Matrix Flow Research Articles

Temperature effect on the mechanical properties and damage mechanisms of a glass/thermoplastic laminate

The aim of this study is to evaluate the temperature effect on the mechanical properties and damage mechanisms of a Glass/Elium 150 laminate composite. Quasi-static indentation tests are carried out at different temperatures to highlight the temperature dependency of different parameters of the samples (stiffness, maximum load, stored elastic energy, and applied energy). The different damage mechanisms involved in the collapse of the composite are observed at the macro-, meso-, and micro-scopic scales using optical and scanning electron microscopy. The influence of temperature on these damage mechanisms is discussed based on post-mortem observations. It has been highlighted that the kind and the severity of damage are strongly temperature dependent. Below 20℃, fiber breakage, strand failure, intra- and inter-laminar crack propagation are identified. At 60℃, plastic flow of the polymer matrix is observed, which modifies micro-crack propagation at the fiber/matrix interface. Above 90℃, only intra-laminar micro-cracking occurs. To conclude, based on all these observations the kinetics of damage appearance are discussed.

A novel framework to study the effect of tree architectural traits on stemflow yield and its consequences for soil-water dynamics

A novel experimental approach and numerical framework are proposed to study the effect of tree architectural traits on stemflow yield and its effects on soil-water dynamics. The framework includes a data mining workflow employing information from two experimental steps: (i) evaluation of the effect of tree aboveground architecture on stemflow yield and (ii) quantification of specific parameters for soil-water dynamics with and without stemflow. We studied double-funnelling (stemflow and root-induced preferential flow) under three sycamore (Acer pseudoplatanus L.) trees growing on a slope in Scotland during the summer season and measured architectural traits. Stemflow yield ranged from 1.3 to 3.8% of the incident rainfall, with funnelling ratios of between 2.2 ± 2.1 and 5.2 ± 3.9. Double-funnelling to a depth of up to 400 mm beneath the soil surface occurred as matrix flow and was significantly and positively correlated with the vertical root distribution. Soil-water dynamics were distinctly different with and without stemflow. Our framework revealed that the number of tree branches, their insertion angle, leaf number, and stem basal diameter influenced stemflow yield within rainfall thresholds of 1.1 and 3.5 mm d-1. The framework also showed that stemflow yield had a negative impact on soil matric suction, while air temperature was the most influential covariate affecting soil-water dynamics, likely due to its strong correlation to evapotranspiration during the summer season. In spite of the study limitations, such as small sample size and differences between individuals, we show that the proposed framework and experimental approach can contribute to our knowledge of how stemflow generated aboveground triggers major responses in soil-water dynamics belowground.

The simulation of transport processes in cementitious materials with embedded healing systems

SummaryA new model for simulating the transport of healing agents in self‐healing (SH) cementitious materials is presented. The model is applicable to autonomic SH material systems in which embedded channels, or vascular networks, are used to supply healing agents to damaged zones. The essential numerical components of the model are a crack flow model, based on the Navier‐Stokes equations, which is coupled to the mass balance equation for simulating unsaturated matrix flow. The driving forces for the crack flow are the capillary meniscus force and the force derived from an external (or internal) pressure applied to the liquid healing agent. The crack flow model component applies to non‐uniform cracks and allows for the dynamic variation of the meniscus contact angle, as well as accounting for inertial terms. Particular attention is paid to the effects of curing on the flow characteristics. In this regard, a kinetic reaction model is presented for simulating the curing of the healing agent and a set of relationships established for representing the variation of rheological properties with the degree of cure. Data obtained in a linked experimental programme of work are employed to justify the choice and form of the constitutive relationships, as well as to calibrate the model's evolution functions. Finally, a series of validation examples are presented that include the analysis of a series of concrete beam specimens with an embedded vascular network. These examples demonstrate the ability of the model to capture the transport behaviour of this type of SH cementitious material system.

