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At least 1,585 records · Page 88

Evaluation of phase shifts for nonrelativistic elastic scattering using quantum computers

Simulations of scattering processes are essential in understanding the physics of our universe. Computing relevant scattering quantities from ab initio methods is extremely difficult on classical devices because of the substantial computational resources needed. Here, this work reports the development of an algorithm that makes it possible to obtain phase shifts for generic nonrelativistic elastic scattering processes on a quantum computer. This algorithm is based on extracting phase shifts from the direct implementation of the real-time evolution. The algorithm is improved by a variational procedure making it more accurate and resistant to the quantum noise. The reliability of the algorithm is first demonstrated by means of classical numerical simulations for different potentials and later tested on existing quantum hardware, specifically on IBM quantum processors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Are Marine Low Cloud Droplet Concentrations Buffered by Entrained Aitken‐Mode Aerosol (Final Technical Report)

During the summertime, the high-latitude oceans come to life with green phytoplankton, which gain their energy from sunlight and are food for sea creatures small and large. When the phytoplankton are eaten or die, sulfur-rich gases are released under the ocean surface and mix into the air. Observations suggest that, over the Southern Ocean, frequent storms lift this air high into the atmosphere while raining out particulates like salt. As a result, the sulfur-rich air then spawns high concentrations of small ‘Aitken-mode’ aerosol particles. We hypothesize that these particles work their way down into the marine boundary layer, where they can replenish the supply of cloud-condensation nuclei scavenged by frequent precipitation. Further, this process maintains high concentrations of liquid cloud droplets in austral summer, promoting more sunlight to be reflected to space. We call this ‘Aitken buffering’. The primary objective of this project has been to document and test what role Aitken-mode aerosols play in clouds over the Southern Ocean and elsewhere. This effort has included three main components: 1) developing a computer model that realistically simulates the aerosol processes and the small-scale turbulent air motions that move aerosols around and create the clouds, 2) using that model to interpret and extend these observations for process understanding, by allowing different factors that contribute to the aerosol budget, such as surface wind speed, precipitation, surface gas exchange, etc. to be separated, and 3) studying Aitken-mode aerosol and its variability with a focus over the Southern Ocean and Antarctica, using data from Atmospheric Radiation Measurement (ARM) sites and other available observations. Initial computer studies in more idealized conditions found that elevated concentrations of Aitken-mode aerosols above the clouds could help prevent the breakup of those clouds by acting as cloud-condensation nuclei after they were entrained into the cloudy boundary layer. Simulations of a day during the ACE-ENA field campaign showed that Aitken-mode aerosols could also prevent cloud breakup under more realistic conditions. A new method that extracts information about Aitken-mode aerosols from measurements of aerosols onto which cloud droplets can form finds that Aitken-mode aerosols do vary seasonally over the Southern Ocean, with a peak in summertime, as described above. Other work during this project has focused on understanding how patterns of water vapor, clouds and precipitation are coupled within low-lying clouds over the oceans, and also on how cloud droplets cluster within clouds and how the distribution of cloud droplet sizes change as dry air is mixed into clouds, with the latter studies also using observations from ACE-ENA.

54 ENVIRONMENTAL SCIENCES↗

Heat Pump Water Heater Using Wrapped-Tank Microchannel Condenser Coil for Charge Reduction – FY19 1st Quarter (Regular) Milestone Report: Development of Wrapped-Tank Condenser Model (Round Tube and Microchannel), Coupled with Water Tank Model

We recently grew the DOE/HPDM model library to enhance its heat pump water heater (HPWH) design and simulation capability. The new additions include wrapped-tank round tube coil, microchannel coil and a one-dimensional stratified water tank. A wrapped-tank condenser coil has strong coupling with a stratified water tank, which leads HPWH simulation a transient process. The new one-dimensional stratified water tank model is an improvement to the open-source EnergyPlus water tank model, by introducing a calibration factor to account for bulk mixing effect due to water draws and circulations, etc. The wrapped-tank condenser coil model, using a segment-to-segment modeling approach to simulate round tubes or microchannel ports. The heat exchanger models can accept arbitrary refrigerant types, e.g. HFCs, HFOs, natural refrigerants like CO 2 and propane, etc.

