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At least 73 records · Page 4

Dynamic Catalysis Fundamentals: I. Fast calculation of limit cycles in dynamic catalysis

Dynamic catalysis—the forced oscillation of catalytic reaction coordinate potential energy surfaces (PES)—has recently emerged as a promising method for the acceleration of heterogeneously-catalyzed reactions. Theoretical study of enhancement of rates and supra-equilibrium product yield via dynamic catalysis has, to-date, been severely limited by onerous computational demands of forward integration of stiff, coupled ordinary differential equations (ODEs) that are necessary to quantitatively describe periodic cycling between PESs. Here, we establish a new approach that reduces, by ≳108×, the computational cost of finding the time-averaged rate at dynamic steady state (i.e. the limit cycle for linear and nonlinear systems of kinetic equations). Our developments are motivated by and conceived from physical and mathematical insight drawn from examination of a simple, didactic case study for which closed-form solutions of rate enhancement are derived in explicit terms of periods of oscillation and elementary step rate constants. Generalization of such closed-form solutions to more complex catalytic systems is achieved by introducing a periodic boundary condition requiring the dynamic steady state solution to have the same periodicity as the kinetic oscillations and solving the corresponding differential equations by linear algebra or Newton-Raphson-based approaches. The methodology is well-suited to extension to non-linear systems for which we detail the potential for multiple solutions or solutions with different periodicities. For linear and non-linear systems alike, the acute decrement in computational expense enables rapid optimization of oscillation waveforms and, consequently, accelerates understanding of the key catalyst properties that enable maximization of reaction rates, conversions, and selectivities during dynamic catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

HLPW-4/GMGW-3: Mesh Adaptation for RANS Technology Focus Group Workshop Summary

The AIAA workshop series helps guide the Computational Fluid Dynamics (CFD) community through publicly available test cases and impartial evaluation to establish the state-of-the-art in applied CFD. A summary of the Mesh Adaptation Technical Focus Group submissions for the joint Fourth CFD High Lift Prediction and Third Geometry & Mesh Generation Workshop is provided. The Common Research Model High-Lift variant (CRM-HL) is the target of this investigation. A 2D high-lift airfoil solution verification case was extracted from the 3D CRM-HL. Low variation is shown between 2D solutions with mesh adaptation to control estimated solution interpolation and output errors. As expected, variation for these mesh adaptation techniques is larger for the 3D CRM-HL than the 2D airfoil. More importantly, the 3D mesh adapted results have a lower variation than expert-crafted meshes of equal or larger size. Suspected multiple solutions to Reynolds-averaged Navier-Stokes with the Spalart-Allmaras turbulence model appear to resolve into a common solution with mesh resolution.

HLPW-4↗

Final Technical Report: Transport of Complex Mixtures in Ion-Containing Polymer Membranes

Permselective ion-containing membranes are an integral component for many applications from water treatment, fuel cells, and solar fuels devices where the selective transport of molecules and ions is desired. In solar fuels devices, ion-containing polymer membranes are responsible for permitting selective transport of ions between electrodes to maintain overall charge neutrality yet limit transport of reaction products produced at the electrodes. While the transport of single solutes through such membranes has been fairly well described, binary and multicomponent transport is poorly understood due to the myriad of interactions that occur in these systems (i.e. between co-permeants and between permeants and the membrane). Solar fuels devices are just one example of an application where understanding the transport of multiple simultaneous species is critically important to improving device performance as product crossover leads to reductions in overall device performance. The objectives of this research was to improve our understanding of the complex array of factors that influence transport behavior of multiple solutes within ion-containing polymer membranes. This experimental project addressed the lack of fundamental understanding of multicomponent transport behavior by synthesizing ion exchange membranes with varied incorporation of comonomers (ionic and neutral moieties) to investigate fundamental relationships between membrane structure, membrane physiochemical properties, and transport behavior of solutes and complex solute mixtures through dense, hydrated membranes.

