# Los Alamos National Laboratory

# Computational Physics Student Summer Workshop

Sponsored by the Los Alamos National Laboratory Advanced Scientific Computing (ASC) Program

Los Alamos National Laboratory's X Computational Physics Division, in cooperation with other related divisions including Theoretical Design and Computer, Computational, and Statistical Sciences, is pleased to sponsor the **annual Computational Physics Student Summer Workshop**.

The workshop seeks to bring to the Laboratory a diverse group of exceptional undergraduate and graduate students for informative, enriching lectures and to work with its staff for 10 weeks on interesting, relevant projects that may culminate in articles or conference presentations. Students are organized into groups of 2-3 working under the guidance of one or more mentors. Each participant is awarded a fellowship that typically ranges from $7,500 to $13,000, based on academic rank (junior, senior, 1st year graduate student, etc.)

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**The workshop is open to U.S. citizens only.**

Each workshop covers a range of research projects. Select a title below for information about the 2019 projects.

Planetary impacts have been invoked to explain a wide range of phenomena from formation of the earth/moon system to extinction of the dinosaurs. With increasing detail, scientists have modeled these impacts and the explosive effects on their environments. Comparatively less well studied are the chemical reactions driven by such incidents. The follow-up chemistry is likely to produce relatively complex substances: atmospheric acids, oxidized interfacial layers that alter the particulate greenhouse, even organic molecules required for the formation of life. Our summer students will extrapolate well-known equilibrium and kinetic approaches to study the extreme conditions created by collisions, using pre-existing Los Alamos impact physics simulations. The results will be applied to problems in the planetary science community plus a variety of energetic Earth-based events (pulses to the crust, ocean and atmosphere). Direct examples are geo-historical collisions such as Tunguska and Chicxulub. Outcomes will feed back valuable information onto environmental models of the Earth, and we will study effects of the chemistry on a spectrum of climate phenomena including -firestorms, marine emissions due to sea ice loss, and hurricanes.

The defining features of turbulent flows are the continuous mixing and churning of fluids in an apparently random fashion. For instance, imagine two fluids, where each has a unique density. Let us call the less dense fluid, f1 and the more dense fluid f2. Then, visualize f1 placed in a clear container with f2 suspended above f1. Now we put a straight ribbon of dye along the interface between the two fluids. Suppose now that gravity is activated in the system. What do you think the dye streak will look like after a short time? The experiment described above is a classical physics problem dubbed the Rayleigh-Taylor instability (RTI). It was named after two brilliant physicists, Lord Rayleigh and Sir G. I. Taylor, for their contributions to solving the problem. Because the heavy fluid, f2, is situated above the light fluid, f1, in a gravitational field, the system is in an unstable configuration. Small perturbations at the fluid interface grow larger and larger as f1 and f2 work to exchange place and find an equilibrium, stable configuration. As the interface perturbations grow, the dye streak will trace the motion along the interface. For a short time, it will evolve into a ribbon of connected s-shaped curves, before eventually dispersing into a dise cloud as the fluid motion becomes more tumultuous. The goal of this project is to develop analytical tools to study the above-described curve (ribbon of dye) as it evolves in time. In particular, we will develop numerical methods to integrate the curve and determine the areas to either side of the interface in two-dimensions. Difficulty arises when the interface begins to fold over on itself and roll up. If you were to plot this curve against the interface-parallel coordinate, you would see that due to the interface roll-up, the curve is a multi-valued function, or a non-function. Plenty of methods exist for integrating functions. However, methods for integrating non-functions are less prolific. Two students will be selected for this project. They will work together as a team to develop the non- function integration code in a compiled language (Fortran, C++, etc.) and tools for analyzing their results (Matlab, Python, etc.). Code will be provided to the students that produces the non-function interface and corresponding data. At project completion, the students will present the results of their work orally and in a written report.

We will use modern hydrodynamic tools developed at Los Alamos to simulate the evolution of protoplanetary disks around young stars to investigate the planet formation processes, including how dust grains (which are building blocks of planets) will interact with the gas in disks and how they coagulate from small sizes to large pebbles. Such simulations are providing insights for interpreting modern observations of such disks as given by ALMA and JVLA, along with other space observations by Hubble and TESS. Students will have opportunities to work with both theorists and observers to utilize advanced tools to solve important problems in such fields.

