = 0$.Plotdoesn't plot anything at all when the value is imaginary. When it happens precisely at the point where they're supposed to meet I guess it becomes a numerical issue, hence whyPlotPointsmay help.
$endgroup$
– C. E.
57 mins ago
$begingroup$
Adding the option PlotPoints->1000 to both your Plots will make those gaps much less visible.
$endgroup$
– Bill
1 hour ago
$begingroup$
Adding the option PlotPoints->1000 to both your Plots will make those gaps much less visible.
$endgroup$
– Bill
1 hour ago
$begingroup$
I think that the problem may be that the functions become imaginary at $epsilon = 0$.
Plot doesn't plot anything at all when the value is imaginary. When it happens precisely at the point where they're supposed to meet I guess it becomes a numerical issue, hence why PlotPoints may help.$endgroup$
– C. E.
57 mins ago
$begingroup$
I think that the problem may be that the functions become imaginary at $epsilon = 0$.
Plot doesn't plot anything at all when the value is imaginary. When it happens precisely at the point where they're supposed to meet I guess it becomes a numerical issue, hence why PlotPoints may help.$endgroup$
– C. E.
57 mins ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
If you turn the equation around and plot $epsilon$ as a function of $rho$, then there are no gaps and no branches:
λ = 685*10^-9;
r = 25*10^-3;
ParametricPlot[Table[10^3 {(m r^3 λ - ρ^4)/(4 r ρ^2), ρ}, {m, -5, 5}],
{ρ, 0, 5*10^-3}, AspectRatio -> 1/GoldenRatio]
answered 1 hour ago
RomanRoman
6,25111132
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
If you turn the equation around and plot $epsilon$ as a function of $rho$, then there are no gaps and no branches:
λ = 685*10^-9;
r = 25*10^-3;
ParametricPlot[Table[10^3 {(m r^3 λ - ρ^4)/(4 r ρ^2), ρ}, {m, -5, 5}],
{ρ, 0, 5*10^-3}, AspectRatio -> 1/GoldenRatio]
answered 1 hour ago
RomanRoman
6,25111132
$endgroup$
add a comment |
$begingroup$
If you turn the equation around and plot $epsilon$ as a function of $rho$, then there are no gaps and no branches:
λ = 685*10^-9;
r = 25*10^-3;
ParametricPlot[Table[10^3 {(m r^3 λ - ρ^4)/(4 r ρ^2), ρ}, {m, -5, 5}],
{ρ, 0, 5*10^-3}, AspectRatio -> 1/GoldenRatio]
answered 1 hour ago
RomanRoman
6,25111132
$endgroup$
add a comment |
$begingroup$
If you turn the equation around and plot $epsilon$ as a function of $rho$, then there are no gaps and no branches:
λ = 685*10^-9;
r = 25*10^-3;
ParametricPlot[Table[10^3 {(m r^3 λ - ρ^4)/(4 r ρ^2), ρ}, {m, -5, 5}],
{ρ, 0, 5*10^-3}, AspectRatio -> 1/GoldenRatio]
answered 1 hour ago
RomanRoman
6,25111132
$endgroup$
If you turn the equation around and plot $epsilon$ as a function of $rho$, then there are no gaps and no branches:
λ = 685*10^-9;
r = 25*10^-3;
ParametricPlot[Table[10^3 {(m r^3 λ - ρ^4)/(4 r ρ^2), ρ}, {m, -5, 5}],
{ρ, 0, 5*10^-3}, AspectRatio -> 1/GoldenRatio]
answered 1 hour ago
RomanRoman
6,25111132
answered 1 hour ago
RomanRoman
6,25111132
answered 1 hour ago
RomanRoman
6,25111132
answered 1 hour ago
RomanRoman
6,25111132
6,25111132
add a comment |
add a comment |
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$begingroup$
Adding the option PlotPoints->1000 to both your Plots will make those gaps much less visible.
$endgroup$
– Bill
1 hour ago
$begingroup$
I think that the problem may be that the functions become imaginary at $epsilon = 0$.
Plotdoesn't plot anything at all when the value is imaginary. When it happens precisely at the point where they're supposed to meet I guess it becomes a numerical issue, hence whyPlotPointsmay help.$endgroup$
– C. E.
57 mins ago