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1
Reimann, Stefan, and Andreas Tupak. "Can constrained percolation be approximated by Bernoulli percolation?" Journal of Physics A: Mathematical and General 35, no. 48 (November 19, 2002): 10219–27. http://dx.doi.org/10.1088/0305-4470/35/48/302.
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de Lima, B. N. B., R. Sanchis, D. C. dos Santos, V. Sidoravicius, and R. Teodoro. "The Constrained-degree percolation model." Stochastic Processes and their Applications 130, no. 9 (September 2020): 5492–509. http://dx.doi.org/10.1016/j.spa.2020.03.014.
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Goyal, Abhay, Nicos S. Martys, and Emanuela Del Gado. "Flow induced rigidity percolation in shear thickening suspensions." Journal of Rheology 68, no. 2 (February 5, 2024): 219–28. http://dx.doi.org/10.1122/8.0000786.
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Discontinuous shear thickening (DST) is associated with a sharp rise in a suspension’s viscosity with increasing applied shear rate or stress. Key signatures of DST, highlighted in recent studies, are the very large fluctuations of the measured stress as the suspension thickens with increasing rate. A clear link between microstructural development and the dramatic increase in stress fluctuations has not been established yet. To identify the microstructural underpinnings of this behavior, we perform simulations of sheared dense suspensions. Through an analysis of the particle contact network, we identify a subset of constrained particles that contributes directly to the rapid rise in viscosity and large stress fluctuations. Indeed, both phenomena can be explained by the growth and percolation of constrained particle networks—in direct analogy to rigidity percolation. A finite size scaling analysis confirms this to be a percolation phenomenon and allows us to estimate the critical exponents. Our findings reveal the specific microstructural self-organization transition that underlies DST.
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Bendisch, Jürgen, Stefan Reimann, and Hartmut von Trotha. "Site percolation for a class of constrained honeycomb lattices." Physica A: Statistical Mechanics and its Applications 307, no. 1-2 (April 2002): 1–14. http://dx.doi.org/10.1016/s0378-4371(01)00611-2.
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Sausset, François, Cristina Toninelli, Giulio Biroli, and Gilles Tarjus. "Bootstrap Percolation and Kinetically Constrained Models on Hyperbolic Lattices." Journal of Statistical Physics 138, no. 1-3 (December 12, 2009): 411–30. http://dx.doi.org/10.1007/s10955-009-9903-1.
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PASTORE, RAFFAELE, MASSIMO PICA CIAMARRA, and ANTONIO CONIGLIO. "PACMAN PERCOLATION AND THE GLASS TRANSITION." Fractals 21, no. 03n04 (September 2013): 1350021. http://dx.doi.org/10.1142/s0218348x13500217.
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We investigate via Monte Carlo simulations the kinetically constrained Kob-Andersen lattice glass model showing that, contrary to current expectations, the relaxation process and the dynamical heterogeneities seems to be characterized by different time scales. Indeed, we found that the relaxation time is related to a reverse percolation transition, whereas the time of maximum heterogeneity is related to the spatial correlation between particles. This investigation leads to a geometrical interpretation of the relaxation processes and of the different observed time scales.
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do Amaral, Charles S. "Constrained volume-difference site percolation model on the square lattice." Physica A: Statistical Mechanics and its Applications 663 (April 2025): 130431. https://doi.org/10.1016/j.physa.2025.130431.
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Yan, Zehao, and Mo Li. "A Stochastic Optimization Model for Agricultural Irrigation Water Allocation Based on the Field Water Cycle." Water 10, no. 8 (August 3, 2018): 1031. http://dx.doi.org/10.3390/w10081031.
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Agricultural water scarcity is a global problem and this reinforces the need for optimal allocation of irrigation water resources. However, decision makers are challenged by the complexity of fluctuating stream condition and irrigation quota as well as the dynamic changes of the field water cycle process, which make optimal allocation more complex. A two-stage chance-constrained programming model with random parameters in the left- and right-hand sides of constraints considering field water cycle process has been developed for agricultural irrigation water allocation. The model is capable of generating reasonable irrigation allocation strategies considering water transformation among crop evapotranspiration, precipitation, irrigation, soil water content, and deep percolation. Moreover, it can deal with randomness in both the right-hand side and the left-hand side of constraints to generate schemes under different flow levels and constraint-violation risk levels, which are informative for decision makers. The Yingke irrigation district in the middle reaches of the Heihe River basin, northwest China, was used to test the developed model. Tradeoffs among different crops in different time periods under different flow levels, and dynamic changes of soil moisture and deep percolation were analyzed. Scenarios with different violating probabilities were conducted to gain insight into the sensitivity of irrigation water allocation strategies on water supply and irrigation quota. The performed analysis indicated that the proposed model can efficiently optimize agricultural irrigation water for an irrigation district with water scarcity in a stochastic environment.
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Beach, Kory, Jeremy A. K. Horwitz, Alyssa Maich, Elida White, Dane Ramos, Ryan S. Crum-Friedman, Minta Akin, and Fady M. Najjar. "Constrained model calibration of grain structure dependent spall dynamics in shock-loaded tantalum." Journal of Applied Physics 132, no. 8 (August 28, 2022): 085904. http://dx.doi.org/10.1063/5.0102611.
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We perform a gas gun experiment by shock loading tantalum samples of varying grain structures to assess the suitability of a numerical model for simulating spall behavior. The observed differences in spall strength, as well spallation and re-compression history, are not captured in uncalibrated hydrodynamic simulations. An optimization is performed on the Johnson spall model to determine the best parameters that fit the observed trends. Linear stability analysis is employed to motivate bounds on those parameters. Herein, optimized simulations agree well with the experimental results, reproducing pullback depth and recompression timescales across the different samples tested. Further, the observed pullback time of the single crystal sample was found to imply, via the stability analysis, a percolation threshold in good agreement with the theoretical value for a body centered cubic lattice. Therefore, the combined linear stability and percolation analysis shows promise and may be applied to other materials with diverse microstructures. Collectively, the findings demonstrate that the model is suitable for reproducing spall-induced free surface behavior across various microstructures, but also points to caution in using model coefficients for uncalibrated microstructures.
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Li, Zhongyang. "Constrained percolation, Ising model, and XOR Ising model on planar lattices." Random Structures & Algorithms 57, no. 2 (May 7, 2020): 474–525. http://dx.doi.org/10.1002/rsa.20924.
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do Amaral, Charles S., A. P. F. Atman, and Bernardo N. B. de Lima. "On the monotonicity of the critical time in the Constrained-degree percolation model." Physica A: Statistical Mechanics and its Applications 561 (January 2021): 125291. http://dx.doi.org/10.1016/j.physa.2020.125291.
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Mossin, Lone, and Ulla L. Ladekarl. "Simple water balance modelling with few data - calibration and evaluation: investigations from a Danish Sitka spruce stand with a high interception loss." Hydrology Research 35, no. 2 (April 1, 2004): 139–51. http://dx.doi.org/10.2166/nh.2004.0010.
