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DOE OSTI2023

Xanthos Output Dataset Under ISIMIP3b Selected CMIP6 Scenarios: 1850 - 2100

Overview Xanthos is an open-source hydrologic model, written in Python, designed to quantify and analyze global water availability. Xanthos simulates historical and future global water availability on a monthly time step at a spatial resolution of 0.5 geographic degrees. Xanthos was designed to be extensible and used by scientists that study global water supply and work with the Global Change Analysis Model (GCAM). Details This dataset includes Xanthos outputs forced by the ISIMIP3b bias-adjusted CMIP6 climate forcing (1850 - 2100). There are 30 scenarios consists of 10 Coupled Model Intercomparison Project phase 6 (CMIP6) General Circulation Models (GCM) and 3 Shared Socioeconomic Pathways (SSP). Each folder is named as cmip6_{gcm}_{ensemble-member}_{ssp}. 10 CMIP6 GCMs: GFDL-ESM4, IPSL-CM6A-LR, MPI-ESM1-2-HR, MRI-ESM2-0, UKESM1-0-LL, CanESM5, CNRM-CM6-1, CNRM-ESM2-1, EC-Earth3, and MIROC6 3 SSP-RCP Scenarios: SSP1-2.6, SSP3-7.0, and SSP5-8.5 The table below summarizes the details of output variables within each scenario folder. | Output Variable | File Short Name | Spatial Resolution | Unit | | ----------------------------------------------- | -------------------------------------- | -------------------------------- | --------------------- | | Runoff | q | 0.5x0.5 degree | km3/month | | Runoff | Basin_runoff | GCAM basin | km3/month | | Runoff | Country_runoff | Country | km3/month | | Runoff | GCAMRegion_runoff | GCAM region | km3/month | | Streamflow | avgchflow | 0.5x0.5 degree | m3/second | | Potential Evapotranspiration | pet | 0.5x0.5 degree | km3/month | | Actual Evapotranspiration | aet | 0.5x0.5 degree | km3/month | | Accessible Water | accessible_water | GCAM basin | km3/year | | Hydropower Generation | actual_hydro | GCAM region | EJ/year |

Climate Change↗

DOE OSTI2025

Quantum simulation of charge and exciton transfer in multi-mode models using engineered reservoirs

Quantum simulation enables studies of open-system dynamics in non-perturbative regimes by programming electronic, vibrational, and environmental interactions on comparable energy scales. Trapped ions offer this capability, combining spins, phonons, and tunable dissipation on one platform. We demonstrate an open-system quantum simulation of charge and exciton transfer in a multi-mode linear vibronic coupling model. Using tailored spin-phonon interactions with reservoir engineering, we emulate a system with two dissipative vibrational modes coupled to donor and acceptor sites and track its non-equilibrium dynamics. We continuously tune the system from the charge transfer regime to the vibrationally assisted exciton transfer regime and find that degenerate modes enhance transfer rates at large energy gaps, while non-degenerate modes activate pathways that reduce the energy-gap dependence. Thus, the presence of one additional vibration introduces interfering pathways and reshapes non-perturbative excitation transfer. Our results establish a scalable, hardware-efficient route to simulate vibronic processes with engineered environments.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2022

A continuum model for heat and mass transfer in moving-bed reactors for thermochemical energy storage

In this work, a continuum heat and mass transfer model coupling transport phenomena and high-temperature thermochemical reactions is developed for stationary packed-bed and counter-flow moving-bed reactors. After presenting the general modeling framework, we focus on the 2D axisymmetric version of the model for which validation is conducted with experimental results for a packed-bed reactor in the literature for manganese-iron oxide reduction/oxidation and an in-house counter-flow moving-bed reactor for magnesium-manganese oxide reduction up to 1450 °C. Transient simulation results including the local distributions of gas/solid temperatures, oxygen concentration and the extent of reaction, as well as the various energy flow components and energy conversion efficiencies are reported. The results based on the 2D axisymmetric model are also compared with those obtained from a previous 1D model. The comparison shows that capturing the radial variation is critical in reactor modeling and the 2D results demonstrate improved agreement with experiments. Specifically, large temperature variations along the radial direction are observed especially in the reaction zone; this non-uniform radial temperature distribution has a significant effect on the chemical reaction extent due to its strong dependence on temperature; and the overall oxygen concentration at the reactor exit and the predicted system efficiency are slightly lower in the 2D model compared to the 1D model. Finally, the present heat and mass transfer model can provide valuable insights into reactor design, scale-up, and operating conditions selection to maximize system energy storage efficiency.

