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Regional surrogates for predictive control of digital twins

Digital twins of complex systems must involve a model that is fast, generalizable, and usable for real-time control. For example, high-fidelity nonlinear multiphysics simulations can capture laser-material interactions, but are too slow for optimization or model predictive control (MPC). Reduced-order models, used to accelerate such computation, frequently fail to generalize to unseen inputs or control states. We show theoretically that this failure is intrinsic, i.e., that a learned model is non-unique outside the sampled subspace when its low-rank structure arises from limited excitation and clustered eigenvalues, rather than from a user-imposed truncation alone. Motivated by this result, we propose a control-ready regional surrogate-construction framework for both autonomous and nonautonomous dynamics; it employs Koopman lifting to represent nonlinearities, while preserving spatial locality. We illustrate our approach by constructing a control-ready surrogate for the digital twin of a thermal component of additive-manufacturing process. Our surrogate, localized in space through a von Neumann stencil, is learned from noisy high-fidelity simulations that emulate thermal-camera images collected during the manufacturing. It is linear in thermo-physically augmented states so that MPC reduces to a convex quadratic program. The surrogate requires no online correction, generalizes to unseen scan paths and power profiles of the laser, and is more than three orders of magnitude faster than a finite-difference solver. Furthermore, when the MPC sequence computed on the digital twin is applied to this solver, closed-loop temperature regulation is recovered, showing that the surrogate preserves control-relevant input-output behavior.

Data-driven model↗

Optimal SCR Control Using Data-Driven Models

We present an optimal control solution for the urea injection for a heavy-duty diesel (HDD) selective catalytic reduction (SCR). The approach taken here is useful beyond SCR and could be applied to any system where a control strategy is desired and input-output data is available. For example, the strategy could also be used for the diesel oxidation catalyst (DOC) system. In this paper, we identify and validate a one-step ahead Kalman state-space estimator for downstream NOx using the bench reactor data of an SCR core sample. The test data was acquired using a 2010 Cummins 6.7L ISB production engine with a 2010 Cummins production aftertreatment system. We used a surrogate HDD federal test procedure (FTP), developed at Michigan Technological University (MTU), which simulates the representative transients of the standard FTP cycle, but has less engine speed/load points. The identified state-space model is then used to develop a tunable cost function that simultaneously minimizes NOx emissions and urea usage. The cost function is quadratic and univariate, thus the minimum can be computed analytically. We show the performance of the closed-loop controller in using a reduced-order discrete SCR simulator developed at MTU. Our experiments with the surrogate HDD-FTP data show that the strategy developed in this paper can be used to identify performance bounds for urea dose controllers.

diesel, emmissions, control, environment, modeling↗

Shubnikov–de Haas oscillations of biaxial-strain-tuned superconductors in pulsed magnetic field up to 60 T

Two-dimensional (2D) materials have gained increasing prominence not only in fundamental research but also in daily applications. However, to fully harness their potential, it is crucial to optimize their properties with an external parameter and track the electronic structure simultaneously. Magnetotransport over a wide magnetic field range is a powerful method to probe the electronic structure and, for metallic 2D materials, quantum oscillations superimposed on the transport signals encode Fermi surface parameters. In this manuscript, we utilize biaxial strain as an external tuning parameter and investigate the effects of strain on the electronic properties of two quasi-2D superconductors, MoTe 2 and RbV 3 Sb 5 , by measuring their magnetoresistance in pulsed magnetic fields up to 60 T. With a careful selection of insulating substrates, we demonstrate the possibility of both the compressive and tensile biaxial strains imposed on MoTe 2 and RbV 3 Sb 5 , respectively. For both systems, the applied strain has led to superconducting critical temperature enhancement compared to their free-standing counterparts, proving the effectiveness of this biaxial strain method at cryogenic temperatures. Clear quantum oscillations in the magnetoresistance—the Shubnikov–de Haas (SdH) effect—are obtained in both samples. In strained MoTe 2 , the magnetoresistance exhibits a nearly quadratic dependence on the magnetic field and remains non-saturating even at the highest field, whereas in strained RbV 3 Sb 5 , two SdH frequencies showed a substantial enhancement in effective mass values, hinting at a possible enhancement of charge fluctuations. Our results demonstrate that combining biaxial strain and pulsed magnetic field paves the way for studying 2D materials under unprecedented conditions.

