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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Analysis of Seismic Signals Generated by Vehicle Traffic with Application to Derivation of Subsurface Q-Values

Correct identification and modeling of anthropogenic sources of ground motion are of considerable importance for many studies, including detection of small earthquakes and imaging seismic properties below the surface. Here, to understand signals generated by common vehicle traffic, we use seismic data recorded by closely spaced geophones normal to roads at two sites on San Jacinto fault zone. To quantify the spatiotemporal and frequency variations of the recorded ground motions, we develop a simple analytical solution accounting for propagation and attenuation of surface waves. The model reproduces well-observed bell-shaped spectrograms of car signals recorded by geophones close to roads, and it can be used to estimate frequency-dependent Q-values of the subsurface materials. The data analysis indicates Q-values of 3–40, for frequencies up to 150 Hz for road-receiver paths at the two examined sites. The derived Q-values are consistent with attenuation factors of surface waves previously obtained with other methods. The analytical results and analysis procedure provide a highly efficient method for deriving Q-values of shallow subsurface materials.

58 GEOSCIENCES↗
DOE OSTI2024

A mixed formulation of the plane-stress problem to facilitate reuse of constitutive models in finite-element programs

Here, the plane-stress assumption can be challenging to support in a finite element program because it traditionally requires separate implementations of constitutive models than those intended for three-dimensional or two-dimensional plane-strain simulations. As a solution to this issue, this paper presents a method to solve the plane-stress problem using a mixed formulation. In this formulation, the out-of-plane strain is treated as a field variable that is solved for in addition to the standard in-plane displacement variables, in a manner that weakly enforces the condition that the out-of-plane stress is zero. The proposed formulation is non-intrusive, requiring no modifications to the constitutive models in contrast to the conventional plane-stress formulation. The proposed mixed formulation has been benchmarked against analytical solutions and numerical solutions, with good performance and accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

An unconditionally stable, time-implicit algorithm for solving the one-dimensional Vlasov–Poisson system

The development of an implicit, unconditionally stable, numerical method for solving the Vlasov–Poisson system in one dimension using a phase-space grid is presented. The algorithm uses the Crank–Nicolson discretization scheme and operator splitting allowing for direct solution of the finite difference equations. This method exactly conserves particle number, enstrophy and momentum. A variant of the algorithm which does not use splitting also exactly conserves energy but requires the use of iterative solvers. This algorithm has no dissipation and thus fine-scale variations can lead to oscillations and the production of negative values of the distribution function. We find that overall, the effects of negative values of the distribution function are relatively benign. We consider a variety of test cases that have been used extensively in the literature where numerical results can be compared with analytical solutions or growth rates. We examine higher-order differencing and construct higher-order temporal updates using standard composition methods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Effects of zero and reversed magnetic shear on resistive wall modes in a straight limiter tokamak with zero beta

Advanced tokamak scenarios often feature equilibriums with zero and reversed magnetic shear. To isolate and investigate their impacts on the resistive wall mode (RWM) instability analytically, we construct a series of cylindrical limiter equilibriums with different magnetic shear in the core and toward plasma edge, as a prototype of the configurations in advanced tokamak scenarios. Equilibriums with zero β are considered so that the analysis focuses on the current-driven RWMs. Analytical solutions for the n=1 resistive wall mode, derived from the reduced ideal magnetohydrodynamics (MHD) equations, consistently demonstrate key insights for both the core and the edge: the growth rate of RWMs is inversely proportional to the averaged magnetic shear when the safety factor at the edge (qa) is held constant. Specifically, an increase in positive averaged magnetic shear results in a decreased growth rate, whereas an increase in negative averaged magnetic shear leads to an increased growth rate. Furthermore, the influence of nqa on the mode's stability significantly surpasses the effects of magnetic shear changes previously discussed. These analytical calculation results provide a verification of NIMROD simulations.

