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Results for “percolation theory”

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2024

Percolative phase transition in few-layered MoSe 2 field-effect transistors using Co and Cr contacts

The metal-to-insulator phase transition (MIT) in two-dimensional (2D) materials under the influence of a gating electric field has revealed interesting electronic behavior and the need for a deeper fundamental understanding of electron transport processes, while attracting much interest in the development of next-generation electronic and optoelectronic devices. Although the mechanism of the MIT in 2D semiconductors is a topic under debate in condensed matter physics, our work demonstrates the tunable percolative phase transition in few-layered MoSe 2 field-effect transistors (FETs) using different metallic contact materials. Here, we attempted to understand the MIT through temperature-dependent electronic transport measurements by tuning the carrier density in a MoSe 2 channel under the influence of an applied gate voltage. In particular, we have examined this phenomenon using the conventional chromium (Cr) and ferromagnetic cobalt (Co) as two metal contacts. For both Cr and Co, our devices demonstrated n-type behavior with a room-temperature field-effect mobility of 16 cm 2 V −1 s −1 for the device with Cr-contacts and 92 cm 2 V −1 s −1 for the device with Co-contacts, respectively. Further, with low temperature measurements at 50 K, the mobilities increased significantly to 65 cm 2 V −1 s −1 for the device with Cr and 394 cm 2 V −1 s −1 for the device with Co-contacts. By fitting our experimental data to the percolative phase transition theory, the temperature-dependent conductivity data show a transition from an insulating-to-metallic behavior at a bias of ∼28 V for Cr-contacts and ∼20 V for Co-contacts. This cross-over of the conductivity can be attributed to an increase in carrier density as a function of the gate bias in temperature-dependent transfer characteristics. By extracting the critical exponents, we find that the transport behavior in the device with Co-contacts aligns closely with the 2D percolation theory. In contrast, the devices with Cr-contacts deviate significantly from the 2D limit at low temperatures.

36 MATERIALS SCIENCE↗
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 OSTI2026

Heterogeneous Corrosion Pathways in Pt–Ni Nanododecahedra Revealed by In Situ Liquid Cell TEM

Unraveling nanoscale corrosion pathways is essential for understanding materials degradation mechanisms and designing corrosion-resistant metal alloys. Here, in this study, we directly visualize the corrosion of Pt–Ni nanododecahedra in 0.1 M HCl using liquid cell TEM. Each nanoparticle features a Ni-rich core and a Pt-rich frame. Our observation reveals that corrosion proceeds in two distinct stages: first the Ni-rich core dissolves without forming porosity, yielding small Pt nanocrystals and transient NiCl 2 ·6H 2 O at the retreating interfaces; then the Pt-rich frame fragments into ∼5 nm Pt 3 Ni nanocrystals that subsequently dissolve uniformly, accompanied by fleeting Pt chlorides. A percolation-based theory explains the observed behaviors: The core’s ∼8% Pt lies below the Pt connectivity threshold, preventing Pt scaffold formation, whereas the frame’s 48% Ni exceeds the Ni percolation threshold and collapses. Ordered Pt 3 Ni suppresses Ni percolation, thereby enforcing uniform dissolution. These findings reveal how composition and structural ordering govern heterogeneous corrosion in Pt–Ni architectured nanoparticles.

Liquid phase TEM↗
DOE OSTI2020

Modeling CO 2 plume migration using an invasion-percolation approach that includes dissolution

Geological carbon dioxide (CO 2 ) sequestration has been proposed as a viable technique to decrease effective emissions of CO 2 into the atmosphere. However, the security of this sequestration is tied to our understanding of the long-term migration of CO 2 in subsurface. The dissolution of CO 2 in the reservoir brine is one of the main long-term trapping mechanisms. However, the assumptions used in large-scale reservoir simulations usually lead to an overestimation of the dissolution volume. We propose a modified approach based on the macroscopic invasion-percolation (MIP) theory that allows the dissolution of CO 2 into brine. We used a high-resolution geological model to compare the Darcy-, modified MIP-, and classic MIP-based simulation results. We observed a significant shrinkage in the nonaqueous plume volume when dissolution is considered during the MIP simulation. In the case of Darcy-based simulation, the plume was completely trapped inside the reservoir with limited migration even after a thousand-year simulation. On the other hand, the majority of the plume migrated out of the simulated reservoir in the case of MIP. Our approach provides more realistic estimation of the dissolution volume and nonaqueous plume extent while leveraging the computational efficiency enjoyed by MIP.