2D materials↗

Shubnikov-de Haas oscillations of biaxial-strain-tuned superconductors in pulsed magnetic field up to 60 T

Two-dimensional (2D) materials have gained increasing prominence not only in fundamental research but also in daily applications. However, to fully harness their potential, it is crucial to optimize their properties with an external parameter and track the electronic structure simultaneously. Magnetotransport over a wide magnetic field range is a powerful method to probe the electronic structure and, for metallic 2D materials, quantum oscillations superimposed on the transport signals encode Fermi surface parameters. In this manuscript, we utilize biaxial strain as an external tuning parameter and investigate the effects of strain on the electronic properties of two quasi-2D superconductors, MoTe 2 and RbV 3 Sb 5 , by measuring their magnetoresistance in pulsed magnetic fields up to 60 T. With a careful selection of insulating substrates, we demonstrate the possibility of both the compressive and tensile biaxial strains imposed on MoTe 2 and RbV 3 Sb 5 , respectively. For both systems, the applied strain has led to superconducting critical temperature enhancement compared to their free-standing counterparts, proving the effectiveness of this biaxial strain method at cryogenic temperatures. Clear quantum oscillations in the magnetoresistance—the Shubnikov–de Haas (SdH) effect—are obtained in both samples. In strained MoTe 2 , the magnetoresistance exhibits a nearly quadratic dependence on the magnetic field and remains non-saturating even at the highest field, whereas in strained RbV 3 Sb 5 , two SdH frequencies showed a substantial enhancement in effective mass values, hinting at a possible enhancement of charge fluctuations. Our results demonstrate that combining biaxial strain and pulsed magnetic field paves the way for studying 2D materials under unprecedented conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A treatment planning approach to spatially fractionated megavoltage grid therapy for bulky lung cancer

The purpose of this study was to explore the treatment planning methods of spatially fractionated megavoltage grid therapy for treating bulky lung tumors using multileaf collimator (MLC). A total of 5 patients with lung cancer who had gross tumor volumes ranging from 277 to 635 cm{sup 3} were retrospectively chosen for this study. The tumors were from 6.5 to 9.6 cm at shortest dimension. Several techniques using either electronic compensation or intensity-modulated radiation therapy (IMRT) were used to create a variety of grid therapy plans on the Eclipse treatment planning system. The dose prescription point was calculated to the volume, and a dose of 20 Gy with 6-MV/15-MV beams was used in each plan. The dose-volume histogram (DVH) curves were obtained to evaluate dosimetric characteristics. In addition, DVH curves from a commercially available cerrobend grid collimator were also used for comparison. The linear-quadratic radiobiological response model was used to assess therapeutic ratios (TRs) and equivalent uniform doses (EUD) for all generated plans. A total of 6 different grid therapy plans were created for each patient. Overall, 4 plans had different electronic compensation techniques: Ecomps-Tubes, Ecomps-Circles, Ecomps-Squares, and Ecomps-Weave; the other 2 plans used IMRT and IMRT-Weave techniques. The DVH curves and TRs demonstrated that these MLC-based grid therapy plans can achieve dosimetric properties very similar to those of the cerrobend grid collimator. However, the MLC-based plans have larger EUDs than those with the cerrobend grid collimator. In addition, the field shaping can be performed for targets of any shape in MLC-based plans. Thus, they can deliver a more conformal dose to the targets and spare normal structures better than the cerrobend grid collimator can. The plans generated by the MLC technique demonstrated the advantage over the standard cerrobend grid collimator on accommodating targets and sparing normal structures. Overall, 6 different plans showed 6 different dosimetric parameters. However, an optimal grid therapy plan selection from among these 6 types requires more information from clinical trials and radiobiological studies.

