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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Fast magnetic reconnection and the ideal evolution of a magnetic field

Regardless of how small non-ideal effects may be, phenomena associated with changes in magnetic field line connections are frequently observed to occur on an Alfvénic time scale. Since it is mathematically impossible for magnetic field line connections to change when non-ideal effects are identically zero, an ideal evolution must naturally lead to states of unbound sensitivity to non-ideal effects. That such an evolution is natural is demonstrated by the use of Lagrangian coordinates based on the flow velocity of the magnetic field lines. The Lagrangian representation of an evolving magnetic field is highly constrained when neither the magnetic field strength nor the forces exerted by the magnetic field increase exponentially with time. The development of a state of fast reconnection consistent with these constraints (1) requires a three-dimensional evolution, (2) has an exponentially increasing sensitivity to non-ideal effects, and (3) has a parallel current density, which lies in exponentially thinning but exponentially widening ribbons, with a magnitude that is limited to a slow growth. The implication is that exponential growth in sensitivity is the cause of fast magnetic reconnection when non-ideal effects are sufficiently small. The growth of the non-ideal effect of the resistivity multiplied by the parallel current density is far too slow to be competitive.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Randomized Algorithms for Scientific Computing (RASC)

Randomized algorithms have propelled advances in artificial intelligence (AI) and represent a foundational research area in advancing AI for Science. Future advancements in DOE Office of Science priority areas such as climate science, astrophysics, fusion, advanced materials, combustion, and quantum computing all require randomized algorithms for surmounting challenges of complexity, robustness, and scalability. Advances in data collection and numerical simulation have changed the dynamics of scientific research and motivate the need for randomized algorithms. For instance, advances in imaging technologies such as X-ray ptychography, electron microscopy, electron energy loss spectroscopy, or adaptive optics lattice light-sheet microscopy collect hyperspectral imaging and scattering data in terabytes, at breakneck speed enabled by state-of-the-art detectors. The data collection is exceptionally fast compared with its analysis. Likewise, advances in high-performance architectures have made exascale computing a reality and changed the economies of scientific computing in the process. Floating-point operations that create data are essentially free in comparison with data movement. Thus far, most approaches have focused on creating faster hardware. Ironically, this faster hardware has exacerbated the problem by making data still easier to create. Under such an onslaught, scientists often resort to heuristic deterministic sampling schemes (e.g., low-precision arithmetic, sampling every nth element) and sacrifice potentially valuable accuracy. Dramatically better results can be achieved via randomized algorithms, reducing the data size as much as or more than naive deterministic subsampling can achieve, while retaining the high accuracy of computing on the full data set. By randomized algorithms we mean those algorithms that employ some form of randomness in internal algorithmic decisions to accelerate time to solution, increase scalability, or improve reliability. Examples include matrix sketching for solving large-scale least-squares problems (see Figure 1) and stochastic gradient descent for training machine learning models. We are not recommending heuristic methods but rather randomized algorithms that have certificates of correctness and probabilistic guarantees of optimality and near-optimality. Such approaches can be useful beyond acceleration, for example, in understanding how to avoid measure zero worst-case scenarios that plague methods such as QR matrix factorization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Lattice Dynamics and Optoelectronic Properties of Vacancy-Ordered Double Perovskite Cs 2 TeX 6 (X = Cl – , Br – , I – ) Single Crystals

