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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Gravitational Cardy limit and AdS black hole entropy

We explore the gravitational implementation of the field theory Cardy-like limit recently used in the successful microstate countings of AdS black hole entropy in various dimensions. On the field theory side, the Cardy-like limit focuses on a particular scaling of conserved electric charges and angular momenta and we first translate this scaling to the gravitational side by a limiting procedure on the black hole parameters. We note that the scaling naturally accompanies a near-horizon region for which these black hole solutions are greatly simplified. Applying the Kerr/CFT correspondence to the near-horizon region, we precisely reproduce the Bekenstein-Hawking entropy of asymptotically AdS 4,5,6,7 BPS black holes. Our results explicitly provide a microscopic and universal low energy description for AdS black holes across various dimensions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Covariance Shaping Over Riemannian Manifolds for Massive MIMO Communication

Acquiring accurate instantaneous channel state information (CSI) is a challenging aspect of massive multi-input multi-output (MIMO) communication. Utilizing statistical information, such as channel covariance matrix, to design statistical beamforming vectors is robust when compared to instantaneous CSI. In this paper, we propose a novel MIMO covariance shaping scheme over Riemannian manifolds. It serves as an effective statistical beamforming solution to a number of close proximity user equipment (UE) that are undergoing substantial channel correlation. Proposed algorithm exploits the Hermitian positive definite nature of covariance matrices lying over Riemannian manifold. We introduce Wasserstein distance function as a Riemannian metric to measure distances between channel covariance matrices. Furthermore, K-means clustering technique is utilized to effectively identify the optimal shape of effective optimal covariance matrices. Our findings suggest that maximizing the geodesic distance between covariance matrices ultimately leads to a corresponding increase in the network throughput, as determined by the beamforming vector used to shape the covariance matrices. Simulation results validate that the proposed solution converges faster than Euclidean-based state-of-the-art, while maintaining the same computational complexity. Finally, the sum rate performance asymptotically achieves full capacity for two-UE case and more than 96% of the upper bound exhaustive search benchmark for multi-UE scenario.

42 ENGINEERING↗
DOE OSTI2022

Collision of localized shocks in AdS 5 as a series expansion in transverse gradients

We introduce a computational framework to more efficiently calculate the collision of localized shocks in five dimensional asymptotically Anti-de Sitter space. We expand the Einstein equations in transverse gradients and find that our numerical results agree well with exact solutions already at first order in the expansion. Moreover, the Einstein equations at first order in transverse gradients can be decoupled into two sets of differential equations. Here, the bulk fields of one of these sets has only a negligible contribution to boundary observables, such that the computation on each time slice can be simplified to the solution of several planar shockwave equations plus four further differential equations for each transverse plane ‘pixel’. At the cost of errors of ≲ 10% at the hydrodynamization time and for low to mid rapidities, useful numerical solutions can be sped up by roughly one order of magnitude.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Bayesian sparse learning with preconditioned stochastic gradient MCMC and its applications

Deep neural networks have been successfully employed in an extensive variety of research areas, including solving partial differential equations. Despite its significant success, there are some challenges in effectively training DNN, such as avoiding overfitting in over-parameterized DNNs and accelerating the optimization in DNNs with pathological curvature. Here, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an adaptive empirical method. That is, one will alternatively sample from the posterior using preconditioned stochastic gradient Langevin Dynamics (PSGLD), and optimize the latent variables via stochastic approximation. The sparsity of the network is achieved while optimizing the hyperparameters with adaptive searching and penalizing. A popular SG-MCMC approach is Stochastic gradient Langevin dynamics (SGLD). However, considering the complex geometry in the model parameter space in nonconvex learning, updating parameters using a universal step size in each component as in SGLD may cause slow mixing. To address this issue, we apply a computationally manageable preconditioner in the updating rule, which provides a step-size parameter to adapt to local geometric properties. Moreover, by smoothly optimizing the hyperparameter in the preconditioning matrix, our proposed algorithm ensures a decreasing bias, which is introduced by ignoring the correction term in the preconditioned SGLD. According to the existing theoretical framework, we show that the proposed algorithm can asymptotically converge to the correct distribution with a controllable bias under mild conditions. Numerical tests are performed on both synthetic regression problems and learning solutions of elliptic PDE, which demonstrate the accuracy and efficiency of the present work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

