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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 OSTI2014

The exit-time problem for a Markov jump process

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Additionally, such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. Finally, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Statistical Analysis of the First Passage Path Ensemble of Jump Processes

The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Nonlocal Convection-Diffusion Problems on Bounded Domains and Finite-Range Jump Processes

In this paper, a nonlocal convection-diffusion model is introduced for the master equation of Markov jump processes in bounded domains. With minimal assumptions on the model parameters, the nonlocal steady and unsteady state master equations are shown to be well-posed in a weak sense. Finally, then the nonlocal operator is shown to be the generator of finite-range nonsymmetric jump processes and, when certain conditions on the model parameters hold, the generators of finite and infinite activity Lévy and Lévy-type jump processes are shown to be special instances of the nonlocal operator.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1978

Optimal estimation for discrete time jump processes

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are derived. The approach used is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. Thus a general representation is obtained for optimum estimates, and recursive equations are derived for minimum mean-squared error (MMSE) estimates. In general, MMSE estimates are nonlinear functions of the observations. The problem is considered of estimating the rate of a DTJP when the rate is a random variable with a beta probability density function and the jump amplitudes are binomially distributed. It is shown that the MMSE estimates are linear. The class of beta density functions is rather rich and explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.

Vaca, M. V.↗
NASA NTRS1977

Optimal estimation for discrete time jump processes

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are obtained. The approach is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. A general representation for optimum estimates and recursive equations for minimum mean squared error (MMSE) estimates are obtained. MMSE estimates are nonlinear functions of the observations. The problem of estimating the rate of a DTJP when the rate is a random variable with a probability density function of the form cx super K (l-x) super m and show that the MMSE estimates are linear in this case. This class of density functions explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.

Vaca, M. V.↗
DOE OSTI2016

Stochastic Games for Continuous-Time Jump Processes Under Finite-Horizon Payoff Criterion

In this paper we study two-person nonzero-sum games for continuous-time jump processes with the randomized history-dependent strategies under the finite-horizon payoff criterion. The state space is countable, and the transition rates and payoff functions are allowed to be unbounded from above and from below. Under the suitable conditions, we introduce a new topology for the set of all randomized Markov multi-strategies and establish its compactness and metrizability. Then by constructing the approximating sequences of the transition rates and payoff functions, we show that the optimal value function for each player is a unique solution to the corresponding optimality equation and obtain the existence of a randomized Markov Nash equilibrium. Furthermore, we illustrate the applications of our main results with a controlled birth and death system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

A fast exact simulation method for a class of Markov jump processes

A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length τ. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze its properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantages of the HLM for large scale problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2019

Frequency comparisons via GPS carrier-phase: jump processing, temperature compensation and zero/short-baseline noise-floors

GPS carrier-phase receivers have been used to produce high quality time/frequency comparisons between clocks and frequency standards. Current ways of processing the carrier-phase data, however, result in phase jumps and data gaps that make the data difficult to use effectively and repeatedly for long datasets. In addition, temperature fluctuations generally perturb receiver output detrimentally. We describe the steps of a simple but effective automated algorithm for comparing frequencies that can compensate for data gaps, day boundary jumps, and other phase jumps as well as for temperature disturbances. We describe process features and focus on zero-baseline noise-floors, measuring Allan deviations of the Deep Space Atomic Clock mission’s receiver down to 1x10-17 at 5x105 seconds, with an upper confidence level of 3x10-17. The zero-baseline noise floors we present give confidence in our algorithm and temperature compensation’s robustness.

Diener, William A.↗
DOE OSTI2019

Comparison of anion and cation dynamics in a carbon-substituted closo-hydroborate salt: 1 H and 23 Na NMR studies of solid-solution Na 2 (CB 9 H 10 )(CB 11 H 12 )

The hexagonal mixed-anion solid solution Na 2 (CB 9 H 10 )(CB 11 H 12 ) shows the highest room-temperature ionic conductivity among all known Na-ion conductors. To study the dynamical properties of this compound, we have measured the 1 H and 23 Na nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation rates in Na 2 (CB 9 H 10 )(CB 11 H 12 ) over the temperature range of 80-435 K. It is found that the diffusive motion of Na+ ions can be described in terms of two jump processes: the fast localized motion within the pairs of tetrahedral interstitial sites of the hexagonal close-packed lattice formed by large anions and the slower jump process via octahedral sites leading to long-range diffusion. Below 350 K, the slower Na + jump process is characterized by the activation energy of 353(11) meV. Although Na + mobility in Na 2 (CB 9 H 10 )(CB 11 H 12 ) found from our NMR experiments is higher than in other ionic conductors, it appears to be an order-of-magnitude lower than that expected on the basis of the conductivity measurements. This result suggests that the complex diffusion mechanism and/or correlations between Na + jumps should be taken into account. The measured 1H spin-lattice relaxation rates for Na 2 (CB 9 H 10 )(CB 11 H 12 ) are consistent with a coexistence of at least two anion reorientational jump processes occurring at different frequency scales. Near room temperature, both reorientational processes are found to be faster than the Na + jump process responsible for the long-range diffusion.

