Welcome to my webpage! My name is Arnaldo RodriguezGonzalez, 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 byandlarge a theoretician and computational scientist, interested in developing mathematical frameworks to understand “exotic” physical phenomena and then applying these models to solve highimpact problems in engineering. Most of the time, this involves highly complicated systems for which a simplified model of the dominant physics can be determined. Fieldspecific descriptions of my interests are shown below.
Mathematics
Applied Functional Analysis
As the infinitedimensional 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
LowReynolds 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.
NonEquilibrium Statistical Mechanics
Most dynamical systems in nature involve the combination of largescale deterministic mechanisms and smallscale 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 bioanalytical 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 ParticleObstacle 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

IUTAM Symposium on Stochastic Approaches to Fluid Flow Transitions, 2018.
Honors and Awards
 2016, Cornell Sloan Fellowship
 2015, UPRMayagüez 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.