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At least 433 records · Page 24

Complete quasilinear model for the acceleration-driven lower hybrid drift instability and a computational assessment of its validity

A complete quasilinear model is derived for the electrostatic acceleration-driven lower hybrid drift instability in a uniform two-species low-beta plasma in which current is perpendicular to the background magnetic field. The model consists of coupled nonlinear velocity space diffusion equations for the volume-averaged ion and electron distribution functions. Each species' diffusion coefficient depends on a time-evolving spectral density of the electric-field energy per unit volume and a time-evolving dispersion relation. The dispersion relation is expressed analytically in integral form without the use of asymptotic limits and applies to arbitrary distribution functions, so long as they can be expressed as a function of one velocity coordinate, e.g., f⁡(vy) or f⁡(v⊥). The quasilinear model conserves energy and is complete in that it fully describes the evolution of the distribution functions, including resonant and nonresonant particle-wave interactions, while accounting for distribution-function-dependent mixed-complex frequencies. Further, the quasilinear diffusion model is solved numerically and self-consistently using a Crank-Nicolson temporal discretization and a second-order finite-volume velocity-space discretization. Numerical solutions are compared to nonlinear fourth-order accurate continuum kinetic Vlasov-Poisson simulations. Evolution of electric-field energy, growth rates, distribution functions, and diffusion coefficients are shown to be in agreement with Vlasov simulations. The quasilinear model is shown to predict anomalous transport terms, like resistivity and heating, to within a factor of order unity. Discrepancies between the quasilinear model and Vlasov simulations are assessed and attributed primarily to lack of damping in the quasilinear description and to the use of unperturbed-orbit susceptibilities in the linear theory dispersion relation. The results illuminate the predictive accuracy of the quasilinear model, place approximate bounds on its validity, and provide much needed vetting of quasilinear theory's ability to predict the nonlinear state of a microturbulent plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Continuum kinetic investigation of the impact of bias potentials in the current saturation regime on sheath formation

In this work, we examine sheath formation in the presence of bias potentials in the current saturation regime for pulsed power fusion experiments. It is important to understand how the particle and heat fluxes at the wall may impact the wall material and affect electrode degradation. Here, simulations are performed using the 1X-1V Boltzmann–Poisson system for a proton–electron plasma in the presence of bias potentials ranging from 0 to 10 kV. The results indicate that the sheath near the anode remains generally the same as that of a classical sheath without the presence of a bias potential. However, the sheath near the cathode becomes more prominent with a larger potential drop, a significant decrease in the electron density, and larger sheath lengths. The spatially constant current density increases to a saturation value with the increasing bias potential. For high bias potentials, the material choice needs to consider that the anode faces significantly larger particle and heat fluxes compared to the cathode. In general, the results trend with theory with differences attributed to the simplified assumptions in the theory and the kinetic effects considered in the simulations. Due to the significant computational cost of a well resolved 1X-2V simulation, only one such simulation is performed for the 5 kV case showing higher current.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Electric-field-tunable electronic nematic order in twisted double-bilayer graphene

Graphene-based moiré systems have attracted considerable interest in recent years as they display a remarkable variety of correlated phenomena. Besides insulating and superconducting phases in the vicinity of integer fillings of the moiré unit cell, there is growing evidence for electronic nematic order both in twisted bilayer graphene and twisted double-bilayer graphene (tDBG), as signaled by the spontaneous breaking of the threefold rotational symmetry of the moiré superlattices. Here, we combine symmetry-based analysis with a microscopic continuum model to investigate the structure of the nematic phase of tDBG and its experimental manifestations. First, we perform a detailed comparison between the theoretically calculated local density of states and recent scanning tunneling microscopy data (arXiv:2009.11645) to resolve the internal structure of the nematic order parameter in terms of the layer, sublattice, spin, and valley degrees of freedom. We find strong evidence that the dominant contribution to the nematic order parameter comes from states at the moiré scale rather than at the microscopic scale of the individual graphene layers, which demonstrates the key role played by the moiré degrees of freedom and confirms the correlated nature of the nematic phase in tDBG. Secondly, our analysis reveals an unprecedented tunability of the orientation of the nematic director in tDBG by an externally applied electric field, allowing the director to rotate away from high-symmetry crystalline directions. Here, we compute the expected fingerprints of this rotation in both STM and transport experiments, providing feasible ways to probe it. Rooted in the strong sensitivity of the flat bands of tDBG to the displacement field, this effect opens an interesting route to the electrostatic control of electronic nematicity in moiré systems.

