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

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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Optimization-based algorithms for nonlinear mechanics and frictional contact

An optimization-based strategy for solving nonlinear mechanics problems is proposed. In contrast to typical nonlinear equation solver algorithms that aim to find zeros in the residual force function, we minimize an energy (or energy-like) function to encourage solutions which are locally stable equilibria. These smooth and potentially non-convex objective functions are minimized using a preconditioned conjugate-gradient trust-region algorithm. Contact is formulated as an inequality constrained minimization problem, and is solved with an augmented Lagrangian algorithm. Friction is included in the approach via a regularized quasi-potential energy, and other dissipative behavior is included through the use of variational constitutive updates. Finally, to accelerate convergence rates for the Lagrange multipliers, we propose a novel multiplier update algorithm utilizing the Fischer-Burmeister function, and demonstrate super-linear solver convergence for some applications.

42 ENGINEERING↗
DOE OSTI2022

Hybrid Hydraulic-Electric Architecture (HHEA) for Mobile Machines (Final Report)

Traditionally, off-road mobile machines such as excavators and wheel loaders are primarily powered by hydraulics, and throttling valves are used to control their work circuits. In recent years, two general trends are towards more energy efficient systems and electrification. With electrification, both efficiency and control performance can be improved by the elimination of throttling losses and the use of high-bandwidth inverter control. Electrification is generally accomplished with Electro-hydraulic actuators (EHA) but they are limited to lower powered systems due to the high cost of electric machines capable of high power or high torque. This project proposes a new system architecture for off-road vehicles - Hybrid Hydraulic Electric Architecture (HHEA) to improve efficiency and control performance without requiring large electric machines. The widely applicable architecture combines hydraulic power and electric power in such a way that the majority of power is provided hydraulically while electric drives are used to modulate this power. In particular, HHEA utilizes multiple common pressure rails to transmit the majority of power and small electric machines to modulate the power. The energy-saving potential of the the HHEA has been validated for the work circuits of a variety of mobile machines, from small 5-ton excavators to medium sized 20-ton excavators and wheel loaders, and representative duty cycles to reduce energy input by 50-80% compared to the commercial state-of-art load-sensing systems. In addition, the corner power requirements of the electrical machines can be downsized by 85% compared to the EHA approach. Various tradeoff studies have also been conducted, including sensitivities to individual components performances, controllers, accumulator sizes, and variations of the system architecture etc. A control strategy has been developed to maintain or exceed the motion control precision compared to current systems. The motion control strategy consists of a nominal controller, based on a passivity-based backstepping design, and a transition controller, based on least-norn feedforward design. The nominal controller is used in between common pressure rail switches whereas the transition controller compensates for any disturbance that common pressure rail switchings inflict on the system. The control strategy has been experimentally validated on both a medium pressure (200bar) hardware-in-the-loop (HIL) testbed and a high pressure (300+bar) HIL testbed. An efficient and power-dense integrated electric-hydraulic machine consisting of an axial flux electric machine and a radial hydrostatic piston hydraulic machine has been designed, constructed and tested. The machine has an active material power density of 6.1kW/kg, a rated speed of 12500 RPM, and a design efficiency of 85%. This is among the highest power density electric machines using conventional materials. While the integrated machine was designed for modulating the hydraulic power within the HHEA, it can also be used in other applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Study of Storage Requirements and Costs for Shaping Renewables and Nuclear Energy (FY23 Summary Report)

To decarbonize electricity generation primarily by using wind and solar resources, it is likely that additional low (or zero) carbon dioxide (CO 2 ) alternatives will be required for ensuring a reliable electricity supply. This study extends the work and modeling framework that we consolidated in FY 2022, by assessing the zero-CO 2 pathways of a Texas power system in which the availability of variable renewable energy (VRE), nuclear energy, and energy storage types (i.e., battery and thermal energy storage [TES]) are considered the sole resources available for expansion. Using the Risk Analysis Virtual Environment (RAVEN) and Holistic Energy Resource Optimization Network (HERON) frameworks, this study investigates the market of two nuclear energy technologies (i.e., large light-water reactors [LWRs] and LWR-type small modular reactors [SMRs]) under two plausible storage coupling scenarios (i.e., electric coupling and direct thermal coupling). We also explore optimal environments for nuclear energy deployment, and identify key performance characteristics that make nuclear energy economically viable in areas with significant intermittent energy sources. Our analysis encompasses 24 cases. We model the least-cost grid systems, highlight the potential for a coupled LWR-TES approach, and utilize SMRs to achieve deep decarbonization in an affordable, technically feasible manner. We also examine seasonal variations in balancing electricity supply and demand, and account for varying performance, costs, and grid constraints. Overall, the findings of our modeling afford valuable insights for supporting future technology investment decisions in the energy sector.

