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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Stability of entrainment of a continuum of coupled oscillators

Complex natural and engineered systems are ubiquitous, and their behavior is challenging to characterize and control. Here, we examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the absence of coupling, an appropriately designed input can result in each oscillator attaining the frequency of the driving signal, with a phase offset determined by its natural frequency. We also consider a special case of interacting oscillators in which the coupling tends to destabilize the phase configuration to which the driving signal would send the collection in the absence of coupling. In this setting, we derive stability results that characterize the trade-off between the effects of driving and coupling, and compare these results to the well-known Kuramoto model of a collection of free-running coupled oscillators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Practical rare event sampling for extreme mesoscale weather

Extreme mesoscale weather, including tropical cyclones, squall lines, and floods, can be enormously damaging and yet challenging to simulate; hence, there is a pressing need for more efficient simulation strategies. Here, we present a new rare event sampling algorithm called quantile diffusion Monte Carlo (quantile DMC). Quantile DMC is a simple-to-use algorithm that can sample extreme tail behavior for a wide class of processes. We demonstrate the advantages of quantile DMC compared to other sampling methods and discuss practical aspects of implementing quantile DMC. To test the feasibility of quantile DMC for extreme mesoscale weather, we sample extremely intense realizations of two historical tropical cyclones, 2010 Hurricane Earl and 2015 Hurricane Joaquin. Our results demonstrate quantile DMC’s potential to provide low-variance extreme weather statistics while highlighting the work that is necessary for quantile DMC to attain greater efficiency in future applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Dynamical commensuration effect in a two-dimensional Yukawa solid modulated by periodic substrates

Transverse depinning dynamics of a periodic-square-substrate modulated two-dimensional dusty plasma solid driven by a constant force in the longitudinal direction are investigated using Langevin dynamical simulations. When the commensuration ratio (the number ratio of particles to substrate potential wells) is increased, there is a nonmonotonic variation of the critical transverse depinning force, and the local maxima and minima of the critical transverse depinning force precisely correspond to the dynamical commensurate and incommensurate conditions, respectively. Here, the dynamical commensuration effect is also clearly visible in the stable one-dimensional channel particle trajectories and the highly ordered structure, while both the particle trajectories and the structure are more disordered under the incommensurate conditions. The nonmonotonic variation of the critical transverse depinning force is attributed to the stability of the lattice structure at specific commensuration ratios.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Mechanical systems with closed orbits on manifolds of revolution

We study natural mechanical systems describing the motion of a particle on a two-dimensional Riemannian manifold of revolution in the field of a central smooth potential. We obtain a classification of Riemannian manifolds of revolution and central potentials on them that have the strong Bertrand property: any nonsingular (that is, not contained in a meridian) orbit is closed. We also obtain a classification of manifolds of revolution and central potentials on them that have the 'stable' Bertrand property: every parallel is an 'almost stable' circular orbit, and any nonsingular bounded orbit is closed. Bibliography: 14 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Optimal deployment of resources for maximizing impact in spreading processes

Significance Spreading processes play an increasingly important role in marketing, opinion setting, and epidemic modeling. Most existing algorithms for optimal resource allocation in spreading processes are based on topological characteristics of the underlying network and aim to maximize impact at infinite time. Clearly, realistic and efficient real-time allocation policies should consider both network properties and details of the dynamics; additionally, control may be applied only to a restricted set of accessible nodes, and impact should be maximized in a limited time window. We introduce a probabilistic targeting framework that incorporates the dynamics and encompasses previously considered optimization formulations. It is based on a scalable dynamic message-passing approach that allows for the solution of large real-world network instances.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Minimum local distance density estimation

We present a local density estimator based on first-order statistics. To estimate the density at a point, $x$, the original sample is divided into subsets and the average minimum sample distance to $x$ over all such subsets is used to define the density estimate at $x$. The tuning parameter is thus the number of subsets instead of the typical bandwidth of kernel or histogram-based density estimators. The proposed method is similar to nearest-neighbor density estimators but it provides smoother estimates. We derive the asymptotic distribution of this minimum sample distance statistic to study globally optimal values for the number and size of the subsets. Simulations are used to illustrate and compare the convergence properties of the estimator. The results show that the method provides good estimates of a wide variety of densities without changes of the tuning parameter, and that it offers competitive convergence performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

