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DOE OSTI2022

Computational models of direct and indirect X‐ray breast imaging detectors for in silico trials

Abstract Background To facilitate in silico studies that investigate digital mammography (DM) and breast tomosynthesis (DBT), models replicating the variety in imaging performance of the DM and DBT systems, observed across manufacturers are needed. Purpose The main purpose of this work is to develop generic physics models for direct and indirect detector technology used in commercially available systems, with the goal of making them available open source to manufacturers to further tweak and develop the exact in silico replicas of their systems. Methods We recently reported on an in silico version of the SIEMENS Mammomat Inspiration DM/DBT system using an open‐source GPU‐accelerated Monte Carlo x‐ray imaging simulation code (MC‐GPU). We build on the previous version of the MC‐GPU codes to mimic the imaging performances of two other Food and Drug Administration (FDA)‐approved DM/DBT systems, such as Hologic Selenia Dimensions (HSD) and the General Electric Senographe Pristina (GSP) systems. In this work, we developed a hybrid technique to model the optical spread and signal crosstalk observed in the GSP and HSD systems. MC simulations are used to track each x‐ray photon till its first interaction within the x‐ray detector. On the other hand, the signal spread in the x‐ray detectors is modeled using previously developed analytical equations. This approach allows us to preserve the modeling accuracy offered by MC methods in the patient body, while speeding up secondary carrier transport (either electron–hole pairs or optical photons) using analytical equations in the detector. The analytical optical spread model for the indirect detector includes the depth‐dependent spread and collection of optical photons and relies on a pre‐computed set of point response functions that describe the optical spread as a function of depth. To understand the capabilities of the computational x‐ray detector models, we compared image quality metrics like modulation transfer function (MTF), normalized noise power spectrum (NNPS), and detective quantum efficiency (DQE), simulated with our models against measured data. Please note that the purpose of these comparisons with measured data would be to gauge if the model developed as part of this work could replicate commercially used direct and indirect technology in general and not to achieve perfect fits with measured data. Results We found that the simulated image quality metrics such as MTF, NNPS, and DQE were in reasonable agreement with experimental data. To demonstrate the imaging performance of the three DM/DBT systems, we integrated the detector models with the VICTRE pipeline and simulated DM images of a fatty breast model containing a spiculated mass and a calcium oxalate cluster. In general, we found that the images generated using the indirect model appeared more blurred with a different noise texture and contrast as compared to the systems with direct detectors. Conclusions We have presented computational models of three commercially available FDA‐approved DM/DBT systems, which implement both direct and indirect detector technology. The updated versions of the MC‐GPU codes that can be used to replicate three systems are available in open source format through GitHub.

Sengupta, Aunnasha↗

DOE OSTI2023

Methodology to Generate the Decay Gamma Source for a Second Target Station Target Wedge

This report details the specifics of applying the Position-Averaged Method methodology for the calculation of the rotating lasagna-style target wedge activation and the resulting decay gamma source terms. The methodology uses MCNP® Code Version 6.2.0 with the RNUCS patch coupled with CINDER2008 from the AARE V1.0 package. The process begins with model preparations that include ensuring impurities are included in the materials in the regions of interest along with segmentation of the geometry in order to capture the decay gamma source gradients. This report also details the physics models and other MCNP®, CINDER2008, and ADVANTG 3.2.0 related options used to calculate the decay gamma source terms. ADVANTG 3.2.0 is used to generate a weight window set to aid in convergence of the neutron fluxes in the initial MCNP® protons-on-target particle transport calculation to calculate the neutron fluxes and spallation products in the regions of interest. The neutron fluxes and spallation products are then used in the CINDER2008 transmutation calculation, and the decay gamma sources are generated by the AARE_GAMMA_SOURCE_SCRIPT as a part of the AARE V1.0 package. These decay gamma sources include the energy distributions as well as the necessary distributions to sample the location of the source using the cell rejection method. The gamma sources that are produced using the methodology may be used for a wide variety of analysis involving the target wedge. This report includes the material specifications, physics options, proton source term description, geometrical configuration, and post-processing details.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS2001

Simulation of Supersonic Jet Noise with the Adaptation of Overflow CFD Code and Kirchhoff Surface Integral

