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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Entanglement phase transitions in random stabilizer tensor networks

Here we explore a class of random tensor network models with “stabilizer” local tensors which we name random stabilizer tensor networks (RSTNs). For RSTNs defined on a two-dimensional square lattice, we perform extensive numerical studies of entanglement phase transitions between volume-law and area-law entangled phases of the one-dimensional boundary states. These transitions occur when either (a) the bond dimension D of the constituent tensors is varied or (b) the tensor network is subject to random breaking of bulk bonds, implemented by forced measurements. In the absence of broken bonds, we find that the RSTN supports a volume-law entangled boundary state with bond dimension D ≥ 3 where D is a prime number, and an area-law entangled boundary state for D = 2. Upon breaking bonds at random in the bulk with probability p, there exists a critical measurement rate p c for each D ≥ 3 above which the boundary state becomes area-law entangled. To explore the conformal invariance at these entanglement transitions for different prime D, we consider tensor networks on a finite rectangular geometry with a variety of boundary conditions, and extract universal operator scaling dimensions via extensive numerical calculations of the entanglement entropy, mutual information, and mutual negativity at their respective critical points. Our results at large D approach known universal data of percolation conformal field theory, while showing clear discrepancies at smaller D, suggesting a distinct entanglement transition universality class for each prime D. We further study universal entanglement properties in the volume-law phase and demonstrate quantitative agreement with the recently proposed description in terms of a directed polymer in a random environment.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Application of the ChIMES Force Field to Nonreactive Molecular Systems: Water at Ambient Conditions

We demonstrate development of the Chebyshev Interaction Model for Efficient Simulation (ChIMES) for molecular systems through application to water under ambient conditions (298 K, 1 g/cm 3 ). These models, which are comprised of linear combinations of Chebyshev polynomials explicitly describing two- and three-body interactions, are largely fit by force matching to Kohn–Sham Density Functional Theory (DFT). Protocols for selecting user-specified parameters and inclusion of stress tensor data are investigated, and structural and dynamical property prediction for resulting models is benchmarked against DFT. We show that the present ChIMES force fields yield excellent agreement with DFT without the need for additional terms such as those for Coulomb interactions. Overall, we show that tractable parametrization and subsequent accuracy of the present models make ChIMES an ideal candidate for extension of DFT dynamics to larger system sizes and longer time scales.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

The Effects of Stochastic Velocity Variations on Estimating Time Dependent Seismic Moment Tensors: Applications to the Blue Mountain Well Perforation Data

Resolving the time dependent terms in the seismic moment tensor provides important information that can be used to interpret the source process of an explosion, including the separation of isotropic explosion terms from shear forces and potentially isolated force couples. In this report, we detail our method of inverting three component seismic data for the seismic moment tensor. We review possible seismic source models from the simplest isotropic explosion type source to those incorporating the six independent moment tensor terms. The inversion we describe is formulated in the frequency domain, and results in estimates of time dependent moment tensor components. The inversion relies on an accurate estimate of the Green's functions of the Earth. However, given the complexity of the Earth, we explore the effects of inaccuracies in the presumed Earth model used to estimate the Green's functions needed for the inversion. Specifically, we explore the effects of stochastic variations in the Earth models on the inversion results. These tests are synthetic throughout, and show that adding stochastic density/velocity heterogeneity in the presumed Earth model results in reduced amplitude seismic moment tensor estimates, as well as degrading the data misfit. We suggest two mitigation strategies. First, produce a suite of Green's functions using different realizations of the stochastic field within the Earth Model. Secondly, perform the in- version in the power spectral domain, eliminating all phase information. Finally, we analyze actual seismic data collected in winter 2017/2018. The seismic data was collected at in active geothermal well site outside of Winnimucca, NV, and was produced during well stimulation operations. In general, the inversion results were poor, with a high degree of data misfit. We hypothesize that the poor results are a function of a poorly constrained Earth model as well as noisy, high-frequency data being used in the inversion.

