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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Universality class for loopless invasion percolation models and a percolation avalanche burst model for hydraulic fracturing

Invasion percolation is a model that was originally proposed to describe growing networks of fractures. In this work, we describe a loopless algorithm on random lattices, coupled with an avalanche-based model for bursts. The model reproduces the characteristic b-value seismicity and spatial distribution of bursts consistent with earthquakes resulting from hydraulic fracturing (“fracking”). We test models for both site invasion percolation and bond invasion percolation. These have differences on the scale of site and bond lengths l. But since the networks are characterized by their large-scale behavior, l << L, we find small differences between scaling exponents. Though data may not differentiate between models, our results suggest that both models belong to different universality classes.

58 GEOSCIENCES↗
DOE OSTI2022

A generalized Flory-Stockmayer kinetic theory of connectivity percolation and rigidity percolation of cytoskeletal networks

Actin networks are essential for living cells to move, reproduce, and sense their environments. The dynamic and rheological behavior of actin networks is modulated by actin-binding proteins such as α-actinin, Arp2/3, and myosin. There is experimental evidence that actin-binding proteins modulate the cooperation of myosin motors by connecting the actin network. In this work, we present an analytical mean field model, using the Flory-Stockmayer theory of gelation, to understand how different actin-binding proteins change the connectivity of the actin filaments as the networks are formed. We follow the kinetics of the networks and estimate the concentrations of actin-binding proteins that are needed to reach connectivity percolation as well as to reach rigidity percolation. We find that Arp2/3 increases the actomyosin connectivity in the network in a non-monotonic way. We also describe how changing the connectivity of actomyosin networks modulates the ability of motors to exert forces, leading to three possible phases of the networks with distinctive dynamical characteristics: a sol phase, a gel phase, and an active phase. Thus, changes in the concentration and activity of actin-binding proteins in cells lead to a phase transition of the actin network, allowing the cells to perform active contraction and change their rheological properties.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2018

Seasonal Monitoring of Melt and Accumulation Within the Deep Percolation Zone of the Greenland Ice Sheet and Comparison with Simulations of Regional Climate Modeling

Increasing melt over the Greenland Ice Sheet (GrIS) recorded over the past several years has resulted in significant changes of the percolation regime of the ice sheet. It remains unclear whether Greenland's percolation zone will act as a meltwater buffer in the near future through gradually filling all pore space or if near-surface refreezing causes the formation of impermeable layers, which provoke lateral runoff. Homogeneous ice layers within perennial firn, as well as near-surface ice layers of several meter thickness have been observed in firn cores. Because firn coring is a destructive method, deriving stratigraphic changes in firn and allocation of summer melt events is challenging. To overcome this deficit and provide continuous data for model evaluations on snow and firn density, temporal changes in liquid water content and depths of water infiltration, we installed an upward-looking radar system (upGPR) 3.4 m below the snow surface in May 2016 close to Camp Raven (66.4779 deg N, 46.2856 deg W) at 2120 m a.s.l. The radar is capable of quasi-continuously monitoring changes in snow and firn stratigraphy, which occur above the antennas. For summer 2016, we observed four major melt events, which routed liquid water into various depths beneath the surface. The last event in mid-August resulted in the deepest percolation down to about 2.3 m beneath the surface. Comparisons with simulations from the regional climate model MAR are in very good agreement in terms of seasonal changes in accumulation and timing of onset of melt. However, neither bulk density of near-surface layers nor the amounts of liquid water and percolation depths predicted by MAR correspond with upGPR data. Radar data and records of a nearby thermistor string, in contrast, matched very well for both timing and depth of temperature changes and observed water percolations. All four melt events transferred a cumulative mass of 56 kg/(sq. m) into firn beneath the summer surface of 2015. We find that continuous observations of liquid water content, percolation depths and rates for the seasonal mass fluxes are sufficiently accurate to provide valuable information for validation of model approaches and help to develop a better understanding of liquid water retention and percolation in perennial firn.