36 MATERIALS SCIENCE↗

Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation

We report the Boltzmann equation with the Bhatnagar-Gross-Krook collision model (Boltzmann-BGK equation) has been employed to describe multiscale flows, i.e., from the hydrodynamic limit to free molecular flow. In this study we employ physics-informed neural networks (PINNs) to solve forward and inverse problems via the Boltzmann-BGK formulation (PINN-BGK), enabling PINNs to model flows in both the continuum and rarefied regimes. In particular, the PINN-BGK is composed of three sub-networks, i.e., the first for approximating the equilibrium distribution function, the second for approximating the non-equilibrium distribution function, and the third one for encoding the Boltzmann-BGK equation as well as the corresponding boundary/initial conditions. By minimizing the residuals of the governing equations and the mismatch between the predicted and provided boundary/initial conditions, we can approximate the Boltzmann-BGK equation for both continuous and rarefied flows. For forward problems, the PINN-BGK is utilized to solve various benchmark flows given boundary/initial conditions, e.g. Kovasznay flow, Taylor-Green flow, cavity flow, and micro Couette flow for Knudsen number up to 5. For inverse problems, we focus on rarefied flows in which accurate boundary conditions are difficult to obtain. We employ the PINN-BGK to infer the flow field in the entire computational domain given a limited number of interior scattered measurements on the velocity without using the (unknown) boundary conditions. Results for the two-dimensional micro Couette and micro cavity flows with Knudsen numbers ranging from 0.1 to 10 indicate that the PINN-BGK can infer the velocity field in the entire domain with good accuracy. Finally, we also present some results on using transfer learning to accelerate the training process. Specifically, we can obtain a three-fold speedup comparted to the standard training process (e.g., Adam plus L-BFG-B) for the two-dimensional flow problems considered in our work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

First principles simulation of reacting hypersonic flow over a blunt wedge

This article presents molecular-level analysis of a reactive, near-continuum, Mach 21 nitrogen flow over a blunt wedge using the direct molecular simulation (DMS) method. The flow conditions lead to internal energy excitation and dissociation in the flow field, resulting in thermal and chemical nonequilibrium in the flow. Thermal nonequilibrium in the vibrational mode is observed to extend to the molecular level, where the vibrational energy distributions at various points in the flow field are observed to be non-Boltzmann. Furthermore, this is the first reactive DMS calculation where the wall is assumed to be isothermal and full momentum accommodation of the particles is enforced, hence incorporating viscous wall effects. Since the DMS method uses a quantum mechanically generated interaction potential as its only modeling input, all thermochemical and transport properties of the flow field can directly be attributed to the ab initio potential energy surface. Using the DMS solution as a benchmark, this article assesses the performance of Navier–Stokes computational fluid dynamics solutions using lower fidelity two-temperature models. Two models are chosen as points of comparison: the well-known Park two-temperature model and the recently developed modified Marrone and Treanor model.

Mechanics↗

A finite micro-rotation material point method for micropolar solid and fluid dynamics with three-dimensional evolving contacts and free surfaces

This paper introduces an explicit material point method designed specifically for simulating the micropolar continuum dynamics in the finite deformation and finite microrotation regime. The material point method enables us to simulate large deformation problems while circumventing the potential mesh distortion without remeshing. To eliminate rotational motion damping and loss of angular momentum during the projection, we introduce the mapping for microinertia and angular momentum between particles and grids through the affine particle-in-cell approach. The microrotation and the curvature at each particle are updated through zero-order forward integration of the microgyration and its spatial gradient. We show that the microinertia and the angular momentum are conserved during the projections between particles and grids in our formulation. We verify the formulation and implementation by comparing with the analytical dispersion relation of micropolar waves under the small strain and small microrotation, as well as the analytical soliton solution for solids undergoing large deformation and large microrotation. Additionally we also demonstrate the capacity of the proposed computational framework to handle a wide spectrum of simulations that exhibit size effects in the geometrical nonlinear regime through three representative numerical examples, i.e., a cantilever beam torsion problem, a fragment-impact penetration problem, and a micropolar fluid discharging problem.

