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At least 685 records · Page 38

Temperature effect on phase state and reactivity controls atmospheric multiphase chemistry and transport of PAHs

Polycyclic aromatic hydrocarbons like benzo(a)pyrene (BaP) in atmospheric particulate matter pose a threat to human health because of their high carcinogenicity. In the atmosphere, BaP is mainly degraded through a multiphase reaction with ozone, but the fate and atmospheric transport of BaP are poorly characterized. Earlier modeling studies used reaction rate coefficients determined in laboratory experiments at room temperature, which may overestimate/underestimate degradation rates when applied under atmospheric conditions. Moreover, the effects of diffusion on the particle bulk are not well constrained, leading to large discrepancies between model results and observations. We show how regional and global distributions and transport of BaP can be explained by a new kinetic scheme that provides a realistic description of the temperature and humidity dependence of phase state, diffusivity, and reactivity of BaP-containing particles. Low temperature and humidity can substantially increase the lifetime of BaP and enhance its atmospheric dispersion through both the planetary boundary layer and the free troposphere. The new scheme greatly improves the performance of multiscale models, leading to better agreement with observed BaP concentrations in both source regions and remote regions (Arctic), which cannot be achieved by less-elaborate degradation schemes (deviations by multiple orders of magnitude). Our results highlight the importance of considering temperature and humidity effects on both the phase state of aerosol particles and the chemical reactivity of particulate air pollutants.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Predicting and Controlling Corrosion (Abbreviated Final Report)

Corrosion accumulates significant replacement costs in the transportation, utility, manufacturing, and infrastructure sectors. It also underpins several of LLNL’s core missions in stockpile stewardship, defense, and energy security. Whereas most corrosion and aging models are empirically parameterized to describe well-defined conditions late in the reaction, the factors that determine the early stages of corrosion—during which mitigation could be most impactful— are poorly understood. This project addressed the critical need for new approaches to predict the kinetics of corrosion initiation based on firm physical and chemical understanding. The activities encompassed degradation of relevant metals in both hydrogen-rich and environmental corrosion scenarios. The team integrated state-of-the-art multiscale simulation, in situ characterization, and data science within three technical thrusts: hydriding of Ti alloys; aqueous corrosion of Al and Ni-Cr alloys; and degradation of additively manufactured 316L stainless steel. In each case, novel capabilities were developed to identify and track the impacts of key atomistic, compositional, and microstructural features on the metal systems. For hydriding, protocols were developed to tightly integrate multiscale models, advanced multimodal characterization, and machine learning to determine how hydrogen interacts with native passivating surface oxides and nucleates new undesired phases, shedding new light on the critical role of grain boundaries, interfaces, and atomically disordered regions. For aqueous corrosion, the project demonstrated methods to predict dissolution rates of metal surfaces in corrosive solutions, to measure and understand microstructural and grain orientation effects on corrosion susceptibility, and to investigate competing growth and dissolution kinetics of surface oxides. For additively manufactured metals, analysis using state-of-the-art microscopy techniques revealed the role of specific heterogeneities invoked during laser processing, including cellular structure, dislocations, and precipitates, on corrosion susceptibility. In addition to new capabilities and understanding, the project provided an avenue for workforce development, as well as key partnerships with stakeholders in corrosion science.

08 HYDROGEN↗

Structural health and prognostics management for offshore wind turbines

Operations and maintenance costs for offshore wind plants are expected to be significantly higher than the current costs for onshore plants. One way in which these costs may be able to be reduced is through the use of a structural health and prognostic management system as part of a condition based maintenance paradigm with smart load management. To facilitate the creation of such a system a multiscale modeling approach has been developed to identify how the underlying physics of the system are affected by the presence of damage and how these changes manifest themselves in the operational response of a full turbine. The developed methodology was used to investigate the effects of a candidate blade damage feature, a trailing edge disbond, on a 5-MW offshore wind turbine and the measurements that demonstrated the highest sensitivity to the damage were the local pitching moments around the disbond. The multiscale method demonstrated that these changes were caused by a local decrease in the blade's torsional stiffness due to the disbond, which also resulted in changes in the blade's local strain field. Full turbine simulations were also used to demonstrate that derating the turbine power by as little as 5% could extend the fatigue life of a blade by as much as a factor of 3. The integration of the health monitoring information, conceptual repair cost versus damage size information, and this load management methodology provides an initial roadmap for reducing operations and maintenance costs for offshore wind farms while increasing turbine availability and overall profit.