The difference between “equivalent” and “not different”

Often, experimenters wish to establish that populations of units can be considered equivalent to each other, in order to leverage improved knowledge about one population for characterizing the new population, or to establish the comparability of items. Equivalence tests have existed for many years, but their use in industry seems to have been largely restricted to biomedical applications, such as for assessing the equivalence of two drugs or protocols. We present the fundamentals of equivalence tests, compare them to traditional two-sample and ANOVA tests that are better suited to establishing differences in populations, and propose the use of a graphical summary to compare p-values across different thresholds of practically important differences.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Rejoinder

First, I would like to thank the discussants for their thoughtful and insightful comments on this topic that I have such passion for. In addition, they raise a number of important areas for further discussion, and I would like to take the opportunity to highlight some of their key ideas.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Quality quandaries: Understanding aspects influencing different types of multiple response optimization

In this study, optimizing with several responses can benefit from an objective approach of eliminating non-contenders, understanding trade-offs between competing responses, and then identifying a final choice that matches optimization priorities. To offer insights that help guide thoughtful decisions, we explore and summarize different patterns of solution sets and their trade-offs for different types of optimization with responses that are to be maximized and/or to achieve a target.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Discussion of “Bayesian design of experiments for industrial and scientific applications via gaussian processes”

First, we would like to commend Dr. Woods on his thought-provoking paper and insightful presentation at the 4th Annual Stu Hunter conference. We think that the material presented highlights some important needs in the area of design of experiments for generalized linear models (GLMs). In addition, we agree with Dr. Woods that design of experiements of GLMs does implicitly require expert judgement about model parameters, and hence using a Bayesian approach to capture this knowledge is a natural strategy to summarize what is known with the opportunity to incorporate associated uncertainty about that information.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Quantifying similarity in reliability surfaces using the probability of agreement

When separate populations exhibit similar reliability as a function of multiple explanatory variables, combining them into a single population is tempting. This can simplify future predictions and reduce uncertainty associated with estimation. However, combining these populations may introduce bias if the underlying relationships are in fact different. The probability of agreement formally and intuitively quantifies the similarity of estimated reliability surfaces across a two-factor input space. An example from the reliability literature demonstrates the utility of the approach when deciding whether to combine two populations or to keep them as distinct. As a result, new graphical summaries provide strategies for visualizing the results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

The weighted priors approach for combining expert opinions in logistic regression experiments

When modeling the reliability of a system or component, it is not uncommon for more than one expert to provide very different prior estimates of the expected reliability as a function of an explanatory variable such as age or temperature. Our goal in this paper is to incorporate all information from the experts when choosing a design about which units to test. Bayesian design of experiments has been shown to be very successful for generalized linear models, including logistic regression models. We use this approach to develop methodology for the case where there are several potentially non-overlapping priors under consideration. While multiple priors have been used for analysis in the past, they have never been used in a design context. The Weighted Priors method performs well for a broad range of true underlying model parameter choices and is more robust when compared to other reasonable design choices. Finally, we illustrate the method through multiple scenarios and a motivating example. Additional figures for this article are available in the online supplementary information.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Choosing a reliability inspection plan for interval censored data

Reliability test plans are important for producing precise and accurate assessment of reliability characteristics. This paper explores different strategies for choosing between possible inspection plans for interval censored data given a fixed testing timeframe and budget. A new general cost structure is proposed for guiding precise quantification of total cost in inspection test plan. Multiple summaries of reliability are considered and compared as the criteria for choosing the best plans using an easily adapted method. Different cost structures and representative true underlying reliability curves demonstrate how to assess different strategies given the logistical constraints and nature of the problem. Results show several general patterns exist across a wide variety of scenarios. Given the fixed total cost, plans that inspect more units with less frequency based on equally spaced time points are favored due to the ease of implementation and consistent good performance across a large number of case study scenarios. Plans with inspection times chosen based on equally spaced probabilities offer improved reliability estimates for the shape of the distribution, mean lifetime, and failure time for a small fraction of population only for applications with high infant mortality rates. The paper uses a Monte Carlo simulation based approach in addition to the common evaluation based on the asymptotic variance and offers comparison and recommendation for different applications with different objectives. Additionally, the paper outlines a variety of different reliability metrics to use as criteria for optimization, presents a general method for evaluating different alternatives, as well as provides case study results for different common scenarios.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Rejoinder