61 RADIATION PROTECTION AND DOSIMETRY↗

WE-E-BRE-07: High-Throughput Mapping of Proton Biologic Effect

Purpose: To systematically relate the relative biological effectives (RBE) of proton therapy to beam linear energy transfer (LET) and dose. Methods: Using a custom irradiation apparatus previously characterized by our group, H460 NSCLCs were irradiated using a clinical 80MeV spot scanning proton beam. Utilizing this system allowed for high-throughput clonogenic assays performed in 96-well tissue culture plates as opposed to the traditional 6-well technique. Each column in the 96-well plate received a set LET-dose combination. By altering the total number of dose repaintings, numerous dose-LET configurations were examined to effectively generate surviving fraction (SF) data over the entire Bragg peak. The clonogenic assay was performed post-irradiation using an INCell Analyzer for colony quantification. SF data were fit to the linear-quadratic model for analysis. Results: Irradiation with increasing LETs resulted in decreased cell survival largely independent of dose. A significant correlation between LET and SF was identified by two-way ANOVA and the extra sum-of-squares F test. This trend was obscured at the lower LET values in the plateau region of the Bragg peak; however, it was clear for LET values at and beyond the Bragg peak. Data fits revealed the SF at a dose of 2Gy (SF2) to be 0.48 for the lowest tested LET (1.55keV/um), 0.47 at the end of the plateau region (4.74keV/um) and 0.33 for protons at the Bragg peak (10.35keV/um). Beyond the Bragg peak we measured SF2s of 0.16 for 15.01keV/um, 0.02 for 16.79keV/um, and 0.004 for 18.06keV/um. Conclusion: We have shown that our methodology enables high-content automated screening for proton irradiations over a range of LETs. The observed decrease in cellular SF in high LET regions confirms an increased RBE of the radiation and suggests further evaluation of proton RBE values is necessary to optimize clinical outcomes. Rosalie B. Hite Graduate Fellowship in Cancer Research, NIH Program Project Grant P01CA021239.

60 APPLIED LIFE SCIENCES↗

Thermo-hydraulic steam pipe models for district heating simulations: Simplifications to balance accuracy and simulation speed

Steam piping networks are essential for optimizing performance in industrial processes and district heating systems. However, dynamic models that balance thermo-hydraulic accuracy with computational efficiency remain limited. In response, this paper presents a new discretized steam pipe model based on the plug flow approach, capturing key thermo-hydraulic behaviors while simplifying steam phase change processes. Implemented in Modelica, the model accurately calculates temperature and pressure distributions along steam pipelines. To improve computational efficiency for district-scale simulations, five model simplifications are introduced: lumped thermo-hydraulic functions, empirical correlations, fluid state approximations, steady-state dynamics and inclusion of flow derivatives. These simplified models achieve 85%-98% accuracy in predicting pressure drop and condensation losses, including dynamic condensate behavior during pipe warm-up—a factor often overlooked in existing models. The models support diverse network configurations, scaling effectively to systems with multiple distribution pipes and connected building loads. Discrete models provide detailed insights but exhibit a cubic increase in simulation time as the network scales by N connected building O(N 2.42 ). In contrast, lumped models simulate 10–28 times faster than discrete, offering quadratic scaling of simulation time O(N 1.73 ). However, they still require 6 times more computation time than a lossless network, highlighting the inherent computational challenges of modeling compressible fluid flow. In conclusion, the steady-state lumped variant, with its near-linear scalability in computational time O(N 1.01 ), emerges as an efficient solution for preliminary design evaluations and extensive parametric studies.

15 GEOTHERMAL ENERGY↗

Spatial Study 2022: Surface Water Samples, Cotton Strip Degradation, and Hydrologic Sensor Data across the Yakima River Basin, Washington, USA (v3)