The Yang-Mills duals of small AdS black holes

Abstract We study the largeNmatrix model for the index of 4d$$ \mathcal{N} $$ N = 4 Yang-Mills theory and its truncations to understand the dual AdS 5 black holes. Numerical studies of the truncated models provide insights on the black hole physics, some of which we investigate analytically with the full Yang-Mills matrix model. In particular, we find many branches of saddle points which describe the known black hole solutions. We analytically construct the saddle points dual to the small black holes whose sizes are much smaller than the AdS radius. They include the asymptotically flat BMPV black holes embedded in large AdS with novel thermodynamic instabilities.

Physics↗
DOE OSTI2024

A new method for solving the linearized 1D Vlasov–Poisson system yielding a new class of solutions

We describe a new method for solving the linearized 1D Vlasov–Poisson system by using properties of Cauchy-type integrals. Our method remedies critical flaws of the two standard methods, reveals a previously unrecognized Gaussian-in-time-like decay, and can also account for an externally applied electric field. The Landau approximation involves deforming the Bromwich contour around the poles closest to the real axis due to the analytically continued dielectric function, finding the long-time behavior for a stable system: Landau damping. Jackson's generalization encircles all poles while sending the contour to infinity, assuming its contribution vanishes, which is not true in general. This gives incorrect solutions for physically reasonable configurations and can exhibit pathological behavior, of which we show examples. The van Kampen method expresses the solution for a stable equilibrium as a continuous superposition of waves, resulting in an opaque integral. Case's generalization includes unstable systems and predicts a decaying discrete mode for each growing discrete mode, an apparent contradiction to both the Jackson solution and ours. We show, without imposing additional constraints, that the decaying modes are never present in the time evolution due to an exact cancellation with part of the continuum. Our solution is free of integral expressions, is obtained using algebra and Laurent series expansions, does not rely on analytic continuations, and results in a correct asymptotically convergent form in the case of infinite sums. The analysis used can be readily applied in higher-dimensional, electromagnetic systems and also provides a new technique for evaluating certain inverse Laplace transforms.

Physics↗
DOE OSTI2024

S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models

While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order dimension. Hyper-reduction techniques are sampling-based methods that further reduce this computational complexity by approximating such terms with a much smaller dimension. The goal of this work is to introduce the points selection algorithm developed by Shin and Xiu as a hyper-reduction method. The selection algorithm was originally proposed as a stochastic collocation method for uncertainty quantification. Since the algorithm aims at maximizing a quantity $\mathcal{S}$ that measures both the column orthogonality and the determinant, we refer to the algorithm as S-OPT. Numerical examples are provided to demonstrate the performance of S-OPT and to compare its performance with a gappy proper orthogonal decomposition (POD) algorithm. Here, we found that using the S-OPT algorithm is shown to predict the full order solutions with higher accuracy than gappy POD especially when the number of sampling points is small, although we note that S-OPT shows slow asymptotic convergence with respect to the number of samples for some applications, e.g., Lagrangian hydrodynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

SDE_quark

This program provides a fixed-grid quadrature algorithm to compute integrals in the self-energy of the quark propagator within the Maris-Tandy model. The quark propagator both on t he spacelike real axis and at complex-valued momenta is determined from its Schwinger-Dyson equation (SDE). We first apply an iterative solver to find the quark propagator on the spacelike real axis. The propagator at complex-valued momenta is then computed from its self-energy based on this solution, where demanding integrals are encountered. In order to compute of these integrals, we apply customized variable transformations for the radial integral after subtracting the asymptotics. We subsequently apply an optional compound of quadrature rules for the angular integral.