25 ENERGY STORAGE↗

Natural convection in steady solidification - Finite element analysis of a two-phase Rayleigh-Benard problem

Galerkin finite-element approximations and Newton's method for solving free boundary problems are combined with computer-implemented techniques from nonlinear perturbation analysis to study solidification problems with natural convection in the melt. The Newton method gives rapid convergence to steady state velocity, temperature and pressure fields and melt-solid interface shapes, and forms the basis for algebraic methods for detecting multiple steady flows and assessing their stability. The power of this combination is demonstrated for a two-phase Rayleigh-Benard problem composed of melt and solid in a veritical cylinder with the thermal boundary conditions arranged so that a static melt with a flat melt-solid interface is always a solution. Multiple cellular flows bifurcating from the static state are detected and followed as Rayleigh number is varied. Changing the boundary conditions to approach those appropriate for the vertical Bridgman solidification system causes imperfections that eliminate the static state. The flow structure in the Bridgman system is related to those for the Rayleigh-Benard system by a continuous evolution of the boundary conditions.

Chang, C. J.↗

Uncertainty estimation of bifurcated solutions in the Rayleigh–Bénard problem for advanced nuclear reactors applications

Multiphysics models of nuclear reactors frequently comprise nonlinear systems of equations. The nonlinear nature of these models could lead to solution bifurcations, where a small change in a certain parameter, e.g., the thermophysical properties of the coolant, can lead to a sudden change in the system’s behavior. At the point in parameter space where this happens, called a critical point, the Jacobian matrix of the model’s nonlinear operator becomes singular potentially permitting multiple solutions to coexist. In this paper, we perform uncertainty estimation (UE) in a parameter range that includes bifurcated solutions within the context of Rayleigh–Bénard problem. We perform this analysis assuming uncertain temperature difference, and tilt angle for the iterative solution algorithm with a unit Prandtl number (Pr = 1). Also, we perform this analysis under uncertain thermophysical properties for both FLiBe molten salt and liquid sodium as working fluid. We deploy two approaches to compute statistical moments for the resulting distributions of selected flow-field variables. The first approach is the blind computation of the mean and the standard deviation without any consideration of solution bifurcation, while the second approach utilizes k-means clustering to cluster each branch’s solutions together and compute separate statistical moments for each branch. The statistical distributions are obtained by perturbing the selected parameters about nominal values that correspond to a solution on one of the valid branches, and that solution is used as initial guess for the iterative solution algorithm. We found that perturbation of any parameter when its nominal value is close to its critical point always leads to branch jumping, i.e., the iterations converge to a solution on a branch different from the branch of the initial guess. This produces a statistical ensemble comprised of fundamentally different solutions leading to wrong mean values and uncertainty estimates, whereas clustering provides an efficient way to deal with this type of computation. This work is important for developing Gen IV nuclear systems because many of these systems rely on natural convection for cooling especially in accident conditions.

97 - MATHEMATICS AND COMPUTING↗

Review of linear compressible stability theory

Aspects of the linear compressible stability theory are considered, with special attention given to the inviscid theory and the additional solutions that arise when there is a region of supersonic flow relative to the phase velocity. For the case of highly cooled flat-plate boundary layers at Mach number 5.8, the unstable region is found to include supersonic outgoing waves. A previously unknown neutral incoming wave has also been identified. An example of viscous multiple solutions is provided, and calculations of higher viscous discrete modes and the compressible counterpart of the Squire mode are presented. It is noted that compressible stability theory is missing a firm connection with boundary-layer transition.

Mack, Leslie M.↗

Slicing Solutions for Wire Arc Additive Manufacturing

Both commercial and research applications of wire arc additive manufacturing (WAAM) have seen considerable growth in the additive manufacturing of metallic components. However, there remains a clear lack of a unified paradigm for toolpath generation when slicing parts for WAAM deposition. Existing toolpath generation options typically lack the appropriate features to account for all complexities of the WAAM process. This manuscript explores the key slicing challenges specific to toolpaths for WAAM geometry and pairs each consideration with multiple solutions to mitigate most negative effects on completed components. These challenges must be addressed to minimize voids, prevent bead collapse, and ensure deposited components accurately approximate the desired geometry. Slicing considerations are grouped into four general categories: geometric, process, thermal, and productivity. Geometric considerations are addressed with overhang compensation, corner-sharpening, and toolpath-smoothing features. Process considerations are addressed with start point configuration and controls for the bead lengths and end points. Thermal and productivity considerations are addressed with island optimization, multi-material printing, and connected insets. Finally, tools for the post-processing of generated G-code are explored. Overall, these solutions represent a critical set of slicing features used to improve generated toolpaths and the quality of the components deposited with those toolpaths.

