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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 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Energy exchange in systems of particles with nonreciprocal interaction

A model is proposed to describe the sources of additional kinetic energy and its redistribution in systems of particles with a nonreciprocal interaction. The proposed model is shown to explain the qualitative specific features of the dust particle dynamics in the sheath region of an RF discharge. Prominence is given to the systems of particles with a quasi-dipole–dipole interaction, which is similar to the interaction induced by the ion focusing effects that occur in experiments on a laboratory dusty plasma, and with the shadow interaction caused by thermophoretic forces and Le Sage’s forces.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Sensitivity of DUNE to long-baseline neutrino oscillation physics

DUNE is an international project, currently in its design phase, for neutrino physics and proton-decay searches. It will consist of two detectors exposed to a megawatt-scale muon neutrino beam that will be produced at Fermilab (Illinois, USA). One detector will record particle interactions near the source of the beam, while a second, much larger, detector comprising four 10-kilotonne liquid argon TPCs will be installed at a depth of 1.5~km at SURF (South Dakota, USA), about 1300 kilometres away of the neutrino source. Among the primary scientific goals of DUNE is the precision measurement of the parameters that govern neutrino mixing, including those still unknown: the octant in which the $\theta_{23}$ mixing angle lies, the neutrino mass ordering and the value of the CP violation phase. This paper discusses the sensitivity of the DUNE experiment to these parameters.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Characterization of the DUNE photodetectors and study of the event burst phenomenon

The Deep Underground Neutrino Experiment (DUNE) is an upcoming neutrino physics experiment that will answer some of the most compelling questions in particle physics and cosmology. The DUNE far detectors employ silicon photomultipliers (SiPMs) to detect light produced by charged particles interacting in a large liquid argon time projection chamber (LArTPC). The SiPMs are photosensors consisting of an array of single-photon avalanche diodes (SPAD) operating in Geiger mode. Their high sensitivity and dynamic range, as well as the possibility to fill large surfaces with high-granularity sensors, makes them an ideal choice for DUNE. An international consortium of research groups is currently engaged in a systematic comparison of the performances of the SiPM models that have been custom developed for DUNE by two manufacturers. Such detailed studies, which include gain measurements and a structure study of the dark count rate at 77 K, are meant to determine the best choice of the photodetection system for DUNE, as well as characterize the response of the chosen detectors for the DUNE simulation. Moreover, an investigation of a newly observed phenomenon, in which quick bursts of tens of events at close range are collected in individual SiPMs, is being carried out, which potentially impacts the design of future models and their implementation in particle physics experiments.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

aosflow3 (a1)

The aerosol observing system (AOS) is the primary platform for in situ aerosol measurements at Earth’s surface. Each AOS has a different complement of instruments, which are selected to ensure the best measurements at each deployment site. The AOS measures aerosol optical properties to better understand how particles interact with solar radiation and influence the Earth's radiation balance. These measurements are useful for calculating parameters used in radiative forcing calculations, such as the aerosol single scattering albedo, asymmetry parameter, mass scattering efficiency, and hygroscopic growth. Measurements made with the AOS form a long-term record at the ARM fixed sites. Shorter measurement records are available from mobile deployments in a wide variety of geographical regions. These measurements are valuable for: identifying long-term changes in aerosol properties identifying atmospheric processes controlling aerosol life cycle and their influence on clouds providing experimental data for developing and testing atmospheric climate models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Millicharged particles in liquid argon neutrino experiments

We investigate the potential of Liquid Argon (LAr) neutrino detectors to search for millicharged particles, a well-motivated extension of the standard model. Detectors located downstream of an intense proton beam that is striking a target may be exposed to a large flux of millicharged particles. Millicharged particles interact primarily through low momentum exchange producing electron recoil events near detector threshold. Recently, sub-MeV detection capabilities were demonstrated by the Fermilab ArgoNeuT detector, a small LAr detector which was exposed to the NuMI neutrino beam. Despite high background rates and its small size, we show that ArgoNeuT is capable of probing unexplored parameter space with its existing dataset. In particular, we show that the excellent spatial resolution in LAr detectors allows rejecting backgrounds by requiring two soft hits that are aligned with the upstream target. We further discuss the prospects of these types of searches in future larger LAr neutrino detectors such as the DUNE near detector.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS2023

