About me

I am a Simons Research Fellow at the University of Cambridge. I study nonlinear partial differential equations, in particular those arising in the study of fluid dynamics.

Before coming to Cambridge I spent some time as Van Vleck Visiting Assistant Professor at the University of Wisconsin-Madison after completing my PhD working with Ian Tice at Carnegie Mellon University. The beginning of my mathematical history can be traced back to the University of Warwick where I carried out my undergraduate studies.

Research interests

I work on nonlinear partial differential equations. I am particularly interested in free boundary problems, geophysical flows, and complex fluids.

Free boundary problems

Many important physical processes occur at interfaces and they are often challenging to describe mathematically. In particular I am interested in the stability of viscous surface waves (see here), studying ferrofluids or the effects of surfactants (here's a fun example of what surfactants can allow you to do: 'soap-powered' boat races!)

Geophysical flows

Ranging from local weather prediction to long-term climate models, the various scales of interest in geophysical flows require an assorted array of mathematical models. In collaboration with Leslie Smith and Sam Stechmann I am currently working on the role of moisture in atmospheric models, where the incorporation of moisture means additional physical processes to consider as well as the introduction of phase boundaries (such as air-cloud interfaces).

Micropolar fluids

Many everyday fluids, such as milk, blood, or liquid crystals (ubiquitous in the electronic displays that surround us) are so-called "complex fluids". This means that they are fluids in which microstructure is present (typically at the microscopic scale) which impacts the overall behaviour of the fluid. More precisely, in these examples, the microstructure corresponds to the fat molecules in milk, the hemoglobin in blood, and the constituting molecules of the liquid crystal themselves.

For a mathematician-friendly introduction to micropolar fluids (i.e. written in mathematical language rather than engineering parlance), see the first chapter of my doctoral thesis. In joint work with Ian Tice we studied the stability of rod-like and pancake-like microstructure (see here and here).

Publications

To appear

  1. A. Remond-Tiedrez and I. Tice, Anisotropic micropolar fluids subject to a uniform microtorque: the stable case, Analysis & PDE [ arxiv, pdf ]

Published

  1. A. Remond-Tiedrez and I. Tice, Anisotropic micropolar fluids subject to a uniform microtorque: the unstable case, Communications in Mathematical Physics (2021) [ arxiv, journal, pdf ]
  2. A. Remond-Tiedrez and I. Tice, The viscous surface wave problem with generalized surface energies, SIAM Journal on Mathematical Analysis (2019) [ arxiv, journal, pdf ]

Thesis

  1. A. Remond-Tiedrez, Nonlinear partial differential equations in fluid dynamics: interfaces, microstructure, and stability ( pdf ). The first chapter of this thesis is a self-contained introduction to micropolar fluids, including a derivation of their equations of motion.

Talks

  1. May 2022: Carnegie Mellon University, Center for Nonlinear Analysis Seminar (Moist potential vorticity inversion: a nonlinear PDE from atmospheric science with free boundaries) [ slides, recording ]
  2. May 2022: Isaac Newton Institute, Junior Isaac Newton Crossover (JINX) Seminar (Instability of an Anisotropic Micropolar Fluid) [ slides, recording ]
  3. Apr. 2022: Twelfth IMACS International Conference on Nonlinear Evolution Equations, Athens (GA) (Instability of an Anisotropic Micropolar Fluid) [slides]
  4. Mar. 2022: Isaac Newton Institute, programme on the mathematical aspects of turbulence (Moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries) [slides]
  5. Nov. 2021: Texas A&M University, Nonlinear PDE Seminar (Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear elliptic PDE from atmospheric dynamics with free boundaries) [slides]
  6. Oct. 2021: University of Wisconsin-Madison, PDE and Geometric Analysis Seminar (Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear elliptic PDE from atmospheric dynamics with free boundaries) [slides]
  7. May 2021: Ohio River Analysis Meeting, Lexington (Instability of an anisotropic micropolar fluid) [slides]
  8. Feb. 2021: University of Wisconsin-Madison, Applied and Computational Mathematics Seminar (Instability of an anisotropic micropolar fluid) [slides]
  9. Oct. 2020: University of Southern California, Analysis and PDE Seminar (Instability of an anisotropic micropolar fluid) [slides]
  10. May 2020: Online North East PDE and Analysis Seminar (jointly organized by Brown, Carnegie Mellon, Princeton, and Toronto) (Instability of an anisotropic micropolar fluid) [slides]
  11. Dec. 2019: SIAM Conference on Analysis of Partial Differential Equations, La Quinta (Instability of a non-isotropic micropolar fluid) [slides]
  12. Jul. 2019: Equadiff, Leiden (The viscous wave problem with generalized surface energies) [slides]
  13. Feb. 2019: SIAM Conference on Computational Science and Engineering, Spokane (Viscous surface waves with generalized surface energies) [slides]
  14. Apr. 2018: Graduate Student Seminar Mini-Conference, Carnegie Mellon University (Decay of surface waves) [slides]
  15. May 2017: Summer School on Mathematical Fluids, University of Southern California (Viscous surface waves and their stability) [slides]

Mentoring

Fall 2021: Directed Reading Program

  1. The Directed Reading Program pairs undergraduate students with mentors that guide the students through readings on a topic of mutual interest for the duration of a semester. In the fall 2021 I supervised David Kwak reading about the Calculus of Variations, following notes by Peter Olver.

Teaching

Lecture notes from previous courses

  1. Fall 2021, Linear Algebra (notes)
  2. Fall 2020, The Theory of Single-Variable Calculus (notes).

Contact

Email: ar2145-at-cam-dot-ac-dot-uk
Office: Isaac Newton Institute F7