Possible pore structure deformation effects on the shale gas enrichment: An example from the Lower Cambrian shales of the Eastern Upper Yangtze Platform, South China

Shale gas reservoir performance and canister desorption experiments of the Lower Cambrian organic-rich shales in the eastern Upper Yangtze Platform reveal a significant difference in shale gas content between the Dabashan arc-like fold-thrust belt in northeastern Chongqing (Deformed Zone) and the slightly folded area in southeastern Chong (Non-deformed Zone). Integrated pore characterization methods including scanning electron microscopy (SEM), low-temperature N2 and CO2 adsorption, and mercury injection capillary pressure (MICP) analyses were comparatively conducted in both areas in order to examine shale gas reservoir pore size variations and thus the possible microscopic pore structure controls on shale gas enrichment.The Lower Cambrian shales in both Deformed Zone (DZ) and Non-deformed Zone (NDZ) were deposited in the deep-water shelf and show similar organic matter richness and thermal maturity. The majority of organic matter (OM)-hosted pores in DZ samples are in nanoscale size range with the dominance of micro-fractures within the OM or at the interface of OM and minerals. In contrast, OM-hosted meso-(2–50 nm) to macropores (>50 nm) are the dominant pore types in the NDZ samples. OM-hosted micropores (<2 nm) are abundant in both zones. Helium ion microscopy observations further confirm the presence of OM-hosted micropores in the studied samples. Mineral-hosted pores in carbonate minerals are abundant in both zones, while dissolution rims around carbonate minerals are more abundant in NDZ samples.The Dabashan arc-like fold-thrust belt took place by the end of the Late Triassic, while the Lower Cambrian shales have reached thermal maturity peak. OM-hosted meso-(2–50 nm) to macropores (>50 nm) in DZ samples are most probably collapsed during structural deformation related to tectonic compression, while micropores due to their smaller size survived the tectonic stress. The OM-hosted micropores are the main storage space for adsorbed gas in the DZ area. The dominance of micro-pores in DZ and lack of connection between those pores and matrix pores led to higher gas content in DZ samples. On the contrary, the well-connected OM-hosted pore network in NDZ allows easier gas flow in the rock matrix that eventually led to significant gas leakage during uplift and exhumation and lower gas content in this zone. The results of this study suggest that structural deformation can potentially change the pore structure of shales and thus shale gas content which has major significance for shale gas exploration and development in south China where had experienced complex tectonic movements.

Volcanic glass leaching and the groundwater geochemistry on the semi-arid Atlantic island of Porto Santo

The groundwater chemistry of the semi-arid volcanic island of Porto Santo, part of the Madeira archipelago, Atlantic Ocean, was investigated. Generally, the groundwater was brackish, containing 2–10 mol % seawater. Groundwater with up to 20 mM alkalinity and a Na enrichment of up to 30 mM, as compared to the Na concentration predicted by the seawater Na/Cl ratio, was found in the main aquifer. Also notable are the high concentrations of F (up to 0.3 mM), B (up to 0.55 mM), As (up to 0.35 μM), all in excess of WHO recommendations, as well as up to 6 μM V. Geochemical modeling, using the PHREEQC code, was used to explore different scenarios that could explain the genesis of the observed bulk groundwater chemistry. First, a model for aquifer freshening with the displacement of resident seawater from the aquifer by infiltrating freshwater, was tested. This scenario leads to the development of NaHCO3 waters as observed in many coastal aquifers. However, the measured alkalinity concentration in the groundwater was far higher than the concentration predicted by the freshening model. In addition, the behavior of modelled pH and PCO2 were at variance with their distributions in the field data. The second model explored the possible effect of volcanic glass leaching on the groundwater chemistry. Using insight derived from studies of volcanic glass surface alteration as well as experimental work on water-volcanic glass interactions, a geochemical model was developed in which the exchange of H+ for Na+ on the volcanic glass surface is the main mechanism but the exchange of other cations on the volcanic glass surface is also included. The uptake of H+ by the glass surface causes the dissociation of carbonic acid, generating bicarbonate. This model is consistent with the local geology and the field data. It requires, however, volcanic glass leaching to occur in the unsaturated zone where there is an unlimited supply of CO2. The exchange reaction of H+ for Na+ is confined to the surface layer of volcanic glass as otherwise the process becomes limited by slow solid state diffusion of H+ into the glass and Na+ out of the glass. Therefore, volcanic ash deposits, with their high volcanic glass surface areas and matrix flow, are the aquifers where this type of high NaHCO3 waters can be expected, rather than in basalts, which predominantly feature fracture flow. The trace components F, B, As and V are believed to originate from hyaloclastites, consisting of predominantly (90%) of trachy-rhyolite volcanic glass. Although stratigraphically older than the main calcarenite aquifer, topographically they are often located at higher altitudes, above the phreatic level and located along the main recharge flow path. In addition, the semi-arid climate conditions provide a long groundwater residence time for the reactions as well as limited aquifer flushing.