42 ENGINEERING↗

Advanced Physics Models for Particle-Particle Interactions (UCD final report)

The LDRD "Advanced Physics Models for Particle-Particle Interactions” collaborative research with Professor Jennifer Sinclair Curtis and PhD student Chanh Nguyen at the University of California, Davis involved meso-scale, discrete element method (DEM) modeling of micron-sized particles impacting a substrate. Using DEM, physical insight into the details of particle response upon impact can be obtained. Such details provide the type of information necessary to enhance existing continuum or macro-scale simulation tools so that modeling for material strength and particle breakage models is based on particle physics versus empirical relationships. While molecular dynamics simulations of atoms can also provide physical insight into the particle response to impact, the scale of particles that are treated is on the order of angstroms, not microns. This study gives evidence to the ability of the DEM simulation technique to provide such fundamental, detailed insight for micron-sized particles as a function of particle properties and impact velocity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Holographic codes from hyperinvariant tensor networks

Holographic quantum-error correcting codes are models of bulk/boundary dualities such as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, where a higher-dimensional bulk geometry is associated with the code’s logical degrees of freedom. Previous discrete holographic codes based on tensor networks have reproduced the general code properties expected from continuum AdS/CFT, such as complementary recovery. However, the boundary states of such tensor networks typically do not exhibit the expected correlation functions of CFT boundary states. In this work, we show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states. Furthermore, these codes exhibit a state-dependent breakdown of complementary recovery as expected from AdS/CFT under small quantum gravity corrections.

97 MATHEMATICS AND COMPUTING↗

Toward a First-Principles Framework for Predicting Collective Properties of Electrolytes

Conspectus Given the universal importance of electrolyte solutions, it is natural to expect that we have a nearly complete understanding of the fundamental properties of these solutions (e.g., the chemical potential) and that we can therefore explain, predict, and control the phenomena occurring in them. In fact, reality falls short of these expectations. But, recent advances in the simulation and modeling of electrolyte solutions indicate that it should soon be possible to make progress toward these goals. In this Account, we will discuss the use of first-principles interaction potentials based in quantum mechanics (QM) to enhance our understanding of electrolyte solutions. Specifically, we will focus on the use of quantum density functional theory (DFT) combined with molecular dynamics simulation (DFT-MD) as the foundation for our approach. The overarching concept is to understand and accurately reproduce the balance between local or short-ranged (SR) structural details and long-range (LR) correlations, allowing the prediction of the thermodynamics of both single ions in solution as well as the collective interactions characterized by activity/osmotic coefficients. In doing so, relevant collective motions and driving forces characterized by chemical potentials can be determined. Here, in this Account, we will make the case that understanding electrolyte solutions requires a faithful QM representation of the SR nature of the ion–ion, ion–water, and water–water interactions. However, the number of molecules that is required for collective behavior makes the direct application of high-level QM methods that contain the best SR physics untenable, making methods that balance accuracy and efficiency a practical goal. Alternatives such as continuum solvent models (CSMs) and empirically based classical molecular dynamics have been extensively employed to resolve this problem but without yet overcoming the fundamental issue of SR accuracy. We will demonstrate that accurately describing the SR interaction is imperative for predicting both intrinsic properties, namely, at infinite dilution, and collective properties of electrolyte solutions. DFT has played an important role in our understanding of condensed phase systems, e.g., bulk liquid water, the air–water interface, ions in bulk, and at the air–water interface. This approach holds huge promise to provide benchmark calculations of electrolyte solution properties that will allow for the development and improvement of more efficient methods, as well as an enhanced understanding of fundamental phenomena. However, the standard protocol using the generalized gradient approximation with van der Waals (vdW) correction requires improvement in order to achieve a high level of quantitative accuracy. Simply simulating with higher level DFT functionals may not be the best route considering the significant computational cost. Alternative methods of incorporating information from higher levels of QM should be explored; e.g., using force matching techniques on small clusters, where high level benchmark calculations are possible, to develop ideal correction terms to the DFT functional is a promising possibility. We argue that DFT with statistical mechanics is becoming an increasingly useful framework enabling the prediction of collective electrolyte properties.

Duignan, Timothy T.↗

The Evolution of the Peridynamics Co-Authorship Network

We report peridynamics is a relatively new field in continuum mechanics that has developed over the past 20 years. This paper studies the evolution of collaborations in the field of peridynamics since its inception using social network analysis. For this purpose, we construct a network for each year from 2000 to 2019 describing co-authorship between scientists in peridynamics. In these networks, each node represents a scientist and each link connects two co-authoring scientists with a link weight representing the frequency and strength of their collaboration; each network as a whole can be thought of as a graph representation of the peridynamics community for the given year. By constructing a network for each year, we are able to analyze the evolution of the network in time and discuss the implications of this evolution for the peridynamics community. Our study demonstrates that the peridynamics community has been growing exponentially in size in recent years. Centrality metrics are also used to identify the most collaborative scientists in the community. Moreover, we compute link recommendations based on both elevating a scientist’s position in the network with respect to certain centrality metrics or closing structural holes in the network identified with persistent homology. We further extend the analysis to higher-order networks whose nodes represent groups of scientists in the community and whose links connect collaborating groups. In some sense, our work studies the past, present, and future of the peridynamics community.