36 MATERIALS SCIENCE↗

Numerical methods for stiff systems of two-point boundary value problems

Numerical procedures are developed for constructing asymptotic solutions of certain nonlinear singularly perturbed vector two-point boundary value problems having boundary layers at one or both endpoints. The asymptotic approximations are generated numerically and can either be used as is or to furnish a general purpose two-point boundary value code with an initial approximation and the nonuniform computational mesh needed for such problems. The procedures are applied to a model problem that has multiple solutions and to problems describing the deformation of thin nonlinear elastic beam that is resting on an elastic foundation.

Flaherty, J. E.↗

Genomic characterization of rare earth binding by Shewanella oneidensis

Abstract Rare earth elements (REE) are essential ingredients of sustainable energy technologies, but separation of individual REE is one of the hardest problems in chemistry today. Biosorption, where molecules adsorb to the surface of biological materials, offers a sustainable alternative to environmentally harmful solvent extractions currently used for separation of rare earth elements (REE). The REE-biosorption capability of some microorganisms allows for REE separations that, under specialized conditions, are already competitive with solvent extractions, suggesting that genetic engineering could allow it to leapfrog existing technologies. To identify targets for genomic improvement we screened 3,373 mutants from the whole genome knockout collection of the known REE-biosorbing microorganism Shewanella oneidensis MR-1. We found 130 genes that increased biosorption of the middle REE europium, and 112 that reduced it. We verified biosorption changes from the screen for a mixed solution of three REE (La, Eu, Yb) using Inductively Coupled Plasma Mass Spectrometry (ICP-MS) in solution conditions with a range of ionic strengths and REE concentrations. We identified 18 gene ontologies and 13 gene operons that make up key systems that affect biosorption. We found, among other things, that disruptions of a key regulatory component of the arc system ( hptA ), which regulates cellular response to anoxic environments and polysaccharide biosynthesis related genes ( wbpQ , wbnJ , SO_3183 ) consistently increase biosorption across all our solution conditions. Our largest total biosorption change comes from our SO_4685 , a capsular polysaccharide (CPS) synthesis gene, disruption of which results in an up to 79% increase in biosorption; and nusA, a transcriptional termination/anti-termination protein, disruption of which results in an up to 35% decrease in biosorption. Knockouts of glnA , pyrD , and SO_3183 produce small but significant increases (≈ 1%) in relative biosorption affinity for ytterbium over lanthanum in multiple solution conditions tested, while many other genes we explored have more complex binding affinity changes. Modeling suggests that while these changes to lanthanide biosorption selectivity are small, they could already reduce the length of repeated enrichment process by up to 27%. This broad exploratory study begins to elucidate how genetics affect REE-biosorption by S. oneidensis , suggests new areas of investigation for better mechanistic understanding of the membrane chemistry involved in REE binding, and offer potential targets for improving biosorption and separation of REE by genetic engineering.

Medin, Sean↗

Quantum protocol for decision making and verifying truthfulness among N ‐quantum parties: Solution and extension of the quantum coin flipping game

Abstract The authors devised a protocol that allows two parties, who may malfunction or intentionally convey incorrect information in communication through a quantum channel, to verify each other's measurements and agree on each other's results. This has particular relevance in a modified version of the quantum coin flipping game. The key innovation of the authors’ work includes the new design of a quantum coin that excludes any advantage of cheating, by which the long‐standing problem of the fair design of the game is, affirmatively, solved. Furthermore, the analysis is extended to N ‐parties communicating with each other, where multiple solutions for the verification of each player's measurement is proposed. The results in the N ‐party scenario could have particular relevance for the implementation of future quantum networks, where verification of quantum information is a necessity.

