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All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Path Integral Formulation of Fractionally Perturbed Lagrangian Oscillators on Fractal

Fractional path integration and particles trajectories in fractional dimensional space are motivating issues in quantum mechanics and kinetics. In this paper, a fractional path integral characterized by a fractional propagator is developed based on the framework of the fractional action-like variational approach. A fractional generalization of the free particle problem is found, the corresponding fractional Schrödinger equation is derived and a fractional path integral formulation of harmonic oscillators characterized by a perturbed Lagrangian is constructed after reducing the fractional action to an integral action on fractal. The new fractal-like path integral offers a number of motivating features which are discussed and analyzed. The main outcome is connected to the possibility of constructing on a fractal a path integral for the oscillators characterized by modified ground energy. In particular for low-temperature case, the fractional perturbed oscillator is characterized by a free energy larger than the standard value E{sub 0}=ħω/2. Such an increase in the ground energy generalizes the uncertainty principle without involving differentiable paths or even invoking new phenomenological theories based on deformed algebra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Functional integrals and inequivalent representations in Quantum Field Theory

We discuss canonical transformations in Quantum Field Theory in the framework of the functional-integral approach. In contrast with ordinary Quantum Mechanics, canonical transformations in Quantum Field Theory are mathematically more subtle due to the existence of unitarily inequivalent representations of canonical commutation relations. When one works with functional integrals, it is not immediately clear how this algebraic feature manifests itself in the formalism. Here we attack this issue by considering the canonical transformations in the context of coherent-state functional integrals. Specifically, in the case of linear canonical transformations, we derive the general functional-integral representations for both transition amplitude and partition function phrased in terms of new canonical variables. By means of this, we show how in the infinite-volume limit the canonical transformations induce a transition from one representation of canonical commutation relations to another one and under what conditions the representations are unitarily inequivalent. We also consider the partition function and derive the energy gap between statistical systems described in two different representations which, among others, allows to establish a connection with continuous phase transitions. We illustrate the inner workings of the outlined mechanism by discussing two prototypical systems: the van Hove model and the Bogoliubov model of weakly interacting Bose gas. - Highlights: • Functional integrals are sensitive to representations of the Heisenberg–Weyl algebra. • Inequivalent representations can be exhibited in the functional integral formalism. • Passage among inequivalent representations is seen as second-order phase transition. • The inequivalence of representations is physically marked by an infinite energy gap.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Optimization of energy requirements for CO 2 post-combustion capture process through advanced thermal integration

The energy optimization modeling work described here was performed to determine efficiency improvements that could be achieved for existing coal-fired power plants to retrofit a partial CO 2 capture from the post-combustion flue gas for carbon sequestration through thermal integration. The work presented includes optimization of the mono-ethanol amine (MEA)-based post-combustion CO 2 capture to reduce energy requirements that could be achieved at existing power plants by thermal integration of the steam turbine cycle, boiler, CO 2 compression train and post-combustion CO 2 capture process to offset efficiency and capacity losses that would be incurred by retrofit or implementation of post-combustion CO 2 capture. Furthermore, partial CO 2 capture, involving treatment of less than 100% of the flue gas leaving the plant and modular design of the CO 2 scrubbing system, was also investigated. Thermal integration of the steam turbine cycle with boiler and CO 2 compression train improved cycle and plant performance and offset, in part, the negative effects of post-combustion CO 2 capture. The best-analyzed integration options improved gross power output by 5% and net unit efficiency by 1.57%, relative to the conventional MEA process. Operating with 40% CO 2 capture increased gross power output by 11.6–14% (depending on the MEA thermal integration option), relative to the conventional MEA integration and 90% CO 2 capture. The improvement in net unit performance is larger compared to the improvement in turbine cycle performance because of the CO 2 compression work, which is also reduced by partial CO 2 capture.