Opacity is a measure of how photons are absorbed as they pass through a material. The opacity of dense plasmas is a key component of modelling energy transport in the sun and other stars. Opacity calculations rely on so-called line broadening methods. Line broadening takes the probability of a particular quantum transition and, accounting for effects such as finite lifetime of the quantum state, produces a line shape that can be compared with experiment, of astrophysical measurement. In this project we will learn the basics of line shape techniques and calculate line shapes with state of the art methods. Starting from a sophisticated electronic structure method will also develop a new method for calculating lines which should have advantages in the dense plasma regime. Comparing these methods we will learn their relative strengths, and then apply them to enigmatic measurements of the opacity of iron at solar interior conditions. These measurements, together with helioseismology, do not agree with current state of the art methods for opacity.

Lagrangian hydrodynamics codes solve complete systems of equations relating kinematic variables such as velocity to thermodynamic variables such as density, pressure, and internal energy. Multi-material cells are commonly introduced during mesh relaxation (strictly speaking, an extension of Lagrangian methods to Arbitrary Lagrangian Eulerian, or ALE hydro), which is performed to avoid mesh tangling during very large deformations. They can also be introduced to resolve physics with fewer computational cells or to simplify model setup. However, once we introduce multi-material cells, the systems of equations are no longer complete (more unknowns than equations) so we must introduce closure models to balance the number of equations with unknowns. Student researchers will learn the basics of Lagrangian hydrodynamics and help us test and verify our modern, high fidelity closure models in the hydrodynamics code FLAG. This will involve developing and running Lagrangian hydrodynamic simulations involving large deformations and shock physics, with multi-material cells, to assess the performance of several closure models in those simulations.

The Laboratory creates the Sesame equation of state (EOS) database, a library of tabular EOS which cover a very wide range of density and temperature, typically to 10^{4} compression in density, and 100 keV (10^{9} K) in temperature. Underlying these EOS tables are a combination of analytic models and approximate first principles calculations. A standard model assumption is that the pressure and internal energy can be written as a sum of cold, ion-thermal, and electron-thermal contributions. A difficult region for models of this type is near solid density and at temperatures that are comparable to the Fermi temperature. In this range, ions are disordered, but still significantly correlated, so that they are neither solid-like nor gas-like. Electronic excitations contribute significantly to the pressure and energy. Ab initio molecular dynamic (AIMD) simulations, which directly simulate trajectories of nuclei under forces determined by solving a quantum mechanical problem for the state of the electrons at every time step, have proven to have good predictive capabilities for EOS, but are limited in the range of states they can cover. We propose to use AIMD simulations to guide improvements to wide ranging EOS models. First we will use AIMD to quantify the accuracy of the additive EOS formulation, through simulations varying the electron and ion temperatures independently. We will then use these results to benchmark models used for full-range Sesame equations of state. We will address issues such as the accuracy of using the melting temperature as a temperature scale for the ion EOS, how fast the ion specific heat interpolates from solid-like to gas-like, how important is realistic ion geometry, as opposed to atomic sphere boundary conditions used in wide-ranging EOS, for the electronic excitation spectrum. We expect these calculations to have a significant impact on the future of EOS modeling and Sesame EOS development.

SuperTimeStepping (STS) schemes are a class of explicit time integration methods that allow for greatly enhanced efficiency for parabolic or mixed parabolic/hyperbolic partial differential equations. The stability restrictions for non-STS explicit time integration schemes require the computational time step to be proportional to the spatial discretization squared. That results in O(N^{2}) time steps, where O(N) is the number of spatial computational cells across a single dimension. For STS schemes, that restriction is brought down by a factor of O(N^{(1/2)}). Typical sizes of N are 10^{2} to 10^{4}, so speed-ups of factors of 10-100 are realized by utilizing STS methods. STS methods have a long history, but only recently [1,2] have important non-linear stability requirements been enhanced to make these methods much more applicable to a wide range of physical systems. The focus of this project will be to explore even more stringent stability restrictions at material interfaces/boundaries. This involves examining discrete recursions and looking for patterns and eventually building new integration methods and exploring their properties. The mentors plan to work with the students, explaining how this was accomplished for the Runge-Kutta-Legendre [1,2] schemes, and how additional restrictions can be utilized to build the next generation of STS schemes with improved properties.

