The Rycroft Group

The Rycroft Group is part of the Department of Mathematics at University of Wisconsin–Madison. 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 six 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!

Prior to summer 2022 the group was located at Harvard University, and some members of the group as still located at Harvard. We collaborate with a wide range of researchers, and we are involved with several collaborative centers such as the Harvard Quantitative Biology Initiative.

We also support teaching a wide range of courses at UW Madison and previously in the Harvard IACS master's program. In particular, from 2014–2021 Chris Rycroft taught and developed Applied Math 205 and Applied Math 225, a year-long graduate course sequence in scientific computing. Many previous and current group members have been involved in providing teaching support for these two courses.
 

Latest news

• October 2022 – Xiaoxiao (Catherine) Ding and Chris Rycroft published a paper in Advanced Materials in collboration with the Bertoldi Group on inverse design of mechanical metamaterials. This paper was featured on the journal cover.
• August 2022 – Our project with the Extavour Lab on modeling the dynamics of nuclei in cricket embryos has been published in Nature Communications. News articles about the work have been published in The Scientist and The New York Times.
• July 2022 – Jovana Andrejevic and Chris Rycroft were finalists in the Nature Awards Science in Shorts competition for their 60 second video on crumpling.
• July 2022 – Danyun He, Nicholas Derr, Yue Sun, and Chris Rycroft attended the SIAM LS22 conference in Pittsburgh and gave talks in the Biological and Bioinspired Fluids and Structures minisymposium.
• July 2022 – The group has moved from the Harvard School of Engineering and Applied Sciences to the Department of Mathematics at the University of Wisconsin–Madison.
• June 2022 – The group had an enjoyable hiking trip based in Bethel, Maine. See photos on Flickr.
• May/April 2022 – Jovana Andrejevic, Nicholas Derr, and Eder Medina successfully defended their Ph.D. theses! We had some in-person celebrations and we also took some group photos following the signature rainbow there. See photos on Flickr.
• April 2022 – Michael Emanuel and Yue Sun successfully passed their Ph.D. qualifying exams.
• April 2022 – Simone Dussi's paper on redox flow battery modeling has been published in the Physics of Fluids and covered on AIP Scilight.
• March 2022 – Jovana Andrejevic, Madelyn Leembruggen, Jiayin Lu, Nicholas Derr, and Changyeob Baek gave talks at the APS March Meeting in Chicago.
• February 2022 – Xiaolin Wang's paper on incorporating rigidity constraints into the reference map technique has been published in the Physics of Fluids.
• February 2022 – Nicholas Derr obtained an instructorship position in the MIT Mathematics Department and will start there in Summer 2022.
• February 2022 – The group has recently submitted several new manuscripts on flow battery modeling, numerical methods for simulating thin sheets, a mathematical analysis of swimming at intermediate Reynolds number, and an undergraduate-focused review of Voronoi cells.
• January 2022 – Chris Rycroft gave a remote talk at Imperial College London on the reference map technique. See associated papers, code, and movies here.
• December 2021 – Our article on three-dimensional simulation using the reference map technique was published in PNAS.
• November 2021 – Chris Rycroft, Yue Sun, and Danyun He attended the APS Division of Fluid Dynamics 2021 meeting in Phoenix, Arizona. We submitted a video to the Gallery of Fluid motion.
• October 2021 – Danyun He successfully passed her Ph.D. qualifying exam.
• August 2021 – Harvard GSAS has published an article about the 2021 Mendelsohn Award winners and an individual profile about Chris Rycroft.
• August 2021 – Luna Lin successfully defended her Ph.D. thesis and will begin a postdoctoral position at the fleXLab at EPFL in November.
• June 2021 – We organized a group outing to New Hampshire to climb Cannon Mountain. By doing this Chris Rycroft completed the 48 New Hampshire four-thousand footers, and has applied to the AMC Four Thousand Footer Club.
• June 2021 – Xiaoxiao (Catherine) Ding and Chris Rycroft are featured in an APS News article about their work on simulating knitted fabrics.
• May 2021 – Chris Rycroft and Jiayin Lu had winning entries in the GSAS Photo Society spring contest, for Spring blossoms, Beacon Hill Dining, The Old Town of Quito, Ecuador, and FishEye Fish.
• May 2021 – Nick Boffi successfully defended his Ph.D. thesis, and Zhao Lyu succesfully defended her master's thesis.
• Apr 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. Additional articles on HowStuffWorks, SEAS News, Popular Mechanics, and Harvard Magazine were published on the work.
• 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.