54 ENVIRONMENTAL SCIENCES↗
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

Continuous Mott Transition in Moiré Semiconductors: Role of Long-Wavelength Inhomogeneities

Recent experiments in moiré transition metal dichalcogenide materials have reported the observation of a continuous bandwidth-tuned transition from a metal to a paramagnetic Mott insulator at a fixed filling of one electron per moiré unit cell. The electrical transport measurements reveal a number of puzzling features that are seemingly at odds with the theoretical expectations of an interaction-induced, but disorder-free, bandwidth-tuned metal-insulator transition. In this Letter, we include the effects of long-wavelength inhomogeneities, building on the results for a continuous metal-insulator transition at fixed filling in the clean limit. We examine the effects of mesoscale inhomogeneities near the critical point on transport using the framework of random resistor networks, highlighting the salient differences from a simple percolation-based picture. Finally, we place our results in the context of recent and ongoing experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Essential role of magnetic frustration in the phase diagrams of doped cobaltites

Doped perovskite cobaltites (e.g., La 1–x Sr x CoO 3 ) have been extensively studied for their spin-state physics, electronic inhomogeneity, and insulator-metal transitions. Ferromagnetically interacting spin-state polarons emerge at low x in the phase diagram of these compounds, eventually yielding long-range ferromagnetism. The onset of long-range ferromagnetism (x≈0.18) is substantially delayed relative to polaron percolation (x≈0.05), however, generating a troubling inconsistency. Here, in this study, Monte Carlo simulations of a disordered classical spin model are used to establish that previously ignored magnetic frustration is responsible for this effect, enabling faithful reproduction of the magnetic phase diagram.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Hydrological connectivity: a review and emerging strategies for integrating measurement, modeling, and management

This review synthesizes methods for measuring, modeling, and managing hydrologic connectivity, offering pathways to improve practices and address environmental challenges (e.g., climate change) and sustainability. As a key driver of water movement and nutrient cycling, hydrologic connectivity influences flood mitigation, water quality regulation, and biodiversity conservation. However, traditional field-based methods (e.g., dye tracing), indirect measurements (e.g., runoff analysis), and remote sensing techniques (e.g., InSAR) often struggle to capture the complexity of catchment-scale interactions. Similarly, modeling approaches—including process-based and percolation theory-based models, graph theory, and entropy-based metrics—face limitations in fully representing these interconnected processes. Both modeling and measurement techniques are constrained by inadequate spatial and temporal coverage, high data demands, computational complexity, and difficulties in representing subsurface connectivity. Subsequently, we critique current management practices that prioritize isolated variables (e.g., streamflow, sediment transport) over system-wide strategies and emphasize the need for adaptive, connectivity-based approaches in water resource planning and restoration. Moving forward, we highlight the importance of interdisciplinary collaboration, technological innovations (e.g., AI-driven modeling, real-time monitoring), and integrated frameworks to improve connectivity measurement, modeling, and adaptive management to restore fragmented hydrologic networks. This integrated approach sets the stage for transformative water resource management, fostering proactive policy development and stakeholder engagement.

Dwivedi, Dipankar↗
DOE OSTI2022

Entanglement phase transitions in random stabilizer tensor networks

Here we explore a class of random tensor network models with “stabilizer” local tensors which we name random stabilizer tensor networks (RSTNs). For RSTNs defined on a two-dimensional square lattice, we perform extensive numerical studies of entanglement phase transitions between volume-law and area-law entangled phases of the one-dimensional boundary states. These transitions occur when either (a) the bond dimension D of the constituent tensors is varied or (b) the tensor network is subject to random breaking of bulk bonds, implemented by forced measurements. In the absence of broken bonds, we find that the RSTN supports a volume-law entangled boundary state with bond dimension D ≥ 3 where D is a prime number, and an area-law entangled boundary state for D = 2. Upon breaking bonds at random in the bulk with probability p, there exists a critical measurement rate p c for each D ≥ 3 above which the boundary state becomes area-law entangled. To explore the conformal invariance at these entanglement transitions for different prime D, we consider tensor networks on a finite rectangular geometry with a variety of boundary conditions, and extract universal operator scaling dimensions via extensive numerical calculations of the entanglement entropy, mutual information, and mutual negativity at their respective critical points. Our results at large D approach known universal data of percolation conformal field theory, while showing clear discrepancies at smaller D, suggesting a distinct entanglement transition universality class for each prime D. We further study universal entanglement properties in the volume-law phase and demonstrate quantitative agreement with the recently proposed description in terms of a directed polymer in a random environment.