42 ENGINEERING↗

Impacts of Microphysical Scheme on Convective and Stratiform Characteristics in Two High Precipitation Squall Line Events

This study investigates the impact of snow, graupel, and hail processes on the simulated squall lines over the Southern Great Plains in the United States. Weather Research and Forecasting (WRF) model is used to simulate two squall line events in May 2007, and the results are validated against radar and surface observations in Oklahoma. Several microphysics schemes are tested in this study, including WRF 5-Class Microphysics Scheme (WSM5), WRF 6-Class Microphysics Scheme (WSM6), Goddard Three Ice scheme (Goddard 3-ice) with graupel, Goddard Two Ice scheme (Goddard 2-ice), and Goddard 3-ice hail scheme. The simulated surface precipitation is sensitive to the microphysics scheme, and especially to whether graupel or hail category is included. All of the three ice (3-ice) schemes overestimated the total precipitation, within which WSM6 has the highest overestimation. Two ice (2-ice) schemes, missing a graupel/hail category, produced less total precipitation than 3-ice schemes. By applying a radar-based convective/stratiform partitioning algorithm, we find that by including the graupel/hail processes, there is an increase in areal coverage, precipitation intensity, updraft and downdraft intensity in convective region and a reduction of areal coverage and its precipitation intensity in stratiform region. For vertical structures, all the bulk schemes, especially 2-ice schemes, have the highest reflectivity located at upper levels (~8 km), which is unrealistic compared to observations. In addition, this study shows the radar-based convective/stratiform partitioning algorithm can reasonably identify WRF simulated precipitation, wind and microphysics fields in both convective and stratiform regions.

characteristics↗

SAM Process Heat Model Development and Validation: Liquid-HTF Trough and Direct Steam Generation Linear Focus Systems

Two new solar industrial process heat (SIPH) models have been added to the System Advisor Model (SAM) energy simulation tool. The two process heat models were: i) liquid-heat transfer fluid (HTF) parabolic troughs; and ii) direct steam generation (DSG) linear-focus collectors. The DSG model can simulate either DSG parabolic troughs (PT) or DSG Linear Fresnel (LF) fields, based on the optical characteristics supplied. These models help to meet the need for independent, validated tools that reliably simulate the effects of adding a solar field to provide heat for potential IPH applications. During the pre-validation of the liquid-HTF model, operational data was provided and preprocessed by SPF and evaluated at ZAE Bayern. The beta liquid-HTF model provided excellent agreement between the simulations and the operational data for the solar thermal yield generation on a yearly and monthly basis (4.4% difference). The final liquid-HTF process heat model has been further optimized with test users such as ZAE Bayern and SPF. Key improvements in the SIPH models to better model SIPH fields include the use of smaller piping systems and heat capacities, a single collector field, and a higher time-step resolution than for electricity generation (down to 10 minutes). Both the final liquid-HTF and DSG models were successfully validated against operational data for respective solar fields, and showed less than 5% deviation to actual results. A brief application where the liquid-HTF process heat model is used for a brewery in California and the value of reliably simulating a potential SIPH solar field are highlighted.

14 SOLAR ENERGY↗

A new Green's function Monte Carlo algorithm for the solution of the two-dimensional nonlinear Poisson–Boltzmann equation: Application to the modeling of the communication breakdown problem in space vehicles during re-entry

The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson–Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals of the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Analysis of Radiation Transport Due to Activated Coolant in the ITER Neutral Beam Injection Cell