The soft, dynamic lattice of inorganic lead halide perovskite CsPbX 3 (X = Cl ⁻ , Br ⁻ , I ⁻ ) leads to the emergence of many interesting photophysical and optoelectronic phenomena. However, probing their lattice dynamics with vibrational spectroscopy remains challenging. The influence of the fundamental octahedral building block in the perovskite lattice can be better resolved in zero-dimensional (0D) vacancy-ordered double perovskites of form A 2 BX 6 . Here we study Cs 2 TeX 6 (X = Cl ⁻ , Br ⁻ , I ⁻ ) single crystals to yield detailed insight into the fundamental octahedral building block and to explore the effect that its isolation in the crystal structure has on structural and electronic properties. The isolated [TeX 6 ] 2- octahedral units serve as the vibrational, absorbing, and emitting centers within the crystal. Serving as the vibrational centers, the isolated octahedra inform the likelihood of a random distribution of 10 octahedral symmetries within the mixed-halide spaces, as well as the presence of strong exciton-phonon coupling and anharmonic lattice dynamics. Serving as the absorbing and emitting centers, the isolated octahedra exhibit compositionally tunable absorption (1.50-3.15 eV) and emission (1.31-2.11 eV) energies. Due to greater molecular orbital overlap between neighboring octahedra with increasing halide anion size, there is a transition from a more molecule-like electronic structure in Cs 2 TeCl 6 and Cs 2 TeBr 6 -as expected from the effective 0D nature of these single crystals-to a dispersive electronic structure in Cs 2 TeI 6 , typical of three-dimensional (3D) bulk single crystals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

The scattering of spinning hadrons from lattice QCD

Hadron spectroscopy is predominantly the study of resonances that decay via the strong interaction into a multitude of stable hadrons, such as the pion. The vast majority of resonances decay via an intermediate hadron with non-zero intrinsic spin. In this thesis, I will present the results of scattering calculations featuring mesons with non-zero intrinsic spin. Before doing so, I will first give a brief introduction to QCD and review the framework necessary to perform lattice QCD calculations in Chapters 1 and 2. In Chapter 3, I present the first lattice calculation of ?? scattering in isospin-2. Here, ?? features in dynamically-coupled 3S1 and 3D1 partial-waves with JP=1+. No resonance enhancement is anticipated in the flavour exotic isospin-2 channel and as such it provides an ideal testing ground for this first calculation. I work at heavier than physical quark masses at the SU(3)F point where the up, down and strange quarks are mass degenerate. Finite-volume spectra are calculated and, utilising the relationship between the discrete energy spectrum and the infinite-volume scattering amplitudes, partial-wave amplitudes with J?3 and the degree of dynamical mixing between the coupled 3S1 and 3D1 channels are determined. In Chapter 4, I investigate ?? in isospin-1 where the a1 axial-vector resonance is expected to feature. Here, I present a discussion on G-parity and Bose-symmetry at the SU(3)F point. Working at heavier than physical quark masses, the resulting finite volume spectrum suggests that the a1 is a bound-state and that the 3S1- and 3D1-wave, ?? scattering amplitudes are similar to those in isospin-2. I present the first calculation of coupled ?? and ?? scattering in Chapter 5 where resonant enhancement is seen experimentally in the JP=1+ channel. Working at a somewhat lighter pion mass than in previous chapters, the finite-volume spectra are determined and the scattering amplitudes are calculated. Analytically continuing the amplitudes into the complex energy plane, a resonance pole is found, interpreted as the analogue of the b1 axial-vector, which couples dominantly to 3S1-wave ??, with a much-suppressed coupling to 3D1-wave ??, and a negligible coupling to ??. In Chapter 6, the exotic JPC=1?+ channel is studied. These quantum numbers are not allowed in the quark model but can be obtained, for example, through a gluonic excitation coupled to a quark-antiquark pair. In this exploratory calculation, performed at the SU(3)F point, the finite-volume spectra and coupled-channel scattering amplitudes are presented. A single resonance pole is found, interpreted as the exotic ?1, and couplings to meson-meson channels, including for example ??{1P1}, ???{1P1} and ??{3P1}, are calculated for the first time in lattice QCD. In order to minimally present the contents of a unitary n-channel scattering matrix, I introduce, in Chapter 7, an n-channel generalisation of the traditional two-channel Stapp parameterisation.