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Simple evapotranspiration models with few data requirements and Penman reference evapotranspiration for grass (Eref) limiting the actual evapotranspiration are often used to estimate chemical fluxes in ecosystems. The aim of this paper is to show how much the interception loss might exceed Eref in a wind-exposed Danish Sitka spruce stand and to demonstrate the importance of the evaluation of model performance, here represented by throughfall measurements and chemical fluxes. Precipitation, throughfall, soil moisture and soil water chemistry were measured monthly for 1.5 years. Model input was daily precipitation, Eref, leaf area index, root distribution and plant available water. The model interception loss was calculated using an empirical relationship between precipitation and interception loss that was calibrated against the measured interception loss. Interception loss was found to be unusually high, on average 58% of precipitation, which was supported by measurements from two other years with interception losses from 62–68% of precipitation. Transpiration and evaporation from soil were constrained by Eref. The modelled percolation was compared to percolation calculated by a chloride mass balance based on measured values. The percolation was only about 20% of precipitation due to the exceptionally high interception loss, which exceeded Eref by almost 50%. Therefore, in wind-exposed forest stands the interception loss should be modelled separately, as done here, and be calibrated on measured values.
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Gao, Xiaolong, Yao Huang, Xiaoxiang He, Xiaojing Fan, Ying Liu, Hong Xu, Daming Wu, and Chaoying Wan. "Mechanically Enhanced Electrical Conductivity of Polydimethylsiloxane-Based Composites by a Hot Embossing Process." Polymers 11, no. 1 (January 2, 2019): 56. http://dx.doi.org/10.3390/polym11010056.
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Electrically conductive polymer composites are in high demand for modern technologies, however, the intrinsic brittleness of conducting conjugated polymers and the moderate electrical conductivity of engineering polymer/carbon composites have highly constrained their applications. In this work, super high electrical conductive polymer composites were produced by a novel hot embossing design. The polydimethylsiloxane (PDMS) composites containing short carbon fiber (SCF) exhibited an electrical percolation threshold at 0.45 wt % and reached a saturated electrical conductivity of 49 S/m at 8 wt % of SCF. When reducing the sample thickness from 1.0 to 0.1 mm by the hot embossing process, a compression-induced percolation threshold occurred at 0.3 wt %, while the electrical conductivity was further enhanced to 378 S/m at 8 wt % SCF. Furthermore, the addition of a second nanofiller of 1 wt %, such as carbon nanotube or conducting carbon black, further increased the electrical conductivity of the PDMS/SCF (8 wt %) composites to 909 S/m and 657 S/m, respectively. The synergy of the densified conducting filler network by the mechanical compression and the hierarchical micro-/nano-scale filler approach has realized super high electrically conductive, yet mechanically flexible, polymer composites for modern flexible electronics applications.
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Starr, Thomas L. "Gas transport model for chemical vapor infiltration." Journal of Materials Research 10, no. 9 (September 1995): 2360–66. http://dx.doi.org/10.1557/jmr.1995.2360.
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A node-bond percolation model is presented for the gas permeability and pore surface area of the coarse porosity in woven fiber structures during densification by chemical vapor infiltration (CVI). Model parameters include the number of nodes per unit volume and their spatial distribution, and the node and bond radii and their variability. These parameters relate directly to structural features of the weave. Some uncertainty exists in the proper partition of the porosity between “node” and “bond” and between intra-tow and inter-tow, although the total is constrained by the known fiber loading in the structure. Applied to cloth layup preforms the model gives good agreement with the limited number of available measurements.
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Lange, F. F. "Constrained network model for predicting densification behavior of composite powders." Journal of Materials Research 2, no. 1 (February 1987): 59–65. http://dx.doi.org/10.1557/jmr.1987.0059.
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Inert particles that do not contribute to the densification of a composite powder compact are visualized as located on network sites; the network is defined by the distribution of the particles in the powder matrix. Because the distances between neighboring network sites are not identical, the strain produced by the sintering powder between all inert particle pairs cannot be the same as that for the powder compact without the inert particles. The constrained network model is based on the hypothesis that the densification of the composite will be constrained by the network and will mimic that of the network. The shrinkage of the network, and thus the densification of the composite, is estimated with a periodic network. A distance between the minimum and maximum site pairs within the unit cell defines the distance between site pairs in the random network where the powder between the particles densifies in the same manner as that for the powder without the inert particle. When the particles form a continuous touching network, composite shrinkage and densification is nil. The chosen lattice must also conform to this condition. A simple relation was developed relating the densification behavior of the composite to that of the matrix without the inert particles and the parameter associated with the chosen lattice. By choosing the lattice formed by the tetrakaidecahedron unit cell (volume fraction of particles for a touching network = 0.277), remarkable agreement was achieved for the experimental data concerning the densification behavior of the ZnO/SiC composite system reported by De Jonghe et al. [L. C. De Jonghe, M. N. Rahaman, and C. H. Hsueh, Acta Metall. 34, 1467 (1986)]. The universal nature of this lattice for other composites is discussed with respect to site percolation theory. The application of this concept to powder compacts containing either whiskers or agglomerates is briefly discussed.
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Hvozd, Taras, Yurij V. Kalyuzhnyi, and Vojko Vlachy. "Aggregation, liquid–liquid phase separation, and percolation behaviour of a model antibody fluid constrained by hard-sphere obstacles." Soft Matter 16, no. 36 (2020): 8432–43. http://dx.doi.org/10.1039/d0sm01014f.
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Ketcheson, Scott J., and Jonathan S. Price. "Comparison of the hydrological role of two reclaimed slopes of different ages in the Athabasca oil sands region, Alberta, Canada." Canadian Geotechnical Journal 53, no. 9 (September 2016): 1533–46. http://dx.doi.org/10.1139/cgj-2015-0391.
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Establishing hydrological connectivity in reconstructed landscapes, and understanding how this connectivity evolves over time, is critical for the development of effective water management strategies after oil sands extraction. In the current study, the dominant controls on the soil water regimes and runoff generation mechanisms on two contrasting reclaimed slopes (2 and 6 years after reclamation) in the Athabasca oil sands region are investigated. The most recently reclaimed slope demonstrated a hydrologic regime with limited soil water storage due to a low surface infiltration capacity that constrained percolation of rainfall. Accordingly, this slope generated a substantial amount of surface runoff controlled primarily by precipitation intensity. Conversely, the older slope had a greater surface infiltration capacity, more dynamic soil water regime, and infrequent surface runoff. Topography controlled soil water distribution on the older slope more strongly than the newer slope due to more efficient water redistribution. This suggests that changes in the hydrophysical properties of reclamation materials following construction result in a shift in the hydrological role of reclaimed slopes at the watershed scale. Thus, over time, reclaimed slopes produce less overland flow and shift from water conveyors to water storage features in constructed watershed systems.
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BAHR, DAVID B., and W. TAD PFEFFER. "Crossover scaling phenomena for glaciers and ice caps." Journal of Glaciology 62, no. 232 (April 2016): 299–309. http://dx.doi.org/10.1017/jog.2016.6.
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ABSTRACTWhile the terms ‘glacier’ and ‘ice cap’ have distinct morphological meanings, no easily defined boundary or transition distinguishes one from the other. Despite this, the exponent of the power law function relating volume to surface area differs sharply for glaciers and ice caps, suggesting a fundamental distinction beyond a smoothly transitioning morphology. A standard percolation technique from statistical physics is used to show that valley glaciers are in fact differentiated from ice caps by an abrupt geometric transition. The crossover is a function of increasing glacier thickness, but it owes its existence more to the nature of the underlying bedrock topography than to specifics of glacier mechanics: the crossover is caused by a switch from directed flow that is constrained by surrounding bedrock topography to unconstrained radial flow of thicker ice that has subsumed the topography. The crossover phenomenon is nonlinear and rapid so that few if any glaciers will have geometries or dynamics that blend the two extremes. The exponents of scaling relationships change abruptly at the crossover from one regime to another; in particular, the volume/area scaling exponent will switch from γ = 1.375 for glaciers to γ = 1.25 for ice caps, with few, if any, ice bodies having exponents that fall between these values.
