Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Exponential distribution”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Measurement and Analysis of the Microphysical Properties of Arctic Precipitation Showing Frequent Occurrence of Riming

Detailed ground-based observations of snow are scarce in remote regions, such as the Arctic. Here, Multi-Angle Snowflake Camera measurements of over 55,000 solid hydrometeors—obtained during a two-year period from August 2016 to August 2018 at Oliktok Point, Alaska—are analyzed and compared to similar measurements from an earlier experiment at Alta, Utah. In general, distributions of hydrometeor fall speed, fall orientation, aspect ratio, flatness, and complexity (i.e., riming degree) were observed to be very similar between the two locations, except that Arctic hydrometeors tended to be smaller. In total, the slope parameter defining a negative exponential of the size distribution was approximately 50% steeper in the Arctic as at Alta. Sixty-six percent of particles were observed to be rimed or moderately rimed with some suggestion that riming is favored by weak boundary layer stability. On average, the fall speed of rimed particles was not notably different from aggregates. However, graupel density and fall speed increase as cloud temperatures approach the melting point.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Near-Optimal Distributed Linear-Quadratic Regulator for Networked Systems

This paper studies the trade-off between the degree of decentralization and the performance of a distributed controller in a linear-quadratic control setting. We study a system of interconnected agents over a graph and a distributed controller, called k-distributed control, which lets the agents make control decisions based on the state information within distance k on the underlying graph. This controller can tune its degree of decentralization using the parameter k and thus allows a characterization of the relationship between decentralization and performance. We show that under mild assumptions, including stabilizability, detectability, and a subexponentially growing graph condition, the performance difference between k-distributed control and centralized optimal control becomes exponentially small in k. Finally, this result reveals that distributed control can achieve near-optimal performance with a moderate degree of decentralization, and thus it is an effective controller architecture for large-scale networked systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Low-overhead transversal fault tolerance for universal quantum computation

Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, we can achieve low logical error rates. However, for many practical quantum error correction codes such as the surface code, owing to syndrome measurement errors, standard constructions require multiple extraction rounds—of the order of the code distance d—for fault-tolerant computation, particularly considering fault-tolerant state preparation. Here we show that logical operations can be performed fault-tolerantly with only a constant number of extraction rounds for a broad class of quantum error correction codes, including the surface code with magic state inputs and feedforward, to achieve ‘transversal algorithmic fault tolerance’. Through the combination of transversal operations7 and new strategies for correlated decoding, despite only having access to partial syndrome information, we prove that the deviation from the ideal logical measurement distribution can be made exponentially small in the distance, even if the instantaneous quantum state cannot be made close to a logical codeword because of measurement errors. We supplement this proof with circuit-level simulations in a range of relevant settings, demonstrating the fault tolerance and competitive performance of our approach. Furthermore, our work sheds new light on the theory of quantum fault tolerance and has the potential to reduce the space–time cost of practical fault-tolerant quantum computation by over an order of magnitude.

Zhou, Hengyun [QuEra Computing, Boston, MA (United↗
DOE OSTI2021

Perspective on Tsallis statistics for nuclear and particle physics

This is a concise introduction to the topic of nonextensive Tsallis statistics meant especially for those interested in its relation to high-energy proton–proton, proton–nucleus and nucleus–nucleus collisions. The three types of Tsallis statistics are reviewed. Only one of them is consistent with the fundamental hypothesis of equilibrium statistical mechanics. The single-particle distributions associated with it, namely Boltzmann, Fermi–Dirac and Bose–Einstein, are derived. These are not equilibrium solutions to the conventional Boltzmann transport equation which must be modified in a rather nonintuitive manner for them to be so. Nevertheless, the Boltzmann limit of the Tsallis distribution is extremely efficient in representing a wide variety of single-particle distributions in high-energy proton–proton, proton–nucleus and nucleus–nucleus collisions with only three parameters, one of them being the so-called nonextensitivity parameter [Formula: see text]. This distribution interpolates between an exponential at low transverse energy, reflecting thermal equilibrium, to a power law at high transverse energy, reflecting the asymptotic freedom of Quantum Chromodynamics (QCD). It should not be viewed as a fundamental new parameter representing nonextensive behavior in these collisions.