58 GEOSCIENCES↗
NASA NTRS1990

Force balance near an X line in a collisionless plasma

The suggestion by Dungey (1988) that the gyroviscosity associated with gradients of the off-diagonal elements of the electron pressure tensor can balance a reconnection electric field along a magnetic X line in a collisionless plasma is investigated. The detailed balance of forces in the vicinity of an X line is evaluated using a two-dimensional magnetic field model and a simple model for particle motion. The results show that the gyroviscosity can indeed provide the force required to balance a reconnection electric field in that region, so that neither collisions nor wave turbulence are necessary for reconnection. The results also show that there should not be a significant increase in current from electron acceleration very near an X line. Reasonable numerical estimates are obtained for conditions expected in the vicinity of the distant X line in the geomagnetic tail.

Lyons, L. R.↗
DOE OSTI2021

Bridging the gap between simulated and experimental ionic conductivities in lithium superionic conductors

Lithium superionic conductors (LSCs) are of major importance as solid electrolytes for next-generation all-solid-state lithium-ion batteries. While ab initio molecular dynamics have been extensively applied to study these materials, there are often large discrepancies between predicted and experimentally measured ionic conductivities and activation energies due to the high temperatures and short time scales of such simulations. Here, we present a strategy to bridge this gap using moment tensor potentials (MTPs). We show that MTPs trained on energies and forces computed using the van der Waals optB88 functional yield much more accurate lattice parameters, which in turn leads to accurate prediction of ionic conductivities and activation energies for the Li 0·33 La 0·56 TiO 3 , Li 3 YCl 6 and Li 7 P 3 S 11 LSCs. NPT MD simulations using the optB88 MTPs also reveal that all three LSCs undergo a transition between two quasi-linear Arrhenius regimes at relatively low temperatures. This transition can be traced to an increase in the number and diversity of diffusion pathways, in some cases with a change in the dimensionality of diffusion. Furthermore, this work presents not only an approach to develop high accuracy MTPs, but also outlines the diffusion characteristics for LSCs which is otherwise inaccessible through ab initio computation.

25 ENERGY STORAGE↗
NASA NTRS1995

Particle acceleration very near an x-line in a collisionless plasma

In a previous paper, we applied a simplified model for particle motion in the vicinity of a magnetic X-line that had been introduced by Dungey. We used the model to quantitatively show that an electric force along an X-line can be balanced by the gyroviscous force associated with the off-diagonal elements of the pressure tensor. Distribution functions near the X-line were shown to be skewed in azimuth about the magnetic field and to include particles accelerated to very high energies. In the present paper, we apply the previous model and use the distribution functions to evaluate the energization that results from particle interactions with the X-line. We find that, in general, this interaction gives a spectrum of energized particles that can be represented by a Maxwellian distribution. A power-law, high-energy tail does not develop. The thermal energy, K, of the Maxwellian can be expressed simply in terms of the field parameters and particle mass and charge. It is independent of the thermal energy, K(sub i), of the particle distribution incident upon the region of the X-line, provided that K(sub i) is less than K. Significant energization is not found for K(sub i) is greater than K.

Lyons, L. R.↗
NASA NTRS1996

Simulation of Two-Fluid Flows by the Least-Squares Finite Element Method Using a Continuum Surface Tension Model