25 ENERGY STORAGE↗
DOE OSTI2026

Assessing shellfish water exposure to fecal bacteria pollution in Salish Sea: three-dimensional modeling and implications for monitoring

Fecal bacteria (FB) contamination poses significant risks to shellfish safety and management in coastal and estuarine waters. Despite extensive pollution identification and correction efforts, FB contamination in shellfish-growing areas persists in the Salish Sea, highlighting the need to identify overlooked sources and better understand FB transport from riverine and shoreline inputs to shellfish beds. To address this, a high-resolution three-dimensional hydrodynamic model coupled with FB kinetics was developed and applied to a case study site in Salish Sea—Portage Bay—to simulate freshwater plume circulation, flushing dynamics, and bacterial transport. Daily FB loading from the major freshwater inflow—Nooksack River was generated by both linear interpolation and integrating a machine learning approach (XGBoost), trained on historical hydrological and meteorological data. The model successfully reproduced both the magnitude and seasonal variation of FB concentrations in Portage Bay for the year of 2021, demonstrating that simplified FB kinetics with first-order decay due to mortality was effective in this dynamic coastal environment with short flushing time. Model results identified the Nooksack River as the dominant far-field FB source, while scenario simulations showed that near-field coastal stormwater outfalls elevated local FB levels following rainfall, particularly under low-flow conditions. The XGBoost prediction provided comparable or superior accuracy to linear interpolation, particularly during periods of missing observational data, by capturing short-term variability and event-driven loading more effectively. Integrating data-driven riverine FB inputs with mechanistic coastal numerical modeling provides a robust framework for operational forecasting of shellfish bed exposure risk and supports adaptive monitoring and management of shellfish growing areas in the Salish Sea and similar coastal systems.

Salish Sea↗
DOE OSTI2023

Sensitivity analysis of a layered piezoelectric system using ZFEM

The complex variable finite element method (ZFEM) is a numerical technique which aims to find the partial derivatives of the independent variables with respect to variation in dependent parameters declared in the physics. This is done by combining the complex Taylor series expansion within the weak formulation of the governing equation in a coupled system of linear equations forming a complex valued block matrix given by the Cauchy–Riemann matrix representation. In this work, two-dimensional linear first-order elements have been implemented in ZFEM to predict the design derivatives of the mechanical displacement field and the voltage potential field for a layered piezoelectric system in a steady-state study with Dirichlet boundary condition applied at the top and bottom edges of the geometry. This approach allows the standard FEM solution to quantify the sensitivity of the mechanical displacement and voltage potential fields with respect to small variations in the material properties through the information obtained from the computation of the derivatives. The domain is formed by a layered body with PZT-4 and PZT-5 stacked together. For result verification, the numerical solution obtained with ZFEM was compared to results from a commercial FEM package and the solution from the imaginary part was compared to the exact solution of a well-known benchmark problem. In conclusion, comparison of the results showed good agreement for both the real and imaginary parts of the solution and the largest sensitivities were found in PZT-5 specifically in C 13 , C 33 , and ε 33 .

42 ENGINEERING↗
DOE OSTI2022

Entropy variations and light ray operators from replica defects

We study the defect operator product expansion (OPE) of displacement operators in free and interacting conformal field theories using replica methods. We show that as n approaches 1 a contact term can emerge when the OPE contains defect operators of twist d - 2. For interacting theories and general states we give evidence that the only possibility is from the defect operator that becomes the stress tensor in the n → 1 limit. This implies that the quantum null energy condition (QNEC) is always saturated for CFTs with a twist gap. As a check, we show independently that in a large class of near vacuum states, the second variation of the entanglement entropy is given by a simple correlation function of averaged null energy operators as studied by Hofman and Maldacena. This suggests that sub-leading terms in the defect OPE are controlled by a defect version of the spin-3 non-local light ray operator and we speculate about the possible origin of such a defect operator. For free theories this contribution condenses to a contact term that leads to violations of QNEC saturation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A mechanistic model for creep and thermal aging in Alloy 709