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Zhou, Tianqi, Chaodong Wu, Zhongkui Shi, Jialin Wang, Wen Zhu, Bo Yuan, and Disheng Yang. "Multi-Scale Quantitative Characterization of Pore Distribution Networks in Tight Sandstone by integrating FE-SEM, HPMI, and NMR with the Constrained Least Squares Algorithm." Energies 12, no. 18 (September 12, 2019): 3514. http://dx.doi.org/10.3390/en12183514.
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The goal of this study was to investigate the impacts of various sedimentary-diagenetic conditions on the macroscopic petrophysical parameters and microscopic pore structures of tight sandstones from the Lower Jurassic Badaowan Formation in the Southern Junggar Basin, China. Based on the traditional methods for establishing pore size distribution, including integrating the results of high-pressure mercury injection, nuclear magnetic resonance, and scanning electron microscopy, the constrained least squares algorithm was employed to automatically determine the porosity contributions of pore types with different origins. The results show that there are six genetic pore types: residual intergranular pores (RIPs), feldspar dissolution pores (FDPs), rock fragment dissolution pores (RFDPs), clay mineral intergranular pores (CIPs), intercrystalline pores of kaolinite (IPKs), and matrix pores (MPs). Four lithofacies were identified: the quartz cemented-dissolution facies (QCDF), carbonate cemented facies (CCF), authigenic clay mineral facies (ACMF), and matrix-caused tightly compacted facies (MCTF). Modified by limited dissolution, the QCDF with a high proportion of macropores (RIPs, FDPs, and RFDPs) exhibited a slightly higher porosity and considerably higher permeability than those of others. A large number of micropores (MPs, CIPs, and IPKs) in MCTF and ACMF led to slightly lower porosities but considerably lower permeabilities. Due to the tightly cemented carbonates in the CCF, its porosity reduced sharply, but the permeability of the CCF remained much higher those of the MCTF and ACMF. The results highlight that a high proportion of macropores with large radii and regular shapes provide more effective percolation paths than storage spaces. Nevertheless, micropores with small radii and complex pore structures have a limited contribution to flow capability. The fractal dimension analysis shows that a high proportion of MPs is the major reason for the heterogeneity in tight sandstones. The formation of larger macropores with smooth surfaces are more conductive for oil and gas accumulation.
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Chen, Siheng, and L. Mahadevan. "Rigidity percolation and geometric information in floppy origami." Proceedings of the National Academy of Sciences 116, no. 17 (April 5, 2019): 8119–24. http://dx.doi.org/10.1073/pnas.1820505116.
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Origami structures with a large number of excess folds are capable of storing distinguishable geometric states that are energetically equivalent. As the number of excess folds is reduced, the system has fewer equivalent states and can eventually become rigid. We quantify this transition from a floppy to a rigid state as a function of the presence of folding constraints in a classic origami tessellation, Miura-ori. We show that in a fully triangulated Miura-ori that is maximally floppy, adding constraints via the elimination of diagonal folds in the quads decreases the number of degrees of freedom in the system, first linearly and then nonlinearly. In the nonlinear regime, mechanical cooperativity sets in via a redundancy in the assignment of constraints, and the degrees of freedom depend on constraint density in a scale-invariant manner. A percolation transition in the redundancy in the constraints as a function of constraint density suggests how excess folds in an origami structure can be used to store geometric information in a scale-invariant way.
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Johnson, M. O., M. Gloor, M. J. Kirkby, and J. Lloyd. "Insights into biogeochemical cycling from a soil evolution model and long-term chronosequences." Biogeosciences Discussions 11, no. 4 (April 23, 2014): 5811–68. http://dx.doi.org/10.5194/bgd-11-5811-2014.
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Abstract. Despite the importance of soil processes for global biogeochemical cycles, our capability for predicting soil evolution over geological timescales is poorly constrained. We attempt to probe our understanding and predictive capability of this evolutionary process by developing a mechanistic soil evolution model, based on an existing model framework, and comparing the predictions with observations from soil chronosequences in Hawaii. Our soil evolution model includes the major processes of pedogenesis: mineral weathering, percolation of rainfall, leaching of solutes, surface erosion, bioturbation and vegetation interactions and can be applied to various bedrock compositions and climates. The specific properties the model simulates over timescales of tens to hundreds of thousand years are, soil depth, vertical profiles of elemental composition, soil solution pH and organic carbon distribution. We demonstrate with this model the significant role that vegetation plays in accelerating the rate of weathering and hence soil profile development. Comparisons with soils that have developed on Hawaiian basalts reveal a remarkably good agreement with Na, Ca and Mg profiles suggesting that the model captures well the key components of soil formation. Nevertheless, differences between modelled and observed K and P are substantial. The fact that these are important plant nutrients suggests that a process likely missing from our model is the active role of vegetation in selectively acquiring nutrients. This study therefore indirectly indicates the valuable role that vegetation can play in accelerating the weathering and thus release of these globally important nutrients into the biosphere.
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Rutishauser, Anja, Kirk M. Scanlan, Baptiste Vandecrux, Nanna B. Karlsson, Nicolas Jullien, Andreas P. Ahlstrøm, Robert S. Fausto, and Penelope How. "Mapping the vertical heterogeneity of Greenland's firn from 2011–2019 using airborne radar and laser altimetry." Cryosphere 18, no. 5 (May 17, 2024): 2455–72. http://dx.doi.org/10.5194/tc-18-2455-2024.
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Abstract. The firn layer on the Greenland Ice Sheet (GrIS) plays a crucial role in buffering surface meltwater runoff, which is constrained by the available firn pore space and impermeable ice layers that limit deeper meltwater percolation. Understanding these firn properties is essential for predicting current and future meltwater runoff and its contribution to global sea-level rise. While very-high-frequency (VHF) radars have been extensively used for surveying the GrIS, their lower bandwidth restricts direct firn stratigraphy extraction. In this study, we use concurrent VHF airborne radar and laser altimetry data collected as part of Operation IceBridge over the 2011–2019 period to investigate our hypothesis that vertical heterogeneities in firn (i.e. ice layers) cause vertical offsets in the radar surface reflection (dz). Our results, corroborated by modelling and firn core analyses, show that a dz larger than 1 m is strongly related to the vertical heterogeneity of a firn profile and effectively delineates between vertically homogeneous and vertically heterogeneous firn profiles over a depth range of ∼ 4 m. Temporal variations in dz align with climatic events and reveal an expansion of heterogeneous firn between 2011–2013 covering an area of ∼ 350 815 km2, followed by firn replenishment over the years 2014–2019 spanning an area of ∼ 667 725 km2. Our approach reveals the firn evolution of key regions on the Greenland Ice Sheet, providing valuable insights for detecting potential alterations in meltwater runoff patterns.
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Floriancic, Marius G., Scott T. Allen, and James W. Kirchner. "Young and new water fractions in soil and hillslope waters." Hydrology and Earth System Sciences 28, no. 18 (September 20, 2024): 4295–308. http://dx.doi.org/10.5194/hess-28-4295-2024.