42 ENGINEERING↗
DOE OSTI2018

Optimal feed flow sequence for multi-effect distillation system integrated with supercritical carbon dioxide Brayton cycle for seawater desalination

Multi-effect distillation is often integrated with a Rankine power cycle for cogeneration (simultaneous production of power and desalinated water). Such integration increases the condenser operating pressure for the Rankine cycle (and increases the heat-rejection temperature) to produce desalinated water, resulting in decreased power-plant efficiency. The supercritical carbon dioxide Brayton cycle has a higher efficiency compared to the Rankine cycle. The waste heat rejected from supercritical carbon dioxide Brayton cycle is at sufficiently hot temperature to have feasible energy integration with multi-effect distillation system. The paper introduces the novel concept of cogeneration without being a parasitic load to the power cycle. For the illustrative example considered, integrating 4-effect distillation system with a 115 MWe power plant can produce 3041 m3 of distillate per day at 1.06 $/m3, at a constant power plant efficiency of 49.2%. The pattern in which feed enters the desalination system often dictates its energy consumption. The two most commonly used feed configurations for multi-effect distillation system are parallel/cross feed and forward feed. With steam as a heat source (i.e., a latent heat source), parallel/cross feed is the most energy-efficient feed configuration. The other objective of this paper is to identify the optimal feed flow configuration for multi-effect distillation system integrated with a supercritical carbon dioxide power cycle (i.e., a sensible heat source). For the simplified network, forward feed is the best feed configuration, which yields a 7.5% increase in distillate production at 2.6% reduced distillate cost. Additionally, different methods for reducing the brine discharge are studied, which can help to achieve zero liquid discharge. Result show increasing the maximum brine concentration gives superior results compared to brine recycling. The system modelling is done using the principle of process integration, and an analytical methodology for cogeneration is derived.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2016

On the performance of exponential integrators for problems in magnetohydrodynamics

Exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations. Over the past decades these methods have been studied theoretically and their performance was evaluated using a range of test problems. While the results of these investigations showed that exponential integrators can provide significant computational savings, the research on validating this hypothesis for large scale systems and understanding what classes of problems can particularly benefit from the use of the new techniques is in its initial stages. Resistive magnetohydrodynamic (MHD) modeling is widely used in studying large scale behavior of laboratory and astrophysical plasmas. In many problems numerical solution of MHD equations is a challenging task due to the temporal stiffness of this system in the parameter regimes of interest. In this paper we evaluate the performance of exponential integrators on large MHD problems and compare them to a state-of-the-art implicit time integrator. Both the variable and constant time step exponential methods of EPIRK-type are used to simulate magnetic reconnection and the Kevin–Helmholtz instability in plasma. Performance of these methods, which are part of the EPIC software package, is compared to the variable time step variable order BDF scheme included in the CVODE (part of SUNDIALS) library. We study performance of the methods on parallel architectures and with respect to magnitudes of important parameters such as Reynolds, Lundquist, and Prandtl numbers. We find that the exponential integrators provide superior or equal performance in most circumstances and conclude that further development of exponential methods for MHD problems is warranted and can lead to significant computational advantages for large scale stiff systems of differential equations such as MHD.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A landing pad system for multicopy gene integration in Issatchenkia orientalis

The robust nature of the non-conventional yeast Issatchenkia orientalis allows it to grow under highly acidic conditions and therefore, has gained increasing interest in producing organic acids using a variety of carbon sources. Recently, the development of a genetic toolbox for I. orientalis, including an episomal plasmid, characterization of multiple promoters and terminators, and CRISPR-Cas9 tools, has eased the metabolic engineering efforts in I. orientalis. However, multiplex engineering is still hampered by the lack of efficient multicopy integration tools. To facilitate the construction of large, complex metabolic pathways by multiplex CRISPR-Cas9-mediated genome editing, we developed a bioinformatics pipeline to identify and prioritize genome-wide intergenic loci and characterized 47 gRNAs located in 21 intergenic regions. These loci are screened for guide RNA cutting efficiency, integration efficiency of a gene cassette, the resulting cellular fitness, and GFP expression level. We further developed a landing pad system using components from these well-characterized loci, which can aid in the integration of multiple genes using single guide RNA and multiple repair templates of the user’s choice. We have demonstrated the use of the landing pad for simultaneous integrations of 2, 3, 4, or 5 genes to the target loci with efficiencies greater than 80%. As a proof of concept, we showed how the production of 5-aminolevulinic acid can be improved by integrating five copies of genes at multiple sites in one step. We have further demonstrated the efficiency of this tool by constructing a metabolic pathway for succinic acid production by integrating five gene expression cassettes using a single guide RNA along with five different repair templates, leading to the production of 9 g/L of succinic acid in batch fermentations. Furthermore, this study demonstrates the effectiveness of a single gRNA-mediated CRISPR platform to build complex metabolic pathways in a non-conventional yeast. This landing pad system will be a valuable tool for the metabolic engineering of I. orientalis.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