This report describes a physics-based model for creep and thermal aging in Alloy 709. Alloy 709 is an advanced austenitic alloy, targeted for use in future Sodium Fast Reactors (SFRs) and other advanced reactors. The material has superior high temperature properties compared to currently qualified 316 and 304 stainless steels. However, the available creep and thermal aging test database for Alloy 709 is significantly more limited compared to the historical materials. The physics-based model developed here is one way to accelerate the qualification of the material by providing more accurate long-term predictions for creep properties and thermal aging, compared to current empirical time-extrapolate techniques. The crystal plasticity finite element model is used to predict the deformation and failure of alloy 709. The same setup for the CPFE model is used in both the baseline model calibration process and the simulation campaigns for parameter inference. Specific constitutive choices are made for Alloy 709 to capture the primary deformation mechanisms. The dislocation creep formulation developed by Hu and Cocks is extended to account for coupled precipitation formation and the grain boundary cavitation model developed by Sham, Needleman, et al. is used to model grain boundary cavitation-induced failure. A novel update algorithm is proposed to render the semi-discrete constitutive update for the Sham-Needleman model unconditionally stable. A progressive calibration approach is adopted based on the observations that several types of material responses can be effectively decoupled. A surrogate model is trained based on full-fledged CPFE simulations to accelerate the forward model evaluations, and stochastic variational inference (SVI) is used to calibrate the unknown microstructural model parameters. The calibrated mechanistic model is used to predict the long-term creep life of Alloy 709, and the predictions are compared against classical empirical approaches.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Lattice-scale variations in viscosity are correlated with solution structure at mineral-water interfaces

At solid-liquid interfaces, the viscosity increases markedly from the bulk due to the collective interactions of ions and water molecules, influencing phenomena relevant to nanofluidics, colloidal dynamics, and electrochemistry. Here, in this study, we investigated dissipative forces at the boehmite-water interface using 3D atomic force microscopy. We observed an increase in interfacial solution viscosity, η, by 10-100-fold as the nanoprobe approached the surface in normal direction, with up to four oscillatory features showing average peaks of η/η bulk = 44-71. Moreover, the viscosity showed sub-nanometer variations within 0.5 nm from the interface, templated by the underlying crystal lattice and correlated with the interfacial solution structure. Beyond a near-wall region of approximately 1.2 nm, the dissipative response was comparable to that in bulk solution. Molecular dynamics simulations, along with statistical mechanical analyses, provided details on hydrodynamic structures near the interface. Specifically, the lattice-dependent dissipative responses are correlated with extensive hydrogen bonding by interfacial water molecules, which increased friction, particularly along the [001] direction. These results demonstrate how solution viscosity at mineral-water interfaces is anisotropic and correlated with the local solution structure, providing insights into the dynamics of nanocrystal attachment.

Viscosity↗
DOE OSTI2022

Quantum error mitigation by hidden inverses protocol in superconducting quantum devices

We present a method to improve the convergence of variational algorithms based on hidden inverses (HIs) to mitigate coherent errors. In the context of error mitigation, this means replacing the hardware implementation of certain Hermitian gates with their inverses. Doing so results in noise cancellation and a more resilient quantum circuit. This approach improves performance in a variety of two-qubit error models where the noise operator also inverts with the gate inversion. We apply the mitigation scheme on superconducting quantum processors running the variational quantum eigensolver (VQE) algorithm to find the H 2 ground-state energy. When implemented on superconducting hardware we find that the mitigation scheme effectively reduces the energy fluctuations in the parameter learning path in VQE, reducing the number of iterations for a converged value. We also provide a detailed numerical simulation of VQE performance under different noise models and explore how HIs and randomized compiling affect the underlying loss landscape of the learning problem. These simulations help explain our experimental hardware outcomes, helping to connect lower-level gate performance to application-specific behavior in contrast to metrics like fidelity which often do not provide an intuitive insight into observed high level performance.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Ensemble Kalman inversion of induced polarization data

