The guiding principle in our research is simplicity. We are drawn to problems which are so complex that others study them using the most advanced and sophisticated numerical approaches. What we try to do, is find simple analytical solutions for these unwieldy problems. Actually, we often don’t seek to find a solution, just as much of one as possible. For computers are very efficient at finding a solution once they are brought in the close vicinity of a solution. Computers are hugely inefficient at finding a solution if they have little information on where to search for the solution. So, our analysis seeks to provide, if not the full solution, then to provide 50% or even just 10% of the solution so as to allow numerical solutions to start with a good idea as to where to go to find the complete solution. With this partial information as initial condition, numerical schemes are vastly faster. For example, the usual computer routines for finding protein structures may take many days or months. But, with some of our analytical advice, we hope, that this time can be reduced to hours or minutes.

We have applied this basic philosophy of looking for simple analytic solutions to complex problems in the areas of turbulence, many-body problems, slip of liquids over solids, and protein folding.