25 ENERGY STORAGE↗

DOE OSTI2021

Retrospective Analysis and Bayesian Model Averaging of CMIP6 Precipitation in the Nile River Basin

The Nile River basin is one of the global hotspots vulnerable to climate change impacts because of a fast-growing population and geopolitical tensions. Previous studies demonstrated that general circulation models (GCMs) frequently show disagreement in the sign of change in annual precipitation projections. Here, we first evaluate the performance of 20 GCMs from phase six of the Coupled Model Intercomparison Project (CMIP6) benchmarked against a high-spatial-resolution precipitation dataset dating back to 1983 from Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks–Climate Data Record (PERSIANN-CDR). Next, a Bayesian model averaging (BMA) approach is adopted to derive probability distributions of precipitation projections in the Nile basin. Retrospective analysis reveals that most GCMs exhibit considerable (up to 64% of mean annual precipitation) and spatially heterogenous bias in simulating annual precipitation. Moreover, it is shown that all GCMs underestimate interannual variability; thus, the ensemble range is underdispersive and is a poor indicator of uncertainty. The projected changes from the BMA model show that the value and sign of change vary considerably across the Nile basin. Specifically, it is found that projected changes in the two headwaters basins, namely, the Blue Nile and Upper White Nile, are 0.03% and -1.65%, respectively; both are statistically insignificant at α = 0.05. The uncertainty range estimated from the BMA model shows that the probability of a precipitation decrease is much higher in the Upper White Nile basin whereas projected change in the Blue Nile is highly uncertain both in magnitude and sign of change.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

The E3SM Diagnostics Package (E3SM Diags v2.7): a Python-based diagnostics package for Earth system model evaluation

Abstract. The E3SM Diagnostics Package (E3SM Diags) is a modern, Python-based Earth system model (ESM) evaluation tool (with Python module name e3sm_diags), developed to support the Department of Energy (DOE) Energy Exascale Earth System Model (E3SM). E3SM Diags provides a wide suite of tools for evaluating native E3SM output, as well as ESM data on regular latitude–longitude grids, including output from Coupled Model Intercomparison Project (CMIP) class models. E3SM Diags is modeled after the National Center for Atmospheric Research (NCAR) Atmosphere Model Working Group (AMWG, 2022) diagnostics package. In its version 1 release, E3SM Diags included a set of core essential diagnostics to evaluate the mean physical climate from model simulations. As of version 2.7, more process-oriented and phenomenon-based evaluation diagnostics have been implemented, such as analysis of the quasi-biennial oscillation (QBO), the El Niño–Southern Oscillation (ENSO), streamflow, the diurnal cycle of precipitation, tropical cyclones, ozone and aerosol properties. An in situ dataset from DOE's Atmospheric Radiation Measurement (ARM) program has been integrated into the package for evaluating the representation of simulated cloud and precipitation processes. This tool is designed with enough flexibility to allow for the addition of new observational datasets and new diagnostic algorithms. Additional features include customizable figures; streamlined installation, configuration and execution; and multiprocessing for fast computation. The package uses an up-to-date observational data repository maintained by its developers, where recent datasets are added to the repository as they become available. Finally, several applications for the E3SM Diags module were introduced to fit a diverse set of use cases from the scientific community.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Evaluating precipitation distributions at regional scales: a benchmarking framework and application to CMIP5 and 6 models