Detailed spatial distributions of the biological dose rate due to a variety of sources are required for the design of the ITER tokamak facility to ensure that all radiological zoning limits are met. During operation, water in the Integrated loop of Blanket, Edge-localized mode and vertical stabilization coils, and Divertor (IBED) cooling system will be activated by plasma neutrons and will flow out of the bioshield through a complex system of pipes and heat exchangers. This paper discusses the methods used to characterize the biological dose rate outside the tokamak complex due to 16 N gamma radiation emitted by the activated coolant in the Neutral Beam Injection (NBI) cell of the tokamak building. Activated coolant will enter the NBI cell through the IBED Primary Heat Transfer System (PHTS), and the NBI PHTS will also become activated due to radiation streaming through the NBI system. To properly characterize these gamma sources, the production of 16 N, the decay of 16 N, and the flow of activated water through the coolant loops were modeled. The impact of conservative approximations on the solution was also examined. Once the source due to activated coolant was calculated, the resulting biological dose rate outside the north wall of the NBI cell was determined through the use of sophisticated variance reduction techniques. The AutomateD VAriaNce reducTion Generator (ADVANTG) software implements methods developed specifically to provide highly effective variance reduction for complex radiation transport simulations such as those encountered with ITER. Using ADVANTG with the Monte Carlo N-particle (MCNP) radiation transport code, radiation responses were calculated on a fine spatial mesh with a high degree of statistical accuracy. In conclusion, advanced visualization tools were also developed and used to determine pipe cell connectivity, to facilitate model checking, and to post-process the transport simulation results.

59 BASIC BIOLOGICAL SCIENCES↗

Nuclear Data Specifications, Utilities, and Libraries

Nuclear data provides descriptions of physical processes used by numerical simulation codes throughout the world. The data is provided in specified formats. Knowledge of the formats and what it represents is important for those that produce and read the data. Nuclear data is typically processed and made available to simulation codes at various temperatures applicable to the general class of problems that the simulation code is designed to model. These libraries are historically pre-processed and made available to the world. The libraries are based on fundamental physical data and are used by scientists and researchers.

Conlin, Jeremy↗

A NEW MODEL FOR MIXING BY DOUBLE-DIFFUSIVE CONVECTION (SEMI-CONVECTION). I. THE CONDITIONS FOR LAYER FORMATION

The process referred to as 'semi-convection' in astrophysics and 'double-diffusive convection in the diffusive regime' in Earth and planetary sciences occurs in stellar and planetary interiors in regions which are stable according to the Ledoux criterion but unstable according to the Schwarzschild criterion. In this series of papers, we analyze the results of an extensive suite of three-dimensional (3D) numerical simulations of the process, and ultimately propose a new 1D prescription for heat and compositional transport in this regime which can be used in stellar or planetary structure and evolution models. In a preliminary study of the phenomenon, Rosenblum et al. showed that, after saturation of the primary instability, a system can evolve in one of two possible ways: the induced turbulence either remains homogeneous, with very weak transport properties, or transitions into a thermo-compositional staircase where the transport rate is much larger (albeit still smaller than in standard convection). In this paper, we show that this dichotomous behavior is a robust property of semi-convection across a wide region of parameter space. We propose a simple semi-analytical criterion to determine whether layer formation is expected or not, and at what rate it proceeds, as a function of the background stratification and of the diffusion parameters (viscosity, thermal diffusivity, and compositional diffusivity) only. The theoretical criterion matches the outcome of our numerical simulations very adequately in the computationally accessible 'planetary' parameter regime and can be extrapolated to the stellar parameter regime. Subsequent papers will address more specifically the question of quantifying transport in the layered case and in the non-layered case.

79 ASTRONOMY AND ASTROPHYSICS↗

Molecular dynamics simulation of graphene growth at initial stage on Ni(100) facet for low flux C energy by CVD

In this study, atomic simulation for graphene growth on Ni (100) at initial stage via chemical vapor deposition method has been developed. The C-C atoms interaction was performed by Terasoff potential mean while Ni-Ni interaction was specified by EAM (Embedded Atom Modified). On the other hand, we used very simple interatomic potential to describe Ni-C interaction during deposition process. From this simulation, it shows that the formation of graphene is not occurs through a combined deposition mechanism on Ni substrate but via C segregation. It means, Ni-C amorphous is source for graphene growth when cooling down of Ni substrate. This result is appropriate with experiments, tight binding and quantum mechanics simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Beam Dynamics Simulations of Optically-Enhanced Field Emission from Structured Cathodes