An acoustic prediction capability for supersonic axisymmetric jets was developed on the basis of OVERFLOW Navier-Stokes CFD (Computational Fluid Dynamics) code of NASA Langley Research Center. Reynolds-averaged turbulent stresses in the flow field are modeled with the aid of Spalart-Allmaras one-equation turbulence model. Appropriate acoustic and outflow boundary conditions were implemented to compute time-dependent acoustic pressure in the nonlinear source-field. Based on the specification of acoustic pressure, its temporal and normal derivatives on the Kirchhoff surface, the near-field and the far-field sound pressure levels are computed via Kirchhoff surface integral, with the Kirchhoff surface chosen to enclose the nonlinear sound source region described by the CFD code. The methods are validated by a comparison of the predictions of sound pressure levels with the available data for an axisymmetric turbulent supersonic (Mach 2) perfectly expanded jet.

Kandula, Max↗

NASA NTRS2002

Simulation of Jet Noise with OVERFLOW CFD Code and Kirchhoff Surface Integral

Kandula, M.↗

DOE OSTI2025

Logical error rates for the surface code under a mixed coherent and stochastic circuit-level noise model inspired by trapped ions

With fault-tolerant quantum computing (FTQC) on the horizon, it is critical to understand sources of logical errors in plausible hardware implementations of quantum error-correcting codes. Detailed error modeling of computational instructions on particular FTQC architectures will enable the better prediction of error propagation in FT-encoded quantum circuits while revealing where greater attention is needed in hardware design. In this work, we consider logical error rates for the surface code implemented on a hypothetical grid-based trapped-ion quantum charge-coupled device architecture. Specifically, we construct logical channels for the idling surface code and examine its diamond error under a mixed coherent and stochastic circuit-level noise model inspired by trapped ions. We include the coherent dephasing noise that is known to accumulate during physical qubit idling and transport in these systems, determining idling and transport durations using the time-resolved output of an open-source trapped-ion surface code compiler. To estimate expectation values of logical Pauli observables following hardware circuits containing non-Clifford sources of noise, we utilize a Monte Carlo technique to sample from an underlying quasiprobability distribution of Clifford circuits that we independently simulate in a phase-sensitive fashion. We verify error suppression up to code distance 𝑑 = 11 at coherent dephasing rates near and below those of current-generation trapped-ion quantum computers and find that logical error rates align with those of analogous fully stochastic simulations in this regime. Exploring higher dephasing rates at 𝑑 = 3−5, we find evidence for growing coherent rotations about all three logical Pauli axes, increased diagonal logical error process matrix elements relative to those of stochastic simulations, and a reduced dephasing rate threshold. Overall, our work paves a way toward realistic hardware emulation of small fault-tolerant quantum processes, e.g., members of an FTQC instruction set.

Quantum benchmarking↗

DOE OSTI2015

User's Guide for RESRAD-OFFSITE

The RESRAD-OFFSITE code can be used to model the radiological dose or risk to an offsite receptor. This User’s Guide for RESRAD-OFFSITE Version 3.1 is an update of the User’s Guide for RESRAD-OFFSITE Version 2 contained in the Appendix A of the User’s Manual for RESRAD-OFFSITE Version 2 (ANL/EVS/TM/07-1, DOE/HS-0005, NUREG/CR-6937). This user’s guide presents the basic information necessary to use Version 3.1 of the code. It also points to the help file and other documents that provide more detailed information about the inputs, the input forms and features/tools in the code; two of the features (overriding the source term and computing area factors) are discussed in the appendices to this guide. Section 2 describes how to download and install the code and then verify the installation of the code. Section 3 shows ways to navigate through the input screens to simulate various exposure scenarios and to view the results in graphics and text reports. Section 4 has screen shots of each input form in the code and provides basic information about each parameter to increase the user’s understanding of the code. Section 5 outlines the contents of all the text reports and the graphical output. It also describes the commands in the two output viewers. Section 6 deals with the probabilistic and sensitivity analysis tools available in the code. Section 7 details the various ways of obtaining help in the code.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2026

Exploring Sustainability in Scientific Software through Code Quality & Test Coverage Metrics

