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At least 793 records · Page 44

A thermodynamics-based damage model for the non-linear mechanical behavior of SiC/SiC ceramic matrix composites in irradiation and thermal environments

A damage model is developed and validated with experimental data for the non-linear mechanical behavior of SiC/SiC composite materials in nuclear applications. Cyclic thermal and mechanical loading associated with neutron irradiation effects of these composites leads to wide-spread and progressive micro-cracking that leads to loss of thermal conductivity and further enhancement of thermo-mechanical damage. A physics-based model of wide-spread micro-cracking is developed within the thermodynamic framework of continuum damage mechanics. Evolution equations for damage parameters that describe the growth of continuum damage are developed, where the material variables are obtained from experiments. The model novelty is in coupling mechanical, thermal, and irradiation damage through a consistent thermodynamic framework, including loss of thermal conductivity due to the evolution of mechanically induced micro-cracks. A number of thermo-mechanical experiments were conducted to confirm model assumptions. The model is shown to be validated with out-of-pile experiments, and then implemented using commercial finite element code COMSOL to the fuel cladding problem with normal and high radiation dose cases.

Materials Science↗

Beyond Ohm's law: Bernoulli effect and streaming in electron hydrodynamics

Recent observations of nonlocal transport in ultraclean two-dimensional materials raised the tantalizing possibility of accessing hydrodynamic correlated transport of a many-electron state. However, it has been pointed out that nonlocal transport can also arise from impurity scattering rather than interaction. At the crux of the ambiguity is the focus on linear effects, i.e., Ohm's law, which cannot easily differentiate among different modes of transport. Furthermore we propose experiments that can reveal rich hydrodynamic features in the system by tapping into the nonlinearity of the Navier-Stokes equation. Three experiments we propose will each manifest a unique phenomenon that is well known in classical fluids: the Bernoulli effect, Eckart streaming, and Rayleigh streaming. Analysis of known parameters confirms that the proposed experiments are feasible and the hydrodynamic signatures are within reach of graphene-based devices. Experimental realization of any one of the three phenomena will provide a stepping stone to formulating and exploring the notions of nonlinear electron fluid dynamics with an eye to celebrated examples from classical nonlaminar flows, e.g., pattern formation and turbulence.

2-dimensional systems↗

A Novel Approach for Computing Rigid Body Motion Using Linear Accelerations

Here, a novel approach is presented for computing general rigid body motion based on a few known linear accelerations. This method utilizes linear acceleration data obtained from three distinct points on the body, all within a body-fixed reference frame. The only requirement is that the three chosen points must not be collinear. A system of differential-algebraic equations is derived, combining principles of rigid body kinematics with theory of the rotation group SO(3). These equations provide a framework for numerically computing various motion parameters, including angular velocity, angular acceleration, body orientation, velocity field, acceleration field, and displacement field. By numerically solving this system of equations, we can fully characterize rigid body motion in three-dimensional space. A numerical example is provided to demonstrate the practical implementation and efficacy of the proposed technique, illustrating its potential for accurate motion computation in various applications.

42 ENGINEERING↗

Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an adjoint analysis, which requires the numerical solution of large high-contrast linear elastic problems with features spanning several length scales. The size of the discretized problems forces the utilization of iterative linear solvers with solution time dependent on the quality of the preconditioner. The lack of clear separation between the scales, as well as the high-contrast, imposes severe challenges on the standard preconditioning techniques. Thus, here we propose new methods for the high-contrast elasticity equation with performance independent of the high-contrast and the multi-scale structure of the elasticity problem. The solvers are based on two-levels domain decomposition techniques with a carefully constructed coarse level to deal with the high-contrast and multi-scale nature of the problem. The construction utilizes spectral equivalence between scalar diffusion and each displacement block of the elasticity problems and, in contrast to previous solutions proposed in the literature, is able to select the appropriate dimension of the coarse space automatically. The new methods inherit the advantages of domain decomposition techniques, such as easy parallelization and scalability. Finally, the presented numerical experiments demonstrate the excellent performance of the proposed methods.