A Multicomponent Reactive Transport Model for Integrated Surface‐Subsurface Hydrology Problems

Abstract Despite the widespread use of integrated hydrology models in a variety of applications, consideration of multicomponent reactive transport is still not common. The implementation of these processes requires coupling transport at the surface‐subsurface interface and efficient solution of the non‐linear geochemical model that is consistent with the integrated hydrology solution. The Advanced Terrestrial Simulator provides a flexible multiphysics framework that facilitated this process. In this work, the integrated reactive transport process kernel (PK) was weakly coupled to the integrated hydrology PK. In turn, integrated transport and reactions were coupled using an operator splitting approach. This splitting enabled an explicit solution of the integrated transport problem, including a novel algorithm to calculate exchange fluxes across the surface‐subsurface interface and a point‐by‐point solution of the geochemical problem. Geochemical capabilities were added using well‐established external codes, but rather than using a custom interface to each, a generic interface was used that clearly specifies the variables and operations used by the chemistry PK. The implementation is demonstrated with two example simulations: transport of a tracer in a soil column as it saturates over time and water ponds on the surface and reactive transport in a hillslope driven by successive wet‐dry cycles that result in infiltration, runoff and exfiltration processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Photonic circuits for laser stabilization with integrated ultra-high Q and Brillouin laser resonators

The integration of stabilized lasers, sources that generate spectrally pure light, will provide compact, low-cost solutions for applications including quantum information sciences, precision navigation and timing, metrology, and high-capacity fiber communications. We report a significant advancement in this field, demonstrating stabilization of an integrated waveguide Brillouin laser to an integrated waveguide reference cavity, where both resonators are fabricated using the same CMOS-compatible integration platform. We demonstrate reduction of the free running Brillouin laser linewidth to a 292 Hz integral linewidth and carrier stabilization to a 4.9 × 10 –13 fractional frequency at 8 ms reaching the cavity-intrinsic thermorefractive noise limit for frequencies down to 80 Hz. We achieve this level of performance using a pair of 56.4 x 10 6 quality factor Si 3 N 4 waveguide ring-resonators that reduce the high-frequency noise by the nonlinear Brillouin process and the low-frequency noise by Pound–Drever–Hall locking to the ultra-low loss resonator. These results represent an important step toward integrated stabilized lasers with reduced sensitivity to environmental disturbances for atomic, molecular, and optical physics (AMO), quantum information processing and sensing, and other precision scientific, sensing, and communications applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Integration of the Full Tokamak Reference Model with the Complex Model for ITER Neutronic Analysis

The ITER International Organization has developed a number of reference Monte Carlo N-Particle (MCNP) models including the tokamak machine C-model, the Tokamak Complex model, and the neutral beam injection (NBI) systems model. The Tokamak Complex model primarily describes building structures beyond the bioshield. Representation of the tokamak and its systems are not included in this model. The Oak Ridge National Laboratory Radiation Transport Group has conducted two ITER neutronic analysis model integrations: (1) integration of the tokamak C-model with the Tokamak Complex model for shutdown dose rate characterization in Port Cell 16 at level B1, and (2) integration of the NBI model with the Tokamak Complex model for estimating the spatial distribution of biological dose rate at levels L1, L2, and L3 of the Tokamak Complex. The integrated models were further extended to include models of system components that are essential to the neutronic analyses. Furthermore, this paper presents the approach and computer tools used to integrate existing reference models, describes the additional design details implemented in the integrated models, and provides representative neutronic calculations based on the extended models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Advanced time integration algorithms for dislocation dynamics simulations of work hardening