Woss, Antoni↗
DOE OSTI2025

Zero-Field NMR and Millitesla-SLIC Spectra for >200 Molecules from Density Functional Theory and Spin Dynamics

NMR is usually performed at magnetic fields of 1 T and above to obtain sufficient sensitivity and spectral dispersion to identify chemicals based on chemical shifts and J couplings. At lower fields, the advent of hyperpolarization technologies and sensitive detectors can address sensitivity concerns. However, it remains disputed whether spectral signatures at zero and ultra-low fields are sufficient for chemical identification. Here, we report an all–electron DFT-based batch calculation of J-coupling constants, which are used to generate J coupling NMR spectra at zero field and 6.5 mT for over 200 small molecules. In the developed computational tool chain, we first used the all-electron FHI-aims code to calculate the molecular J couplings and chemical shifts. We then fed the calculated NMR parameters into the NMR simulation package SPINACH to simulate both heteronuclear J coupling spectra at zero-field, and homonuclear J coupling spectra as spin-lock induced crossing (SLIC) spectra at ultra-low field (6.5 mT). The resulting spectra demonstrate that zero and ultra-low field NMR spectra can represent unique identifiers of chemical structure for small molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Dynamics of straight vortex filaments in a Bose–Einstein condensate with the Gaussian density profile

The dynamics of interacting quantized vortex filaments in a rotating Bose–Einstein condensate existing in the Thomas–Fermi regime at zero temperature and obeying the Gross–Pitaevskii equation has been considered in the hydrodynamic “nonelastic” approximation. A noncanonical Hamilton equation of motion for the macroscopically averaged vorticity has been derived for a smoothly inhomogeneous array of filaments (vortex lattice) taking into account spatial nonuniformity of the equilibrium density of the condensate, which is determined by the trap potential. The minimum of the corresponding Hamiltonian describes the static configuration of the deformed vortex lattice against the preset density background. The condition of minimum can be reduced to a nonlinear second-order partial differential vector equation for which some exact and approximate solutions are obtained. It has been shown that if the condensate density has an anisotropic Gaussian profile, the equation of motion for the averaged vorticity has solutions in the form of a vector exhibiting a nontrivial time dependence, but homogeneous in space. An integral representation has also been obtained for the matrix Green function that determines the nonlocal Hamiltonian of a system of several quantized vortices of an arbitrary shape in a Bose–Einstein condensate with the Gaussian density. In particular, if all filaments are straight and oriented along one of the principal axes of the ellipsoid, we have a finitedimensional reduction that can describe the dynamics of the system of pointlike vortices against an inhomogeneous background. A simple approximate expression is proposed for the 2D Green function with an arbitrary density profile and is compared numerically with the exact result in the Gaussian case. The corresponding approximate equations of motion, describing the long-wavelength dynamics of interacting vortex filaments in condensates with a density depending only on transverse coordinates, have been derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Non-adiabatic quantum reactive scattering in hyperspherical coordinates

A new electronically non-adiabatic quantum reactive scattering methodology is presented based on a time-independent coupled channel formalism and the adiabatically adjusting principal axis hyperspherical coordinates of Pack and Parker [J. Chem. Phys. 87, 3888 (1987)]. The methodology computes the full state-to-state scattering matrix for A + B 2 (v, j) ↔ AB(v', j') + B and A + AB(v, j) → A + AB(v', j') reactions that involve two coupled electronic states which exhibit a conical intersection. The methodology accurately treats all six degrees of freedom relative to the center-of-mass which includes non-zero total angular momentum J and identical particle exchange symmetry. The new methodology is applied to the ultracold hydrogen exchange reaction for which large geometric phase effects have been recently reported [B. K. Kendrick et al., Phys. Rev. Lett. 115, 153201 (2015)]. Rate coefficients for the H/D + HD(v = 4, j = 0) → H/D + HD(v', j') reactions are reported for collision energies between 1 μK and 100 K (total energy ≈1.9 eV). A new diabatic potential energy matrix is developed based on the Boothroyd, Keogh, Martin, and Peterson (BKMP2) and double many body expansion plus single-polynomial (DSP) adiabatic potential energy surfaces for the ground and first excited electronic states of H 3 , respectively. The rate coefficients computed using the new non-adiabatic methodology and diabatic potential matrix reproduce the recently reported rates that include the geometric phase and are computed using a single adiabatic ground electronic state potential energy surface (BKMP2). The dramatic enhancement and suppression of the ultracold rates due to the geometric phase are confirmed as well as its effects on several shape resonances near 1 K. In conclusion, the results reported here represent the first fully non-adiabatic quantum reactive scattering calculation for an ultracold reaction and validate the importance of the geometric phase on the Wigner threshold behavior.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Spectral function of the $J_1$ – $J_2$ Heisenberg model on the triangular lattice