Context: Scientific open-source software (SciOSS) plays a foundational role in research and engineering, yet its long-term sustainability has often been overlooked and remains a significant concern. Objective: This study investigates the long-term sustainability of SciOSS through code and test quality metrics. Method: We analyze CASS Software Portfolio projects, classifying them by sustainability and comparing their code structure, test coverage, and links between code quality and testing across the dataset. Results: Sustainable projects show higher, more consistent test coverage and clearer code-test correlations, while unsustainable ones show weaker patterns. Overall, test coverage is low in scientific software, and high complexity and coupling reduce testability. Conclusion: In this study, we present a practical, data-driven approach for assessing sustainability in scientific software, offering a foundation for evaluating long-term software health and supporting future efforts in quality assurance and sustainability monitoring.

Md mushfiqur rahman, Sheikh [University of Tenness↗

DOE OSTI2016

Balmer-α spectrum measurements of the LHD one-third ion source

Wavelength spectra of Balmer-α light from plasmas in the extraction region of the Large Helical Device-R&D negative ion source, or the LHD one-third ion source have exhibited a blue shift as a negative bias voltage was applied to the plasma grid. The blue shift increased as the negative bias voltage with respect to the local plasma potential was increased. The measured spectra were compared with the velocity distributions of surface reflected hydrogen atoms calculated by atomic collisions in amorphous target code. The arc power and the source H{sub 2} pressure also affected the shift and broadening in the observed Balmer-α spectra. The possibility of identifying the negative hydrogen ions produced at the low work function plasma grid surface by high resolution spectroscopy is discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2015

SU-E-T-462: Impact of the Radiochromic Film Energy Response On Dose Measurements of Low Energy Electronic Brachytherapy Sources

Purpose: We investigated the effect of the EBT3 GafChromicTM film model absorbed dose energy response when used for percent depth dose (PDD) measurements in low-energy photon beams. Methods: We measured PDDs in water from a Xoft 50 kVp source using EBT3 film, and compared them to PDD measurements acquired with a PTW-TN34013 parallel-plate ionization chamber. For the x-ray source, we simulated spectra using the EGSnrc (BEAMnrc) Monte Carlo code, and calculated Half Value Layer (HVL) at different distances from the source in water. Pieces of EBT3 film were irradiated in air and calibration curves were created in terms of air-kerma in air ((Kair)air) for different beam qualities. Pieces of EBT3 film were positioned at distances of 2–6 cm from the Xoft source in a water phantom using a custom-made holder, and irradiated at the same time. As scatter is incorporated in the measured film signal in water, measured (Kair)wat was subsequently converted into absorbed dose to water by the ratio of mass energy absorption coefficients following the AAPM TG-61 dosimetry protocol. Results: Our results show that film calibration curves obtained at beam qualities near the effective energy of the Xoft 50 kVp source in water lead to variation in absorbed dose energy dependence of the response of around 3%. However, if the calibration curve was established at MV beam quality, the error in absorbed dose could be as large as 15%. We observed agreement within 1% between PDD measurements using EBT3 film model (using a calibration curve obtained at 80 kVp, HVL=2.18 mm Al, Eeff=29.5 keV) and the parallel-plate ionization chamber. Conclusion: Accurate dose measurements using radiochromic films at low photon energies require that the radiochromic film dosimetry system be calibrated at corresponding low energies, as large absorbed dose errors are expected for calibrations performed at MV beam qualities.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2024

SCALE 6.3 Modeling Strategies for Reactivity, Nuclide Inventory, and Decay Heat of Non-LWRs

To assess modeling and simulation capabilities for thermal hydraulics, accident progression, source term, and consequence analysis for non–light-water reactor (LWR) technologies, the US Nuclear Regulatory Commission (NRC) initiated a collaborative project between Oak Ridge National Laboratory (ORNL) and Sandia National Laboratories (SNL) in FY20, which is detailed in “Volume 3: Computer Code Development Plans for Severe Accident Progression, Source Term, and Consequence Analysis.” This project demonstrated the capabilities of the MELCOR and SCALE codes to calculate accident scenarios during operation of relevant non-LWRs. The following five non-LWR concepts were selected for capability demonstration based on recently renewed industry interest in the United States to develop and deploy such reactor technologies: pebble-bed high temperature gas-cooled reactors (HTGRs), pebble-bed fluoride salt-cooled reactors (FHRs), molten salt–fueled reactors (MSRs), heat pipe reactors (HPRs), and sodium-cooled fast reactors (SFRs).