97 MATHEMATICS AND COMPUTING↗

The influence of physical and algorithmic factors on simulated far-field waveforms and source–time functions of underground explosions using unsupervised machine learning

SUMMARY Characterizing explosion sources and differentiating between earthquake and underground explosions using distributed seismic networks becomes non-trivial when explosions are detonated in cavities or heterogeneous ground material. Moreover, there is little understanding of how changes in subsurface physical properties affect the far-field waveforms we record and use to infer information about the source. Simulations of underground explosions and the resultant ground motions can be a powerful tool to systematically explore how different subsurface properties affect far-field waveform features, but there are added variables that arise from how we choose to model the explosions that can confound interpretation. To assess how both subsurface properties and algorithmic choices affect the seismic wavefield and the estimated source functions, we ran a series of 2-D axisymmetric non-linear numerical explosion experiments and wave propagation simulations that explore a wide array of parameters. We then inverted the synthetic far-field waveform data using a linear inversion scheme to estimate source–time functions (STFs) for each simulation case. We applied principal component analysis (PCA), an unsupervised machine learning method, to both the far-field waveforms and STFs to identify the most important factors that control variance in the waveform data and differences between cases. For the far-field waveforms, the largest variance occurs in the shallower radial receiver channels in the 0–50 Hz frequency band. For the STFs, both peak amplitude and rise times across different frequencies contribute to the variance. We find that the ground equation of state (i.e. lithology and rheology) and the explosion emplacement conditions (i.e. tamped versus cavity) have the greatest effect on the variance of the far-field waveforms and STFs, with the ground yield strength and fracture pressure being secondary factors. Differences in the PCA results between the far-field waveforms and STFs could possibly be due to near-field non-linearities of the source that are not accounted for in the estimation of STFs and could be associated with yield strength, fracture pressure, cavity radius and cavity shape parameters. Other algorithmic parameters are found to be less important and cause less variance in both the far-field waveforms and STFs, meaning algorithmic choices in how we model explosions are less important, which is encouraging for the further use of explosion simulations to study how physical Earth properties affect seismic waveform features and estimated STFs.

58 GEOSCIENCES↗

Quantum time dynamics employing the Yang-Baxter equation for circuit compression

Quantum time dynamics (QTD) is considered a promising problem for quantum supremacy on near-term quantum computers. However, QTD quantum circuits grow with increasing time simulations. This study focuses on simulating the time dynamics of one-dimensional (1D) integrable spin chains with nearest-neighbor interactions. We have proved the existence of a reflection symmetry in the quantum circuit employed for simulating the time evolution of certain classes of 1D Heisenberg model Hamiltonians by virtue of the quantum Yang-Baxter equation, and how this symmetry can be exploited to compress and produce a shallow quantum circuit. With this compression scheme, the depth of the quantum circuit becomes independent of step size and only depends on the number of spins. We show that the depth of the compressed circuit is rigorously a linear function of the system size for the studied Heisenberg model Hamiltonians in the present work. As a consequence, the number of CNOT gates in the compressed circuit only scales quadratically with the system size, which allows for the simulations of time dynamics of very large 1D spin chains. We derive the compressed circuit representations for different special cases of the Heisenberg Hamiltonian. We compare and demonstrate the effectiveness of this approach by performing simulations on quantum computers.

