Skip to main content

plotting - DensityPlot, ScalingFunctions, and small values



Edit: I figured out I can use Rescale to retrieve the plot as well as get the correct plot legend. I still can't figure out how to rescale the axes from 10^-9 to 1 though...


enter image description here


Original


I'm trying to make a density plot of a 2D potential energy, but mathematica fails to produce the plots. The system is of relevance for nano-technology so everything is in nano scale, I believe this is the source of my problems.


My code looks like


cont = DensityPlot[(c1 + c2 q^2) (1 - Cos[2 Pi (x - c4 q)/a]) + (c5 + c6 q^2) 
(1 - Cos[c7 2 Pi (x)/a]) + c3 q^4, {x, 0, 3*^-9},{q, 0, 1.5*^-10},
PlotPoints -> 200, FrameLabel -> {"x[t]", "q[t]"},
ImageSize -> 400, PlotLegends -> Automatic, ScalingFunctions ->
{{1*^-9 # &, 1*^9 # &}, {1*^-9 # &, 1*^9 # &}, # &}]


it results in something that looks like this


enter image description here


there are two issues with this image:



  1. It has been flatly colored blue, however, the the PlotLegend seems to have picked up the right values (edit: this is solved now, see top)

  2. The axes have not been rescaled by 10^9


I would also like to rescale the potential itself by a factor 10^18, to have values around 1, but I couldn't figure out how to do that, so that's not in the code above.


Any ideas what could have gone wrong and how to fix any of those issues?



For reference, here's the parameter values:


c11 = 4.0*^-20;
c22 = 3.0;

c1 = c11;
c2 = c22;
c3 = 14*^20;
c4 = 7.0;
c5 = 0.5 c11;
c6 = 0.5 c22;

c7 = 1.0;

The density plot looks fine if I scale all constants by some large number. But then the rescaling still doesn't work...




Comments

Popular posts from this blog

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]

plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1....