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1,385 records · Page 36

Thermo-Poro-Mechanical Modeling of RTV Intumescence

Room temperature vulcanizing (RTV) silicone is a high-temperature adhesive used as a gap-filler between heatshield tiles in numerous entry missions. Its propensity to intumesce, or swell upon exposure to heat, is a well-known effect that needs to be carefully quantified during design. At tile interfaces of charring ablators, intumescence, combined with differential recession, could cause the gap filler to protrude past the ablator outer mold line, forming a “fence”. Fencing can in turn cause transition to turbulence of the flow wetting the heat shield, leading to augmented surface heating. Recent experiments conducted at the Plasmatron X facility, the high enthalpy wind tunnel of the Center for Hypersonics and Entry Systems Studies, have shown prominent fencing of RTV gap fillers in PICA, under both nitrogen and air plasmas. Similar observations are well known in the arcjet literature. Further experiments under controlled environment, performed using in situ X-ray micro-computed tomography (micro-CT) at the Advanced Light Source (ALS), have shown heating rate-dependent swelling and shrinkage of RTV during pyrolysis. To simulate RTV intumescence, a novel model was introduced in the Porous Materials Analysis Toolbox based on OpenFOAM, PATO, to account for pore-pressure buildup within both closed- and open-pores. The governing equation for the thermo-poro-mechanical response were developed, assuming linear elasticity for the charring silicone. A new multi-pyrolysis model that tracks non-monotonic advancement of material properties with pyrolysis was proposed. This model addresses the limitations of state-of-the-art ablator models to capture the different stages of thermal degradation and coupled thermomechanics. Swelling of RTV was simulated using the new thermo-poro-mechanical model and compared against in situ micro-CT data. Results showed good agreement in intumescence height and temperature profiles at all heating rates, indicating that the key factor contributing to RTV swelling is the internal pressure build-up within closed- and open-pores. As RTV is cured into a soft (rubbery) compound with low-porosity and permeability, initial temperature increase and pyrolysis gas production cause a significant increase of internal pressure, causing a pronounced volume growth. As thermal degradation progresses, rigidization of the silicone occurs due to char hardening which counteract volume shrinkage after gas pressure relief. Overall, our model shows that accounting for changes in properties such porosity, permeability and key thermomechanical coefficients is crucial for capturing the RTV volume change during ablation and enable a predictive capability for heatshield tile interface response. A plan for future calibration of thermomechanical properties evolution during degradation is discussed, as a key next step to close the new model.

RTV

Thermo-Poro-Mechanical Modeling of RTV Intumescence

Room temperature vulcanizing (RTV) silicone is a high-temperature adhesive used as a gap-filler between heatshield tiles in numerous entry missions. Its propensity to intumesce, or swell upon exposure to heat, is a well-known effect that needs to be carefully quantified during design. At tile interfaces of charring ablators, intumescence, combined with differential recession, could cause the gap filler to protrude past the ablator outer mold line, forming a “fence”. Fencing can in turn cause transition to turbulence of the flow wetting the heat shield, leading to augmented surface heating. Recent experiments conducted at the Plasmatron X facility, the high enthalpy wind tunnel of the Center for Hypersonics and Entry Systems Studies, have shown prominent fencing of RTV gap fillers in PICA, under both nitrogen and air plasmas. Similar observations are well known in the arcjet literature. Further experiments under controlled environment, performed using in situ X-ray micro-computed tomography (micro-CT) at the Advanced Light Source (ALS), have shown heating rate-dependent swelling and shrinkage of RTV during pyrolysis. To simulate RTV intumescence, a novel model was introduced in the Porous Materials Analysis Toolbox based on OpenFOAM, PATO, to account for pore-pressure buildup within both closed- and open-pores. The governing equation for the thermo-poro-mechanical response were developed, assuming linear elasticity for the charring silicone. A new multi-pyrolysis model that tracks non-monotonic advancement of material properties with pyrolysis was proposed. This model addresses the limitations of state-of-the-art ablator models to capture the different stages of thermal degradation and coupled thermomechanics. Swelling of RTV was simulated using the new thermo-poro-mechanical model and compared against in situ micro-CT data. Results showed good agreement in intumescence height and temperature profiles at all heating rates, indicating that the key factor contributing to RTV swelling is the internal pressure build-up within closed- and open-pores. As RTV is cured into a soft (rubbery) compound with low-porosity and permeability, initial temperature increase and pyrolysis gas production cause a significant increase of internal pressure, causing a pronounced volume growth. As thermal degradation progresses, rigidization of the silicone occurs due to char hardening which counteract volume shrinkage after gas pressure relief. Overall, our model shows that accounting for changes in properties such porosity, permeability and key thermomechanical coefficients is crucial for capturing the RTV volume change during ablation and enable a predictive capability for heatshield tile interface response. A plan for future calibration of thermomechanical properties evolution during degradation is discussed, as a key next step to close the new model.