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Abstract. The transport processes and corresponding timescales of water's infiltration into and percolation through the shallow subsurface are poorly understood. Here, we characterize the transport of recent precipitation through a forested hillslope using a continuous 3-year record of O and H stable isotopes in precipitation, streamflow, and soil waters from various depths. We found that the fractions of recent precipitation decreased with depth, both in waters extracted using suction-cup lysimeters and in waters extracted from bulk soil samples using cryogenic distillation. Fractions of recent precipitation found in soils and streamflow were much larger with wet antecedent conditions, showing that wet landscapes can transmit recent precipitation quicker than dry landscapes. Approximately 18 % of streamflow was younger than 2–3 months, 11 % was younger than 3 weeks, and 7 % was younger than 1 week; these new water fractions were similar to those seen in 20 to 80 cm deep soils. Mobile soil waters below 2 m depth contained much less recent precipitation (1.2 ± 0.4 % younger than 2 weeks) than streamflow did (12.3 ± 2.1%), indicating that they are not the dominant source of streamflow. Instead, streamflow must be generated from a mixture of deep subsurface waters, with very little isotopic seasonality and short-term variability, and shallow soil waters, with more pronounced isotopic seasonality and short-term variability. This study illustrates how flow, storage, and mixing processes linking precipitation to streamflow and evapotranspiration can be constrained by measuring isotopic variability across different hillslope positions, subsurface depths, and timescales.
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Johnson, M. O., M. Gloor, M. J. Kirkby, and J. Lloyd. "Insights into biogeochemical cycling from a soil evolution model and long-term chronosequences." Biogeosciences 11, no. 23 (December 10, 2014): 6873–94. http://dx.doi.org/10.5194/bg-11-6873-2014.
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Abstract. Despite the importance of soil processes for global biogeochemical cycles, our capability for predicting soil evolution over geological timescales is poorly constrained. We attempt to probe our understanding and predictive capability of this evolutionary process by developing a mechanistic soil evolution model, based on an existing model framework, and comparing the predictions with observations from soil chronosequences in Hawaii. Our soil evolution model includes the major processes of pedogenesis: mineral weathering, percolation of rainfall, leaching of solutes, surface erosion, bioturbation, the effects of vegetation in terms of organic matter input and nutrient cycling and can be applied to various bedrock compositions and climates. The specific properties the model simulates over timescales of tens to hundreds of thousand years are, soil depth, vertical profiles of elemental composition, soil solution pH and organic carbon distribution. We demonstrate with this model the significant role that vegetation plays in accelerating the rate of weathering and hence soil profile development. Comparisons with soils that have developed on Hawaiian basalts reveal a remarkably good agreement with Na, Ca and Mg profiles suggesting that the model captures well the key components of soil formation. Nevertheless, differences between modelled and observed K and P are substantial. The fact that these are important plant nutrients suggests that a process likely missing from our model is the active role of vegetation in selectively acquiring nutrients. This study therefore indirectly indicates the valuable role that vegetation can play in accelerating the weathering and thus release of these globally important nutrients into the biosphere.
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Chan, Kristian, Cyril Grima, Anja Rutishauser, Duncan A. Young, Riley Culberg, and Donald D. Blankenship. "Spatial characterization of near-surface structure and meltwater runoff conditions across the Devon Ice Cap from dual-frequency radar reflectivity." Cryosphere 17, no. 5 (May 5, 2023): 1839–52. http://dx.doi.org/10.5194/tc-17-1839-2023.
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Abstract. Melting and refreezing processes in the firn of the Devon Ice Cap control meltwater infiltration and runoff across the ice cap, but their full spatial extent and effect on near-surface structure is difficult to measure with surface-based traverses or existing satellite remote sensing. Here, we derive the coherent component of the near-surface return from airborne ice-penetrating radar surveys over the Devon Ice Cap, Canadian Arctic, to characterize firn containing centimeter- to meter-thick ice layers (i.e., ice slabs) formed from refrozen meltwater in firn. We assess the use of dual-frequency airborne ice-penetrating radar to characterize the spatial and vertical near-surface structure of the Devon Ice Cap by leveraging differences in range resolution of the radar systems. Comparison with reflectivities using a thin layer reflectivity model, informed by surface-based radar and firn core measurements, indicates that the coherent component is sensitive to the near-surface firn structure composed of quasi-specular ice and firn layers, limited by the bandwidth-constrained radar range resolution. Our results suggest that average ice slab thickness throughout the Devon Ice Cap percolation zone ranges from 4.2 to 5.6 m. This implies conditions that can enable lateral meltwater runoff and potentially contribute to the total surface runoff routed through supraglacial rivers down glacier. Together with the incoherent component of the surface return previously studied, our dual-frequency approach provides an alternative method for characterizing bulk firn properties, particularly where high-resolution radar data are not available.
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Turkeltaub, Tuvia, Daniel Kurtzman, and Ofer Dahan. "Real-time monitoring of nitrate transport in the deep vadose zone under a crop field – implications for groundwater protection." Hydrology and Earth System Sciences 20, no. 8 (August 2, 2016): 3099–108. http://dx.doi.org/10.5194/hess-20-3099-2016.
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Abstract. Nitrate is considered the most common non-point pollutant in groundwater. It is often attributed to agricultural management, when excess application of nitrogen fertilizer leaches below the root zone and is eventually transported as nitrate through the unsaturated zone to the water table. A lag time of years to decades between processes occurring in the root zone and their final imprint on groundwater quality prevents proper decision-making on land use and groundwater-resource management. This study implemented the vadose-zone monitoring system (VMS) under a commercial crop field. Data obtained by the VMS for 6 years allowed, for the first time known to us, a unique detailed tracking of water percolation and nitrate migration from the surface through the entire vadose zone to the water table at 18.5 m depth. A nitrate concentration time series, which varied with time and depth, revealed – in real time – a major pulse of nitrate mass propagating down through the vadose zone from the root zone toward the water table. Analysis of stable nitrate isotopes indicated that manure is the prevalent source of nitrate in the deep vadose zone and that nitrogen transformation processes have little effect on nitrate isotopic signature. The total nitrogen mass calculations emphasized the nitrate mass migration towards the water table. Furthermore, the simulated pore-water velocity through analytical solution of the convection–dispersion equation shows that nitrate migration time from land surface to groundwater is relatively rapid, approximately 5.9 years. Ultimately, agricultural land uses, which are constrained to high nitrogen application rates and coarse soil texture, are prone to inducing substantial nitrate leaching.
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Yan, Tingting, Shengbo Hu, and Jinrong Mo. "Path Formation Time in the Noise-Limited Fractionated Spacecraft Network with FDMA." International Journal of Aerospace Engineering 2018 (October 2, 2018): 1–12. http://dx.doi.org/10.1155/2018/9124132.
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Connectivity and path formation time are very important for the design and optimization in fractionated spacecraft network. Taking frequency division multiple access (FDMA) with subcarrier binary phase-shift keying (BPSK) modulation as an example, this paper focuses on the issues of constraint to orbital elements and path formation time for the noise-limited fractionated spacecraft network percolating. First, based on the proposed evolution of the dynamic topology graph in the fractionated spacecraft network, we prove the constraint condition of orbital elements for noise-limited fractionated spacecraft network percolating, and the definition of path formation time is provided and the mobility model is established. Next, we study the relationship between first docking time and spatial initial distribution and the relationship between first separating time and spatial initial distribution. These relationships provide an important basis for the orbit design in the fractionated spacecraft network. Finally, the numerical results show that the network topology for fractionated spacecraft is time-varying and dynamic. The path formation time and hop length scale linearly with path length within each orbital hyperperiod and change periodically. Besides, the time constant gradually tends to a stable value with path formation time increasing, that is, path length. These results powerfully support percolation theory further under the environment of the noise-limited fractionated spacecraft network.