Spectral probes, such as neutron scattering, are crucial for characterizing excitations in quantum many-body systems and the properties of quantum materials. Among the most elusive phases of matter are quantum spin liquids, which have no long-range order even at zero temperature and host exotic fractionalized excitations with nontrivial statistics. These phases can occur in frustrated quantum magnets, such as the paradigmatic Heisenberg model with nearest- and next-nearest-neighbor exchange interactions on the triangular lattice, the so-called $J_1$ – $J_2$ model. In this work, we compute the spectral function using large-scale matrix product state simulations across the three different phases of this model's phase diagram, including a quantum spin-liquid phase at intermediate $J_2$/$J_1$. Despite a plethora of theoretical and experimental studies, the exact nature of this phase is still contested, with the dominant candidates being a gapped $\mathbb{Z}_2$, a gapless U(1) Dirac, and a spinon Fermi surface quantum spin-liquid state. We find a V-shaped spectrum near the center of the Brillouin zone ($Γ$ point), a key signature of a spinon Fermi surface, observed in prior neutron scattering experiments. However, we find a small gap near the $Γ$ point, ruling out such a phase. Furthermore, we find localized gapless excitations at the corner of the Brillouin zone boundary (K point) and the middle of the edge of the Brillouin zone boundary (M point), ruling out the gapped $\mathbb{Z}_2$ spin-liquid phase. Here, our results imply that the intermediate spin-liquid phase is a gapless $U(1)$ Dirac spin liquid, and provide clear signatures to detect this phase in future neutron scattering experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Self-organized Segregation on the Grid

We consider an agent-based model with exponentially distributed waiting times in which two types of agents interact locally over a graph, and based on this interaction and on the value of a common intolerance threshold τ, decide whether to change their types. This is equivalent to a zero-temperature ising model with Glauber dynamics, an asynchronous cellular automaton with extended Moore neighborhoods, or a Schelling model of self-organized segregation in an open system, and has applications in the analysis of social and biological networks, and spin glasses systems. Some rigorous results were recently obtained in the theoretical computer science literature, and this work provides several extensions. We enlarge the intolerance interval leading to the expected formation of large segregated regions of agents of a single type from the known size ϵ>0 to size ≈0.134. Namely, we show that for 0.433<τ<1/2 (and by symmetry 1/2<τ<0.567), the expected size of the largest segregated region containing an arbitrary agent is exponential in the size of the neighborhood. We further extend the interval leading to expected large segregated regions to size ≈0.312 considering “almost segregated” regions, namely regions where the ratio of the number of agents of one type and the number of agents of the other type vanishes quickly as the size of the neighborhood grows. In this case, we show that for 0.344<τ≤0.433 (and by symmetry for 0.567≤τ<0.656) the expected size of the largest almost segregated region containing an arbitrary agent is exponential in the size of the neighborhood. This behavior is reminiscent of supercritical percolation, where small clusters of empty sites can be observed within any sufficiently large region of the occupied percolation cluster. The exponential bounds that we provide also imply that complete segregation, where agents of a single type cover the whole grid, does not occur with high probability for p=1/2 and the range of intolerance considered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

High-Field Magnetoelectric and Spin-Phonon Coupling in Multiferroic (NH 4 ) 2 [FeCl 5 ·(H 2 O)]