This dataset supports a broader study examining the drivers of spatial variability in sediment respiration rates in the Yakima River Basin. The dataset provides data and photos generated from sample collection during the same one-week period at 48 sites within multiple rivers throughout the Yakima River Basin in Washington, USA. The contents include surface water geochemistry data; river substrate grain size photos; stream depth data; manual chamber open channel respiration data; and field metadata (including qualitative information on instream and river corridor characteristics). Grain size photos can be used to improve estimates of channel substrate D50 data. The dataset also includes tensile strength and photos from cotton strip field degradation experiments; five-week sensor time series temperature, dissolved oxygen, pressure, pH, specific conductance, chlorophyll A, and turbidity data; plots of the sensor data; and R scripts used to generate the plots. Samples collected during this study were labeled as “Second Spatial Study” or “SSS.” A subset of data from the SSS samples were published in the contiguous United States (CONUS)-Scale Model-Sample (CM) study data package available at https://data.ess-dive.lbl.gov/view/doi:10.15485/1923689 that presents data from across the CONUS. SSS data published in the CM data package were not included in this data package. They include dissolved organic carbon (DOC, measured as non-purgeable organic carbon, NPOC), total nitrogen (TN), grain size, aerobic sediment respiration, dissolved oxygen (DO), and temperature. Parent IDs and Site IDs are consistent between the SSS and CM data packages, and they can be mapped directly so data across packages can be used together. Additionally, sensor data from a similar 2021 spatial study can be found at https://data.ess-dive.lbl.gov/view/doi:10.15485/1892052 and 2021 sample data can be found at https://data.ess-dive.lbl.gov/view/doi:10.15485/1898914. The 2021 spatial study had some sites in common with this 2022 spatial study. This dataset is comprised of three photo folders and one main data folder with six subfolders. The photo folders contain photographs and videos of cotton strip retrieval and sediment quadrats. The main data folder consists of (1) file-level metadata; (2) data dictionary; (3) field metadata; (4) total suspended solids (TSS) data and cotton strip tensile strength data and averages; (5) field protocol; (6) readme; (7) methods codes; (8) international generic sample number (IGSN) mapping file; (9) sensor installation methods summary; (10) stream depth and averages; and (11) Ultrameter data and averages. The Sonar subfolder consists of Sonar time-series depth data and a processing script. The BarotrollAtm, DepthHOBO, MantaRiver, miniDOT, and miniDOTManualChamber subfolders contain time-series data, plots, and summary files. All files are .csv, .pdf, .txt, .R, .Rmd, .jpg, .jpeg, .AVI, .mp4, or .mov. The data package was originally published in April 2023. It was updated in August 2023 (v2; modified files) and September 2024 (v3; modified files). See the change history section in the readme for details. We acknowledge the Yakama Nation as owners and caretakers of the lands where we collected these data. We thank the Confederated Tribes and Bands of the Yakama Nation Tribal Council and Yakama Nation Fisheries for working with us to facilitate sample collection and optimization of data usage according to their values and worldview.

54 ENVIRONMENTAL SCIENCES↗

Voltage linearity modulation and polarity dependent conduction in metal-insulator-metal capacitors with atomic-layer-deposited Al{sub 2}O{sub 3}/ZrO{sub 2}/SiO{sub 2} nano-stacks

Excellent voltage linearity of metal-insulator-metal (MIM) capacitors is highly required for next generation radio frequency integration circuits. In this work, employing atomic layer deposition technique, we demonstrated how the voltage linearity of MIM capacitors was modulated by adding different thickness of SiO{sub 2} layer to the nano-stack of Al{sub 2}O{sub 3}/ZrO{sub 2}. It was found that the quadratic voltage coefficient of capacitance (α) can be effectively reduced from 1279 to −75 ppm/V{sup 2} with increasing the thickness of SiO{sub 2} from zero to 4 nm, which is more powerful than increasing the thickness of ZrO{sub 2} in the Al{sub 2}O{sub 3}/ZrO{sub 2} stack. This is attributed to counteraction between the positive α for Al{sub 2}O{sub 3}/ZrO{sub 2} and the negative one for SiO{sub 2} in the MIM capacitors with Al{sub 2}O{sub 3}/ZrO{sub 2}/SiO{sub 2} stacks. Interestingly, voltage-polarity dependent conduction behaviors in the MIM capacitors were observed. For electron bottom-injection, the addition of SiO{sub 2} obviously suppressed the leakage current; however, it abnormally increased the leakage current for electron top-injection. These are ascribed to the co-existence of shallow and deep traps in ZrO{sub 2}, and the former is in favor of the field-assisted tunnelling conduction and the latter contributes to the trap-assisted tunnelling process. The above findings will be beneficial to device design and process optimization for high performance MIM capacitors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Simulator evaluation of system identification with on-line control law update for the controls and astrophysics experiment in space