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Vance, S. D., and M. Melwani Daswani. "Serpentinite and the search for life beyond Earth." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2165 (January 6, 2020): 20180421. http://dx.doi.org/10.1098/rsta.2018.0421.
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Hydrogen from serpentinization is a source of chemical energy for some life forms on Earth. It is a potential fuel for life in the subsurface of Mars and in the icy ocean worlds in the outer solar system. Serpentinization is also implicated in life’s origin. Planetary exploration offers a way to investigate such theories by characterizing and ultimately searching for life in geochemical settings that no longer exist on Earth. At present, much of the current context of serpentinization on other worlds relies on inference from modelling and studies on Earth. While there is evidence from orbital spectral imaging and martian meteorites that serpentinization has occurred on Mars, the extent and duration of that activity has not been constrained. Similarly, ongoing serpentinization might explain hydrogen found in the ocean of Saturn’s tiny moon Enceladus, but this raises questions about how long such activity has persisted. Titan’s hydrocarbon-rich atmosphere may derive from ancient or present-day serpentinization at the bottom of its ocean. In Europa, volcanism or serpentinization may provide hydrogen as a redox couple to oxygen generated at the moon’s surface. We assess the potential extent of serpentinization in the solar system’s wet and rocky worlds, assuming that microfracturing from thermal expansion anisotropy sets an upper limit on the percolation depth of surface water into the rocky interiors. In this bulk geophysical model, planetary cooling from radiogenic decay implies the infiltration of water to greater depths through time, continuing to the present. The serpentinization of this newly exposed rock is assessed as a significant source of global hydrogen. Comparing the computed hydrogen and surface-generated oxygen delivered to Europa’s ocean reveals redox fluxes similar to Earth’s. Planned robotic exploration missions to other worlds can aid in understanding the planetary context of serpentinization, testing the predictions herein. This article is part of a discussion meeting issue ‘Serpentinite in the Earth System’.
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Ray, P., and I. Bose. "Percolation under a spiralling constraint." Journal of Physics A: Mathematical and General 21, no. 2 (January 21, 1988): 555–59. http://dx.doi.org/10.1088/0305-4470/21/2/033.
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Li, Daqing, Guanliang Li, Kosmas Kosmidis, H. E. Stanley, Armin Bunde, and Shlomo Havlin. "Percolation of spatially constraint networks." EPL (Europhysics Letters) 93, no. 6 (March 1, 2011): 68004. http://dx.doi.org/10.1209/0295-5075/93/68004.
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Mistroni, Alberto, Felix Reichmann, Yuji Yamamoto, Marvin Hartwig Zöllner, Giovanni Capellini, Laura Diebel, Dominique Bougeard, and Marco Lisker. "Low Disorder and High Mobility 2DEG in Si/SiGe Fabricated in 200 mm BiCMOS Pilot line." ECS Meeting Abstracts MA2024-02, no. 32 (November 22, 2024): 2320. https://doi.org/10.1149/ma2024-02322320mtgabs.
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In 1997, Loss and DiVincenzo proposed that the fundamental unit of a quantum computer, the quantum bit, could be physically encoded as the spin of a single electron confined within a semiconductor quantum dot. Since then, silicon-based spin qubits have emerged as a leading platform for the advancement of large-scale quantum computation systems [1]. Silicon-based spin qubits present notable advantages, including extended coherence times and high fidelities, due to weak spin-orbit coupling and hyperfine interactions. Additionally, their compatibility with complementary metal-oxide-semiconductor (CMOS) technologies enables the efficient fabrication of numerous physical qubits on a single quantum chip. However, the production of complex quantum circuits, such as multi-qubit quantum processors, requires all quantum dot devices to be as uniform and consistent as possible. This is a crucial condition for practical control and manipulation of the qubits. Hence, comprehensive characterization of quantum devices and heterostructures quality becomes imperative for the scalability of spin qubit technology. Hall bar shaped FETs fabricated on the heterostructures provide a practical platform for extensive material stack characterization, their relatively large area facilitates efficient assessment of material uniformity. Most importantly, magneto-transport measurements of Hall bars allow for the extrapolation the figures of merit that indicate the quality of 2D electron gas (2DEG), that is directly related to quantum dot quality eventually fabricated on such heterostructure. [2,3]. High density mobility, constrained by scattering from within and around the quantum well [4,5], measures disorder in high-density regimes, while percolation density probes disorder in low-density regimes, which is where quantum dots operate. These are two of the main relevant metrics assessing device quality. This study investigates the properties of the 2DEG within a Si/SiGe heterostructure through magneto-transport measurements conducted at cryogenic temperatures. Our hall bar-shaped FET were fabricated entirely using the IHP 200 mm BiCMOS pilot line, demonstrating complete compatibility with industry standards. The heterostructure under examination comprises a 7 nm Si quantum well and a 35 nm Si0.66Ge0.34 barrier, grown via reduced pressure chemical vapor deposition (RP-CVD) on 200 mm Si wafers with an optimized buffer structure. A notable advancement compared to prior studies is the complete consumption of the epitaxial Si-cap of the heterostructure and the utilization of a low-temperature, high-density plasma SiO2. Our findings reveal that the heterostructure exhibits a remarkable low percolation threshold density of 6.3x1010 cm⁻², and a high maximum mobility μ of over 320000 cm²/Vs (figure 1), suggesting a low disorder and good scattering properties of the 2DEG. These measurement outcomes underscore the high quality achieved by IHP's optimized heterostructure compared to similar state-of-the-art studies [3]. In figure 1a, the fitting of the mobility power-law density dependence confirms that scattering from impurities inside or close the quantum well to be the main limiting mechanism of mobility in high density regimes (μ ∝ n0.3), while remote impurities scattering hinders mobility in the low density (μ ∝ n2.1) [4,5]. This, combined with low percolation threshold density indicates the high quality of the interface formed between the SiGe top barrier and the HDP Si oxide in our heterostructure. To assess additional metrics relevant to spin qubit operation, we also investigate our device at 300 mK and discuss the results. Finally, density measurements on our uncapped heterostructure confirm the absence of secondary channel formation at higher gate voltages, consistent with observations in the literature on standard heterostructures with a Si cap layer [6]. These results motivate further in-depth investigation of the properties of these heterostructures to characterize other important parameters relevant for spin qubit applications. This work is part of the joint project QUASAR „Halbleiter-Quantenprozessor mit shuttlingbasierter skalierbarer Architektur“ and is supported by the German Federal Ministry of Education and Research. [1] Philips, S.G.J., et al. Universal control of a six-qubit quantum processor in silicon. Nature 609, 919–924 (2022). [2] Davide Degli Esposti, et al Wafer-scale low-disorder 2DEG in 28Si/SiGe without an epitaxial Si cap. Appl. Phys. Lett. 2 May (2022). [3] Degli Esposti, et al. Low disorder and high valley splitting in silicon. npj Quantum Inf 10, 32 (2024). [4] Mi, X. et al, Magnetotransport studies of mobility limiting mechanisms in undoped Si/SiGe heterostructures, Phys. Rev. B 92, 035304 (2015). [5] D. Laroche, et al; Scattering mechanisms in shallow undoped Si/SiGe quantum wells. AIP Advances 1 October 2015; 5 (10): 107106. [6] Di Zhang et al 2023 J. Phys. D: Appl. Phys. 56 085302. Figure 1
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Lecacheur, Kilian, Olivier Fabbri, Francesca Piccoli, Pierre Lanari, Philippe Goncalves, and Henri Leclère. "High-pressure Ca metasomatism of metabasites (Mont Avic, Western Alps): insights into fluid–rock interaction during subduction." European Journal of Mineralogy 36, no. 5 (September 12, 2024): 767–95. http://dx.doi.org/10.5194/ejm-36-767-2024.
