#### Title

Flocks, Digraphs, and Oscillator Arrays

#### Date

11-8-2021 3:00 PM

#### Abstract

A flock is a collective of decentralized, self-propelled agents striving towards altering their motion to adhere to some formation. In this paper, we discuss the mathematical representation of flocks, construct a linear model to approximate their behavior, and study a special case to exhibit a few features of this model. Along the way, we establish connections to the theory of directed graphs, circulant matrices, and control theory.

#### Biographies

**Choomno Moos, Mathematics**

Choomno is an undergraduate student at Portland State University majoring in mathematics. He is a first-generation college student from a low-income family, having been raised by a single immigrant mother. Despite the difficult circumstances of his upbringing, Choomno has managed to achieve great success in his studies. In addition to having elected to take numerous graduate mathematics courses, from 2018 onward he has been researching an application of information theory to crystallographic image processing with Professor Peter Moeck in the Nanocrystallography physics group at Portland State and is now working with Professor J.J.P. Veerman on the dynamics of flocks. In recognition of his achievements, Portland State’s Fariborz Maseeh Department of Mathematics and Statistics has awarded Choomno their competitive David and Laura Brose Memorial and Dave Fitzpatrick departmental scholarships. Throughout the course of his studies, Choomno has accrued an appreciation for the miracle that is the unreasonable effectiveness of mathematics in the sciences (cf. Eugene Wigner). This has motivated a broad interest in mathematics. Among Choomno’s favorite mathematical subjects are dynamical systems, algebraic and geometric topology, functional analysis, and category theory, and he intends to pursue research in at least one of those directions. As such, Choomno plans to start a doctoral program in mathematics in Fall 2022, immediately following the completion of his undergraduate degree. Choomno also has an interest in teaching mathematics and has been working as a mathematics and physics tutor at Portland State’s Learning Center since the Fall of 2019.

**Dr. Peter Veerman, Faculty Mentor, Department of Mathematics **

J. J. P. VEERMAN is Professor of Mathematics and Affiliate Professor of Physics at Portland State University in Oregon, USA. He received his Ph.D. from Cornell University in 1986. After postdocs in Spain (1 year) and at Cornell University/Rockefeller University (2 years), he held visiting positions in the U.S. (Rockefeller University, CUNY, Stony Brook University, Georgia Tech, Penn State), as well as in Spain (Aut ́oma Madrid, Aut ́onoma Barcelona), Brazil (IMPA, PUC-Rio, UFPe). He came to Portland State University in 2000. He has since held visiting positions in Spain (Granada), Italy (Pisa, Salerno), Greece (University of Crete), and Rockefeller University in NYC. In Fall 2000, he was the Gorenstein Professor of Mathematics at CUNY-Queens. Since 2015, he is Scientific Adviser to the International Center for Nonlinear Dynamics and Complex Systems, “Gabriele d’Annunzio” University, Pescara, Italy. More recently, he was offered the (full year) Fulbright-Czech Distinguished Professorship for 2019-2020 at the Czech Technical University in Prague. These awards are viewed as among the most prestigious appointments in the Fulbright Scholar Program. Portland State University policies rendered it impossible to accept this prestigious award.

#### Disciplines

Mathematics

#### Persistent Identifier

https://archives.pdx.edu/ds/psu/36209

Flocks, Digraphs, and Oscillator Arrays

A flock is a collective of decentralized, self-propelled agents striving towards altering their motion to adhere to some formation. In this paper, we discuss the mathematical representation of flocks, construct a linear model to approximate their behavior, and study a special case to exhibit a few features of this model. Along the way, we establish connections to the theory of directed graphs, circulant matrices, and control theory.