Heilig, Achim↗
DOE OSTI2026

Deciphering the Conflict Between Ion and Electron Percolating Networks in Solid-State Battery Cathodes

High-energy- and power-density solid state batteries require an optimal cathode composition and microstructural arrangement of cathode active material, solid-state electrolyte, conductive carbon, and binder to simultaneously support lithium-ion transport, electron conduction, and storage capacity. The ion and electron conducting phases in solid-state cathodes counteract each other's percolating networks as their mass ratios increase or decrease relative to each other. Here, we investigate targeted mass ratio variations of argyrodite solid electrolyte and two different types of conductive carbon (particles and fibers) in composite LiNi0.8Mn0.1Co0.1O2 (NMC811) solid-state cathodes to ascertain the ionic-electronic tradeoffs in cathode performance. Through ionic and electronic conductivity measurements on composite cathodes, as well as rate-testing and cycling performance in full cells, it is shown that the conductive carbon fibers form a percolative electronic network within the composite at a lower mass ratio (3-5 wt%) than particulate carbon (>5 wt%). The threshold to achieve electronic percolation coincides with higher accessible capacity in the cathode as the active material particles become electronically connected. However, carbon loadings beyond this percolation threshold lead to increased ion transport resistance, arising from disruptions to ionic conduction pathways and degraded contact at the interface between the electrolyte and active materials. Imaging, spectroscopy, and physics-based models quantitatively describe the relationship between carbon and electrolyte compositions and the cell's capacity and rate performance through percolation theory. This work demonstrates the importance of quantitatively understanding percolating networks in solid-state cells and that strategic engineering of conductive carbon morphologies can further increase the energy- and power-density of solid-state cells.

25 ENERGY STORAGE↗
DOE OSTI2020

Percolated Ionic Aggregate Morphologies and Decoupled Ion Transport in Precise Sulfonated Polymers Synthesized by Ring-Opening Metathesis Polymerization

Here, we describe a set of precise single-ion conducting polymers that form self-assembled percolated ionic aggregates in glassy polymer matrices and have decoupled transport of metal cations. These precise single-ion conductors (SICs), synthesized by a scalable ring-opening metathesis polymerization, consist of a polyethylene backbone with a sulfonated phenyl group pendant on every fifth carbon and are fully neutralized by a counterion X + (Li + , Na + , or Cs + ). Experimental X-ray scattering measurements and fully atomistic molecular dynamics (MD) simulations are in good agreement. The MD simulations show that the ionic groups nanophase separate from the polymer backbone to form percolating ionic aggregates. Using graph theory, we find that within the Li + - and Na + -neutralized polymers the percolated aggregates exhibit planar and ribbon-like configurations at intermediate length scales, while the percolated aggregates within the Cs + -neutralized polymers are more isotropic. Electrical impedance spectroscopy measurements show that the ionic conductivities exhibit Arrhenius behavior, with conductivities of 10 –7 to 10 –6 S/cm at 180 °C. In the MD simulations, the cations move between sulfonate groups in the percolated aggregates, larger ions travel further, and overall cations travel further than the polymer backbones, indicating a decoupled ion-transport mechanism. Thus, the percolated ionic aggregates in these polymers can serve as pathways to facilitate decoupled ion motion through a glassy polymer matrix.

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

Soil water percolation and nutrient fluxes as a function of topographical, seasonal and soil texture variation in Central Amazonia, Brazil

Abstract Understanding soil water dynamics and transport of nutrients is challenging in tropical rainforests due to the uniqueness of several properties related to soils, vegetation and seasonality that make relating patterns found in temperate environments to tropical sites difficult. We address the need for better edaphic characterization in tropical environments by investigating soil water percolation rates and chemistry across topographic, soil texture and seasonal gradients in a mature tropical rainforest in Central Amazonia, Brazil. We utilized a passive wick flux meter (e.g., drainage lysimeter) to directly measure real‐time percolation fluxes at 60‐cm depth, and to sample a suite of chemical species across plateau, slope and valley topographic positions. We found percolation flux volume and chemical exports generally increase with decreasing elevation and clay content, which was lowest in the valley. Daily percolation flux was observed to be 2.39 ± 0.44 in plateau, 3.01 ± 0.50 in slope and 6.16 ± 0.83 mm in valley. Most solutes were present in small amounts of <1 mg L −1 , such as PO₄ 3− , Fe 2+ /Fe 3+ and Mn 2+ ; however, NO 3 − concentrations were >20 mg L −1 , even exceeding 100 mg L −1 in the valley. Based on additional isotopic analysis, we speculate high NO 3 − concentrations are partially an artefact of root decomposition following installation of the flux meters. The empirical relationships we show among percolation volume and nutrient exports under varying topographies and soil textures can improve Earth System Model performance by better constraining ecohydrological relationships to nutrient fluxes, which can in‐turn better illuminate the important factors that govern their behaviour.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Predicting Water Cycle Characteristics from Percolation Theory and Observational Data