Jia, Shaoyang↗
DOE OSTI2020

Multigrid-Reduction-in-Time for the Rotating Shallow Water Equations

We consider multilevel time-parallel methods for the numerical solution of the rotating shallow water equations. In particular, the multigrid-reduction-in-time (MGRIT) algorithm is used for the parallel time integration. An asymptotic model is used at the coarse levels while the full model is employed at the finer levels. The asymptotic model is well-suited for highly oscillatory partial differential equations like the rotating shallow water equations because it can accurately and stably take the required large time-steps on coarse levels. Our work exploits the flexibility of the MGRIT algorithm in terms of the number of levels and relaxation schemes to show some computational benefits, especially with respect to FCF-relaxation and data reuse.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Richtmyer–Meshkov instability when a shock is reflected for fluids with arbitrary equation of state

First predicted by Richtmyer in 1960 and experimentally confirmed by Meshkov in 1969, the Richtmyer–Meshkov instability (RMI) is crucial in fields such as physics, astrophysics, inertial confinement fusion and high-energy-density physics. These disciplines often deal with strong shocks moving through condensed materials or high-pressure plasmas that exhibit non-ideal equations of state (EoS), thus requiring theoretical models with realistic fluid EoS for accurate RMI simulations. Approximate formulae for asymptotic growth rates, like those proposed by Richtmyer, are helpful but rely on heuristic prescriptions for compressible materials. These prescriptions can sometimes approximate the RMI growth rate well, but their accuracy remains uncertain without exact solutions, as the fully compressible RMI growth rate is influenced by both vorticity deposited during shock refraction and multiple sonic wave refractions. This study advances previous work by presenting an analytic, fully compressible theory of RMI for reflected shocks with arbitrary EoS. It compares theoretical predictions with heuristic prescriptions using ideal gas, van der Waals gas and three-term constitutive equations for simple metals, the latter being analysed with detailed and simplified ideal-gas-like EoS. We additionally offer an alternative explicit approximate formula for the asymptotic growth rate. The comprehensive model also incorporates the effects of constant-amplitude acoustic waves at the interface, associated with the D'yakov–Kontorovich instability in shocks.

Napieralski, Mario (ORCID:0009000692344901)↗
DOE OSTI2024

A robust spectral element implementation of the $k - τ$ RANS model in Nek5000/NekRS

The $k - ω$ Reynolds Averaged Navier Stokes (RANS) model is one of the industry standard approaches for modeling of turbulent flows. It performs better than the $k - ϵ$ model for low Reynolds number flows and is also more suitable for boundary layers with adverse pressure gradients. Major drawback of the model, however, is that the asymptotic value of $ω$ at the walls is singular, necessitating the use of a contrived “sufficiently” large value for $ω$ as the boundary condition for its transport equation. Here, this invariably leads to the solution being sensitive to near wall grid spacing. While an acceptable solution for low order (finite volume) methods, the excessive near wall gradients lead to persistent numerical stability issues in high order codes. To alleviate the problem, specifically in the context of the high order spectral element code Nek5000, a regularized $k - ω$ approach was formulated in our prior work (Tomboulides et al., 2018). The formulation, however, relies on the use of wall distance and its gradients for modeling the closure terms and can pose problems for simulations in complex geometries. This work presents a novel implementation of the $k - τ$ RANS model in Nek5000, where $τ = 1/ω$, eliminating the need for regularization, owing to the asymptotically bounded behavior of the source terms in the $τ$ transport equation, and also eliminating dependence on wall distance. Robustness and stability of the $k - τ$ model is ensured through implicit treatment of the source terms and their careful numerical implementation and demonstrated through several cases aimed at verification and validation. Studies include both canonical and engineering relevant problems, viz., turbulent channel flow, pipe flow, backward facing step, flow over NACA 0012 airfoil and flow in a T-junction. Results from the $k - τ$ model are shown to be consistent with regularized $k - ω$ model and also with the $k - ω$ SST model in OpenFOAM (for select studies). Comparison with experimental data is also shown, where available, to bolster validation efforts for the $k - τ$ model implementation through prediction of key turbulent quantities of interest.