We combine high field polarization, magneto-infrared spectroscopy, and lattice dynamics calculations with prior magnetization to explore the properties of (NH 4 ) 2 [FeCl 5 ·(H 2 O)]-a type II molecular multiferroic in which the mixing between charge, structure, and magnetism is controlled by intermolecular hydrogen and halogen bonds. Electric polarization is sensitive to the series of field-induced spin reorientations, increasing linearly with the field and reaching a maximum before collapsing to zero across the quasi-collinear to collinear-sinusoidal reorientation due to the restoration of inversion symmetry. Magnetoelectric coupling is on the order of 1.2 ps/m for the P∥c, H∥c configuration between 5 and 25 T at 1.5 K. In this range, the coupling takes place via an orbital hybridization mechanism. Other forms of mixing are active in (NH 4 ) 2 [FeCl 5 ·(H 2 O)] as well. Magneto-infrared spectroscopy reveals that all of the vibrational modes below 600 cm –1 are sensitive to the field-induced transition to the fully saturated magnetic state at 30 T. We analyze these local lattice distortions and use frequency shifts to extract spin-phonon coupling constants for the Fe–O stretch, Fe–OH 2 rock, and NH 4 + libration. Inspection also reveals subtle symmetry breaking of the ammonium counterions across the ferroelectric transition. Here, the coexistence of such varied mixing processes in a platform with intermolecular hydrogen- and halogen-bonding opens the door to greater understanding of multiferroics and magnetoelectrics governed by through-space interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems

We develop a new robust methodology for the stochastic Navier–Stokes equations based on the dynamically-orthogonal (DO) and bi-orthogonal (BO) methods . Both approaches are variants of a generalized Karhunen–Loève (KL) expansion in which both the stochastic coefficients and the spatial basis evolve according to system dynamics, hence, capturing the low-dimensional structure of the solution. The DO and BO formulations are mathematically equivalent , but they exhibit computationally complimentary properties. Specifically, the BO formulation may fail due to crossing of the eigenvalues of the covariance matrix, while both BO and DO become unstable when there is a high condition number of the covariance matrix or zero eigenvalues. To this end, we combine the two methods into a robust hybrid framework and in addition we employ a pseudo-inverse technique to invert the covariance matrix. The robustness of the proposed method stems from addressing the following issues in the DO/BO formulation: (i) eigenvalue crossing: we resolve the issue of eigenvalue crossing in the BO formulation by switching to the DO near eigenvalue crossing using the equivalence theorem and switching back to BO when the distance between eigenvalues is larger than a threshold value; (ii) ill-conditioned covariance matrix: we utilize a pseudo-inverse strategy to invert the covariance matrix; (iii) adaptivity: we utilize an adaptive strategy to add/remove modes to resolve the covariance matrix up to a threshold value. In particular, we introduce a soft-threshold criterion to allow the system to adapt to the newly added/removed mode and therefore avoid repetitive and unnecessary mode addition/removal. When the total variance approaches zero, we show that the DO/BO formulation becomes equivalent to the evolution equation of the Optimally Time-Dependent modes . We demonstrate the capability of the proposed methodology with several numerical examples, namely (i) stochastic Burgers equation: we analyze the performance of the method in the presence of eigenvalue crossing and zero eigenvalues; (ii) stochastic Kovasznay flow: we examine the method in the presence of a singular covariance matrix; and (iii) we examine the adaptivity of the method for an incompressible flow over a cylinder where for large stochastic forcing thirteen DO/BO modes are active.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Shuttling Majorana zero modes in disordered and noisy topological superconductors

