Mario Juha

A Framework For Studying The RKEM Representation of Discrete Point Sets

The application of engineering analysis to new areas, such as nanomechanics and the life sciences, often involves geometric problem domains defined by discrete point sets as measured from diagnostic equipment. The development of a suitable mesh for finite element analysis can be a tedious task. One approach to simplifying the geometric description is to use a parametrized set of basis functions, and fit the parameters to the data set. In this paper, we discuss the problem of determining suitable parameters for the Reproducing Kernel Element Method representation of discrete point sets, and in particular the solution of the inverse problem of determining pre-image evaluation points in the parametric space that correspond to a given input point. We justify our solution by posing a theoretical framework and an error indicator.

Experimental Approach for Developing and Testing Predictive Self-Assembly Models

Testing methods and apparatus for studying capillary self-assembly processes are presented. This system permits the control of key self-assembly process variables so that relationships between process rates and yields and the process variables can be tested. Part arrival energies and angles are controlled by dropping through a fluid at terminal velocity onto fixed substrate binding sites. Using this system, the assembly probability at the low energy limit is shown to match a simple area fraction relationship.Copyright