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DOE OSTI2024

Open-closed string duality, branes, and topological recursion

We consider matrix models exhibiting open-closed string duality in two-dimensional string theories with various amounts of supersymmetry. In particular, a relationship between matrix models in the β = 2 Wigner-Dyson class and models in the (1 + 2Γ, 2) Altland-Zirnbauer class relates the perturbative solutions of the two systems’ string equations. Point-like operator insertions in the closed string theory are mapped to the topological expansion of the free energy in the open string theory. We compute correlation functions of macroscopic loop operators and FZZT branes in a general topological gravity background. The relationship between the topological recursion of moduli space volumes and branes is discussed by analyzing the Virasoro conditions in the matrix models.

2D Gravity↗

DOE OSTI2021

Literary review and modeling outlook for radiation damage in fused-silica optical fibers

The purpose of this document is to distill, from literature, the effects of radiation damage in fused-silica optical fibers. This information will be used to design a theoretical framework capable of predictive modeling that will be published elsewhere. By inspection of the relevant literature, the devised method is calculation of defect amorphous structures by molecular dynamic techniques, and computation of the macroscopic dielectric function using density functional theory. The dielectric function is then used to directly compute the transmittance of the core material before and after irradiation via solution of Maxwell’s equations in a homogeneous medium.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

On Relative Importance of Vehicular and Structural Motions in Defining Electrolyte Transport

Molecular motions of ionic and neutral electrolyte species determine transport properties at the continuum scale. These molecular motions can be classified as vehicular (e.g., cations moving with a solvation shell of neighboring solvent molecules) and structural (e.g., cations hopping from one solvation shell to another) motions. While literature studies have described the presence, and relative importance, of each of these motions in various electrolytes, a clear link to macroscopic transport properties has not been made. We herein establish this link by using the fluctuation-dissipation theorem to develop theoretical expressions connecting the molecular displacements to Stefan-Maxwell diffusivities. To illustrate the usefulness of the proposed equations, we study LiPF 6 in propylene carbonate as an exemplar electrolyte. We show that its transport behavior improves at all concentrations when structural diffusion of cations is promoted. On the other hand, boosting the cation vehicular diffusion negatively affects the concentrated compositions. We extend this understanding to a generalized electrolyte of a salt dissolved in a solvent. Our theory suggests that while structural diffusion influences Stefan-Maxwell diffusivities globally, vehicular diffusion is only relevant under certain conditions. Such guidelines are critical for a bottom-up design of electrolyte transport.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

GLUE Code: A framework handling communication and interfaces between scales

Many scientific applications are inherently multiscale in nature. Such complex physical phenomena often require simultaneous execution and coordination of simulations spanning multiple time and length scales. This is possible by combining expensive small-scale simulations (such as molecular dynamics simulations) with larger scale simulations (such continuum limit/hydro solvers) to allow for considerably larger systems using task and data parallelism. However, the granularity of the tasks can be very large and often leads to load imbalance. Traditionally, we use approximations to streamline the computation of the more costly interactions and this introduces trade-offs between simulation cost and accuracy. In recent years, the available computational power and the advances in machine learning have made computing these scale-bridging interactions and multiscale simulations more feasible. One driving application has been plasma modeling in inertial confinement fusion (ICF), which is fundamentally multiscale in nature. This requires deep understanding of how to extrapolate microscopic information into macroscopically relevant scales. For example, in ICF one needs an accurate understanding of the connection between experimental observables and the underlying microphysics. The properties of the larger scales are often affected by the microscale behavior incorporated usually into the equations of state and ionic and electronic transport coefficients (Liboff, 1959; Rinderknecht et al., 2014; Rosenberg et al., 2015; Ross et al., 2017). Instead of incorporating this information using reliable molecular dynamics (MD) simulations, one often needs to use theoretical models, due to the inability of MD to reach engineering scales (Glosli et al., 2007; Marinak et al., 1998). One approach to resolve this issue is by coupling two MD simulations of different scales via force interpolation, e.g., the AdResS method (Krekeler et al., 2018; Nagarajan et al., 2013). Another approach, which we will pursue in the scope of this work, is by enabling scale bridging between MD simulations and meso/macro-scale models through the development and support of application programming interfaces that these different applications can interact through.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