We would like to thank all of the discussants for their thoughtful and insightful comments. We heartily agree with Willis Jensen’s remark that the collection of views from multiple different perspectives possible with a discussion paper has added greatly to the overall contribution. Roger Hoerl compactly and eloquently summarized our thoughts about the role of statisticians on teams: “to objectively lead a team of subject matter experts through the minefield of problem resolution.” We agree with Benjamin Slade that this leadership role can be achieved either through formally leading the team or by being an active, engaged member of the team with an eye on the overall goals of the team and impacting the structure of the decision-making process. Hoerl also highlights what solutions interdisciplinary teams should be seeking – namely those that are “the best business … or scientific solution[s], rather than the best statistical solutions.” If this is how we define the objective of the team’s problem-solving or decision-making efforts, then establishing ourselves as fully-included team members or even working towards leading the team efforts should become easier.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Where did the tumor start? An inverse solver with sparse localization for tumor growth models

In this work, we present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction–diffusion partial differential equation (PDE) for the tumor concentration. We use a PDE-constrained optimization formulation for the inverse problem. The unknown parameters are the reaction coefficient (proliferation), the diffusion coefficient (infiltration), and the initial condition field for the tumor PDE. Segmentation of magnetic resonance imaging (MRI) scans drive the inverse problem where segmented tumor regions serve as partial observations of the tumor concentration. Like most cases in clinical practice, we use data from a single time snapshot. Moreover, the precise time relative to the initiation of the tumor is unknown, which poses an additional difficulty for inversion. We perform a frozen-coefficient spectral analysis and show that the inverse problem is severely ill-posed. We introduce a biophysically motivated regularization on the structure and magnitude of the tumor initial condition. In particular, we assume that the tumor starts at a few locations (enforced with a sparsity constraint on the initial condition of the tumor) and that the initial condition magnitude in the maximum norm is equal to one. We solve the resulting optimization problem using an inexact quasi-Newton method combined with a compressive sampling algorithm for the sparsity constraint. Our implementation uses PETSc and AccFFT libraries. We conduct numerical experiments on synthetic and clinical images to highlight the improved performance of our solver over a previously existing solver that uses standard two-norm regularization for the calibration parameters. The existing solver is unable to localize the initial condition. Our new solver can localize the initial condition and recover infiltration and proliferation. In clinical datasets (for which the ground truth is unknown), our solver results in qualitatively different solutions compared to the two-norm regularized solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Kinetics of diffusion-controlled annihilation with sparse initial conditions

Here, we study diffusion-controlled single-species annihilation with sparse initial conditions. In this random process, particles undergo Brownian motion, and when two particles meet, both disappear. We also focus on sparse initial conditions where particles occupy a subspace of dimension δ that is embedded in a larger space of dimension d. Furthermore, we find that the co-dimension Δ = d - δ governs the behavior. All particles disappear when the co-dimension is sufficiently small, Δ ≤ 2; otherwise, a finite fraction of particles indefinitely survive. We establish the asymptotic behavior of the probability S(t) that a test particle survives until time t. When the subspace is a line, δ = 1, we find inverse logarithmic decay, $S\sim {(\mathrm{ln}t)}^{-1}$, in three dimensions, and a modified power-law decay, $S\sim (\mathrm{ln}t){t}^{-1/2}$, in two dimensions. In general, the survival probability decays algebraically when Δ < 2, and there is an inverse logarithmic decay at the critical co-dimension Δ = 2.

97 MATHEMATICS AND COMPUTING↗