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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows

Herein we demonstrate that the reformulation of renormalization group (RG) flow equations as nonlinear heat equations has severe implications on the understanding of RG flows in general. We demonstrate by explicitly constructing an entropy function for a zero-dimensional Z 2 -symmetric model that the dissipative character of generic nonlinear diffusion equations is also hard-coded in the functional RG equation. This renders RG flows manifestly irreversible, revealing the semigroup property of RG transformations on the level of the flow equation itself. Additionally, we argue that the dissipative character of RG flows, its irreversibility and the entropy production during the RG flow may be linked to the existence of a so-called C– / A-function. In total, this introduces an asymmetry in the so-called RG time—in complete analogy to the thermodynamic arrow of time—and allows for an interpretation of infrared actions as equilibrium solutions of dissipative RG flows equations. The impossibility of resolving microphysics from macrophysics is evident in this framework. Furthermore, we directly link the irreversibility and the entropy production in RG flows to an explicit numerical entropy production, which is manifest in diffusive and non-linear partial differential equations (PDEs) and a standard mathematical tool for the analysis of PDEs. Using exactly solvable zero-dimensional Z 2 -symmetric models, we explicitly compute the (numerical) entropy production related to the total variation nonincreasing property of the PDE during RG flows toward the infrared limit. Finally, we discuss generalizations of our findings and relations to the C– / A-theorem as well as how our work may help to construct truncations of RG flow equations in the future, including numerically stable schemes for solving the corresponding PDEs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

The expressivity of classical and quantum neural networks on entanglement entropy

Abstract Analytically continuing the von Neumann entropy from Rényi entropies is a challenging task in quantum field theory. While then-th Rényi entropy can be computed using the replica method in the path integral representation of quantum field theory, the analytic continuation can only be achieved for some simple systems on a case-by-case basis. In this work, we propose a general framework to tackle this problem using classical and quantum neural networks with supervised learning. We begin by studying several examples with known von Neumann entropy, where the input data is generated by representing$${\text {Tr}}\rho _A^n$$ Tr ρ A n with a generating function. We adopt KerasTuner to determine the optimal network architecture and hyperparameters with limited data. In addition, we frame a similar problem in terms of quantum machine learning models, where the expressivity of the quantum models for the entanglement entropy as a partial Fourier series is established. Our proposed methods can accurately predict the von Neumann and Rényi entropies numerically, highlighting the potential of deep learning techniques for solving problems in quantum information theory.

Physics↗
DOE OSTI2024

Reactive flash sintering and characterization of bulk high entropy nitrides

Over the past decade, numerous high-entropy ceramics have been synthesized, often displaying attractive properties. However, the study on facile preparation of bulk high entropy nitrides (HEN) are limited, despite its broad potential applications. This research demonstrates for the first time rapid fabrication (within ∼6 min) of bulk high-entropy nitrides, especially (Al 0.17 Nb 0.17 Ta 0.17 Ti 0.32 Zr 0.17 )N, from binary nitride powder mixtures using a highly efficient reactive flash sintering (RFS) technique. X-ray diffraction (XRD) shows the HENs from RFS are near single-phase solid solutions with a rock salt crystal structure, while in situ synchrotron study carried out during RFS captured in real time the formation of HEN, which was preserved upon cooling, suggesting thermodynamic stability of the HEN phase, even up to extreme pressure (∼35.6 GPa). Microscopic analyses using SEM, STEM, and EDS reveal decent uniformity for HEN with no obvious segregation of elements, even to submicron scale. Some properties of the obtained bulk HENs are consistent with expectations. For example, their hardness and bulk modulus are close to estimates based on rule-of-mixture (ROM) values from the constituent binary nitrides. Meanwhile, some other measured properties seem to show surprises. For example, the fracture toughness for the HENs (e.g., 7.81 ± 1.40 MPa•m 1/2 or higher) turns out to be more than double of the expected ROM estimates. The significantly improved fracture toughness is attributed to the observed nano-layered structure of the HENs, despite the HEN’s cubic crystal structure and high hardness. In addition, the oxidation resistance shows improvement up till ∼800°C, possibly due to Ta doping that suppress oxygen vacancy formation in the oxide shell, while the 5-metal HEN of (Al 0.17 Nb 0.17 Ta 0.17 Ti 0.32 Zr 0.17 )N displays superconductivity (T c of ∼5–7 K from magnetism and resistivity measurements, slightly lower than ROM estimate), despite insulating property of starting AlN. Furthermore, future study combining experimental investigation using larger samples to confirm the observed increase in fracture toughness and oxidation resistance, theoretical modeling at different length scale, and more detailed structural/chemical characterization, especially at the atomic scale, are all needed to fully understand the inter-relationships between composition, processing, structure, and novel properties for these HENs and the development of related new materials for different applications.