Ikeda, Kazuki↗

Optimizing and Exploring Untapped Micro-Hydro Hybrid Systems: a Multi-Objective Approach for Crystal Lake as a Large-Scale Energy Storage Solution

Increasing electricity demand and concerns about climate change and fossil fuel consumption have highlighted the importance of renewable energy resources and storage systems. This paper proposes a method for exploring untapped pumped hydro storage potentials to accommodate intermittent renewable energy generation profiles. Hourly measured data from 2022 in Benzie County, Michigan, United States, were gathered for system sizing and a thorough, realistic analysis. By employing the multi-objective grey wolf optimization algorithm, we formulated optimal sizing and energy-management strategies for three different scenarios. Unlike similar studies, the 3rd with triple objective functions (OFs) scenario aims to maximize both reliability and ecological OFs while minimizing the cost OF. It has shown promising results with multiple solutions, considering economic, environmental, and reliability factors. A case study conducted in Crystal Lake, Michigan, revealed that although Crystal Lake would function only as a micro-hydro power facility, it is a promising and huge storage unit with a substantial storage capacity of around 14.9734GWh. The system investigated is significant in the USA due to its rapid deployment capabilities, minimal construction requirements, and ease of integration with the distribution grid. The fuzzy logic method was employed to identify the best non-dominant solution among the other solutions. Furthermore, these outcomes include a notably low levelized cost of energy at 0.046147$/kWh, a robust index of reliability of 99.705%, and a significant reduction in CO₂ emissions amounting to 7.9142×10 3 tons/year, when considering the triple OFs. The paper’s methodology provides valuable insights for regions aiming to utilize renewable energy from untapped storage sources.

13 HYDRO ENERGY↗

Check-Cases for Verification of 6-Degree-of-Freedom Flight Vehicle Simulations

The rise of innovative unmanned aeronautical systems and the emergence of commercial space activities have resulted in a number of relatively new aerospace organizations that are designing innovative systems and solutions. These organizations use a variety of commercial off-the-shelf and in-house-developed simulation and analysis tools including 6-degree-of-freedom (6-DOF) flight simulation tools. The increased affordability of computing capability has made highfidelity flight simulation practical for all participants. Verification of the tools' equations-of-motion and environment models (e.g., atmosphere, gravitation, and geodesy) is desirable to assure accuracy of results. However, aside from simple textbook examples, minimal verification data exists in open literature for 6-DOF flight simulation problems. This assessment compared multiple solution trajectories to a set of verification check-cases that covered atmospheric and exo-atmospheric (i.e., orbital) flight. Each scenario consisted of predefined flight vehicles, initial conditions, and maneuvers. These scenarios were implemented and executed in a variety of analytical and real-time simulation tools. This tool-set included simulation tools in a variety of programming languages based on modified flat-Earth, round- Earth, and rotating oblate spheroidal Earth geodesy and gravitation models, and independently derived equations-of-motion and propagation techniques. The resulting simulated parameter trajectories were compared by over-plotting and difference-plotting to yield a family of solutions. In total, seven simulation tools were exercised.

Murri, Daniel G.↗

Mass action model of solution activity via speciation by solvation and ion pairing equilibria

Abstract Solutes and their concentrations influence many natural and anthropogenic solution processes. Electrolyte and solution models are used to quantify and predict such behavior. Here we present a mechanistic solution model based on mass action equilibria. Solvation and ion pairing are used to model speciated solute and solvent concentrations such that they correlate to a solution’s vapor pressure (solvent activity) according to Raoult’s law from dilute conditions to saturation. This model introduces a hydration equilibrium constant ( K ha ) that is used with either an ion dissociation constant ( K id ) or a hydration modifier ( m ) with an experimentally determined ion dissociation constant, as adjustable parameters to fit vapor–liquid equilibrium data. The modeled solvation equilibria are accompanied by molecular dynamics (MD) studies that support a decline in the observed degree of solvation with increased concentration. MD calculations indicate this finding is a combination of a solvent that solvates multiple solutes, and changes in a solute’s solvation sphere, with the dominant factor changing with concentration. This speciation-based solution model is lateral to established electrostatics-based electrolyte theories. With its basis in mass action, the model can directly relate experimental data to the modeled solute and solvent speciated concentrations and structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Qualitative Headspace GCMS Analysis of Lunar Regolith and Volatile Simulant Mixtures