The kinetic origin of the fluid helicity—A symmetry in the kinetic phase space

Helicity, a topological degree that measures the winding and linking of vortex lines, is preserved by ideal (barotropic) fluid dynamics. In the context of the Hamiltonian description, the helicity is a Casimir invariant characterizing a foliation of the associated Poisson manifold. Casimir invariants are special invariants that depend on the Poisson bracket, not on the particular choice of the Hamiltonian. The total mass (or particle number) is another Casimir invariant, whose invariance guarantees the mass (particle) conservation (independent of any specific choice of the Hamiltonian). In a kinetic description (e.g., that of the Vlasov equation), the helicity is no longer an invariant (although the total mass remains a Casimir of the Vlasov’s Poisson algebra). The implication is that some “kinetic effect” can violate the constancy of the helicity. To elucidate how the helicity constraint emerges or submerges, we examine the fluid reduction of the Vlasov system; the fluid (macroscopic) system is a “sub-algebra” of the kinetic (microscopic) Vlasov system. In the Vlasov system, the helicity can be conserved if a special helicity symmetry condition holds. To put it another way, breaking helicity symmetry induces a change in the helicity. We delineate the geometrical meaning of helicity symmetry and show that for a special class of flows (the so-called epi-two-dimensional flows), the helicity symmetry is written as ∂γ = 0 for a coordinate γ of the configuration space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Emergence of vorticity and viscous stress in finite-scale quantum hydrodynamics

The Madelung equations offer a hydrodynamic description of quantum systems, from single particles to quantum fluids. In this formulation, the probability density is mapped onto the fluid density and the phase is treated as a scalar potential generating the velocity field. As examples of potential flows, quantum fluids described in this way are inherently irrotational, but quantum vortices may arise at discrete points where the phase is undefined. In this paper, starting from this irrotational description of a quantum fluid, a coarse-graining procedure is applied to arrive at a macroscopic description of the quantum fluid in terms of a hierarchy of moments in which the role of velocity is played by a Favre average of the microscopic velocity field. This hierarchy is truncated using an explicit closure derived from an expansion in a finite length scale. The resulting coarse-grained fields are shown to allow for finite vorticity at any point in the fluid. Additionally, it is shown that this vorticity obeys a similar equation to the vorticity equation in classical hydrodynamics and includes a vortex-stretching term. The particular closure employed here also gives rise to a novel stress term in the fluid equations, which in the appropriate limit appears analogous to an artificial viscous stress from computational fluid dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Decoherence and Brownian motion of a polarizable particle near a medium

Optically levitated nanoparticles are ideal experimental testbeds for investigating macroscopic superpositions and microscopic thermodynamics. Integrating such levitated nanoparticles with photonic structures can enable strong coupling between their center-of-mass motion and guided photonic modes, facilitating enhanced control and probing of their motion. When coupling a particle to a photonic structure, such as a waveguide, the effects of fluctuations become prominent at nanoscales. In this work, we analyze the classical and quantized center-of-mass motion of a polarizable particle interacting with the fluctuations of the electromagnetic field in the presence of a medium. We derive a position localization master equation for the particle's quantized center of mass, and examine its classical center-of-mass momentum diffusion, elucidating correspondences between classical and quantum Brownian motion of polarizable particles near media. We study the decoherence rate of the particle in the presence of a planar surface as a function of temperature and distance from the surface, comparing it to common sources of decoherence. Our results are pertinent to experiments aimed at preparing levitated nanospheres in macroscopic quantum states and investigating their Brownian dynamics.

Brownian motion↗

DOE OSTI2023

The theory of kinetic effects on resistive wall mode stability in tokamaks

Tokamak fusion plasmas benefit from high pressures but are then susceptible to modes of instability. These magnetohydrodynamic (MHD) modes are macroscopic distortions of the plasma, but certain collective motions of individual particles can provide stabilizing effects opposing them. The presence of a resistive wall slows the mode growth, converting a kink to a resistive wall mode (RWM). A kinetic MHD model includes Maxwell's equations, ideal MHD constraints, and kinetic effects included through the pressure tensor, calculated with the perturbed drift-kinetic distribution function of the particles. The kinetic stabilizing effects on the RWM arise through resonances between the plasma rotation and particle drift motions: precession, bounce, and transit. A match between particle motions and the mode allows efficient transfer of energy that would otherwise drive the growth of the mode, thus damping the growth. The first approach to calculating RWM stability is to write a set of equations for the complex mode frequency in terms of known quantities and then to solve the system. The “energy principle” approach, which has the advantage of clarity in distinguishing the various stabilizing and destabilizing effects, is to change the force balance equation into an equation in terms of changes of kinetic and potential energies, and then to write a dispersion relation for the mode frequency in terms of those quantities. These methods have been used in various benchmarked codes to calculate kinetic effects on RWM stability. Importantly, the theory has illuminated the important roles of plasma rotation, energetic particles, and collisions in RWM stability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Interaction of cosmological domain walls with large classical objects, like planets and satellites, and the flyby anomaly