silicone intumescence

Two-dimensional non-equilibrium melting of charged colloids

Thermodynamic two-dimensional melting has been extensively studied in experiments and simulations, and is well predicted by theory. For systems in equilibrium, this transition is well described by the Kosterlitz–Thouless–Halperin–Nelson–Young theory, where melting is directly linked to the unbinding of topological defects. For driven, non-equilibrium melting and other non-equilibrium phase transitions, the picture is less clear. Here, in this work, we study the two-dimensional melting of a crystal of charged colloids. By randomly replacing some charged colloids with magnetic colloids, we can melt our system by rotating a fraction of the particles to create non-equilibrium, hydrodynamic random flows and local stresses. We can also melt it thermally by changing the particle number density. We find that an effective temperature approach cannot explain the results of our driven system. Rather, in both experiments and simulations, we observe that plotting the hexatic order parameter and the hexatic correlation’s exponent versus the density of disclinations and dislocations, respectively, yields universal curves. This implies that in our systems, two-dimensional melting depends directly on the density of topological defects and is independent of whether thermal or non-equilibrium forces generate them.

critical phenomena

Time-History Statistics of Soot Formation in A Model Gas Turbine Combustor

Soot formation is a complex dynamic and intermittent process determined by properties of the fuel, combustor design, and combustor operation. Although the major steps in soot formation (i.e., formation of precursors, inception, growth and evolution) are similar for a variety of carbonaceous fuels, applications, and operating conditions, it remains unclear when the temporal transition between these steps occurs. An engineering prediction tool coupled with computational fluid physics (CFD), therefore needs to accurately model all these complex steps. To develop such a model, we propose the time-history concept for understanding the time dependency of soot formation as a function of local properties (i.e., temperature, velocity, local fuel air ratio, etc.). We continue our previous work with modeling the DLR aero-combustor [1] with our updated in-house CFD code, Open National Combustion Code (OpenNCC), that now includes a Multiple Time-Scale Flamelet Progress Variable approach and a the semi-empirical two-equation soot model. We injected massless tracer particles upstream of the injector region of the combustor to collect time-history statistics of the solution variables. The correlations between the collected statistics with respect to the experimental soot volume fraction data showed that time-history effect of certain flow variables, including turbulent kinetic energy (TKE), and multiple species is indeed important for soot formation. We then conducted a time-history based correlation analysis to determine the key species and the concentration ranges critical for soot formation (C6H5-based nucleation, acetylene-based surface growth, and oxidation with OH and O2). Based on the time-history correlation coefficient (THCC) analysis, we propose possible modifications to improve the current two-equation model.

LES

Turbo-Design: Open-Source Radial Equilibrium Turbomachinery Solver: Part I - Turbines

Advances in 3D Geometrical Designs and Cooling have played a significant role in improving the efficiency of turbomachinery. However, these advancements must be effectively translated back to the modeler. Machine learning can facilitate this transition. Specifically, machine learning–based loss models can bridge the gap between 3D and 1D designs, enabling modelers not only to predict velocity triangles but also to extract additional geometric features. Currently, the design tools used at NASA have not been updated to support such integration—until now. TurboDesign is an open-source, Python-based framework that replaces TD2 (LEW-11029-1) and AXOD2 (LEW-16323-1), both of which are radial equilibrium solvers for axial turbines. The goal of this update is to enable the integration of machine learning loss models into radial equilibrium equations. Additionally, TurboDesign is designed to support radial machines. This paper presents the governing equations, the assumptions underlying the code, the integration of legacy loss models, an example of machine learning model integration, and a validation comparison with CFD. All code, tutorials, and documentation are available at: https://www.github.com/nasa/turbo-design