Flash sintering↗
DOE OSTI2023

Model-Free Approach for Profiling of Polydisperse Soft Matter Using Small Angle Scattering

A strategy for determining the size polydispersity of systems from their small angle coherent scattering is outlined. Here, using the method of moment expansion, we show that the various central moments representing the average particle size, variance of particle size, and skewness of size distribution function (SDF) for polydisperse systems can be extracted from spectral analysis without bias. When the degree of polydispersity is moderate, SDF can be further reconstructed based on the maximum entropy principle. Numerical benchmarking of a model study over a wide range of size nonuniformity demonstrates the validity of this analytical approach for quantifying the size distribution of general soft matter systems in a model-free manner. Furthermore, the efficacy of this method was validated by successfully applying it to the fitting of small-angle neutron scattering data obtained from L64 Pluronic micelles using various form factor models. The numerical and experimental verification underscores the reliability and versatility of this method in accurately characterizing the size distribution of complex soft matter systems.

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

Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations

Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a semi-discrete entropy inequality under appropriate boundary conditions. Here in this work, we describe a discretization of viscous terms in the compressible Navier-Stokes equations which enables a simple and explicit imposition of entropy stable no-slip and reflective (symmetry) wall boundary conditions for discontinuous Galerkin (DG) discretizations. Specifically, we derive methods for imposing adiabatic no-slip and reflective (symmetry) boundary conditions for modal entropy stable DG formulations which preserve a semi-discrete entropy inequality. Numerical results confirm the robustness and accuracy of the proposed approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Empirical correlations between the function of entropy ( Z S ) and net artificial viscous work in a shock physics hydrocode

Entropy is a state variable that may be obtained from any thermodynamically complete equation of state (EOS). However, hydrocode calculations that output the entropy often contain numerical errors; this is not because of the EOS, but rather the solution techniques that are used in hydrocodes (especially Eulerian) such as convection, remapping, and artificial viscosity. Here, in this work, empirical correlations are investigated to reduce the errors in entropy without altering the solution techniques for the conservation of mass, momentum, and energy. Specifically, these correlations are developed for the function of entropy Z S , and they depend upon the net artificial viscous work, as determined via Sandia National Laboratories’ shock physics hydrocode CTH. These results are a continuation of a prior effort to implement the entropy-based CREST reactive burn model in CTH, and they are presented here to stimulate further interest from the shock physics community. Future work is planned to study higher-dimensional shock waves, shock wave interactions, and possible ties between the empirical correlations and a physical law.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Model-Free Measurement of Local Entropy Production and Extractable Work in Active Matter

Time-reversal symmetry breaking and entropy production are universal features of nonequilibrium phenomena. Despite its importance in the physics of active and living systems, the entropy production of systems with many degrees of freedom has remained of little practical significance because the high dimensionality of their state space makes it difficult to measure. Here, in this work, we introduce a local measure of entropy production and a numerical protocol to estimate it. We establish a connection between the entropy production and extractability of work in a given region of the system and show how this quantity depends crucially on the degrees of freedom being tracked. We validate our approach in theory, simulation, and experiments by considering systems of active Brownian particles undergoing motility-induced phase separation, as well as active Brownian particles and E.coli in a rectifying device in which the time-reversal asymmetry of the particle dynamics couples to spatial asymmetry to reveal its effects on a macroscopic scale.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting

In this paper, we develop high-order nodal discontinuous Galerkin (DG) methods for hyperbolic conservation laws that satisfy invariant domain preserving properties using subcell flux corrections and convex limiting. These methods are based on a subcell flux corrected transport (FCT) methodology that involves blending a high-order target scheme with a robust, low-order invariant domain preserving method that is obtained using a graph viscosity technique. Furthermore, the new low-order discretizations are based on sparse stencils which do not increase with the polynomial degree of the high-order DG method. As a result, the accuracy of the low-order method does not degrade when used with high-order target methods. The method is applied to both scalar conservation laws, for which the discrete maximum principle is naturally enforced, and to systems of conservation laws such as the Euler equations, for which positivity of density and a minimum principle for specific entropy are enforced. Numerical results are presented on a number of benchmark test cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Energetically consistent model reduction for metriplectic systems

The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not preserve the metriplectic structure which governs long-term stability of the system. Based on proper orthogonal decomposition, a provably convergent metriplectic reduced-order model is formulated which is guaranteed to maintain the algebraic structure necessary for energy conservation and entropy formation. Further, numerical results on benchmark problems show that the proposed method is remarkably stable, leading to improved accuracy over long time scales at a moderate increase in cost over naive methods.