36 MATERIALS SCIENCE↗
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 OSTI2023

Experimental and modeling studies of IPDI-based polyurea elastomers – The role of hard segment fraction

Segmented polyureas (PUa) are industrially important class of polymers widely used in coatings, sealant, and adhesive applications. Here, in this paper, we report synthesis, characterization, and modeling of Isophorone Diisocyanate-Diethyl-Toluene-Diamine-Polyether amine (IPDI-DETDA-PO PUa) with varied hard segment contents of 20, 30, and 40 weight percent. For each of the three materials, we study its structure and phase behavior using FTIR, DSC, and TEM, and clearly show the presence of microphase separation between the hard and soft nanodomains. We then measure the linear viscoelastic response of the PUa-s using DMA (frequency sweeps at multiple temperatures). The DMA data are shown to obey the time-temperature superposition. Finally, we develop a new micromechanical model describing the DMA results; the model describes a phase-separated PUa as two “Fractional-order Maxwell gels” branches, connected in parallel, with the first FMG branch representing the “percolated hard phase" and the second one modeling the “filled soft phase". In agreement with the earlier thermodynamic theories, the volume-fraction of the percolated hard phase is related to the hard segment weight-fraction (HSWF), defined as the combined mass of IPDI and DETDA normalized to the total mass of the polymer. The data and model are found to be in a good qualitative and quantitative agreement.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Measurement-induced criticality in random quantum circuits

We investigate the critical behavior of the entanglement transition induced by projective measurements in (Haar) random unitary quantum circuits. Using a replica approach, we map the calculation of the entanglement entropies in such circuits onto a two-dimensional statistical-mechanics model. In this language, the area- to volume-law entanglement transition can be interpreted as an ordering transition in the statistical-mechanics model. We derive the general scaling properties of the entanglement entropies and mutual information near the transition using conformal invariance. We analyze in detail the limit of infinite on-site Hilbert space dimension in which the statistical-mechanics model maps onto percolation. In particular, we compute the exact value of the universal coefficient of the logarithm of subsystem size in the n th Rényi entropies for n ≥ 1 in this limit using relatively recent results for the conformal field theory describing the critical theory of two-dimensional (2D) percolation, and we discuss how to access the generic transition at finite on-site Hilbert space dimension from this limit, which is in a universality class different from 2D percolation. Here, we also comment on the relation to the entanglement transition in random tensor networks, studied previously in Vasseur et al. [Phys. Rev. B 100, 134203 (2019)].

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

A probabilistic-phase field model for the fracture of brittle materials

Abstract We develop a computational method to determine the failure probability of brittle materials under general mechanical loading conditions. The method is a combination of two parts: (1) numerical simulations of materials with multiple cracks using phase field theory, where the complete fracture process is viewed as ‘damage percolation’ along critical paths or clusters of cracks, rather than the traditional weak-link failure mechanism of Weibull, and (2) an extension of the Batdorf statistical theory of fracture to finite domains, where it is implemented within the finite element framework. The results of phase-field simulations at the ‘percolation threshold’ are used as failure data in the Batdorf theory to determine the overall probability of failure. The input to this approach is the size distribution of cracks in a pristine material. An example is shown, where alumina samples that were previously tested by Abe and coworkers (Abeet al2003J. Am. Ceram. Soc.861019–21) in four-point loading are compared to the results of our numerical simulations. The approach developed here has the advantage of being extendable to more complex thermomechanical loading.

