Search NASA⌕ Search

SEARCH · Search NASA

Results for “operator exponential”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14

Almost strong zero modes at finite temperature

Interacting fermionic chains exhibit extended regions of topological degeneracy of their ground states as a result of the presence of Majorana or parafermionic zero modes localized at the edges. In the opposite limit of infinite temperature, the corresponding nonintegrable spin chains, obtained via generalized Jordan-Wigner mapping, are known to host so-called almost strong zero modes, which are long-lived with respect to any bulk excitations. Here we study the fairly unexplored territory that bridges these two extreme cases of zero and infinite temperature. We blend two established techniques for states, the Lanczos series expansion and a tensor network ansatz, uplifting them to the level of operator algebra. This allows us to efficiently simulate large system sizes for arbitrarily long timescales and to extract the temperature-dependent decay rates. We observe that for the Kitaev-Hubbard model, the decay rate of the edge mode depends exponentially on the inverse temperature 𝛽, and on an effective energy scale Δ eff that is greater than the thermodynamic gap of the system Δ.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Snowmelt runoff modeling in simulation and forecasting modes with the Martinec-Mango model

The Martinec-Rango snowmelt runoff model was applied to two watersheds in the Rio Grande basin, Colorado-the South Fork Rio Grande, a drainage encompassing 216 sq mi without reservoirs or diversions and the Rio Grande above Del Norte, a drainage encompassing 1,320 sq mi without major reservoirs. The model was successfully applied to both watersheds when run in a simulation mode for the period 1973-79. This period included both high and low runoff seasons. Central to the adaptation of the model to run in a forecast mode was the need to develop a technique to forecast the shape of the snow cover depletion curves between satellite data points. Four separate approaches were investigated-simple linear estimation, multiple regression, parabolic exponential, and type curve. Only the parabolic exponential and type curve methods were run on the South Fork and Rio Grande watersheds for the 1980 runoff season using satellite snow cover updates when available. Although reasonable forecasts were obtained in certain situations, neither method seemed ready for truly operational forecasts, possibly due to a large amount of estimated climatic data for one or two primary base stations during the 1980 season.

Shafer, B.↗

Brief Communication: Mapping Greenland’s Perennial Firn Aquifers Using Enhanced-Resolution L-Band Brightness Temperature Image Time Series

Enhanced-resolution L-band brightness temperature (TB) image time series generated from observations collected over the Greenland Ice Sheet by NASA’s Soil Moisture Active Passive (SMAP) satellite are used to map Greenland’s perennial firn aquifers from space. Exponentially decreasing L-band T(sub B) signatures are correlated with perennial firn aquifer areas identified via the Center for Remote Sensing of Ice Sheets (CReSIS) Multi-Channel Coherent Radar Depth Sounder (MCoRDS) that was flown by NASA’s Operation IceBridge (OIB) campaign. An empirical algorithm to map extent is developed by fitting these signatures to a set of sigmoidal curves. During the spring of 2016, perennial firn aquifer areas are found to extend over ~ 66 000 km(exp 2).

Julie Z Miller↗

Data-Informed Evaluation Framework for Integrated Energy Systems: Insights from Power, Process Heat, and Hydrogen Production Applications

The multi-criteria decision analysis (MCDA) framework provides a systematic evaluation of the diverse preferences and performance metrics associated with alternative solutions. This approach is advantageous over a single-criterion methodology, which are only valid under conditions that assume ceteris paribus or an "apples-to-apples" comparison. However, selecting suitable technologies for integrated energy systems (IES) can be likened to an "apples-to-oranges" comparison, given the heterogeneous factors at stake. These factors include economics and performance parameters, geological compatibility, and environmental impacts. Consequently, past research has often employed a mixture of qualitative and quantitative criteria tailored to the specific interests of each study. While the method proves effective in handling the intricate interplay of criteria, the resulting rankings and scores can vary from study to study. This inconsistency is introduced from the use of subjectively defined thresholds and weights. As a result, decision-makers frequently find it challenging to establish clear connections between specific criteria and the resulting scores, as the transformation of criteria into ordinal scores results in a substantial loss of information. To address this challenge, we introduce a data-informed IES evaluation framework that offers comprehensive, interpretable, and traceable evaluations backed by quantifiable rationale. First, we identified key IES evaluation criteria from a decade of literature, focusing on relevant IES applications in power, process heat, and hydrogen production. We leveraged state-of-the-art cost estimates from the Idaho National Laboratory (INL) and technical data from 78 reactor designs from the International Atomic Energy Agency (IAEA) and the Organization for Economic Co-operation and Development - Nuclear Energy Agency (OECD-NEA). Lastly, we established thresholds by analyzing the mean, variance, root mean square, and slope of values across alternatives, categorizing the preferences of decision-makers into distinct utility functions, such as linear, saturating, exponential, and stepwise. Our approach yielded two main outcomes: (1) it provided consistent assessments across different stakeholder groups and (2) it visualized uncertainties in the decision-making context via comprehensive sensitivity analysis. To demonstrate the impact of our framework, we conducted case studies on 6 reactor designs (AP1000, NuScale, BWRX-300, Xe-100, eVinci, iMSR) for the three applications. Our data-driven framework proved to be highly effective in addressing heterogenous uncertainties faced by varied decision-makers? preferences and IES applications, as well as cost and technical estimates of advanced reactors.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Performance of a near-optimum receiver for optical antipodal signals

