Editing IVAJ/Level1 (section)

==<font color="#0000DD">Base Workflow</font>==

[[Image:Figure1_Tohline.jpg |border|center|600px|Figure 1.  Screenshots of the window within the VisTrails builder that displays user-designed visualization workflows. (a = left panel) The base workflow we constructed from standard VTK-based modules.  (b = inset panel) A segment of the workflow that's hidden inside the <font face="Courier">Draw_Streamlines</font> group module. (c = right panel) The customized workflow we used to create Figure 2, in which we inserted the <font face="Courier">SwitchCoord</font> module containing our customized Python script into the base workflow.]]
<center>'''Figure 1:''' (scroll over image for caption)</center>

Within [http://www.vistrails.org VisTrails], we initially selected various VTK-based modules to do the following, in sequence (see Figure 1a):
*''Read simulation data.'' We used <font face="Courier">vtkPLOT3DReader</font> to read in one file containing the <math>(x, y, z)</math> coordinate locations of every vertex on our 3D cylindrical coordinate mesh and a separate file containing the fluid's mass-density (scalar) and momentum-density (3D vector) at every grid vertex.
*''Outline cylindrical domain boundary.'' As shown, we enlisted <font face="Courier">vtkStructuredGridOutlineFilter</font>, <font face="Courier">vtkPolyDataMapper</font>, and <font face="Courier">vtkActor</font>.
*''Define isodensity surfaces.'' We rendered two nested isodensity surfaces to outline high- (red) and low-density (blue) flow regions.  The <font face="Courier">Red_contour</font> and <font face="Courier">Blue_contour</font> module groups each contain <font face="Courier">vtkContourFilter</font>, <font face="Courier">vtkDataSetMapper</font>, <font face="Courier">vtkProperty</font>, and <font face="Courier">vtkActor</font>.
*''Draw streamlines.'' As Figure 1b shows, each of the eight separate <font face="Courier">Draw_Streamlines</font> module groups uses <font face="Courier">vtkStreamLine</font>, <font face="Courier">vtkTubeFilter</font>, <font face="Courier">vtkDataSetMapper</font>, <font face="Courier">vtkProperty</font>, <font face="Courier">vtkActor</font>, <font face="Courier">vtkSphereSource</font>, <font face="Courier">vtkPolyDataMapper</font>, and <font face="Courier">vtkLODActor</font> to trace an individual streamline within the flow.  Streamline lengths are set by feeding a common <font face="Courier">Propagation_Time</font> into all eight module groups.

[http://www.vistrails.org VisTrails] renders the output from the various workflow actors in a composite scene using <font face="Courier">vtkRenderer</font> as viewed by an observer located at a position that <font face="Courier">vtkCamera</font> specifies.  Finally, the module <font face="Courier">vtkCell</font> directs this scene to the VisTrails interactive spreadsheet.

In this initially constructed ''base workflow,'' [http://www.vistrails.org VisTrails] pipes the 3D vector field representing the momentum density distribution from the <font face="Courier">vtkPLOT3DReader</font> module directly into each of the eight <font face="Courier">Draw_Streamline</font> module groups.  This base workflow &#8212; which [http://www.vistrails.org VisTrails] assembles using generically available <font face="Courier">vtk</font> modules &#8212; lets us examine the behavior of streamlines in our binary mass-transfer simulations, but only from the frame of reference, <math>\Omega_0</math>, in which we originally performed each simulation (see Figure 2b, labeled <math>\Delta\Omega = 0.00</math>).

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'''<font size="+1"color="darkblue">TERMINOLOGY</font>'''<br>
One well-defined characteristic of a binary star system is it orbital period, <math>P</math>.  If the stars are in circular orbit around one another, a binary system will appear to be stationary when viewed from a frame that's rotating with an angular frequency <math>\Omega_\mathrm{frame} = 2\pi/P</math>.  When modeling mass-transferring binary star systems, we've found it advantageous to perform each computational fluid dynamic (CFD) simulation on a cylindrical-coordinate grid that rotates with a frequency <math>\Omega_0 = 2\pi/P_0</math>, where <math>P_0</math> is the binary system's orbital period at the beginning of the simulation.  As mass and angular momentum are transferred from one star to the other throughout the simulation, however, the binary system's orbital period &#150; and associated value of <math>\Omega_\mathrm{frame}</math> &#150; will vary.  As explained in the main text, we used [http://www.vistrails.org VisTrails] to measure <math>\Delta\Omega = (\Omega_\mathrm{frame} - \Omega_0)</math> and, hence, the instantaneous orbital period <math>P = P_0/(1 + P_0 \Delta\Omega/2\pi)</math> at any time during a simulation.
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