In this paper a numerical procedure for simulating two-fluid flows is presented. This procedure is based on the Volume of Fluid (VOF) method proposed by Hirt and Nichols and the continuum surface force (CSF) model developed by Brackbill, et al. In the VOF method fluids of different properties are identified through the use of a continuous field variable (color function). The color function assigns a unique constant (color) to each fluid. The interfaces between different fluids are distinct due to sharp gradients of the color function. The evolution of the interfaces is captured by solving the convective equation of the color function. The CSF model is used as a means to treat surface tension effect at the interfaces. Here a modified version of the CSF model, proposed by Jacqmin, is used to calculate the tension force. In the modified version, the force term is obtained by calculating the divergence of a stress tensor defined by the gradient of the color function. In its analytical form, this stress formulation is equivalent to the original CSF model. Numerically, however, the use of the stress formulation has some advantages over the original CSF model, as it bypasses the difficulty in approximating the curvatures of the interfaces. The least-squares finite element method (LSFEM) is used to discretize the governing equation systems. The LSFEM has proven to be effective in solving incompressible Navier-Stokes equations and pure convection equations, making it an ideal candidate for the present applications. The LSFEM handles all the equations in a unified manner without any additional special treatment such as upwinding or artificial dissipation. Various bench mark tests have been carried out for both two dimensional planar and axisymmetric flows, including a dam breaking, oscillating and stationary bubbles and a conical liquid sheet in a pressure swirl atomizer.

Wu, Jie↗
NASA NTRS1984

An analysis of the high-latitude thermospheric wind pattern calculated by a thermospheric general circulation model. I - Momentum forcing

A diagnostic processor (DP) was developed for analysis of hydrodynamic and thermodynamic processes predicted by the NCAR thermospheric general circulation model (TGCM). The TGCM contains a history file on the projected wind, temperature and composition fields at each grid point for each hour of universal time. The DP assimilates the history file plus ion drag tensors and drift velocities, specific heats, coefficients of viscosity, and thermal conductivity and calculates the individual forcing terms for the momentum and energy equations for a given altitude. Sample momentum forcings were calculated for high latitudes in the presence of forcing by solar radiation and magnetospheric convection with a 60 kV cross-tail potential, i.e., conditions on Oct. 21, 1981. It was found that ion drag and pressure forces balance out at F region heights where ion drift velocities are small. The magnetic polar cap/auroral zone boundary featured the largest residual force or net acceleration. Diurnal oscillations were detected in the thermospheric convection, and geostrophic balance was dominant in the E layer.

Killeen, T. L.↗
DOE OSTI2012

Comparison of various approaches to the calculation of optically induced forces

Various approaches used for the calculation of optically induced forces applied to a transparent optical medium imbedded in a close plane optical resonator are analyzed. The forces are calculated by means of analysis of a change in the eigen frequency and energy stored in the resonator at various positions of the medium. It is shown that results obtained are identical to those calculated by means of approaches based on the Maxwell stress tensor, based on an analysis of a change in the momentum of light. An exception is for results obtained on the base of last versions of the Lorentz density force. - Highlights: Black-Right-Pointing-Pointer There are no Lorentz forces in a homogeneous optical medium. Black-Right-Pointing-Pointer A net force produced by an inhomogeneous electrostriction pressure is equal to zero. Black-Right-Pointing-Pointer Any distributions of the Lorentz force in a homogeneous optical medium are misleading.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1996

Element Library for Three-Dimensional Stress Analysis by the Integrated Force Method

The Integrated Force Method, a recently developed method for analyzing structures, is extended in this paper to three-dimensional structural analysis. First, a general formulation is developed to generate the stress interpolation matrix in terms of complete polynomials of the required order. The formulation is based on definitions of the stress tensor components in term of stress functions. The stress functions are written as complete polynomials and substituted into expressions for stress components. Then elimination of the dependent coefficients leaves the stress components expressed as complete polynomials whose coefficients are defined as generalized independent forces. Such derived components of the stress tensor identically satisfy homogenous Navier equations of equilibrium. The resulting element matrices are invariant with respect to coordinate transformation and are free of spurious zero-energy modes. The formulation provides a rational way to calculate the exact number of independent forces necessary to arrive at an approximation of the required order for complete polynomials. The influence of reducing the number of independent forces on the accuracy of the response is also analyzed. The stress fields derived are used to develop a comprehensive finite element library for three-dimensional structural analysis by the Integrated Force Method. Both tetrahedral- and hexahedral-shaped elements capable of modeling arbitrary geometric configurations are developed. A number of examples with known analytical solutions are solved by using the developments presented herein. The results are in good agreement with the analytical solutions. The responses obtained with the Integrated Force Method are also compared with those generated by the standard displacement method. In most cases, the performance of the Integrated Force Method is better overall.

