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At least 613 records · Page 34

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DOE OSTI2016

Light propagation in stratified media with soft interfaces

The propagation of light through materials in which the density of charge carriers varies smoothly on a scale smaller than or comparable to the wavelength requires a description that goes beyond the commonly used Fresnel equations. We propose a method to solve Maxwell’s equations in such a way that any linear response theory for the bulk material can be combined with a given smooth density profile for the (free or bound) charge carriers. This method is implemented for linearly polarized monochromatic light impinging on inhomogeneous multilayer systems, leading to a fast algorithm that yields reflectance and transmittance for such systems. We apply our algorithm to investigate the difference in optical response between smooth interfaces and abrupt interfaces in stratified systems where the materials can have complex bulk permittivities, and find that the smoothening of the interface on a wavelength scale significantly reduces reflection in favor of absorption. This result is of importance to current experiments that aim to detect metallic hydrogen and deuterium films using their optical response. Furthermore, our results show that for a correct interpretation of these experiments it is important to consider the smoothness of the density profile of the metallic layer. Also, for nonabsorbing layers, a smooth, rather than abrupt transition, can have an important impact on the design of optical filters.

08 HYDROGEN↗

DOE OSTI2016

Fast Bayesian blind deconvolution with Huber Super Gaussian priors

We report expectation Maximization (EM) based inference has already proven to be a very powerful tool to solve blind image deconvolution (BID) problems. Unfortunately, three important problems still impede the application of EM in BID: the undesirable saddle points and local minima caused by highly nonconvex priors, the instability around zero of some of the most interesting sparsity promoting priors, and the intrinsic high computational cost of the corresponding BID algorithm. In this paper we first show how Super Gaussian priors can be made numerically tractable around zero by introducing the family of Huber Super Gaussian priors and then present a fast EM based blind deconvolution method formulated in the image space. In the proposed computational approach, image and kernel estimation are performed by using the Alternating Direction Method of Multipliers (ADMM), which allows to exploit the advantages of FFT computation. For highly nonconvex priors, we propose a Smooth ADMM (SADMM) approach to avoid poor BID estimates. In conclusion, extensive experiments demonstrate that the proposed method significantly outperforms state-of-the-art BID methods in terms of quality of the reconstructions and speed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Adaptive Urban Traffic Signal Control for Multiple Intersections: An LQR Approach

Traffic congestion leads to severe problems especially in urban traffic networks. It increases the chance of accidents, energy waste, and social costs. In order to address these problems, an adaptive linear quadratic regulator (LQR) approach is developed for traffic signal control at multiple intersections in an urban area. The proposed method controls the green time of the traffic signals to reduce traffic congestion and smooth traffic flow. Real-world data from vision-based traffic sensors are used to build the traffic network model, which mimics the real-world traffic behavior. In addition, the proposed control utilizes recursive least square parameter estimation, which is capable of tracking dynamic changes in traffic conditions. Simulation of Urban MObility (SUMO) is used to analyze the efficacy of the proposed method. Results of the simulation show that the proposed method outperforms pretimed control in various aspects.

adaptive LQR control↗

NASA NTRS2017

A Smoothed Eclipse Model for Solar Electric Propulsion Trajectory Optimization

Solar electric propulsion (SEP) is the dominant design option for employing low-thrust propulsion on a space mission. Spacecraft solar arrays power the SEP system but are subject to blackout periods during solar eclipse conditions. Discontinuity in power available to the spacecraft must be accounted for in trajectory optimization, but gradient-based methods require a differentiable power model. This work presents a power model that smooths the eclipse transition from total eclipse to total sunlight with a logistic function. Example trajectories are computed with differential dynamic programming, a second-order gradient-based method.

trajectory design↗

NASA NTRS2017

A Smoothed Eclipse Model for Solar Electric Propulsion Trajectory Optimization

optimization↗

NASA NTRS1990

Reaction-compensation technology for microgravity laboratory robots

Robots operating in the microgravity environment of an orbiting laboratory should be capable of manipulating payloads such that the motion of the robot does not disturb adjacent experiments. The current results of a NASA Lewis Research Center technology program to develop smooth, reaction-compensated manipulation based on both mechanism technology and trajectory planning strategies are present. Experimental validation of methods to reduce robot base reactions through the use of redundant degrees of freedom is discussed. Merits of smooth operation roller-driven robot joints for microgravity manipulators are also reviewed.