Structured cathodes - cathodes with a segmented emission surface - are finding an increasing number of applications and can be combined with a variety of emission mechanisms, including photoemission and field emission. These cathodes have been used to enhance the quantum efficiency of metallic cathodes when operated as plasmonic cathodes, have produced high-current electron bunches though field emission from multiple tips, and can be used to form beams with transverse segmentations necessary for improving the performance of accelerator-based light sources. In this report we present recent progress towards the development of finite-difference time-domain particle-in-cell simulations using the emission process in structured cathodes based on the WARP framework. The simulations give further insight on the localized source of the emitted electrons which could be used for additional high-fidelity start-to-end simulations of electron accelerators that employ this type of electron source.

43 PARTICLE ACCELERATORS↗

Simulation system for testing a radar system

A simulation system for use in testing a radar system comprises a coarse delay module, a fine delay module, and a doppler shift module. The coarse delay module is configured to receive a first stream of digital data samples that are sampled from a radar signal at a sample time period or a second stream of digital data samples that are processed by another simulation system component and delay the digital data samples by a selectable first delay time that is greater than or equal to the sample time period. The fine delay module is configured to receive the digital data samples and filter the digital data samples to represent delay by a selectable second delay time that is less than the sample time period. The doppler shift module is configured to receive the digital data samples and adjust a value of a frequency content of the fine delayed samples.

Chritton, Audrey L.↗

Multi-scale models of whole cells: progress and challenges

Whole-cell modeling is “the ultimate goal” of computational systems biology and “a grand challenge for 21st century”. These complex, highly detailed models account for the activity of every molecule in a cell and serve as comprehensive knowledgebases for the modeled system. Their scope and utility far surpass those of other systems models. In fact, whole-cell models (WCMs) are an amalgam of several types of “system” models. The models are simulated using a hybrid modeling method where the appropriate mathematical methods for each biological process are used to simulate their behavior. Given the complexity of the models, the process of developing and curating these models is labor-intensive and to date only a handful of these models have been developed. While whole-cell models provide valuable and novel biological insights, and to date have identified some novel biological phenomena, their most important contribution has been to highlight the discrepancy between available data and observations that are used for the parametrization and validation of complex biological models. Another realization has been that current whole-cell modeling simulators are slow and to run models that mimic more complex (e.g., multi-cellular) biosystems, those need to be executed in an accelerated fashion on high-performance computing platforms. In this manuscript, we review the progress of whole-cell modeling to date and discuss some of the ways that they can be improved.

59 BASIC BIOLOGICAL SCIENCES↗

System-based identification of toxicity pathways associated with multi-walled carbon nanotube-induced pathological responses

The fibrous shape and biopersistence of multi-walled carbon nanotubes (MWCNT) have raised concern over their potential toxicity after pulmonary exposure. As in vivo exposure to MWCNT produced a transient inflammatory and progressive fibrotic response, this study sought to identify significant biological processes associated with lung inflammation and fibrosis pathology data, based upon whole genome mRNA expression, bronchoaveolar lavage scores, and morphometric analysis from C57BL/6J mice exposed by pharyngeal aspiration to 0, 10, 20, 40, or 80 μg MWCNT at 1, 7, 28, or 56 days post-exposure. Using a novel computational model employing non-negative matrix factorization and Monte Carlo Markov Chain simulation, significant biological processes with expression similar to MWCNT-induced lung inflammation and fibrosis pathology data in mice were identified. A subset of genes in these processes was determined to be functionally related to either fibrosis or inflammation by Ingenuity Pathway Analysis and was used to determine potential significant signaling cascades. Two genes determined to be functionally related to inflammation and fibrosis, vascular endothelial growth factor A (vegfa) and C-C motif chemokine 2 (ccl2), were confirmed by in vitro studies of mRNA and protein expression in small airway epithelial cells exposed to MWCNT as concordant with in vivo expression. This study identified that the novel computational model was sufficient to determine biological processes strongly associated with the pathology of lung inflammation and fibrosis and could identify potential toxicity signaling pathways and mechanisms of MWCNT exposure which could be used for future animal studies to support human risk assessment and intervention efforts. - Highlights: • A novel computational model identified toxicity pathways matching in vivo pathology. • Systematic identification of MWCNT-induced biological processes in mouse lungs • MWCNT-induced functional networks of lung inflammation and fibrosis were revealed. • Two functional, representative genes, ccl2 and vegfa, were validated in vitro.