Kaljevic, Igor↗
DOE OSTI2017

Bound-Preserving Reconstruction of Tensor Quantities for Remap in ALE Fluid Dynamics

We analyze several new and existing approaches for limiting tensor quantities in the context of deviatoric stress remapping in an ALE numerical simulation of elastic flow. Remapping and limiting of the tensor component-by-component is shown to violate radial symmetry of derived variables such as elastic energy or force. Therefore, we have extended the symmetry-preserving Vector Image Polygon algorithm, originally designed for limiting vector variables. This limiter constrains the vector (in our case a vector of independent tensor components) within the convex hull formed by the vectors from surrounding cells – an equivalent of the discrete maximum principle in scalar variables. We compare this method with a limiter designed specifically for deviatoric stress limiting which aims to constrain the J 2 invariant that is proportional to the specific elastic energy and scale the tensor accordingly. We also propose a method which involves remapping and limiting the J 2 invariant independently using known scalar techniques. The deviatoric stress tensor is then scaled to match this remapped invariant, which guarantees conservation in terms of elastic energy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Quantum-Based Molecular Dynamics Simulations Using Tensor Cores

Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary computational speed and energy efficiency but with the caveat that they were designed for tensor contractions (matrix–matrix multiplications) using only low-precision floating-point operations. Despite this perceived limitation, we demonstrate how tensor cores can be applied with high efficiency to the challenging and numerically sensitive problem of quantum-based Born–Oppenheimer molecular dynamics, which requires highly accurate electronic structure optimizations and conservative force evaluations. The interatomic forces are calculated on-the-fly from an electronic structure that is obtained from a generalized deep neural network, where the computational structure naturally takes advantage of the exceptional processing power of the tensor cores and allows for high performance in excess of 100 Tflops on a single Nvidia A100 GPU. Stable molecular dynamics trajectories are generated using the framework of extended Lagrangian Born–Oppenheimer molecular dynamics, which combines computational efficiency with long-term stability, even when using approximate charge relaxations and force evaluations that are limited in accuracy by the numerically noisy conditions caused by the low-precision tensor core floating-point operations. A canonical ensemble simulation scheme is also presented, where the additional numerical noise in the calculated forces is absorbed into a Langevin-like dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2011

Several versions of the compensated compactness principle

The convergence of the product of a solenoidal vector w{sub {epsilon}} and a gradient {nabla}u{sub {epsilon}} in L{sup 1}({Omega}) (where {Omega} is a region in R{sup d}) is investigated in the case when the factors converge weakly in the spaces L{sup {gamma}({Omega})}{sup d} and L{sup {alpha}({Omega})}{sup d}, respectively, with 1/{gamma}+1/{alpha}>1, which means that the main assumption of the classical div-curl lemma fails. Nevertheless, the same convergence (in the sense of distributions in {Omega}) as in the framework of the div-curl lemma, survives under certain additional assumptions. The new versions of the compensated compactness principle proved in the paper can be used in homogenization and in the theory of G-convergence of monotone operators with non-standard coercivity and growth properties, for instance, some degenerate operators. Bibliography: 20 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A consistent and unified picture for critical phenomena of f(R) AdS black holes

