Percolation Limit Research Articles

The Free Boundary Schur Process and Applications I

We investigate the free boundary Schur process, a variant of the Schur process introduced by Okounkov and Reshetikhin, where we allow the first and the last partitions to be arbitrary (instead of empty in the original setting). The pfaffian Schur process, previously studied by several authors, is recovered when just one of the boundary partitions is left free. We compute the correlation functions of the process in all generality via the free fermion formalism, which we extend with the thorough treatment of “free boundary states.” For the case of one free boundary, our approach yields a new proof that the process is pfaffian. For the case of two free boundaries, we find that the process is not pfaffian, but a closely related process is. We also study three different applications of the Schur process with one free boundary: fluctuations of symmetrized last passage percolation models, limit shapes and processes for symmetric plane partitions and for plane overpartitions.

Multi-arm incipient infinite clusters in 2D: Scaling limits and winding numbers

Nous étudions le cluster infini conditionné (IIC) à $k$-bras alternants pour la percolation par site sur le réseau triangulaire $\mathbb{T}$. En utilisant le résultat de Camia et Newman montrant que la limite d’échelle de la percolation par site sur $\mathbb{T}$ est le CLE$_{6}$, nous prouvons l’existence de la limite d’échelle de l’IIC à $k$ bras pour $k=1,2,4$. Conditionnellement à l’événement qu’il y ait un bras ouvert et un bras fermé connectant l’origine à $\partial\mathbb{D}_{R}$, nous montrons que la variance du nombre d’enroulements est $(3/2+o(1))\log R$ quand $R\rightarrow\infty$, ce qui confirme la prédiction de Wieland et Wilson [Phys. Rev. E 68 (2003) 056101]. Notre preuve utilise le SLE$_{6}$ radial à deux côtés ainsi que des arguments de couplage. En utilisant ce résultat, nous obtenons une forme explicite pour le CLT sur le nombre d’enroulements, et obtenons des résultats analogues pour le IIC à deux bras, améliorant ainsi notre résultat précédent.

Hydrological Connectivity in Vegetated River Deltas: The Importance of Patchiness Below a Threshold

AbstractHydrological connectivity in coastal deltas is important for delivering flow, sediment, and nutrients to the island interiors. The roughness of island vegetation limits connectivity, but how important is the spatial distribution of vegetation? Using hydrodynamic modeling, we test the influence of vegetated percent cover, patch size, and stem density on the discharge‐fraction allocated to the islands of an idealized delta complex, modeled after Wax Lake Delta. We find that heterogeneity has negligible effects when vegetation is relatively sparse but is important when vegetation is relatively dense and covers less than a “disconnectivity” threshold of 40–50% of the islands, near the theoretical percolation limit. Below this threshold, preferential flow paths develop in the islands, which alter the hydraulics and residence time distribution of the delta complex and enhance potential sediment transport with respect to model runs with uniform vegetation. Patchiness has hydrogeomorphic and biogeochemical implications, which should be considered when modeling deltaic systems.

Spin glass, single-ion and dense Kondo effects in La1−xCexFePO

We investigated a series of La1−xCexFePO , and constructed a rich phase diagram by transport, magnetic, and thermodynamic measurements. Upon Ce doping, superconductivity is suppressed and disappears near . For the broad doping region , the Ce moments behave as single-ion Kondo impurities. With further Ce doping, the system evolves into a coherent Kondo lattice, with the critical concentration far exceeding the percolation limit of for a two-dimensional square lattice. No long-range magnetic ordering is identified on this phase diagram, while short-range spin-glass behavior is suggested to coexist with the single-ion Kondo phase. Within the spin-glass phase, the dominant magnetic correlation is found to change from antiferromagnetic-like to ferromagnetic-like as Ce concentration increases. We discuss the results based on the disordered Kondo lattice model, and ascribe the phase diagram to the high frustration of the Ce moments introduced by the superexchange interactions bridged by O and P anions. Our work hence provides an intriguing platform to study the disordered Kondo effect in the high-frustration limit.

Robustness of functional networks at criticality against structural defects.

