I have two coupled second-order systems. So the total dimension is four (x,y,z,p). I want to plot the sector fields of any 2 dimensions of them (y,p). Is there any method available in mathematica or elsewhere?
I highly recommend Tecplot. Here are two examples of 4D data (x, y, z, color) sliced in three planes. I have even plotted 5D data (x, y, z, color, size) plus added vector arrows. http://dudleybenton.altervista.org/projects/miscellaneous/cooling_tower_approach.gif http://dudleybenton.altervista.org/projects/miscellaneous/cooling_tower_rating.gif TP2 will also slice data. You can download it free here http://dudleybenton.altervista.org/software/TP2_610.zip I have attached a sliced volume seen from three directions. You can also print it on paper and fold to form a cube.
In Mathematica, if 4-D discrete field can be represented as a list a={{x1,y1,z1,p1},...,{xN,yN,zN,pN}}, then its 2-D section (for example, b={{y1,p1},...,{yN,pN}}) has a form
b = Table[a[[i]][[2 ;; 4 ;; 2]], {i, Length[a]}];
Then ListPlot[b] can be used for visualization.
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