97 MATHEMATICS AND COMPUTING↗

Overset-Grid Method with Smooth Orbital Partitioning for Molecular Scattering Calculations

To solve molecular photoionization and electron scattering problems, we use an overset-grid representation of electronic continuum functions, which has an extended central spherical grid that overlaps small spherical grids (subgrids) centered on each atom of a polyatomic molecule. Here, in this work, we present an improved algorithm that smoothly partitions the total wave function between the central grid and the atomic subgrids. The smooth partitioning allows one to use approximately one-fourth the number of partial waves on the central grid compared to our previous implementation with switching functions. The resulting numerical method for treating electron scattering and photoionization of polyatomic molecules combines the accuracy and flexibility of pure numerical grid representations with the rapid convergence of hybrid combinations of atom-centered basis-set expansions and grid methods. The overset-grid representation is implemented using the complex Kohn variational principle for scattering and photoionization amplitudes. The faster convergence with respect to the number of central grid partial waves is demonstrated and accuracy is verified by comparisons with the previous implementation and with far more computationally demanding single-center numerical expansions in electron-molecule scattering and photoionization calculations on the neon dimer (Ne 2 ) system, carbon tetrafluoride (CF 4 ) molecule, and the pyridine (C 5 H 5 N) molecule in the static-exchange approximation.

Molecules↗

Modeling Heat Pipe Startup And Noncondensable Gases In Sockeye

A one-dimensional gas mixture flow model was developed and implemented in the heat pipe code Sockeye to model the effects of non-condensable gases. Additionally a startup model based on the dusty gas model was implemented to model the transition from rarefied gas dynamics to continuum flow, which occurs during the frozen startup of high-temperature heat pipes. Multiple startup models and non-condensable gas models were tested against experimental data for sodium heat pipes, showing excellent agreement. Additionally, the newly developed gas mixture model for modeling non-condensable gas is further tested with a theoretical case study with arbitrary heating configurations. Finally, several recommendations and conclusions are made from the studies in this work to guide future heat pipe modeling efforts.

97 - MATHEMATICS AND COMPUTING↗

Time-dependent density functional theory of charge, energy, and spin transport, and quantum continuum mechanics (Final Report)

The overarching goal of this project, which unfolded over a period of seventeen years, including two no-cost extensions in the last two years, was to extend and deepen our ability to use time-dependent density functional theory and related theoretical methods for the description of the transport of charge, spin, or energy in quantum electronic systems at the nanoscale. The output of our efforts is contained in 52 papers, listed below, which we have published since 2006. There have also been many presentations at international conferences, workshops, colloquia and seminars. This body of work has been carried out with the essential input of 8 postdoctoral students (who were supported by the grant) and several external senior collaborators and their postdocs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multi-scale modeling of the electric field assisted sintering process

The electric field assisted sintering (EFAS) process involves tightly coupled physics that influence microstructural evolution in the particles being compacted. It is also an inherently multi-scale phenomenon, with the microstructure of the compact influencing the subsequent engineering-scale response of the sintering system. To improve understanding of how processing parameters influence microstructural evolution, we have developed a multi-scale modeling approach that couples a continuum-level model of the sintering system with a phase-field model for microstructural evolution of particles within the compact. The phase-field model couples the effect of chemical and electrical driving forces on microstructural evolution and includes the effect of charged defect segregation to surfaces and grain boundaries; this segregation leads to enhanced defect transport and heat generation at these interfaces in response to applied electric field. The effect of enhanced heat generation on particle neck growth and the influence of microstructural evolution on the engineering-scale model are demonstrated.