The robustness of dynamical properties of neuronal networks against structural damages is a central problem in computational and experimental neuroscience. Research has shown that the cortical network of a healthy brain works near a critical state and, moreover, that functional neuronal networks often have scale-free and small-world properties. In this work, we study how the robustness of simple functional networks at criticality is affected by structural defects. In particular, we consider a two-dimensional Ising model at the critical temperature and investigate how its functional network changes with the increasing degree of structural defects. We show that the scale-free and small-world properties of the functional network at criticality are robust against large degrees of structural lesions while the system remains below the percolation limit. Although the Ising model is only a conceptual description of a two-state neuron, our research reveals fundamental robustness properties of functional networks derived from classical statistical mechanics models.

Low percolation threshold in highly conducting graphene nanoplatelets/glass composite coatings

Thermal sprayed thick glass coatings with a small percentage of multilayer graphene nanoplatelets (GNP) demonstrate electrical functionality with a quite remarkable low percolation limit (1.18 vol.%). This low critical content and the high electrical conductivity (∼40 S m−1) observed for the in-plane direction are related to the peculiar coating microstructure, formed by the pileup of lamellar amorphous particles decorated by GNP mostly following a surface parallel orientation. The general effective media model fitting to the electrical conductivity data for these coatings suggests a 3D connectivity of graphene and estimates an upper limit conductivity for the GNP of 105 S m−1. Hall effect shows the n-type behavior intrinsic to the SiO2/graphene interface, and carrier density and mobility rising with the GNP content. In addition, the coatings evidence a very high solar absorptivity that jointly with their high electrical conductivity broadens their potential applications, among others, for electromagnetic interference shielding or as photothermal detector and solar absorber for solar steam generation and water desalination.

Large Dielectric Constant Enhancement in MXene Percolative Polymer Composites.

We demonstrate that poly(vinylidene fluoride) (PVDF)-based percolative composites using two-dimensional (2D) MXene nanosheets as fillers exhibit significantly enhanced dielectric permittivity. The poly(vinylidene fluoride-trifluoro-ethylene-chlorofluoroehylene) (P[VDF-TrFE-CFE]) polymer embedded with 2D Ti3C2T x nanosheets reaches a dielectric permittivity as high as 105 near the percolation limit of about 15.0 wt % MXene loading, which surpasses all previously reported composites made of carbon-based fillers in the same polymer. With up to 10 wt % MXene loading, the dielectric loss of the MXene/P(VDF-TrFE-CFE) composite indicates only an approximately 5-fold increase (from 0.06 to 0.35), while the dielectric constant increased by 25 times over the same composition range. Furthermore, the ratio of permittivity to loss factor of the MXene-polymer composite is superior to that of all previously reported fillers in this same polymer. The dielectric constant enhancement effect is demonstrated to exist in other polymers as well when loaded with MXene. We show that the dielectric constant enhancement is largely due to the charge accumulation caused by the formation of microscopic dipoles at the surfaces between the MXene sheets and the polymer matrix under an external applied electric field.

AC and DC electrical behavior of MWCNT/epoxy nanocomposite near percolation threshold: Equivalent circuits and percolation limits

This study attempts to comprehensively investigate the effects of multi-walled carbon nanotubes (MWCNTs) on the AC and DC electrical conductivity of epoxy nanocomposites. The samples (0.2, 0.3, and 0.5 wt. % MWCNT) were produced using a combination of ultrason and shear mixing methods. DC measurements were performed by continuous measurement of the current-voltage response and the results were analyzed via a numerical percolation approach, while for the AC behavior, the frequency response was studied by analyzing phase difference and impedance in the 10 Hz to 0.2 MHz frequency range. The results showed that the dielectric parameters, including relative permittivity, impedance phase, and magnitude, present completely different behaviors for the frequency range and MWCNT weight fractions studied. To better understand the nanocomposites electrical behavior, equivalent electric circuits were also built for both DC and AC modes. The DC equivalent networks were developed based on the current-voltage curves, while the AC equivalent circuits were proposed by using an optimization problem according to the impedance magnitude and phase at different frequencies. The obtained equivalent electrical circuits were found to be highly useful tools to understand the physical mechanisms involved in MWCNT filled polymer nanocomposites.