The well known photon-counting, heterodyning and homodyning optical receivers (operating over a free-space channel) do not achieve the performance of the optimum quantum receiver, which attains significantly lower error-probabilities than the above receiver structures. A demonstration and analysis are given of a binary antipodal optical receiver that exponentially approaches the performance of the optimum quantum receiver. A general mathematical model is developed, and subsequently used to evaluate the effects of external interference and internal error-sources on receiver performance.

Vilnrotter, V. A.↗

Data-Informed Evaluation Framework for Integrated Energy Systems: Insights from Power, Process Heat, and Hydrogen Production Applications

The multi-criteria decision analysis (MCDA) framework provides a systematic evaluation of the diverse preferences and performance metrics associated with alternative solutions. This approach is advantageous over a single-criterion methodology, which are only valid under conditions that assume ceteris paribus or an "apples-to-apples" comparison. However, selecting suitable technologies for integrated energy systems (IES) can be likened to an "apples-to-oranges" comparison, given the heterogeneous factors at stake. These factors include economics and performance parameters, geological compatibility, and environmental impacts. Consequently, past research has often employed a mixture of qualitative and quantitative criteria tailored to the specific interests of each study. While the method proves effective in handling the intricate interplay of criteria, the resulting rankings and scores can vary from study to study. This inconsistency is introduced from the use of subjectively defined thresholds and weights. As a result, decision-makers frequently find it challenging to establish clear connections between specific criteria and the resulting scores, as the transformation of criteria into ordinal scores results in a substantial loss of information. To address this challenge, we introduce a data-informed IES evaluation framework that offers comprehensive, interpretable, and traceable evaluations backed by quantifiable rationale. First, we identified key IES evaluation criteria from a decade of literature, focusing on relevant IES applications in power, process heat, and hydrogen production. We leveraged state-of-the-art cost estimates from the Idaho National Laboratory (INL) and technical data from 78 reactor designs from the International Atomic Energy Agency (IAEA) and the Organization for Economic Co-operation and Development - Nuclear Energy Agency (OECD-NEA). Lastly, we established thresholds by analyzing the mean, variance, root mean square, and slope of values across alternatives, categorizing the preferences of decision-makers into distinct utility functions, such as linear, saturating, exponential, and stepwise. Our approach yielded two main outcomes: (1) it provided consistent assessments across different stakeholder groups and (2) it visualized uncertainties in the decision-making context via comprehensive sensitivity analysis. To demonstrate the impact of our framework, we conducted case studies on 6 reactor designs (AP1000, NuScale, BWRX-300, Xe-100, eVinci, iMSR) for the three applications. Our data-driven framework proved to be highly effective in addressing heterogenous uncertainties faced by varied decision-makers? preferences and IES applications, as well as cost and technical estimates of advanced reactors.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Systematically localizable operators for quantum simulations of quantum field theories

Correlations and measures of entanglement in ground-state wave functions of relativistic quantum field theories are spatially localized over length scales set by the mass of the field. We utilize this localization to design digital quantum circuits for preparing the ground states of lattice scalar quantum field theories. Controlled rotations that are exponentially localized in their position-space extent are found to provide exponentially convergent wave function fidelity. These angles scale with the correlation between sites and the classical two-point correlation function, as opposed to the more localized mutual information or the hyperlocalized (1×1)-site negativity. We anticipate that further investigations will uncover quantum circuit designs with controlled rotations dictated by the measures of entanglement. This work is expected to impact quantum simulations of systems of importance to nuclear physics, high-energy physics, and basic energy sciences research.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Simple and General Unitarity Conserving Numerical Real-Time Propagators of the Time-Dependent Schrödinger Equation Based on Magnus Expansion

Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. Here, we use this property and explicit integration of Lagrange interpolation formulas for the time-dependent Hamiltonian within each time interval and derive approximations that preserve unitarity for the differential time evolution operators of general time-dependent Hamiltonians. The resulting second-order approximation is the same as using the average of Hamiltonians for two end points of time. We identify three fourth-order approximations involving commutators of Hamiltonians at different times and also derive a sixth-order expression. A test of these approximations along with other available expressions for a two-state time-dependent Hamiltonian with sinusoidal time dependences provides information on the relative performance of these approximations and suggests that the derived expressions can serve as useful numerical tools for time evolution in time-resolved spectroscopy, quantum control, quantum sensing, real-time ab initio quantum dynamics, and open system quantum dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Block encoding of the three-dimensional heterogeneous Poisson equation with application to fracture flow

Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as state preparation, data loading, and efficient information extraction. In this work, we study the feasibility of applying QLS algorithms to solve discretized three-dimensional (3D) heterogeneous Poisson equations, with specific examples relating to groundwater flow through geologic fracture networks. We explicitly construct a block encoding for the 3D heterogeneous Poisson matrix by leveraging the sparse local structure of the discretized operator. While classical solvers benefit from preconditioning, we show that block encoding the system matrix and preconditioner separately does not improve the effective condition number that dominates the QLS run-time. This differs from classical approaches where the preconditioner and the system matrix can often be implemented independently. Nevertheless, due to the structure of the problem in three dimensions, the quantum algorithm achieves a run-time of 𝑂⁡(𝑁 2/3 polylog 𝑁 ⋅log (1/𝜖)), outperforming the best classical methods (with run times of 𝑂⁡(𝑁⁢log 𝑁 ⋅log (1/𝜖))) and offering exponential memory savings. These results highlight both the promise and limitations of QLS algorithms for practical scientific computing, and point to effective condition-number reduction as a key barrier in achieving quantum advantages.

58 GEOSCIENCES↗

The scalar chemical potential in cosmological collider physics

Non-analyticity in co-moving momenta within the non-Gaussian bispectrum is a distinctive sign of on-shell particle production during inflation, presenting a unique opportunity for the “direct detection” of particles with masses as large as the inflationary Hubble scale ( H ). However, the strength of such non-analyticity ordinarily drops exponentially by a Boltzmann-like factor as masses exceed H . In this paper, we study an exception provided by a dimension-5 derivative coupling of the inflaton to heavy-particle currents, applying it specifically to the case of two real scalars. The operator has a “chemical potential” form, which harnesses the large kinetic energy scale of the inflaton, \( {\overset{\cdot }{\phi}}_0^{1/2}\approx 60H \) , to act as an efficient source of scalar particle production. Derivative couplings of inflaton ensure radiative stability of the slow-roll potential, which in turn maintains (approximate) scale-invariance of the inflationary correlations. We show that a signal not suffering Boltzmann suppression can be obtained in the bispectrum with strength f NL ~ \( \mathcal{O} \) (0 . 01–10) for an extended range of scalar masses \( \lesssim {\overset{\cdot }{\phi}}_0^{1/2} \) , potentially as high as 10 15 GeV, within the sensitivity of upcoming LSS and more futuristic 21-cm experiments. The mechanism does not invoke any particular fine-tuning of parameters or breakdown of perturbation-theoretic control. The leading contribution appears at tree-level , which makes the calculation analytically tractable and removes the loop-suppression as compared to earlier chemical potential studies of non-zero spins. The steady particle production allows us to infer the effective mass of the heavy particles and the chemical potential from the variation in bispectrum oscillations as a function of co-moving momenta. Our analysis sets the stage for generalization to heavy bosons with non-zero spin.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Crowded electrolytes containing redoxmers in different states of charge: Solution structure, properties, and fundamental limits on energy density

