Patrick Shipman

Department of Mathematics
Colorado State University


Patrick Shipman

Nanoscale Pattern Formation at Surfaces

Collaborator: Mark Bradley, CSU Department of Physics

Bombarding a solid surface with a broad ion beam can lead to the spontaneous formation of a remarkable variety of self-assembled nanoscale patterns, including periodic height modulations or "ripples," mounds arranged in hexagonal arrays of astonishing regularity, and arrays of sharply pointed conical protrusions.  The emergence of these patterns is fascinating in its own right, but active experimental investigations are aimed at developing ion bombardment as an important tool in the fabrication of nanostructures for a wide range of applications.  Our team has developed a theory that explains the genesis of patterns that form spontaneously when a binary solid is subjected to ion bombardment.  We are investigating defects in these patterns, with the aim of suggesting techniques whereby defects may be minimized.  

Patrick Shipman Diffusion to Capture

Collaborators: Stephen Thompson, CSU Department of Chemistry; Jaime Shinn, Department of Mathematics

We are seeking a universal mathematical description of experiments involving diffusion and nucleation and growth processes that are being performed in The Laboratory for Mathematics in the Sciences.  This includes gas-phase periodic precipitation phenomena and patterns produced by polymer-gas interactions.

Patrick Shipman Phyllotaxis and Growth in Biological Systems

Collaborators: Alan Newell, University of Arizona; Todd Cooke, University of Maryland-College Park

Through mathematical models for the formation of phyllotactic patterns on plants from biochemical and biomechanical mechanisms, we suggest ways to understand both universal aspects of phyllotactic patterns as well as how interacting mechanisms can cooperate or compete to produce the array of phyllotactic lattices and polygonal planforms seen in nature.

Supported by NSF Grant DMS-000000


Invasive Species Spread

Collaborators:  Christopher Strickland, Department of Mathematics; Gerhard Dangelmayr, Department of Mathematics; Sunil Kumar, Natural Resource Ecology Lab; Tom Stohlgren, Natural Resource Ecology Lab

Many scientists now recognize invasive species as the number one environmental threat of the 21st Century. Invasive species pose threats to global ecosystems, including processes, functions, and the life they sustain. The invasion of non-native plants, animals and pathogens has escalated dramatically over the last few decades with the increase of trade, transportation and other elements of globalization.  Impacts include loss of native species and habitat, economic suppression, reduced food and water security, and direct threats to human health.

Our focus species is cheatgrass, which is one of the worst invaders in the western United States.  Cheatgrass has also invaded many parts of the Rocky Mountain National Park (RMNP) and is spreading further into the park. Our team has developed a prototype model, using as a basis data available for the invasive cheatgrass (Bromus tectorum) in RMNP.  We are working to incorporate more available data into the model, and we are in the beginning stages of mathematical analysis of the model to extract information useful for managers at RMNP.

Patrick Shipman Natural Language Vowel Systems

Collaborator: Sergio Faria, Basque Center for Climate Change

We are applying the mathematical framework of continuous diversity to form a model for vowel chain shifts.

Patrick Shipman Orthogonal Coordinate Systems

Collaborator: Barbara Shipman, Department of Mathematics, University of Texas--Arlington

We investigate a Lie-algebraic framework for the Gauss-Mainardi-Codazzi equations governing coordinate systems that are orthogonal with respect to various metrices.

   Other Publications

Past publications include topics in mathematical epidemiology with Henry Tuckwell, Max-Planck-Institute for Mathematics in the Sciences.