The Kinematic Match

We are all happy calculating the trajectory of an object in free-fall. But how do we actually solve what happens just after that, during an inelastic collision?. The interactions involved are highly nonlinear and oftentimes the colliding objects are free to deform as they are in contact.

This problem is relevant because it has plenty of applications, from soft robots, to gear teeth and even astrophysics. In general, you have a PDE under and some nonlinear constraints that represents the problem. The KM sets a new constraint on the contacting surface by imposing that the angle of incidence between the two objects is smooth. It has the advantage of introducing an intuitive idea (easy to code = can be quickly implemented in industrial setups), while enhancing accuracy. This framework is agnostic to the technique used to approximate the PDE, so it can be implemented using a finite difference scheme, or finite elements, or even a variational method. We have successfully implemented the KM for the case of a rigid sphere impacting against an elastic membrane, and are currently working on other cases, most notably a deformable droplet impacting different surfaces -either rigid or not.

Foundational Spintronics Experiments

It is known that current electronics will become unfeasible as devices (transistors, among others) further decrease in size. State-of-the-art computer chips have around 100 billion transistors, accompanied by significant heat generation, while the quantum limit is on the horizon. In this scenario, Spintronics emerges as a proposal. Unlike traditional electronics, Spintronics considers not only the charge of electrons but also their spin. The generation, manipulation, and detection of spin currents have gathered great interest academically and industrially due to minimal thermal dissipation in current propagation and, consequently, information.

Under the guidance of Flávio Garcia and Luiz Sampaio (and their amazing lab members) at the Brazilian Center for Research in Physics, we investigated which materials are suitable to generate spin currents. We grew thin bilayer films of permalloys together with different pure elements, and using ferromagnetic resonance, we measured their energy dissipation in the form of angular momentum. As the theory of magnetic susceptibility predicts, this dissipation is proportional to the damping mechanism in the LLG equation. Finally, we employed the inverse spin hall effect as an experimental means to measure the amount of angular momenta in the form of coherent spin current. A final report paper is available here.

Promoting Science Olympiads

Science Olympiads have reshaped the way I see the world. Through OMAPA, an NGO that invested in Science Olympiads when I was in high school, I was lucky enough to receive proper training and have another chance in life. Several years have passed, now I'm ready to start a PhD and extremely enthusiastic to share with others what I've received. Since 2019, I mentor brilliant students at "Jovenes Talentos", a program that introduces students to critical thinking and college-level math topics. If you are enthusiastic and have initiatives in mind to promote these kinds of projects, contact me!

If you ever wondered how to approach a new, challenging problem, Polya's four steps are always a safe pick to enhance your problem-solving habilities

Mathura³

Paraguay has a mediocre mean years of schooling when compared to other countries. To mitigate this, Paraguay's government offers full-tuition scholarships to pursue undergraduate degrees in our country for high-school students. In order to qualify, students must met a minimum score in math and literature tests taken nationwide. However, high-schoolers systematically fail to get the bare minimum to qualify for this scholarship, and sometimes hundreds of scholarships don't get awarded because of this. There's obviously a systematic flaw causing this issue. However, it's such a pity that all these scholarships never get awarded because most of these students come from underserved contexts.

Mathura is a regional initiative founded by a long friend of mine. We gave free Math and Literature classes to these students to mitigate the aforementioned issue.

ReAcción

ReAcción aims to catalize community innovation against corruption using civic education, collective construction, strategic communication, and social technology to promote transparency and good governance, especially in the education sector.

You probably agree with me that transactions made by the government must be tractable and transparent. There are guidelines to achieve this goal, given by the Open Contracting Data Standards.

Up until a couple of years, Paraguay had little to no infrasctructure on this matter. Public contracts were mainly scanned and their metadata were unavailable to the public.

We analyzed hundreds of contracts before the digitalization to show our government that there was demand for transparency among civil society. After the first steps towards digitalization were taken, I authored a simple Google Scripts project that extracted the metadata of all public contracts in the period 2012-2019. From that data, a couple of articles were written.

Project Euler

I'll back Evan Chen on this one. Please learn to code. Project Euler is not the best resource to learn coding from first principles, but rather to spark your curiosity into algorithmic thinking. Here's a cool problem to think about:

How many numbers of the form 2n²-1 are primes, for 1≤n≤50000000?.