A consistent and unified picture for critical phenomena of charged AdS black holes in f ( R ) gravity is drawn in this paper. Firstly, we investigate the phase transition in canonical ensemble. We derive the explicit solutions corresponding to the divergence of C {sub Q} . The two solutions merge into one when the condition Q {sub c} =√(−1/3 R {sub 0}) is satisfied. The curve of specific heat for Q < Q {sub c} has two divergent points and can be divided into three regions. Both the large radius region and the small radius region are thermodynamically stable with positive specific heat while the medium radius region is unstable with negative specific heat. However, when Q > Q {sub c} , the specific heat is always positive, implying the black holes are locally stable and no phase transition will take place. Secondly, both the T − r {sub +} curve and T − S curve f ( R ) AdS black holes are investigated and they exhibit Van der Vaals like behavior as the P − v curve in the former research. Critical physical quantities are obtained and they are consistent with those derived from the specific heat analysis. We carry out numerical check of Maxwell equal area law for the cases Q =0.2 Q {sub c} , 0.4 Q {sub c} , 0.6 Q {sub c} , 0.8 Q {sub c} . The relative errors are amazingly small and can be negligible. So the Maxwell equal area law holds for T − S curve of f ( R ) black holes. Thirdly, we establish geometrothermodynamics for f ( R ) AdS black hole to examine the phase structure. It is shown that the Legendre invariant scalar curvature R would diverge exactly where the specific heat diverges. To summarize, the above three perspectives are consistent with each other, thus providing a unified picture which deepens the understanding of critical phenomena of f ( R ) AdS black holes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Lifshitz theory of van der Waals pressure in dissipative media

We derive a first-principles method of determining the van der Waals or Casimir pressure in a dissipative and dispersive planar multilayered system by calculating the Maxwell stress tensor in a fictitious layer of vacuum, that is eventually made to vanish, introduced in the structure. This is illustrated by calculating the van der Waals pressure in a thin film with dissipative properties embedded between two semi-infinite media.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces

It has been known for several decades that Einstein's field equations, when projected onto a null surface, exhibit a structure very similar to the nonrelativistic Navier-Stokes equation. I show that this result arises quite naturally when gravitational dynamics is viewed as an emergent phenomenon. Extremizing the spacetime entropy density associated with the null surfaces leads to a set of equations which, when viewed in the local inertial frame, becomes identical to the Navier-Stokes equation. This is in contrast to the usual description of the Damour-Navier-Stokes equation in a general coordinate system, in which there appears a Lie derivative rather than a convective derivative. I discuss this difference, its importance, and why it is more appropriate to view the equation in a local inertial frame. The viscous force on fluid, arising from the gradient of the viscous stress-tensor, involves the second derivatives of the metric and does not vanish in the local inertial frame, while the viscous stress-tensor itself vanishes so that inertial observers detect no dissipation. We thus provide an entropy extremization principle that leads to the Damour-Navier-Stokes equation, which makes the hydrodynamical analogy with gravity completely natural and obvious. Several implications of these results are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Possible Explanation of the Geograv Detector Signal during the Explosion of SN 1987A in Modified Gravity Models

A change in the law of attraction in some regimes is predicted in the modified gravity models being actively developed at present. The set of up-to-date observational data leaves a wide range of admissible parameters for the theory. In this paper, we consider the possibility that the signal recorded by the Geograv resonant gravitational-wave detector in 1987 during the explosion of SN 1987A was produced by an abrupt change in the metric during the passage of a powerful neutrino flux through the detector. Such an impact on the detector is possible, in particular, in extended scalar–tensor theories in which the local matter density gradient affects the gravitational force. The first short neutrino pulse emitted at the initial stage of stellar core collapse before the onset of neutrino opacity could exert a major influence on the detector, because it could produce the detector response at the first resonance frequency. In contrast, the influence of the subsequent broad pulse (with a duration of several seconds) in the resonant detector is exponentially suppressed, despite the fact that the second pulse carries an order-of-magnitude more neutrino energy, and it could generate a signal in the LSD neutrino detector. This explains the time delay of 1.4 s between the Geograv and LSD signals. The consequences of this effect of modified gravity for future LIGO/Virgo observations are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