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Tree-based solvers for adaptive mesh refinement code FLASH – III: a novel scheme for radiation pressure on dust and gas and radiative transfer from diffuse sources

Radiation is an important contributor to the energetics of the interstellar medium, yet its transport is difficult to solve numerically. We present a novel approach towards solving radiative transfer of diffuse sources via backwards ray tracing. Here, we focus on the radiative transfer of infrared radiation and the radiation pressure on dust. The new module, TREERAY/RADPRESSURE, is an extension to the novel radiative transfer method TREERAY implemented in the grid-based Magneto-Hydrodynamics code FLASH. In TREERAY/RADPRESSURE, every cell and every star particle is a source of infrared radiation. We also describe how gas, dust, and radiation are coupled via a chemical network. This allows us to compute the local dust temperature in thermal equilibrium, leading to a significantly improvement over the classical grey approximation. In several tests, we demonstrate that the scheme produces the correct radiative intensities as well as the correct momentum input by radiation pressure. Subsequently, we apply our new scheme to model massive star formation from a collapsing, turbulent core of 150 M ⊙ . We include the effects of both, ionizing and infrared radiation on the dynamics of the core. We find that the newborn massive star prevents fragmentation in its proximity due to radiative heating. Over time, dust and radiation temperature equalize, while the gas temperature can be either warmer due to shock heating or colder due to insufficient dust–gas coupling. Compared to gravity, the effects of radiation pressure are insignificant for the stellar mass on the simulated time-scale in this work.

(ISM:) HII regions↗

DOE OSTI2014

SU-E-T-240: Monte Carlo Modelling of SMC Proton Nozzles Using TOPAS

Purpose: To simulate the 60Co beam from a novel Gamma—Tomo SBRT system and to calculate the output factors and dose rates for different source configurations and collimator sizes. Methods: The BEAM-Monte Carlo code is used to realistically model the system geometry, including 32 source capsules, source housing, primary collimator and 4 different changeable collimators. The sources (6.22 mm of diameter) are located in 2 rows with different angles and distances to the longitudinal axis and the beams can be collimated to obtain four different circular field sizes at the isocenter (35 mm, 16 mm, 7mm, and 3.5mm). Since the dose distributions will be determined in a spherical polystyrene phantom of 8cm radius centered at the isocenter, a new geometry module is designed for the dose calculation. Results: : The caracteristics of the particle spectra emerging from each source are determined and the influence of the source position on the spectra reaching the isocenter is found to be minimal (<2%). We found that the scattered photons represent about 15% of the total number of photons reaching the scoring plane immediately (1 mm) below the source and primary collimator. The radial photon fluence does not vary significantly inside the collimator opening and decreases quickly beyond the 3cm radius (projected at the isocenter plane). Conclusion: Our preliminary results indicate that the position of the source and primary collimator assembly does not affect the energy spectra and fluence distributions reaching the isocenter significantly. This allows the use of a well-represented source model for all the sources to perform the dose calculations for all the changeable collimators for this novel Gamma-Tomo SBRT system.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1993

Estimating the size of Huffman code preambles

Data compression via block-adaptive Huffman coding is considered. The compressor consecutively processes blocks of N data symbols, estimates source statistics by computing the relative frequencies of each source symbol in the block, and then synthesizes a Huffman code based on these estimates. In order to let the decompressor know which Huffman code is being used, the compressor must begin the transmission of each compressed block with a short preamble or header file. This file is an encoding of the list n = (n(sub 1), n(sub 2)....,n(sub m)), where n(sub i) is the length of the Hufffman codeword associated with the ith source symbol. A simple method of doing this encoding is to individually encode each n(sub i) into a fixed-length binary word of length log(sub 2)l, where l is an a priori upper bound on the codeword length. This method produces a maximum preamble length of mlog(sub 2)l bits. The object is to show that, in most cases, no substantially shorter header of any kind is possible.