Energetic Proton Acceleration By EMIC Waves in Io’s Footprint Tail

In this study, we present a survey of energetic proton observations associated with Io’s footprint tail (FPT) and compare their signatures with in situ measurements of the plasma waves and lower-energy electron environments. We find further supporting evidence that proton acceleration in Io’s FPT is likely a consequence of wave–particle interactions via electromagnetic ion cyclotron waves that are generated by precipitating electrons into Jupiter’s ionosphere. This idea was originally proposed by Clark et al. (2020) and Sulaiman et al. (2020) based on NASA’s Juno mission likely transiting Io’s Main Alfvén Wing (MAW) during its twelfth orbit (i.e., PJ12). Additionally, the analysis of > 50 keV protons presented here highlights important observational details about the Io–Jupiter interaction as follows: 1) proton acceleration in Io’s FPT is a persistent feature and the energy flux carried by the protons is highest at smaller Io-Alfvén tail distances; 2) energetic protons exhibit positive correlations with both plasma waves and <100 keV/Q electrons; 3) during a small number of Io FPT crossings, the protons display finer spatial/temporal structure reminiscent of the electron observations reported by Szalay et al. (2018); and 4) the proton pitch angle distributions are characterized by two types: conic distributions in or near Io’s MAW and isotropic elsewhere.

space physics↗
NASA NTRS2021

ARTEMIS Observations of Plasma Waves in Laminar and Perturbed Interplanetary Shocks

The ‘Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction with the Sun’ (ARTEMIS) mission provides a unique opportunity to study the structure of interplanetary shocks and the associated generation of plasma waves with frequencies between ~50-8000 Hz due to its long duration electric and magnetic field burst waveform captures. We compare wave properties and occurrence rates at 11 quasi-perpendicular interplanetary shocks with burst data within 10 minutes (~3200 proton gyroradii upstream, ~1900 downstream) of the shock ramp. A perturbed shock is defined as possessing a large amplitude whistler precursor in the quasi-static magnetic field with an amplitude greater than ⅓ the difference between the upstream and downstream average magnetic field magnitudes; laminar shocks lack these large precursors and have a smooth, step function-like transition. In addition to wave modes previously observed, including ion acoustic, whistler, and electrostatic solitary waves, waves in the ion acoustic frequency range that show rapid temporal frequency change are common. Three shocks had burst captures in the ramp; of these, the two laminar shocks with burst data in the ramp contained a wide range of large amplitude wave modes in the ramp whereas the one perturbed shock contained no such waves. Thus, energy dissipation through wave-particle interactions is more prominent in these two laminar shocks than in the perturbed shock. Based on observations from all 11 shocks, the The wave occurrence rates for laminar shocks are higher in the transition region, especially the ramp, than downstream. In contrast, perturbed shocks have approximately 2-3 times the wave occurrence rate downstream than laminar shocks.

L. A. Davis↗
DOE OSTI2017

IceCube can constrain the intrinsic charm of the proton [IC at IC: IceCube can constrain the intrinsic charm of the proton]

Here, the discovery of extraterrestrial neutrinos in the ~30 TeV–PeV energy range by IceCube provides new constraints on high energy astrophysics. An important background to the signal are the prompt neutrinos which originate from the decay of charm hadrons produced by high energy cosmic-ray particles interacting in the Earth’s atmosphere. It is conventional to use the calculations of charm hadroproduction using gluon splitting g → c¯c alone. However, QCD predicts an additional “intrinsic" component of the heavy quark distribution which arises from diagrams where heavy quarks are multiply connected to the proton’s valence quarks. We estimate the prompt neutrino spectrum due to intrinsic charm. We find that the atmospheric prompt neutrino flux from intrinsic charm is comparable to those calculated using QCD computations not including intrinsic charm, once we normalize the intrinsic charm differential cross sections to the ISR and the LEBC-MPS collaboration data. In the future, IceCube will constrain the intrinsic charm content of the proton and will contribute to one of the major questions in high energy physics phenomenology.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Phonon Sensor Dynamics for Cryogenic Dark Matter Search Experiment