Characterization of preferential flow in soils near Zarqa river (Jordan) using in situ tension infiltrometer measurements

BackgroundThe Zarqa River (ZR) is located in the northern part of Jordan and supplies King Talal Dam (KTD). The streamflow that discharges into KTD is composed of treated wastewater from the Khirbat Es-Samra water treatment plant (KTP) and runoff generated during the winter season. Thus, during the summer, the streamflow of the ZR is dominated by effluent from the KTP. Due to the severe scarcity of water in Jordan, a portion of the streamflow is utilized for irrigated agriculture in the ZR valley, located between the KTP and KTD. The groundwater in the vicinity of the ZR is vulnerable to contamination—a risk that may be exacerbated by the potential occurrence of preferential flow (PF). Therefore, the PF in the soils near the ZR should be carefully considered.MethodsThe macropore flux fraction (Qmacro) and macroscopic capillary length (λc) were determined from in situ measurements using a tension infiltrometer equipped with an infiltration disc with a diameter of 20 cm. The macropore was defined as the pore size that drains at a tension of less than —-3— cm. The λc less than 80 mm was considered to be an indication of PF. The measurements were taken at 69 sites along the ZR between the KTP and KTD. At each measurement site, the soil organic matter content (OM) and soil texture were determined using a composite soil sample obtained by excavating the soil beneath the infiltration disc to a depth of 10 cm.ResultsThe data was split into two groups: the matrix flow group (MF), which includes data associated with λc > 80 mm, and the PF group, which includes data associated with λc < 80 mm. The Qmacro values of 0.67 and 0.57, respectively, for PF and MF were significantly different at p < 0.01 (t-test). The flow rates at h=0 were generally well associated with λc, as attested to by a significant difference between the averages of PF (57.8 mm/hr) and MF (21.0 mm/hr) at p < 0.01 (t-test). The OM was positively associated with PF. This was statistically confirmed by a t-test at p < 0.01. The average sand and clay contents of PF and MF were not statistically different. Analysis of the ratio of Soil Organic Carbon (SOC) to clay showed that the average SOC/clay of the PF (14%) was larger than that of the MF (13.3%). After the exclusion of soils with clay content less than 8%, the differences between the SOC/clay averages of PF (9.8%) and MF (7.5%) were significant at p < 0.05, as shown by a WM-test.ConclusionThe OM was positively associated with PF. Soil texture—and clay content in particular—influenced the λcvalues. However, the association of clay content with PF was not statistically significant. Consideration of the SOC/clay ratio showed that the tendency toward PF increases as the complexation of the clay content increases. This was most obvious in soils with a clay content of greater than 8% and SOC/clay of approximately 10%. The OM either influences or is inter-correlated with the processes responsible for the formation of macropores.

Anomalously enhanced toughness of poly (lactic acid) nanocomposites by core-shell particles with high thickness soft shell

The anomalous improvement in ductility and toughness of biodegradable poly (lactic acid) (PLA) was achieved by incorporating the silica-g-poly(caprolactone-co-lactide) (SiO2-PCLLA) core-shell nanoparticle with high thickness rubber shell. The variation of mechanical properties and toughening mechanism of nanocomposites with rubber shell thickness were investigated via tensile tests and surface morphology observation, X-ray scattering (SAXS) and diffraction (WAXD). The experimental results showed that the core-shell nanoparticle with high thickness rubber shell of 25 nm extremely remarkably improved the ductility and toughness of nanocomposite, about 34 times higher than those of neat PLA, particularly nearly without reducing its strength. This considerable increment of toughness is attributed to that the cavitation occurred in thick rubber shell can induce the intense plastic flow of matrix, forming the fibrillated structure like ‘bamboo joint’. In addition, it was found that the toughening of PLA is not only related to the rubber shell thickness, but also to the added nanofiller content.

