The Rycroft Group

The Rycroft Group is part of the John A. Paulson School of Engineering and Applied Sciences at Harvard University. The group is led by Chris Rycroft and focuses on mathematical modeling and scientific computation, particularly for interdisciplinary applications in science and engineering.

The Rycroft Group works on a wide range of topics. A hallmark of the group's approach is to develop new computational methods while working directly with domain scientists. Three particular focus areas are listed below.

Numerical methods for material mechanics

Many materials of scientific importance are hard to simulate, due to challenges resolving multiple phases or components, disparate timescales, and large deformations. We developed a new numerical method for bulk metallic glasses and used it to predict their failure properties, which were later verified experimentally. We co-developed the reference map technique, a new approach for simulating fluid–structure interaction.

Data-driven discovery

Many scientific fields are increasingly awash in data. We develop new computational approaches for processing data and extracting scientific insight, particularly those that combine traditional analysis and modeling with new machine learning methods. For example, we have a sequence of papers on the physics of crumpling, covering experimental observations, new machine learning approaches, and analysis and modeling.

Computational geometry

Geometry problems appear across many scales, from the arrangements of atoms to the structure of galaxies, and techniques for geometric analysis enter into many group projects. Chris Rycroft developed Voro++, a software library for calculating the Voronoi tessellation. The library is widely used, and the Rycroft Group has used it for problems as diverse as modeling insect wing patterning and finding materials for carbon dioxide capture.

The team

The Rycroft Group currently consists of twelve graduate students, along with postdocs, undergraduates, and sabbatical visitors. Members have a diverse range of backgrounds and have education in applied mathematics, physics, engineering, and computer science. We also like obsessive color coordination!

We collaborate with a wide range of researchers at Harvard and beyond, and we are involved in a several collaborative centers including the Harvard MRSEC and the Quantitative Biology Initiative.

We also support teaching a wide range of courses in the Harvard Applied Mathematics program and in the Harvard IACS master's program. In particular, since 2014 Chris Rycroft has taught and developed Applied Math 205 and Applied Math 225, a year-long graduate course sequence in scientific computing. Many group members have been involved as Teaching Fellows for these two courses.
 

Latest news

• Mar 2021 – Chris Rycroft has received the Everett Mendelsohn Award for Excellence in Mentorship.
• Mar 2021 – Our article on understanding the physics of crumpling has been published in Nature Communications. An story featuring Jovana Andrejevic and Chris Rycroft about the work has published in the New York Times. Jovana was also interviewed by BYU Radio about the project.
• Feb 2021 – Chris Rycroft and Gary Pui-Tung Choi have published a paper on using the reference map technique for creating density-equalized maps in the Journal of Scientific Computing.
• Jan 2021 – Graduate student Nick Boffi was awarded the NSF Postdoctoral Fellowship in Mathematical Sciences. Nick plans to start as position as a Courant Instructor at New York University in Summer 2021.
• Oct 2020 – Our collaborative project with the Mahadevan Group on modeling and simulation of erosion was published in Physical Review Letters.
• Sep 2020 – Chris Rycroft is teaching Applied Math 205 on advanced scientific computing. This is online-only due to the COVID-19 pandemic, and some parts have been redesigned. A sequence of online group activities have been introduced, and a YouTube video sequence was created.
• Sep 2020 – Graduate student Dan Fortunato defended his Ph.D. thesis and will start a postdoctoral fellowship at the Flatiron Institute.
• Sep 2020 – Graduate students Madelyn Leembruggen and Xiaoxiao (Catherine) Ding passed their Ph.D. qualification exams.
• May 2020 – Graduate student Gary Pui-Tung Choi defended his Ph.D. thesis and was awarded the NSF Postdoctoral Fellowship in Mathematical Sciences. He will start as an instructor in the MIT Mathematics Department in Summer 2020.
• April 2020 – Our paper on using the reference map for simulating incompressible fluid–structure interaction was published in the Journal of Fluid Mechanics. Complete source code to reproduce all of the results in this paper is available on GitHub.