The braiding of Majorana zero modes (MZMs) forms the fundamental building block for topological quantum computation. Braiding protocols which involve the physical exchange of MZMs are typically envisioned on a network of topological superconducting wires. An important component of these protocols is the transport of MZMs, which can be performed by using electric gates to locally tune sections of the wire between topologically trivial and nontrivial phases. In this work, we numerically simulate this transport by tuning a single section of a superconducting wire which contains either disorder (uncorrelated and correlated) or noise. We focus on the impact of these additional effects on the diabatic error, which describes unwanted transitions between the ground state and excited states. We show that the behavior of the average diabatic error is predominantly controlled by the statistics of the minimum bulk energy gap which is suppressed in the presence of disorder. The increase in diabatic error can be several orders of magnitude and is most deleterious when the disorder correlation length is a finite fraction of the transport distance and negligible when these lengths are far apart. In the presence of noise, the diabatic error is significantly enhanced due to optical transitions which depend on the minimum bulk energy gap as well as the frequency modes present in the noise. The results presented here serve to further characterize the diabatic error in disordered and noisy settings, which are important considerations in practical implementations of physical braiding schemes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Quantifying uncertainty in analysis of shockless dynamic compression experiments on platinum. I. Inverse Lagrangian analysis

Absolute measurements of solid-material compressibility by magnetically driven shockless dynamic compression experiments to multi-megabar pressures have the potential to greatly improve the accuracy and precision of pressure calibration standards for use in diamond anvil cell experiments. Here, to this end, we apply characteristics-based inverse Lagrangian analysis (ILA) to 11 sets of ramp-compression data on pure platinum (Pt) metal and then reduce the resulting weighted-mean stress–strain curve to the principal isentrope and room-temperature isotherm using simple models for yield stress and Grüneisen parameter. We introduce several improvements to methods for ILA and quasi-isentrope reduction, the latter including calculation of corrections in wave speed instead of stress and pressure to render results largely independent of initial yield stress while enforcing thermodynamic consistency near zero pressure. More importantly, we quantify in detail the propagation of experimental uncertainty through ILA and model uncertainty through quasi-isentrope reduction, considering all potential sources of error except the electrode and window material models used in ILA. Compared to previous approaches, we find larger uncertainty in longitudinal stress. Monte Carlo analysis demonstrates that uncertainty in the yield-stress model constitutes by far the largest contribution to uncertainty in quasi-isentrope reduction corrections. We present a new room-temperature isotherm for Pt up to 444 GPa, with 1-sigma uncertainty at that pressure of just under ±1.2%; the latter is about a factor of three smaller than uncertainty previously reported for multi-megabar ramp-compression experiments on Pt. The result is well represented by a Vinet-form compression curve with (isothermal) bulk modulus K 0 = 270.3 ± 3.8 GPa, pressure derivative K$^{'}_{0}$= 5.66 ± 0.10, and correlation coefficient $R_{K_{0},K^{'}_{0}}$= –0.843.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Dynamics of disordered mechanical systems with large connectivity, free probability theory, and quasi-Hermitian random matrices

Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the systems studied in this paper have all their degrees of freedom coupled to each other. Thus, the problem of linearized small oscillations of such systems involves two full positive-definite and non-commuting matrices, as opposed to the sparse matrices associated with disordered crystals. Consequently, the familiar methods for determining the averaged vibrational spectra of disordered crystals, introduced many years ago by Dyson and Schmidt, are inapplicable for highly connected disordered systems. In this paper we apply random matrix theory (RMT) to calculate the averaged vibrational spectra of such systems, in the limit of infinitely large system size. At the heart of our analysis lies a calculation of the average spectrum of the product of two positive definite random matrices by means of free probability theory techniques. We also show that this problem is intimately related with quasi-hermitian random matrix theory (QHRMT), which means that the ‘hamiltonian’ matrix is hermitian with respect to a non-trivial metric. This extends ordinary hermitian matrices, for which the metric is simply the unit matrix. The analytical results we obtain for the spectrum agree well with our numerical results. The latter also exhibit oscillations at the high-frequency band edge, which fit well the Airy kernel pattern. We also compute inverse participation ratios of the corresponding amplitude eigenvectors and demonstrate that they are all extended, in contrast with conventional disordered crystals. Finally, we compute the thermodynamic properties of the system from its spectrum of vibrations. In addition to matrix model analysis, we also study the vibrational spectra of various multi-segmented disordered pendula, as concrete realizations of highly connected mechanical systems. A universal feature of the density of vibration modes, common to both pendula and the matrix model, is that it tends to a non-zero constant at vanishing frequency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