Introduction: Future Artemis missions aim to return the volatile-bearing samples collected near lunar polar craters. We, as advanced curation scientists, are responsible for developing techniques and methodologies for preserving the integrity of returned samples and the science value those samples contain. The extent to which that preservation is possible, and the trade-offs preservation requires (e.g. monetary costs, sample volume limitations) all must be considered. Even less-than pristine volatile-bearing samples will be of tremendous value to the scientific community seeking to unravel the history of lunar surface volatiles and, more broadly, volatiles in the solar system. A sample collected on the lunar surface will experience at least five distinctive periods during which any changes here referred to as “alteration” will certainly occur at some scale: collection on the lunar surface; transportation back to Earth; long-term storage; curatorial processing; and allocation/distribution. The Planetary Exploration and Astromaterials Research Lab (PEARL) seeks to understand temperature and pressure effects on returned volatile samples by working with high-fidelity volatile-containing regolith simulants, setting the foundation for the future of cold curation. This abstract is focused on gas-surface interactions between LCROSS volatiles and readily available lunar regolith simulants. Experiments involved analyzing differences in headspace gas composition for various combinations of volatile and regolith simulants using gas chromatography/mass spectrometry (GC/MS). Experimental Procedure: The volatile simulants were chosen based on the molecules detected during the LCROSS mission.1 Stock solutions of condensed lunar volatile analytes were: methanol, 7 N ammonia in methanol, and 0.4% hydrogen sulfide in water. The regolith simulants used were primarily JSC-1A and NU-LHT-4M. Additional regolith simulant control studies were conducted with <150 μm sieved sand and KBr. A nested vial sample preparation approach separated the liquid stock solutions from the regolith, eliminating potential matrix effects between liquid and solid phases. Fifteen microliter aliquots of liquid volatile simulants were added to a 2 mL liquid GC vial and capped in atmosphere. An 18G needle punctured the 2 mL GC vial immediately before being transferred and sealed in a 20 mL GC vial containing 0-0.3 g of regolith simulant, see Figure 1. Separating the analytes ensures any changes observed in the total headspace gases is a result of gas-surface and/or gas-gas interactions. Equipment and Method: Initial GC/MS method development for the separation and identification of relevant headspace gases can be found in Amick, et al. 2023.2 The only hardware change is a different column: a TG-1701MS 30 m × 0.25 mm × 1.00 μm column. The vials were sampled at 10°C, room temperature (~25°C) and 50°C. Low temperature samples were kept in a chilled autosampler stage for at least 1 hour prior to sampling. High temperature samples were agitated at 50°C for 5 minutes immediately prior to injection onto the column. Headspace chromatograms were collected for each combination of temperature, regolith, and volatile simulant, including controls without one or both types of analytes, in triplicate. The chromatogram elution window for each analyte or significant atmospheric gas was identified using the peak mass spectrum cross-referenced with Figure 1.Picture of the nested vial set-up. a NIST MS library search. Each analyte peak was integrated after filtering the mass spectrum trace for the parent or most unique mass-to-charge ratio. For example, the mass-to-charge ratio used to identify, filter for, and integrate the carbon dioxide peak was centered around 44 m/z. Results: Figure 2 shows the integrated peak area for hydrogen sulfide in all combinations of regolith simulants, temperatures, and the addition of ammonia in methanol solution. Multiple repeat experiments with H2S and regolith simulants have confirmed hydrogen sulfide is removed from the headspace within 1 hour when exposed to JSC-1A, NU-LHT-4M and sand (not pictured). The consumption of H2S by lunar regolith simulants at different temperatures indicates surface chemistry will be an integral component in sample integrity and preservation. It is important to note that while the effect of surface chemistry on gaseous hydrogen sulfide is intriguing, further investigation into more chemically accurate regolith simulants is necessary and ongoing. The sulfur in hydrogen sulfide is in its most reduced state while off-the-shelf, terrestrially sourced JSC-1A and NU-LHT-4M are more oxidized than most lunar materials,3which likely leads to different oxidation-reduction reactions than would be expected in lunar regolith. Figure 3 shows the integrated peak area of carbon dioxide for each sample combination that contained ammonia in methanol solution. The addition of ammonia to the GC vials results in a consistent and reproducible decrease in carbon dioxide gas, even at 50°C. The effect became more pronounced when JSC-1A or NU-LHT-4M were present. This set of experiments demonstrated that the sample composition will affect the chemical and physical state of each component present. Future spectroscopic and microscopy experiments will be geared towards identifying the cause for the CO2(g) concentration decrease and the consumption of hydrogen sulfide. As cold and volatile curation scientists, this information provides necessary insight on how to appropriately handle and analyze volatile bearing returned samples, as well as predict the effect chemical composition has on the various sample phases we will analyze upon return to Earth. Unlike traditional curation of geologic materials, the molecules in a sample cannot be identified or processed using the naked eye or even an optical microscope. Volatile curation will require a combination of analytical techniques, including but not limited to highly sensitive gas and solid/condensed phase spectroscopy. This set of experiments has demonstrated the need for more detailed studies of volatile mixtures with mineralogically and geochemically analogous lunar regolith simulants to prepare for the curation of volatile-rich lunar samples from the south polar region of the Moon. References: [1] Colaprete, A., et al. (2010) Science, 330, (463-468). [2] Amick, C. L., et al.(2023) Houston, Texas, [3] Heiken, G. H., et al.(1991) (778-778)