Nek5000↗
DOE OSTI2022

Shock Formation and Vorticity Creation for 3d Euler

Abstract We analyze the shock formation process for the 3D nonisentropic Euler equations with the ideal gas law, in which sound waves interact with entropy waves to produce vorticity. Building on our theory for isentropic flows in [3, 4], we give a constructive proof of shock formation from smooth initial data. Specifically, we prove that there exist smooth solutions to the nonisentropic Euler equations which form a generic stable shock with explicitly computable blowup time, location, and direction. This is achieved by establishing the asymptotic stability of a generic shock profile in modulated self‐similar variables, controlling the interaction of wave families via: (i) pointwise bounds along Lagrangian trajectories, (ii) geometric vorticity structure, and (iii) high‐order energy estimates in Sobolev spaces. © 2022 Wiley Periodicals LLC.

Mathematics↗
DOE OSTI2021

Black hole induced false vacuum decay from first principles

We provide a method to calculate the rate of false vacuum decay induced by a black hole. The method uses complex tunneling solutions and consistently takes into account the structure of different quantum vacua in the black hole metric via boundary conditions. The latter are connected to the asymptotic behavior of the time-ordered Green’s function in the corresponding vacua. We illustrate the technique on a two-dimensional toy model of a scalar field with inverted Liouville potential in an external background of a dilaton black hole. We analytically derive the exponential suppression of tunneling from the Boulware, Hartle-Hawking and Unruh vacua and show that they are parametrically different. The Unruh vacuum decay rate is exponentially smaller than the decay rate of the Hartle-Hawking state, though both rates become unsuppressed at high enough black hole temperature. We interpret the vanishing suppression of the Unruh vacuum decay at high temperature as an artifact of the two-dimensional model and discuss why this result can be modified in the realistic case of black holes in four dimensions.

2D Gravity↗
DOE OSTI2026

A buoyancy–shear–drag–scalar-based turbulence model for power-law acceleration-driven Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing

A previously developed phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing based on a general buoyancy–shear–drag model [O. Schilling, “A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing,” Physica D 402, 132238 (2020)] is extended to include active or passive scalar mixing and power-law acceleration-driven Rayleigh–Taylor mixing. The buoyancy–shear–drag equations are coupled to a scalar variance equation that is used to define the molecular mixing parameter θ m , and when the scalar is active, modifies the Rayleigh–Taylor and Kelvin–Helmholtz mixing layer growth parameters to depend on the asymptotic value of this parameter, θ mol . Here, the scalar variance equation is closed by algebraically or differentially modeling the scalar variance dissipation rate. Nonlinear analytical solutions of the model are obtained in the total and separate bubble and spike mixing layer width formulations with the algebraic scalar variance dissipation rate for each instability, which are then used to calibrate the mechanical and scalar equation coefficients to predict specific values of physical observables and molecular mixing parameters. Surrogate mechanical and scalar turbulent fields can be constructed by multiplying a presumed self-similar spatial profile by appropriate functions of the width and its time derivative, and of the scalar obtained by solving the ordinary differential model equations. The explicit modeling and solution of turbulent transport equations are not required. The bubble and spike mixing layer width and scalar variance equations are then solved numerically for constant-acceleration Rayleigh–Taylor, impulsively reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing, confirming that the prescribed level of molecular mixing is correctly predicted and illustrating the spatiotemporal evolution of the scalar fields.

