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At least 109 records · Page 6

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NASA NTRS1960

The Numerical Calculation of Flow Past Conical Bodies Supporting Elliptic Conical Shock Waves at Finite Angles of Incidence

The inverse method, with the shock wave prescribed to be an elliptic cone at a finite angle of incidence, is applied to calculate numerically the supersonic perfect-gas flow past conical bodies not having axial symmetry. Two formulations of the problem are employed, one using a pair of stream functions and the other involving entropy and components of velocity. A number of solutions are presented, illustrating the numerical methods employed, and showing the effects of moderate variation of the initial parameters.

Briggs, Benjamin R.↗

DOE OSTI2022

Entropy Measurement of a Strongly Coupled Quantum Dot

The spin 1/2 entropy of electrons trapped in a quantum dot has previously been measured with great accuracy, but the protocol used for that measurement is valid only within a restrictive set of conditions. Here, in this work, we demonstrate a novel entropy measurement protocol that is universal for arbitrary mesoscopic circuits and apply this new approach to measure the entropy of a quantum dot hybridized with a reservoir. The experimental results match closely to numerical renormalization group (NRG) calculations for small and intermediate coupling. For the largest couplings investigated in this Letter, NRG calculations predict a suppression of spin entropy at the charge transition due to the formation of a Kondo singlet, but that suppression is not observed in the experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Simulating lossy Gaussian boson sampling with matrix-product operators

Gaussian boson sampling, a computational model that is widely believed to admit quantum supremacy, has already been experimentally demonstrated and is claimed to surpass the classical simulation capabilities of even the most powerful supercomputers today. However, whether the current approach limited by photon loss and noise in such experiments prescribes a scalable path to quantum advantage is an open question. Here, to understand the effect of photon loss on the scalability of Gaussian boson sampling, we analytically derive the asymptotic operator entanglement entropy scaling, which relates to the simulation complexity. As a result, we observe that efficient tensor network simulations are likely possible under the N out ∝ √N scaling of the number of surviving photons N out in the number of input photons N. We numerically verify this result using a tensor network algorithm with U⁡(1) symmetry, and we overcome previous challenges due to the large local Hilbert-space dimensions in Gaussian boson sampling with hardware acceleration. Additionally, we observe that increasing the photon number through larger squeezing does not increase the entanglement entropy significantly. Finally, we numerically find the bond dimension necessary for fixed accuracy simulations, providing more direct evidence for the complexity of tensor networks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Entanglement transitions from restricted Boltzmann machines

The search for novel entangled phases of matter has lead to the recent discovery of a new class of “en- tanglement transitions,” exemplified by random tensor networks and monitored quantum circuits. Most known examples can be understood as some classical ordering transitions in an underlying statistical mechanics model, where entanglement maps onto the free-energy cost of inserting a domain wall. In this paper we study the possibility of entanglement transitions driven by physics beyond such statistical mechanics mappings. Motivated by recent applications of neural-network-inspired variational Ansätze, we investigate under what conditions on the variational parameters these Ansätze can capture an entanglement transition. We study the entanglement scaling of short-range restricted Boltzmann machine (RBM) quantum states with random phases. For uncorrelated random phases, we analytically demonstrate the absence of an entanglement transition and reveal subtle finite-size effects in finite-size numerical simulations. Introducing phases with correlations decaying as 1/r α in real space, we observe three regions with a different scaling of entanglement entropy depending on the exponent α. We study the nature of the transition between these regions, finding numerical evidence for critical behavior. Furthermore, our work establishes the presence of long-range correlated phases in RBM-based wave functions as a required ingredient for entanglement transitions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1992

Numerical simulation of entry flow over blunt swept-wing planes

Viscous, heat-conducting flow with chemical and vibrational relaxation processes of the constituent gases surrounding winged spacecraft is considered in the continuum regime. The Navier-Stokes equations are appended by additional vibrational energy and species rate equations and supplemented by the equations of state and the phenomenological laws based on mixture rules or collisional cross sections. Numerical convective flux can be obtained from several forms of one-dimensional Riemann solver, with or without entropy correction. High-order accuracy is obtained from two types of reconstructive interpolation. A number of explicit and implicit numerical schemes have been implemented as a means to yield converged solutions. Both shock-fitting, finite-difference and shock-capturing, finite-volume techniques have been tested for configurations such as a sphere, double ellipsoid, blunt-edge delta wing, a European Hermes vehicle, and the U.S. Shuttle Orbiter. The shock-fitting code provides excellent results only for simple configurations, whereas the shock-capturing code leads to overall satisfying solutions for complex geometries.