A procedure for optimizing the performance of large flexible spacecraft that require active vibration suppression to achieve required performance is presented. The procedure is to conduct on-orbit testing and system identification followed by a control system design. It is applied via simulation to a spacecraft configuration currently being considered for flight test by NASA - the Controls, Astrophysics, and Structures Experiment in Space (CASES). The system simulator is based on a NASTRAN finite element structural model. A finite number of modes is used to represent the structural dynamics. The system simulator also includes models of the electronics, actuators, sensors, the digital controller, and the internal and external disturbances. Nonlinearities caused by quantization are included in the study to examine tolerance of the procedure to modelling errors. Disturbance and sensor noise is modelled as a Gaussian process. For system identification, the system is excited using sinusoidal inputs at the resonant frequencies of the structure using each actuator. Mode shapes, frequencies, and damping ratios are identified from the unforced response sensor data after each excitation. Then, the excitation data is used to identify the actuator influence coefficients. The results of the individual parameter identification analyses are assembled into an aggregate system model. The control design is accomplished based only on the identified model using multi-input/output linear quadratic Gaussian theory. Its performance is evaluated based on time-to-damp as compared with the uncontrolled structure.

Montgomery, Raymond C.↗

A Mechanism-Based Approach to Predict the Relative Biological Effectiveness of Protons and Carbon Ions in Radiation Therapy

Purpose: The physical and potential biological advantages of proton and carbon ions have not been fully exploited in radiation therapy for the treatment of cancer. In this work, an approach to predict proton and carbon ion relative biological effectiveness (RBE) in a representative spread-out Bragg peak (SOBP) is derived using the repair-misrepair-fixation (RMF) model. Methods and Materials: Formulas linking dose-averaged linear-quadratic parameters to DSB induction and processing are derived from the RMF model. The Monte Carlo Damage Simulation (MCDS) software is used to quantify the effects of radiation quality on the induction of DNA double-strand breaks (DSB). Trends in parameters {alpha} and {beta} for clinically relevant proton and carbon ion kinetic energies are determined. Results: Proton and carbon ion RBE are shown to increase as particle energy, dose, and tissue {alpha}/{beta} ratios decrease. Entrance RBE is {approx}1.0 and {approx}1.3 for protons and carbon ions, respectively. For doses in the range of 0.5 to 10 Gy, proton RBE ranges from 1.02 (proximal edge) to 1.4 (distal edge). Over the same dose range, the RBE for carbon ions ranges from 1.5 on the proximal edge to 6.7 on the distal edge. Conclusions: The proposed approach is advantageous because the RBE for clinically relevant particle distributions is guided by well-established physical and biological (track structure) considerations. The use of an independently tested Monte Carlo model to predict the effects of radiation quality on DSB induction also minimizes the number of ad hoc biological parameters that must be determined to predict RBE. Large variations in predicted RBE across an SOBP may produce undesirable biological hot and cold spots. These results highlight the potential for the optimization of physical dose for a uniform biological effect.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Isotherm Modeling and Techno-Economic Analysis of Contactor Technologies for New Tetraamine-Appended MOF for NGCC Applications

Recently, a family of tetraamine-functionalized metal-organic frameworks (MOF) has been reported as promising sorbent materials for capturing CO2 from flue gas conditions relevant to natural gas combined cycle (NGCC) applications. The main advantages of these materials are their two-step cooperative CO2 adsorption, which gives rise to unusual two step-shaped CO2 adsorption profiles and their high thermal stability. This work presents the modelling of the two-transition isotherm of the tetraamine-appended MOF, N,N'-bis(3-aminopropyl)-1,4-diaminobutane (3-4-3)-appended Mg2(dobpdc), and the techno-economic analysis (TEA) of carbon capture processes utilizing this sorbent. Due to the unusual isotherm shapes of the experimental CO2 adsorption data for tetraamine-appended Mg2(dobpdc) and the strong nonlinearity of CO2 loading with respect to temperature and pressure, we tested two different models which use logistic functions for representing the different isotherm behaviors in the different pressure ranges. The first model uses the quadratic isotherm model in the low-pressure region, the Langmuir isotherm model in the middle pressure range, and the dual site Langmuir isotherm model in the high-pressure range. To model the transition between regions we used the arctangent functions independent of temperature and the thermal effect was accounted by using the Clausius-Clapeyron relation]. The second model is an extension of the weighted dual-site Langmuir isotherm model presented by Hughes et al.. In this extended model, the dual-site Langmuir isotherm is employed in the three transition regions, using temperature-dependent logistic functions to activate or deactivate the isotherm model in the low, middle, and high-pressure ranges. Both models fit the experimental data quite well with root mean squared errors (RMSE’s) of 0.41 and 0.17 for model 1 and model 2, respectively. Since model 2 resulted in a lower RMSE, it was leveraged for the development of the gas/solid contactor models used by the TEA. Specifically, two different contactor models, an axial-flow fixed bed and moving bed contactor, were developed as part of this work. These models are dynamic, pressure-driven, and consist of mass, energy, and momentum conservation equations. A kinetic model was also developed by performing parameter estimation using experimental fixed bed breakthrough data. These models are then used to simulate CO2 capture processes from the flue gas generated from a ~600 gross MW NGCC power plant. A cost model was developed which considers the capital cost of the reactors and the significant operating costs such as steam and electricity. Using NETL’s Framework for the Optimization and Quantification of Uncertainty of Uncertainty and Surrogates tool (FOQUS), which has the capability of linking models built using numerous modelling platforms with derivative-free optimization solvers, a techno-economic optimization of the carbon capture processes was performed which minimizes the cost of capture.