Buoyancy–drag↗
DOE OSTI2024

A collision-based hybrid method for the BGK equation

In this article, we apply the collision-based hybrid method introduced by Hauck and McClarren to the Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of the source term is used to handle stiffness associated with the BGK operator. Although it helps the numerical scheme become stable with a large time step size, it is still not obvious to achieve the desired order of accuracy due to the relationship between the size of the spatial cell and the mean free path. Without asymptotic preserving property, a very restricted grid size is required to resolve the mean free path, which is not practical. Our approaches are based on the noncollision-collision decomposition of the BGK equation. We introduce the arbitrary order of nodal discontinuous Galerkin (DG) discretization in space with a semi-implicit time-stepping method; we employ the backward Euler time integration for the uncollided equation and the 2nd order predictor-corrector scheme for the collided equation, i.e., both source terms in uncollided and collided equations are treated implicitly and only streaming term in the collided equation is solved explicitly. This improves the computational efficiency without the complexity of the numerical implementation. Numerical results are presented for various Knudsen numbers to present the effectiveness and accuracy of our hybrid method. Also, we compare the solutions of the hybrid and non-hybrid schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Helicity at small x: oscillations generated by bringing back the quarks

We construct a numerical solution of the recently-derived large-N c &N f small-x helicity evolution equations with the aim to establish the small-x asymptotics of the quark helicity distribution beyond the large-N c limit explored previously in the same framework. (Here N c and N f are the numbers of quark colors and flavors.) While the large-N c helicity evolution involves gluons only, the large-N c &N f evolution includes contributions from quarks as well. We find that adding quarks to the evolution makes quark helicity distribution oscillate as a function of x. Our numerical results in the large-N c &N f limit lead to the x-dependence of the flavor-singlet quark helicity distribution which is well-approximated by $$ {\left.\Delta \Sigma \left(x,{Q}^2\right)\right|}_{\mathrm{large}\hbox{-} {N}_c\&{N}_f}\sim {\left(\frac{1}{x}\right)}^{\alpha_h^q}\cos \left[{\omega}_q\ln \left(\frac{1}{x}\right)+{\varphi}_q\right]. $$. The power $α^{q}_{h}$ exhibits a weak N f -dependence, and, for all Nf values considered, remains very close to $α^{q}_{h}$(N f =0)=$\left(4/\sqrt{3}\right)\sqrt{\alpha_s{N}_c/\left(2\pi \right)}$ obtained earlier in the large-N c limit. The novel oscillation frequency ω q and phase shift φ q depend more strongly on the number of flavors N f (with ω q = 0 in the pure-glue large-N c limit). The typical period of oscillations for ΔΣ is rather long, spanning many units of rapidity. We speculate whether the oscillations we find are related to the sign variation with x seen in the strange quark helicity distribution extracted from the data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

A Quantum-Inspired Tensor Network Algorithm for Constrained Combinatorial Optimization Problems

Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we propose a quantum-inspired tensor-network-based algorithm for general locally constrained combinatorial optimization problems. Our algorithm constructs a Hamiltonian for the problem of interest, effectively mapping it to a quantum problem, then encodes the constraints directly into a tensor network state and solves the optimal solution by evolving the system to the ground state of the Hamiltonian. We demonstrate our algorithm with the open-pit mining problem, which results in a quadratic asymptotic time complexity. Our numerical results show the effectiveness of this construction and potential applications in further studies for general combinatorial optimization problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Tracking and Rejection of Biased Sinusoidal Signals Using Generalized Predictive Controller

Some novel applications require the tracking/rejection of biased sinusoidal reference/distur-bances. According to the internal model principle (IMP), a controller must embed the model of a biased sinusoidal signal to track references and also reject perturbations modeled through the aforementioned signal. However, the design of that kind of controller is not straightforward, especially when they are implemented in digital processors. This paper presents a controller, based on generalized predictive control (GPC), designed for tracking/rejection of biased sinusoidal signals. In general, GPC is based on the prediction of the plant responses through an augmented prediction model. The proposed approach develops an augmented model that predicts the future errors. The prediction model and the control law used in the proposed approach embed the discrete-time model of a biased sinusoidal signal. Thus, the proposed controller can track/reject biased sinusoidal references/disturbances. The predicted errors and the future inputs of the proposed augmented model are used to define the cost function that measures the control performance. An optimization technique was applied to obtain the solution of the cost function, which is the optimal sequence of future model inputs that allows defining the control law. Experimental tests prove that the proposed controller can asymptotically track and reject biased sinusoidal signals.

42 ENGINEERING↗