Understanding the quasiparticle diffusion process inside sputtered aluminum (Al thin films (∼ 0.1-1 μm is critical for the Cryogenic Dark Matter Search (CDMS experiment to further optimize its detectors to directly search for dark matter. An initial study with Al films was undertaken by our group ∼ 20 years ago, but some important questions were not answered at the time. This thesis can be considered a continuation of that critical study. The CDMS experiment utilizes high purity silicon and germanium crystals to simultaneously measure ionization and phonons created by particle interactions. In addition to describing some of the rich physics involved in simultaneously detecting ionization and phonons with a CDMS detector, this thesis focuses on the detailed physics of the phonon sensors themselves, which are patterned onto CDMS detector surfaces. CDMS detectors use thin sputtered Al films to collect phonon energy when it propagates to the surfaces of the detector crystals. The phonon energy breaks Cooper pairs and creates quasiparticles (qps). These qps diffuse until they get trapped in an proximitized “overlap” region where lower-Tc tungsten films connect to the Al film. These tungsten films are the transition edge sensors (W-TESs CDMS uses to readout phonon signals. We performed a wide range of experiments using several sets of test devices designed and fabricated specifically for this work. The devices were used mostly to study quasiparticle (qp transport in Al films and qp transmission through Al/W interfaces. The results of this work are being used to optimize the design of detectors for SuperCDMS SNOLAB. This thesis is intended for CDMS collaborators who are interested in knowing more about the detailed fundamentals of how our phonon sensors work so they can take full advantage of their benefits. However, this work can also be read by general readers who are interested in particle detection using TES technology. This thesis contains eight chapters. The first chapter gives basic background information about dark matter and searches for it. We then describe the basic CDMS detector technology in Chapter two. Chapter three focuses on superconductivity and explains some of the solid state physic most relevant to our Al and W film studies. We then turn our attention to the fabrication processes used to make test devices, and describe some of the studies done to characterize our W and Al film properties. Chapter five explains the experimental setup including how a 3He/4He dilution refrigerator works, and how our electronics were configured. We then get to chapter six where we present key experimental results. Chapter seven covers the TES model we used for our test devices to simulate the data pulse shapes and reconstruct the pulse energies. We also describe the diffusion models used to fit our data. Finally, we end with a short summary of our findings and provide a few suggestions for future studies.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

Conformational sampling enhancement of replica exchange molecular dynamics simulations using swarm particle intelligence

In this paper, we present a new method based on swarm particle social intelligence for use in replica exchange molecular dynamics simulations. In this method, the replicas (representing the different system configurations) are allowed communicating with each other through the individual and social knowledge, in additional to considering them as a collection of real particles interacting through the Newtonian forces. The new method is based on the modification of the equations of motion in such way that the replicas are driven towards the global energy minimum. The method was tested for the Lennard-Jones clusters of N = 4, 5, and 6 atoms. Our results showed that the new method is more efficient than the conventional replica exchange method under the same practical conditions. In particular, the new method performed better on optimizing the distribution of the replicas among the thermostats with time and, in addition, ergodic convergence is observed to be faster. We also introduce a weighted histogram analysis method allowing analyzing the data from simulations by combining data from all of the replicas and rigorously removing the inserted bias.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Simulated X-Ray Radiographic Performance of a Bismuth-Loaded PVT Array

