Brennon L. Shanks

Postdoctoral Researcher

Energy Frontier Research Center

Biography

I am a statistical thermodynamics researcher that applies molecular dynamics, statistical mechanics, and machine learning to study liquid state materials. My current research projects include developing machine learning approaches for neutron scattering analysis, thermodynamic characterization of high pressure and temperature liquids and liquid metals, and fundamental analysis of many-body interactions from neutron scattering experiments.

This website contains posts, projects, publications, talks, teaching and course materials. I will also occasionally post Jupyter notebooks highlighting useful machine learning techniques as well as derivations of statistical and quantum mechanical relations that are relevant to the investigation of atomic structure and interactions.

Interests

Neutron Scattering
Molecular Dynamics
Statistical Mechanics
Quantum Mechanics
Probabilistic Machine Learning
Gaussian Processes

Education

Ph.D. in Chemical Engineering, 2024
University of Utah
B.E. in Chemical Engineering and Mathematics, 2019
Ohio State University

Posts

The Ornstein-Zernike Equation

Introduction In Ornstein and Zernike’s seminal work, Accidental deviations of density and opalescence at the critical point of a single substance, in: KNAW, Proceedings, 17 II, 1914, pp. 793-806, it was shown that the total correlation between molecules in a statistical mechanical system must obey an integral equation of the form,

Brennon L. Shanks

Last updated on Oct 24, 2024 15 min read

Ohia Lehua Population Model with a Spatial Gaussian Process Classifier

Airborn imaging spectroscopy is a valuable method to characterize the distribution of plant life for ecological, agricultural, and environmental research. In this study, spectroscopy measurements of ‘Ohi’a Lehua, a keystone tree species on the Big Island of Haw’aii, were collected for tree samples at various locations across the island.

Brennon L. Shanks, Megan M. Seeley

Last updated on Oct 24, 2024 6 min read

Thermodynamic Stability Criterion

The thermodynamic requirement that the second derivative of energy be positive gives rise to some interesting results on thermodynamic system stability. To see this, let’s first construct an intrinsic system and a complimentary subsystem from a composite, isolated system.

Brennon L. Shanks

Last updated on Jul 15, 2023 4 min read

The Henderson Inverse Theorem

The Henderson Inverse Theorem is an important result on the relationship between the radial distribution function and pairwise additive potential in a statistical ensemble. This theorem is the basis for the structure-optimized potential refinement algorithm and provides a variational solution to the statistical mechanical inverse problem.

Brennon L. Shanks

Last updated on Dec 29, 2023 4 min read

Kirkwood-Buff Theory of Fluid Thermodynamics

The Kirkwood-Buff solution theory was presented in a landmark paper in 1951. The theory relates particle number fluctuations in the grand canonical ensemble to integrals of the radial distribution function. In this short introduction to the topic, we will introduce the statistical mechanics required to understand Kirkwood-Buff solution theory.

Brennon L. Shanks

Last updated on Jun 13, 2023 7 min read

Projects

Structure Optimized Potential Refinement (SOPR)

Structure-optimized potential refinement (SOPR) is a machine learning assisted iterative Boltzmann inversion method designed to predict accurate and transferable interaction potentials from a provided set of site-site partial radial distribution functions.

Bayesian Force Field Optimization

Structure and self-assembly are complex, emergent properties of matter that are often misrepresented by existing molecular simulation models. In this project, we use Bayesian optimization, an accurate and robust statistical method, to optimize novel force fields based on experimental neutron/X-ray diffraction data to better model the structural behavior of liquid state systems.

Many-Body Effects from Neutron Scattering

Neutron/X-ray diffraction measurements can be utilized to quantify many-body interactions at the same length scale as the interatomic interactions. We use a combination of electron structure theory and structure-optimized potential refinement to directly quantify the influence of third- and higher-order effects for real fluid ensembles.