Wan, Sui (ORCID:0009000464121677)↗
DOE OSTI2021

Uranium hydride corrosion. I New insights into the Condon-Kirkpatrick model of uranium hydride formation rate

An analytic solution to the uranium hydride formation rate equation of Condon and Kirkpatrick (CK) has been developed, which is directly solved via algebraic operations and requires only gaseous hydrogen (H 2 ) pressure and temperature as inputs. The solution does not depend on the specific functional forms of the hydriding and dehydriding rate constants, nor of key physical parameters. Furthermore, a modified form of the CK model has also been developed, where replacement of the hydrogen solubility function results in an improved fit to published experimental data as H 2 pressure decreases toward the corrosion threshold value.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Coupled Lattice Boltzmann Modeling Framework for Pore-Scale Fluid Flow and Reactive Transport

In this paper, we propose a modeling framework for pore-scale fluid flow and reactive transport based on a coupled lattice Boltzmann model (LBM). We develop a modeling interface to integrate the LBM modeling code parallel lattice Boltzmann solver and the PHREEQC reaction solver using multiple flow and reaction cell mapping schemes. The major advantage of the proposed workflow is the high modeling flexibility obtained by coupling the geochemical model with the LBM fluid flow model. Consequently, the model is capable of executing one or more complex reactions within desired cells while preserving the high data communication efficiency between the two codes. Meanwhile, the developed mapping mechanism enables the flow, diffusion, and reactions in complex pore-scale geometries. We validate the coupled code in a series of benchmark numerical experiments, including 2D single-phase Poiseuille flow and diffusion, 2D reactive transport with calcite dissolution, as well as surface complexation reactions. The simulation results show good agreement with analytical solutions, experimental data, and multiple other simulation codes. In addition, we design an AI-based optimization workflow and implement it on the surface complexation model to enable increased capacity of the coupled modeling framework. Compared to the manual tuning results proposed in the literature, our workflow demonstrates fast and reliable model optimization results without incorporating pre-existing domain knowledge.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Semicomputational calculation of Bragg shift in stratified materials

The fiber Bragg grating (FBG) may be viewed as a one dimensional photonic band-gap crystal by virtue of the periodic spatial perturbation imposed on the fiber core dielectric material. Similar to media supporting Bloch waves, the engraved weak index modulation, presenting a periodic “potential” to an incoming guided mode photon of the fiber, yields useful spectral properties that have been the basis for sensing applications and emerging quantum squeezing and solitons. The response of an FBG sensor to arbitrary external stimuli represents a multiphysics problem without a known analytical solution despite the growing use of FBGs in classical and quantum sensing and metrology. Here, we study this problem by first presenting a solid mechanics model for the thermal and elastic states of a stratified material. Additionally, the model considers an embedded optical material domain that represents the Bragg grating, here in the form of an FBG. Using the output of this model, we then compute the optical modes and their temperature- and stress-induced behavior. The developed model is applicable to media of arbitrary shape and composition, including soft matter and materials with nonlinear elasticity and geometric nonlinearity. Finally, we employ the computed surface stress and temperature distributions along the grating to analytically calculate the Bragg shift, which is found to be in reasonable agreement with our experimental measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Modeling gas release from a Bingham plastic slurry and deconvoluting measured data

Physics-based models for predicting the off-gassing characteristics of agitated slurries are presented. This approach decomposes the system into two separate but coupled slurry and headspace models. The physics driving bubble transport through the slurry and gas mixing within the headspace are discussed. An analytical expression for predicting the time evolution of the headspace concentration using first principles theory is also presented. Predictions from the numerical models, as well as expectations from the analytical solution, both agree with measured off gassing data for two different experimental operating conditions. After benchmarking the numerical model predictions against experimental data, the model was used to make predictions for gas release from a full-scale vessel and to perform sensitivity analyses to examine the sensitivity of gas release to parameters such as yield stress, consistency index, slurry density, bubble size, bubble concentration, and impeller speed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Finite domain solution of a KGD hydraulic fracture in the viscosity-dominated regime