A detailed investigation on thermal and micro-structural properties of hexagonal boron nitride composites

This work reports on the processing and characterization of Boron Nitride filled polyester composites. It emphasizes the details of the test procedures and results in regard to the thermal and micro-structural characteristics of the polyester composites filled with micro-sized boron nitride (BN) with different concentrations. The estimation of effective thermal conductivity of the composites using the proposed theoretical models is done and the results are validated by corresponding experimental results. The effects of inclusion of BN on the effective thermal conductivity (keff), glass transition temperature (Tg), coefficient of thermal expansion (CTE) of composites are also studied. With the addition of BN, the thermal conductivity enhances. Again, the embedment of BN fillers results in lowering the CTE of the composites whereas the Tg of the composites is improved manifold. The other theoretical models as well as the proposed theoretical correlation can serve as very good empirical models for particulate fillers to estimate keff for composites within the percolation limit. Again, the polyester composites serve to be a better option than the epoxy composites as polyester tends to impart better mechanical and thermal properties. By enhancement of conduction capability the light weight and micro-sized BN filled polyester composites can be used for applications such as space flight and aviation industry,electronic encapsulations,engine parts etc. Similarly a hybrid composite is fabricated with another organic filler which showed even more distinctive properties suitable for particular applications

Interplay between key variables of peroxide cured EPDM and evaluation of electromechanical efficiency for MV cables

ABSTRACTExtensive work has been done on ethylene‐propylene‐diene monomer (EPDM) vulcanizates and the main factors influencing their cure efficiency. However, very little attention has been given to the evolution of material properties and the interplay between key variables formulation. The effect of ethylene/propylene content and concentration of peroxide and type on viscoelastic and dielectric properties of EPDM elastomers was investigated using dynamic mechanical analysis and electric property measurements at room temperature. In order to compare results, these measurements were obtained by FTIR spectroscopy. Differences between real and imaginary (loss) part of the permittivity of EPDM/ dicumyl peroxide (DCP) composites were more significant than those in EPDM/di(tert‐butylperoxyisopropyl)benzene (DTBPIB) composites. For peroxide DTBPIB, the dielectric percolation limit moves further with the increase of ethylene content of EPDM. The dielectric percolation limit of the peroxide DTBPIB is found to be approximately 60 g at a 75% of ethylene in EPDM. The FTIR analysis showed that a termoxidative degradation was promoted at mixes with peroxide DCP at 45 and 75% of ethylene in EPDM. Therefore, we could interestingly show the decrease in electrical properties particularly associated with termoxidative degradation of peroxide DCP. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018, 135, 46139.

Spin pumping and inverse spin Hall effect in ultrathin SrRuO3 films around the percolation limit

Spin pumping and inverse spin Hall effect in ultrathin <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>SrRuO</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> films around the percolation limit

La chirurgie valvulaire à cœur ouvert

Composites of single-walled carbon nanotubes (SWNT) and conjugated polymers are highly interesting as active semiconducting layers in solution-processable and flexible electronics. Understanding the percolation behavior and percolation threshold for electrical conductivity in these composites is a prerequisite for future applications. Here, we investigate the concentration and length dependence of on-currents and apparent mobilities for selectively dispersed, semiconducting (6,5) single-walled carbon nanotubes in a matrix of the dispersing polyfluorene-bipyridine copolymer (PFO-BPy) through field-effect transistor measurements. More importantly, we directly visualize the percolation paths at and above the percolation limit by near-infrared electroluminescence (EL) imaging with high spatial resolution. EL imaging reveals the various shapes of critical percolation paths at the threshold and the non-uniformity of charge transport even at high SWNT concentrations. We also find that percolation paths differ depending on the assignment of the injecting electrodes probably due to different injection barriers and variation of nanotube density at the electrodes.

Direct visualization of percolation paths in carbon nanotube/polymer composites

Composites of single-walled carbon nanotubes (SWNT) and conjugated polymers are highly interesting as active semiconducting layers in solution-processable and flexible electronics. Understanding the percolation behavior and percolation threshold for electrical conductivity in these composites is a prerequisite for future applications. Here, we investigate the concentration and length dependence of on-currents and apparent mobilities for selectively dispersed, semiconducting (6,5) single-walled carbon nanotubes in a matrix of the dispersing polyfluorene-bipyridine copolymer (PFO-BPy) through field-effect transistor measurements. More importantly, we directly visualize the percolation paths at and above the percolation limit by near-infrared electroluminescence (EL) imaging with high spatial resolution. EL imaging reveals the various shapes of critical percolation paths at the threshold and the non-uniformity of charge transport even at high SWNT concentrations. We also find that percolation paths differ depending on the assignment of the injecting electrodes probably due to different injection barriers and variation of nanotube density at the electrodes.