Griffith, Daniel Todd↗

Optimizing Discharge Capacity of Li-O 2 Batteries by Design of Air-Electrode Porous Structure: Multifidelity Modeling and Optimization

We develop a new mathematical framework to study the optimal design of air electrode microstructures for lithium-oxygen (Li-O2) batteries. It can eectively reduce the number of expensive experiments for testing dierent air-electrodes, thereby minimizing the cost in the design of Li-O2 batteries. The design parameters to characterize an air-electrode microstructure include the porosity, surface-to-volume ratio, and parameters associated with the pore-size distribution. A surrogate model (also known as response surface) for discharge capacity is rst constructed as a function of these design parameters. The surrogate model is accurate and easy to evaluate such that an optimization can be performed based on it. In particular, a Gaussian process regression method, co-kriging, is employed due to its accuracy and eciency in predicting high-dimensional responses from a combination of multidelity data. Specically, a small amount of data from high-delity simulations are combined with a large number of data obtained from computationally ecient low-delity simulations. The high-delity simulation is based on a multiscale modeling approach that couples the microscale (pore-scale) and macroscale (device-scale) models. Whereas, the low-delity simulation is based on an empirical macroscale model. The constructed response surface provides quantitative understanding and prediction about how air electrode microstructures aect the discharge performance of Li-O2 batteries. The succeeding sensitivity analysis via Sobol indices and optimization via genetic algorithm ultimately oer a reliable guidance on the optimal design of air electrode microstructures. The proposed mathematical framework can be generalized to investigate other new energy storage techniques and materials.

25 ENERGY STORAGE↗

Studying the effect of phenyl group content on the physical properties of un-crosslinked PDMS (Progress Summary)

Over the last couple of years, the emphasis on our A&L efforts has been on developing a thermal-age-aware constitutive model for foam cushions. From our studies so far, it appears that an $N = 2$ Ogden hyperfoam model within the framework of a two-network Tobolsky scheme is appropriate to describe the age-aware stress-strain response of both stochastic and additively manufactured (AM) foams. The models have so far been fitted only to a limited number of silicone-based materials systems, i.e., M97 and M9763 stochastic foams and AM foams made of SE1700 rubber. As we explore new and different rubber formulations for improved structural as well as A&L properties, we find it important to develop a deeper understanding of the effect of functional groups on the physical, mechanical, and flow properties of the constituent elastomer. To this end, in Q2 FY19, we have begun a project on multiscale modeling of polymers that realistically incorporates from bond-level dynamics to terminal dynamics of whole chains (e.g., tube dynamics). In such mesoscale simulations the polymer tube dynamics is modeled through coarse-graining of monomers to mesoscale “beads”, with the bead-bead potential being systematically fitted to accurate atomic-level forcefields. The aim of this collaboration is to develop a fully physical constitutive model that predicts the mechanical response of polymers of our interest based on structure and modeled dynamics alone.

36 MATERIALS SCIENCE↗

The self-assembly of particles with isotropic interactions: Using DNA coated colloids to create designer nanomaterials

Self-consistent field theory equations are presented that are suitable for use as a coarse-grained model for DNA coated colloids, polymer-grafted nanoparticles and other systems with approximately isotropic interactions. The equations are generalized for arbitrary numbers of chemically distinct colloids. The advantages and limitations of such a coarse-grained approach for DNA coated colloids are discussed, as are similarities with block copolymer self-assembly. In particular, preliminary results for three species self-assembly are presented that parallel results from a two dimensional ABC triblock copolymer phase. The possibility of incorporating crystallization, dynamics, inverse statistical mechanics and multiscale modelling techniques are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE ASR Final Report on “Use of ARM Observations to Investigate the Role of Tropical Radiative Processes and Cloud Radiative Effects in Climate Simulations”