60 APPLIED LIFE SCIENCES↗

Cold-Air Outbreaks in the Marine Boundary Layer Experiment (COMBLE) Science Implementation Plan

Boreal regions have experienced warming faster than the rest of the Earth, and the arctic ice cover has declined at a rate faster than predicted by most climate models. Uncertainties in climate projections for this region are large, in part due to the lack of observational guidance to constrain the treatment of aerosol-cloud-precipitation linkages in climate models. To remedy this shortfall, field campaigns have been conducted to collect integrated, comprehensive measurements under specific atmospheric regimes. While considerable efforts have been devoted to subtropical marine boundary-layer clouds, as well as to clouds in the stable arctic environment, very few targeted observations exist of convective boundary-layer clouds that form over open water when cold airmasses are advected off ice-covered regions or boreal continents. There is an urgent need to shed light on the dynamics and microphysical properties of clouds and precipitation in the high-latitude marine boundary layer during cold-air outbreaks. Despite the common occurrence of linear and cellular cloud patterns that typify cold-air outbreaks, little is known about the properties of these clouds; how they vary with surface, environmental, and aerosol conditions; the role of cold-air outbreaks in the global atmospheric and ocean circulation; and the accuracy of the treatment of this atmospheric regime in climate models. Thus, we proposed to conduct the Cold-Air Outbreaks in the Marine Boundary Layer Experiment (COMBLE), to focus on marine boundary-layer clouds during cold-air outbreaks. COMBLE will deploy the first ARM Mobile Facility (AMF1) and an AMF “satellite” station in the far North Atlantic in January–May 2020. COMBLE will take advantage of the synergy with several coincident campaigns, notably MOSAIC, which will characterize the source airmasses of cold-air outbreaks over the arctic ice, and (AC) 3 , which will operate several aircraft between northern Scandinavia and the MOSAIC deployment to document evolution of these airmasses. COMBLE and its sister campaigns will compose a four-member array of supersites between northern Scandinavia and the Arctic, each with profiling and in situ cloud, precipitation, radiation, and aerosol measurements. COMBLE will be guided by six science themes. The first five deal with boundary-layer convection in cold-air outbreaks: (1) the fetch-dependent mesoscale organization of clouds and precipitation, including linear and cellular convection; (2) surface heat and momentum fluxes and vertical profiles of temperature, humidity, wind, and turbulence; (3) vertical structure of clouds and precipitation; (4) the sources and sinks of aerosol, including ice-nucleating particles, and the role of cloud-active aerosol on cloud processes and radiative fluxes; and (5) the influence of these four themes on polar cyclogenesis and polar low vertical structure. The overarching sixth theme is that COMBLE will provide integrated data sets of dynamical, thermodynamic, and cloud microphysical characteristics of marine boundary-layer convection in cold-air outbreaks, including cloud and aerosol properties, that will enable constraining high-resolution numerical simulations, developing process-level understanding, and, subsequently, evaluating and improving representations of shallow convection in weather and climate models.

