Associate Professor of Mathematics
Rose-Hulman Institute of Technology

an Undergraduate Research Project,
funded by National Science Foundation REU grants
DMS-0352940, DMS-0647121
Rose-Hulman Math REU page
Participants Results Preprints
When baking a drop sugar cookie, one starts with a drop of cookie dough on the cookie sheet. As the dough gets heated, it becomes a liquid and starts to achieves its equilibrium shape. Then as it bakes it solidifies to its final equilibrium shape. See pictures below.

Drop of Cookie Dough
(becoming a liquid)

Cookie Baking
(attaining shape)

Baked Cookie
(cooling to final shape)
Once the cookie is baked, can one recover the shape of the cookie knowing only its wetted surface (the region that it is in contact with the cookie sheet), and properties of the cookie dough (density, stiffness) and the size (volume) of the cookie?
General Modelling Results:
  • (with Hari Ravindran) Fit of Sessile Drop Model to Vanilla Wafers. Model seems to be accurate at least to accuracy of measurement at least for circular vanilla wafers. Question is model accurate for elliptical wafers? Preliminary investigation indicates that model remains accurate. Some investigation on the structure of the level curves.
  • (with Robert Lemke Oliver and Yvette Monachino) Investigation of the Location of the Maximum of a Linearized Cookie. Question: Given a domain U, where in the domain is maximum height of the cookie located. The study is on a linearized version of a sessile drop, i.e. a variant of Laplace's equation. The location of the maximum is determined by various methods.
  • (with Erik Perkins) Formulation of Cooling Model. Modelling a cookie as an elastic body, this invesitgation proposes a modification of the Navier equations for the cooling of a cookie. The deformation of the elastic body is driven by the heat equation by coupling the thermal properties of the elasticity to the temperature of the cookie and using heat to determine the interior pressure of the gas bubbles supporting the cookie.
  • (with the 2007 REU group) Use Capillary Surface to Model the Shape of French Bread as example of a 1-D cookie. The model is at least as accurate as an elliptical fit of data from slices of bread.
  • (with Matt Lundy and Kyla Quillin) Investigation of Structure of Periodic Bread Shapes An investigation into periodic capillary shapes under gravity.
Elliptical Cookies
  • (with Emma Norborthen) Level Curves of Elliptical Cookies Determine whether level curves of elliptical sessile drops are ellipses. They are not exactly ellipses. This is accomplished by direct calculation using Frobenius expansion of the solution as solution to system of ODEs and symmetry of an elliptical sessile drop. The solution of the ODE is shown to be close to a solution of the PDE by numerical results lending evidence that the solution is close to elliptical.
  • (with Meredith Perrie) Oval Cookies Determine whether level curves of elliptical sessile drops are ellipses. Alternate approach. Look at Frobenius-Fourier expansion of solution to the PDE in general. Numerical and algebraic approach to show how close level curves are to ellipses. They are close to ellipses if not exactly ellipses.
  • (with Brian Shourd) Turnover Points for Elliptic Cookies Determine whether the first points where horizontal normal lines appear (vertical tangent planes) are along the minor axis of the ellipse. Corresponding this means the highest turnover point is on the minor axis.
Double Bubble Cookies
  • (with Blake Hartz) Investigation into the Structure of a Double Bubble Cookie. Is a cookie obtained by two cookies running together modelled by a sessile drop. No. The interaction at the crease where they run together is not accounted for by a sessile drop. This is also a first look at non-convex domains and the double bubble type cookie. Results on the structure of the solution are obtained, mostly topological in terms of whether the maximum is obtained along the crease or in the middle.
  • (with Matt Donahue and Pam Welch) Further Investigation into the Structure of a Double Bubble Cookie. Introduction of a crease energy and the effect of the crease energy on the crease. Numerical results and conjectures on different aspects of the model.
  • (with Mark Pengitore) Investigation of Triple Bubble Symmetric Cookies Qualitative investigation of the shape of symmetric triple bubble cookies.

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