The overall objective of this ASR funded project is to investigate the role of cloud radiative effects, especially those associated with tropical thin cirrus clouds in the tropical tropopause layer, by analyzing the ARM observations combined with numerical models. In particular, we have processed and analyzed the observations from the Raman lidar at the ARM SGP and TWP sites. In the tenure of the project (8/15/2013 – 8/14/2016 and with a no-cost extension to 8/14/2017), we have been concentrating on (i) developing an automated feature detection scheme of clouds and aerosols for the ARM Raman lidar; (ii) developing an automated retrieval of cloud and aerosol extinctions for the ARM Raman lidar; (iii) investigating cloud radiative effects based on the observations on the simulated temperatures in the tropical tropopause layer using a radiative-convective model; and (iv) examining the effect of changes of atmospheric composition on the tropical lower-stratospheric temperatures. In addition, we have examined the biases in the CALIPSO-inferred aerosol direct radiative effects using ground-based Raman lidars at the ARM SGP and TWP sites, and estimated the impact of lidar detection sensitivity on assessing global aerosol direct radiative effects. We have also investigated the diurnal cycle of clouds and precipitation at the ARM site using the cloud radar observations along with simulations from the multiscale modeling framework. The main results of our research efforts are reported in the six referred journal publications that acknowledge the DOE Grant DE-SC0010557.

47 OTHER INSTRUMENTATION↗

Workshop Report on Basic Research Needs for Scientific Machine Learning: Core Technologies for Artificial Intelligence

Scientific Machine Learning (SciML) and Artificial Intelligence (AI) will have broad use and transformative effects across the Department of Energy. Accordingly, the January 2018 Basic Research Needs workshop identified six Priority Research Directions (PRDs). The first three PRDs describe foundational research themes that correspond to the need for domain-awareness (PRD #1), interpretability (PRD #2), and robustness (PRD #3). The other three PRDs describe capability research themes and correspond to the three major use cases for massive scientific data analysis (PRD #4), machine learning-enhanced modeling and simulation (PRD #5), and intelligent automation and decision-support for complex systems (PRD #6). The Priority Research Directions provide a sound basis for a coherent, long-term research and development strategy in SciML and AI. Over the last decade, DOE investments in applied mathematics have laid the groundwork for the type of basic research that will underpin key advances in the six PRDs. Such advances will build on the work from leading researchers in optimization, linear algebra, high-performance solvers and algorithms, multiscale modeling and simulation, complex systems research, uncertainty quantification, and the new basic research areas that will emerge from the pursuit of transformative technologies.

97 MATHEMATICS AND COMPUTING↗

Brochure on Basic Research Needs for Scientific Machine Learning: Core Technologies for Artificial Intelligence [Slides]

Scientific Machine Learning (SciML) and Artificial Intelligence (AI) will have broad use and transformative effects across the Department of Energy. Accordingly, the January 2018 Basic Research Needs workshop identified six Priority Research Directions (PRDs). The first three PRDs describe foundational research themes that correspond to the need for domain-awareness (PRD #1), interpretability (PRD #2), and robustness (PRD #3). The other three PRDs describe capability research themes and correspond to the three major use cases for massive scientific data analysis (PRD #4), machine learning-enhanced modeling and simulation (PRD #5), and intelligent automation and decision-support for complex systems (PRD #6). The Priority Research Directions provide a sound basis for a coherent, long-term research and development strategy in SciML and AI. Over the last decade, DOE investments in applied mathematics have laid the groundwork for the type of basic research that will underpin key advances in the six PRDs. Such advances will build on the work from leading researchers in optimization, linear algebra, high-performance solvers and algorithms, multiscale modeling and simulation, complex systems research, uncertainty quantification, and the new basic research areas that will emerge from the pursuit of transformative technologies.

