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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Asymmetric oligomerization state and sequence patterning can tune multiphase condensate miscibility

Endogenous biomolecular condensates, composed of a multitude of proteins and RNAs, can organize into multiphasic structures with compositionally distinct phases. This multiphasic organization is generally understood to be critical for facilitating their proper biological function. However, the biophysical principles driving multiphase formation are not completely understood. Here we use in vivo condensate reconstitution experiments and coarse-grained molecular simulations to investigate how oligomerization and sequence interactions modulate multiphase organization in biomolecular condensates. We demonstrate that increasing the oligomerization state of an intrinsically disordered protein results in enhanced immiscibility and multiphase formation. Interestingly, we find that oligomerization tunes the miscibility of intrinsically disordered proteins in an asymmetric manner, with the effect being more pronounced when the intrinsically disordered protein, exhibiting stronger homotypic interactions, is oligomerized. Our findings suggest that oligomerization is a flexible biophysical mechanism that cells can exploit to tune the internal organization of biomolecular condensates and their associated biological functions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

A Voltage Injection-Based Current Harmonics Suppression Strategy for Six-Phase PMSM With Nonsinusoidal Back EMF

This article presents a voltage injection-based current harmonic minimization method for wide bandgap device-based six-phase permanent magnet synchronous machine (PMSM) drives. The presence of low-order harmonics is common in the back EMF of PMSMs with low slot and high pole numbers. The back EMF harmonics generate low-order harmonic currents that increase torque ripples. Furthermore, zero-sequence current (ZSC) is also observed if all six phases are connected to a common neutral point. ZSC does not affect the torque ripple but reduces the system efficiency. A special technique is required to reduce ZSC for variable speed drives as direct ac component to synchronous reference frame (SRF) dc transformation is not possible for ZSC. In this article, a voltage injection-based current harmonics reduction method is proposed. The injected harmonic voltage coefficients are calculated from the harmonic estimations of back EMF and updated using closed-loop harmonic compensators to improve steady-state performance. For ZSC reduction, third harmonics power controller, and for 6n ± 1 (n = 1, 2,...) order harmonic current reduction, SRF current controllers are presented in this article. Furthermore, the current harmonics minimization method is experimentally verified using a GaN-based three-level active neutral point clamped inverter-driven six-phase PMSM.

42 ENGINEERING↗
DOE OSTI2024

Postfault Operation of Three-Level Inverter Driven Six-Phase PMSM With Enhanced Torque–Speed Region

This article presents an open-switch postfault operational technique with enhanced torque–speed region for three-level (3L) active neutral point clamped (ANPC) inverter-driven symmetrical six-phase (SSP) permanent magnet synchronous machines (PMSMs). Maximum torque (MT), minimum loss (ML), and single three-phase (STP) operations are commonly used for the postfault operations of six-phase drives. The maximum possible torque and speed in these operations are generally limited by voltage, current ratings, and the neutral point configuration of the motor. To enhance the postfault torque and speed operating region, the torque and speed limits in different postfault operational techniques are determined based on the voltage, current constraints, and neutral point configuration of the SSP-PMSM. In this work, a unified postfault operation is proposed that increases the postfault operational limits by combining MT, ML, and STP operations and modifying the neutral point configuration of the SSP-PMSM. In addition, a technique is also presented that modifies the pulsewidth modulation technique to enable full torque operation below 0.5 p.u. speed. The proposed postfault operational technique enables full-speed (1 p.u.) operation by operating in STP mode and full torque operation (1 p.u.) below 0.5 p.u. speed. Furthermore, the postfault operational technique is experimentally validated using a Gallium Nitride (GaN) device-based3L-ANPC inverter-driven SSP-PMSM.