Radial Equilibrium

Commutative Algebra Modeling in Materials Science – A Case Study on Metal–Organic Frameworks (MOFs)

Metal-organic frameworks (MOFs) are a class of important crystalline and highly porous materials whose hierarchical geometry and chemistry hinder interpretable predictions in materials properties. Commutative algebra is a branch of abstract algebra that has been rarely applied in data and material sciences. We introduce the first ever commutative algebra modeling and prediction in materials science. Specifically, category-specific commutative algebra (CSCA) is proposed as a new framework for MOF representation and learning. It integrates element-based categorization with multiscale algebraic invariants to encode both local coordination motifs and global network organization of MOFs. These algebraically consistent, chemically aware representations enable compact, interpretable, and data efficient modeling of MOF properties such as Henry’s constants and uptake capacities for common gases. Compared to traditional geometric and graph-based approaches, CSCA achieves comparable or superior predictive accuracy while substantially improving interpretability and stability across data sets. By aligning commutative algebra with the chemical hierarchy, the CSCA establishes a rigorous and generalizable paradigm for understanding structure and property relationships in porous materials and provides a nonlinear algebra-based framework for data-driven material discovery.

Khaemba, Caleb S.

Used Nuclear Fuel Management Using the Next Generation System Analysis Model

The U.S. Department of Energy (DOE) is leading the National effort to manage the back end of the nuclear fuel cycle, encompassing the safe transportation, storage/staging, and/or eventual disposal of used nuclear fuel (UNF) and high-level radioactive waste. The Next Generation System Analysis Model (NGSAM) is DOE’s discrete-event, agent-based simulation tool designed to model the full life cycle of UNF from reactor discharge to final disposal. NGSAM supports the DOE Office of Spent Fuel and High-Level Waste Disposition by enabling a detailed, scenario-based analysis of logistics, infrastructure, and shipping strategies. NGSAM replaces legacy models with a modern, flexible platform built on Repast Simphony and enhanced by the Process Analysis Tool. NGSAM simulates the movement and interaction of individual fuel assemblies with system components such as canisters, casks, railcars, and facilities. The model integrates with the Java Transportation Operations Model to plan and execute transportation scenarios, supporting both constrained and unconstrained resource allocation. Key features include customizable allocation and acceptance algorithms, detailed facility-level operations, and a Quick Edit tool for rapid scenario adjustments. NGSAM supports multimodal transportation modeling (e.g. rail, road, barge) and provides comprehensive cost, schedule, and infrastructure data. NGSAM utilizes data from sources such as DOE’s STANDARDS UNF database and DOE’s Stakeholder Tool for Assessing Radioactive Transportation, while also allowing user-defined inputs for scenario customization. NGSAM enables stakeholders to evaluate complex UNF management strategies, assess system performance under varying assumptions, and inform decision making for future infrastructure investments. Its modular architecture and integration with other Integrated Waste Management System tools make it a critical asset for planning the safe and efficient disposition of the Nation’s growing UNF inventory.

Craig, Brian [Argonne National Laboratory (ANL)]

Computational modeling of coupled mechanical damage and electrochemistry in ternary oxide composite electrodes

Performance degradation of ternary layered oxide cathodes largely originates from their loss of structural integrity in cyclic usage. Mechanical damage, such as intergranular fracture of the active particles, is not only a mechanical cleavage process but also interferes with electrochemical kinetics such as infiltration of liquid electrolyte, surface corrosion of the constituent primary particles, and may eventually isolate the primary grains from the electron conducting network. Here, in this work, we develop a computational framework that integrates electrochemistry of a LiNi x Mn y Co 1−x−y O 2 (NMC) composite cathode with mechanical damage of the active particles. To fully examine the intricate chemomechanical behavior of the electrode, we evaluate the effects of the anisotropic material properties, the influence of mechanical potential on Li transport, and the concurrent intergranular fracture and electrolyte penetration along the grain boundaries upon multiple cycles. Electrolyte infiltration benefits capacity retention but aggravates further mechanical damage by corrosion. Structural failure mostly occurs in the first charging due to the anisotropic mechanical strain between the primary grains, while the resulting damage remains stable in the later few cycles. The results are consistent with experimental observations and the integration of electrochemistry and mechanical failure enables a step further understanding of the complex mechanism of battery degradation.