Caballero, Daison↗

Carbon dioxide in an ionic liquid: Structural and rotational dynamics

Ionic liquids (ILs), which have widely tunable structural motifs and intermolecular interactions with solutes, have been proposed as possible carbon capture media. In order to inform the choice of an optimal ionic liquid system, it can be useful to understand the details of dynamics and interactions on fundamental time scales (femtoseconds to picoseconds) of dissolved gases, particularly carbon dioxide (CO 2 ), within the complex solvation structures present in these uniquely organized materials. The rotational and local structural fluctuation dynamics of CO 2 in the room temperature ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EmimNTf2) were investigated by using ultrafast infrared spectroscopy to interrogate the CO 2 asymmetric stretch. Polarization-selective pump probe measurements yielded the orientational correlation function of the CO 2 vibrational transition dipole. It was found that reorientation of the carbon dioxide occurs on 3 time scales: 0.91 ± 0.03, 8.3 ± 0.1, 54 ± 1 ps. The initial two are attributed to restricted wobbling motions originating from a gating of CO 2 motions by the IL cations and anions. The final (slowest) decay corresponds to complete orientational randomization. Two-dimensional infrared vibrational echo (2D IR) spectroscopy provided information on structural rearrangements, which cause spectral diffusion, through the time dependence of the 2D line shape. Analysis of the time-dependent 2D IR spectra yields the frequency-frequency correlation function (FFCF). Polarization-selective 2D IR experiments conducted on the CO 2 asymmetric stretch in the parallel- and perpendicular-pumped geometries yield significantly different FFCFs due to a phenomenon known as reorientation-induced spectral diffusion (RISD), revealing strong vector interactions with the liquid structures that evolve slowly on the (independently measured) rotation time scales. To separate the RISD contribution to the FFCF from the structural spectral diffusion contribution, the previously developed first order Stark effect RISD model is reformulated to describe the second order (quadratic) Stark effect—the first order Stark effect vanishes because CO 2 does not have a permanent dipole moment. Through this analysis, we characterize the structural fluctuations of CO 2 in the ionic liquid solvation environment, which separate into magnitude-only and combined magnitude and directional correlations of the liquid’s time dependent electric field. This new methodology will enable highly incisive comparisons between CO 2 dynamics in a variety of ionic liquid systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Versatile Nonlinear Method for Predictive Modeling

As computational fluid dynamics techniques and tools become widely accepted for realworld practice today, it is intriguing to ask: what areas can it be utilized to its potential in the future. Some promising areas include design optimization and exploration of fluid dynamics phenomena (the concept of numerical wind tunnel), in which both have the common feature where some parameters are varied repeatedly and the computation can be costly. We are especially interested in the need for an accurate and efficient approach for handling these applications: (1) capturing complex nonlinear dynamics inherent in a system under consideration and (2) versatility (robustness) to encompass a range of parametric variations. In our previous paper, we proposed to use first-order Taylor expansion collected at numerous sampling points along a trajectory and assembled together via nonlinear weighting functions. The validity and performance of this approach was demonstrated for a number of problems with a vastly different input functions. In this study, we are especially interested in enhancing the method's accuracy; we extend it to include the second-orer Taylor expansion, which however requires a complicated evaluation of Hessian matrices for a system of equations, like in fluid dynamics. We propose a method to avoid these Hessian matrices, while maintaining the accuracy. Results based on the method are presented to confirm its validity.