Recent material advancements in organic plastic scintillators enable marked increases in material detection efficiency, light yield, and pulse shape discrimination properties. These advances may resolve significant capability gaps for lowcost, portable, and durable dual-particle imaging (DPI) systems for nuclear safety, security, and safeguard purposes. One such material, a 21% bismuth-loaded polyvinyl toluene (BiPVT), is computationally evaluated as a small, pixelated radiographic array using Monte Carlo N-Particle (MCNP) and Zemax OpticStudio, and it is compared to identical evaluations of EJ-200 and EJ-256 arrays. MCNP software enables estimates of particle interaction and energy deposition, while OpticStudio computes optical light transport within each material. Here, computational estimates of spatial resolution and relative light collection at 370 kVp are found to agree with experimental results for both EJ-200 and EJ-256 arrays, thereby validating predictions of the same for the BiPVT array. As such, for equivalent exposures at 370 kVp, a BiPVT array may provide ~20× the light collection expected from EJ-200 and ~10× that expected from EJ-256. Similar comparisons of estimated light collection are also computed at 150 and 270 kVp, and these results suggest that BiPVT will provide significantly improved performance over EJ-200 and EJ-256 across all energies practical for portable X-ray radiography.

42 ENGINEERING↗
DOE OSTI2022

Direct observation of the dead-cone effect in quantum chromodynamics

In particle collider experiments, elementary particle interactions with large momentum transfer produce quarks and gluons (known as partons) whose evolution is governed by the strong force, as described by the theory of quantum chromodynamics (QCD). These partons subsequently emit further partons in a process that can be described as a parton shower, which culminates in the formation of detectable hadrons. Studying the pattern of the parton shower is one of the key experimental tools for testing QCD. This pattern is expected to depend on the mass of the initiating parton, through a phenomenon known as the dead-cone effect, which predicts a suppression of the gluon spectrum emitted by a heavy quark of mass m Q and energy E, within a cone of angular size m Q /E around the emitter. Previously, a direct observation of the dead-cone effect in QCD had not been possible, owing to the challenge of reconstructing the cascading quarks and gluons from the experimentally accessible hadrons. We report the direct observation of the QCD dead cone by using new iterative declustering techniques to reconstruct the parton shower of charm quarks. This result confirms a fundamental feature of QCD. Furthermore, the measurement of a dead-cone angle constitutes a direct experimental observation of the non-zero mass of the charm quark, which is a fundamental constant in the standard model of particle physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Physics of the Aurora: Laboratory Measurements of Electron Acceleration by Inertial Alfven Waves (Final Technical Report)

The physics of the aurora is one of the foremost unsolved problems of space physics. The mechanisms responsible for accelerating electrons that precipitate onto the ionosphere are not fully understood. For more than three decades, particle interactions with Alfven waves have been proposed as a possible means for accelerating electrons and generating auroras. Due to the limitations of spacecraft conjunction studies and other multi-spacecraft approaches, it is unlikely that it will ever be possible, through spacecraft observations alone, to confirm definitively the proposed electron acceleration mechanism by making simultaneous measurements of both the accelerated electrons and the inertial Alfven wave responsible for the acceleration. Here, we show laboratory measurements of the resonant transfer of energy from Alfven waves to electrons under conditions relevant to the auroral zone. Experiments are performed by launching Alfven waves and simultaneously recording the electron velocity distribution. Numerical simulations and analytical theory support that the measured energy transfer process produces accelerated electrons capable of reaching auroral energies. The experiments, theory, and simulations demonstrate a clear causal relationship between Alfven waves and accelerated electrons that directly cause auroras.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Enhancing the sensitivity of the LUX-ZEPLIN (LZ) dark matter experiment to low energy signals

