Research
I am interested in the mathematical modeling of physics relevant to the ocean.
I am focused on the ocean submesoscale, where wave and balanced motion coexist and interact nonlinearly.
I am excited about many mathematical tools: stochastic methods, asymptotic analysis, and statistical inference. Numerically solving equations also plays an important part in my work.
Presentations:
Next-order balanced model captures submesoscale physics and statistics (talk),
at AGU Ocean Sciences Meeting (OSM), February 2024.
SQG+1 as a Model for Submesoscale Asymmetry (Poster),
at FilaChange 2022, August 2022 (funded by the conference travel grant).
Domain dependence of wave turbulence theory for the Majda-McLaughlin-Tabak (MMT) model (Poster),
at the 23rd Conference on Atmospheric and Oceanic Fluid Dynamics (AOFD23), June 2022;
and the 2022 Gordon Conference: Ocean Mixing, June 2022 (partially funded by the conference).
Modeling Systems of Drop Carrier Particles Through Energy Minimization (Poster),
at the 72nd Annual Meeting of the Division of Fluid Dynamics (APS DFD), Nov 2019.
Presenting at Ocean Sciences meeting 2024
Writings:
(the PDFs of the papers/preprints are available in my Zotero Profile)
In preparation:
Dù, R.S., Smith K.S., Bühler, O., 2024. Next-order balanced model captures submesoscale physics and statistics. In preparation for Journal of Physical Oceanography.
Peer reviewed:
Dù, R.S., Bühler, O., 2023. The Impact of Frequency Bandwidth on a One-Dimensional Model for Dispersive Wave Turbulence. J Nonlinear Sci 33, 81. [doi][pdf]
Du, R.S., Liu, L., Ng, S., Sambandam, S., Hernandez Adame, B., Perez, H., Ha, K., Falcon, C., de Rutte, J., Di Carlo, D., Bertozzi, A.L., 2021. Statistical energy minimization theory for systems of drop-carrier particles. Phys. Rev. E 104, 015109. [doi][pdf]
Reports:
Lindstrom, M.R., Du, R.S., Ng, X.Y., Diaz, D., Koulikova, M., Nero, M., Ross, H., Shukla, S., Bertozzi, A., Brantingham, P.J., 2019. Using local geographic features to predict changes in the Los Angeles homeless population. UCLA CAM Report 19-62. [ftp]
Unrefereed short notes:
These are short notes that I think are useful to share but will not become articles.
Dù, R.S., 2023. Learning the Evolution of Statistical Moments and Extreme Values from Data. [pdf]
This note presents an easy way to diagnose the change in statistical moments and extremes from time-series data. It is simple to implement and versatile. We think it is most useful as a tool to quickly explore the time evolution of interesting quantities in data.
Dù, R.S., 2023. Plotting and Fitting Power-Laws. [pdf]
Data following power-laws are ubiquitous in applied fields. In this note, we examine how one should diagnose the power-law exponent from data and how one should plot these data. One of our conclusion is that: linear regression on the log-log form of the data is not always appropriate.