This paper describes a numerical algorithm for solving the classic problem of a plane strain (KGD) fracture propagating in an impermeable elastic medium with zero toughness. The method, which takes advantage of the self-similar nature of the solution, combines a domain-based scheme to solve the elasticity equations and a finite volume method to solve the nonlinear lubrication equation. This work represents a first step towards developing a model able to account for pore pressure diffusion in the medium and corresponding poroelastic effects, noting that these processes are more efficiently solved using a domain-based rather than a boundary integral method. To enhance the efficiency and accuracy of the numerical scheme, the far-field crack asymptotics is embedded in the discretized elastic relationship between the fluid pressure and the crack opening, while the coupled fluid-solid tip asymptote is enforced in a weak form when solving the nonlinear lubrication equation. The proposed technique yields results that closely match the analytical solution, even with a coarse mesh. This approach offers potential for addressing more complex hydraulic fracturing problems in the future.

Domain-based method↗
DOE OSTI2021

Micro-continuum approach for mineral precipitation

Abstract Rates and extents of mineral precipitation in porous media are difficult to predict, in part because laboratory experiments are problematic. It is similarly challenging to implement numerical methods that model this process due to the need to dynamically evolve the interface of solid material. We developed a multiphase solver that implements a micro-continuum simulation approach based on the Darcy–Brinkman–Stokes equation to study mineral precipitation. We used the volume-of-fluid technique in sharp interface implementation to capture the propagation of the solid mineral surface. Additionally, we utilize an adaptive mesh refinement method to improve the resolution of near interface simulation domain dynamically. The developed solver was validated against both analytical solution and Arbitrary Lagrangian–Eulerian approach to ensure its accuracy on simulating the propagation of the solid interface. The precipitation of barite (BaSO 4 ) was chosen as a model system to test the solver using variety of simulation parameters: different geometrical constraints, flow conditions, reaction rate and ion diffusion. The growth of a single barite crystal was simulated to demonstrate the solver’s capability to capture the crystal face specific directional growth.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Exploring the working range of automated standard dilution analysis of nutrient elements in foods by inductively coupled plasma optical emission spectrometry

Inductively coupled plasma optical emission spectrometry (ICP-OES) is an important tool for measuring nutrient elements in food. ICP-OES methods typically determine analytical concentrations using external standard calibration but can be susceptible to matrix effects. The method of standard additions does not suffer from matrix effects but is time consuming and labor intensive. Automated standard dilution analysis (SDA) allows for online matrix matched calibration without preparing individual standard additions for each sample matrix. This approach may solve both time and matrix issues and has been described in the literature as an attractive alternative to standard additions. The working range of the method for nutrient elements, however, is an understudied feature of SDA that may be a potential drawback to routine analysis of foods. We evaluated automated SDA performance through the analysis of 10 reference materials and four fortified (i.e., spiked) foods spanning the AOAC food triangle. We evaluated the working range, accuracy, and precision for analyses of nutrient elements in foods. Accepted accuracy (80–120% recovery) was achieved for 10 nutrient elements, Ca, Cu, Fe, K, Mg, Mn, Na, P, S, and Zn, when the analytical solution concentration to standard concentration ratio was less than 10. This equates to a working range for each element spanning at least two orders of magnitude. Removing outliers, Z scores (n = 95) ranged from –1.8 to 0.88, and the average recovery (n = 85) from fortification experiments was 97 ± 12% (2σ). Therefore, automated SDA applied to ICP-OES may be used for nutrient elemental analyses in samples with difficult matrices such as foods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Entanglement properties of disordered quantum spin chains with long-range antiferromagnetic interactions