Abstract. As the resolution of global Earth system models increases, regional-scale evaluations are becoming ever more important. This study presents a framework for quantifying precipitation distributions at regional scales and applies it to evaluate Coupled Model Intercomparison Project (CMIP) 5 and 6 models. We employ the Intergovernmental Panel on Climate Change (IPCC) sixth assessment report (AR6) climate reference regions over land and propose refinements to the oceanic regions based on the homogeneity of precipitation distribution characteristics. The homogeneous regions are identified as heavy-, moderate-, and light-precipitating areas by K-means clustering of Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (GPM) version 6 final run product (IMERG) precipitation frequency and amount distributions. With the global domain partitioned into 62 regions, including 46 land and 16 ocean regions, we apply 10 established precipitation distribution metrics. The collection includes metrics focused on the maximum peak, lower 10th percentile, and upper 90th percentile in precipitation amount and frequency distributions; the similarity between observed and modeled frequency distributions; an unevenness measure based on cumulative amount; average total intensity on all days with precipitation; and number of precipitating days each year. We apply our framework to 25 CMIP5 and 41 CMIP6 models, as well as six observation-based products of daily precipitation. Our results indicate that many CMIP5 and 6 models substantially overestimate the observed light-precipitation amount and frequency, as well as the number of precipitating days, especially over midlatitude regions outside of some land regions in the Americas and Eurasia. Improvement from CMIP5 to 6 is shown in some regions, especially in midlatitude regions, but it is not evident globally, and over the tropics most metrics point toward degradation.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

A time-dependent chloride diffusion model for predicting initial corrosion time of reinforced concrete with slag addition

The effect of granulated blast furnace slag (GBFS) addition on the threshold chloride concentration (TCC) for rebar corrosion was investigated. A modified diffusion model, coupled with a time-dependent effective diffusion coefficient and surface chloride concentration, was proposed to predict the chloride profile. The corrosion initiation time was estimated based on the model predictions and the measured TCC. The results indicate that adding GBFS decreases the TCC by lowering the pH value of the pore solution. The evolution of corrosion potential and current density is found to obey a 3-parameter Weibull distribution. MIP tests show that adding GBFS contributes to refinement of pore structure by decreasing the fraction of large capillary pores. The time-dependent model exhibits good predictive strength and helps understand how GBFS addition delays the corrosion initiation by retarding the chloride diffusion, though a lower TCC is obtained.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Characterizing and quantifying uncertainty in projections of climate change impacts on air quality

Climate change can aggravate air pollution, with important public health and environmental consequences. While major sources of uncertainty in climate change projections - greenhouse gas (GHG) emissions scenario, model response, and internal variability - have been investigated extensively, their propagation to estimates of air quality impacts has not been systematically assessed. Here, we compare these uncertainties using a coupled modeling framework that includes a human activity model, an Earth system model of intermediate complexity, and a global atmospheric chemistry model. Uncertainties in projections of U.S. air quality under 21st century climate change are quantified based on a climate-chemistry ensemble that includes multiple initializations, representations of climate sensitivity, and climate policy scenarios, under constant air pollution emissions. We find that climate-related uncertainties are comparable at mid-century, making it difficult to distinguish the impact of variations in GHG emissions on ozone and particulate matter pollution. While GHG emissions scenario eventually becomes the dominant uncertainty based on the scenarios considered, all sources of uncertainty are significant through the end of the century. The results provide insights into intrinsically different uncertainties in projections of air pollution impacts and the potential for large ensembles to better capture them.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Ripening of Rh Nanoparticle Catalysts in Reverse Water–Gas Shift via a Data-Driven Model Combining Physics, Theory, and Experiment