1-dimensional spin chains↗

Transport coefficients for magnetic-field evolution in inviscid magnetohydrodynamics

The magnetized resistivity and electrothermal tensors when substituted into the induction equation lead to electrothermal magnetic field generation, resistive magnetic diffusion, and magnetic field advection due to resistivity gradients, temperature gradients and currents. Here, the advection terms driven by temperature gradient and current have cross-field components (perpendicular to both the magnetic field and the driving term) that depend on significantly modified versions of Braginskii’s transport coefficients. The improved fits to Braginskii’s coefficients given by Epperlein and Haines and Ji and Held give physically incorrect results for cross-field advection at small Hall parameters (product of cyclotron frequency and collision time). The errors in Epperlein and Haines’ fits are particularly severe, giving increasing advection velocities below a Hall parameter of one when they should decrease linearly to zero. Epperlein and Haines’ fits can also give erroneous advection terms due to variations in effective atomic number. The only serious error in Braginskii’s fits is an overestimate in advection due to perpendicular resistivity. New fits for the cross-field advection terms are obtained from a direct numerical solution of the Fokker-Planck equation and Ji and Held’s higher order expansion approach that are continuous functions of the effective atomic number.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Piecewise polyhedral formulations for a multilinear term

Herein, we present a mixed-integer linear programming (MILP) formulation of a piecewise, polyhedral relaxation (PPR) of a multilinear term using its convex-hull representation. Based on the PPR’s solution, we also present a MILP formulation whose solutions are feasible for nonconvex, multilinear equations. We then present computational results showing the effectiveness of proposed formulations on standard benchmark nonlinear programs (NLPs) with multilinear terms and compare with a traditional formulation that is built using recursive bilinear groupings of multilinear terms.

42 ENGINEERING↗

Numerical simulations of three-dimensional ion crystal dynamics in a Penning trap using the fast multipole method

We simulate the dynamics, including laser cooling, of three-dimensional (3-D) ion crystals confined in a Penning trap using a newly developed molecular dynamics-like code. The numerical integration of the ions’ equations of motion is accelerated using the fast multipole method to calculate the Coulomb interaction between ions, which allows us to efficiently study large ion crystals with thousands of ions. In particular, we show that the simulation time scales linearly with ion number, rather than with the square of the ion number. By treating the ions’ absorption of photons as a Poisson process, we simulate individual photon scattering events to study laser cooling of 3-D ellipsoidal ion crystals. Initial simulations suggest that these crystals can be efficiently cooled to ultracold temperatures, aided by the mixing of the easily cooled axial motional modes with the low frequency planar modes. In our simulations of a spherical crystal of 1000 ions, the planar kinetic energy is cooled to several millikelvin in a few milliseconds while the axial kinetic energy and total potential energy are cooled even further. This suggests that 3-D ion crystals could be well suited as platforms for future quantum science experiments.

Zaris, John (ORCID:0009000196476323)↗

Instabilities of a vortex-ring-bright soliton in trapped binary three-dimensional Bose-Einstein condensates

Instabilities of vortex-ring-bright coherent structures in harmonically trapped two-component three-dimensional Bose-Einstein condensates are studied numerically within the coupled Gross-Pitaevskii equations and interpreted analytically. Interestingly, the filled vortex core with a sufficiently large amount of the bright component is observed to reduce the parametric interval of stability of the vortex ring. Here, we have identified the mechanisms of several linear instabilities and one nonlinear parametric instability in this connection. Two of the linear instabilities are qualitatively different from ones reported earlier and are associated with azimuthal modes of m = 0 and m = 1, i.e., deviations of the vortex from the stationary ring shape. Our nonlinear parametric resonance instability occurs between the m = 0 and m = 2 modes and signals the exchange of energy between them.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Stability analysis of a one-dimensional multiphysics model of a molten salt fast reactor

Reactor designs with a fast neutron spectrum have recently moved into the research focus for possible Generation IV reactor concepts - a representative of which is the molten salt fast reactor (MSFR). In order to assess the safety and reliability of this reactor concept, it is necessary to obtain knowledge of the system behaviour. An important part of this research concerns the dynamical stability of the MSFR. Research regarding the MSFR stability so far has either been using linearized models for stability criteria or only been examining certain transients at fixed parameter values. This work delivers a comprehensive stability analysis for a non-linearized MSFR model, and a wide range of values for all relevant parameters. For this purpose, a one-dimensional MSFR model was set up, taking neutron kinetics and thermal hydraulics in the form of a system of differential equations into account. The stability of this model was investigated by means of the numerical tool MATCONT, which was used to monitor the evolution of a so-called fixed-point solution, here referring to the steady state at operating conditions of the system, while system parameters got varied. The MATCONT analyses showed no loss of stability for any of the considered parameter variations and no solutions that might co-exist in parallel with the steady-state fixed-point solution. Therefore these results indicate a stable fixed point to which all solution transients converge, making the considered MSFR model insusceptible to deviations from the equilibrium. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Exact-Factorization-Based Surface Hopping without Velocity Adjustment