Physics↗
DOE OSTI2020

A software package for modeling and simulating fault graphs

This report describes a novel fault graph modeling language and a simulation tool for executing models specified in the language. The modeling language has three primary features that distinguish it from similar reliability analysis tools. These are (1) a random variable modeling several distinct outcomes of a single fault; (2) chains of faults in which one fault triggers another; and (3) time to fail sampled from probability distributions including positive normal, exponential, Weibull with a minimum, or immediate. These features are motivated by their use in a historical analysis of centrifuge reliability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fault Graph (fg)

This software package offers a novel fault graph modeling language and a simulation tool for executing models specified in the language. The modeling language has three primary features that distinguish it from similar reliability analysis tools. These are (1) a random variable modeling several distinct outcomes of a single fault; (2) chains of faults in which one fault triggers another; and (3) time to fail sampled from probability distributions including positive normal, exponential, Weibull with a minimum, or immediate.

Nutaro, James↗
DOE OSTI2025

Pair momentum dependence of a tilted source in heavy-ion collisions

In noncentral heavy-ion collisions, the particle-emitting source can be tilted away from the beam direction, an effect that becomes particularly significant at collision energies of a few GeV and lower. This phenomenon, manifest itself in many observables such as directed flow, polarization, and vorticity, is therefore important to investigate. Here, in this paper, we study the consistency between the tilt extracted directly from the freeze-out distribution of pions and the tilt parameter obtained using the azimuthally sensitive femtoscopy (asHBT) method. Using the Ultrarelativistic Quantum Molecular Dynamics model, we demonstrate a strong dependence of the tilt parameter extracted with asHBT on the momentum of the particle pair. Considering the experimental challenges in accessing low particle momenta—where the tilt parameter extracted with asHBT closely matches the tilt of the freeze-out distribution of pions—we propose an exponential extrapolation method to obtain the tilt of the entire freeze-out distribution. This approach aims to enhance the accuracy of experimental measurements of tilt in noncentral heavy-ion collisions.

particle correlations & fluctuations↗
DOE OSTI2023

Approximate Boltzmann distributions in quantum approximate optimization

Approaches to compute or estimate the output probability distributions from the quantum approximate optimization algorithm (QAOA) are needed to assess the likelihood it will obtain a quantum computational advantage. We analyze output from QAOA circuits solving 7200 random MaxCut instances, with $n$ = 14–23 qubits and depth parameter $p$ ≤ 12 and find that the average basis state probabilities follow approximate Boltzmann distributions: The average probabilities scale exponentially with their energy (cut value), with a peak at the optimal solution. Furthermore, we describe the rate of exponential scaling or effective temperature in terms of a series with a leading-order term $T$ ~ $C$ min /$n$ $\sqrt{p}$, with $C$ min the optimal solution energy. Using this scaling, we generate approximate output distributions with up to 38 qubits and find these give accurate accounts of important performance metrics in cases we can simulate exactly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Quantum Information Science in High Energy Physics at the Large Hadron Collider (Final Report-QuantISED)

We pursue scientific research at the interface of High Energy Physics and Quantum Information Science. This includes studies of thermal radiation and quantum entanglement in high-energy collisions at the Large Hadron Collider (LHC), with special emphasis on entanglement entropy and the Higgs boson. This project has also been extended to include quantum entanglement and charged current weak interactions using Fermilab results. And most recently, we have begun tests of the temporal entanglement using LHC data. Collider experiments such as proton-proton collisions at the LHC yield hadrons that exhibit an exponential behavior at low transverse momenta. This surprising behavior is seen in data from both the ATLAS and CMS collaborations. We attribute this phenomenon to quantum entanglement between the regions in the nucleon wave function. The exponential component to the transverse momentum distribution is a result of thermal radiation that is akin to Hawking or Unruh radiation that should exist at the event horizon of astrophysical black holes and neutron stars. The Principal Investigator, in collaboration with a theoretical physicist at Stony Brook University and Brookhaven National Laboratory, and with Yale University students, has shown evidence for this thermal radiation in several production and decay processes in the ATLAS and CMS data, and its connection to entanglement entropy (O.K. Baker and D.E Kharzeev, Phys. Rev. D 98, 054007 (2018)), including even the Higgs boson sector. Interestingly, this thermal behavior is also seen in momentum distributions of charged current weak interactions according to our studies. These findings suggest a deep connection between quantum entanglement (entanglement entropy) and thermalization in both hadron collisions at the energy frontier and neutrino scattering at the intensity frontier. We have confirmed the proposed relation between the effective temperature and the hard-scattering scale at lower energies using the most recent LHC data for the following systems: Higgs bosons, top quarks, and charged hadrons. Additionally, we have results for hadron production in neutrino scattering from nuclei using Fermilab weak interaction data. This study is carried out using data from the MINERvA collaboration. In those cases where entanglement is expected, there is an exponential component to the momentum distribution, while this component is absent in those processes where no entanglement is expected. This research thus tests the hypothesis about a link between quantum entanglement and thermalization in strong and weak interactions. See Phys Lett B 811, 135948 (2020). We also initiated research applying a quantum search algorithm (Grover's Algorithm) to LHC data. This quantum algorithm was used to show how rare events in LHC data can be searched for in large, unsorted databases, with quadratic speedup compared to classical search algorithms on classical computers. See "Application of a Quantum Search Algorithm to High- Energy Physics Data at the Large Hadron Collider", arXiv:2010.00649 [quant-ph].