54 ENVIRONMENTAL SCIENCES↗

High-Resolution WRF-Based Downscaling of Earth System Model Projections for Energy Applications across CONUS

Evaluating energy resources under future scenarios requires meteorological information that adequately resolves regional-scale variability and is suitable for regional energy system studies. Although Earth system model (ESM) outputs provide essential large-scale context, their coarse resolution and inherent biases limit direct use in energy system applications. This work presents a high-resolution dynamical downscaling framework using the Weather Research and Forecasting (WRF) model to generate energy-relevant regional fields for future scenarios over the contiguous United States (CONUS). The framework first identifies an optimal WRF configuration through sensitivity experiments, then evaluates raw and bias-corrected ESM initial and boundary conditions, with soil moisture and soil temperature bias correction implemented as an integral component of the bias-corrected ESM atmospheric forcing prior to WRF dynamical downscaling to improve land-atmosphere interactions. Simulations performed at 4-km resolution show that uncorrected ESM forcing leads to systematically dry and cold soil states, which propagate into elevated near-surface air temperature and solar irradiance biases, particularly during summer for the period 2000-2014. Incorporating bias-corrected atmospheric forcing together with soil state bias correction substantially reduces these errors and improves the representation of surface energy processes in WRF simulations. The results highlight the importance of bias-aware initialization strategies in high-resolution dynamical downscaling for future energy system analysis and planning.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Simulations of flaming combustion and flaming-to-smoldering transition in wildland fire spread at flame scale

Our objective in the present study is to provide basic insights into the coupling between external-gas and solid biomass vegetation processes that control the dynamics of flame spread in wildland fire problems. Here we focus on a modeling approach that resolves processes occurring at vegetation and flame scales, i.e., the formation of flammable vapors due to the thermal degradation of the solid biomass, the subsequent combustion in ambient air, the thermal feedback to the biomass through radiative and convective heat transfer, and the possible transition from flaming combustion (taking place outside of the solid biomass) to smoldering combustion (taking place inside the solid biomass). The capability uses a multiphase combustion framework and treats external-gas processes through a Large Eddy Simulation solver and solid biomass processes through a discrete particle model. The discrete particle model adopts a one-dimensional porous medium formulation, includes descriptions of drying, thermal pyrolysis, oxidative pyrolysis, and char oxidation, as well as a description of the external-gas-to-solid-biomass diffusion of oxygen mass; the discrete particle model thereby provides a treatment of in-depth oxidative processes and allows the simulation of smoldering combustion. The modeling capability is applied to the simulation of fire spread across a surrogate biomass vegetation bed corresponding to a discrete array of cylindrical-shaped, vertically-oriented, pine wood sticks, characterized by a monomodal size distribution, in horizontal flat terrain and under wind-aided conditions. The numerical results demonstrate that the model can simulate successful flaming-to-smoldering transition followed by complete biomass consumption.

01 COAL, LIGNITE, AND PEAT↗

Numerical Investigation of the Spark Discharge Process in a Crossflow

The present study numerically investigates the spark discharge process under crossflow conditions using a thermal equilibrium plasma solver that fully couples the electromagnetic physics and fluid dynamics in a computational framework. Numerical results are validated by the comparison with experimental data. Here, the spark discharge experiment is performed in a constant volume vessel using an inductive coil ignition system for automotive applications, and the evolution of the spark channel is measured using high-speed imaging. The crossflow in the gap between the spark-plug electrodes is generated by a rotating fan with two different fan speeds, and the flow velocity across the gap is characterized by particle image velocimetry (PIV) measurement. A computational fluid dynamics (CFD) solver is employed to simulate the crossflow and provide the flow field variables (velocity, pressure, temperature) to the plasma solver. The crossflow velocity predicted in the flow simulation agrees well with the PIV data in that the non-uniform velocity profiles at monitoring points are reproduced by the CFD code. With the crossflow initialization in the plasma solver, the simulated spark discharge process from the breakdown to spark discharge matches the experimental data, including the voltage and circuit waveforms and the high-speed images of the spark channel evolution. The stretch of spark channel captured by plasma simulations agrees with the measured data. The plasma simulation reveals that the mean temperature of the spark channel is maintained at 5000 K during the discharge phase, and the temperature varies along the spark channel so that the highest value is obtained at the spark root on the center electrode. Overall, the results presented in this paper are meant to provide valuable information about the properties of the plasma generated by the spark discharge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