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Abstract. The study of rock chemistry is a milestone in understanding fluid–rock interactions and fluid migration in subduction zones. When combined with thermodynamic models, it can provide direct insight into fluid composition, metasomatic reactions, and pressure–temperature (P–T) conditions, as well as their role in rock deformation. Here, a shear zone – located in the Mont Avic area of the Zermatt-Saas zone (Western Alps) – is analyzed. This shear zone consists of several blocks of different lithotypes, including a Ca-rich metasomatite block embedded in a serpentinite mylonitic matrix, and structurally underlies a coherent eclogitic mafic unit. This work aims to estimate the pressure–temperature conditions of the Ca-rich metasomatism and the amount of fluid involved. The brecciation exhibits mosaic breccia textures with clasts comprising ∼80 vol % of garnet, together with omphacite, epidote, titanite, rutile, and apatite hosted in an omphacite matrix. Quantitative chemical mapping of the garnet reveals primary garnet cores with embayment and lobate edges with a chemical composition similar to unaltered reference eclogite garnet. These primary garnet cores are overlain by Ca-rich metasomatic garnet rims with oscillatory chemical zoning. The oscillatory chemical zoning, together with the morphology of the primary garnet cores, suggests repeated influxes of external Ca-rich fluid that destabilized the primary garnet cores and promoted the growth of Ca-rich rims. Mass balance calculations between precursor metabasite and Ca-metasomatite indicate multiple fluid sources involving dehydrated serpentinite, calcic metasediments, and metabasites with time-integrated fluid fluxes calculated between 11.5×103 and 5.5×104 mfluid3 mrock-2, consistent with channelized fluid flow in an open system. Thermodynamic modeling of garnet from unbrecciated and non-metasomatized metabasites – from the Savoney eclogitic mafic unit – indicates peak metamorphic conditions of 2.5±0.1 GPa and 535±40 °C, consistent with regional estimates. Pressure–temperature conditions of metasomatism were constrained using P–X and T–X phase modeling (where X represents changes in bulk CaO and Na2O composition) between 2.6–2.2 GPa and 570–500 °C, showing that Ca-rich fluid percolation occurred close to the metamorphic peak (i.e., prograde to the peak or early exhumation path).
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Huang, Rui-heng Ray. "Deriving Chinese alternative questions." Concentric. Studies in Linguistics 46, no. 2 (October 28, 2020): 206–39. http://dx.doi.org/10.1075/consl.00018.hua.
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Abstract This study proposes an approach which derives Chinese alternative questions by means of feature percolation and LF movement. This approach is argued to fare better than a movement approach as proposed by C.-T. Huang (1998) and a non-movement binding approach as proposed by R.-H. Huang (2010) in that it may successfully explain why Chinese alternative questions are only sensitive to the wh-island constraint, but not to other types of island constraints. The LF movement analysis may receive empirical support from the observed fact that Chinese alternative questions exhibit focus-intervention effects, generally assumed to be induced by LF movement.
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Phillips, J. C., and M. F. Thorpe. "Constraint theory, vector percolation and glass formation." Solid State Communications 53, no. 8 (February 1985): 699–702. http://dx.doi.org/10.1016/0038-1098(85)90381-3.
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Yakunina, T. V., and V. N. Udodov. "Correlation length critical exponent as a function of the percolation radius for one-dimensional chains in bond problems." Journal of Physics: Conference Series 2094, no. 2 (November 1, 2021): 022038. http://dx.doi.org/10.1088/1742-6596/2094/2/022038.
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Abstract A one-dimensional lattice percolation model is constructed for the problem of constraints flowing along non-nearest neighbors. In this work, we calculated the critical exponent of the correlation length in the one-dimensional bond problem for a percolation radius of up to 6. In the calculations, we used a method without constructing a covering lattice or an adjacency matrix (to find the percolation threshold). The values of the critical exponent of the correlation length were obtained in the one-dimensional bond problem depending on the size of the system and at different percolation radii. Based on original algorithms that operate on a computer faster than standard ones (associated with the construction of a covering lattice), these results are obtained with corresponding errors.
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Basch, Valentin, Elisabetta Rampone, Laura Crispini, Carlotta Ferrando, Benoit Ildefonse, and Marguerite Godard. "Multi-stage Reactive Formation of Troctolites in Slow-spreading Oceanic Lithosphere (Erro–Tobbio, Italy): a Combined Field and Petrochemical Study." Journal of Petrology 60, no. 5 (March 29, 2019): 873–906. http://dx.doi.org/10.1093/petrology/egz019.
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Abstract Many recent studies have investigated the replacive formation of troctolites from mantle protoliths and the compositional evolution of the percolating melt during melt–rock interaction processes. However, strong structural and geochemical constraints for a replacive origin have not yet been established. The Erro–Tobbio impregnated mantle peridotites are primarily associated with a hectometre-size troctolitic body and crosscutting gabbroic dykes, providing a good field control on melt–rock interaction processes and subsequent magmatic intrusions. The troctolitic body exhibits high inner complexity, with a host troctolite (Troctolite A) crosscut by a second generation of troctolitic metre-size pseudo-tabular bodies (Troctolite B). The host Troctolite A is characterized by two different textural types of olivine, corroded deformed millimetre- to centimetre-size olivine and fine-grained rounded undeformed olivine, both embedded in interstitial to poikilitic plagioclase and clinopyroxene. Troctolite A shows melt–rock reaction microstructures indicative of replacive formation after percolation and impregnation of mantle dunites by a reactive melt. The evolution of the texture and crystallographic preferred orientation (CPO) of olivine are correlated and depend on the melt/rock ratio involved in the impregnation process. A low melt/rock ratio allows the preservation of the protolith structure, whereas a high melt/rock ratio leads to the disaggregation of the pre-existing matrix. The mineral compositions in Troctolite A define reactive trends, indicative of the buffering of the melt composition by assimilation of olivine during impregnation. The magmatic Troctolite B bodies are intruded within the pre-existing Troctolite A and are characterized by extreme textural variations of olivine, from decimetre-size dendritic to fine-grained euhedral crystals embedded in poikilitic plagioclase. This textural variability is the result of olivine assimilation during melt–rock reaction and the correlated increase in the degree of undercooling of the percolating melt. In the late gabbroic intrusions, mineral compositions are consistent with the fractional crystallization of melts modified after the reactive crystallization of Troctolites A and B. The Erro–Tobbio troctolitic body has a multi-stage origin, marked by the transition from reactive to fractional crystallization and diffuse to focused melt percolation and intrusion, related to progressive exhumation. During the formation of the troctolitic body, the melt composition was modified and controlled by assimilation and concomitant crystallization reactions occurring at low melt supply. Similar processes have been described in ultraslow-spreading oceanic settings characterized by scarce magmatic activity.
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Yang, Yi, and Canlong Wu. "Modelling for the electrical conductivity of graphite-modified asphalt concrete based on micromechanics." Journal of the Croatian Association of Civil Engineers 76, no. 09 (October 2024): 803–12. http://dx.doi.org/10.14256/jce.3753.2023.