Two-phase xenon detectors, such as that at the core of the forthcoming LZ dark matter experiment, use photomultiplier tubes to sense the primary (S1) and secondary (S2) scintillation signals resulting from particle interactions in their liquid xenon target. This paper describes a simulation study exploring two techniques to lower the energy threshold of LZ to gain sensitivity to low-mass dark matter and astrophysical neutrinos, which will be applicable to other liquid xenon detectors. The energy threshold is determined by the number of detected S1 photons; typically, these must be recorded in three or more photomultiplier channels to avoid dark count coincidences that mimic real signals. To lower this threshold: a) we take advantage of the double photoelectron emission effect, whereby a single vacuum ultraviolet photon has a $\sim20\%$ probability of ejecting two photoelectrons from a photomultiplier tube photocathode; and b) we drop the requirement of an S1 signal altogether, and use only the ionization signal, which can be detected more efficiently. For both techniques we develop signal and background models for the nominal exposure, and explore accompanying systematic effects, including the dependence on the free electron lifetime in the liquid xenon. When incorporating double photoelectron signals, we predict a factor of $\sim 4$ sensitivity improvement to the dark matter-nucleon scattering cross-section at $2.5$ GeV/c$^2$, and a factor of $\sim1.6$ increase in the solar $^8$B neutrino detection rate. Dropping the S1 requirement may allow sensitivity gains of two orders of magnitude in both cases. Finally, we apply these techniques to even lower masses by taking into account the atomic Migdal effect; this could lower the dark matter particle mass threshold to $80$ MeV/c$^2$.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Enhancing the sensitivity of the LUX-ZEPLIN (LZ) dark matter experiment to low energy signals

Two-phase xenon detectors, such as that at the core of the forthcoming LZ dark matter experiment, use photomultiplier tubes to sense the primary (S1) and secondary (S2) scintillation signals resulting from particle interactions in their liquid xenon target. This paper describes a simulation study exploring two techniques to lower the energy threshold of LZ to gain sensitivity to low-mass dark matter and astrophysical neutrinos, which will be applicable to other liquid xenon detectors. The energy threshold is determined by the number of detected S1 photons; typically, these must be recorded in three or more photomultiplier channels to avoid dark count coincidences that mimic real signals. To lower this threshold: a) we take advantage of the double photoelectron emission effect, whereby a single vacuum ultraviolet photon has a $\sim20\%$ probability of ejecting two photoelectrons from a photomultiplier tube photocathode; and b) we drop the requirement of an S1 signal altogether, and use only the ionization signal, which can be detected more efficiently. For both techniques we develop signal and background models for the nominal exposure, and explore accompanying systematic effects, including the dependence on the free electron lifetime in the liquid xenon. When incorporating double photoelectron signals, we predict a factor of $\sim 4$ sensitivity improvement to the dark matter-nucleon scattering cross-section at $2.5$ GeV/c$^2$, and a factor of $\sim1.6$ increase in the solar $^8$B neutrino detection rate. Dropping the S1 requirement may allow sensitivity gains of two orders of magnitude in both cases. Finally, we apply these techniques to even lower masses by taking into account the atomic Migdal effect; this could lower the dark matter particle mass threshold to $80$ MeV/c$^2$.

Akerib, DS↗
DOE OSTI2014

Collecting high-order interactions in an effective pairwise intermolecular potential using the hydrated ion concept: The hydration of Cf{sup 3+}

This work proposes a new methodology to build interaction potentials between a highly charged metal cation and water molecules. These potentials, which can be used in classical computer simulations, have been fitted to reproduce quantum mechanical interaction energies (MP2 and BP86) for a wide range of [M(H{sub 2}O){sub n}]{sup m+}(H{sub 2}O){sub ℓ} clusters (n going from 6 to 10 and ℓ from 0 to 18). A flexible and polarizable water shell model (Mobile Charge Density of Harmonic Oscillator) has been coupled to the cation-water potential. The simultaneous consideration of poly-hydrated clusters and the polarizability of the interacting particles allows the inclusion of the most important many-body effects in the new polarizable potential. Applications have been centered on the californium, Cf(III) the heaviest actinoid experimentally studied in solution. Two different strategies to select a set of about 2000 structures which are used for the potential building were checked. Monte Carlo simulations of Cf(III)+500 H{sub 2}O for three of the intermolecular potentials predict an aquaion structure with coordination number close to 8 and average R{sub Cf−−O} in the range 2.43–2.48 Å, whereas the fourth one is closer to 9 with R{sub Cf−−O} = 2.54 Å. Simulated EXAFS spectra derived from the structural Monte Carlo distribution compares fairly well with the available experimental spectrum for the simulations bearing 8 water molecules. An angular distribution similar to that of a square antiprism is found for the octa-coordination.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