42 ENGINEERING↗
DOE OSTI2024

Should We Conserve Entropy or Energy when Computing CAPE with Mixed-Phase Precipitation Physics?

Abstract The rapidly increasing resolution of global atmospheric reanalysis and climate model datasets necessitates finding methods for computing convective available potential energy (CAPE) both efficiently and accurately. To this end, this article compares two common methods for computing CAPE which conserve either energy or entropy. Inaccuracies in these computations arise from both physical and numerical errors. For instance, computing CAPE with entropy conserved results in physical errors from nonequilibrium phase transitions but minimizes numerical errors because solutions are analytic at each height. In contrast, computing CAPE with energy conserved avoids these physical errors, but accumulates numerical errors that are grid-resolution-dependent because the numerical integration of a differential equation is required. Analysis of CAPE computed with large databases of soundings from the tropical Amazon and midlatitude storm environments shows that physical errors from the entropy method are typically 1%–3% as large as CAPE, which is comparable to the numerical errors from conserving energy with grid spacing of 25 and 250 m using explicit first-order and second-order integration schemes, respectively. Errors in entropy-based CAPE calculations are also insensitive to vertical grid spacing, in contrast to energy-based calculations whose error strongly scales with the grid spacing. It is shown that entropy-based methods are advantageous when intercomparing datasets with differing vertical resolution because they produce accurate and reasonably fast results that are insensitive to grid resolution, whereas a second-order energy-based method is advantageous when analyzing data with a consistent vertical resolution because of its superior computational efficiency. Significance Statement Convective available potential energy (CAPE) is a measure of instability in the atmosphere that helps forecasters and researchers understand when and where thunderstorms will form. The purpose of this article is to identify the most efficient and accurate methods for computing CAPE. Two methods are considered here, one that relates to the entropy (a measure of thermodynamic disorder) of an air parcel and one that relates to the energy of an air parcel. Results indicate that the entropy method is most accurate and insensitive to the resolution of the data used for the calculation (which can vary considerably), whereas the energy method uses the least computation time.

Peters, John M.↗
DOE OSTI2020

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

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

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

A simple method for obtaining heat capacity coefficients of minerals

Abstract Heat capacity data are unavailable or incomplete for many minerals at geologically relevant temperatures. Despite the availability of entropy and enthalpy values in numerous thermodynamic tables (even sometimes at elevated temperatures), there remains need for extrapolation beyond, or interpolation between, temperatures. This approach inevitably results in estimates for entropy and enthalpy values because the heat capacity coefficients required for optimal thermodynamic treatment are less frequently available. Here we propose a simple method for obtaining heat capacity coefficients of minerals. This method requires only the empirically measured temperature-specific heat capacity for calculation via a matrix algorithm. The system of equations solver is written in the Python computing language and has been made accessible in an online repository. Thermodynamically, the solution to a system of equations represents the heat capacity coefficients that satisfy the mineral-specific polynomial. Direct coefficient calculation will result in more robust thermodynamic data, which are not subject to fitting uncertainties. Using hematite as an example, this method provides results that are comparable to conventional means and is applicable to any solid material. Coefficients vary within the traditional large 950 K temperature interval, indicating that best results should instead utilize a smaller 400 K temperature interval. Examples of large-scale implications include the refinement of geothermal gradient estimation in rapidly subsiding sedimentary basins or metamorphic and hydrothermal evolution.

Geochemistry & Geophysics↗
DOE OSTI2024

Sequential formulation of all‐way coupled finite strain thermoporomechanics for largely deformable gas hydrate deposits

We develop a numerically stable sequential formulation of thermoporomechanics for largely deformable gas hydrate deposits, extended from the fixed stress split of infinitesimal transformation. Constitutive equations are based on the total Lagrangian approach for both flow and geomechanics, including dynamic full tensor permeability and thermal conductivity updated from the deformation gradient. For space discretization, we take the cell-centered finite volume and node-based finite element method for flow and geomechanics, respectively. Then, we propose a sequential implicit method for all-way coupled thermoporomechanics, where the nonisothermal multiphase flow problem of gas hydrates is solved implicitly first and then the geomechanics problem is solved implicitly at the next step. During solution of the flow problem, we fix the rate of first Pioal total stress for numerical stability as well as apply porosity correction and entropy correction to account for geomechanical effects. We test numerical examples where flow and geomechanics parameters are based on deep oceanic gas hydrate deposits. When applying depressurization, even though the results between the infinitesimal transformation and finite strain geomechanics are similar in the early stages due to small deformation, we find differences between them in the late times as deformation becomes large. Accordingly, permeability and thermal conductivity tensors become nonisotropic full tensors although they are initially isotropic. Furthermore, we identify numerical stability of the developed sequential method from the test cases that exhibit the highly complex coupled gas hydrate systems with large deformation. Thus, the proposed sequential formulation can be applied in largely deformable gas hydrate systems.