36 - MATERIALS SCIENCE↗

Quantitative study of the effect of grain boundary parameters on the slip system level Hall-Petch slope for basal slip system in Mg-4Al

Several theoretical studies have reported that the geometry and structure of grain boundaries in polycrystalline materials could impose a significant effect on the Hall-Petch slope. However, experimental observations are primarily limited by the ability of the techniques to accurately quantify the grain boundary strength and validate these theoretical models. Using high-resolution electron backscatter diffraction (HR-EBSD), the local stress tensor ahead of a slip band blocked by a grain boundary was quantified and coupled with a continuum dislocation pile-up model to assess the barrier strength of specific grain boundaries to specific slip systems, referred to as micro-Hall-Petch coefficient. For basal slip system in a deformed Mg-4Al alloy, the micro-Hall-Petch coefficient ($k^{basal}_{μ}$) varied significantly, from 0.054 to 0.184 MPa - m 1/2 for nine different grain boundaries. These results were correlated with geometric descriptors of the respective grain boundaries, with three-dimensional GB profile additionally measured via focused ion beam milling. It was found that the angle between the two slip plane traces on the grain boundary plane was the most sensitive parameter affecting $k^{basal}_{μ}$, followed by the angle between the slip directions. A functional form for calculation of $k^{basal}_{μ}$ depending on these two angles is proposed to augment crystal plasticity constitutive models with slip resistance dependent on some measure of the grain size. The method allows a new pathway to calibrate grain size strengthening parameters in crystal plasticity models, allowing further computational investigations of the interrelationship between texture, grain morphology, and the Hall Petch effect.

36 MATERIALS SCIENCE↗

Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions. However, material identification is a challenging task, especially when the characteristic of the material is highly nonlinear in nature, as is common in biological tissue. In this work, we identify unknown material properties in continuum solid mechanics via physics-informed neural networks (PINNs). To improve the accuracy and efficiency of PINNs, we develop efficient strategies to nonuniformly sample observational data. We also investigate different approaches to enforce Dirichlet-type boundary conditions (BCs) as soft or hard constraints. Finally, we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space. The estimated material parameters achieve relative errors of less than 1%. As such, this work is relevant to diverse applications, including optimizing structural integrity and developing novel materials.

97 MATHEMATICS AND COMPUTING↗

Multi-Scale Modeling Framework for Mercury Biogeochemistry

Multi-Scale modeling of mercury (Hg) geochemical speciation and reactions has been performed by integrating atomistic quantum chemical calculations with continuum scale speciation models. Major progress has been made in the improvement of quantum chemical models to calculate critical thermodynamic data for Hg complexes in aquatic environments. Rapid and reliable quantum chemical approaches have been developed for calculating acid dissociation constants (pK a ) and stability constants (log K), with calculated mean unsigned errors of 0.5 and 1.5 log units, respectively for ligand molecules and Hg complexes. At the continuum scale, systematic analysis of uncertainty propagation in mercury (Hg) speciation modeling has been conducted and was used to identify environmental conditions under which thermodynamic constant uncertainties are significant and recommended to be accounted for. The integrated framework for multi-scale modeling of mercury geochemistry is open to the research community through the web-based multiscale modeling aqueous speciation resource, AQUA-MER. The improved quantum chemical approaches for thermodynamic constant calculations are accessible through AQUA-MER and can be used to provide the missing constants in the continuum scale speciation calculations. In addition to low molecular mass Hg complex speciation, modeling natural aquatic environments also involve the transport of high molecular weight dissolved organic matter (DOM) in reactive flows simultaneously with equilibrium and kinetic reactions. To this end, atomistic MD simulations were performed to capture the details of aggregation, mechanisms and distribution of functional groups in DOM at the molecular level. The elemental composition and calculated bulk properties of the DOM models are in close agreement with experimental measurements. A travel-time based reactive transport model in the hyporheic zone of stream corridors was established for the multicomponent Hg-DOM-S system and implemented through PFLOTRAN.

54 ENVIRONMENTAL SCIENCES↗

Protein drift-diffusion dynamics and phase separation in curved cell membranes and dendritic spines: Hybrid discrete-continuum methods

We develop methods for investigating protein drift-diffusion dynamics in heterogeneous cell membranes and the roles played by geometry, diffusion, chemical kinetics, and phase separation. Our hybrid stochastic numerical methods combine discrete particle descriptions with continuum-level models for tracking the individual protein drift-diffusion dynamics when coupled to continuum fields. We show how our approaches can be used to investigate phenomena motivated by protein kinetics within dendritic spines. The spine geometry is hypothesized to play an important biological role regulating synaptic strength, protein kinetics, and self-assembly of clusters. We perform simulation studies for model spine geometries varying the neck size to investigate how phase-separation and protein organization is influenced by different shapes. We also show how our methods can be used to study the roles of geometry in reaction-diffusion systems including Turing instabilities. Furthermore, our methods provide general approaches for investigating protein kinetics and drift-diffusion dynamics within curved membrane structures.

97 MATHEMATICS AND COMPUTING↗