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This paper proposes a novel micromechanics theory to model the electrical conductivity of graphite-modified asphalt concrete. The constraint range of electrical conductivity was derived according to the Hashin–Shtrikman (H–S) method. Based on the self-consistent (SC) method and percolation theory, A modified self-consistent (MSC) method was used to develop an electrical conductivity model based on the SC method and percolation theory. The results predicted by the MSC model were compared with the test data by adjusting the aspect ratio and percolation exponent. We highlight this new theory and its application to graphite-modified asphalt concrete, and demonstrate that the predicted values are in close agreement with the test data.
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SANTRA, S. B. "STUDY OF FINITE SIZE EFFECTS ON DIRECTED SPIRAL PERCOLATION." International Journal of Modern Physics B 17, no. 29 (November 20, 2003): 5555–64. http://dx.doi.org/10.1142/s0217979203023252.
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Percolation under both directional and rotational constraints is studied numerically on the square lattice of different finite sizes L. The critical percolation threshold pc≈0.655 of the infinite network is determined by extrapolating the finite size data. The fractal dimension df of the infinite percolation clusters is found df≈1.72 from the finite size scaling, S∞~Ldf where S∞ is the mass of the infinite cluster. The critical exponents are estimated as a function of the system size L. It is seen that the results of smaller systems converge to that of the large systems. The results are then extrapolated to the infinite network. The extrapolated results for the infinite network are compared with Monte Carlo results on a single large lattice. A good agreement is found.
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Prosandeev, S. A., V. S. Vikhnin, and S. Kapphan. "Percolation with constraints in the highly polarizable oxide KTaO." European Physical Journal B 15, no. 3 (2000): 469. http://dx.doi.org/10.1007/s100510051148.
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SINHA, SANTANU, and S. B. SANTRA. "DIRECTED SPIRAL PERCOLATION HULL ON THE SQUARE AND TRIANGULAR LATTICES." International Journal of Modern Physics C 16, no. 08 (August 2005): 1251–68. http://dx.doi.org/10.1142/s0129183105007868.
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Critical properties of hulls of directed spiral percolation clusters are studied on the square and triangular lattices in two dimensions (2D). The hull fractal dimension (dH) and some of the critical exponents associated with different moments of the hull size distribution function of the anisotropic DSP clusters are reported here. The values of dH and other critical exponents are found the same within error bars on both the lattices. The universality of the hull's critical exponents then holds true between the square and triangular lattices in 2D unlike the cluster's critical exponents which exhibit a breakdown of universality. The hull fractal dimension (dH ≈ 1.46) is also found close to 4/3 and away from 7/4, that of ordinary percolation cluster hull. A new conjecture is proposed for dH in terms of two connectivity length exponents (ν‖ and ν⊥) of the anisotropic clusters generated here. The values of dH and other critical exponents obtained here are very close to that of the spiral percolation cluster hull. The hull properties of the DSP clusters are then mostly determined by the rotational constraint and almost independent of the directional constraint present in the model.
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Santra, S. B., and I. Bose. "Percolation under rotational constraint: a finite-size scaling study." Journal of Physics A: Mathematical and General 24, no. 10 (May 21, 1991): 2367–75. http://dx.doi.org/10.1088/0305-4470/24/10/021.
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Jasna, C. K., V. Krishnadev, and V. Sasidevan. "Percolation in semicontinuum geometries." Journal of Statistical Mechanics: Theory and Experiment 2025, no. 1 (January 1, 2025): 013201. https://doi.org/10.1088/1742-5468/ad9c4c.
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Abstract We study percolation problems of overlapping objects where the underlying geometry is such that in D − dimensions, a subset of the directions has a lattice structure, while the remaining directions have a continuum structure. The resulting semicontinuum problem describes the percolation of overlapping shapes in parallel layers or lanes with positional constraints for the placement of the objects along the discrete directions. Several semicontinuum percolation systems are analyzed like hypercuboids with a particular focus on 2D and 3D cases, disks, and parallelograms. Adapting the excluded volume arguments to the semicontinuum setting, we show that for the semicontinuum problem of hypercuboids, for fixed side-lengths of the hypercuboids along the directions in which a lattice structure is maintained, the percolation threshold is always independent of the side-lengths along the continuum directions. The result holds even when there is a distribution for the side-lengths along the continuum directions. Trends in the variation of the thresholds, as we vary the linear measure of the shapes along the continuum directions, are obtained for other semicontinuum models like disks and parallelograms in 2D. The results are compared with those of corresponding continuum and lattice models. For the 2D and 3D models considered, using Monte Carlo simulations, we verify the excluded volume predictions for the trends and numerical values of the percolation thresholds. Very good agreement is seen between the predicted numerical values and the simulation results. The semicontinuum setting also allows us to establish a connection between the percolation problem of overlapping shapes in 2D continuum and the triangular lattice. We also verify that the isotropy of the threshold for anisotropic shapes and standard percolation universality class is maintained in the semicontinuum setting.
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Liu, Tongjing, Liwu Jiang, Jinju Liu, Juan Ni, Xinju Liu, and Pengxiang Diwu. "A Novel Workflow for Early Time Transient Pressure Data Interpretation in Tight Oil Reservoirs with Physical Constraints." Energies 16, no. 1 (December 26, 2022): 245. http://dx.doi.org/10.3390/en16010245.
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In this work, a novel workflow has been proposed, validated and applied to interpret the early time transient pressure data in tight oil reservoirs with physical constraints. More specifically, the theoretical model was developed to obtain the transient pressure response for a vertical well in tight oil reservoirs with consideration of pseudo threshold pressure gradient (TPG). Then, a physical constraint between the skin factor and formation permeability has been proposed based on the physical meaning of percolation theory. This physical constraint can be applied to determine the lower limit of the skin factor which can reduce the uncertainty during the interpretation process. It is found that the influence range of the skin factor and permeability may partially overlap during the interpretation process without consideration of physical constraints. Additionally, it is found that the equivalent wellbore radius is more reasonable by considering the skin factor constraints. Furthermore, the short-time asymptotic method was applied to separate the small pressure signal at the early time period and a novel type curve was proposed to better analyze the early time pressure response. Subsequently, sensitivity analyses were conducted to investigate the influence of different parameters on the new type curves. It is found that the new type curves are more dispersed and sensitive to the parameters at the early time period which can be beneficial for the early time transient pressure analysis in a tight formation. The proposed method has been validated and then extended to a field application, demonstrating that the transient pressure for a vertical well in a tight formation can be analyzed in a reasonable and accurate manner with only early time transient pressure data.
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Prosandeev, S. A., V. S. Vikhnin, and S. Kapphan. "Percolation with constraints in the highly polarizable oxide KTaO :Li." European Physical Journal B 15, no. 3 (May 2000): 469–74. http://dx.doi.org/10.1007/pl00011047.
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Shannon, M. C., and C. B. Agee. "High pressure constraints on percolative core formation." Geophysical Research Letters 23, no. 20 (October 1, 1996): 2717–20. http://dx.doi.org/10.1029/96gl02817.
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Le Roux, Véronique, and Yan Liang. "Ophiolitic Pyroxenites Record Boninite Percolation in Subduction Zone Mantle." Minerals 9, no. 9 (September 18, 2019): 565. http://dx.doi.org/10.3390/min9090565.
