Wolfram Computation Meets Knowledge

Wolfram Summer School


Dominique Djanal-Mann

Summer School

Class of 2015


I was born in Cameroon and raised in Florida, US. I graduated with a BS in electrical engineering from the University of Florida in 2011. I am currently pursuing an MSc in microsystems engineering at the Masdar Institute in Abu Dhabi, UAE, where I am a research assistant in the Nanophotonic and Optoelectronic Laboratory, conducting research on silicon photonic waveguide sensors in the mid IR range. I am increasingly developing an interest, however, in applied mathematics and computer science, particularly different computational paradigms, as well as the physical and theoretical interface between hardware and software. NKS has also caused me to view reality differently, and to envision a theory of everything based on a simple program instead of a simple equation. My other interests include space colonization, resource-based economics, future urbanization, and transhumanism.

Project: Modal Analysis Based on Geometric Classification

Modal analysis is the study of the dynamic properties of structures under vibrational excitation. It has proven to be a highly accurate and versatile method for studying different waveguide structures, with the capability of accounting for multiple reflections within the device, stored energy, and higher-order propagating modes. Traditionally, the finite element method (the computational solution of the interior Helmholtz eigenvalue problem) has been used to obtain mode shapes of an enclosed region, in which continuous quantities are approximated as a set of quantities at discrete points. The scope of my project consists of conducting the modal analysis of different waveguide geometries using the methods described in NKS. I will study the relationship between different waveguide geometries and their modal characteristics.

My methodology will include starting with primitive waveguide geometries in the form of polyominoes and observing the types of modes seen within them. Initially I will begin with two dimensions and determine the lowest mode, with the eventual hope of modelling three-dimensional waveguides. The main question I will try to answer is if it is possible to classify excitations based on a given geometry. This project also has machine learning implications, in which I will also investigate if there are signatures of behavior that allow for the prediction of modes without solving the paraxial Helmholtz equation.

Wolfram Summer School | Champaign, IL, USA | July 3 29–July 22, 2022