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Efficient verification of anticoncentrated quantum states

I present a method for estimating the fidelity F(μ, τ) between a preparable quantum state μ and a classically specified pure target state τ=|τ> <τ|, using simple quantum circuits and on-the-fly classical calculation (or lookup) of selected amplitudes of |τ>. The method is sample efficient for anticoncentrated states (including many states that are hard to simulate classically), with approximate cost 4ϵ –2 (1 – F)dpcoll where ϵ is the desired precision of the estimate, d is the dimension of the Hilbert space, and pcoll is the collision probability of the target distribution. Furthermore, this scaling is exponentially better than that of any method based on classical sampling. I also present a more sophisticated version of the method that uses any efficiently preparable and well-characterized quantum state as an importance sampler to further reduce the number of copies of μ needed. Though some challenges remain, this work takes a significant step toward scalable verification of complex states produced by quantum processors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Firewalls at exponentially late times

We consider a version of the typical state firewall setup recently reintroduced by Stanford and Yang, who found that wormholes may create firewalls. We examine a late-time scaling limit in JT gravity in which one can resum the expansion in the number of wormholes, and we use this to study the exact distribution of interior slices at times exponential in the entropy. We consider a thermofield double with and without early perturbations on a boundary. These perturbations can appear on interior slices as dangerous high energy shockwaves. For exponentially late times, wormholes tend to teleport the particles created by perturbations and render the interior more dangerous. In states with many perturbations separated by large times, the probability of a safe interior is exponentially small, even though these would be safe without wormholes. With perturbation, even in the safest state we conceive, the odds of encountering a shock are fifty-fifty. One interpretation of the phenomenon is that wormholes can change time-ordered contours into effective out-of-time-ordered folds, making shockwaves appear in unexpected places.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Microhardness Distribution of Long Magnesium Block Processed through Powder Metallurgy

Powder metallurgy is a popular method of making raw powders into specific shaped samples. However, the pressure distribution and the microhardness difference within the sample are nonnegligible and unclear when the sample is long or exceeds a specific size. In this study, the long magnesium blocks, with a ratio of about 2.8 between the sample height and the sample side length, are successfully synthesized under three uniaxial and two biaxial conditions. Then, the sample hardness values on the outer surface and the center plane are tested to study the microhardness distribution. The modified analytical expression indicates that the normal pressure exponentially decreases along the compression direction, which is consistent with the hardness distribution trend. Because higher pressure leads to a more compact arrangement of the powders, more metal bonds are formed after sintering. During the first pressing, the sidewall pressure makes the surface hardness higher. The secondary reverse compression mainly improves the bottom and core hardness due to the re-orientation and re-location of the powders. The obtained relationship between the applied pressure and the hardness distribution is instructive in predicting and improving the sample quality.

Wang, Jiaying↗
DOE OSTI2025

Scientific Data Management Beyond Traditional Computing Boundaries

Scientific data management is undergoing a fundamental transformation driven by the convergence of artificial intelligence (AI)/machine learning workflows, distributed computing and storage environments, and exponential data growth. Here, we analyze how these developments address current limitations while enabling new capabilities for cross-facility collaboration and AI-driven research.

