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
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).
Scientific Publications
Paper 1, accepted to Small (stay tuned!)
Talks/Presentations
- 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.
Conferences Attended
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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
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.