Rohn, Douglas A.↗

NASA NTRS1990

Reaction-compensation technology for microgravity laboratory robots

Rohn, Douglas A.↗

NASA NTRS1980

Numerical generation of two-dimensional orthogonal curvilinear coordinates in an Euclidean space

A noniterative method for the numerical generation of orthogonal curvilinear coordinates for plane annular regions between two arbitrary smooth closed curves was developed. The basic generating equation is the Gaussian equation for an Euclidean space which is solved analytically. The method is applied in many cases and these test results demonstrate that the proposed method can be readily applied to a wide variety of problems. The method can also be used for simply connected regions only by obtaining the solution of the linear equation under the changed boundary conditions.

Warsi, Z. U. A.↗

DOE OSTI2022

Combining DPG in space with DPG time-marching scheme for the transient advection–reaction equation

In this article, we present a general methodology to combine the Discontinuous Petrov–Galerkin (DPG) method in space and time in the context of methods of lines for transient advection–reaction problems. We first introduce a semidiscretization in space with a DPG method redefining the ideas of optimal testing and practicality of the method in this context. Then, we apply the recently developed DPG-based time-marching scheme, which is of exponential-type, to the resulting system of Ordinary Differential Equations (ODEs). Further, we also discuss how to efficiently compute the action of the exponential of the matrix coming from the space semidiscretization without assembling the full matrix. Finally, we verify the proposed method for 1D+time advection–reaction problems showing optimal convergence rates for smooth solutions and more stable results for linear conservation laws comparing to the classical exponential integrators.

42 ENGINEERING↗

DOE OSTI2017

A single-stage flux-corrected transport algorithm for high-order finite-volume methods

We present a new limiter method for solving the advection equation using a high-order, finite-volume discretization. The limiter is based on the flux-corrected transport algorithm. Here, we modify the classical algorithm by introducing a new computation for solution bounds at smooth extrema, as well as improving the preconstraint on the high-order fluxes. We compute the high-order fluxes via a method-of-lines approach with fourth-order Runge-Kutta as the time integrator. For computing low-order fluxes, we select the corner-transport upwind method due to its improved stability over donor-cell upwind. Several spatial differencing schemes are investigated for the high-order flux computation, including centered- difference and upwind schemes. We show that the upwind schemes perform well on account of the dissipation of high-wavenumber components. The new limiter method retains high-order accuracy for smooth solutions and accurately captures fronts in discontinuous solutions. Further, we need only apply the limiter once per complete time step.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1981

General relaxation schemes in multigrid algorithms for higher order singularity methods

Relaxation schemes based on approximate and incomplete factorization technique (AF) are described. The AF schemes allow construction of a fast multigrid method for solving integral equations of the second and first kind. The smoothing factors for integral equations of the first kind, and comparison with similar results from the second kind of equations are a novel item. Application of the MD algorithm shows convergence to the level of truncation error of a second order accurate panel method.

Oskam, B.↗

DOE OSTI2015

Identifying finite-time coherent sets from limited quantities of Lagrangian data

A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that “leak” from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, “data rich” test problems, and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or “mesh-free” methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1986

Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite volume, time marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier Stokes equations. The entire calculation is performed in the physical domain. The method is currently limited to the calculation of attached flows. The features of the current method can be summarized as follows. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is now needed. Different time steps are used in the different governing equations to improve the convergence speed of the viscous calculations. A new pressure interpolation scheme is introduced which improves the shock capturing ability of the method. A multi-volume method for pressure changes in the boundary layer allows calculations which use very long and thin control volumes. A special discretization technique is also used to stabilize these calculations. A special formulation of the energy equation is used to provide improved transient behavior of solutions which use the full energy equation. The method is then compared with a wide variety of test cases. The freestream Mach numbers range from 0.075 to 2.8 in the calculations. Transonic viscous flow in a converging diverging nozzle is calculated with the method; the Mach number upstream of the shock is approximately 1.25. The agreement between the calculated and measured shock strength and total pressure losses is good. Essentially incompressible turbulent boundary layer flow in a adverse pressure gradient is calculated and the computed distribution of mean velocity and shear stress are in good agreement with the measurements. At the other end of the Mach number range, a flat plate turbulent boundary layer with a freestream Mach number of 2.8 is calculated using the full energy equation; the computed total temperature distribution and recovery factor agree well with the measurements when a variable Prandtl number is used through the boundary layer.

Nicholson, S.↗

DOE OSTI2016

A real-space Green’s function method for thenumerical solution of Maxwell’s equations

A new method for solving the transverse part of the free-space Maxwell equations in three dimensions is presented. By taking the Helmholtz decomposition of the electric field and current sources and considering only the divergence-free parts, we obtain an explicit real-space representation for the transverse propagator that explicitly respects finite speed of propagation. Because the propagator involves convolution against a singular distribution, we regularize via convolution with smoothing kernels (B-splines) prior to sampling based on a method due to Beyer and LeVeque (1992). We show that the ultimate discrete convolutional propagator can be constructed to attain an arbitrarily high order of accuracy by using higher-order regularizing kernels and finite difference stencils and that it satisfies von Neumann’s stability condition. Furthermore, the propagator is compactly supported and can be applied using Hockney’s method (1970) and parallelized using the same observation as made by Vay, Haber, and Godfrey (2013), leading to a method that is computationally efficient.