Widener, Patrick [Oak Ridge National Laboratory (O↗
DOE OSTI2023

Maximum entropy distributions of dark matter in ΛCDM cosmology

Context. Small-scale challenges to ΛCDM cosmology require a deeper understanding of dark matter physics. Aims. This paper aims to develop the maximum entropy distributions for dark matter particle velocity (denoted by X ), speed (denoted by Z ), and energy (denoted by E ) that are especially relevant on small scales where system approaches full virialization. Methods. For systems involving long-range interactions, a spectrum of halos of different sizes is required to form to maximize system entropy. While the velocity in halos can be Gaussian, the velocity distribution throughout the entire system, involving all halos of different sizes, is non-Gaussian. With the virial theorem for mechanical equilibrium, we applied the maximum entropy principle to the statistical equilibrium of entire system, such that the maximum entropy distribution of velocity (the X distribution) could be analytically derived. The halo mass function was not required in this formulation, but it did indeed result from the maximum entropy. Results. The predicted X distribution involves a shape parameter α and a velocity scale, v 0 . The shape parameter α reflects the nature of force ( α → 0 for long-range force or α → ∞ for short-range force). Therefore, the distribution approaches Laplacian with α → 0 and Gaussian with α → ∞. For an intermediate value of α , the distribution naturally exhibits a Gaussian core for v ≪ v 0 and exponential wings for v ≫ v 0 , as confirmed by N -body simulations. From this distribution, the mean particle energy of all dark matter particles with a given speed, v , follows a parabolic scaling for low speeds (∝ v 2 for v ≪ v 0 in halo core region, i.e., “Newtonian”) and a linear scaling for high speeds (∝ v for v ≫ v 0 in halo outskirt, i.e., exhibiting “non-Newtonian” behavior due to long-range gravity). We compared our results against N -body simulations and found a good agreement.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Vectorization techniques for probability distribution functions using VecCore

Probability distribution functions (PDFs) are very used in modeling random processes and physics simulations. Improving the performance of algorithms that generate many random numbers under complex PDFs is often a very challenging task when methods as direct functions are not available. In this work we present general strategies on how to vectorize some PDFs using VecCore library. We show the results for the Exponential, Gaussian, discrete Poisson and Gamma probability distributions.

Chaparro Amaro, Oscar R.↗
DOE OSTI2025

Convex relaxation for Fokker–Planck equation

We propose an approach to directly estimate the moments or marginals for a high-dimensional equilibrium distribution in statistical mechanics by solving the high-dimensional Fokker–Planck equation in terms of low-order cluster moments or marginals. With this approach, we bypass the exponential complexity of estimating the full high-dimensional distribution and directly solve the simplified partial differential equations for low-order moments/marginals. Moreover, the proposed moment/marginal relaxation is fully convex and can be solved via off-the-shelf solvers. We further propose a time-dependent version of the convex programs to study non-equilibrium dynamics. In a specific setting, we show the proposed method can recover a mean-field-type equilibrium density. Numerical results are provided to demonstrate the performance of the proposed algorithm for high-dimensional systems.

Chen, Yian↗
DOE OSTI2024

Solving differential‐algebraic equations in power system dynamic analysis with quantum computing

Abstract Power system dynamics are generally modeled by high dimensional non‐linear differential‐algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing penetration of distributed energy resources, whereas their computation time becomes sensitive due to the increasing interconnection of the power grid with other energy systems. This paper demonstrates the use of quantum computing algorithms to solve DAEs for power system dynamic analysis. We leverage a symbolic programming framework to equivalently convert the power system's DAEs into ordinary differential equations (ODEs) using index reduction methods and then encode their data into qubits using amplitude encoding. The system non‐linearity is captured by Hamiltonian simulation with truncated Taylor expansion so that state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can solve the power system's DAEs accurately with a computational complexity polynomial in the logarithm of the system dimension. We also illustrate the use of recent advanced tools in scientific machine learning for implementing complex computing concepts, that is, Taylor expansion, DAEs/ODEs transformation, and quantum computing solver with abstract representation for power engineering applications.

computational complexity↗