Session D47: Undergraduate Research V

Particle Dynamics Through the Earth: A Study of Non-Zero Tunnel Diameters

A standard problem in undergraduate mechanics derives the trajectory of a particle that has been dropped through a gravity tunnel passing through the center of the Earth as simple harmonic oscillation, assuming constant earth density and negligible tunnel diameter. We show that when the more accurate PREM density profile and non-negligible tunnel diameters are taken into consideration, significant deviations from harmonic oscillations are observed along with reduced particle speeds. Furthermore, we report that a particle traveling perpendicular to the axis of the gravity tunnel is unable to reach the center of the earth beyond a critical tunnel diameter of 71.36% of the earth's diameter under a constant density, or 72.36% of the diameter under the PREM density model. When the rotation of the earth is incorporated, the particle trajectories occasionally extend beyond the surface of the earth at large tunnel diameters, owing to tunnel-induced non-uniformity of the earth's potential energy surface. In addition, we numerically calculate the brachistochrones connecting two points on the surface for various tunnel diameters using the PREM density profile. Our results highlight the effect of non-negligible tunnel diameters on the overall potential energy surface and particle dynamics.   

A Study of Composition, Texture and Space Weathering Effects on Asteroid (101955) Bennu

The focus of our work has been asteroid (101955) Bennu, target of NASA’s OSIRIS-REx mission. The first part of our work was creating two-component laboratory simulations of the asteroid surface’s texture and composition. We found a physical model whose composition and texture best fit the near-infrared spectrum of the asteroid, as observed from the spacecraft: a dry mixture of 90% saponite (SAP105) with 10% carbon lampblack (LCA101) dissolved in a 1:2 powder to water slurry, then baked and broken into rough chunks.

 

Next, we worked on constraining space weathering processes on the asteroid. Qualitative and quantitative analyses of previous work and mission findings have led to our preferred hypothesis: the major agent of surface evolution on Bennu is dehydration of phyllosilicates and nanophase magnetite opaque formation due to surface irradiation. 

 

Nakauchi et al. 2021 (Icarus Vol. 355, 114140) suggest that there are distinct peaks at 2.72 μm, 2.77 μm, and 2.85 μm, each of which correspond to OH, H₂O, and Si-OH, respectively. We are writing a machine learning algorithm that will fit Gaussians at each peak, and are hoping to compare the depth of each Gaussian when applied to irradiated and unirradiated sample spectra to see exactly which type of hydration feature is attenuated.   

Modeling and Manufacturing Baffle Panels to Reduce the Impact of Sidelobes in Cosmic Microwave Background Telescopes

Three Mirror Anastigmat (TMA) Cosmic Microwave Background (CMB) telescopes experience a substantial reduction in image quality caused by significant sidelobe pickup.  TMA telescopes have specularly reflecting internal walls that can amplify the effects of the scattered light entering the instrument at wide angles, thus worsening the resulting sidelobes.  We aim to reduce the contrast of the sidelobes by lining the cabin in white noise surfaces, called baffle panels, designed to scatter light over a wide range of angles, thus diffusing the sidelobe specular peaks into a DC base.  Our research focuses on modeling the scattering caused by the white noise surfaces using phase-sensitive ray tracing and manufacturing such surfaces at a larger scale.  We hope to see our analytical model confirm our previous experimental results from the 90-110 GHz range.     

Analysis of Non-Prompt Lepton Backgrounds in Four-Lepton Events at the ATLAS Experiment

In the search for new physics beyond the Standard Model (SM), the ATLAS detector at the Large Hadron Collider (LHC) is collecting an ever-growing collision dataset requiring an increasingly precise understanding of background sources. An ideal candidate for high-precision studies of the SM are four-lepton events, which have final states of two same-flavor opposite-charge lepton pairs. These events have contributions from several interesting SM processes including single Z boson production, Higgs boson production, and on-shell ZZ production, as well as sensitivity to new physics beyond the SM. However, non-prompt leptons produced by secondary hadron decays or as artifacts of mis-reconstructions contaminate the dataset and must be suppressed. These backgrounds are subject to rare detector effects, and are therefore preferentially studied using data driven methods. Through comparisons with Monte Carlo simulated data, I studied a sample of collision data in which the final states include a pair of leptons, and any additional third lepton is likely to be non-prompt. I investigated the non-prompt lepton suppression methods, and refined the non-prompt lepton region to reduce systematic uncertainties on background measurements.   

