# Research Projects

Research projects focus on the development and enhancement of algorithms, models, and software for applications in multiple domains that require high-performance computing resources.These domains include computational chemistry, biology, astrophysics, mathematics, big data science, and computational electromagnetics.

#### Accelerating Reactive Molecular Dynamics Simulations on Modern Architectures

#### Mentors: H. Metin Aktulga, Yue Qi

The objective of this project is to significantly improve the performance and scalability of reactive molecular dynamics (MD) simulations on massively parallel architectures with hardware accelerators. The proposed efforts will focus on the ReaxFF model and the PuReMD codebase.

Students working in this group must have experience programming in C. Some knowledge of algorithms and data structures will be useful but is not required.

#### Phase Retrieval Algorithms for Molecular Imaging

#### Mentor: Mark Iwen

We will learn about phase retrieval algorithms used by scientists to image complex molecules of interest. Our group will have two focuses: (i) implementing a method for recovering a simple "molecule" from phaseless Fourier measurements, and (ii) proving that it always works given some simplifying assumptions.

Current methods are either very slow, or else are not guaranteed to work in even the simplest settings. We will work to understand how one might develop a better alternative. A fast method that is still guaranteed to work in realistic conditions.

Students should be familiar with undergraduate Fourier analysis, and basic linear algebra. The students working on this project will be interacting with real imaging research at an introductory level. The methods we will be considering require some working knowledge of linear algebra (eigenvalues, and eigenvectors) as well as basic Fourier analysis (discrete Fourier transforms and convolutions). Experience taking an engineering or math course that has introduced each of these topics is strongly recommended.

#### Comparing Methods for Solving Scattering Problems with Non-Local Interactions

#### Mentor: Filomena Nunes

Nuclear reaction is a powerful probe into the properties of unstable nuclei, but the understanding requires a reliable reaction theory. Some reaction theories for direct reactions require the solution of a Schrodinger equation with non-local interactions and scattering boundary conditions.

In our current implementation of the problem, we solve the integral-differential equation by iteration. The goal of the project is to explore other methods of solving the problem and compare the benefits.

#### Simulating Astrophysical Fluid Flow

#### Mentors: Brian O'Shea, Sean Couch

In this project, a team of students will study turbulence and fluid instabilities in fluids that are relevant to a range of astrophysical environments, including supernovae and the intergalactic medium. This will be done by running, analyzing, and visualizing simulations that include fluid dynamics, magnetic fields, and radiation. In addition, over the course of the project students will learn about the numerical methods used in the software packages they use and will write their own fluid dynamics code. [NOTE: This project will be jointly mentored by Prof. Sean Couch and Prof. Brian O'Shea]

Experience with the Unix command line and Python, C, C++, or Fortran are strongly desired.

#### Representing Complex Data with Topology

#### Mentor: Jose Perea

The goal of topology, much like in geometry, is to measure the shape of mathematical objects. The main objective of this project is to learn how topology can be used to probe the shape of complex data sets. Students will develop new tools, and explore real data sets from fields including the biological, social and physical sciences.

Statistics and familiarity with R are highly desirable, but not required.

#### Omics Approaches to Microbiomes

#### Mentor: Ashley Shade

Students will develop bioinformatic skills in microbial metagenomics and other 'omics approaches to probe microbiome dynamics, diversity, and function. Bioinformatics experience is useful but not required.

#### Robust CAD tools for THz Integrated Circuits and Systems

#### Mentors: B. Shanker, Leo Kempel, John Verboncoeur

The electromagnetics research group develops tools specifically geared to THz Monolithic Integrated Circuits (TMIC) analysis and design. By nature, TMICs are broadband and multiscale. As a result, principal difficulties occur on two fronts:(i) Tyranny of scales wherein one needs to find fields in geometrically complex and electrically large structures, and (ii) Inclusion of material properties that are dispersive with complex frequency response,and often non-linear.

To address these challenges, his group will: (i) develop a hierarchical domain decomposition analysis framework that constructs and integrates stable multi-region time domain integral equation based methods with space-time adaptive discontinuous Gelerkin methods, (ii) develop and augment integral equation kernels with broadband accelerators, and (iii) develop tunable parallel algorithms that are architecture independent.

Students applying to this project must have taken coursework in electromagnetics.

High-Order Numerical Methods for Anomalous Transport Phenomena

#### Mentor: Mohsen Zayernouri

Students will examine the performance (accuracy and speed) of several high-order numerical methods in different applications, including

- sub-to-super diffusion problems
- advection-dispersion in porous media
- non-local turbulent mixing flows
- visco-elasto-plastic materials

In each case, students will first learn about the underlying physics in addition to the associated mathematical modelling. Next, they will focus on several existing codes, developed for solving the aforementioned problems, where they might make the necessary changes/modifications in order to run at different regimes/conditions.

#### Predicting Biodiversity Hotspots and Coldspots in Space and Time

##### Mentors: Phoebe Zarnetske, Kyla Dahlin Patricia, Soranno , Kendra Cheruvelil, Andrew Finley, Lifeng Luo

A major challenge for scientists is to generate robust models that describe and predict biodiversity in space and time. With these models, we can identify hotspots (highs) and coldspots (lows) of biodiversity change, which are likely linked with shifts in ecosystem functions and services. Students will have the opportunity to study and forecast the effects of climate change on biodiversity and ecosystem functioning, using a variety of computational tools and spatial analysis. Key aspects of the project include: analyzing “big data” from the NSF National Ecological Observatory Network (NEON) and Global Biodiversity Information Facility (GBIF), learning remote sensing techniques, conducting statistical spatial analysis in R (including species distribution modeling), learning Python and QGIS, and learning to run models on the MSU HPCC.

Prior coursework in biology, ecology, or environmental science is a plus but not required.