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The peridotite section of supra-subduction zone ophiolites is often crosscut by pyroxenite veins, reflecting the variety of melts that percolate through the mantle wedge, react, and eventually crystallize in the shallow lithospheric mantle. Understanding the nature of parental melts and the timing of formation of these pyroxenites provides unique constraints on melt infiltration processes that may occur in active subduction zones. This study deciphers the processes of orthopyroxenite and clinopyroxenite formation in the Josephine ophiolite (USA), using new trace and major element analyses of pyroxenite minerals, closure temperatures, elemental profiles, diffusion modeling, and equilibrium melt calculations. We show that multiple melt percolation events are required to explain the variable chemistry of peridotite-hosted pyroxenite veins, consistent with previous observations in the xenolith record. We argue that the Josephine ophiolite evolved in conditions intermediate between back-arc and sub-arc. Clinopyroxenites formed at an early stage of ophiolite formation from percolation of high-Ca boninites. Several million years later, and shortly before exhumation, orthopyroxenites formed through remelting of the Josephine harzburgites through percolation of ultra-depleted low-Ca boninites. Thus, we support the hypothesis that multiple types of boninites can be created at different stages of arc formation and that ophiolitic pyroxenites uniquely record the timing of boninite percolation in subduction zone mantle.
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Thorpe, M. F., and R. B. Stinchcombe. "Two exactly soluble models of rigidity percolation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2008 (February 13, 2014): 20120038. http://dx.doi.org/10.1098/rsta.2012.0038.
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We summarize results for two exactly soluble classes of bond-diluted models for rigidity percolation, which can serve as a benchmark for numerical and approximate methods. For bond dilution problems involving rigidity, the number of floppy modes F plays the role of a free energy. Both models involve pathological lattices with two-dimensional vector displacements. The first model involves hierarchical lattices where renormalization group calculations can be used to give exact solutions. Algebraic scaling transformations produce a transition of the second order, with an unstable critical point and associated scaling laws at a mean coordination 〈 r 〉=4.41, which is above the ‘mean field’ value 〈 r 〉=4 predicted by Maxwell constraint counting. The order parameter exponent associated with the spanning rigid cluster geometry is β =0.0775 and that associated with the divergence of the correlation length and the anomalous lattice dimension d is dν =3.533. The second model involves Bethe lattices where the rigidity transition is massively first order by a mean coordination 〈 r 〉=3.94 slightly below that predicted by Maxwell constraint counting. We show how a Maxwell equal area construction can be used to locate the first-order transition and how this result agrees with simulation results on larger random-bond lattices using the pebble game algorithm.
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Aleshkin, A. S. "Stochastic Models of Traffic Management." International Journal of Open Information Technologies 12, no. 4 (April 1, 2024): 15–22. http://dx.doi.org/10.25559/injoit.2307-8162.12.202404.15-22.
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This article discusses the problem of blocking nodes in road networks and percolation thresholds for the transport infrastructure of a modern metropolis. For metropolitan networks, the values of percolation thresholds are calculated and displayed, considering the different density of connections between network nodes. Further, it is shown that the dependence of the values of the percolation thresholds on the network’s density can be described by functional dependencies with a high degree of correlation. The obtained results can be used to assess the reliability of transport infrastructure and to check the increase in the capacity of selected sections of the road network. Further, the article discusses obtaining a description of road infrastructure from open sources (obtaining data from OpenStreetMap using the SUMO - Simulation of Urban MObility package), after which it is possible to build a graph of the road network and determine its percolation properties. For the constructed nodes of the graph described a model of the stochastic dynamics of blocking a single road lane in the transport network. The threshold value L of number of cars that can be placed in the lane (based on the length of the road lane) is used as constraints and the incoming and outgoing flows of cars are also determined as income parameters of a model. The constructed model allows us to obtain the predicted blocking time of a road network line, for a given probability of such blocking, where the probability of blocking a single road network line is taken from the percolation properties of this network discussed earlier. The resulting blocking times of road network nodes make it possible to build an algorithm for controlling traffic light regulation.
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Miller, Brian J. "A percolation theory analysis of continuous functional paths in protein sequence space affirms previous insights on the optimization of proteins for adaptability." PLOS ONE 19, no. 12 (December 5, 2024): e0314929. https://doi.org/10.1371/journal.pone.0314929.
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A key question in protein evolution and protein engineering is the prevalence of evolutionary paths between distinct proteins. An evolutionary path corresponds to a continuous path of functional sequences in sequence space leading from one protein to another. Natural selection could direct a mutating coding region in DNA along a continuous functional path (CFP), so a new protein could arise far more easily than if a coding region were randomly mutating without any constraints. The distribution and length of CFPs undergird theories on the origin of natural proteins and strategies for engineering artificial proteins. This study examined the distribution of long CFPs within the framework of percolation theory, which addresses the proportion of randomly filled sites in a lattice above which long continuous paths of neighboring filled sites become common (aka percolation threshold). It also used a simulation to demonstrate that the percolation threshold in protein sequence space approximates the reciprocal of the average number of protein variants that could result from a single mutation. For diverse proteins, the ratio was calculated between the percolation threshold and the proportion of sequences reported to perform a protein’s function, relative to the total number of sequences of that protein’s length. This ratio represents a measure of the biasing in the distribution of functional sequences required for evolutionary paths to possibly exist, so it provides a means to quantify the specificity in protein sequence and structure required to allow for a protein to develop new catalytic functions. The consistently high ratio demonstrates that CFPs can only connect distinct proteins if the biasing in the distribution of functional sequences in sequence space is often extremely large. Regions in sequence space are identified where the biasing is sufficient to allow for extensive CFPs. The calculated levels of required biasing and the identified regions of high biasing reinforce the conclusion of previous studies that some proteins are highly optimized, so mutations can enable or enhance catalytic functions while maintaining the protein’s structure. The conclusions of this study also challenge the results of a previous application of percolation theory to sequence space that did not properly incorporate the percolation threshold. Steps are outlined for integrating the percolation threshold and the biasing measure into studies of protein sequence space.
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Fuller, L., A. Baker, I. J. Fairchild, C. Spötl, A. Marca-Bell, P. Rowe, and P. F. Dennis. "Isotope hydrology of dripwaters in a Scottish cave and implications for stalagmite palaeoclimate research." Hydrology and Earth System Sciences Discussions 5, no. 2 (March 3, 2008): 547–77. http://dx.doi.org/10.5194/hessd-5-547-2008.
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Abstract. Dripwater hydrology and hydrogeochemistry is particularly useful to constrain the meaning of speleothem palaeoclimate archives, for example using δ18O signatures. Here, we calibrate the relationship between δ18O in precipitation, percolation waters and contemporary calcite deposits, at Tartair cave, Sutherland, NW Scotland, an Atlantic site sensitive to regional changes both of temperature and precipitation. Monthly precipitation displayed a 7.1‰ range in δ18O, a negative linear relationship with rainfall amount, and no correlation with temperature. Autogenically-derived cave percolation waters show little variation in δ18O during the same period and their annual weighted mean is the same as that of the local precipitation. This evidence together with hydrological data and electroconductivity values indicates that percolation waters are well mixed and dominated by stored water. Calculated values of δ18O of calcite deposited in this cave environment indicate that the cave deposits are forming close to isotopic equilibrium and kinetic effects are negligible. Comparison of a high-resolution δ18O stalagmite record with the instrumental record of climate indicates that isotopically heavy values are reflective of relatively cold, dry conditions (and vice-versa for warm, wet condition) and hence that stalagmite oxygen isotopes provide an appropriate means of investigating the palaeoclimate in this location.