Efficient time integration is a necessity for dislocation dynamics simulations of work hardening to achieve experimentally relevant strains. In this work, an efficient time integration scheme using a high order explicit method with time step subcycling and a newly-developed collision detection algorithm are evaluated. First, time integrator performance is examined for an annihilating Frank–Read source, showing the effects of dislocation line collision. The integrator with subcycling is found to significantly out-perform other integration schemes. The performance of the time integration and collision detection algorithms is then tested in a work hardening simulation. The new algorithms show a 100-fold speed-up relative to traditional schemes. As a result, subcycling is shown to improve efficiency significantly while maintaining an accurate solution, and the new collision algorithm allows an arbitrarily large time step size without missing collisions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Integrals of motion for one-dimensional Anderson localized systems

Anderson localization is known to be inevitable in one-dimension for generic disordered models. Since localization leads to Poissonian energy level statistics, we ask if localized systems possess ‘additional’ integrals of motion as well, so as to enhance the analogy with quantum integrable systems. Weanswer this in the affirmative in the present work. We construct a set of nontrivial integrals of motion for Anderson localized models, in terms of the original creation and annihilation operators. These are found as a power series in the hopping parameter. The recently found Type-1 Hamiltonians, which are known to be quantum integrable in a precise sense, motivate our construction.Wenote that these models can be viewed as disordered electron models with infinite-range hopping, where a similar series truncates at the linear order.Weshow that despite the infinite range hopping, all states but one are localized.Wealso study the conservation laws for the disorder free Aubry–Andre model, where the states are either localized or extended, depending on the strength of a coupling constant.Weformulate a specific procedure for averaging over disorder, in order to examine the convergence of the power series. Using this procedure in the Aubry–Andre model, we show that integrals of motion given by our construction are well-defined in localized phase, but not so in the extended phase. Lastly, we also obtain the integrals of motion for a model with interactions to lowest order in the interaction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

BraggNet: integrating Bragg peaks using neural networks

Neutron crystallography offers enormous potential to complement structures from X-ray crystallography by clarifying the positions of low-Z elements, namely hydrogen. Macromolecular neutron crystallography, however, remains limited, in part owing to the challenge of integrating peak shapes from pulsed-source experiments. To advance existing software, this article demonstrates the use of machine learning to refine peak locations, predict peak shapes and yield more accurate integrated intensities when applied to whole data sets from a protein crystal. The artificial neural network, based on the U-Net architecture commonly used for image segmentation, is trained using about 100 000 simulated training peaks derived from strong peaks. After 100 training epochs (a round of training over the whole data set broken into smaller batches), training converges and achieves a Dice coefficient of around 65%, in contrast to just 15% for negative control data sets. Integrating whole peak sets using the neural network yields improved intensity statistics compared with other integration methods, including k-nearest neighbours. These results demonstrate, for the first time, that neural networks can learn peak shapes and be used to integrate Bragg peaks. In conclusion, it is expected that integration using neural networks can be further developed to increase the quality of neutron, electron and X-ray crystallography data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Evaluating the Impact of Price-Responsive Load on Power Systems Using Integrated T&D Simulation

This paper explores the differences between simulating price-responsive load (PRL) interactions with power systems using integrated transmission and distribution (T&D) models and transmission-only (T-only) models. This analysis uses the Integrated Grid Modeling System (IGMS) software to capture 'ISO-to-appliance' simulations using a synthetic T&D model built on the PJM 5-Bus transmission network with multiple full-scale taxonomy feeders that include physics-based models of thousands of customers and PRLs. The results show important differences in the impacts of PRLs between integrated T&D and T-only models. Experiments with the synthetic integrated T&D dataset demonstrated that integrated T&D simulation revealed notably larger differences between the PRL and no-PRL cases for load, and prices compared to T-only simulation. Similarly, differences are observed between the price response of individual buildings and distribution feeders and the corresponding transmission bus in the integrated T&D simulations, which are difficult to capture in traditional T-only simulations.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2015

Integrated PEV Charging Solutions and Reduced Energy for Occupant Comfort [Brochure]