Entanglement measures are useful tools in characterizing otherwise unknown quantum phases and indicating transitions between them. Here we examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $\textit{α}$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $α > \frac{1}{2}$ . A numerical implementation of the SDRG method yields a power-law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading-order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $\textit{α}$, corresponding to a critical behavior with an effective central charge $\textit{c}$ = ln(2), independent of $\textit{α}$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $\textit{α}$. For a wide range of partition size $\textit{l}$, the EE fits a critical behavior with a central charge close to $\textit{c}$ = 1, which is the same as for the clean Haldane-Shastry model with a power-law-decaying interaction with $\textit{α}$ = 2. Only for small $l \ll L$, in a range which increases with the number of spins N, we find deviations which are rather consistent with the strong disorder fixed point central charge $\textit{c}$ = ln(2). Furthermore, we find using ED that the concurrence shows power-law decay, albeit with smaller power exponents than obtained by SDRG. Finally, we also present results obtained with DMRG and find agreement with ED for sufficiently small $\textit{α}$ < 2, whereas for larger $\textit{α}$ DMRG tends to underestimate the entanglement entropy and finds a faster decaying concurrence.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Solidification dynamics in metal additive manufacturing: analysis of model assumptions

Solidification characteristics in the meltpool drive the process-microstructure relationship which helps dictate the material properties of as-built parts in additive manufacturing; therefore, being able to accurately and quickly simulate the size, shape, and solidification characteristics in the melt pool is of great interest to the field. In this study, we investigate various important physical phenomena (dynamic material properties, fluid-flow, radiation and vaporization) which can either be included or neglected in a continuum finite volume model (FVM) and their effect on the solidification conditions. Additionally, since the simplest form of such a model (conduction only) has an analytic solution which is much faster, its viability is also considered. Since the inclusion of some of these physical phenomena will inherently change the net energy input as well as the amount of energy needed to achieve melting of a control volume, each set of included phenomena had an effective absorption efficiency which was calibrated to closely match the dimensions of the melt pool to that of the ground truth data. The ground truth data for this study was defined to be the output of the FVM which included all the physical phenomena (OF). This study then goes on to compare the effects on solidification conditions each of these calibrated models has. It was found that most of the change in solidification conditions comes from the inclusion of latent heat. A posterior correlation factor (PCF) is then introduced to enable an analytic model to predict similar solidification conditions to OF model.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Exact and locally implicit source term solvers for multifluid-Maxwell systems

Recently, a family of models that couple multifluid systems to the full Maxwell equations have been used in laboratory, space, and astrophysical plasma modeling. These models are more complete descriptions of the plasma than reduced models like magnetohydrodynamic (MHD) since they are derived more closely from the full kinetic Vlasov-Maxwell system, without assumptions like quasi-neutrality, negligible electron mass, etc. Thus these models naturally retain non-ideal MHD effects like electron inertia, Hall term, pressure anisotropy/nongyrotropy, displacement current, among others. One obstacle to broader application of these model is that an explicit treatment of their source terms leads to the need to resolve rapid processes like plasma oscillation and electron cyclotron motion, even when these are not important. In this paper, we suggest two ways to address this issue. First, we derive the analytic solutions to the source update equations, which can be implemented as a practical, but less generic solver. We then develop a time-centered, locally implicit algorithm to update the source terms, allowing stepping over the fast kinetic time-scales. For a plasma with S species, the locally implicit algorithm involves inverting a local (3 S + 3) × (3 S + 3) matrix only, thus is very efficient. The performance can be further increased by using the direct update formulas to skip null calculations. In this paper, we present benchmarks illustrating the exact energy-conservation of the locally implicit solver, as well as its efficiency and robustness for both small-scale, idealized problems and largescale, complex systems. The locally implicit algorithm can be also easily extended to include other local sources, like collisions and ionization, which are difficult to solve analytically.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Beam focusing and consequences for Doppler backscattering measurements