SUMMARY This paper explores the applicability of ensemble Kalman inversion (EKI) with level-set parametrization for solving geophysical inverse problems. In particular, we focus on its extension to induced polarization (IP) data with uncertainty quantification. IP data may provide rich information on characteristics of geological materials due to its sensitivity to characteristics of the pore–grain interface. In many IP studies, different geological units are juxtaposed and the goal is to delineate these units and obtain estimates of unit properties with uncertainty bounds. Conventional inversion of IP data does not resolve well sharp interfaces and tends to reduce and smooth resistivity variations, while not readily providing uncertainty estimates. Recently, it has been shown for DC resistivity that EKI is an efficient solver for inverse problems which provides uncertainty quantification, and its combination with level set parametrization can delineate arbitrary interfaces well. In this contribution, we demonstrate the extension of EKI to IP data using a sequential approach, where the mean field obtained from DC resistivity inversion is used as input for a separate phase angle inversion. We illustrate our workflow using a series of synthetic and field examples. Variations with uncertainty bounds in both DC resistivity and phase angles are recovered by EKI, which provides useful information for hydrogeological site characterization. Although phase angles are less well-resolved than DC resistivity, partly due to their smaller range and higher percentage data errors, it complements DC resistivity for site characterization. Overall, EKI with level set parametrization provides a practical approach forward for efficient hydrogeophysical imaging under uncertainty.

Geochemistry & Geophysics↗
DOE OSTI2021

Coding and noncoding variants in EBF3 are involved in HADDS and simplex autism

Abstract Background Previous research in autism and other neurodevelopmental disorders (NDDs) has indicated an important contribution of protein-coding (coding) de novo variants (DNVs) within specific genes. The role of de novo noncoding variation has been observable as a general increase in genetic burden but has yet to be resolved to individual functional elements. In this study, we assessed whole-genome sequencing data in 2671 families with autism (discovery cohort of 516 families, replication cohort of 2155 families). We focused on DNVs in enhancers with characterized in vivo activity in the brain and identified an excess of DNVs in an enhancer named hs737. Results We adapted the fitDNM statistical model to work in noncoding regions and tested enhancers for excess of DNVs in families with autism. We found only one enhancer (hs737) with nominal significance in the discovery (p = 0.0172), replication (p = 2.5 × 10 −3 ), and combined dataset (p = 1.1 × 10 −4 ). Each individual with a DNV in hs737 had shared phenotypes including being male, intact cognitive function, and hypotonia or motor delay. Our in vitro assessment of the DNVs showed they all reduce enhancer activity in a neuronal cell line. By epigenomic analyses, we found that hs737 is brain-specific and targets the transcription factor gene EBF3 in human fetal brain. EBF3 is genome-wide significant for coding DNVs in NDDs (missense p = 8.12 × 10 −35 , loss-of-function p = 2.26 × 10 −13 ) and is widely expressed in the body. Through characterization of promoters bound by EBF3 in neuronal cells, we saw enrichment for binding to NDD genes (p = 7.43 × 10 −6 , OR = 1.87) involved in gene regulation. Individuals with coding DNVs have greater phenotypic severity (hypotonia, ataxia, and delayed development syndrome [HADDS]) in comparison to individuals with noncoding DNVs that have autism and hypotonia. Conclusions In this study, we identify DNVs in the hs737 enhancer in individuals with autism. Through multiple approaches, we find hs737 targets the gene EBF3 that is genome-wide significant in NDDs. By assessment of noncoding variation and the genes they affect, we are beginning to understand their impact on gene regulatory networks in NDDs.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Mycorrhizal status and host genotype interact to shape plant nutrition in field grown maize ( Zea mays ssp. mays )