Mceliece, R. J.↗

DOE OSTI2020

Survey and Assessment of Computational Capabilities for Advanced (Non-LWR) Reactor Mechanistic Source Term Analysis.

A vital part of the licensing process for advanced (non-LWR) nuclear reactor developers in the United States is the assessment of the reactor’s source term, i.e., the potential release of radionuclides from the reactor system to the environment during normal operations and accident sequences. In comparison to source term assessments which follow a bounding approach with conservative assumptions, a mechanistic approach to modeling radionuclide transport, which realistically accounts for transport and retention phenomena, is expected to be used for advanced reactor systems. As the designs of advanced reactors increase in maturity and progress towards licensing, there is a need to advance modeling and simulation capabilities in analyzing the mechanistic source term (MST) of a prospective reactor concept. In the present work, a survey is provided of existing computational capabilities for the modeling of advanced reactors MSTs. The following reactors are considered: high temperature gas reactors (HTGR); molten salt reactors (MSR) which include salt-fueled reactors and fluoride salt-cooled high temperature reactors (FHR); and sodium- and lead-cooled fast reactors (SFR, LFR). A review of relevant codes which may be useful in providing information to MST analyses is also completed, including codes that have been used for source term analyses of LWRs, as well as those being developed for other aspects of advanced reactor system modeling such as reactor physics, thermal hydraulics, and chemistry. A discussion of MST modeling capabilities for each reactor type is provided with additional focus on important phenomena and functional requirements. Additionally, a comprehensive survey is provided of tools for consequence modeling such as atmospheric transport and dispersion (ATD).

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2018

Steady-State Thermal-Hydraulic Analysis and Bowing Reactivity Evaluation Methods Based on Neutron and Gamma Transport Calculations

With the advancement of computer technology, the variational nodal transport code VARIANT is now routinely used for sodium-cooled fast reactor (SFR) design analysis. In particular, VARIANT transport calculations are usually performed for whole core neutronics analyses and for fuel cycle analyses with REBUS-3. However, the steady-state thermal hydraulics analysis with the SE2-ANL coed and the assembly bowing reactivity calculation with the structural analysis with the NUBOW-3D code are still performed with the DIF3D finite difference diffusion theory code. Furthermore, the DIF3D diffusion calculation for these applications is performed with only six triangular meshes per hexagonal assembly, and the SE2-ANL code determines the pin power distributions approximately by assuming that the power distribution within an assembly is separable in the radial and axial directions. In order to overcome the limitations and to improve the accuracy of the existing methods, it was proposed to develop the relevant computational methods based on the transport calculations with the VARIANT and PROTEUS-SN codes. The objectives of this study are to develop a new heating calculation method based on the coupled neutron and gamma transport calculations with VARIANT, to implement the new heating calculation method into the SE2-ANL steady-state thermal-hydraulics analysis code with improved numerical algorithms and additional capabilities for automatic flow allocation calculations, and to develop a method to calculate bowing reactivity coefficients based on the VARIANT core solutions and the PROTEUS-SN assembly solutions, which can be used in NUBOW-3D calculations. A new, coupled neutron and gamma heating calculation procedure has been developed based on VARIANT transport calculations. In the new heating calculation procedure, the neutron flux distribution is first determined by solving an eigenvalue transport problem using the VARIANT transport code. Using the calculated neutron flux, the intra-nodal gamma source distributions are calculated to be consistent with the neutron flux distribution with the GAMSOR code. For this, the GAMSOR code has been updated to generate the intra-nodal gamma source distributions in the form of the VARSRC dataset of VARIANT. With this gamma source distribution, the gamma flux distribution is determined by solving a fixed source gamma transport problem using VARIANT again. With the neutron and gamma flux distributions, the heat generation rates are evaluated at individual fuel pins and assembly duct walls, without assuming separable axial and radial profiles for the intra-assembly power distribution.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1983

Some practical universal noiseless coding techniques, part 2

This report is an extension of earlier work (Part 1) which provided practical adaptive techniques for the efficient noiseless coding of a broad class of data sources characterized by only partially known and varying statistics (JPL Publication 79-22). The results here, while still claiming such general applicability, focus primarily on the noiseless coding of image data. A fairly complete and self-contained treatment is provided. Particular emphasis is given to the requirements of the forthcoming Voyager II encounters of Uranus and Neptune. Performance evaluations are supported both graphically and pictorially. Expanded definitions of the algorithms in Part 1 yield a computationally improved set of options for applications requiring efficient performance at entropies above 4 bits/sample. These expanded definitions include as an important subset, a somewhat less efficient but extremely simple "FAST' compressor which will be used at the Voyager Uranus encounter. Additionally, options are provided which enhance performance when atypical data spikes may be present.