An analysis of the spatio-temporal resolution of the immersed boundary method with direct forcing

The immersed boundary method (IBM) with direct forcing is very popular in the simulation of rigid particulate flows. In the IBM, an interaction force is introduced at the interface between fluid and particle in order to approximate the no-slip boundary condition. The interaction force is calculated through dividing the velocity difference (or error) between fluid and particle at the interface by the time step. Here, a dynamic equation for the velocity difference is derived. Additionally, analyses on the dynamic equation provide a few new findings: (i) The interaction force is the solution of a least-squares error problem, with the direct implication that the Lagrangian marker distribution has no effect on the large scale flow structure once the distribution of Lagrangian markers become saturated along the interface (i.e., each marker remains properly correlated with all its neighbors); (ii) The Lagrangian volume-weight is a relaxation factor to control how fast the velocity error decays to the ideal value of zero; (iii) The optimal choice of the Lagrangian volume-weight is the largest value permissible by a stability condition. A comprehensive convergence analysis with regard to the spatial and temporal resolution is presented for the velocity error and also for the shear-stress and surface pressure. In three simple canonical problems, it is analytically and numerically shown that the IBM results converge to the theoretical solutions obtained with precise imposition of no-slip and no-penetration boundary conditions. It is observed that it is not necessary to match the Lagrangian marker volume-weight to that of the local Eulerian cell volume and in fact this matching leads to lower than optimal computational efficiency. However, it is found that extremely high Eulerian grid resolution and small time step have to be used to obtain high precision simulation results. Especially, the time step should be inversely proportional to the particle Reynolds number for low Reynolds number flows. For high frequency oscillation problems, the grid size needs to be reduced by a factor of the square root of the frequency, and the time step to be reduced by a factor of the frequency. The theoretical findings here can be used to alleviate the technical difficulties in simulating non-spherical particles by not requiring the Lagrangian marker distribution to match the Eulerian grids and also in the implementation of IBM on non-uniform Eulerian grids. The present work also provides simple practical guidance on the choice of temporal and spatial resolution so as to control the simulation error a priori.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Modeling Dynamic Fracture of Cryogenic Pellets

This work is part of an investigation with the long-range objective of predicting the size distribution function and velocity dispersion of shattered pellet fragments after a large cryogenic pellet impacts a solid surface at high velocity. The study is vitally important for the shattered pellet injection (SPI) technique, one of the leading technologies being implemented at ORNL for the mitigation of disruption damage on current tokamaks and ITER. The report contains three parts that are somewhat interwoven. In Part I we formulated a self-similar model for the expansion dynamics and velocity dispersion of the debris cloud following pellet impact against a thick (rigid) target plate. Also presented in Part I is an analytical fracture model that predicts the nominal or mean size of the fragments in the debris cloud and agrees well with known SPI data. The aim of Part II is to gain an understanding of the pellet fracturing process when a pellet is shattered inside a miter tube with a sharp bend. Because miter tubes have a thin stainless steel (SS) wall a permanent deformation (dishing) of the wall is produced at the site of the impact. A review of the literature indicates that most projectile impact on thin plates are those for which the target is deformed and the projectile is perfectly rigid. Such impacts result in “projectile embedding” where the projectile speed is reduced to zero during the interaction so that all the kinetic energy (KE) of the projectile goes into the energy stored in plastic deformation. Much of the literature deals with perforation of the target. The problem here is quite different; the softer pellet easily undergoes complete material failure causing only a small transfer of KE to stored energy of wall deformation. For the real miter tube, we derived a strain energy function for the wall deflection using a non-linear (plastic) stress-strain relation for 304 SS. Using a dishing profile identical to the linear Kirchkoff-Love profile (for lack of a rigorously derived profile) we derived the strain energy associated with the deflection and applied a virtual work principle to find a relationship between the impact (load) pressure to the measured wall deflection depth. The inferred impact pressure was in good agreement with the expected pressure for oblique cryogenic pellet impacts where the pellet shear stress causing cleavage fracture is well above the yield stress for pure shear. The section is concluded with additional discussion on how this wall deformation data lends further support to the analytical fracture model presented in Part I. In Part III we present three different size distribution models. A summary, with a few brief suggestions for a follow on study, is provided at the end of this report.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Active- and transfer-learning applied to microscale-macroscale coupling to simulate viscoelastic flows