Degradation via sintering is an ongoing challenge that impedes the broad commercial success of supported metallic nanoparticle catalysts. To mitigate degradation via informed catalyst design and process operations, here we aim to disambiguate the underlying mechanisms of sintering by combining theory and experiment in a quantitative framework. While mechanistic sintering models exist, they only model a single sintering pathway, even though multiple sintering mechanisms can occur simultaneously or dominate at different stages of the process. Data-driven machine learning models have emerged as a means to represent complex processes through data regression. However, machine learning models have very large data needs and lack mechanistic insights due to their black-box encoding. To develop an interpretive model of catalyst degradation via sintering, we constructed a hybrid model combining mechanistic “physics-based” models and data-driven methods to obtain both reliable predictions and mechanistic insights regarding experimentally observed sintering phenomena. Focusing on nanoparticle sintering in the Rh–TiO 2 catalyst for the reverse water–gas shift (RWGS) reaction, the hybrid model couples a mechanistic term for Ostwald ripening with energy values calculated via density functional theory (DFT) with a parametric, data-driven discrepancy function term for unmodeled mechanisms. The hybrid model is trained using Bayesian inference with data collected from small-angle X-ray scattering (SAXS) in situ experiments wherein average nanoparticle diameter versus time was measured at three relevant operating temperatures. The calibrated hybrid model results show that an Ostwald ripening-only model parameterized with fixed DFT energies does not fully capture the time and temperature dependence of the SAXS-observed sintering kinetics, and that an additional functional contribution, or DFT energy calibration, is required to reconcile simulation and experiment. Analysis of the hybrid-model error confirms that the hybrid model outperforms both the purely mechanistic and purely data-driven alternatives in terms of expected predictive accuracy for time-evolving average particle sizes. Furthermore, the results support the hypothesis that the Ostwald ripening mechanism is less important for explaining the sintering phenomena as operating temperature increases under an assumed fixed DFT parameterization. This could be explained in one of two ways: either latent, unmodeled sintering mechanisms dominate at higher temperatures, or the DFT uncertainty increases with temperature. The proposed modeling approach directly links theory to experiments and simulations via a statistical hybrid modeling framework and can be extended to other catalytic systems to improve predictive models and mechanistic understanding.

Bayesian hybrid modeling↗

DOE OSTI2021

Significant impact of forcing uncertainty in a large ensemble of climate model simulations

Forcing due to solar and volcanic variability, on the natural side, and greenhouse gas and aerosol emissions, on the anthropogenic side, are the main inputs to climate models. Reliable climate model simulations of past and future climate change depend crucially upon them. Here we analyze large ensembles of simulations using a comprehensive Earth System Model to quantify uncertainties in global climate change attributable to differences in prescribed forcings. The different forcings considered here are those used in the two most recent phases of the Coupled Model Intercomparison Project (CMIP), namely CMIP5 and CMIP6. We show significant differences in simulated global surface air temperature due to volcanic aerosol forcing in the second half of the 19th century and in the early 21st century. The latter arise from small-to-moderate eruptions incorporated in CMIP6 simulations but not in CMIP5 simulations. We also find significant differences in global surface air temperature and Arctic sea ice area due to anthropogenic aerosol forcing in the second half of the 20th century and early 21st century. These differences are as large as those obtained in different versions of an Earth System Model employing identical forcings. In simulations from 2015 to 2100, we find significant differences in the rates of projected global warming arising from CMIP5 and CMIP6 concentration pathways that differ slightly but are equivalent in terms of their nominal radiative forcing levels in 2100. Our results highlight the influence of assumptions about natural and anthropogenic aerosol loadings on carbon budgets, the likelihood of meeting Paris targets, and the equivalence of future forcing scenarios.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Validation of ablation model for polyethylene using pulsed x-ray and proton exposures

The surface erosion of polyethylene is interrogated using pulsed x rays at the Z Machine (Sandia National Laboratories) and with proton beams at the Gamble II generator (Naval Research Laboratory) to validate a coupled model for volumetric thermal ablation, photoionization, finite-rate decomposition, and molecular recombination of radicals. The intense radiation pulses (up to ∼1014W/m2 over tens of nanoseconds) are used to generate one-dimensional vapor flows with low ionization fractions and a simplified geometry compared to typical laser ablation, allowing for evaluation of the model under local thermal equilibrium conditions. Areal momentum carried by the ensuing uniaxial hydrodynamic shock is used to indicate the extent of ablation. The threshold fluence for ablation is found to be in close correspondence with the bulk melt transition, and reasonable agreement with the model is obtained for peak temperatures in polyethylene up to 5500 K and heating rates up to 1011K/s where thermal decomposition reactions are also active.