42 ENGINEERING↗
DOE OSTI2023

A Six-Phase Space Vector PWM Technique for Wide Bandgap Device-Based Three-Level Inverters

This article presents a space vector pulsewidth modulation (SVPWM) technique for wide bandgap (WBG) device-based three-level (3L) six-phase inverters. Implementation of the SVPWM techniques for any six-phase inverter is complex for its high number of possible voltage vectors. Different six-phase load configurations are also possible depending on the angle between two consecutive phases and neutral point connections. The implementation techniques change depending on the load configuration. Moreover, a common neutral point for all six phases leads to circulating currents. Capacitor voltage balancing is also needed for 3L inverters. Capacitor voltage balancing and addressing the circulating current problem further increases the implementation complexity. In this article, a generalized SVPWM technique is proposed for the six-phase 3L inverters that is implementable using two three-phase 3L SVPWM blocks. The SVPWM technique also ensures dc bus capacitor voltage balancing and minimizes circulating current. Here, the SVPWM technique is experimentally verified using a GaN-based 3L six-phase active neutral point clamped (ANPC) inverter prototype, and the results are presented in this article.

42 ENGINEERING↗
DOE OSTI2025

The Design of a Multiphase CO2 Turbine Test Facility

As the energy market continues to evolve with increased renewables, such as solar and wind energy, the need to balance energy demand with its availability has become increasingly more challenging. The country’s aggressive decarbonization goals in the upcoming decades will increase renewable energy market penetration, thus exacerbating the disparity between energy demand and renewable resource availability. Long-duration energy storage technologies, such as pumped thermal energy storage (PTES), are potential solutions to this challenge with high potential round-trip efficiency (RTE), no geological or geographical constraints, and low safety risks. The charge mode of a PTES system operates a heat pump cycle, converting input power to thermal energy in hot and cold reservoirs. Fundamentally, heat pumps are commonly used in daily life, but the operating conditions required by high RTE PTES systems are outside the design experience of these systems. The low-pressure side of the cycle for a supercritical CO2 (sCO2) PTES operates just above the vapor-dome and potentially drives the turbine to expand into the dome, resulting in multiphase operation in the rear stages of the turbine. This paper presents the design of the test facility for an advanced multiphase-tolerant sCO2 turbine for the heat pump of a PTES system. Heat rejection and pressure loss estimations for the multiphase sections of the test loop presented unforeseen challenges.

25 ENERGY STORAGE↗
DOE OSTI2021

Active motion of multiphase oil droplets: emergent dynamics of squirmers with evolving internal structure

Synthetic soft matter systems, when driven beyond equilibrium by active processes, offer the potential to achieve dynamical states and functions of a complexity found in living matter. Emulsions offer the basis of a simple yet versatile system for identification of the physicochemical principles underlying active soft matter, but how multiple internal phases within emulsion droplets (e.g., Janus morphologies) organize to impact emergent dynamics is not understood. Here, we create multiphase oil droplets with ultralow interfacial tensions but distinct viscosities, and drive them into motion in aqueous micellar solutions. Preferential solubilization of select components of the oil both drives the droplet motion and yields a progression of internal phase morphological states with distinct symmetries. In this work, we find the active droplets to exhibit five dynamical states during morphogenesis. By quantifying microscopic flow fields, we show that it is possible to map the diverse droplet behaviors to squirmer models of spherical microswimmers in Stokes flow, thus showing that multiphase droplets offer the basis of a versatile platform with which to study and engineer the hydrodynamics of microswimmers.

36 MATERIALS SCIENCE↗
DOE OSTI2022

The driving mode of shock-driven turbulence

Turbulence in the interstellar medium (ISM) is crucial in the process of star formation. Shocks produced by supernova explosions, jets, radiation from massive stars, or galactic spiral-arm dynamics are amongst the most common drivers of turbulence in the ISM. However, it is not fully understood how shocks drive turbulence, in particular whether shock driving is a more solenoidal (rotational, divergence-free) or a more compressive (potential, curl-free) mode of driving turbulence. The mode of turbulence driving has profound consequences for star formation, with compressive driving producing three times larger density dispersion, and an order of magnitude higher star formation rate than solenoidal driving. Here, we use hydrodynamical simulations of a shock inducing turbulent motions in a structured, multiphase medium. This is done in the context of a laser-induced shock, propagating into a foam material, in preparation for an experiment to be performed at the National Ignition Facility (NIF). Specifically, we analyse the density and velocity distributions in the shocked turbulent medium, and measure the turbulence driving parameter $b=(\sigma _{\rho /\langle \rho \rangle }^{2\Gamma }-1)^{1/2}(1-\sigma _{\rho /\langle \rho \rangle }^{-2})^{-1/2}\mathcal {M}^{-1}\Gamma ^{-1/2}$, with the density dispersion σρ/<ρ>, the turbulent Mach number $\mathcal {M}$, and the polytropic exponent Γ. Purely solenoidal and purely compressive driving correspond to b ~ 1/3 and b ~ 1, respectively. As a result, using simulations in which a shock is driven into a multiphase medium with structures of different sizes and Γ < 1, we find b ~ 1 for all cases, showing that shock-driven turbulence is consistent with strongly compressive driving.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Effects of Carbonic Acid-Rock Interactions on CO2/Brine Multiphase Flow Properties in the Upper Minnelusa Sandstones

Summary Carbon dioxide (CO2) injection into a deep saline aquifer can dissolve into formation brine and generate carbonic acid. The resulting acid can drive fluid-rock geochemical reactions. The impact of these fluid-rock geochemical reactions on porosity, permeability, and multiphase flow responses is relevant to the determination of CO2 storage capacity of deep saline aquifers. In this research, carbonic acid flooding experiments were performed on core samples consisting of poorly sorted, quartz-rich sand with laminated bedding from a possible CO2 storage target in northwest Wyoming. Complementary pre- and post-injection porosity and permeability, thin-section, Brunauer-Emmett-Teller (BET) surface area, mercury intrusion capillary pressure (MICP), and time-domain nuclear magnetic resonance (TD-NMR) measurements were conducted. Overall, both core porosity and permeability increased after a 7-day carbonic acid injection, from 6.2 to 8.4% and 1.6 to 3.7 md, respectively. We attributed these changes to carbonate mineral dissolution, which was evidenced by the effluent brine geochemistry, pore-throat size distribution (PTSD), and BET surface area. To be more specific, within the more-permeable section of core samples containing larger pore size, the permeability increment is apparent due to dolomite mineral grains and cements dissolution. However, for the lower-permeability section corresponding to the smaller pore size, mineral precipitation possibly lessened dissolution effects, leading to insignificant petrophysical properties changes. Consequently, the observed heterogeneous carbonic acid-rock interactions resulted in alterations of CO2/brine relative permeability (i.e., the initial CO2 saturation decreased and the CO2 flow capacity was enhanced). This research provides a fundamental understanding regarding effects of fluid-rock reactions on changes in static and multiphase flow properties of eolian sandstones, which lays the foundation for more accurate prediction/simulation of CO2 injection into deep saline aquifers.

Engineering↗
DOE OSTI2025

Population Balance Models for Catalytic Depolymerization: From Elementary Steps to Multiphase Reactors

Here, the ongoing accumulation of plastic waste in landfills and in the environment is driving research on chemical processes and catalysts to recycle polymers. Traditional modeling strategies are not applicable to these processes because they involve too many reactants and intermediates, one for each molecular weight and each functionalization. To model the kinetics, we have developed population balance models (PBMs) that account for macromolecular reactants in the bulk and macromolecular catalytic intermediates. These PBMs couple to each other through polymer adsorption and desorption models and to traditional rate equations for small molecule products and co-reactants (like hydrogen or ethylene). The models, in combination with experimental data, are being used in many ways: (i) to test mechanistic hypotheses, (ii) to extract rate parameters, (iii) to quantitatively compare catalyst activities, (iv) to account for mass transfer and vapor–liquid partitioning in two-phase reactors, and (v) to design novel support architectures and catalysts that mimic the processive action of natural depolymerization enzymes. Some key theoretical advances allow PBMs to be constructed from elementary rates and mechanisms, as opposed to traditional formulations with pseudoelementary rate parameters invoked as fitting parameters. We discuss ways to build these models “bottom-up” from first-principles calculations and ways to extract model parameters from “top down” analyses of rate data. The combination provides a quantitative bridge between first-principles calculations and the kinetics of complex macromolecular transformations for polymer upcycling and beyond.

