CVT_BASIS_TCELL - Flow Solutions in a T-Cell

CVT_BASIS_TCELL is a set of velocity solutions to a flow problem in a T-cell, used by the CVT_BASIS program.

The "T-Cell" region is a channel open to the left and right, with a rectangular recess in the bottom:

        ----------------------
     -->                      -->
     -->                      -->
     -->                      -->
        -----+          +-----
             |          |
             |          |
             +----------+

Specifically, a partial differential equation (PDE) has been defined, specifying the time dependent flow of a fluid through a region. The PDE specification includes a parameter ALPHA whose value strongly affects the behavior of the flow. The steady state solution S0 is computed for a particular value of ALPHA. Then the time dependent problem is solved over a fixed time interval, with ALPHA varying from time to time. A set of several hundred solutions S(T(I),ALPHA(I)) are saved.

The need is to try to extract from this solution data the typical modes of behavior of the solution. Such a set of modes may then be used as a finite element basis that is highly tuned to the physics of the problem, so that a very small set of basis functions can be used to closely approximate the behavior of the solution over a range of values of ALPHA.

The method of extracting information from the solution data uses a form of K-Means clustering.

The data to be examined is assumed to be stored in a file. The file is assumed to contain a number of records, with each record stored on its own line. Each record, in turn, contains a fixed number of data values that describe a particular gene expression experiment. Each record will be regarded as a point in N dimensional space.

Files you may copy include:

xy.txt, the XY coordinates associated with the nodes.
steady.txt, the steady state solution.

There are 500 files containing solutions of the time-dependent PDE with varying values of the parameter. The solutions are ordered by time step, but no information is supplied about the value of ALPHA at any time.

up001.txt.
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up500.txt.

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Last revised on 20 June 2002.