Rice, R. F.↗

NASA NTRS2011

Soft-Decision-Data Reshuffle to Mitigate Pulsed Radio Frequency Interference Impact on Low-Density-Parity-Check Code Performance

This presentation briefly discusses a research effort on mitigation techniques of pulsed radio frequency interference (RFI) on a Low-Density-Parity-Check (LDPC) code. This problem is of considerable interest in the context of providing reliable communications to the space vehicle which might suffer severe degradation due to pulsed RFI sources such as large radars. The LDPC code is one of modern forward-error-correction (FEC) codes which have the decoding performance to approach the Shannon Limit. The LDPC code studied here is the AR4JA (2048, 1024) code recommended by the Consultative Committee for Space Data Systems (CCSDS) and it has been chosen for some spacecraft design. Even though this code is designed as a powerful FEC code in the additive white Gaussian noise channel, simulation data and test results show that the performance of this LDPC decoder is severely degraded when exposed to the pulsed RFI specified in the spacecraft s transponder specifications. An analysis work (through modeling and simulation) has been conducted to evaluate the impact of the pulsed RFI and a few implemental techniques have been investigated to mitigate the pulsed RFI impact by reshuffling the soft-decision-data available at the input of the LDPC decoder. The simulation results show that the LDPC decoding performance of codeword error rate (CWER) under pulsed RFI can be improved up to four orders of magnitude through a simple soft-decision-data reshuffle scheme. This study reveals that an error floor of LDPC decoding performance appears around CWER=1E-4 when the proposed technique is applied to mitigate the pulsed RFI impact. The mechanism causing this error floor remains unknown, further investigation is necessary.

Ni, Jianjun David↗

DOE OSTI2018

The multi-assumption architecture and testbed (MAAT v1.0): R code for generating ensembles with dynamic model structure and analysis of epistemic uncertainty from multiple sources

Abstract. Here, computer models are ubiquitous tools used to represent systems across many scientific and engineering domains. For any given system, many computer models exist, each built on different assumptions and demonstrating variability in the ways in which these systems can be represented. This variability is known as epistemic uncertainty, i.e. uncertainty in our knowledge of how these systems operate. Two primary sources of epistemic uncertainty are (1) uncertain parameter values and (2) uncertain mathematical representations of the processes that comprise the system. Many formal methods exist to analyse parameter-based epistemic uncertainty, while process-representation-based epistemic uncertainty is often analysed post hoc, incompletely, informally, or is ignored. In this model description paper we present the multi-assumption architecture and testbed (MAAT v1.0) designed to formally and completely analyse process-representation-based epistemic uncertainty. MAAT is a modular modelling code that can simply and efficiently vary model structure (process representation), allowing for the generation and running of large model ensembles that vary in process representation, parameters, parameter values, and environmental conditions during a single execution of the code. MAAT v1.0 approaches epistemic uncertainty through sensitivity analysis, assigning variability in model output to processes (process representation and parameters) or to individual parameters. In this model description paper we describe MAAT and, by using a simple groundwater model example, verify that the sensitivity analysis algorithms have been correctly implemented. The main system model currently coded in MAAT is a unified, leaf-scale enzyme kinetic model of C 3 photosynthesis. In the Appendix we describe the photosynthesis model and the unification of multiple representations of photosynthetic processes. The numerical solution to leaf-scale photosynthesis is verified and examples of process variability in temperature response functions are provided. For rapid application to new systems, the MAAT algorithms for efficient variation of model structure and sensitivity analysis are agnostic of the specific system model employed. Therefore MAAT provides a tool for the development of novel or toy models in many domains, i.e. not only photosynthesis, facilitating rapid informal and formal comparison of alternative modelling approaches.

54 ENVIRONMENTAL SCIENCES↗