The phenomenon of focusing of microwave beams in a plasma near a turning-point caustic is discussed by exploiting the analytical solution to the Gaussian beam-tracing equations in the two-dimensional (2-D) linear-layer problem. The location of maximum beam focusing and the beam width at that location are studied in terms of the beam initial conditions. This focusing must be taken into account to interpret Doppler backscattering (DBS) measurements. We find that the filter function that characterises the scattering intensity contribution along the beam path through the plasma is inversely proportional to the beam width, predicting enhanced scattering from the beam focusing region. We show that the DBS signal enhancement for decreasing incident angles between the beam path and the density gradient is due to beam focusing and not due to forward scattering, as was originally proposed by (Gusakov et al., (Plasma Phys. Contr. Fusion, vol. 56, 2014, p. 0250092014, 2017); Plasma Phys. Rep. vol. 43(6), 2017, pp. 605–613). The analytic beam model is used to predict the measurement of the k y density-fluctuation wavenumber power spectrum via DBS, showing that, in an NSTX-inspired example, the spectral exponent of the turbulent, intermediate-to-high k y density-fluctuation spectrum might be quantitatively measurable via DBS, but not the spectral peak corresponding to the driving scale of the turbulent cascade.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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↗
DOE OSTI2021

Numerical and Analytical Modeling of Flow Partitioning in Partially Saturated Fracture Networks

Infiltration processes in fractured-porous media remain a crucial, yet not very well understood component of recharge and vulnerability assessment. Under partially-saturated conditions flows in fractures, percolating fracture networks, and fault zones contribute to the fastest spectrum of infiltration velocities via preferential pathways. Specifically, the partitioning dynamics at fracture intersections determine the magnitude of flow fragmentation into vertical and horizontal components and hence the bulk flow velocity and dispersion of fracture networks. In this work, we derive an approximate analytical solution for the partitioning process and validate it using smoothed particle hydrodynamics simulations. The developed transfer function is conceptually based on simulation results and laboratory experiments carried out in previous works. It allows to efficiently simulate flow through fracture networks with simple cubic structure and arbitrary number of fractures and aperture sizes via linear response theory and convolution of a given input signal. We derive a non-dimensional bulk flow velocity ($\widetilde{v}$) and dispersion coefficient ($\widetilde{D}$) to characterize fracture networks in terms of dimensionless horizontal and vertical time scales $\tau_m$ and $\tau_0$. The dispersion coefficient is shown to strongly depend on the horizontal time scale and converges towards a constant value of $0.08$ within reasonable fluid and geometrical parameter ranges, while the non-dimensional velocity exhibits a characteristic $\widetilde{v} \sim \tau_m^{-1/2}$ scaling. Given that hydraulic information is often only available at limited places within (fractured-porous) aquifer system, such as boreholes or springs, our study intends to provide a rudimentary analytical concept to potentially reconstruct internal fracture network geometries from external boundary information, e.g., the dispersive properties of discharge (groundwater level fluctuations).

42 ENGINEERING↗
DOE OSTI2020

Coordinate parameterisation and spectral method optimisation for Beltrami field solver in stellarator geometry

The numerical solution of the stepped pressure equilibrium (Hudson et al 2012 Phys. Plasmas 19 112502) requires a fast and robust solver to obtain the Beltrami field in three-dimensional geometry such as stellarators. The spectral method implemented in the stepped pressure equilibrium code (SPEC) is efficient when the domain is a hollow torus, but ill-conditioning of the discretised linear equations occurs in the (solid) toroid due to the artificially singular coordinate parameterisation near the axis. Here, we propose an improved choice for the reference axis to prevent coordinates surfaces from overlapping. Then, we examine the parity and asymptotics of the magnetic vector potential near the axis and suggest the use of recombined and rescaled Zernike radial basis functions. The maximum relative error in the magnetic field of the Wendelstein 7-X geometry is shown to reach 10 –9 at high resolution in a series of convergence tests and benchmarks against the boundary integral equation solver for Taylor states. The new method is also reported to significantly improve the accuracy of multi-volume SPEC calculations. A comparison between free-boundary SPEC and the analytical Dommaschk potential is presented with higher-than-usual Fourier resolution. It is illustrated that we are able to resolve low amplitude current sheets when an interface is placed where there is no flux surface in the analytic solution. This was previously concealed because of insufficient numerical resolution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