Overlay of two functions leaves gaps












2












$begingroup$


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:



enter image description here



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







share|improve this question









$endgroup$












  • $begingroup$
    Adding the option PlotPoints->1000 to both your Plots will make those gaps much less visible.
    $endgroup$
    – Bill
    7 hours 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.
    7 hours ago
















2












$begingroup$


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:



enter image description here



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







share|improve this question









$endgroup$












  • $begingroup$
    Adding the option PlotPoints->1000 to both your Plots will make those gaps much less visible.
    $endgroup$
    – Bill
    7 hours 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.
    7 hours ago














2












2








2





$begingroup$


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:



enter image description here



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







share|improve this question









$endgroup$




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:



enter image description here



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






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked 8 hours ago









RodrigoRodrigo

1056




1056












  • $begingroup$
    Adding the option PlotPoints->1000 to both your Plots will make those gaps much less visible.
    $endgroup$
    – Bill
    7 hours 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.
    7 hours ago


















  • $begingroup$
    Adding the option PlotPoints->1000 to both your Plots will make those gaps much less visible.
    $endgroup$
    – Bill
    7 hours 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.
    7 hours ago
















$begingroup$
Adding the option PlotPoints->1000 to both your Plots will make those gaps much less visible.
$endgroup$
– Bill
7 hours ago




$begingroup$
Adding the option PlotPoints->1000 to both your Plots will make those gaps much less visible.
$endgroup$
– Bill
7 hours 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.
7 hours 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.
7 hours ago










1 Answer
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oldest

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5












$begingroup$

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]


enter image description here






share|improve this answer









$endgroup$














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    1 Answer
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    active

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    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    5












    $begingroup$

    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]


    enter image description here






    share|improve this answer









    $endgroup$


















      5












      $begingroup$

      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]


      enter image description here






      share|improve this answer









      $endgroup$
















        5












        5








        5





        $begingroup$

        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]


        enter image description here






        share|improve this answer









        $endgroup$



        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]


        enter image description here







        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 7 hours ago









        RomanRoman

        6,29611132




        6,29611132






























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