The fate of water and water-soluble toxic wastes in the subsurface is of high importance for many scientific and practical applications. Although solute transport is proportional to water flow rates, theoretical and experimental studies show that heavy-tailed (power-law) solute transport distribution can cause chemical transport retardation, prolonging clean-up time-scales greatly. However, no consensus exists as to the physical basis of such transport laws. In percolation theory, the scaling behavior of such transport rarely relates to specific medium characteristics, but strongly to the dimensionality of the connectivity of the flow paths (for example, two- or three-dimensional, as in fractured-porous media or heterogeneous sediments), as well as to the saturation characteristics (i.e., wetting, drying, and entrapped air). In accordance with the proposed relevance of percolation models of solute transport to environmental clean-up, these predictions also prove relevant to transport-limited chemical weathering and soil formation, where the heavy-tailed distributions slow chemical weathering over time. The predictions of percolation theory have been tested in laboratory and field experiments on reactive solute transport, chemical weathering, and soil formation and found accurate. Recently, this theoretical framework has also been applied to the water partitioning at the Earth’s surface between evapotranspiration, ET, and run-off, Q, known as the water balance. A well-known phenomenological model by Budyko addressed the relationship between the ratio of the actual evapotranspiration (ET) and precipitation, ET/P, versus the aridity index, ET 0 /P, with P being the precipitation and ET 0 being the potential evapotranspiration. Existing work was able to predict the global fractions of P represented by Q and ET through an optimization of plant productivity, in which downward water fluxes affect soil depth, and upward fluxes plant growth. In the present work, based likewise on the concepts of percolation theory, we extend Budyko’s model, and address the partitioning of run-off Q into its surface and subsurface components, as well as the contribution of interception to ET. Using various published data sources on the magnitudes of interception and information regarding the partitioning of Q, we address the variability in ET resulting from these processes. The global success of this prediction demonstrated here provides additional support for the universal applicability of percolation theory for solute transport as well as guidance in predicting the component of subsurface run-off, important for predicting natural flow rates through contaminated aquifers.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Evaluation of the rheological and electrical percolation of high‐density polyethylene/carbon black composites using mathematical models

Abstract In this work, conductive polymer composites (CPCs) of bio‐based polyethylene (BioPe) containing different concentrations of carbon black (CB) were developed. By using oscillatory rheology analysis, a Newtonian plateau was observed in BioPe, and all BioPe/CB composites had a behavior of a pseudo‐solid and that composites with volume fractions ranging from 0.24 to 0.56 presented higher viscosity, storage, and loss modulus. This suggests the formation of a percolated network and by using the power‐law models, it was observed that the electrical percolation threshold was higher than the rheological percolation threshold. The electrical conductivity was measured using the four‐point probe method and a sigmoid model was used to predict the CPCs' electrical conductivity percolation threshold. The results indicated that the four‐point probe method presented satisfactory results according to the calculated standard deviations and voltage–current characteristics for each round of measurements considering the same ranging as used in rheology analysis. The analytical model used showed a coefficient of determination ( R 2 ) higher than 95%, allowing the prediction of the electrical conductivity of the CPC and the percolation threshold as a function of the volumetric fraction of the CB.

da SiIva, Moacy P.↗
DOE OSTI2019

A 3D percolation model for multicomponent nanocarbon composites: the critical role of nematic transition

A three-dimensional (3D) continuum percolation model has been developed on the basis of Monte Carlo simulation to investigate the percolation behavior of an electrically insulating matrix reinforced with multiple conductive fillers of different dimensionalities. Impenetrable fillers of large aspect ratio are found to preferentially align with each other to maximize the packing entropy rather than forming randomly oriented clusters. This entropy-driven transition from isotropic to nematic phase is shown to critically affect the percolation threshold. It suggests that an isotropic phase with a smaller nematic order parameter leads to a reduction in percolation threshold. In addition, a combination of two fillers with different dimensionalities can achieve a working concentration below the percolation threshold of single component system, which is further validated by the experiments of electrical conductivity in multicomponent multidimensional nanocarbon composites.