42 ENGINEERING↗
DOE OSTI2020

Real-time observations of TRIP-induced ultrahigh strain hardening in a dual-phase CrMnFeCoNi high-entropy alloy

Abstract Strategies involving metastable phases have been the basis of the design of numerous alloys, yet research on metastable high-entropy alloys is still in its infancy. In dual-phase high-entropy alloys, the combination of local chemical environments and loading-induced crystal structure changes suggests a relationship between deformation mechanisms and chemical atomic distribution, which we examine in here in a Cantor-like Cr 20 Mn 6 Fe 34 Co 34 Ni 6 alloy, comprising both face-centered cubic ( fcc ) and hexagonal closed packed ( hcp ) phases. We observe that partial dislocation activities result in stable three-dimensional stacking-fault networks. Additionally, the fraction of the stronger hcp phase progressively increases during plastic deformation by forming at the stacking-fault network boundaries in the fcc phase, serving as the major source of strain hardening. In this context, variations in local chemical composition promote a high density of Lomer-Cottrell locks, which facilitate the construction of the stacking-fault networks to provide nucleation sites for the hcp phase transformation.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Exploring Parameter Redundancy in the Unitary Coupled-Cluster Ansätze for Hybrid Variational Quantum Computing

One of the commonly used chemical-inspired approaches in variational quantum computing is the unitary coupled-cluster (UCC) ansatze. Despite being a systematic way of approaching the exact limit, the number of parameters in the standard UCC ansatze exhibits unfavorable scaling with respect to the system size, hindering its practical use on near-term quantum devices. Efforts have been taken to propose some variants of UCC ansatze with better scaling. In this paper we explore the parameter redundancy in the preparation of unitary coupled-cluster singles and doubles (UCCSD) ansatze employing spin-adapted formulation, small amplitude filtration, and entropy-based orbital selection approaches. Numerical results of using our approach on some small molecules have exhibited a significant cost reduction in the number of parameters to be optimized and in the time to convergence compared with conventional UCCSD-VQE simulations. Further, we also discuss the potential application of some machine learning techniques in further exploring the parameter redundancy, providing a possible direction for future studies.

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

Adaptive Deep Reinforcement Learning Algorithm for Distribution System Cyber Attack Defense With High Penetration of DERs

With grid modernization, smart inverters are increasingly used to execute advanced controls for distribution network reliability. However, this also increases the cyber-attack space. Here this paper focuses on the defense approaches to restore the system to normal operation circumstances in the presence of cyber-attacks. A unique deep reinforcement learning (DRL) method is developed to minimize voltage violations and reduce power losses for impacted feeders. The defense problem is reformulated as a Markov decision-making process to dynamically control DERs while minimizing load shedding. This is achieved via an improved soft actor-critic (SAC)-based DRL algorithm, which can govern DER set points and load-shedding scenarios in discrete and continuous modes via the auto-tune entropy and Gaussian policy features. Numerical comparison results on the modified IEEE 123-node system with other control approaches, such as Volt-VAR (VV), Volt-Watt (VW), and model predictive control (MPC) show that the proposed method can eliminate voltage violations and provide feasible control actions that perform complete mitigation of cyber-threats.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

High-dimensional maximum-entropy phase space tomography using normalizing flows

Particle accelerators generate charged-particle beams with tailored distributions in six-dimensional position-momentum space (phase space). Knowledge of the phase space distribution enables model-based beam optimization and control. In the absence of direct measurements, the distribution must be tomographically reconstructed from its projections. In this paper, we highlight that such problems can be severely underdetermined and that entropy maximization is the most conservative solution strategy. We leverage —invertible generative models—to extend maximum-entropy tomography to six-dimensional phase space and perform numerical experiments to validate the model's performance. Our numerical experiments demonstrate consistency with exact two-dimensional maximum-entropy solutions and the ability to fit complicated six-dimensional distributions to large measurement sets in reasonable time. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