While surface hopping has emerged as a powerful method for simulating non-adiabatic dynamics in large molecules, the ad hoc nature of the necessary velocity adjustments and decoherence corrections in the algorithm somewhat reduces its reliability. Here we propose a new scheme that eliminates these aspects by combining the nuclear equation from the quantum-trajectory surface-hopping approach with the electronic equation derived from the exact-factorization approach. Furthermore, the resulting method, denoted QTSH-XF, yields a surface-hopping method on firmer ground than previous and is shown to successfully capture dynamics in Tully models and in a linear vibronic coupling model of the photoexcited uracil cation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ballooning theory for micro-tearing mode in tokamak

This paper aims to investigate the impact of magnetic drift on the linear micro-tearing mode by using a kinetic approach to derive a reduced two-field eigen system in real space. Here, since the magnetic drift in real space has derivatives, it is more efficient to solve the mode equations in a Fourier-ballooning representation using the two-dimensional (2D) ballooning transform. The lowest-order eigen system in the Fourier-ballooning representation consists of two integral equations, which are numerically solved using the finite difference method for both eigenvalues and wave functions. The main results will be presented through graphical eigenvalue scans for each parameter. Furthermore, we present a graphical comparison between the predictions of the ballooning theory and GENE gyrokinetic code simulation in the pedestal region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Quantum tracking control of the orientation of symmetric-top molecules

The goal of quantum tracking control is to identify shaped fields to steer observable expectation values along designated time-dependent tracks. The fields are determined via an iteration-free procedure, which is based on inverting the underlying dynamical equations governing the controlled observables. In this paper, we generalize the ideas in [Phys. Rev. A 98, 043429 (2018)] to the task of orienting symmetric top molecules in three dimensions. To this end, we derive equations for the control fields capable of directly tracking the expected value of the three-dimensional dipole orientation vector along a desired path in time. In conclusion, we show this framework can be utilized for tracking the orientation of linear molecules as well, and present numerical illustrations of these principles for symmetric-top tracking control problems.

74 ATOMIC AND MOLECULAR PHYSICS↗

Addendum to SAND2023-09604 Xyce lumped-element transmission line model verification to support Empire-Cable cable SGEMP analyses

This report supplements the Verification of Empire-Cable SAND report by expanding on the use of Xyce to simulate the coupling to a transmission line cable model. While Empire-Cable solves its governing equations on a high-order, finite-element mesh with an an implicit-in-time formulation, Xyce must use a first order graph for the circuit and explicit-in-time approach to be compatible with non-linear electrical device models. Thus, given the different solution methodologies in Xyce as compared to Empire-Cable, the convergence rates are expected to be different but the overall quality of the solution should be the same. The original four canonical problems studied in the Empire-Cable verification report are replicated here running in Xyce using transmission line modeling parameters from the verification report. Overall, agreement between the codes is excellent with Xyce’s convergence rates being limited mostly to first order due to the circuit network approximation of a transmission line being a first order approximation.