Battery degradation

Spectroscopy in Nanoscopic Cavities: Models and Recent Experiments

The ability of nanophotonic cavities to confine and store light to nanoscale dimensions has important implications for enhancing molecular, excitonic, phononic, and plasmonic optical responses. Spectroscopic signatures of processes that are ordinarily exceedingly weak such as pure absorption and Raman scattering have been brought to the single-particle limit of detection, while new emergent polaritonic states of optical matter have been realized through coupling material and photonic cavity degrees of freedom across a wide range of experimentally accessible interaction strengths. In this review, we discuss both optical and electron beam spectroscopies of cavity-coupled material systems in weak, strong, and ultrastrong coupling regimes, providing a theoretical basis for understanding the physics inherent to each while highlighting recent experimental advances and exciting future directions.

Chemistry

A Parametric Battery Model for the Conceptual Design of Electric Aircraft

Electric aircraft conceptual designs usually have an assumed specific power and specific energy for the aircraft’s energy storage system that dictates the total capacity and the peak power available. The specific energy and power are inherently linked to the state-of-charge and discharge rate from which they were derived; therefore, they will not directly correspond to the diverse circumstances encountered in various aircraft missions and flight segments. These parameters turn the battery system into a black box, disregard potential electrical restrictions, and disallow the aircraft and battery to be optimized as a system. Peering into this box, this study highlights the importance of incorporating a parametric battery model into the conceptual design workflow by splitting high-level terms such as power into voltage and current and investigating their variability during the discharge process. Through the modeling of these more detailed parameters, this methodology shows the feasibility of using low states-of-charge for contingency operations, including the end of the reserve mission, expanding the amount of usable capacity for electric aircraft. Stark differences in aircraft capabilities can arise between varying fidelity battery models due to late-mission, high-power flight operations. This parametric battery model effectively captures these differences by evaluating the limitations that arise within the individual battery cells and the aircraft powertrain. This paper shows that the unusable charge of a battery is set by the balked landing power requirement and can realistically range from 5% to 44% based on assumptions. This sets the analog to unusable fuel capacity in aircraft with liquid fuel systems. Needing only aircraft- and mission-level inputs and only seconds of run time, this model is a prime fit for the fast, accurate exploration of the electric aircraft conceptual design space.

Battery

Design and Modeling of the Charge Readout of a SiMOS Quantum Dot with a Single Electron Transistor and CryoCMOS

Single electron spin qubits trapped in SiMOS quantum dots are a promising technology for scaling to thousand- or million-qubit systems due to their compatibility with mature CMOS manufacturing processes. A readout system that combines a single electron transistor with a custom cryogenic CMOS amplification and digitization chain offers key advantages by avoiding the use of bulky RF components or room-temperature interconnects. We present design techniques and simulation results for an optimized qubit-SET cryoCMOS interface, culminating in the design of the QNDR1 ASIC, the first cryogenic readout ASIC designed under the Quandarum project, which targets the development of a many-channel spin qubit based detector for use in high energy physics.

Quinn, Adam [Fermilab] (ORCID:0009000605056371)

Advanced Model Development for Large Eddy Simulation of Oxy-Combustion and Supercritical Carbon Dioxide Power Cycles

A joint experimental and numerical study is performed to observe the characteristics of a supercritical carbon dioxide turbulent mixing layer in the presence of strong nonlinearities in the thermodynamic and transport properties. A bespoke experimental setup is designed and employed for this purpose and provides insight into macroscopic mixing behavior. The mixing is experimentally observed using two techniques: shadowgraphy and spontaneous Raman scattering. Qualitative and quantitative intensity fields obtained via these techniques yield instantaneous and mean density data. Spanwise temperature data is also collected using analogue resistance temperature detectors. These measurements are used to quantify the level of mixed material within the field. The experimental data are supplemented by a companion high-fidelity numerical study. The numerical results are obtained through fully resolved, three-dimensional direct numerical simulation. The numerical dataset permits observation of the near-field mixing characteristics, which are difficult to measure experimentally due to the rapid dynamics and sharp thermophysical gradients in this area. Qualitative field visualizations are presented, followed by quantitative mixed material results and observations regarding thermodynamic property trends at select locations within the field. One-dimensional spectra of the turbulent kinetic energy and solenoidal dissipation are provided to observe the spectral characteristics of the flow. Reynolds stress anisotropy is analyzed graphically through anisotropy invariance maps (Lumley triangles). The mixing quantification, spectral data and anisotropy analysis of a flow at these thermodynamic conditions represent the main outcomes of the work.

