I am a Van Vleck Visiting Assistant Professor at the University of Wisconsin-Madison. I study nonlinear partial differential equations, in particular those arising in the study of fluid dynamics.
Before coming to Madison I completed my PhD under the supervision of 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.
I work on nonlinear partial differential equations. I am particularly interested in the nonlinear stability analysis of viscous surface waves and complex fluids, studying ferrofluids or the effects of surfactants (here's a fun example of what surfactants can allow you to do: 'soap-powered' boat races!)
I am also interested in micropolar fluids, which are fluids in which a microstructure is present (typically at the microscopic scale) which impacts the overall dynamics of the fluid. For example, milk, blood, and liquid crystals are all micropolar fluids, where the microstructure corresponds to the fat molecules in milk, the hemoglobin in blood, and the constituting molecules of the liquid crystal themselves.
As an undergraduate student I got tangled up with liquid crystals and knotted fields under the supervision of Gareth Alexander. As a graduate student I juggled juggling epsilons and deltas, applying tools from mathematical analysis to questions inspired by the physical sciences. In particular, under the supervision of Ian Tice, I am carried out work on free-boundary problems arising from fluid mechanics and on complex fluids.
- A. Remond-Tiedrez and I. Tice, Anisotropic micropolar fluids subject to a uniform microtorque: the stable case, submitted [ arxiv, pdf ]
- A. Remond-Tiedrez and I. Tice, Anisotropic micropolar fluids subject to a uniform microtorque: the unstable case, to appear in Communications in Mathematical Physics [ arxiv, pdf ]
- Oct. 2020: Instability of an anisotropic micropolar fluid (Analysis and PDE Seminar, University of Southern California)
- May 2020: Instability of an anisotropic micropolar fluid (Online North East PDE and Analysis Seminar (jointly organized by Brown, Carnegie Mellon, Princeton, and Toronto) [slides]
- Dec. 2019: Instability of a non-isotropic micropolar fluid (SIAM Conference on Analysis of Partial Differential Equations, La Quinta) [slides]
- Jul. 2019: The viscous wave problem with generalized surface energies (Equadiff, Leiden) [slides]
- Feb. 2019: Viscous surface waves with generalized surface energies (SIAM Conference on Computational Science and Engineering, Spokane) [slides]
- Apr. 2018: Decay of surface waves (Graduate Student Seminar Mini-Conference, Carnegie Mellon University) [slides]
- May 2017: Viscous surface waves and their stability (Summer School on Mathematical Fluids, University of Southern California) [slides]
Fall 2020: The Theory of Single-Variable CalculusThis semester I am teaching MATH 421 which introduces students to mathematical proofs through the lens of calculus.
Office: Van Vleck 607