Manis, Lela K. [University of Illinois at Urbana-C↗
DOE OSTI2024

Unveiling the Essential Parameters Driving Mineral Reactions during CO2 Storage in Carbonate Aquifers through Proxy Models

Numerical simulation is a commonly employed technique for studying carbon dioxide (CO2) storage processes in porous media, particularly saline aquifers. It enables the representation of diverse trapping mechanisms and the assessment of CO2 retention capacity within the subsurface. The intricate physicochemical phenomena involved necessitate the incorporation of multiphase flow, accurate depiction of fluid and rock properties, and their interactions. Among these factors, geochemical reaction rates and mechanisms are pivotal for successful CO2 trapping in carbonate reactive rocks. However, research on kinetic parameters and the influence of lithology on CO2 storage remains limited. This limitation is partly due to the challenges faced in laboratory experiments, where the time scale of the reactions and the lack of in situ conditions hinder accurate measurement of mineral reaction rates. This study employs proxy models constructed using response surfaces calibrated with simulation results to address uncertainties associated with geochemical reactions. Monte Carlo simulation is utilized to explore a broader range of parameters and identify influential factors affecting CO2 mineralization. The findings indicate that an open database containing kinetic parameters can support uncertainty assessment. Additionally, the proxy models effectively represent objective functions related to CO2 injectivity and mineralization, with calcite dissolution playing a predominant role. pH, calcite concentration, and CO2 injection rate significantly impact dolomite precipitation, while quartz content remains unaffected.

58 GEOSCIENCES↗
DOE OSTI2020

Hydrodynamic computations of high-power laser drives generating metal ejecta jets from surface grooves

Understanding dynamic fragmentation in shock-loaded metals and predicting properties of the resulting ejecta are of considerable importance for both basic and applied science. The nature of material ejection has been shown to change drastically when the free surface melts on compression or release. In this work, we present hydrodynamic simulations of laser-driven microjetting from micron-scale grooves on a tin surface. We study microjet formation across a range of shock strengths from drives that leave the target solid after release to drives that induce shock melting in the target. The shock-state particle velocity (Up) varies from 0.3 to 3 km/s and the shock breakout pressure is 3–120 GPa. The microjet tip velocity is 1–8 km/s and the free-surface velocity varies from 0.1 to 5 km/s. Two tin equations of state are examined: a “soft” model (LEOS 501) where the target melts for U p > 1 km/s and a more detailed multiphase model (SESAME 2161) that melts for U p > 1.4 km/s. We use these two models to examine the influence of phase change and the choice of the material model on microjet formation and evolution. We observe in our computational results that jet formation can be classified into three regimes: a low-energy regime where material strength affects jet formation, a moderate-energy regime dominated by the changing phase of tin material, and a high-energy regime where results are insensitive to the material model and jet formation is described by an idealized steady-jet theory. Using an ensemble of 2D simulations, we show that these trends hold across a wide range of drive energies and groove angles.

36 MATERIALS SCIENCE↗
DOE OSTI2020

High pressure/high temperature multiphase simulations of dodecane injection to nitrogen: Application on ECN Spray-A

The present work investigates the complex phenomena associated with pressure/high temperature dodecane injection for the Engine Combustion Network (ECN) Spray-A case, employing more elaborate thermodynamic closures, to avoid well known deficiencies concerning density and speed of sound prediction using traditional cubic models. A tabulated thermodynamic approach is proposed here, based on log 10 (p)-T tables, providing very high accuracy across a large range of pressures, spanning from 0 to 2500 bar, with only a small number of interpolation points. The tabulation approach is directly extensible to any thermodynamic model, existing or to be developed in the future. Here NIST REFPROP properties are used, combined with PC-SAFT Vapor-Liquid-Equilibrium to identify the liquid in mixtures penetration, hence avoiding the use of an arbitrary threshold for mass fraction. Identified liquid and vapour penetration are compared against experimental data from the ECN database showing a good agreement, within approximately 3–8% for axial penetration of liquid, 2% for vapor axial penetration and within experimental uncertainty for radial distribution of mass fraction. Analysis of the vortex evolution indicates that driving mechanisms behind the jet break-up are vortex tilting/stretching, then baroclinic torque, leading to Rayleigh-Taylor instabilities, closely followed by vortex dilation and finally viscous effects.

42 ENGINEERING↗
DOE OSTI2025

Chromium segregation-induced oxide evolution in Ni-10Cr alloys during high-temperature oxidation

The oxidation behavior of a Ni-10(wt%)Cr alloy under high-temperature O 2 conditions is investigated using transmission electron microscopy and first-principles calculations. Results reveal that chromium segregation plays a central role in driving the evolution of complex oxide phase structures during oxidation. At low Cr concentrations, Cr preferentially segregates to NiO grain boundaries or internal pores, substituting for Ni atoms and forming Ni(Cr)O solid solutions. As Cr content increases, enhanced diffusion promotes Cr penetration into the NiO lattice, leading to the formation of multiphase oxide structures. First-principles modeling corroborates these findings: at low Cr concentrations, Cr atoms favor surface and grain-boundary segregation, while higher concentrations lead to Cr aggregation within the NiO bulk. Furthermore, the integrated experimental-theoretical approach provides atomistic insights into Cr-mediated mass transport mechanisms during alloy oxidation and offers valuable guidance for controlling oxide growth kinetics and phase stability in Ni-Cr alloys, with implications for improving oxidation resistance in high-temperature structural applications.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Robust hierarchical dispatch for residential distribution network management considering home thermal flexibility and model predictive control

In the transactive energy (TE) paradigm, the devices of participative consumers, or prosumers, may be aggregated and employed to drive operational objectives at the network level. Home heating, ventilation and air-conditioning (HVAC) systems in particular are well-suited to modulate their behaviours based on both home thermal flexibility and requests from the utility grid. This paper develops a robust, hierarchical power dispatch scheme in the context of a residential distribution network. The formulation couples a unique, multiphase linear distribution optimal power flow (OPF) at the upper level with model predictive control (MPC)-based HVAC fleet controllers at the lower level. The proposed approach is tested on nearly 2000 homes with a three-phase distribution network in an intraday market setting, where two major applications are explored and analysed.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Exploring Whether Subsurface Fluid Production Can Minimize Triggered Seismicity in Geothermal Fields

Fluid injection and production related to energy recovery and other industrial operations alter the pressure and stress state of subsurface reservoirs which can lead to induced seismicity. Here, the primary goal is to investigate the hypothesis that the modulation of stress state in subsurface reservoirs through fluid injection/production operations can reduce the likelihood of inducing seismicity. Validation of this mitigation strategy will provide an active operational method to control induced seismicity in subsurface reservoir exploitations such as geothermal energy recovery and carbon storage. In this project, we analyze the relationship between extensive fluid production and the paucity of aftershock activity at the Coso Geothermal plant (CGP) following the 2019 Ridgecrest earthquake sequence, where high rates of aftershock triggering were expected. We developed a high-fidelity multiphase coupled thermo-hydro-mechanical (THM) model to simulate fluid injection/production activities at the CGP between 1986 and 2020. THM results of surface subsidence due to high rates of fluid production agree well with field observations from global positioning system (GPS) and interferometric synthetic aperture radar (InSAR). Subsequently, the variations of pore pressure, temperature and stress state were used to drive numerical earthquake simulations of the aftershock response to the 2019 Ridgecrest earthquakes. The earthquake simulations show that seismic quiescence may occur following the Ridgecrest event, depending on the initial stress state at the time of the mainshock and at the initiation of geothermal energy production. Seismic quiescence occurs in 20% of the cases we explored, where rates are decreased by 50% of the background rate in the two years following the mainshock. In circumstances where aftershock rates increase near the CGP following Ridgecrest, the average rate change is a factor of two larger than background rates from simulations with no operations. These findings indicate that unlike many other operations that bring faults closer to failure, operations at the CGP are acting to stabilize faults such that triggering in the current stress state is minimal.