Arbuscular mycorrhizal fungi (AMF) establish symbioses with the major cereal crops, providing plants with increased access to nutrients while enhancing their tolerance to toxic heavy metals. However, not all plant varieties benefit equally from this association. In this study, we used quantitative trait loci (QTL) mapping to evaluate the combined effect of host genotypic variation (G) and AMF across 141 genotypes on the concentration of 20 mineral elements in the leaves and grain of field grown maize (Zea mays spp. mays). Our mapping design included selective incorporation of a castor AMF-incompatibility mutation, allowing estimation of AMF, QTL and QTLxAMF effects by comparison of mycorrhizal and non-mycorrhizal plants. Overall, AMF compatibility was associated with higher concentrations of boron (B), copper (Cu), molybdenum (Mo), phosphorus (P), selenium (Se) and zinc (Zn) and lower concentrations of arsenic (As), iron (Fe), magnesium (Mg), manganese (Mn), potassium (K) and strontium (Sr). In addition to effects on individual elements, pairwise correlation matrices for element concentration differed between mycorrhizal and non-mycorrhizal plants. We mapped 22 element QTLs, including 18 associated with QTLxAMF effects that indicate plant genotype-specific differences in the impact of AMF on the host ionome. Although there is considerable interest in AMF as biofertilizers, it remains challenging to estimate the impact of AMF in the field. Our design illustrates an effective approach for field evaluation of AMF effects. Furthermore, we demonstrate the capacity of the ionome to reveal host genotype-specific variation in the impact of AMF on plant nutrition.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Relativistic resolution-of-the-identity with Cholesky integral decomposition

In this study, we present an efficient integral decomposition approach called the restricted-kinetic-balance resolution-of-the-identity (RKB-RI) algorithm, which utilizes a tunable RI method based on the Cholesky integral decomposition for in-core relativistic quantum chemistry calculations. The RKB-RI algorithm incorporates the restricted-kinetic-balance condition and offers a versatile framework for accurate computations. Notably, the Cholesky integral decomposition is employed not only to approximate symmetric large-component electron repulsion integrals but also those involving small-component basis functions. In addition to comprehensive error analysis, we investigate crucial conditions, such as the kinetic balance condition and variational stability, which underlie the applicability of Dirac relativistic electronic structure theory. Here we compare the computational cost of the RKB-RI approach with the full in-core method to assess its efficiency. To evaluate the accuracy and reliability of the RKB-RI method proposed in this work, we employ actinyl oxides as benchmark systems, leveraging their properties for validation purposes. This investigation provides valuable insights into the capabilities and performance of the RKB-RI algorithm and establishes its potential as a powerful tool in the field of relativistic quantum chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Method-independent cusps for atomic orbitals in quantum Monte Carlo

Here, we present an approach for augmenting Gaussian atomic orbitals with correct nuclear cusps. Like the atomic orbital basis set itself and unlike previous cusp corrections, this approach is independent of the many-body method used to prepare wave functions for quantum Monte Carlo. Once the basis set and molecular geometry are specified, the cusp-corrected atomic orbitals are uniquely specified, regardless of which density functionals, quantum chemistry methods, or subsequent variational Monte Carlo optimizations are employed. We analyze the statistical improvement offered by these cusps in a number of molecules and find them to offer similar advantages as molecular-orbital-based approaches while remaining independent of the choice of many-body method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Atomic‐Scale Surface Imaging of Bulk Epitaxial CsPbBr 3 Perovskite Single Crystals on Mica Using Light Assisted Scanning Tunneling Microscopy at Low‐Temperature (80 K)

Epitaxial single-crystalline CsPbBr 3 perovskite films on mica, prepared ex situ, are explored using a low-temperature scanning tunneling microscope (STM) by probing the unoccupied electronic states of their surface in ultra-high vacuum (UHV) at 80 K. Light-assisted STM measurements under a broadband illumination with visible light were employed to enhance and stabilize surface conductivity. STM imaging across the surface of macroscopic bulk CsPbBr 3 films reveals large flat terraces characterized by a specific type of surface reconstruction, consisting of parallel rows of U-shaped atomic nanostructures. These structures are spaced by 12 Å and exhibit an internal feature size of 5.1 Å. Density functional theory (DFT) calculations reproduce the experimental observations and reveal a competition between different orthorhombic CsPbBr 3 (110) surface reconstructions: a Cs-rich structure, identified as the most energetically stable, and three alternative Pb–Br-rich reconstructions, which are slightly higher in energy yet remain consistent with the STM data. Additional analyses that explicitly account for the mica substrate exclude the cubic CsPbBr 3 phase and other orthorhombic surface orientations, while showing that variations in the mica surface termination do not alter the preferred CsPbBr 3 (110) reconstruction. In conclusion, this combined approach thereby confirms our assignment and resolves previous STM interpretations of CsPbBr 3 .

36 MATERIALS SCIENCE↗
DOE OSTI2021

Time-Resolved Geometric Feature Tracking Elucidates Laser-Induced Keyhole Dynamics

In this report, during laser melting of metals, localized metal evaporation resulting in the formation of a keyhole shaped cavity can occur if processing conditions are chosen with high power density. An unstable keyhole can have deleterious effects in certain applications (e.g., laser powder bed fusion) as it increases the likelihood of producing defects such as porosity. In this work, we propose a pipeline that enables complete segmentation and extraction of various geometric features in keyholing conditions. In situ synchrotron high-speed X-ray visualization at the Advanced Photon Source provides large datasets of experimental images with a high spatio-temporal resolution across a range of laser parameters for Ti-6Al- 4 V. Computer vision image processing techniques were used to extract time-resolved quantitative geometric features (e.g., depth, width, front wall angle) throughout keyhole evolution which were subsequently analyzed to understand the relationship between the variation of local keyhole geometry and processing conditions. This analysis is the first to employ a data-driven approach to further our understanding of the keyholing process regime.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Grain structure and texture selection regimes in metal powder bed fusion

Additive manufacturing (AM) offers opportunities to produce complex part geometries not possible with conventional processing and in some cases even improve part performance. However, adoption has been slowed by difficulties assessing microstructure variability and there is no straightforward approach to relate processing to grain structure characteristics. In this study, datasets from AdditiveFOAM heat transport simulations of laser powder bed fusion (LPBF) are used to drive ExaCA simulations of grain structure. The GPU utilization of ExaCA and an algorithmic update for modeling melt pool overlap region solidification enabled rapid and parallel simulation across a wider range of process conditions than previously explored with cellular automata-based solidification models. A texture selection angle $θ_s$ is defined based on melt pool overlap geometry, and the range of $θ_s$ over which a commonly observed texture transition occurs in characterized AM builds was well-reproduced by ExaCA simulations over a wide range of melt pool shape, hatch spacing, and layer height. ExaCA simulations with 90 degree rotation of the scan direction on every other layer reproduced a number of trends from the AM literature including grain refinement, the dominance of layers with larger melt pools on the final grain structure, and the weakening or strengthening of texture depending on odd and even layer melt pool overlap geometry. EBSD data from a benchmark AM part is used to validate the simulated mechanism of a layer rotation-induced texture strengthening effect. Importantly, these results expand the understanding of the mechanisms for texture selection in alloys with cubic crystal symmetry and offer an approach to easily evaluate processing conditions. With this new understanding, these modeling tools will enable anticipation of previously unexpected variations in grain structure and target specific microstructures and properties.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A new phenomenological model to describe root-soil interactions based on percolation theory

In his paper on net primary productivity of terrestrial communities predicted from climatological data, Rosenzweig (1968) argued that variability in productivity is well accounted for by (evapo)-transpiration, and that water from transpiration is, on global scales, the most variable component in the photosynthesis reaction. The goal of this paper is to investigate whether variability in plant growth on local scales and within species is primarily related to transpiration under several scenarios including different terrain curvature, slope aspect, soil characteristics, and climate ranges. Here, we test the hypothesis that this relationship exists because root growth into the surface soil layers (0–2 m) tends to follow paths with minima in resistance, which in turn maximizes water flow and nutrient delivery rates that regulate growth. The set of all connected paths with individual pore-to-pore flow resistances less than a critical, percolating, value forms a cluster with mass fractal dimensionality, d f . We propose that roots follow paths through the 2D percolation cluster, defining the set of all optimal flow paths, making the 2D value of d f from percolation relevant to root fractal dimensionality. The tortuosity of such optimal paths as defined in percolation theory should then relate root length to root radial extent, linking the parameters of root tortuosity and plant productivity. Our analysis of large data sets across species implies that root radial extent and tree height are both proportional to cumulative transpiration until trees approached maximum height, and their growth rates are proportional to the transpiration rate, not to the moisture content. Local variations in tree height as functions of the variables investigated appear generally consistent with deduced variations in transpiration. Here this correlation is investigated more closely in the context of studies addressing individual tree species.

54 ENVIRONMENTAL SCIENCES↗