Synthesis and Properties of Poly(ether sulfone)s with Clustered Sulfonic Groups for PEMFC Applications under Various Relative Humidity.

Novel sulfonated poly(ether sulfone) copolymers (S4PH-x-PSs) based on a new aromatic diol containing four phenyl substituents at the 2, 2', 6, and 6' positions of 4,4'-diphenyl ether were synthesized. Sulfonation was found to occur exclusively on the 4 position of phenyl substituents by NMR spectroscopy. The ion exchange capacity (IEC) values can be controlled by adjusting the mole percent (x in S4PH-x-PS) of the new diol. The fully hydrated sulfonated poly(ether sulfone) copolymers had good proton conductivity in the range 0.004-0.110 S/cm at room temperature. The surface morphology of S4PH-x-PSs and Nafion 212 was investigated by atomic force microscopy (tapping-mode) and related to the percolation limit and proton conductivity. Single H2/O2 fuel cell based on S4PH-40-PS loaded with 0.25 mg/cm2 catalyst (Pt/C) exhibited a peak power density of 462.6 mW/cm2, which was close to that of Nafion 212 (533.5 mW/cm2) at 80 °C with 80% RH. Furthermore, fuel cell performance of S4PH-35-PS with various relative humidity was investigated. It was confirmed from polarization curves that the fuel cell performance of S4PH-35-PS was not as high as that of Nafion 212 under fully hydrated state due to higher interfacial resistance between S4PH-35-PS and electrodes. While under low relative humidity (53% RH) at 80 °C, fuel cells based on S4PH-35-PS showed higher peak power density (234.9 mW/cm2) than that (214.0 mW/cm2) of Nafion 212.

Understanding the anomalous frequency responses of composite materials using very large random resistor-capacitor networks

In this paper large resistor-capacitor (RC) networks that consist of randomly distributed conductive and capacitive elements which are much larger than those previously explored are studied using an efficient algorithm. We investigate the emergent power-law scaling of the conductance and the percolation and saturation limits of the networks at the high and low frequency bounds in order to compare with a modification of the classical Effective Medium Approximation (EMA) that enables its extension to finite network sizes. It is shown that the new formula provides a simple analytical description of the network response that accurately predicts the effects of finite network size and composition and it agrees well with the new numerical calculations on large networks and is a significant improvement on earlier EMA formulae. Avenues for future improvement and explanation of the formula are highlighted. Finally, the statistical variation of network conductivity with network size is observed and explained. This work provides a deeper insight into the response of large resistor-capacitor networks to understand the AC electrical properties, size effects, composition effects and statistical variation of properties of a range of heterogeneous materials and composite systems.

Electrochemical properties of composite cathodes using Sm doped layered perovskite for intermediate temperature-operating solid oxide fuel cell

SmBaCo2O5+d (SBCO) showed the lowest observed Area Specific Resistance (ASR) value in the LnBaCo2O5+d (Ln: Pr, Nd, Sm, and Gd) oxide system for the overall temperature ranges tested. The ASR of a composite cathode (mixture of SBCO and Ce0.9Gd0.1O2−d) on a Ce0.9Gd0.1O2−d (CGO91) electrolyte decreased with respect to the CGO91 content; the percolation limit was also achieved for a 50wt% SBCO and 50wt% CGO91 (SBCO50) composite cathode.The ASRs of SBCO50 on the dense CGO91 electrolyte in the overall temperature range of 500–750°C were relatively lower than those of SBCO50 on the CGO91 coated dense 8mol% yttria-stabilized zirconia (8YSZ) electrolyte for the same temperature range. From 750°C and for all higher temperatures tested, however, the ASRs of SBCO50 on the CGO91 coated dense 8YSZ electrolyte were lower than those of the CGO91 electrolyte.The maximum power densities of SBCO50 on the Ni-8YSZ/8YSZ/CGO91 buffer layer were 1.034Wcm−2 and 0.611Wcm−2 at 800°C and 700°C.