Ni, Xiaojuan↗
DOE OSTI2019

Ultrabroadband infrared near-field spectroscopy and imaging of local resonators in percolative gold films

Percolation processes are ubiquitous in nature and are responsible for many critical phenomena such as first-order phase transitions and infectious epidemic networks. The optical properties of a percolative medium can generally be captured by the effective medium approximation (EMA) when the degree of percolation and the properties of the constituent materials are properly addressed. However, the important local collective responses of nanoclusters in the deep subwavelength regime are often only phenomenologically addressed in the standard EMA formalism. Additionally, a comprehensive method that measures local light–matter interactions and registers how the local responses influence global optical properties has yet to be established on a firm basis. In this paper, we use infrared nanoimaging/spectroscopy to investigate percolative gold films in the vicinity of the critical percolation threshold. We demonstrate experimentally and theoretically that the near-field spectra yield quantitative information of the characteristic length scale of the local gold clusters and their relative oscillator strengths. As a result, EMA analysis can be augmented with near-field nano-spectroscopy to yield better predictability of the far-field reflection spectrum at the corresponding spectral range.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Percolation technique for galaxy clustering

We study percolation in mass and galaxy distributions obtained in 3D simulations of the CDM, C + HDM, and the power law (n = -1) models in the Omega = 1 universe. Percolation statistics is used here as a quantitative measure of the degree to which a mass or galaxy distribution is of a filamentary or cellular type. The very fast code used calculates the statistics of clusters along with the direct detection of percolation. We found that the two parameters mu(infinity), characterizing the size of the largest cluster, and mu-squared, characterizing the weighted mean size of all clusters excluding the largest one, are extremely useful for evaluating the percolation threshold. An advantage of using these parameters is their low sensitivity to boundary effects. We show that both the CDM and the C + HDM models are extremely filamentary both in mass and galaxy distribution. The percolation thresholds for the mass distributions are determined.

Klypin, Anatoly↗
DOE OSTI2021

Postprocessing techniques for gradient percolation predictions on the square lattice

In this work, we revisit the classic problem of site percolation on a regular square lattice. In particular, we investigate the effect of quantization bias errors on percolation threshold predictions for large probability gradients and propose a mitigation strategy. We demonstrate through extensive computational experiments that the assumption of a linear relationship between probability gradient and percolation threshold used in previous investigations is invalid. Moreover, we demonstrate that, due to skewness in the distribution of occupation probabilities visited the average does not converge monotonically to the true percolation threshold. Furthermore, we identify several alternative metrics which do exhibit monotonic (albeit not linear) convergence and document their observed convergence rates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Expandable Li Percolation Network: The Effects of Site Distortion in Cation-Disordered Rock-Salt Cathode Material

Cation-disordered rock-salt (DRX) materials receive intensive attention as a new class of cathode candidates for high-capacity lithium-ion batteries (LIBs). Unlike traditional layered cathode materials, DRX materials have a three-dimensional (3D) percolation network for Li + transportation. The disordered structure poses a grand challenge to a thorough understanding of the percolation network due to its multiscale complexity. In this work, we introduce the large supercell modeling for DRX material Li 1.16 Ti 0.37 Ni 0.37 Nb 0.10 O 2 (LTNNO) via the reverse Monte Carlo (RMC) method combined with neutron total scattering. Here, through a quantitative statistical analysis of the material’s local atomic environment, we experimentally verified the existence of short-range ordering (SRO) and uncovered an element-dependent behavior of transition metal (TM) site distortion. A displacement from the original octahedral site for Ti 4+ cations is pervasive throughout the DRX lattice. Density functional theory (DFT) calculations revealed that site distortions quantified by the centroid offsets could alter the migration barrier for Li + diffusion through the tetrahedral channels, which can expand the previously proposed theoretical percolating network of Li. The estimated accessible Li content is highly consistent with the observed charging capacity. The newly developed characterization method here uncovers the expandable nature of the Li percolation network in DRX materials, which may provide valuable guidelines for the design of superior DRX materials.

25 ENERGY STORAGE↗
DOE OSTI2021

Critical percolation on the kagome hypergraph

In this report we study the percolation critical surface of the kagome lattice in which each triangle is allowed an arbitrary connectivity. Using the method of critical polynomials, we find points along this critical surface to high precision. This kagome hypergraph contains many unsolved problems as special cases, including bond percolation on the kagome and (3, 12 2 ) lattices, and site percolation on the hexagonal, or honeycomb, lattice, as well as a single point for which there is an exact solution. We are able to compute enough points along the critical surface to find a very accurate fit, essentially a Taylor series about the exact point, that allows estimations of the critical point of any system that lies on the surface to precision rivaling Monte Carlo and traditional techniques of similar accuracy. We find also that this system sheds light on some of the surprising aspects of the method of critical polynomials, such as why it is so accurate for certain problems, like the kagome and (3, 12 2 ) lattices. The bond percolation critical points of these lattices can be found to 17 and 18 digits, respectively, because they are in close proximity, in a sense that can be made quantitative, to the exact point on the critical surface. We also discuss in detail a parallel implementation of the method which we use here for a few calculations.

97 MATHEMATICS AND COMPUTING↗
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↗