Cosmological domain walls can be formed as a result of symmetry breaking at any epoch during the evolution of our universe. We study their interaction with a classical macroscopic object, like Earth or a satellite in Earth’s orbit. We set up an action that includes the interaction term between the massive classical object and the scalar field that the domain wall is made of. We use numerical calculations to solve the coupled equations of motion which describe the crossing between the domain wall and the classical object. Depending on the strength of the interaction, relative velocity and size, the object can be either stopped by the wall, or it can pass through it inducing deformations in the wall that cost energy. At the same time, the coupling to the scalar filed might change the object’s mass during the crossover. The fact that satellites in Earth’s orbit (or planets in Sun’s orbit) can change their mass and/or lose energy interacting with walls can be used as a new domain wall detection probe. For example, a typical velocity precision of a satellite is about 0.5 mm/s, which directly puts an upper limit on its mass change to ΔM/M ≲ 5 × 10 –17 . Alternatively, a known satellite flyby anomaly can easily be explained as an interaction with a closed domain wall. We also show that the presence of matter modifies the scalar filed potential and can locally create a bubble of the true vacuum, and thus trigger the decay of the false vacuum. For a critical bubble which is able to expand, such an interaction with the domain wall must be strong enough.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Magnetic-Confinement Fusion—Plasma Theory: Tokamak Magnetohydrodynamic Equilibrium and Stability

Magnetohydrodynamics (MHD) provides a useful model to describe the crucial plasma macroscopic equilibrium and stability behaviors in toroidal tokamak devices by considering the plasma as a conducting fluid interacting with a surrounding confining electromagnetic field. MHD is the most basic plasma model, incorporating most large-scale phenomena, including plasma equilibrium and all major instabilities. MHD equations are obtained by taking moments of the Boltzmann equations for different plasma species. They provide a set of comprehensive physics constrains to compute and optimize the equilibrium plasma shape and pressure and current profiles that are critical to its stability and performance. In the ideal case, the equations have special properties that lead to efficient numerical calculation schemes, the most important of which is the ideal MHD energy principle for linear stability against small departures from equilibrium. In a tokamak plasma, equilibrium pressure is mostly destabilizing for MHD modes, whereas equilibrium current is also often a major driving force. Plasma resistivity creates new freedom for a MHD instability to grow, but there are also cases where the plasma resistivity plays a stabilizing role. Equilibrium toroidal flow and/or flow shear can affect MHD instabilities. Principal MHD instabilities include the internal kink mode, sawtooth, fishbone, external kink, resistive wall mode, resistive interchange, tearing and neoclassical tearing modes (NTMs), locked modes, toroidal Alfven eigenmodes (TAEs), and edge localized modes (ELMs). Fast-growing MHD instabilities can lead to an abrupt plasma disruption and termination that can potentially damage the device plasma facing components (PFCs) and in-vessel structures. Furthermore, an important MHD application is to develop robust techniques to mitigate and control MHD instabilities.

Dispersive pellet injection↗

DOE OSTI2026

Structural Aspects of Neutron Survival Probabilities

The neutron survival probability (and related quantities including probabilities of extinction and initiation) is a central element of the broader stochastic theory of neutron populations and finds application in fields including reactor start-up, analysis of reactor power bursts and criticality accidents, and safeguards. In a full neutron transport formulation, the equation governing the single-neutron survival probability is a backward or adjoint-like integro-partial differential equation with the added complexity of being highly nonlinear. Analogous formulations of this equation exist in the context of many approximate theories of neutron transport, with the point kinetics formulation having received significant theoretical attention since the 1940s. This work continues this tradition by providing a novel analysis of the single-neutron survival probability equation using the tools of boundary layer theory. The analysis reveals that the “fully dynamic” solution of the single-neutron survival probability equation—and some key probability distributions derived from it—may be cast as a singular perturbation around the underlying quasi-static single-neutron probability of initiation. In this perturbation solution, the expansion parameter is the ratio of the neutron generation time to a macroscopic time scale characterizing the overall system evolution; this interpretation illuminates some of the fundamental structural aspects of neutron survival phenomena.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Deducing the EOS of dense neutron star matter with machine learning