Synthesis and characterization of supported Sn/γ-Al2O3 and Sn/ZSM5 catalysts for CO2 reduction in electrochemical cell

To improve CO2 conversion efficiency at the cathode of an electroreduction cell, different loadings of Sn on high surface area supports, γ-Al2O3 and ZSM5, were synthesized by wet impregnation followed by hydrogen reduction. As synthesized catalysts were characterized using X-Ray diffraction (XRD), thermal gravimetric analysis (TGA), transmission electron microscope (TEM) and cyclic voltammetry studies. By comparing voltammetry results it is found that 20wt% Sn catalyst is electrochemically more active towards CO2 reduction than other lower and higher loadings of Sn on both the supports. The reason for such observation is explained based on physical characterization of γ-Al2O3 and ZSM5. In 20wt% Sn catalyst, the Sn remains in dispersed form adhering to the porous wall of γ-Al2O3 and ZSM5 satifying percolation limit. Whereas, at lower loadings, electronic connectivity between Sn particles are lost and, at higher loadings, Sn particles agglomerate blocking the pores of the support. Reduction of CO2 using 20Sn/Al2O3 and 20Sn/ZSM5 catalyst is found to be selective towards methane and carbon monoxide formation from the product analysis of the electroreduction cell using gas chromatograph. In electroreduction cell, 20Sn/ZSM5 cathode produced higher current and more faradaic efficiency (20.4%) towards methane formation compared to 20Sn/Al2O3 cathode (12.9%).

Orthogonally weaved silver nanowire networks for very efficient organic optoelectronic devices

We demonstrate a simple but effective method to control the orientation of silver nanowires (AgNWs). Shear-flow-induced AgNW preferable orientation is realized by judiciously controlling the process parameters in the bar-coating method. This controllability of the NW direction enables the formation of AgNW cross-linking networks for transparent conductive electrode (TCE) applications. We experimentally demonstrate that the orthogonally weaved AgNW networks possess predominant advantages of lower percolation limit, higher transmission, and lower sheet resistance compared with the randomly orientated AgNW counterparts. The phenomenon is also confirmed with theoretical calculation by the Monte Carlo method. These high-quality AgNW TCEs exhibit a high transmittance of ∼94% with a sheet resistance of ∼20 Ω/sq, which meet the requirements of modern optoelectronic devices. Very efficient organic light-emitting diodes (OLEDs) and organic solar cells (OSCs) prepared by these AgNW TCEs are demonstrated. The OLED exhibits exceptionally high luminance efficiency, power efficacy, and external quantum efficiency of 92 cd/A, 111 lm/W, and 26.8%, respectively. The OSCs also deliver a high power conversion efficiency of up to 7.5%.

Synthesis and characterization of Zr-based in situ crystal precipitated and liquid phase separated bulk metallic glass composite

The aim of this study was to evaluate new Zr-based bulk metallic composites with crystallized dendrites or droplets which have the volume fraction below the critical one (the percolation limit). The Cu36Zr48Al8Ag8 alloy was chosen as matrix. Dendrites formed by in-situ solidification due to Ni addition. It was found that a new monotectic alloy system can be created successfully owing to Y addition (1–7at.%) to the matrix. Small amount of dendrites with non-random distribution has a strong influence on the compressive strength. Experiment showed that the alloy with 4.1at.% Ni has the maximum compressive strength (1998MPa) and Young's modulus (86GPa) within the examined samples. The results of compression test reveal that the cracks propagate near the small droplets below 1μm in diameter which generate weakening in the microstructure. In contrast, the large droplets especially above 3μm in diameter create a strong barrier for the shear band propagation.

Monitoring Damage Propagation in Glass Fiber Composites Using Carbon Nanofibers.

In this work, we report the potential use of novel carbon nanofibers (CNFs), dispersed during fabrication of glass fiber composites to monitor damage propagation under static loading. The use of CNFs enables a transformation of the typically non-conductive glass fiber composites into new fiber composites with appreciable electrical conductivity. The percolation limit of CNFs/epoxy nanocomposites was first quantified. The electromechanical responses of glass fiber composites fabricated using CNFs/epoxy nanocomposite were examined under static tension loads. The experimental observations showed a nonlinear change of electrical conductivity of glass fiber composites incorporating CNFs versus the stress level under static load. Microstructural investigations proved the ability of CNFs to alter the polymer matrix and to produce a new polymer nanocomposite with a connected nanofiber network with improved electrical properties and different mechanical properties compared with the neat epoxy. It is concluded that incorporating CNFs during fabrication of glass fiber composites can provide an innovative means of self-sensing that will allow damage propagation to be monitored in glass fiber composites.