Pressure and rate transient modeling of multi fractured horizontal wells in shale gas condensate reservoirs

Gas condensate production using technology of multi-stage hydraulically fracturing in shale gas condensate reservoirs' horizontal wells is a new topic of unconventional resources studies. Thus, shale gas condensate as a new source of energy can be considered as an important issue for development and further studies. In this work, a semi-analytical solution of gas and oil two-phase flow is presented for pressure transient analysis (PTA) and rate transient analysis (RTA) of a shale gas condensate reservoir's production data. Fluid flow assumption here is flow in a pseudo triple-porosity porous media, which are matrix, natural fractures and adsorbed gas. Adsorbed gas is a form of gas in porous rock pores like free gas, but unlike that, it is not free to flow initially and requires pressure drop to desorb from micro- (or even nano-) pores of rock to flow in matrix and then in fracture. In this study, desorption of the adsorbed gas is modeled with Langmuir isotherm theory. Based on the results, type curves of two-phase pseudo-pressure and also two-phase rate decline are plotted. These type curves are analyzed with different sensitivities to Langmuir volume, interporosity flow parameters, horizontal well length, number of multiple-fractures and Corey model relative permeability exponents. Τhe strength of this work is to plot type curves of pressure and rate transient analysis of multi-stage hydraulically fractured well (MHFW) in shale gas condensate reservoir in terms of rich gas production of the well.

History matching and pressure analysis with stress-dependent permeability using the In Salah CO2 storage case study

Using the In Salah CO2 storage case study, this study demonstrates how reservoir simulation history-matching and pressure analysis can be used to improve conformance assurance. By adopting a holistic approach to reservoir simulation and history matching, in conjunction with the injection pressure analysis and use of microseismic monitoring data, an improved understanding of the injection processes at the In Salah storage site was gained, revealing distinctively different responses to CO2 injection at each of the three injection wells. It has been shown that injection well performance at wells KB-501 and KB-503 was characterised by periods of matrix and fracture flow, the latter being due to shear reactivation of existing fractures in the vicinity of the wellbore. In contrast, the analysis at KB-502 revealed that CO2 injection has resulted in fracture reactivation in both shear and tensile modes with propagation both laterally and vertically.The findings of this study have shown that the injection-induced microseismic events recorded close to the KB-502 well is mainly caused by injecting CO2 into a 4-kilometer long fracture-zone intersecting the borehole. This fracture zone experienced tensile opening of fractures during injection and then subsequent partial closure after the injection was suspended. It is furthermore clear that the rather unique combination of microseismic and InSAR monitoring data and reservoir history matching around the injection well KB-502 provide highly valuable insights into injection-induced seismicity and fracture flow behaviour for CO2 storage projects. Episodes of flow in natural fractures can be separated from flow in induced fractures and the need for a dynamic, stress-dependent, permeability variable have been demonstrated.

Formal analysis of the Schulz matrix inversion algorithm: A paradigm towards computer aided verification of general matrix flow solvers

This paper pilots Schulz generalised matrix inverse algorithm as a paradigm in demonstrating how computer aided reachability analysis and theoretical numerical analysis can be combined effectively in developing verification methodologies and tools for matrix iterative solvers. It is illustrated how algorithmic convergence to computed solutions with required accuracy is mathematically quantified and used within computer aided reachability analysis tools to formally verify convergence over predefined sets of multiple problem data. In addition, some numerical analysis results are used to form computational reliability monitors to escort the algorithm on-line and monitor the numerical performance, accuracy and stability of the entire computational process. For making the paper self-contained, formal verification preliminaries and background on tools and approaches are reported together with the detailed numerical analysis in basic mathematical language. For demonstration purposes, a custom made reachability analysis program based on affine arithmetic is applied to numerical examples.