Lo, Boris↗

DOE OSTI2020

Detecting Low-level Radiation Sources Using Border Monitoring Gamma Sensors

We consider a problem of detecting a low-level radiation source using a network of Gamma spectral sensors placed on the periphery of a monitored region. We propose a computationally light-weight, correlation-based method which is primarily intended for systems with limited computing capacity. Sensor measurements are combined at the fusion by first generating decisions at each time step and then taking their majority vote within a time widow. At each time step, decisions are generated using two strategies: (i) SUM method based on a threshold decision on a correlation statistic derived from measurements from all sensors, and (ii) OR method based on logical-OR of threshold decisions based on correlations statistics of individual sensor measurements. We derive analytical performance bounds for false alarm rates of SUM and OR methods, and show that their performance is enhanced by the temporal smoothing of majority vote within a time window. Using measurements from a test campaign, we generate a border monitoring scenario with twelve 2"x2" NaI Gamma sensors deployed on the periphery of 42m x 42m outdoor region. A Cs-137 source is moved in a straight-line across this region, starting several meters outside and finally moving away from it. We illustrate the performance of both correlation-based detection methods, and compare their performances with each other and with a particle filter method. Overall, under small false-alarm conditions, the OR fusion is found to produce better detection performance.

Sen, Satyabrata↗

DOE OSTI2025

A discontinuous Galerkin spectral element method for compressible reacting flows

High-order methods have recently been shown to be an effective tool for high-fidelity flow computations like direct numerical simulations and large-eddy simulations because of their strong balance between accuracy and computational cost. In this work, a high-order discontinuous Galerkin spectral element method (DGSEM) is developed to solve the chemically reacting Navier-Stokes equations. To handle the disparate length and time scales associated with these equations, we develop a novel method which combines the spectral accuracy of the SEM with the flexibility of the DG approach. The framework, implemented in the spectral element code Nek5000, is well suited to capture turbulence in smooth regions of the flow, while maintaining numerical stability in the presence of shocks. An entropy-residual based artificial viscosity is added to smooth shocked regions of flow, and a positivity-preserving limiter is implemented to suppress non-physical oscillations. These enhancements support the numerical stability of the hydrodynamic sub-step, which is decoupled from the chemistry integration through a second-order operator splitting method. Here, a series of smooth and discontinuous validation cases are presented in increasing physical and computational complexity for both inviscid and viscous flows. In particular, simulations of canonical one-dimensional and two-dimensional detonations are performed, and the high-order numerical results are validated against available literature data. Additional validation studies are carried out for classical three-dimensional numerical simulations of incompressible and compressible turbulent flows.

Compressible reacting flows↗

DOE OSTI2020

Four-Switch Buck-Boost Converter Based on Model Predictive Control with Smooth Mode Transition Capability

Four-switch buck-boost converter supports both voltage step-up and step-down functionalities, but it suffers from mode transfer challenge that would need reliable mode detection when designed to operate in multi different modes. In this paper, a novel control method based on model predictive current control is proposed for such converter with inherent smooth mode transfer capability without extra design on mode detection and transfer scheme. Modulator and mode detection are replaced by an optimization process through cost function. This largely simplifies the design and makes it easily implemented. Therefore, seamless transfer between buck and boost modes is achieved with many other system level benefits. Simulation and experimental results are provided to verify the effectiveness of proposed method for the four-switch buck-boost converter.

42 ENGINEERING↗

DOE OSTI2021

Laplacian Smoothing Stochastic Gradient Markov Chain Monte Carlo

As an important Markov chain Monte Carlo (MCMC) method, the stochastic gradient Langevin dynamics (SGLD) algorithm has achieved great success in Bayesian learning and posterior sampling. Furthermore, SGLD typically suffers from a slow convergence rate due to its large variance caused by the stochastic gradient. In order to alleviate these drawbacks, we leverage the recently developed Laplacian smoothing technique and propose a Laplacian smoothing stochastic gradient Langevin dynamics (LS-SGLD) algorithm. We prove that for sampling from both log-concave and non-log-concave densities, LS-SGLD achieves strictly smaller discretization error in 2-Wasserstein distance, although its mixing rate can be slightly slower. Experiments on both synthetic and real datasets verify our theoretical results and demonstrate the superior performance of LS-SGLD on different machine learning tasks including posterior sampling, Bayesian logistic regression, and training Bayesian convolutional neural networks.

97 MATHEMATICS AND COMPUTING↗