Li, C. P.↗

DOE OSTI2023

Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state

Here, this paper is concerned with the approximation of the compressible Euler equations supplemented with an arbitrary or tabulated equation of state. The proposed approximation technique is robust, formally second-order accurate in space, invariant-domain preserving, and works for every equation of state, tabulated or analytic, provided the pressure is nonnegative. An entropy surrogate functional that grows across shocks is proposed. The numerical method is verified with novel analytical solutions and then validated with several computational benchmarks seen in the literature including problems with composite waves.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Adsorbate Free Energies from DFT-Derived Translational Energy Landscapes

Adsorption free energies are fundamental to surface chemistry and catalysis. Standard models combine some assumed analytical form of the translational potential energy surface, often parameterized against density functional theory (DFT) calculations, with an analytical expression for the resultant translational densities of states (DOS), free energy, and entropy. Here we compare the performance of such models against numerical evaluations of the DOS and thermodynamic functions derived from solutions to the translational Schrodinger equation. We compare results for a translational potential energy surface (PES) derived from nudged eleastic band calculations with those obtained from adsorbate rastering across a series of monatomic (O, S, C, N, H) and polyatomic (NH x ) adsorbates on (100) Pt and Au facets. We find that analytical models as commonly parameterized have mixed performance for describing the translational PES and that the consequences for computed free energies are modest but potentially significant in microkinetic models. Here, numerical solutions are possible for modest to no additional computational cost over analytical models and thus should be considered when reliable free energy estimates are needed or translational potential energy surfaces are available.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2004

Flow field topology of transient mixing driven by buoyancy

Transient mixing driven by buoyancy occurs through the birth of a symmetric Rayleigh-Taylor morphology (RTM) structure for large length scales. Beyond its critical bifurcation the RTM structure exhibits self-similarity and occurs on smaller and smaller length scales. The dynamics of the RTM structure, its nonlinear growth and internal collision, show that its genesis occurs from an explosive bifurcation which leads to the overlap of resonance regions in phase space. This event shows the coexistence of regular and chaotic regions in phase space which is corroborated with the existence of horseshoe maps. A measure of local chaos given by the topological entropy indicates that as the system evolves there is growth of uncertainty. Breakdown of the dissipative RTM structure occurs during the transition from explosive to catastrophic bifurcation; this event gives rise to annihilation of the separatrices which drives overlap of resonance regions. The global bifurcation of explosive and catastrophic events in phase space for the large length scale of the RTM structure serves as a template for which mixing occurs on smaller and smaller length scales. Copyright 2004 American Institute of Physics.

Nonlinear Dynamics↗

DOE OSTI2021

Scaling functions for eigenstate entanglement crossovers in harmonic lattices

For quantum matter, eigenstate entanglement entropies obey an area law or log-area law at low energies and small subsystem sizes and cross over to volume laws for high energies and large subsystems. This transition is captured by crossover functions, which assume a universal scaling form in quantum critical regimes. We demonstrate this for the harmonic lattice model, which describes quantized lattice vibrations and is a regularization for free scalar field theories, modeling, e.g., spin-0 bosonic particles. In one dimension, the ground-state entanglement obeys a log-area law. For dimensions d ≥ 2, it displays area laws, even at criticality. The distribution of excited-state entanglement entropies is found to be sharply peaked around subsystem entropies of corresponding thermodynamic ensembles in accordance with the eigenstate thermalization hypothesis. Numerically, we determine crossover scaling functions for the quantum critical regime of the model and do a large-deviation analysis. We show how infrared singularities of the system can be handled and how to access the thermodynamic limit using a perturbative trick for the covariance matrix. Eigenstates for quasi-free bosonic systems are not Gaussian. Here, we resolve this problem by considering appropriate squeezed states instead. For these, entanglement entropies can be evaluated efficiently.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Continuous polyamorphic transition in high-entropy metallic glass

Polyamorphic transition (PT) is a compelling and pivotal physical phenomenon in the field of glass and materials science. Understanding this transition is of scientific and technological significance, as it offers an important pathway for effectively tuning the structure and property of glasses. In contrast to the PT observed in conventional metallic glasses (MGs), which typically exhibit a pronounced first-order nature, herein we report a continuous PT (CPT) without first-order characteristics in high-entropy MGs (HEMGs) upon heating. This CPT behavior is featured by the continuous structural evolution at the atomic level and an increasing chemical concentration gradient with temperature, but no abrupt reduction in volume and energy. The continuous transformation is associated with the absence of local favorable structures and chemical heterogeneity caused by the high configurational entropy, which limits the distance and frequency of atomic diffusion. As a result of the CPT, numerous glass states can be generated, which provides an opportunity to understand the nature, atomic packing, formability, and properties of MGs. Moreover, this discovery highlights the implication of configurational entropy in exploring polyamorphic glasses with an identical composition but highly tunable structures and properties.