Representation of a new physics-based non-Darcy equation for low-velocity flow in tight reservoirs

There has been a growing interest in the study of low-velocity non-Darcy flow in tight reservoirs. Most existing non-Darcy equations, however, are flawed in model assumption, equation derivation or field practicability. For another, current non-Darcy simulations are based on the traditional methods, which are incapable of describing the fracture-rich feature of tight reservoir geology. In light of this, this paper introduces a new physics-based non-Darcy equation for low-velocity flow from four aspects: equation derivation, experimental validation, flow simulation and flow analysis. The rigorous derivations of the new equation are presented with a modified Buckingham-Reiner equation in which the boundary layer effect and the Bingham fluid behavior are described. The non-Darcy coefficient controlled by the boundary layer parameter and threshold pressure gradient (TPG) is incorporated into Darcy's equation. The equation validations are performed by liquid column experiment and core flow experiment, which yields good matching relationship between modeled values and observed values. The non-Darcy flow simulation is based on the triangle-gridded discrete fracture-matrix model (DFM) which can model arbitrary fractures. The upstream weighting scheme for computing the non-Darcy transmissibility is proposed to improve numerical robustness. Then the scheme is implemented by constructing non-Darcy operators, consisting of half-face upstream weighting operator and gradient operator, and further setting up the Automatic Differentiation (AD)-style discrete equations. The studies on non-Darcy flow in matrix coupled with Darcy flow in fracture are performed by modeling two types of fractured reservoirs. Detailed analyses are illustrated with pressure transient, long-term well bottom pressure and pressure map.

Modelling root growth and soil suction due to plant competition

Previous experimental results show that planting spacing has significant effects on root distribution and soil suction (negative pore water pressure) due to inter-plant competition. However, there is a lack of theoretical study on this aspect. This study proposes a new physically based mathematical model to capture planting spacing effects on root growth and soil suction considering three key factors, namely hydrotropism, soil mechanical impedance and inter-plant competition. The model is mainly composed of four parts: (i) extension of root zone front; (ii) increase in root density; (iii) root water uptake and (iv) water flow in soil matrix. Root growth and root water uptake are fully coupled. In order to validate the model, laboratory and field tests were conducted on one tree (Schefflera heptaphylla) and one shrub species (Schefflera arboricola), respectively, with different planting spacings. Even though the investigated tree and shrub species had different values of leaf area index and root length density, consistent conclusions on planting spacing effects can be drawn. When planting spacing became smaller, the size of root system decreased while root density increased, hence causing higher soil suction. The model can capture the root distributions as well as induced soil suction during both evapotranspiration and rainfall events quite well for both tree and shrub species.

Calibration and field application of an innovative passive sampler for monitoring groundwater quality

This study describes the development of a novel Empore™ disk-based passive sampler specially adapted to groundwater monitoring. The sampler was calibrated in the laboratory using conditions that corresponded to groundwater (i.e. matrix medium, water temperature, flow rate and water flow across the disks). The retention and elution performance for sixteen semi-polar and polar pollutants on the Empore™ disk (47 mm diameter, SDB-XC) was evaluated. Recoveries were ~80% for the majority of compounds. Sampler uptake kinetics were measured over fourteen days at three concentrations (10, 100 and 500 ng L−1) and the sampling rate (RS) calculated for four compounds. There was no influence of concentration of the test analyte on the uptake profile; with mean RS varying between 0.018 ± 0.007 L day−1 and 0.047 ± 0.001 L day−1. Passive samplers were deployed in twelve characterized groundwater wells near Lyon (France). Atrazine, atrazine-desethyl and diuron were the main pollutants found with a maximum time-weighted concentration of 61 ± 3, 62 ± 24 and 127 ± 49 ng L−1 respectively.

The hyperbolic constitutive equations and modified dynamic material model of TiBw/Ti-6.5Al-2.5Zr-1Mo-1V-0.5Si composites

The hot deformation behaviors TiBw/Ti-6.5Al-2.5Zr-1Mo-1V-0.5Si composite were studied via hot compression tests at the temperature ranged from 870 °C to 1100 °C and strain rate ranged from 1 s−1 to 0.001 s−1. Hyperbolic constitutive equations were calculated for α+β and β phase region respectively. The processing maps were constructed based on a modified dynamic material modeling (MDMM), in which an integration method bonded by linear regression was employed to reduce the uncertainty caused by interpolation. The microstructure evolution of metallic matrix and TiBw reinforcement were investigated by scanning electronic microscopy and transmitting electronic microscopy. The hot deformation activation energy of the present composite was determined to be 593.7 kJ mol−1 in α+β region and 338.1 kJ mol−1 in β region. No trace of macroscopic defects was found on the compressed specimens, showing the present composite has a good workability. The ideal hot working regions for the present composite are 0.003 s−1/900 °C and 0.06 s−1/950 °C in α+β region, 0.003 s−1/1020 °C and 0.01 s−1/1060 °C in β phase region. The refinement in microstructure was caused by globularization and dynamic recrystallization, which also caused the peaks of heat dissipation efficiency in the processing maps. The flow of metallic matrix lead to the rotation of TiBw, forming a sharp (1 0 0)TiBw || CD texture. TiBw fracture was caused by the stress concentration induced by dislocation pileups around them, and the fracture of TiBw can be reduced by decreasing strain rate or increasing deformation temperature.