Cecilia L Amick↗

Insights on the continuous representations of piecewise-smooth nonlinear systems: limits of applicability and effectiveness

Dynamical systems subject to intermittent contact are often modeled with piecewise-smooth contact forces. However, the discontinuous nature of the contact can cause inaccuracies in numerical results or failure in numerical solvers. Representing the piecewise contact force with a continuous and smooth function can mitigate these problems, but not all continuous representations may be appropriate for this use. Here, five representations used by previous researchers (polynomial, rational polynomial, hyperbolic tangent, arctangent, and logarithm-arctangent functions) are studied to determine which ones most accurately capture nonlinear behaviors including super- and subharmonic resonances, multiple solutions, and chaos. The test case is a single-DOF forced Duffing oscillator with freeplay nonlinearity, solved using direct time integration. This work intends to expand on past studies by determining the limits of applicability for each representation and what numerical problems may occur.

42 ENGINEERING↗

nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius $\delta$ goes to zero, and to the fractional Laplacian as $\delta$ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We also provide theoretical convergence rates with respect to $\delta$ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, $\delta$ and $\alpha$, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order $\alpha(y)$, which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as $\delta$. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

97 MATHEMATICS AND COMPUTING↗

One Stomatal Model to Rule Them All? Toward Improved Representation of Carbon and Water Exchange in Global Models

Abstract Stomatal conductance schemes that optimize with respect to photosynthetic and hydraulic functions have been proposed to address biases in land‐surface model (LSM) simulations during drought. However, systematic evaluations of both optimality‐based and alternative empirical formulations for coupling carbon and water fluxes are lacking. Here, we embed 12 empirical and optimization approaches within a LSM framework. We use theoretical model experiments to explore parameter identifiability and understand how model behaviors differ in response to abiotic changes. We also evaluate the models against leaf‐level observations of gas‐exchange and hydraulic variables, from xeric to wet forest/woody species spanning a mean annual precipitation range of 361–3,286 mm yr −1 . We find that models differ in how easily parameterized they are, due to: (a) poorly constrained optimality criteria (i.e., resulting in multiple solutions), (b) low influence parameters, (c) sensitivities to environmental drivers. In both the idealized experiments and compared to observations, sensitivities to variability in environmental drivers do not agree among models. Marked differences arise in sensitivities to soil moisture (soil water potential) and vapor pressure deficit. For example, stomatal closure rates at high vapor pressure deficit range between −45% and +70% of those observed. Although over half the new generation of stomatal schemes perform to a similar standard compared to observations of leaf‐gas exchange, two models do so through large biases in simulated leaf water potential (up to 11 MPa). Our results provide guidance for LSM development, by highlighting key areas in need for additional experimentation and theory, and by constraining currently viable stomatal hypotheses.

54 ENVIRONMENTAL SCIENCES↗

Analysis of nonlinear features associated with radio-frequency sheaths

An analytic study is conducted of nonlinear features that arise when radio-frequency (RF) sheath boundary conditions are solved self-consistently with the electromagnetic fields in a magnetized plasma. An instability associated with RF sheath–plasma interactions is identified and shown to be closely linked with sheath–plasma resonance and the occurrence of multiple solutions. It is proposed that this instability serves as a physical mechanism that enables jumping from one solution branch to another, providing a physical basis for the prediction of an RF sheath hysteresis in the time domain. It is further shown that this instability can lead to non-intuitive features such as spontaneous symmetry breaking in an otherwise completely symmetric problem. In plane-stratified geometry, two analytically solvable examples are considered for the cases of an unbounded half-space and a bounded domain

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