25 ENERGY STORAGE↗
NASA NTRS2022

Simulating the Diffusion of Hydrogen in Amorphous Silicates: A ‘Jumping’ Migration Process and its Implications for Solar Wind Implanted Lunar Volatiles

We use molecular dynamics (MD) simulations to better explain the movement of atomic hydrogen in amorphous silica and quantify the planetary science implications of these findings. Previous MD simulations had a large range of predicted values and did not agree well with experiment. Our simulations sample atomic motion for a longer duration and consider a wider range of temperatures than previous simulations. In contrast to constant atomic motion, the hydrogen atoms were shown to undergo random intermittent jumps from one oxygen atom to another, the number of which increase with temperature. Predicted diffusion coefficients had a better agreement to experimental values than previous MD simulations, suggesting the importance of longer simulation durations for better statistics. The low activation energy and jumps observed at lunar temperatures do not support the theory of diurnal variations in OH content for an undamaged amorphous silica surface. Instead, we conclude that energetic solar wind impacts can induce two competing atomic hydrogen motion processes in the exposed surface: A prompt effect that induces jumps in the temperature spike volume, but also a long term effect of damage in the structure that traps atomic hydrogen. We then use SDTrimSP to quantify the damage created during exposure and MD to demonstrate the H retention and trapping near these defects. Damage was shown to be dependent on impact energy, with defects easily retaining implanted hydrogen. MD results like those presented herein on unweathered surfaces are therefore most relevant to magnetic anomalies. As a result, we demonstrate the importance of lunar volatile models to account for the damage state of the substrate when modelling hydrogen diffusion, retention, and subsequent OH/water production.

Liam S. Morrissey↗
DOE OSTI2023

Stochastic Price Generation for Evaluating Wholesale Electricity Market Bidding Strategies

This work presents a novel method for generating electricity price scenarios from statistical properties of past electricity prices using a hybrid statistical and reduced-form stochastic model. Previous work in applying stochastic differential equations (SDE) to model electricity prices has focused on daily average prices. To extend stochastic price generation methods to hourly or sub-hourly pricing, we address several weaknesses in the state-of-the-art: (1) we replace the mean-reversion component of the SDE with an ARIMA process that is better able to characterize the daily and weekly trends; (2) we extend the price-spike, or jump process to account for conditional probabilities of price spikes occurring in consecutive time steps by replacing the traditional Poisson process for modeling jumps with a generalized point process model inspired by brain neuron models; and (3) we replace the traditional method of estimating spike intensity with empirical variance with a Markov process based on observed price spike intensity transitions. The method is demonstrated with electricity prices from the US ERCOT market and a use-case example is provided for bidding an energy storage unit into the day-ahead and real-time energy markets of ERCOT using stochastic optimization methods. Results show that the the synthetic price model out performs a (naive) persistence forecast model by resulting in 24% to 47% more in profits over 168 simulated days.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS1981

Singular perturbation, state aggregation and nonlinear filtering

Consideration is given to a state process evolving in R(n), whose motion is that of a pure jump process in R(n) in the 0(1) time scale, upon which is superimposed a continuous motion along the orbits of a gradient-like vector field g in R(n) in the 0(1/epsilon) time scale. The infinitesimal generator of the state process is, in other words, of the form L + (1/epsilon)g. It follows from the main results presented that the projected filters converge to the finite state Wonham filter corresponding to the problem of estimating the finite state process in the presence of additive white noise.

Hijab, O.↗
NASA NTRS1971

A stochastic model for eye movements during fixation on a stationary target.

A stochastic model describing small eye movements occurring during steady fixation on a stationary target is presented. Based on eye movement data for steady gaze, the model has a hierarchical structure; the principal level represents the random motion of the image point within a local area of fixation, while the higher level mimics the jump processes involved in transitions from one local area to another. Target image motion within a local area is described by a Langevin-like stochastic differential equation taking into consideration the microsaccadic jumps pictured as being due to point processes and the high frequency muscle tremor, represented as a white noise. The transform of the probability density function for local area motion is obtained, leading to explicit expressions for their means and moments. Evaluation of these moments based on the model is comparable with experimental results.

Vasudevan, R.↗
NASA NTRS1992

Stochastic stability properties of jump linear systems

Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented.

Feng, Xiangbo↗