36 MATERIALS SCIENCE↗

DOE OSTI2023

KiT-RT: An Extendable Framework for Radiative Transfer and Therapy

Here, in this article, we present Kinetic Transport Solver for Radiation Therapy (KiT-RT), an open-source C++-based framework for solving kinetic equations in therapy applications available at https://github.com/CSMMLab/KiT-RT . This software framework aims to provide a collection of classical deterministic solvers for unstructured meshes that allow for easy extendability. Therefore, KiT-RT is a convenient base to test new numerical methods in various applications and compare them against conventional solvers. The implementation includes spherical harmonics, minimal entropy, neural minimal entropy, and discrete ordinates methods. Solution characteristics and efficiency are presented through several test cases ranging from radiation transport to electron radiation therapy. Due to the variety of included numerical methods and easy extendability, the presented open-source code is attractive for both developers, who want a basis to build their numerical solvers, and users or application engineers, who want to gain experimental insights without directly interfering with the codebase.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Data-driven, structure-preserving approximations to entropy-based moment closures for kinetic equations

In this study, we present a data-driven approach for approximating entropy-based closures of moment systems from kinetic equations. The proposed closure learns the entropy function by fitting the map between the moments and the entropy of the moment system, and thus does not depend on the spacetime discretization of the moment system or specific problem configurations such as initial and boundary conditions. With convex and C 2 approximations, this data-driven closure inherits several structural properties from entropy-based closures, such as entropy dissipation, hyperbolicity, and H-Theorem. We construct convex approximations to the Maxwell–Boltzmann entropy using convex splines and neural networks, test them on the plane source benchmark problem for linear transport in slab geometry, and compare the results to the standard, entropy-based systems which solve a convex optimization problem to find the closure. Numerical results indicate that these data-driven closures provide accurate solutions in much less computation time than that required by the optimization routine.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Minimum entropy filtering for a single output non-Gaussian stochastic system using state transformation

This paper presents a novel filter design for the single-output stochastic non-linear systems subjected to non-Gaussian noises and the proposed assumptions. Based on a state transformation, the unmeasurable states of the systems can be estimated where non-linear terms in the systems have been eliminated. It has been shown that the estimation error is linearly dynamical regarding to the presented vector-valued filter gain which can be optimised by minimising the entropy-based performance criterion. In addition, the convergence of the presented algorithm is analysed in mean-square sense and a numerical example is given to verify the effectiveness of the presented filtering algorithm. Meanwhile, the extended Kalman filter, unscented particle filter and minimum entropy filter are given for the comparisons of the filtering performance. Following the presented framework, some extensions of the presented filtering algorithm are discussed to indicate the flexibility of the filter design. The contribution of this paper can be summarised as establishing a novel minimum entropy filtering framework which consists of model transformation, entropy optimisation and convergence analysis.

42 ENGINEERING↗

DOE OSTI2024

A note on higher-order and nonlinear limiting approaches for continuously bounds-preserving discontinuous Galerkin methods

In Dzanic (2024), a limiting approach for high-order discontinuous Galerkin schemes was introduced which allowed for imposing constraints on the solution continuously (i.e., everywhere within the element). While exact for linear constraint functionals, this approach only imposed a sufficient (but not the minimum necessary) amount of limiting for nonlinear constraint functionals. This short note shows how this limiting approach can be extended to allow exactness for general nonlinear quasiconcave constraint functionals through a nonlinear limiting procedure, reducing unnecessary numerical dissipation. Finally, some examples are shown for nonlinear pressure and entropy constraints in the compressible gas dynamics equations, where both analytic and iterative approaches are used.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Z 3 Parafermion in the Double Charge Kondo Model

Quantum impurity models with frustrated Kondo interactions can support quantum critical points with fractionalized excitations. Recent experiments [arXiv:2108.12691] on a circuit containing two coupled metal-semiconductor islands exhibit transport signatures of such a critical point. Here we show using bosonization that the double charge-Kondo model describing the device can be mapped in the Toulouse limit to a sine-Gordon model. Its Bethe-ansatz solution shows that a Z 3 parafermion emerges at the critical point, characterized by a fractional $\frac{1}{2}$ln(3) residual entropy, and scattering fractional charges e/3. Finally, we also present full numerical renormalization group calculations for the model and show that the predicted behavior of conductance is consistent with experimental results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1984

Entropy condition satisfying approximations for the full potential equations of transonic flow

A class of conservative difference approximations for the steady full potential equation was presented. They are, in general, easier to program than the usual density biasing algorithms, and in fact, differ only slightly from them. Rigorous proof indicated that these new schemes satisfied a new discrete entropy inequality, which ruled out expansion shocks, and that they have sharp, steady, discrete shocks. A key tool in the analysis is the construction of a new entropy inequality for the full potential equation itself. Results of some numerical experiments using the new schemes are presented.

Osher, S.↗

NASA NTRS1985

Entropy condition satisfying approximations for the full potential equation of transonic flow

Osher, S.↗

NASA NTRS1990

Encoding Y,I,Q component estimates of an NTSC composite signal

Several new techniques for reducing the entropy of a Y,I,Q component digital transmission are presented. A discussion of each technique is presented along with objective and subjective analysis. For a set of four test pictures, the average Y,I,Q entropy/pixel was reduced by nearly 80 percent. An initial component system entropy of 11.08 bits/pixel was reduced to 2.33 bits/pixel. Although exact numeric results are dependent on the separation technique used, the methods presented may be applied to systems using other component separation methods.

Border, David A.↗