Brochure on Vehicle Testing and Integration Facility, featuring the Vehicle Modification Facility, Vehicle Test Pad and ReCharge Integrated Demonstration System. Plug-in electric vehicles (PEVs) offer the opportunity to shift transportation energy demands from petroleum to electricity, but broad adoption will require integration with other systems. While automotive experts work to reduce the cost of PEVs, fossil fueled cars and trucks continue to burn hundreds of billions of gallons of petroleum each year - not only to get from point A to point B, but also to keep passengers comfortable with air conditioning and heat. At the National Renewable Energy Laboratory (NREL), three installations form a research laboratory known as the Vehicle Testing and Integration Facility (VTIF). At the VTIF, engineers are developing strategies to address two separate but equally crucial areas of research: meeting the demands of electric vehicle-grid integration and minimizing fuel consumption related to vehicle climate control. Part of NREL's Center for Transportation Technologies and Systems (CTTS), the VTIF is dedicated to renewable and energy efficient solutions. This facility showcases technology and systems designed to increase the viability of sustainably powered vehicles. NREL researchers instrument every class of on-road vehicle, conduct hardware and software validation for electric vehicle (EV) components and accessories, and develop analysis tools and technology for the Department of Energy, other government agencies and industry partners. Research conducted at the VTIF examines the interaction of building energy systems, utility grids, renewable energy sources and PEVs, integrating energy management solutions, and maximizing potential greenhouse gas (GHG) reduction, while smoothing the transition and reducing costs for EV owners. NREL's collaboration with automakers, charging station manufacturers, utilities and fleet operators to assess technologies using VTIF resources is designed to enable PEV communication with the smart grid and create opportunities for vehicles to play an active role in building and grid management. Ultimately, this creates value for the vehicle owner and will help renewables be deployed faster and more economically, making the U.S. transportation sector more flexible and sustainable.

02 PETROLEUM↗
DOE OSTI2018

Integrated Testing of a Membrane CO 2 Capture Process with a Coal-Fired Boiler

This final technical report describes work conducted by Membrane Technology and Research, Inc. (MTR) for the Department of Energy, National Energy Technology Laboratory (DOE NETL) to demonstrate integrated operation of the MTR small pilot membrane CO 2 capture system with Babcock & Wilcox Enterprises, Inc.’s (B&W) Small Boiler Simulator-II (SBS-II) pilot coal boiler (award number DE-FE0026414). The work was performed from July 1, 2015 through March 31, 2018. The overall goal of this project was to operate the existing MTR small pilot membrane CO 2 capture system at an appropriately-sized coal-fired boiler to test integrated operation with CO 2 recycle to the boiler. MTR was assisted in this project by B&W, which hosted the integrated membrane-boiler field test at the B&W Research Facility in Barberton, OH. This report details the work performed to prepare the B&W site, modify the existing MTR membrane system, install the MTR system at B&W, and operate an integrated membrane-boiler field test with CO 2 recycle to the boiler. Detailed analysis of the integrated membrane-boiler test data was conducted to validate prior B&W computational fluid dynamics (CFD) modeling and SBS-II boiler tests with CO 2 -laden air that showed modest effects of recycled CO 2 on boiler performance. The integrated test results also demonstrated how various membrane parameters impact the performance of a dynamic boiler system. Key results for all tasks and recommendations for future research are discussed in this report.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2023

Observations and Lessons Learned From Installing Residential Roofing-Integrated Photovoltaics