97 MATHEMATICS AND COMPUTING↗

From Cell to System: Accelerated hpc Simulations of BESS Aging under Frequency Regulation and Arbitrage use cases

Lithium-ion battery energy storage systems (BESS) packs have emerged as a leading solution for grid-scale energy storage, enhancing resiliency and balancing load fluctuations. Yet, experimental characterization of large-format LIB packs-particularly to assess performance and degradation over hundreds of cycles - demands substantial hardware investment and multi-year testing campaigns. In this work, we couple a hierarchical, physics-based modeling framework agnostic to electrode chemistries with high-performance computing to accelerate systems level evaluation by upto two orders of magnitude. Building on the open-source liionpack platform, we implement cell, module, and pack-scale electrochemical models enriched with mechanistic aging mechanisms and deploy them on an HPC cluster to simulate 150−200kWh systems over 500 - 1,000 cycles with in days. We subject these virtual B ESS to both constant-current cycling and realistic grid service profiles spanning frequency regulation, ramp-rate support, and energy arbitrage-and quantify the resulting degradation patterns. Our results reveal that localized cell aging can induce substantial nonuniformity at module and pack levels, with service-specific cycling protocols driving distinct aging modes. This rapid, multiscale modeling approach provides a powerful design-space exploration tool for optimizing electrical architecture, control strategies, and operational schedules to prolong pack lifetime and lower total cost of ownership.

Ayalasomayajula, Surya [ORNL] (ORCID:0009000860788↗

Effect of Ionizing Radiation on the Redox Chemistry of Penta- and Hexavalent Americium

The recent development of facile methods to oxidize trivalent americium to its higher valence states holds promise for the discovery of new chemistries and critical insight into the behavior of the 5f electrons. However, progress in understanding high valent americium chemistry has been hampered by americium’s inherent ionizing radiation field, and its concomitant effects on americium redox chemistry. Any attempt to understand high valent americium reduction and/or disproportionation must account for the effects of these radiolytic processes. Fortunately, the effects of ionizing radiation on water and aqueous nitric acid solutions are well known. Values for the yields of the major radiolytically produced reactive species that could conceivably react with americium, and their rate coefficients, are available for use in radiation chemical modeling. Therefore, we present a complete, quantitative, mechanistic description of the radiation-induced redox chemistry of the americyl oxidation states in aerated, aqueous nitric acid, as a function of radiation quality (type and energy) and solution composition using multi-scale modeling calculations supported by experiment. The reduction of Am(VI) to Am(V) was found to be most sensitive to the effects of ionizing radiation, undergoing rapid reductions with the steady-state products of aqueous HNO 3 radiolysis, i.e., HNO 2 , H 2 O 2 , and HO 2 •, which dictated its practical lifetime under acidic conditions. In contrast Am(V) is only susceptible to radiolytic oxidation, mainly through its reactions with NO 3 •, and is notably radiation resistant with respect to direct one-electron reduction to produce Am(IV). Our multiscale modeling calculations predict that the lifetime of Am(V) is dictated by its rate of disproportionation, 2AmO 2 + + 4 Haq + → AmO 2 2+ + Am 4+ + 2H 2 O, with a fourth-order dependence on [H aq + ] in agreement with previous experimental findings, giving an optimized rate coefficient of $k$ = 2.27 × 10 -6 M -5 s -1 . This disproportionation initially produces Am(IV) and Am(VI) species, but the lack of any spectroscopic evidence in our study for Am(IV) suggests that solvent reduction of this cation occurs rapidly. The ultimate product of all the Am(VI)/Am(V) irradiations is Am(III), which shows great stability in an irradiation field.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multiscale Investigation on Biofilm Distribution and Its Impact on Macroscopic Biogeochemical Reaction Rates