[1] Meyer, Chad D., Dinshaw S. Balsara, and Tariq D. Aslam. "A second-order accurate Super TimeStepping formulation for anisotropic thermal conduction." Monthly Notices of the Royal Astronomical Society 422.3 (2012): 2102-2115.

[2]Meyer, Chad D., Dinshaw S. Balsara, and Tariq D. Aslam. "A stabilized Runge-Kutta-Legendre method for explicit super-time-stepping of parabolic and mixed equations." Journal of Computational Physics 257 (2014): 594-626.

Understanding how matter behaves in extreme conditions is of importance to many areas of study, such as earth science, astrophysics, and weapons physics. The behavior of matter is particularly intriguing when molecules are involved. We intend to use molecular quantum mechanics and statistical physics to study the behavior of molecular matter. We will do this by optimizing and developing models to reproduce observed behavior of molecular matter. Working on this project will offer several different avenues of work from which to pick. Summaries of potential projects are shown below. We will seek to study molecular behavior in extreme environments with ab initio methods. We would like to improve numerical solvers required for equation of state modeling. We would like optimize models to reproduce observed behavior of molecular matter using Bayesian techniques. We will seek to improve the implementation of a constrained optimization problem and visualize the solutions.

Using the Branson Monte Carlo mini-app (https://github.com/lanl/branson) student researchers on this project will research and develop new variance reduction techniques for surface tallies in thermal radiation transport (TRT) calculations. The emphasis of this project will be to explore existing variance reduction techniques such as source biasing, event biasing, spatial weight windows, and Consistent Adjoint Driven Importance Sampling (CADIS) methods. Many of these methods have been explored for computer graphics and neutron transport applications but few have been extended to TRT applications. In particular this project will emphasize implementing a variance reduction techniques that performs well on TRT simulations such as supernovae with circumstellar media.

Using both highly-resolved FLAG and molecular dynamics (MD) simulations, the students will create complex ejecta profiles. These calculations will include different shock & release profiles (including two shocks), as well as different material states. One of our collaborators, Gerald Stevens at MSTS STL, has demonstrated the ability of high-resolution hydrodynamic simulations to capture details of experimental data that cannot be captured using current reduced-order ejecta models. These calculations show acceleration of slower ejecta and deceleration of faster ejecta after a second shock occurs, which is consistent with the Silverleaf data, but is not captured by continuum ejecta models. A challenge in using these calculations is the large diversity of physics that are occurring in these models including ejecta production, porous damage and recompaction, surface structures, ejecta interactions, and so on. Here, we aim to use unsupervised machine learning approaches to decompose the ejecta signatures into the salient features so that the time evolution of those components can be better interrogated, as well as the impact of these prominent features on the ejecta dispositioning. A comparison between FLAG and MD will provide a means to assess the impacts of physics missing in FLAG such as surface tension. This proposal will involve using existing tools to model ejecta production in both FLAG and MD, as well as learning unsupervised machine learning techniques and applying them to the resulting simulations.

Optical potentials, which provide a phenomenological prescription to describe the interaction between two nuclei (often projectile and target), are just one of the many models that are needed to describe the fission process. Many global optical potentials have been developed, typically to describe scattering properties of spherical, close-shelled, stable nuclei. Introducing these potentials into the Monte Carlo fission code CGMF gives rise to differences between prompt fission observables, in particular the neutron energy spectrum. The project would involve disentangling the effects of the optical potential from any averaging effects due to the variety of fission fragments, as well as investigating other causes of these similarities (e.g. unique parameterizations can give rise to similar results due to correlations between the parameters). This could lead to the development of a potential that is more suitable to the nuclei produced in a fission reaction, in itself an interesting large-scale, computational optimization problem.

We will conduct a computational study of the behavior of high speed jets. Two cases will be considered on for the inject of a light gas into a heavy fluid and the other for the reverse condition of a heavy fluid into a light gas. Simulations will be performed in both rectangular and axisymmetric geometries. The simulations will be motivated by experiments described in “An Album of Fluid Motion” assembled by Milton Van Dyke.