42 ENGINEERING↗

Simulating coupled surface–subsurface flows with ParFlow v3.5.0: capabilities, applications, and ongoing development of an open-source, massively parallel, integrated hydrologic model

Surface flow and subsurface flow constitute a naturally linked hydrologic continuum that has not traditionally been simulated in an integrated fashion. Recognizing the interactions between these systems has encouraged the development of integrated hydrologic models (IHMs) capable of treating surface and subsurface systems as a single integrated resource. IHMs are dynamically evolving with improvements in technology, and the extent of their current capabilities are often only known to the developers and not general users. This article provides an overview of the core functionality, capability, applications, and ongoing development of one open-source IHM, ParFlow. ParFlow is a parallel, integrated, hydrologic model that simulates surface and subsurface flows. ParFlow solves the Richards equation for three-dimensional variably saturated groundwater flow and the two-dimensional kinematic wave approximation of the shallow water equations for overland flow. The model employs a conservative centered finite-difference scheme and a conservative finite-volume method for subsurface flow and transport, respectively. ParFlow uses multigrid-preconditioned Krylov and Newton–Krylov methods to solve the linear and nonlinear systems within each time step of the flow simulations. The code has demonstrated very efficient parallel solution capabilities. ParFlow has been coupled to geochemical reaction, land surface (e.g., the Common Land Model), and atmospheric models to study the interactions among the subsurface, land surface, and atmosphere systems across different spatial scales. This overview focuses on the current capabilities of the code, the core simulation engine, and the primary couplings of the subsurface model to other codes, taking a high-level perspective.

58 GEOSCIENCES↗

Techniques for studying materials under extreme states of high energy density compression

The properties of materials under extreme conditions of pressure and density are of key interest to a number of fields, including planetary geophysics, materials science, and inertial confinement fusion. In geophysics, the equations of state of planetary materials, such as hydrogen and iron, under ultrahigh pressure and density provide a better understanding of their formation and interior structure [Celliers et al., “Insulator-metal transition in dense fluid deuterium,” Science 361, 677–682 (2018) and Smith et al., “Equation of state of iron under core conditions of large rocky exoplanets,” Nat. Astron. 2, 591–682 (2018)]. The processes of interest in these fields occur under conditions of high pressure (100 GPa–100 TPa), high temperature (>3000 K), and sometimes at high strain rates (>103 s−1) depending on the process. With the advent of high energy density (HED) facilities, such as the National Ignition Facility (NIF), Linear Coherent Light Source, Omega Laser Facility, and Z, these conditions are reachable and numerous experimental platforms have been developed. To measure compression under ultrahigh pressure, stepped targets are ramp-compressed and the sound velocity, measured by the velocity interferometer system for any reflector diagnostic technique, from which the stress-density of relevant materials is deduced at pulsed power [M. D. Knudson and M. P. Desjarlais, “High-precision shock wave measurements of deuterium: Evaluation of exchange-correlation functionals at the molecular-to-atomic transition,” Phys. Rev. Lett. 118, 035501 (2017)] and laser [Smith et al., “Equation of state of iron under core conditions of large rocky exoplanets,” Nat. Astron. 2, 591–682 (2018)] facilities. To measure strength under high pressure and strain rates, experimenters measure the growth of Rayleigh–Taylor instabilities using face-on radiography [Park et al., “Grain-size-independent plastic flow at ultrahigh pressures and strain rates,” Phys. Rev. Lett. 114, 065502 (2015)]. The crystal structure of materials under high compression is measured by dynamic x-ray diffraction [Rygg et al., “X-ray diffraction at the national ignition facility,” Rev. Sci. Instrum. 91, 043902 (2020) and McBride et al., “Phase transition lowering in dynamically compressed silicon,” Nat. Phys. 15, 89–94 (2019)]. Medium range material temperatures (a few thousand degrees) can be measured by extended x-ray absorption fine structure techniques, Yaakobi et al., “Extended x-ray absorption fine structure measurements of laser-shocked V and Ti and crystal phase transformation in Ti,” Phys. Rev. Lett. 92, 095504 (2004) and Ping et al., “Solid iron compressed up to 560 GPa,” Phys. Rev. Lett. 111, 065501 (2013), whereas more extreme temperatures are measured using x-ray Thomson scattering or pyrometry. This manuscript will review the scientific motivations, experimental techniques, and the regimes that can be probed for the study of materials under extreme HED conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