Biofilms are critical locations for biogeochemical reactions in the subsurface environment. The occurrence and distribution of biofilms at microscale as well as their impacts on macroscopic biogeochemical reaction rates are still poorly understood. This paper investigated the formation and distributions of biofilms in heterogeneous sediments using multiscale models, and evaluated the effects of biofilm heterogeneity on local and macroscopic biogeochemical reaction rates. Sediment pore structures derived from X-ray computed tomography were used to simulate the microscale flow dynamics and biofilm distribution in the sediment column. The response of biofilm formation and distribution to the variations in hydraulic and chemical properties was first examined. One representative biofilm distribution was then utilized to evaluate its effects on macroscopic reaction rates using nitrate reduction as an example. The results revealed that microorganisms primarily grew on the surfaces of grains and aggregates near preferential flow paths where both electron donor and acceptor were readily accessible, leading to the heterogeneous distribution of biofilms in the sediments. Furthermore, the heterogeneous biofilm distribution decreased the macroscopic rate of biogeochemical reactions as compared with those in homogeneous cases. Operationally considering the heterogeneous biofilm distribution in macroscopic reactive transport models such as using dual porosity domain concept can significantly improve the prediction of biogeochemical reaction rates. Overall, this study provided important insights into the biofilm formation and distribution in soils and sediments as well as their impacts on the macroscopic manifestation of reaction rates.

42 ENGINEERING↗

Progress update on lower length scale research and development on U3Si2 fuel and FeCrAl cladding

This report summarizes the lower length scale model development and studies in regards to two accident tolerant (ATF) concepts, U 3 Si 2 and FeCrAl. U 3 Si 2 is proposed to replace UO 2 fuel for its high thermal conductivity and higher uranium density. FeCrAl alloys are proposed to replace Zr based cladding for their high mechanical strength and good corrosion resistance. Before applying them in reactors, sufficient data are needed to establish their predictable in-pile performance, but largely missing, and they are costly and time consuming to obtain by experimental approaches. Under the NEAMS ATF high-impact-problem (HIP), multiscale modeling and simulations are used to develop atomistic and mesoscale tools, obtain fundamental material properties, and assess the behaviors of these two ATF concepts. The accomplishments in FY17 are briefly introduced in this report including the development of interatomic potentials, assessment of swelling in U 3 Si 2 , and Cr precipitation in FeCrAl alloys.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

E3SM: Improved Climate Prediction with Exascale Capability

The Energy Exascale Earth System Model (E3SM) project is an ongoing, state-of-the-science earth system modeling, simulation, and prediction effort that optimizes Department of Energy (DOE) computing resources to meet the science needs of the nation and the agency’s mission objectives. Climate simulation has become a proven tool for identifying and quantifying the impacts of climate change, but even greater accuracy is required at all levels to improve forecast precision. Understanding the impact of climate change on global and regional water cycles is one of the highest priorities and most difficult challenges in climate change prediction. As part of a subproject of DOE’s Exascale Computing Project, a multidisciplinary team including geophysical and computational scientists developed a multiscale modeling framework (MMF) to refine cloud representation in E3SM climate simulation on GPU accelerated supercomputers, making higher resolution, more computationally efficient predictions possible.

54 ENVIRONMENTAL SCIENCES↗

Research for Sustainable Bioenergy: Linking Genomic and Ecosystem Sciences, Workshop, October 2-4, 2013 Report