Materials Science↗
DOE OSTI2024

Cylinders’ percolation: Decoupling and applications

In this paper we establish a strong decoupling inequality for the cylinder’s percolation process introduced by Tykesson and Windisch (Probab. Theory Related Fields 154 (2012) 165–191). This model features a very strong dependency structure, making it difficult to study, and this is why such decoupling inequalities are desirable. It is important to notice that the type of dependencies featured by cylinder’s percolation is particularly intricate, given that the cylinders have infinite range (unlike some models like Boolean percolation) while at the same time being rigid bodies (unlike processes such as random interlacements). Here our work introduces a new notion of fast decoupling, proves that it holds for the model in question and finishes with an application. More precisely, we prove that for a small enough density of cylinders, a random walk on a connected component of the vacant set is transient for all dimensions d≥3.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Effect of Fluorination on Lithium Transport and Short-Range Order in Disordered-Rocksalt-Type Lithium-Ion Battery Cathodes

Fluorine substitution is a critical enabler for improving the cycle life and energy density of disordered rocksalt (DRX) Li-ion battery cathode materials which offer prospects for high energy density cathodes, without the reliance on limited mineral resources. Due to the strong Li–F interaction, fluorine also is expected to modify the short-range cation order in these materials which is critical for Li-ion transport. In this work, density functional theory and Monte Carlo simulations are combined to investigate the impact of Li–F short-range ordering on the formation of Li percolation and diffusion in DRX materials. Additionally, the modeling reveals that F substitution is always beneficial at sufficiently high concentrations and can, surprisingly, even facilitate percolation in compounds without Li excess, giving them the ability to incorporate more transition metal redox capacity and thereby higher energy density. It is found that for F levels below 15%, its effect can be beneficial or disadvantageous depending on the intrinsic short-range order in the unfluorinated oxide, while for high fluorination levels the effects are always beneficial. Using extensive simulations, a map is also presented showing the trade-off between transition-metal capacity, Li-transport, and synthetic accessibility, and two of the more extreme predictions are experimentally confirmed.

25 ENERGY STORAGE↗
DOE OSTI2025

Non-equilibrium simulations of hydraulic permeation: Role of mechanical boundary conditions in dense membranes

Understanding the mechanisms of water transport in reverse osmosis membranes is critical for improving membrane performance and guiding material design. While classical models describe transport as either solution-diffusion (SD)—involving concentration-driven diffusion through a homogeneous medium—or pore-flow (PF)—involving pressure-driven convection through percolated water channels—their applicability to crosslinked polyamide membranes remains debated. Here, using non-equilibrium molecular dynamics simulations, we investigate the impact of mechanical support conditions on pressure-driven water transport in polyamide membranes across varying crosslink densities and pressure differentials (1000–5000 bar). Two support conditions are considered: graphene-restrained, representing experimentally relevant supported membranes, and freeze-restrained, mimicking a self-supported structure. In graphene-restrained systems, water concentration gradients and constant pressure profiles emerge, consistent with SD theory and incompatible with PF assumptions due to the absence of percolated pores and sub-nanometer voids. In contrast, freeze-restrained systems display uniform water concentration and linearly decreasing pressure at 1000 bar, and exhibit compressibility-induced water gradients and partial percolation at 5000 bar, resembling PF-like behavior. However, the underlying assumptions of PF theory—continuous solvent pathways and pressure transmission through water-filled pores—are not met under most conditions. Our results demonstrate that accurate modeling of reverse osmosis membranes must incorporate realistic mechanical boundary conditions to distinguish between transport mechanisms. For dense polyamide membranes supported by porous substrates, graphene-restrained simulations best reflect experimental setups and support the SD model as the dominant mechanism of water permeation.

molecular dynamics↗
DOE OSTI2022

The effect of metal–insulator interface interactions on electrical transport in granular metals

Here, we present an in-depth study of metal–insulator interfaces within granular metal (GM) films and correlate their interfacial interactions with structural and electrical transport properties. Nominally 100 nm thick GM films of Co and Mo dispersed within yttria-stabilized zirconia (YSZ), with volumetric metal fractions (φ) from 0.2–0.8, were grown by radio frequency co-sputtering from individual metal and YSZ targets. Scanning transmission electron microscopy and DC transport measurements find that the resulting metal islands are well-defined with 1.7–2.6 nm average diameters and percolation thresholds between φ = 0.4–0.5. The room temperature conductivities for the φ = 0.2 samples are several orders of magnitude larger than previously-reported for GMs. X-ray photoemission spectroscopy indicates both oxygen vacancy formation within the YSZ and band-bending at metal–insulator interfaces. The higher-than-predicted conductivity is largely attributed to these interface interactions. In agreement with recent theory, interactions that reduce the change in conductivity across the metal–insulator interface are seen to prevent sharp conductivity drops when the metal concentration decreases below the percolation threshold. These interface interactions help interpret the broad range of conductivities reported throughout the literature and can be used to tune the conductivities of future GMs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