Building-sited solar photovoltaics (PV) could play a key role in decarbonizing the building sector either through racked and mounted PV or through Building-integrated PV (BIPV). BIPV is installed into the building envelope itself, with solar cells and/or modules forming the outer layer of a building structure, thus transforming a single-purpose structure into one that serves the dual purposes of the building envelope and electricity. BIPV can be applied to building roofs, facades, awnings, pergolas, windows, skylights, balustrades, and other external surfaces. Given BIPV products vary widely, the focus of this research is residential roofing integrated PV (RIPV), where solar is incorporated into or otherwise replaces the roofing material. Previous research suggests that residential RIPV could reduce customer acquisition, labor, supply chain, and equipment costs. These products have yet to realize these cost savings and deployment remains significantly less than conventional rooftop PV as a relative share of the addressable market in the US. One potential barrier to broader residential roofing integrated PV deployment may be higher costs relative to conventional rooftop PV, primarily because the design and installation of these products is still evolving. Here, we explore residential RIPV cost-reduction opportunities by analyzing installation processes. Our study documents residential RIPV installations at 2 reroofing sites and the equivalent of 9 new construction sites in California through a methodology known as time and motion study. We also conducted interviews with subject-matter experts to identify barriers and solutions to maximize these products' market penetration. Our time and motion study breaks the RIPV installation process into four steps: 1) staging, unloading, and roof preparation; 2) fire resistant underlayment(s) (synthetic material laid between roof shingles and roof deck); 3) flashings and PV installation; and 4) wiring and monitoring. We measure the time required for each step in terms of worker-hours, representing an hour of labor from a single worker. We further normalize process time by dividing worker-hours by kilowatt (kW) of system capacity. The most time-intensive step was flashings and PV installation, taking around 2.4 worker-hours per kW on average and accounting for around 60% of the process time for an average installation. The total installation process took on average about 6.4 and 3.5 worker-hours per kW at the reroofing sites and new construction sites, respectively. For comparison, a previous time and motion study documented a time of 6.9 worker-hours per kW for conventional rooftop PV. The shorter RIPV installation times are consistent with previous studies suggesting that RIPV could be installed faster than conventional rooftop PV. The time and motion results and feedback from interviewees provide insights into potential residential RIPV cost reduction opportunities. Several interviewees suggested that these products would be more efficient if PV installation was more fully integrated into the roofing/construction industries, which currently use separate supply chains and skillsets. Further integration could reduce supply chain delays and labor force redundancies. Future research could explore specific ways to integrate these industries to help realize the cost savings potential of RIPV.

14 SOLAR ENERGY↗
DOE OSTI2021

Findings from the NETL Well Integrity Workshop: Insights for multiple subsurface energy operations

Wells are a core aspect of subsurface energy infrastructure. Ensuring the resilience of that infrastructure relies on the integrity of wells as engineered pathways that safely extract, inject, and store fluids in the subsurface. To identify areas where focused research can yield new insights to improve integrity and extend the operational life of wells, the United States (US) Department of Energys (DOE) National Energy Technology Laboratory (NETL) organized and hosted a workshop on well integrity research needs in May and June of 2021. The three-day workshop consisted of six technical sessions and 18 presentations from international well integrity experts on topics of geologic storage of carbon dioxide, natural gas, and hydrogen, as well as hydrocarbon and geothermal energy production. There were over 350 registrants from more than 10 countries, 4 major oil & gas companies, 14 US states, 8 US DOE National Laboratories, US Departments of Interior, Transportation, and Energy, and regulators from eight of ten US Environmental Protection Agency (EPA) regions and US EPA headquarters. Through presentations, moderated discussions, and an attendee survey several important areas for future research were identified. In this presentation, we highlight the findings of the NETL well integrity workshop and discuss future well integrity research needs.

carbon capture utilization and storage (CCUS)↗
DOE OSTI2017

NUMERICAL INTEGRAL OF RESISTANCE COEFFICIENTS IN DIFFUSION

The resistance coefficients in the screened Coulomb potential of stellar plasma are evaluated to high accuracy. I have analyzed the possible singularities in the integral of scattering angle. There are possible singularities in the case of an attractive potential. This may result in a problem for the numerical integral. In order to avoid the problem, I have used a proper scheme, e.g., splitting into many subintervals where the width of each subinterval is determined by the variation of the integrand, to calculate the scattering angle. The collision integrals are calculated by using Romberg’s method, therefore the accuracy is high (i.e., ∼10{sup −12}). The results of collision integrals and their derivatives for −7 ≤ ψ ≤ 5 are listed. By using Hermite polynomial interpolation from those data, the collision integrals can be obtained with an accuracy of 10{sup −10}. For very weakly coupled plasma ( ψ ≥ 4.5), analytical fittings for collision integrals are available with an accuracy of 10{sup −11}. I have compared the final results of resistance coefficients with other works and found that, for a repulsive potential, the results are basically the same as others’; for an attractive potential, the results in cases of intermediate and strong coupling show significant differences. The resulting resistance coefficients are tested in the solar model. Comparing with the widely used models of Cox et al. and Thoul et al., the resistance coefficients in the screened Coulomb potential lead to a slightly weaker effect in the solar model, which is contrary to the expectation of attempts to solve the solar abundance problem.

79 ASTRONOMY AND ASTROPHYSICS↗