The design of sustainable biofuel systems requires knowledge about key plant-microbe-environment interactions that provide a range of ecosystem services. Most critical is a mechanistic understanding of how candidate biofuel plants interact with biotic and abiotic factors to affect the ecosystem outcomes that define sustainability. Recent advances in the genomic sciences can contribute immensely to the knowledge needed to design such systems. For example, progress in plant genomics will enable the inclusion of sustainability traits in future feedstocks, and advances in microbial genomics will allow insights into plantmicrobe-soil interactions that might be used to manage and support plant productivity and vigor. Linking these advances to breakthroughs in ecosystem science enables the use of systems biology in the fundamental design of sustainable biofuel systems. To identify research opportunities in developing such systems, the Department of Energy’s (DOE) Office of Biological and Environmental Research (BER) held the Research for Sustainable Bioenergy Workshop on Oct. 2–4, 2013, in Germantown, Maryland. The workshop convened more than 30 researchers with a broad and diverse range of expertise, including ecology, microbiology, plant genetics, genomics, computational biology, and modeling. Participants discussed and identified research gaps, challenges, and opportunities for enhancing the understanding of influences that biotic, abiotic, and genetic factors have on long-term plant feedstock performance and the delivery of ecosystem services at multiple scales. This report identifies the key topics and questions that could be addressed effectively to achieve this understanding. Research opportunities are organized into four categories: (1) plant systems, encompassing plant productivity, resource use efficiency, genotype/phenotype breeding, and crop diversity; (2) the plant microbiome, which includes microbes living in close association within or adjacent to plants; (3) ecosystem processes, such as carbon capture, greenhouse gas mitigation, and hydrologic processes; and (4) multiscale modeling, which integrates and extends results across spatiotemporal scales.

59 BASIC BIOLOGICAL SCIENCES↗

An adaptive multi-level simulation algorithm for stochastic biological systems

Discrete-state, continuous-time Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms (SSA) to estimate system statistics. The Gillespie algorithm is exact, but computationally costly as it simulates every single reaction. As such, approximate stochastic simulation algorithms such as the tau-leap algorithm are often used. Potentially computationally more efficient, the system statistics generated suffer from significant bias unless tau is relatively small, in which case the computational time can be comparable to that of the Gillespie algorithm. The multi-level method [Anderson and Higham, “Multi-level Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics,” SIAM Multiscale Model. Simul. 10(1), 146–179 (2012)] tackles this problem. A base estimator is computed using many (cheap) sample paths at low accuracy. The bias inherent in this estimator is then reduced using a number of corrections. Each correction term is estimated using a collection of paired sample paths where one path of each pair is generated at a higher accuracy compared to the other (and so more expensive). By sharing random variables between these paired paths, the variance of each correction estimator can be reduced. This renders the multi-level method very efficient as only a relatively small number of paired paths are required to calculate each correction term. In the original multi-level method, each sample path is simulated using the tau-leap algorithm with a fixed value of τ. This approach can result in poor performance when the reaction activity of a system changes substantially over the timescale of interest. By introducing a novel adaptive time-stepping approach where τ is chosen according to the stochastic behaviour of each sample path, we extend the applicability of the multi-level method to such cases. We demonstrate the efficiency of our method using a number of examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Predictive Chemical Kinetic Modeling: Where We Succeed, Where We Struggle, and What Comes Next

Chemical kinetic modeling plays a foundational role in fields ranging from energy to environmental science, pharmaceuticals, and advanced materials. The past two decades have seen remarkable progress, particularly in modeling gas-phase reactions for thermochemical processes, leading to impactful industrial applications such as steam cracking and air quality management. However, new challenges are emerging. The successful development of systematic methodologies for the description of gas-phase kinetics opens the possibility to apply the same approach to the study of more challenging systems. Here, we review recent advances, including ab initio transition state theory-based master equation estimation of elementary rates, automated mechanism generation, machine-learning-assisted kinetics, and uncertainty quantification, and discuss the advances needed to apply the same methodological approach in areas such as heterogeneous catalysis, electrochemistry, liquid-phase and solid-state reactivity, and multiscale model integration. We advocate for the development of targeted tools, especially methods that go beyond empirical tuning toward first-principles-based predictions. We highlight the need for accessible software and AIaugmented workflows to democratize modeling for industry and academia alike. In this perspective, we call attention to not only what has worked but also what remains unsolved, advocating to avoid overemphasizing successes in scientific works at the expense of realism. The next decade should focus on predictive capability, physical accuracy, and community infrastructure (e.g., databases and services) to enable innovation across diverse fields. We argue that kinetic modeling, properly equipped, can accelerate discovery far beyond its traditional domains.

ab initio calculations↗

Multi-level methods and approximating distribution functions

Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie’s direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparable to Gillespie’s direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146–179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