Nonaqueous redox flow batteries use liquid electrolytes containing redox-active organic molecules (redoxmers) as their energy storage medium. To maximize energy density, the redoxmer concentration needs to be maximized while maintaining low viscosity and high ionic conductivity. During charge, a redoxmer molecule pairs with an ion in the electrolyte while another ion migrates across the membrane to maintain electric neutrality. In a crowded electrolyte, this reconstitution changes physical and chemical properties of the solution. To explore these behaviors, a phenothiazine redoxmer fully miscible with acetonitrile was used, and electrochemical charge was mimicked by chemical oxidation. The solutions were examined using small-angle X-ray scattering, nuclear magnetic resonance, and conductometry and modeled using classical molecular dynamics. Overall, our study indicates that physical and structural properties of redoxmer solutions in both states of charge make it exceedingly difficult to increase the redoxmer concentrations over 2 M at any temperature without compromising dynamic properties of such solutions. The cause for this limitation is proximity to a gel-like regime in which fluidity, diffusivity, and ionic conductivity exponentially decrease with increasing concentration. This tendency is compounded by non-Arrhenius behavior of the electrolyte: a small increase in the concentration outruns gains in fluidity and conductivity at a higher temperature. Thus the properties of crowded electrolytes generally make it impossible to operate when gel-like behavior sets in. Pushing the redoxmer concentration to 2.5-3 M might be possible for small redoxmer molecules, but it would require the use of ionic liquid electrolytes at 340-360 K. (C) 2021 Elsevier B.V. All rights reserved.

25 ENERGY STORAGE↗

Hydrogen evolution in nickel-water heat pipes.

A study was made of the evolution of hydrogen gas in nickel-water heat pipes for the purpose of investigating methods of accelerated life testing. The data were analyzed in terms of a phenomenological corrosion model of heat pipe degradation which incorporates corrosion and oxidation theory and contains parameters which can be determined by experiment. The gas was evolved with a linear time dependence and an exponential temperature dependence with an activation energy of 1.03 x 10 to the minus 19th joules. A flow-rate dependence of the gas evolution was found in the form of a threshold. The results were used to predict usable lifetimes of heat pipes operated at normal operating conditions from results taken under accelerated operating conditions.

Anderson, W. T.↗

The Ground Flash Fraction Retrieval Algorithm Employing Differential Evolution: Simulations and Applications

The ability to estimate the fraction of ground flashes in a set of flashes observed by a satellite lightning imager, such as the future GOES-R Geostationary Lightning Mapper (GLM), would likely improve operational and scientific applications (e.g., severe weather warnings, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method, called the Ground Flash Fraction Retrieval Algorithm (GoFFRA), was recently developed for estimating the ground flash fraction. The method uses a constrained mixed exponential distribution model to describe a particular lightning optical measurement called the Maximum Group Area (MGA). To obtain the optimum model parameters (one of which is the desired ground flash fraction), a scalar function must be minimized. This minimization is difficult because of two problems: (1) Label Switching (LS), and (2) Parameter Identity Theft (PIT). The LS problem is well known in the literature on mixed exponential distributions, and the PIT problem was discovered in this study. Each problem occurs when one allows the numerical minimizer to freely roam through the parameter search space; this allows certain solution parameters to interchange roles which leads to fundamental ambiguities, and solution error. A major accomplishment of this study is that we have employed a state-of-the-art genetic-based global optimization algorithm called Differential Evolution (DE) that constrains the parameter search in such a way as to remove both the LS and PIT problems. To test the performance of the GoFFRA when DE is employed, we applied it to analyze simulated MGA datasets that we generated from known mixed exponential distributions. Moreover, we evaluated the GoFFRA/DE method by applying it to analyze actual MGAs derived from low-Earth orbiting lightning imaging sensor data; the actual MGA data were classified as either ground or cloud flash MGAs using National Lightning Detection Network[TM] (NLDN) data. Solution error plots are provided for both the simulations and actual data analyses.

Koshak, William↗

The International Space Station (ISS) Port 1 (P1) External Active Thermal Control System (EATCS) Ammonia Leak

Ammonia is used in the Starboard 1 (S1) and Port 1 (P1) External Active Thermal Control System (EATCS) to cool the pressurized modules, and some of the external electrical power distribution hardware. Leaks that develop in these critical cooling systems that deplete in-line tanks can ultimately result in loss of cooling, which can have devastating impacts to the mission, science and crew onboard the ISS. A slow ammonia leak was initially observed from the P1 EATCS in 2011, but later in 2013 the leak rate began to accelerate. The ammonia inventory eventually began to decay exponentially, raising concerns that the inventory could drop to levels where the system would not be operational.The Robotic External Leak Locator (RELL) was built and launched to the ISS to detect and help locate ammonia leaks using the ISS Robotic Arm and remote ground operator control without constant crew involvement. RELL pinpointed the ammonia leak to the two flexible jumper hose assemblies connecting one of two fluid loops in one of the three deployable radiators to the P1 EATCS. The ammonia inside the two hose assemblies and that radiator fluid loop was isolated and vented to space in 2017. This stopped the leak and an Extravehicular Activity was conducted to remove the two hose assemblies so they could be returned to ground for further Test, Teardown and Evaluation (TT&E). The purpose of this presentation is to discuss this leakage scenario and the TT&E efforts.