nonlinear modeling↗

GENPLAT: an Automated Platform for Biomass Enzyme Discovery and Cocktail Optimization

The high cost of enzymes for biomass deconstruction is a major impediment to the economic conversion of lignocellulosic feedstocks to liquid transportation fuels such as ethanol. We have developed an integrated high throughput platform, called GENPLAT, for the discovery and development of novel enzymes and enzyme cocktails for the release of sugars from diverse pretreatment/biomass combinations. GENPLAT comprises four elements: individual pure enzymes, statistical design of experiments, robotic pipeting of biomass slurries and enzymes, and automated colorimeteric determination of released Glc and Xyl. Individual enzymes are produced by expression in Pichia pastoris or Trichoderma reesei, or by chromatographic purification from commercial cocktails or from extracts of novel microorganisms. Simplex lattice (fractional factorial) mixture models are designed using commercial Design of Experiment statistical software. Enzyme mixtures of high complexity are constructed using robotic pipeting into a 96-well format. The measurement of released Glc and Xyl is automated using enzyme-linked colorimetric assays. Optimized enzyme mixtures containing as many as 16 components have been tested on a variety of feedstock and pretreatment combinations. GENPLAT is adaptable to mixtures of pure enzymes, mixtures of commercial products (e.g., Accellerase 1000 and Novozyme 188), extracts of novel microbes, or combinations thereof. To make and test mixtures of ˜10 pure enzymes requires less than 100 μg of each protein and fewer than 100 total reactions, when operated at a final total loading of 15 mg protein/g glucan. We use enzymes from several sources. Enzymes can be purified from natural sources such as fungal cultures (e.g., Aspergillus niger, Cochliobolus carbonum, and Galerina marginata), or they can be made by expression of the encoding genes (obtained from the increasing number of microbial genome sequences) in hosts such as E. coli, Pichia pastoris, or a filamentous fungus such as T. reesei. Proteins can also be purified from commercial enzyme cocktails (e.g., Multifect Xylanase, Novozyme 188). An increasing number of pure enzymes, including glycosyl hydrolases, cell wall-active esterases, proteases, and lyases, are available from commercial sources, e.g., Megazyme, Inc. (www.megazyme.com), NZYTech (www.nzytech.com), and PROZOMIX (www.prozomix.com). Design-Expert software (Stat-Ease, Inc.) is used to create simplex-lattice designs and to analyze responses (in this case, Glc and Xyl release). Mixtures contain 4-20 components, which can vary in proportion between 0 and 100%. Assay points typically include the extreme vertices with a sufficient number of intervening points to generate a valid model. In the terminology of experimental design, most of our studies are "mixture" experiments, meaning that the sum of all components adds to a total fixed protein loading (expressed as mg/g glucan). The number of mixtures in the simplex-lattice depends on both the number of components in the mixture and the degree of polynomial (quadratic or cubic). For example, a 6-component experiment will entail 63 separate reactions with an augmented special cubic model, which can detect three-way interactions, whereas only 23 individual reactions are necessary with an augmented quadratic model. For mixtures containing more than eight components, a quadratic experimental design is more practical, and in our experience such models are usually statistically valid. All enzyme loadings are expressed as a percentage of the final total loading (which for our experiments is typically 15 mg protein/g glucan). For "core" enzymes, the lower percentage limit is set to 5%. This limit was derived from our experience in which yields of Glc and/or Xyl were very low if any core enzyme was present at 0%. Poor models result from too many samples showing very low Glc or Xyl yields. Setting a lower limit in turn determines an upper limit. That is, for a six-component experiment, if the lower limit for each single component is set to 5%, then the upper limit of each single component will be 75%. The lower limits of all other enzymes considered as "accessory" are set to 0%. "Core" and "accessory" are somewhat arbitrary designations and will differ depending on the substrate, but in our studies the core enzymes for release of Glc from corn stover comprise the following enzymes from T. reesei: CBH1 (also known as Cel7A), CBH2 (Cel6A), EG1(Cel7B), BG (βglucosidase), EX3 (endo-β1,4-xylanase, GH10), and BX (β-xylosidase).

09 BIOMASS FUELS↗