20 FOSSIL-FUELED POWER PLANTS

Lightweight bipolar storage battery

An apparatus [10] is disclosed for a lightweight bipolar battery of the end-plate cell stack design. Current flow through a bipolar cell stack [12] is collected by a pair of copper end-plates [16a,16b] and transferred edgewise out of the battery by a pair of lightweight, low resistance copper terminals [28a,28b]. The copper terminals parallel the surface of a corresponding copper end-plate [16a,16b] to maximize battery throughput. The bipolar cell stack [12], copper end-plates [16a,16b] and copper terminals [28a,28b] are rigidly sandwiched between a pair of nonconductive rigid end-plates [20] having a lightweight fiber honeycomb core which eliminates distortion of individual plates within the bipolar cell stack due to internal pressures. Insulating foam [30] is injected into the fiber honeycomb core to reduce heat transfer into and out of the bipolar cell stack and to maintain uniform cell performance. A sealed battery enclosure [ 22] exposes a pair of terminal ends [26a,26b] for connection with an external circuit.

Rowlette, John J.

Elastic-plastic models for multi-site damage

This paper presents recent developments in advanced analysis methods for the computation of stress site damage. The method of solution is based on the p-version of the finite element method. Its implementation was designed to permit extraction of linear stress intensity factors using a superconvergent extraction method (known as the contour integral method) and evaluation of the J-integral following an elastic-plastic analysis. Coarse meshes are adequate for obtaining accurate results supported by p-convergence data. The elastic-plastic analysis is based on the deformation theory of plasticity and the von Mises yield criterion. The model problem consists of an aluminum plate with six equally spaced holes and a crack emanating from each hole. The cracks are of different sizes. The panel is subjected to a remote tensile load. Experimental results are available for the panel. The plasticity analysis provided the same limit load as the experimentally determined load. The results of elastic-plastic analysis were compared with the results of linear elastic analysis in an effort to evaluate how plastic zone sizes influence the crack growth rates. The onset of net-section yielding was determined also. The results show that crack growth rate is accelerated by the presence of adjacent damage, and the critical crack size is shorter when the effects of plasticity are taken into consideration. This work also addresses the effects of alternative stress-strain laws: The elastic-ideally-plastic material model is compared against the Ramberg-Osgood model.

Actis, Ricardo L.

Characterizing the subglacial environment of lower Thwaites Glacier using radar modeling

Understanding the spatial heterogeneity beneath Thwaites Glacier, West Antarctica, is vital to projecting its impact on future sea levels. Radar-echo sounding (RES) is commonly used to infer subglacial conditions, but these data can be challenging to interpret. We assess basal heterogeneity across Thwaites Glacier by comparing RES returns to a radar backscattering simulator for over 400 km of RES data. The modeled variations in bed returned power exhibited a strong correlation with actual RES data in 40% of our simulated flight segments, which we consider evidence for a relatively homogeneous glacier bed. Other sites (40%) demonstrated improved fit quality when hydrology or substrate transitions were introduced in the bed material model. The remaining simulated segments (20%) were diagnosed as having more complex basal heterogeneity. The spatial distribution of complex heterogeneity appears to coincide with asymmetric patterns in the RES specularity content, which has been interpreted in previous studies as a signature for channelized hydrology. Conversely, the homogeneous substrate locations coincide with areas of fast-moving ice in western Thwaites. Our simulation method can isolate power variations induced by material heterogeneity vs topography, which is an important limitation of existing RES analysis methods.