Moore, N. W. (ORCID:0000000272259674)↗

DOE OSTI2020

Little influence of Arctic amplification on mid-latitude climate

Observations and model simulations show enhanced warming in the Arctic under increasing greenhouse gases, a phenomenon known as the Arctic amplification (AA), that is likely caused by sea-ice loss. AA reduces meridional temperature gradients linked to circulation, thus mid-latitude weather and climate changes have been attributed to AA, often on the basis of regression analysis and atmospheric simulations. However, other modelling studies show only a weak link. This inconsistency may result from deficiencies in separating the effects of AA from those of natural variability or background warming. In this work, using coupled model simulations with and without AA, we show that cold-season precipitation, snowfall and circulation changes over northern mid-latitudes come mostly from background warming. AA and sea-ice loss increase precipitation and snowfall above ~60° N and reduce meridional temperature gradients above ~45° N in the lower–mid troposphere. However, minimal impact on the mean climate is seen below ~60° N, with weak reduction in zonal wind over 50°–70° N and 150–700 hPa, mainly over the North Atlantic and northern central Asia. These results suggest that the climatic impacts of AA are probably small outside the high latitudes, thus caution is needed in attributing mid-latitude changes to AA and sea-ice loss on the basis of statistical analyses that cannot distinguish the impact of AA from other correlated changes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

A proof of concept for matchete: an automated tool for matching effective theories

Abstract Studying the impact of new-physics models on low-energy observables necessitates matching to effective field theories at the relevant mass thresholds. We introduce the first public version of , a computer tool for matching weakly-coupled models at one-loop order. It uses functional methods to directly compute all matching contributions in a manifestly gauge-covariant manner, while simplification methods eliminate redundant operators from the output. We sketch the workings of the program and provide examples of how to match simple Standard Model extensions. The package, documentation, and example notebooks are publicly available at https://gitlab.com/matchete/matchete .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI1995

Nuclear Safety [Vol. 36, No. 2, July-December 1995]

Nuclear Safety is a journal that covers significant issues in the field of nuclear safety. Its primary scope is safety in the design, construction, operation, and decommissioning of nuclear power reactors worldwide and the research and analysis activities that promote this goal, but it also encompasses the safety aspects of the entire nuclear fuel cycle, including fuel fabrication, spent-fuel processing and handling, and nuclear waste disposal, the handling of fissionable materials and radioisotopes, and the environmental effects of all these activities. Table of Contents for this issue follows. THE CHORNOBYL ACCIDENT: 195 The Chornobyl Accident Revisited, Part III: Chernobyl Source Term Release Dynamics and Reconstruction of Events During the Active Phase, A. R. Sich; GENERAL SAFETY CONSIDERATIONS: 218 Second ANS Workshop on the Safety of Soviet-Designed Nuclear Power Plants, R. A. Bari; 234 Elements of a Nuclear Criticality Safety Program, C. M. Hopper; 243 Rickover, Excellence, and Criticality Safety Programs, R. E. Wilson; ACCIDENT ANALYSIS: 249 Transient Analysis of the PIUS Advanced Reactor Design with the TRAC-PF1/MOD2 Code, B. E. Boyack, J. L Steiner, S. C. Harmony, H. J. Stumpf, and J. F. Lime; 278 The Hierarchy-By-Interval Approach to Identifying Important Models that Need Improvement in Severe-Accident Simulation Codes, T. J. Heames, M. Khatib-Rahbar, J. E. Kelly, R. P. Jenks-Johnson, and Y.-S. Chen; 290 RELAP5/MOD3 Code Coupling Model, R. P. Martin; 299 Missiles Caused by Severe Pressurized-Water Reactor Accidents, R. Krieg; DESIGN FEATURES: 310 Validation of COMMIX with Westinghouse AP-600 PCCS Test Data, J. G. Sun, T. H. Chien, J. Ding, and W T. Sha; ENVIRONMENTAL EFFECTS: 321 Spent Nuclear Fuel Characterization for a Bounding Reference Assembly for the Receiving Basin for Off-Site Fuel, S. D. Kahook, R. L. Garrett, L. R. Canas, and M J. Beckum; OPERATING EXPERIENCES: 332 Reactor Shutdown Experience, Compiled by J. W. Cletcher; U.S. NUCLEAR REGULATORY COMMISSION INFORMATION AND ANALYSES: 335 Reactor Coolant System Blowdown at Wolf Creek on September 17, 1994, J. V. Kauffman and S. L. Israel; RECENT DEVELOPMENTS: 344 Reports, Standards, and Safety Guides, D. S. Oueener; 349 Proposed Rule Changes as of June 30, 1995; ANNOUNCEMENTS: 320 Symposium on Acceptability of Risk From Radiation—Application to Manned Space Flight; 320 24th DOE/NRC Nuclear Air Cleaning and Treatment Conference; 361 Radiation Biology and Radiation Protection— Modern Developments and Tendencies in Radiation Biology; 362 1997 IEEE Sixth Conference on Human Factors and Power Plants; 354 The Authors; 360 Reviewers of Nuclear Safety, Vol. 36.

05 NUCLEAR FUELS↗

DOE OSTI1995

Nuclear Safety [Vol. 36, No. 2, July-December 1995]

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

CMIP6-based Multi-model Streamflow Projections over the Conterminous US, Version 1.1

This dataset presents an ensemble of streamflow projections covering the conterminous United States (CONUS), developed to support the SECURE Water Act Section 9505 Assessment for the US Department of Energy (DOE) Water Power Technologies Office (WPTO). Multiple Coupled Models Intercomparison Project phase 6 (CMIP6) Global Climate Models (GCMs) were downscaled using either statistical (DBCCA) or dynamical (RegCM) downscaling methods, based on two meteorological reference datasets (Daymet and Livneh). Subsequently, the downscaled precipitation, temperature, and wind speed data were used to drive two calibrated hydrologic models (VIC and PRMS), with total runoff routed through the Routing Application for Parallel computatIon of Discharge (RAPID) routing model, producing an ensemble of streamflow projections across 2.7 million NHDPlusV2 stream reaches across the CONUS. Each ensemble member covers the 1980-2019 baseline and 2020-2059 near-future periods under the high-end (SSP585) emission scenario. Additionally, using only DBCCA and Daymet, the projections extend to the 2060-2099 far-future period and encompass three additional emission scenarios (SSP370, SSP245, and SSP126). This dataset is designed to support the SECURE Water Act Section 9505 Assessment for the US Department of Energy (DOE) Water Power Technologies Office (WPTO). For further details, refer to Kao et al. (2022), Rastogi et al. (2022), and Ghimire et al. (2023).

13 HYDRO ENERGY↗

DOE OSTI2020

Multiscale formulation of frictional contact mechanics at the pore scale

Direct numerical simulation (DNS) yields the highest fidelity predictions of mechanical deformation at the pore scale, but is prohibitively expensive for analyzing large or many samples. Discrete element methods (DEM) are an efficient alternative, but are limited to granular media and incapable of estimating or controlling prediction errors. We present a pore-level multiscale method (PLMM) that approximates DNS efficiently and with controllable accuracy. We focus on the linear elastic response of a consolidated geologic porous medium with arbitrary microstructure, heterogeneous mineralogy, containing cracks or defects. PLMM decomposes the solid phase into non-overlapping subdomains, on which local basis functions are constructed. The bases are then coupled with a global interface problem that accounts for slip or stick contact conditions between the subdomains. PLMM produces an initial, but accurate, approximation to DNS that can be iteratively improved. It is amenable to parallelism and allows for different mesh, models, and physics in each subdomain. An algebraic interpretation of PLMM as a preconditioner is also presented to allow non-intrusive implementation into existing solvers. Lastly, this work extends previous developments of PLMM in fluid dynamics to solid mechanics and enables future extensions towards modeling coupled flow and mechanics problems.

42 ENGINEERING↗

DOE OSTI2022

Dynamics of homogeneous cavitation with pressure feedback

Theoretical studies of homogeneous cavitation have largely been based on the classical nucleation theory. However, existing cavitation models cannot adequately describe its dynamics at nanosecond timescale, which has been called for in other fields. We develop a model coupling nucleation kinetics with cavity growth and pressure feedback as saturation mechanisms. Our numerical studies reveal the exponential dependence of cavitation characteristics such as saturation cavity density and most probable cavity radius on model parameters: Tolman length and initial pressure. This work also sheds light on the possibility of accurately determining Tolman length, whose value has a large spread in the literature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