Cowan, Darnell T.↗

Recycled dark matter

Here, we outline a new production mechanism for dark matter that we dub “recycling”: dark sector particles are kinematically trapped in the false vacuum during a dark phase transition; the false pockets collapse into primordial black holes (PBHs), which ultimately evaporate before Big Bang Nucleosynthesis (BBN) to reproduce the dark sector particles. The requirement that all PBHs evaporate prior to BBN necessitates high scale phase transitions and hence high scale masses for the dark sector particles in the true vacuum. Our mechanism is therefore particularly suited for the production of ultra heavy dark matter (UHDM) with masses above ~10 12 GeV. The correct relic density of UHDM is obtained because of the exponential suppression of the false pocket number density. Recycled UHDM has several novel features: the dark sector today consists of multiple decoupled species that were once in thermal equilibrium and the PBH formation stage has extended mass functions whose shape can be controlled by IR operators coupling the dark and visible sectors.

79 ASTRONOMY AND ASTROPHYSICS↗

Quantum Markov chain Monte Carlo with digital dissipative dynamics on quantum computers

Modeling the dynamics of a quantum system connected to the environment is critical for advancing our understanding of complex quantum processes, as most quantum processes in nature are affected by an environment. Modeling a macroscopic environment on a quantum simulator may be achieved by coupling independent ancilla qubits that facilitate energy exchange in an appropriate manner with the system and mimic an environment. This approach requires a large, and possibly exponential number of ancillary degrees of freedom which is impractical. In contrast, we develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. By combining periodic modulation of the ancilla energies, or spectral combing, with periodic reset operations, we are able to mimic interaction with a large environment and generate thermal states of interacting many-body systems. We evaluate the algorithm by simulating preparation of thermal states of the transverse Ising model. Our algorithm can also be viewed as a quantum Markov chain Monte Carlo process that allows sampling of the Gibbs distribution of a multivariate model. To illustrate this we evaluate the accuracy of sampling Gibbs distributions of simple probabilistic graphical models using the algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

AdS/CFT unitarity at higher loops: high-energy string scattering

What is the space of weakly-coupled, gravitational theories which contain massive, higher-spin particles? This class of theories is highly constrained and it is conjectured their ultraviolet completion must be string theory. We provide more evidence for this conjecture by studying the Regge limit in large N, 4d CFTs with single-trace operators of unbounded spin. We show that in the Regge limit, these theories have bulk scattering amplitudes which are consistent with the string theory prediction to all orders in 1/N for large, but finite, coupling. In the language of Regge theory, we show Pomeron exchange naturally exponentiates in the 1/N expansion. To do this, we solve the bootstrap equations at tree-level and then use the Lorentzian inversion formula to find the one-loop correlator in the Regge limit. This is a unitarity method for AdS/CFT which can be repeated iteratively to make all orders statements. We also explain under what conditions the tree-level result exponentiates in the 1/N expansion at arbitrary coupling. Finally, we comment on further inelastic effects and show they give subleading contributions at large coupling. As a consistency check, we recover results from bulk Einstein gravity in the limit where all higher-spin particles decouple.

1/N Expansion↗

Simulating nonlinear optical processes on a superconducting quantum device

Simulating plasma physics on quantum computers is difficult because most problems of interest are nonlinear, but quantum computers are not naturally suitable for nonlinear operations. In weakly nonlinear regimes, plasma problems can be modelled as wave–wave interactions. In this paper, we develop a quantization approach to convert nonlinear wave–wave interaction problems to Hamiltonian simulation problems. We demonstrate our approach using two qubits on a superconducting device. Unlike a photonic device, a superconducting device does not naturally have the desired interactions in its native Hamiltonian. Nevertheless, Hamiltonian simulations can still be performed by decomposing required unitary operations into native gates. To improve experimental results, we employ a range of error-mitigation techniques. Apart from readout error mitigation, we use randomized compilation to transform undiagnosed coherent errors into well-behaved stochastic Pauli channels. Moreover, to compensate for stochastic noise, we rescale exponentially decaying probability amplitudes using rates measured from cycle benchmarking. We carefully consider how different choices of product-formula algorithms affect the overall error and show how a trade-off can be made to best utilize limited quantum resources. This study provides an example of how plasma problems may be solved on near-term quantum computing platforms.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