Effect of cavity-induced long-range interactions between two-component fermions on optical lattices

We study interacting two-component fermions subjected to a periodic optical lattice potential and an optical cavity. In addition to the tunneling interaction and on-site interaction modified by the optical lattice potential, the cavity photons mediate long-range interactions between Fermi atoms. At the steady-state limit of the cavity photon decay, the photon mediated long-range interaction that contains a spin-flip term. After decoupling this spin-flip interaction term using a mean-field theory, we introduce a unitary transformation to convert our Hamiltonian into an effectively site-dependent population-imbalance quasi-fermion system. We then solve our effective Hamiltonian to study the effect of the long-range interactions on physical properties using standard theoretical approaches.     

Ground state properties of many-body quantum systems: chaos vs integrability

We study the distribution of the ground state energy of different many-body quantum systems and compare it with analytical expressions obtained for small and large random matrices. We find that weak differences in distribution tails can be attributed to the regularity or the chaoticity of the model.   

Can banded random matrices describe realistic many-body quantum systems?

Despite the success of full random matrices in describing statistically the spectrum of complex systems, they imply the unphysical scenario of all particles interacting simultaneously. Banded random matrices were introduced in an effort to better approach random matrices to realistic systems. We study power-law banded random matrices and show that they capture very well many features of the evolution of realistic disordered spin-1/2 chains both in their chaotic regime and in intermediate regions between chaos and localization.   

Weak disorder perturbation expansion for random resistance networks

Random resistance networks are a popular paradigm in statistical physics for modeling transport in disordered media such as semiconductors, spin glasses, and even porous rocks. We study a square lattice where the resistances at each bond are chosen from a statistical distribution. We derive the moments of the nodal voltages and bond currents exactly up to second order in a perturbation expansion in the disorder strength. Further, we construct an order parameter using the bond currents at arbitrary and infinite disorder, which provides a characterization of the behaviour of the system in the weak as well as strong disorder regimes. We predict a square law scaling with weak disorder, which is verified through numerical simulations. Scalings for the strong disorder regime are also obtained numerically, and the susceptibility of the order parameter is shown to diverge at a critical disorder. We compare our results with previous studies that use exponentially distributed resistances at each bond.   

Dynamic 3D Simulations of Tree and Network Sea Fan Structures

Sea fans are a variety of corals structured in a flat fanlike pattern of numerous cylindrical polyps. Their morphology has been previously studied through 2D images and digitized data points depicting the structures have been obtained. The project employs polymer physics and molecular simulations to study samples of tree-like and network structures and analyze differences in their dynamics. The sea fans' motion was initially simulated with the Large-scale Atomic/Molecular Massively Parallel Simulator Molecular Dynamics software by connecting the data points through harmonic bonds and modulating the flexibility/bending stiffness through an angle potential between three particles. Next, hydrodynamics was integrated using Smooth Particle Hydrodynamics and the Constant Energy Dissipative Particle Dynamics. Preliminary analysis of the output through particle displacements computations suggests that tree structures tend to be more dynamic than networks and that the greatest displacements correspond to outer particles, a result consistent with experimental findings. Further analysis of all available structures is necessary to conclusively find the correlation between the morphology of sea fans and their environment.   

The Effect of Finite Element Mesh Style and Size on Nano-Optic Computational Electromagnetic Simulations

Finite element method analysis produces highly accurate computational models for electromagnetics, especially the field of plasmonics. However, mesh size can vary across studies, and how it affects simulation accuracy for nanoscale electromagnetic could use further investigation. Larger mesh elements can reduce computation time, and so an understanding of mesh size upon model accuracy is significant. The purpose of our work is to investigate the relationship between mesh element size and deviancy from expected values of optical characteristics of the nanostructures. Specifically, we are trying to define a maximum mesh element size that retains acceptable deviance from expected values. 

Additionally, mesh creation style has some effect on the impact of mesh size on optical enhancement. Two methods of mesh creation have been investigated. One, the “Allmesh” method, used one unified mesh across the entire structure. The second, the “Mesh-Scalar” method, used multiple meshes to simulate different elements of the nanostructure.

Results for plasmonics structures indicate that mesh element sizes beyond 10 nm resulted in severe deviancy in optical enhancement, and that the “mesh-scalar” method was more sensitive to change in element size. Next we will investigate photonic crystals.   

New Condensed Matter Physics Model of Water Material in its Three Dimensions and Phases Solid (Ice), Liquid (Fluid Water) and Gas (Vapor)

In pure water, electrical mobility of hydroxide ion (OH)^– and hydronium ion (H₃O)⁺=(H₂O)H⁺ are 5 times higher than impurity ions (Na⁺, Cl^–). In 2013, Chihtang Sah delayed retiring from transistor manufacturing and college teaching, to find out why.  In June of 2017, he accepted me to work on this project. I noticed at 0°K, only half of the trisector sites between the adjacent tetrahedral oxygens of the hexagonal closed packed ice are occupied by protons, p⁺, forming a band of proton filled sites. The other half are unoccupied by p⁺, forming a band of proton unfilled sites. When ice warms up from 0°K, some p⁺ in proton filled band are excited to proton unfilled band, by absorbing propagating longitudinal proton vibrations, leaving some proton-filled sites unoccupied by protons, or occupied by prohols.  From pH measurements in liquid water, this proton-prohol pair has an activation energy of 540meV. Proton and prohol traps are also formed, but by localized proton vibrations which are fed by the traveling proton and prohol vibrations from the surrounding heat source through the fluid water tank and by the number of Born-Von Karman primitive unit cells in the tank.  This water lattice model is applicable to Nuclear, Particle, Astro and Cosmo physics at their kinetic energies.   

First principles thermodynamic modeling of aqueous lead corrosion

The corrosion of lead water pipes is a major public health concern. Treatment strategies aim to induce passivation, the formation of a protective solid layer between the pipe and the water. While prevention of lead corrosion is understood from engineering practices, computational models using decades old data remain unable to accurately predict the behavior of real pipes using thermodynamics alone. Here we calculate free energies of formation for solid lead compounds with density functional theory (DFT) and construct electrochemical phase diagrams for various water conditions. We find that the Perdew-Burke-Ernzerhof revised for solids (PBEsol) functional with spin-orbit coupling is the best choice for this Pb-H2O system. Our phase diagrams predict the corrosion of lead in standard state water conditions, confirming the need for corrosion inhibitors. We find that lead carbonates form in broad water conditions. However, our model did not find stable lead phosphates, contrary to the historical success of orthophosphate treatments, indicating the need for further investigation. Our work demonstrates the potential for computational materials physics techniques to provide insight into the thermodynamics of lead corrosion.   

Path Integral Construction of Quantum Propagators for Time-Dependent Potentials to Evaluate Work Statistics

The path integral approach to quantum mechanics is an alternative to the Schrödinger equation for finding quantum propagators. This approach generalizes the action principle in classical mechanics with a sum over the infinite number of possible trajectories. It can also be used to calculate the propagator in the case of a time-dependent potential. Here, I describe several of these potentials and illustrate the case of a particle in a rigid box with one wall moving uniformly in time, using a semi-classical approximation. Time-dependent potentials can be used in quantum thermodynamics as a work parameter, which does work on the system when controlled by an external agent. This leads to a path integral approach to quantum thermodynamics. I illustrate the calculation of the work statistics for the rigid box with one wall moving uniformly in time.