Active- and transfer-learning are applied to microscale dynamics of polymer flows for the multiscale discovery of effective constitutive approximations required in viscoelastic flow simulation. The result is macroscopic rheology directly connected to a microstructural model. Micro and macroscale simulations are adaptively coupled by means of Gaussian process regression (GPR) to run the expensive microscale computations only as necessary. This multiscale method is demonstrated with flows of a polymer solution as a model system. At the microscale level dissipative particle dynamics (DPD) is employed to model the fluid as a suspension of bead-spring micro-structures subjected to steady shear flow. The results yield the non-Newtonian viscosity and the first normal stress difference at strain rates as training data used in a GPR model. DPD parameters are calibrated with respect to experimental data for a real polymer solution. Compliance with these data requires adjustment of the DPD model's cutoff radius, which then becomes a function of the second invariant of the strain rate tensor. The FENE-P model is chosen for the macroscale description using the spectral element method (SEM) to simulate channel flow and flow past a circular cylinder. The DPD results at the lowest possible shear strain rate yield an estimate of the zero-shear rate viscosity, which allows the initiation of the macroscale flow by SEM as a Newtonian fluid. The resulting strain-rate field is surveyed to determine additional shear strain rate sampling points for the DPD system. This new information allows an initial fitting of parameters of the constitutive equation followed by new SEM simulations at the macroscale. Additionally, guided by active-learning GPR to select new sampling points, this process continues until convergence is achieved. The effectiveness of this new simulation paradigm for viscoelastic flows is tested with different macroscale operating conditions. The effective closure learned in the channel simulation is then transferred directly to the flow past a circular cylinder at low Reynolds number, where the results show that only two additional DPD simulations are required to achieve a satisfactory constitutive model. With an increase of the Reynolds number, the active-learning scheme automatically detects the inaccuracy of the learned constitutive model, and initiates additional DPD simulations for the extra data needed to once again close the microscale-macroscale coupled system. This new paradigm of active- and transfer-learning for multiscale modeling is readily applicable to other microscale-macroscale coupled simulations of complex fluids and other materials. Furthermore, the coupling between microscale and macroscale solvers can be seamlessly implemented with our open source multiscale universal interface (MUI) library.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Electrical switching of a p-wave magnet

Magnetic states with zero magnetization but non-relativistic spin splitting are outstanding candidates for the next generation of spintronic devices. Their electronvolt (eV)-scale spin splitting, ultrafast spin dynamics and nearly vanishing stray fields make them particularly promising for several applications. A variety of such magnetic states with non-trivial spin textures have been identified recently, including even-parity d-wave, g-wave or i-wave altermagnets and odd-parity p-wave magnets. Achieving voltage-based control of the non-uniform spin polarization of these magnetic states is of great interest for realizing energy-efficient and compact devices for information storage and processing. Spin-spiral type II multiferroics are optimal candidates for such voltage-based control, as they exhibit an inversion-symmetry-breaking magnetic order that directly induces ferroelectric polarization, allowing for symmetry-protected cross-control between spin chirality and polar order. Here we combine photocurrent measurements, first-principles calculations and group-theory analysis to provide direct evidence that the spin polarization of the spin-spiral type II multiferroic NiI 2 exhibits odd-parity character connected to the spiral chirality. The symmetry-protected coupling between chirality and polar order enables electrical control of a primarily non-relativistic spin polarization. Our findings represent an observation of p-wave magnetism in a spin-spiral type II multiferroic, which may lead to the development of voltage-based switching of non-relativistic spin polarization in compensated magnets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