58 GEOSCIENCES↗
DOE OSTI2021

ORNL Input to GDSA Repository Systems Analysis FY21

This document satisfies the M3 milestone M3SF-21OR010304082 titled “ORNL Input to GDSA Repository Systems.” This document describes the current status of Oak Ridge National Laboratory’s (ORNL’s) efforts related to analyses of dual-purpose canister (DPC) disposal in unsaturated alluvium with a focus on thermal hydrological constraints on criticality timing and power output. This analysis updates previous analyses of thermal hydrological constraints on timing and power output of a potential criticality event in Dual-Purpose Canisters (DPCs) in a hypothetical repository in unsaturated alluvium using a more realistic representation of heat transport inside dry DPCs. PFLOTRAN was used for the simulations of multiphase thermal hydrology near a single DPC. The scenario considers a DPC failure at 9000 years, allowing water to enter and eventually fill the DPC. Once the DPC is filled to a level that could support a criticality event, different values for criticality power output were added to the decay heat. The main objective is to bound the power output that could be produced by a criticality event without driving water out of the package. For the conditions analyzed here, following a package breach, the alluvial formation could supply enough water to allow enough accumulation in the DPC to support a criticality event. However, the power output that would be generated is limited to modest values by loss of water moderator due to evaporation and vapor diffusion. In the reference case scenario, the DPC would not start to fill with water until about 16,000 years post closure and would not fill to a level that allows a criticality event until approximately 25,000 years post closure. The long-term average power output that could be sustained without driving off the water and terminating the criticality event is limited to approximately 100 W. Sensitivity to assumed conditions and parameters in the reference case, especially the deep percolation rate, need to be addressed but could not be undertaken because of numerical failures of the PFLOTRAN code running in general mode in the dry conditions of an unsaturated alluvium repository

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Microstructure-Dependent Rate Theory Model of Radiation-Induced Segregation in Binary Alloys

Conventional rate theory often uses the mean field concept to describe the effect of inhomogeneous microstructures on the evolution of radiation induced defect and solute/fission product segregation. However, the spatial and temporal evolution of defects and solutes determines the formation and spatial distribution of radiation-induced second phase such as precipitates and gas bubbles/voids, especially in materials with complicated microstructures and subject to high dose radiation. In this work, a microstructure-dependent model of radiation-induced segregation (RIS) has been developed to investigate the effect of inhomogeneous thermodynamic and kinetics properties of defects on diffusion and accumulations of solute A in AB binary alloys. Four independent concentrations: atom A, interstitial A, interstitial B, and vacancy on [A, B] sublattice are used as field variables to describe temporal and spatial distribution and evolution of defects and solute A. The independent concentrations of interstitial A and interstitial B allow to describe their different generation rates, thermodynamic and kinetic properties, and release the assumptions of interstitial generation and sink strength used in the conventional rate theory. Microstructure and concentration dependent chemical potentials of defects are used to calculate the driving forces of defect diffusions. With the model, the effects of defect chemical potentials and mobilities on the RIS in polycrystalline AB model alloys have been simulated. The results demonstrated the model capability in predicting defect evolution in materials with inhomogeneous thermodynamic and kinetic properties of defects. The model can be extended to materials with complicated microstructures such as a wide range of grain size distribution, coating structure and multiphases as well as radiation-induced precipitation subject to severe radiation damage.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Alquimia v1.0: a generic interface to biogeochemical codes – a tool for interoperable development, prototyping and benchmarking for multiphysics simulators

Alquimia v1.0 is a generic interface to geochemical solvers that facilitates development of multiphysics simulators by enabling code coupling, prototyping and benchmarking. The interface enforces the function arguments and their types for setting up, solving, serving up output data and carrying out other common auxiliary tasks while providing a set of structures for data transfer between the multiphysics code driving the simulation and the geochemical solver. Alquimia relies on a single-cell approach that permits operator splitting coupling and parallel computation. We describe the implementation in Alquimia of two widely used open-source codes that perform geochemical calculations: PFLOTRAN and CrunchFlow. We then exemplify its use for the implementation and simulation of reactive transport in porous media by two open-source flow and transport simulators: Amanzi and ParFlow. We also demonstrate its use for the simulation of coupled processes in novel multiphysics applications including the effect of multiphase flow on reaction rates at the pore scale with OpenFOAM, the role of complex biogeochemical processes in land surface models such as the E3SM Land Model (ELM) and the impact of surface–subsurface hydrological interactions on hydrogeochemical export from watersheds with the Advanced Terrestrial Simulator (ATS). These applications make it apparent that the availability of a well-defined yet flexible interface has the potential to improve the software development workflow, freeing up resources to focus on advances in process models and mechanistic understanding of coupled problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