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!
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.
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.
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.
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.
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).
Paper 1, accepted to Small (stay tuned!)
- Invariance as Information: Exploiting Symmetries in Mathematical Models, SiGMA Seminar, November 2018.
- Manipulating Colloidal Particle Dynamics in Microfluidic Channels with Particle-Obstacle Interactions, Cornell Fluids Seminar, February 2018.
- Open Problems in Theoretical Mechanics: A Bird’s Eye View, SiGMA Seminar, October 2017.
- Microscale Fluid Mechanics: Concepts and Innovations, Summer STEM Colloquium, August 2017.
IUTAM Symposium on Stochastic Approaches to Fluid Flow Transitions, 2018.
Honors and Awards
- 2016, Cornell Sloan Fellowship
- 2015, UPR-Mayagüez Honor Roll (top 5% of class)
- 2010, Rafael Carrión Jr. Academic Excellence Award
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.