Antarctic glaciology

A SIMULINK Environment for Flight Dynamics and Control Analysis - Application to the DHC-2 'Beaver', Part 1. Implementation of a Model Library in SIMULINK

The design of advanced Automatic Aircraft Control Systems (AACS's) can be improved upon considerably if the designer can access all models and tools required for control system design and analysis through a graphical user-interface, from within one software environment. This MSc-thesis presents the first step in the development of such an environment, which is currently being done at the Section for Stability and Control of Delft University of Technology, Faculty of Aerospace Engineering. The environment is implemented within the commercially available software package MATLAB/SIMULINK. The report consists of two parts. Part I gives a detailed description of the AACS design environment. The heart of this environment is formed by the SIMULINK implementation of a nonlinear aircraft model in block-diagram format. The model has been worked out for the old laboratory aircraft of the Faculty, the De Havilland DHC-2 'Beaver', but due to its modular structure, it can easily be adapted for other aircraft. Part I also describes MATLAB programs which can be applied for finding steady-state trimmed-flight conditions and for linearization of the aircraft model, and it shows how the built-in simulation routines of SIMULINK have been used for open-loop analysis of the aircraft dynamics. Apart from the implementation of the models and tools, a thorough treatment of the theoretical backgrounds is presented. Part II of this report presents a part of an autopilot design process for the 'Beaver' aircraft, which clearly demonstrates the power and flexibility of the AACS design environment from part I. Evaluations of all longitudinal and lateral control laws by means of nonlinear simulations are treated in detail. The AACS design environment from part I proved to be a very useful tool for designing the control laws of the 'Beaver' autopilot within a very tight time-schedule. The autopilot design process itself will be used as a guideline for future AACS research at the Faculty of Aerospace Engineering. Flight tests of the 'Beaver' autopilot, done after evaluating the control laws in the SIMULINK package, proved to be quite successful. In the future, the AACS design package will evolve into a standardized, integrated design environment which can be applied to virtually any type of aircraft. The AACS design cycle will be shortened further by developing tools for automatically porting control laws from the MATLAB/SIMULINK environment to a piloted real-time flight simulator and the Flight Control Computers of the aircraft.

Aircraft Modelling

Computing the Critical Temperature of the Affine-Transformed $D=3$ Ising Model Using Masked Autoregressive Flow

The simple Ising model provides a rich environment to build and study lattice field theories. As part of an ongoing project to construct a conformal field theory (CFT) on an arbitrarily curved manifold, in this work we develop methods to measure the critical temperature $β_c$ of the affine-transformed Ising model on the face-centered cubic (FCC) lattice. The main challenge in this endeavor is finding a computationally efficient and accurate method of interpolating and extrapolating Monte Carlo observables with respect to coupling coefficients and temperature. Herein, we compare two such methods. A traditional statistical approach uses the multiple histogram (MH) method, while a newer machine learning approach uses a masked autoregressive flow (MAF) to estimate the underlying probability density function of a set of observables. While the MH method is specifically designed to interpolate and extrapolate Monte Carlo observables, we find that MAF is a viable alternative for measuring $β_c$ with a computational cost that scales more favorably. Furthermore, we comment on additional advantages of MAF relevant to our work, such as extrapolating in system volume.

Svenson, Kai [Texas U.]

Sustainable Triacetic Acid Lactone Production from Sugarcane by Fermentation and Crystallization

Triacetic acid lactone (TAL) has the potential to serve as a bioderived platform chemical for commercial products including sorbic acid and recyclable polydiketoenamine plastics. In this study, we leveraged BioSTEAM to design, simulate, and evaluate (via techno-economic analysis, TEA, and life cycle assessment, LCA) TAL production from sugarcane. We experimentally characterized TAL solubility, calibrated solubility models, and designed a process to separate TAL from fermentation broths by crystallization. The biorefinery could produce TAL at a minimum product selling price (MPSP) of $\$3.73$–5.86·kg –1 (5th–95th percentiles; baseline at $\$4.60$·kg –1 ) and a carbon intensity (CI) of 5.31 [2.60–8.71] kg CO 2 -eq·kg –1 , which could enable financially viable, low-CI production of sorbic acid and polydiketoenamines. To drive down costs and CI, we explored the theoretical fermentation space (titer, yield, productivity combinations), operation scheduling and capacity expansion strategies (e.g., integrated sorghum processing), and potential separation improvements (mitigating TAL loss through pH control). Advancements in key design and technological parameters could further reduce MPSP by 51% to $\$2.26$·kg –1 [$\$1.97$–2.80·kg –1 ] and CI by 43% to 3.05 [1.91–4.15] kg CO 2 -eq·kg –1 . This research highlights the ability of agile TEA-LCA to screen promising designs, navigate sustainability trade-offs, prioritize research needs, and chart quantitative roadmaps to advance bioproducts and biofuels.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH