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At least 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Structure constants in $ \mathcal{N} $ = 4 SYM at finite coupling as worldsheet g-function

We develop a novel nonperturbative approach to a class of three-point functions in planar $ \mathcal{N} $ N = 4 SYM based on Thermodynamic Bethe Ansatz (TBA). More specifically, we study three-point functions of a non-BPS single-trace operator and two determinant operators dual to maximal Giant Graviton D-branes in AdS 5 × S 5 . They correspond to disk one-point functions on the worldsheet and admit a simpler and more powerful integrability description than the standard single-trace three-point functions. We first introduce two new methods to efficiently compute such correlators at weak coupling; one based on large N collective fields, which provides an example of open-closed-open duality discussed by Gopakumar, and the other based on combinatorics. The results so obtained exhibit a simple determinant structure and indicate that the correlator can be interpreted as a generalization of g -functions in 2d QFT; an overlap between an integrable boundary state and a state corresponding to the single-trace operator. We then determine the boundary state at finite coupling using the symmetry, the crossing equation and the boundary Yang-Baxter equation. With the resulting boundary state, we derive the ground-state g -function based on TBA and conjecture its generalization to other states. This is the first fully nonperturbative proposal for the structure constants of operators of finite length. The results are tested extensively at weak and strong couplings. Finally, we point out that determinant operators can provide better probes of sub-AdS locality than single-trace operators and discuss possible applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Renormalization and scale evolution of the soft-quark soft function

Soft functions defined in terms of matrix elements of soft fields dressed by Wilson lines are central components of factorization theorems for cross sections and decay rates in collider and heavy-quark physics. While in many cases the relevant soft functions are defined in terms of gluon operators, at subleading order in power counting soft functions containing quark fields appear. We present a detailed discussion of the properties of the soft-quark soft function consisting of a quark propagator dressed by two finite-length Wilson lines connecting at one point. This function enters in the factorization theorem for the Higgs-boson decay amplitude of the h → γγ process mediated by light-quark loops. We perform the renormalization of this soft function at one-loop order, present a conjecture for its two-loop anomalous dimension and discuss solutions to its renormalization-group evolution equation in momentum space, in Laplace space and in the “diagonal space”, where the evolution is strictly local in the momentum variable.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

The Epidermal Microbiome Within an Aggregation of Leopard Sharks ( Triakis semifasciata ) Has Taxonomic Flexibility with Gene Functional Stability Across Three Time-points

The epidermis of Chondrichthyan fishes consists of dermal denticles with production of minimal but protein-rich mucus that collectively, influence the attachment and biofilm development of microbes, facilitating a unique epidermal microbiome. Here, we use metagenomics to provide the taxonomic and functional characterization of the epidermal microbiome of the Triakis semifasciata (leopard shark) at three time-points collected across 4 years to identify links between microbial groups and host metabolism. Our aims include (1) describing the variation of microbiome taxa over time and identifying recurrent microbiome members (present across all time-points); (2) investigating the relationship between the recurrent and flexible taxa (those which are not found consistently across time-points); (3) describing the functional compositions of the microbiome which may suggest links with the host metabolism; and (4) identifying whether metabolic processes are shared across microbial genera or are unique to specific taxa. Microbial members of the microbiome showed high similarity between all individuals (Bray–Curtis similarity index = 82.7, where 0 = no overlap, 100 = total overlap) with the relative abundance of those members varying across sampling time-points, suggesting flexibility of taxa in the microbiome. One hundred and eighty-eight genera were identified as recurrent, including Pseudomonas, Erythrobacter, Alcanivorax, Marinobacter, and Sphingopxis being consistently abundant across time-points, while Limnobacter and Xyella exhibited switching patterns with high relative abundance in 2013, Sphingobium and Sphingomona in 2015, and Altermonas, Leeuwenhoekiella, Gramella, and Maribacter in 2017. Of the 188 genera identified as recurrent, the top 19 relatively abundant genera formed three recurrent groups. The microbiome also displayed high functional similarity between individuals (Bray–Curtis similarity index = 97.6) with gene function composition remaining consistent across all time-points. These results show that while the presence of microbial genera exhibits consistency across time-points, their abundances do fluctuate. Microbial functions however remain stable across time-points; thus, we suggest the leopard shark microbiomes exhibit functional redundancy. We show coexistence of microbes hosted in elasmobranch microbiomes that encode genes involved in utilizing nitrogen, but not fixing nitrogen, degrading urea, and resistant to heavy metal.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Results of a Multi-institutional Phase 2 Clinical Trial for 4DCT-ventilation Functional Avoidance Thoracic Radiation Therapy

Radiation pneumonitis remains a major limitation in the radiation therapy treatment of patients with lung cancer. Functional avoidance radiation therapy uses functional imaging to reduce pulmonary toxic effects by designing radiation therapy plans that reduce doses to functional regions of the lung. Lung functional imaging has been developed that uses 4-dimensional computed tomography (4DCT) imaging to calculate 4DCT-based lung ventilation (4DCT-ventilation). A phase 2 multicenter study was initiated to evaluate 4DCT-ventilation functional avoidance radiation therapy. The study hypothesis was that functional avoidance radiation therapy could reduce the rate of grade ≥2 radiation pneumonitis to 12% compared with a 25% historical rate, with the trial being positive if ≤16.4% of patients experienced grade ≥2 pneumonitis.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2021

Machine learning reveals sequence-function relationships in family 7 glycoside hydrolases

Family 7 glycoside hydrolases (GH7) are among the principal enzymes for cellulose degradation in nature and industrially. These important enzymes are often bimodular, including a catalytic domain and carbohydrate binding module (CBM) attached via a flexible linker, and exhibit an active site that binds cello-oligomers of up to ten glucosyl moieties. GH7 cellulases consist of two major subtypes: cellobiohydrolases (CBH) and endoglucanases (EG). Despite the critical importance of GH7 enzymes, there remain gaps in our understanding of how GH7 sequence and structure relate to function. Here, we employed machine learning to gain data-driven insights into relationships between sequence, structure, and function across the GH7 family. Machine-learning models, trained only on the number of residues in the active-site loops as features, were able discriminate GH7 CBHs and EGs with up to 99% accuracy, demonstrating that the lengths of loops A4, B2, B3, and B4 strongly correlate with functional subtype across the GH7 family. Classification rules were derived such that specific residues at 42 different sequence positions each predicted the functional subtype with accuracies surpassing 87%. A random forest model trained on residues at 19 positions in the catalytic domain predicted the presence of a CBM with 89.5% accuracy. Our ML results recapitulate, as top-performing features, a substantial number of the sequence positions determined by previous experimental studies to play vital roles in GH7 activity. We surmise that the yet-to-be-explored sequence positions among the top-performing features also contribute to GH7 functional variation and may be exploited to understand and manipulate function.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Adaptive Activation Functions Accelerate Convergence in Deep and Physics-informed Neural Networks

We employ adaptive activation functions for regression in deep and physics-informed neural networks (PINNs) to approximate smooth and discontinuous functions as well as solutions of linear and nonlinear partial differential equations. In particular, we solve the nonlinear Klein-Gordon equation, which has smooth solutions, the nonlinear Burgers equation, which can admit high gradient solutions, and the Helmholtz equation. We introduce a scalable hyper-parameter in the activation function, which can be optimized to achieve best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. The adaptive activation function has better learning capabilities than the traditional one (fixed activation) as it improves greatly the convergence rate, especially at early training, as well as the solution accuracy. To better understand the learning process, we plot the neural network solution in the frequency domain to examine how the network captures successively different frequency bands present in the solution. We consider both forward problems, where the approximate solutions are obtained, as well as inverse problems, where parameters involved in the governing equation are identified. Our simulation results show that the proposed method is a very simple and effective approach to increase the efficiency, robustness and accuracy of the neural network approximation of nonlinear functions as well as solutions of partial differential equations, especially for forward problems. We theoretically prove that in the proposed method, gradient descent algorithms are not attracted to suboptimal critical points or local minima.

machine leaning, Bad minima, Inverse problems, Phy↗
DOE OSTI2025

Anti-symmetric barron functions and their approximation with sums of determinants

A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The architecture of neural network models for the electron wave function typically comprises an equivariant component followed by a summation of determinants. The recently introduced Generic Antisymmetric (GA) block is designed to enhance the expressivity of such neural wave functions, and it was found that the 2-layer GA block achieved more accurate energies than the corresponding single-determinant FermiNet architecure, suggesting its promise as a way to improve the expressivity of neural wave functions. In this paper we show how the function expressed by the 2-layer GA block can be decomposed into a sum of determinants. We formalize this result by defining the antisymmetric Barron space as a generalized version of the 2-layer GA block and providing an appromation theorem for this function class. This result can be viewed as a negative result showing that the 2-layer GA block is not more expressive than using multiple determinants.

Abrahamsen, Nilin↗
DOE OSTI2021

The discrete Green's function paradigm for two-way coupled Euler–Lagrange simulation

We outline a methodology for the simulation of two-way coupled particle-laden flows. The drag force that couples fluid and particle momentum depends on the undisturbed fluid velocity at the particle location, and this latter quantity requires modelling. We demonstrate that the undisturbed fluid velocity, in the low particle Reynolds number limit, can be related exactly to the discrete Green's function of the discrete Stokes equations. In addition to hydrodynamics, the method can be extended to other physics present in particle-laden flows such as heat transfer and electromagnetism. The discrete Green's functions for the Navier–Stokes equations are obtained at low particle Reynolds number in a two-plane channel geometry. We perform verification at different Reynolds numbers for a particle settling under gravity parallel to a plane wall, for different wall-normal separations. Compared with other point-particle schemes, the Stokesian discrete Green's function approach is the most robust at low particle Reynolds number, accurate at all wall-normal separations. To account for degradation in accuracy away from the wall at finite Reynolds number, we extend the present methodology to an Oseen-like discrete Green's function. The extended discrete Green's function method is found to be accurate within 6% at all wall-normal separations for particle Reynolds numbers up to 24. Furthermore, the discrete Green's function approach is well suited to dilute systems with significant mass loading and this is highlighted by comparison against other Euler–Lagrange as well as particle-resolved simulations of gas–solid turbulent channel flow. Strong particle–turbulence coupling is observed in the form of turbulence modification and turbophoresis suppression, and these observations are placed in context of the different methods.

42 ENGINEERING↗
DOE OSTI2022

Functionalization of Electrodes with Tunable [EMIM] x [Cl] x +1 – Ionic Liquid Clusters for Electrochemical Separations

Functionalization of electrodes with clusters of hydrophobic molecules may improve the energy efficiency and selectivity of electrochemical separations by modulating the desolvation process occurring at the interface. Ionic liquids (IL), which have a broad range of compositions and properties, are potential candidates for controlling the transport, desolvation, and adsorption of target ions at electrochemical interfaces. We report a joint experimental and theoretical investigation of the structure, stability, and selective adsorption properties of the IL clusters 1-ethyl-3-methylimidazolium chloride [EMIM] x [Cl] x+1 - (x = 1 – 10) and demonstrate their ability to adsorb and separate ions from solution. The structure and stability of the IL clusters are determined experimentally using high-mass-resolution electrospray ionization mass spectrometry, collision-induced dissociation, and negative ion photoelectron spectroscopy. Global optimization theory and ab initio molecular dynamics simulations provide molecular-level insight into the bonding and structural fluxionality of these species. Ion soft landing is used to selectively functionalize the surface of highly oriented pyrolytic graphite (HOPG) working electrodes with [EMIM] 1 [Cl] 2 - , [EMIM] 3 [Cl] 4 - , and [EMIM] 5 [Cl] 6 - clusters. Kelvin probe microscopy provides insight into the relative stability of the clusters on HOPG and their effect on the work function of IL-functionalized electrodes. Cyclic voltammetry measurements reveal irreversible adsorption of Fe(CN) 6 4-/3- anions during redox cycling, while electrochemical impedance spectroscopy indicates a substantial decrease in the electron transfer resistance of the IL-functionalized electrodes due to adsorption of Fe(CN) 6 4-/3- . Overall, our findings demonstrate that IL clusters with different size and stoichiometry may be used to increase the efficiency of electrochemical separations, opening new horizons in selective electrode functionalization.

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

Assessing the Limitations of Self-Interaction-Corrected Functionals for Describing the Hydrated Electron

Simulating the hydrated electron using density functional theory is challenging due to the prevalence of self-interaction error in standard functionals. Hybrid functionals like PBEh(40) can reasonably describe the chemistry of an excess electron in water and partially mitigate self-interaction error by incorporating exact Hartree–Fock exchange, but they are computationally expensive making them impractical for large-scale and long-time ab initio molecular dynamics simulations. Explicit self-interaction correction schemes that are applied on an orbital-by-orbital basis offer a potential alternative when the correction is limited to the singly occupied molecular orbital obtained with a generalized gradient approximation functional. Here, we examine whether the Perdew–Zunger self-interaction correction scheme applied to the revPBE functional can provide a computationally efficient and physically sensible alternative to PBEh(40) for the hydrated electron. We find that functionals incorporating a self-interaction correction scheme should be viewed with caution when applied to the hydrated electron and its reactivity. Furthermore, we show that it is critical to consider extensive sampling and diverse chemical environments when validating their performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Assessment of Performance of Density Functionals for Predicting Potential Energy Curves in Hydrogen Storage Applications

We report the availability of accurate computational tools for modeling and simulation is vital to accelerate the discovery of materials capable of storing hydrogen (H 2 ) under given parameters of pressure swing and temperature. Previously, we compiled the H2Bind275 data set consisting of equilibrium geometries and assessed the performance of 55 density functionals over this data set (Veccham, S. P.; Head-Gordon, M. J. Chem. Theory Comput. 2020, 16, 4963-4982). As it is crucial for computational tools to accurately model the entire potential energy curve (PEC), in addition to the equilibrium geometry, we extended this data set with 389 new data points to include two compressed and three elongated geometries along 78 PECs for H 2 binding, forming the H2Bind78 × 7 data set. By assessing the performance of 55 density functionals on this significantly larger and more comprehensive H2Bind78 × 7 data set, we identified the best performing density functionals for H 2 binding applications: PBE0-DH, ωB97X-V, ωB97M-V, and DSD-PBEPBE-D3(BJ). The addition of Hartree-Fock exchange improves the performance of density functionals, albeit not uniformly throughout the PEC. We recommend the usage of ωB97X-V and ωB97M-V density functionals as they offer good performance for both geometries and energies. In addition, we also identified B97M-V and B97M-rV as the best semilocal density functionals for predicting H 2 binding energy at its equilibrium geometry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

A Theoretical Benchmark of the Geometric and Optical Properties for 3d Transition Metal Nanoclusters via Density Functional Theory

Understanding structure–property relationships in atomically precise metal nanoclusters is vital in finding selective and tunable catalysts. Here, in this study, density functional theory (DFT) was used to benchmark seven exchange correlation functionals at different basis sets for 17 atomically precise nanoclusters against experimentally determined geometries, band gaps, and optical gaps. The set contains both monometallic and bimetallic clusters that possess at least two types of 3d transition metals (specifically, Cu, Ni, Fe, or Co). The benchmark highlights that PBE0 is a good functional to use regardless of the basis set, and Minnesota functionals do well with respect to specific metals. Further, while long-range corrected functionals overestimate band and optical gaps, they model absorption features better than the other considered functionals. The study additionally looks at the photoinduced hydrogen evolution reaction (HER) and the CO 2 reduction mechanism on nanoclusters reported from the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Surface-Functionalized Cellulose Nanocrystals as Nanofillers for Crosslinking Processes: Implications for Thermosetting Resins

Understanding the response of fillers in the epoxy resin crosslinking process and characterizing polymer–filler dynamics are the key features that guide the engineering of new thermosetting resin composites. Here, in this work, X-ray photon correlation spectroscopy (XPCS) is used as a thermal analysis tool to track the microscopic changes occurring during the cure of a functionalized cellulose nanocrystal (mCNC)–epoxy composite. In contrast, traditional methods such as differential scanning calorimetry (DSC) and curing rheology are used to understand the kinetics and properties on macroscopic length scales. Of interest is the influence of the mCNC on the curing kinetics and properties of the thermosetting resin. Two levels of modification (increasing hydrophobicity) were chosen to observe the effect of functionalization. Before cure, the highly functionalized CNC (mCNC3) shows a 44% increase in complex viscosity (η*), while the less functionalized CNC (mCNC2) shows a η* value similar to that of the neat resin. As the cure cycle progresses, results from DSC, rheology, and XPCS further show the enhancement in dispersion for mCNC3. The results show a clear difference in the maximum drift velocity, maximum heat flow, and complex viscosity during the ramp to the isothermal cure temperature (T cure ). Such results suggest that mCNC3 contains a well-dispersed network of particles due to the higher level of functionalization. During T cure , a transition in elastic modulus (G') occurs only for the highly functionalized CNC particle system. We believe that heat-induced aggregation occurs, and the crosslinked resin ultimately dominates the macroscopic properties of the final cured system for all samples. The results from the three techniques are in good agreement and showcase XPCS as a beneficial experimental tool for characterizing the microscopic dynamics of particulate-filled thermosetting resins. Hence, we envision this to be a fundamental curing study for the design of thermosetting resin composites.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Increasing Branching and Functionalization Decreases Crystallinity and Crystallization Rate in Linear EVOH

Here, we report the crystallization behavior of a linear poly(ethylene-co-vinyl alcohol) (LEVOH) under isothermal crystallization as a function of both OH incorporation and undercooling, and compare the results to conventional branched EVOH. This LEVOH is synthesized by post-polymerization functionalization of polycyclooctene, and it exhibits a half-crystallization time and primary crystallization rate nearly an order of magnitude faster than branched EVOH at ~ 6 mol% OH incorporation. While the LEVOH obtains approximately twice the extent of crystallization compared to the branched equivalent, as OH incorporation increases, the crystallization kinetics and crystallinity of LEVOH decrease. The crystal structure of LEVOH is orthorhombic at low functionalization (≤ 11 mol% OH), a mixture of orthorhombic and hexagonal at moderate functionalization (17 - 21 mol%), and hexagonal at high functionalization (23 %). The LEVOH crystallizes into plates, with crystallite widths ~ 20 - 60 times the crystallite thickness. Ultimately, we show LEVOH crystallizes faster and to a greater extent than commercial branched EVOH, a potential advantage of post-polymerization functionalization as part of polymer-to-polymer upcycling.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Increasing Functional Diversity in a Global Land Surface Model Illustrates Uncertainties Related to Parameter Simplification

Abstract Simulations of the land surface carbon cycle typically compress functional diversity into a small set of plant functional types (PFT), with parameters defined by the average value of measurements of functional traits. In most earth system models, all wild plant life is represented by between five and 14 PFTs and a typical grid cell (≈100 × 100 km) may contain a single PFT. Model logic applied to this coarse representation of ecological functional diversity provides a reasonable proxy for the carbon cycle, but does not capture the non‐linear influence of functional traits on productivity. Here we show through simulations using the Energy Exascale Land Surface Model in 15 diverse terrestrial landscapes, that better accounting for functional diversity markedly alters predicted total carbon uptake. The shift in carbon uptake is as great as 30% and 10% in boreal and tropical regions, respectively, when compared to a single PFT parameterized with the trait means. The traits that best predict gross primary production vary based on vegetation phenology, which broadly determines where traits fall within the global distribution. Carbon uptake is more closely associated with specific leaf area for evergreen PFTs and the leaf carbon to nitrogen ratio in deciduous PFTs.

58 GEOSCIENCES↗
DOE OSTI2026

Informing Robust Functional Relationship Benchmarks: An Evaluation of the Temperature Sensitivity of Ecosystem Respiration Across the Arctic-Boreal Region

During land model development, simulated carbon dynamics are often benchmarked against observational data sets to evaluate model performance. Functional relationship benchmarks are the relationship between a driving variable (e.g., temperature) and a response variable (e.g., ecosystem respiration) and are a promising tool for assessing model performance by evaluating modeled sensitivities to changing environmental conditions. However, observed functional relationships can be influenced by choices made during data collection and throughout the benchmarking process, impacting the inferred skill of land models. To avoid misrepresenting a model's true performance, it is necessary to systematically evaluate best practices when constructing functional relationship benchmarks. We developed a set of guidelines for constructing functional relationship benchmarks, considering the choice of data set, number of daily observations, temporal extent, and temporal resolution across Alaska and Canada over a 20-year period from 2001 to 2020. The temperature sensitivity of ecosystem respiration from observations, evaluated through an apparent Q 10 , is highly variable both spatially and as a result of the data processing approach applied in the benchmark formation. When benchmarking 13 models from the Warming Permafrost Model Intercomparison Project (WrPMIP), the range in inferred model skill is substantially impacted by the choices applied in constructing functional relationship benchmarks. The inferred performance of a given model is most sensitive to the number of daily observations and temporal extent, followed by choice of benchmark data set and temporal averaging. Results from this analysis can guide the development of consistent and robust functional relationships for future model evaluation studies.

Poe, Jeralyn [Northern Arizona University, Flagsta↗
DOE OSTI2021

Long-term warming in a Mediterranean-type grassland affects soil bacterial functional potential but not bacterial taxonomic composition

Abstract Climate warming is known to impact ecosystem composition and functioning. However, it remains largely unclear how soil microbial communities respond to long-term, moderate warming. In this study, we used Illumina sequencing and microarrays (GeoChip 5.0) to analyze taxonomic and functional gene compositions of the soil microbial community after 14 years of warming (at 0.8–1.0 °C for 10 years and then 1.5–2.0 °C for 4 years) in a Californian grassland. Long-term warming had no detectable effect on the taxonomic composition of soil bacterial community, nor on any plant or abiotic soil variables. In contrast, functional gene compositions differed between warming and control for bacterial, archaeal, and fungal communities. Functional genes associated with labile carbon (C) degradation increased in relative abundance in the warming treatment, whereas those associated with recalcitrant C degradation decreased. A number of functional genes associated with nitrogen (N) cycling (e.g., denitrifying genes encoding nitrate-, nitrite-, and nitrous oxidereductases) decreased, whereas nifH gene encoding nitrogenase increased in the warming treatment. These results suggest that microbial functional potentials are more sensitive to long-term moderate warming than the taxonomic composition of microbial community.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Discerning the thermodynamic feasibility of the spontaneous coexistence of multiple functional vegetation groups

Can the Second Law of Thermodynamics explain why ecosystems naturally organize into a complex structure composed of multiple vegetation species and functional groups? Ecosystem structure, which refers to the number and type of plant functional groups, is the result of self-organization, or the spontaneous emergence of order from random fluctuations. By considering ecosystems as open thermodynamic systems, we model and study these fluctuations of throughput signatures on short timescales to determine the drivers and characteristics of ecosystem structure. This diagnostic approach allows us to use fluxes of energy and entropy to calculate an ecosystem’s estimated work and understand the thermodynamic behavior of the system. We use a multi-layer canopy-root-soil model to calculate the energy and entropy fluxes of different scenarios for field sites across various climates. At each site, scenarios comprised of native individual plant functional groups and a coexisting multi-group composition scenario including all functional groups observed at the site are compared. Ecosystem-scale calculations demonstrate that entropy fluxes and work efficiency—the work performed for the amount of radiation entering the ecosystem—are greatest in the multi-group scenario when its leaf area is significantly larger than each of its individual functional groups. Thus, we conclude that ecosystems self-organize towards the vegetation structure with the greatest outgoing entropy flux and work efficiency, resulting in the coexistence of multiple functional groups and performing the maximum amount of work within the constraints of locally available energy, water, and nutrients.

54 ENVIRONMENTAL SCIENCES↗