On the Effect of Beating during Nonlinear Frequency Chirping

Spectroscopic analyses of energetic particle (EP) driven bursts of MHD fluctuations in magnetically confined plasmas often exhibit chirps that occur simultaneously in groups of two or more. While the superposition of oscillations at multiple frequencies necessarily causes beating in the signal acquired by a localized external probe, self-consistent hybrid simulations of chirping EP modes in a JT-60U tokamak plasma have demonstrated the possibility of global beating, where the mode's electromagnetic field vanishes globally between beats and reappears with opposite phase [Bierwage et al., Nucl. Fusion 57, 016036 (2017)]. This implies that there can be a single coherent field mode that oscillates at multiple frequencies simultaneously when it is resonantly driven by multiple density waves in EP phase space. Conversely, this means that the EP density waves are mutually coupled and interfere with each other via the jointly driven field, a mechanism ignored in some theories of chirping. In this thesis-style treatise, we study the role of field pulsations in general and beating in particular using the Hamiltonian guiding center orbit-following code ORBIT with a reduced wave-particle interaction model in realistic geometry. Beating is found to drive the evolution of EP phase space structures. Additionally, a key mechanism is the pulsation of effective phase space islands combined with the alternation of their effective O- and X-points due to phase jumps between each beat. Observations: (1) Beating causes density wave fronts to advance radially in a pulsed manner and the resulting chirps become staircase-like. (2) The pulsations facilitate convective transfer of material between neighboring layers of phase space density waves. On the one hand, this may inhibit the early detachment of solitary phase space vortices. On the other hand, it facilitates the accumulation of hole and clump fragments into larger structures. (3) Long-range chirping is observed when massive holes or clumps detach and drift away from the turbulent belt around the seed resonance. It is remarkable that the detached vortices remain robust and,on average, maintain their concentric nested layers while being visibly perturbed by the field's continued beating.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2010

Hidden Statistics Approach to Quantum Simulations

Recent advances in quantum information theory have inspired an explosion of interest in new quantum algorithms for solving hard computational (quantum and non-quantum) problems. The basic principle of quantum computation is that the quantum properties can be used to represent structure data, and that quantum mechanisms can be devised and built to perform operations with this data. Three basic non-classical properties of quantum mechanics superposition, entanglement, and direct-product decomposability were main reasons for optimism about capabilities of quantum computers that promised simultaneous processing of large massifs of highly correlated data. Unfortunately, these advantages of quantum mechanics came with a high price. One major problem is keeping the components of the computer in a coherent state, as the slightest interaction with the external world would cause the system to decohere. That is why the hardware implementation of a quantum computer is still unsolved. The basic idea of this work is to create a new kind of dynamical system that would preserve the main three properties of quantum physics superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. In other words, such a system would reinforce the advantages and minimize limitations of both quantum and classical aspects. Based upon a concept of hidden statistics, a new kind of dynamical system for simulation of Schroedinger equation is proposed. The system represents a modified Madelung version of Schroedinger equation. It preserves superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. Such an optimal combination of characteristics is a perfect match for simulating quantum systems. The model includes a transitional component of quantum potential (that has been overlooked in previous treatment of the Madelung equation). The role of the transitional potential is to provide a jump from a deterministic state to a random state with prescribed probability density. This jump is triggered by blowup instability due to violation of Lipschitz condition generated by the quantum potential. As a result, the dynamics attains quantum properties on a classical scale. The model can be implemented physically as an analog VLSI-based (very-large-scale integration-based) computer, or numerically on a digital computer. This work opens a way of developing fundamentally new algorithms for quantum simulations of exponentially complex problems that expand NASA capabilities in conducting space activities. It has been illustrated that the complexity of simulations of particle interaction can be reduced from an exponential one to a polynomial one.

Zak, Michail↗