Abstract The interior of a neutron star is a unique astrophysical laboratory for studying matter at extreme densities and pressures beyond what is replicable in terrestrial experiments. While there is no direct way to simulate the interior of these stars, one promising avenue to learning more about the equation of state (EOS) of such matter is through X‐rays emitted from the star's surface. The current state‐of‐the‐art method for inference of EOS from a star's X‐ray spectra uses piece‐wise, simulation‐based likelihoods that rely on theoretical assumptions complicated by systematic uncertainties. To reduce the dimensionality of the problem, this method infers macroscopic properties of the star (mass and radius) from emitted X‐ray spectra, and from those quantities infers the EOS. This work approaches the same problem using machine learning techniques, demonstrating a series of enhancements to the current state‐of‐the‐art by realistic uncertainty quantification and reducing the need for theoretical assumptions. We also demonstrate novel inference of the EOS directly from high‐dimensional simulated X‐ray spectra from neutron stars that negate the need for a piece‐wise approach. This inference allows for a natural propagation of uncertainties from the X‐ray spectra by conditioning the discussed networks on realistic sources of uncertainty for each star.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Nyström type exponential integrators for strongly magnetized charged particle dynamics

Solving for charged particle motion in electromagnetic fields (i.e. the particle pushing problem) is a computationally intensive component of particle-in-cell (PIC) methods for plasma physics simulations. This task is especially challenging when the plasma is strongly magnetized due numerical stiffness arising from the wide range of time scales between highly oscillatory gyromotion and long term macroscopic behavior. A promising approach to solve these problems is by a class of methods known as exponential integrators that can solve linear problems exactly and are A-stable. This work extends the standard exponential integration framework to derive Nyström-type exponential integrators that integrates the Newtonian equations of motion as a second-order differential equation directly. In particular, we derive second-order and third-order Nyström-type exponential integrators for strongly magnetized particle pushing problems. Numerical experiments show that the Nyström-type exponential integrators exhibit significant improvement in computation speed over the standard exponential integrators.

general physics↗

DOE OSTI2023

COWALKER:EFFECTIVE TRANSPORT PROPERTIES OF COMPOSITE MATERIALS

SF-23-026 This software computes effective transport properties of composite materials involving fibers and nanoparticles using a random-walk algorithm that efficiently scales to an arbitrary number of processes and cores. Effective transport properties (thermal, electrical) are key to bridge the microstructure of complex materials with its macroscopic behavior. Traditional approaches either use effective medium approximations (closed mathematical expressions that are approximation for certain conditions) or continuum simulation models such as finite element or finite volume, which require the generation of a mesh for each configuration explored. cowalker leverages the equivalence between laplacian or heat equation-based models and random walks to compute the asymptotic transport properties from an ensemble of first sojourn times of a random walker moving through the composite material. This allows us to directly define a composite material as a collection of particles and use algorithms developed for molecular dynamics to quickly compute the intersection of the walker with the different interfaces in the material. cowalker is developed in C++, and it relies on the GNU Scientific Library for random generation. cowalker is currently delivered as source code, so the GSL library is not included in cowalker's distribution. A more userfriendly version, cowalker.jl is currently in development and will be released as part of cowalker.

YANGUAS-GIL, ANGEL↗

DOE OSTI2024

Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model

In this work, we propose a semi-Lagrangian (SL) nodal discontinuous Galerkin (DG) solver for the BGK equation. The BGK model was introduced by Bhatnagar, Gross, and Krook [1] as a relaxation model for the fundamental Boltzmann equation [5], which describes the kinetic dynamic of rarefied gases with a probability distribution function. The challenges of designing efficient numerical schemes for the Boltzmann equation mainly come from its high dimensionality and complicated nonlinear collision operator. The BGK model gains interests since it has much lower computational cost, due to the relatively simple structure of the relaxation operator in replacement of the collision operator, while simultaneously preserving several important physical properties, such as macroscopic quantities and dissipation of entropy.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Equilibrium Thermodynamic Properties of Aqueous Solutions of Ionic Liquid 1-Ethyl-3-Methylimidazolium Methanesulfonate [EMIM][MeSO3]

