Associate Professor, Mathematics
Scholarly Work
Dr. Buchmann is an applied mathematician working in the field of mathematical biology. She studies complex biological systems using mathematical and computational models. Modeling can provide valuable insights when traditional experiments are either too expensive or impossible.
These models often require a wide variety of mathematics and computer science. The mathematics courses at USD that are most relevant to her research are: Math 250 Calculus III, Math 310/311 Applied Math for Science and Engineering I/II, Math 320 Linear Algebra, Math 330 Ordinary Differential Equations, Math 331 Partial Differential Equations, Math 340 Numerical Analysis, and Math 445 Mathematical Modeling.
Dr. Buchmann uses some of the mathematics from these courses to create mechanical models of microorganisms to study their coordinated behavior and interactions with their environment. She has written several papers on mathematical models of bacteria flagella. She models bacteria as rigid, rotating helices immersed in a viscous fluid.
Some questions she is interested in answering are:
· How can machine learning algorithms be used to classify the separation of particles resulting from the rotation of two helices?
· What helical placement would maximize particle mixing between three helices?
· How are vesicles transported by rigid, rotating helices?