About

Welcome to my webpage! My name is Arnaldo Rodriguez-Gonzalez, and I’m currently a Ph.D. student in Theoretical & Applied Mechanics at Cornell. Here you’ll find a comprehensive listing of my works, scientific or otherwise, along with other assorted miscellanea. Enjoy!

Research Interests

I am by-and-large a theoretician and computational scientist, interested in developing mathematical frameworks to understand “exotic” physical phenomena and then applying these models to solve high-impact problems in engineering. Most of the time, this involves highly complicated systems for which a simplified model of the dominant physics can be determined. Field-specific descriptions of my interests are shown below.

Mathematics

Applied Functional Analysis

As the infinite-dimensional extension of linear algebra, I strive to use functional analysis as a framework to generate approximations, constructive algorithms, & estimates in mathematical systems whose elements are far more abstract than column vectors and whose mappings are more pathological than matrix operations.

Nonlinear Dynamics & Chaos Theory

Particularly in abstract systems, the temporal evolution of quantifiable characteristics of a system will fail to be captured by linear mappings; I seek to understand and manipulate the dynamics of such systems by using the mathematical tools of nonlinear dynamical systems and chaos theory.

Physics

Low-Reynolds Electrohydrodynamics

Whereas most physicists study the intersection of electromagnetism and hydrodynamics at the high Reynolds number limit (plasma physics), I work to discern the dominant physics of electrohydrodynamic systems where the length scales and speeds of the fluid are relatively small—such as in electrolytic solutions.

Non-Equilibrium Statistical Mechanics

Most dynamical systems in nature involve the combination of large-scale deterministic mechanisms and small-scale stochastic processes—I like to explore those processes in which these scales blend together in unexpected ways, causing unexpected dynamical and equilibrium behavior.

Engineering

Micro- and Nanofluidics

The complex interplay between colloidal hydrodynamics, microscale forces, and microfluidic device architectures leads to a bounty of physical phenomena that I can exploit to engineer chemical and bio-analytical microdevices for suspensions with key engineering value (such as cell colonies, atmospheric particulate samples, etc).

Computational Inverse Design

Whether developing a device, a mechanical design, or a chemical solution, I as an engineer strive to obtain general protocols for designing and creating these systems that both adapt to a specific user’s needs and have quantifiable performance guarantees for any possible user specifications.

Scientific Publications

  • Liu, X., Qi, G., Park, A. M. G., Rodriguez‐Gonzalez, A., Enotiadis, A., Pan, W. Y., Kosma, V., Fuchs, G. D., Kirby, B. J., Giannelis, E. P., Scalable Synthesis of Switchable Assemblies of Gold Nanorod Lyotropic Liquid Crystal Nanocomposites. Small 2019, 1901666. https://doi.org/10.1002/smll.201901666
  • Rodriguez‐Gonzalez, A., Gleghorn, J. P., Kirby, B. J., Rational Design Protocols for Size-Based Particle Sorting Microdevices Using Symmetry-Induced Cyclical Dynamics. Submitted to Physical Review E, https://arxiv.org/abs/1911.01201

Talks/Presentations

Conferences Attended

  • 13th International Symposium on Electrokinetics (ELKIN), 2019 (Poster)
  • IUTAM Symposium on Stochastic Approaches to Fluid Flow Transitions, 2018.

Honors and Awards

  • 2019, H. D. Block Teaching Prize
  • 2016, Cornell Sloan Fellowship
  • 2015, UPR-Mayagüez Honor Roll (top 5% of class)
  • 2010, Rafael Carrión Jr. Academic Excellence Award

Education

Ph.D. (Current) Cornell University, theoretical & applied mechanics.

B.S. (2015) University of Puerto Rico at Mayagüez, mechanical engineering (magna cum laude), minor in applied mathematics.