Abstract The ionic liquid 1-ethyl-3-methylimidazolium methanesulfonate ([EMIM][MeSO 3 ]) has been considered as a promising alternative desiccant to triethylene glycol and lithium bromide commonly used in the industry. In this paper, the water activity coefficient of this binary system was measured from 303 K to 363 K with water concentration from 18% to 92%. The interaction energies between the ionic liquid molecules ( $${g}_{22}$$ g 22 ) and between the ionic liquid and water molecules ( $${g}_{12}$$ g 12 ) for the [EMIM][MeSO 3 ]/water binary system were determined from the water activity coefficient data using the Non-Random Two-Liquid (NRTL) model. The magnitude of the interaction energy between the [EMIM][MeSO 3 ] and water molecules ( $${g}_{12}$$ g 12 ) was found to be in the range of 45~49 kJ/mol, which was about 20% larger than that between the water molecules ( $${g}_{11}$$ g 11 ) in the [EMIM][MeSO 3 ]/water system. The large ( $${g}_{12}$$ g 12 ) can explain many observed macroscopic thermodynamic properties such as strong hygroscopicity in the ionic liquid [EMIM][MeSO 3 ]. These interaction energies were used to determine the heat of desorption of the [EMIM][MeSO 3 ]/water system, and the obtained heat of desorption was in good agreement with that calculated from the conventional Clausius-Clapeyron Equation.

42 ENGINEERING↗

DOE OSTI2020

High-speed x-ray phase contrast imaging and digital image correlation analysis of microscale shock response of an additively manufactured energetic material simulant

The performance of energetic materials subjected to dynamic loading significantly depends on their micro- and meso-scale structural morphology. The geometric versatility offered by additive manufacturing opens new pathways to tailor the performance of these materials. Additively manufactured energetic materials (AMEMs) have a wide range of structural characteristics with a hierarchy of length scales and process-inherent heterogeneities, which are hitherto difficult to precisely control. It is important to understand how these features affect AMEMs’ response under dynamic/shock loading. Therefore, temporally and spatially resolved measurements of both macroscopic behavior and micro- and meso-level processes influencing macroscopic behavior are required. In this paper, we analyze the shock compression response of an AMEM simulant loaded under several impact conditions and orientations. Furthermore, x-ray phase contrast imaging (PCI) is used to track features across the observed shock front and determine the linear shock velocity vs particle velocity equation of state, as well as to quantify the interior deformation fields via digital image correlation (DIC) analyses. Photon Doppler velocimetry is simultaneously used to measure the particle velocities of the specimens, which are consistent with those obtained from x-ray PCI. The DIC analyses provide an assessment of the average strain fields inside the material, showing that the average axial strain depends on the loading intensity and reaches as high as 0.23 for impact velocities up to 1.5 km/s. The overall results demonstrate the utility of x-ray PCI for probing “in-material” equation of state and interior strains associated with dynamic shock compression behavior of the AMEM simulant.

3D printing↗

DOE OSTI2021

A multi-dimensional Child–Langmuir law for any diode geometry

While prior theoretical studies of multi-dimensional space-charge limited current (SCLC) assumed emission from a small patch on infinite electrodes, none have considered emission from an entire finite electrode. In this paper, we apply variational calculus (VC) and conformal mapping, which have previously been used to derive analytic solutions for SCLC density (SCLCD) for nonplanar one-dimensional geometries, to obtain mathematical relationships for any multi-dimensional macroscopic diode with finite cathode and anode. We first derive a universal mathematical relationship between space-charge limited potential and vacuum potential for any diode and apply this technique to determine SCLCD for an eccentric spherical diode. We then apply VC and the Schwartz–Christoffel transformation to derive an exact equation for SCLCD in a general two-dimensional planar geometry with emission from a finite emitter. Particle-in-cell simulations using VSim agreed within 4%–13% for a range of ratios of emitter width to gap distance using the thinnest electrodes practical for the memory constraints of our hardware, with the difference partially attributed to the theory's assumption of infinitesimally thin electrodes. After generalizing this approach to determine SCLCD for any orthogonal diode as a function of only the vacuum capacitance and vacuum potential, we derive an analytical formulation of the three-dimensional Child–Langmuir law for finite parallel rectangular and disk geometries. These results demonstrate the utility for calculating SCLCD for any diode geometry using vacuum capacitance and vacuum potential, which are readily obtainable for many diode geometries, to guide experiment and simulation development.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