An unfitted finite element method for the Darcy problem in a fracture network

The paper develops an unfitted finite element method for solving the Darcy system of equations posed in a network of fractures embedded in a porous matrix. The approach builds on the Hughes–Masud stabilized formulation of the Darcy problem and the trace finite element method. The system of fractures is allowed to cut through the background mesh in an arbitrary way. Moreover, the fractures are not triangulated in the common sense and the junctions of fractures are not fitted by the mesh. To couple the flow variables at multiple fracture junctions, we extend the Hughes–Masud formulation by including penalty terms to handle interface conditions. One observation made here is that by over-penalizing the pressure continuity interface condition one can avoid including additional jump terms along the fracture junctions. This simplifies the formulation while ensuring the optimal convergence order of the method. The application of the trace finite element method allows to treat both planar and curvilinear fractures with the same ease. The paper presents convergence analysis and assesses the performance of the method in a series of numerical experiments. For the background mesh we use an octree grid with cubic cells. The flow in the fracture can be easily coupled with the flow in matrix, but we do not pursue the topic of discretizing such coupled system here.

Zhang Neural Networks for fast and accurate computations of the field of values

In this paper, a new and different neural network, called Zhang Neural Network (ZNN) is appropriated from discrete time-varying matrix problems and applied to the angle parameter-varying matrix field of values (FoV) problem. This problem acts as a test bed for newly discovered convergent 1-step ahead finite difference formulas of high truncation error orders. The ZNN method that uses a look-ahead finite difference scheme of error order 6 gives us 15+ accurate digits of the FoV boundary points in record time when applied to hermitian matrix flows .

Karst conduit contribution to spring discharge and aquifer cross-sectional area

Groundwater flow discharging to springs from carbonate aquifers is governed by the interaction of slow matrix flow and fast fracture/conduit flow, which creates highly complex flow and transport conditions. An important unknown is the relative contribution of matrix and conduit flow to the total discharge. This study experimentally investigated groundwater fluxes in the Floridan aquifer within the springshed of Silver Springs, FL, one of the largest freshwater springs in the world with mean discharge of approximately 20 m3/s. Using in situ passive flux meters (PFMs, n = 48 at 16 wells) and a new karstic borehole dilution (KBHD, n = 21 at 7 wells) technique we measured groundwater fluxes in rock matrix and non-matrix (conduit and fracture) zones of 0.06 ± 0.003 m/day and 3.05 ± 1.8 m/day (mean ± standard error). These data, combined with previously conducted tracer tests (n = 12 at 3 sites), were coupled with simple analytical and numerical solutions to identify the proportion of the aquifer that contributes most significantly to water flow to the spring with three different modeling scenarios: single domain, dual domain including matrix and non-matrix zones, and triple domain including matrix, fracture, and conduit zones. The analytical and numerical models coupled with the in situ measured fluxes for the dual and triple domain scenarios showed good agreement with measured head profiles (Nash-Sutcliffe E > 0.90), when compared to the homogeneous porous domain scenario (E = −1.84). Conduit and fracture zones were estimated to represent between 2% and 22% of the aquifer cross-sectional area (at radial distance of 3 km from the spring outlet), yet these zones contributed between 75 and 96% of the total groundwater flow. The results of this study offer field-measured hydrogeologic data that can be used for active resource management in springsheds, and the simple modeling approach presented here may be applicable to other springsheds with fairly simple geometry to estimate the relative contributions of fast and slow water flow and solute transport pathways to the spring outlet.

Spatial–Temporal Soil Water Dynamics beneath a Tree Monitored by Tensiometer-Time Domain Reflectometry Probes

Tensiometer-coiled time domain reflectometry (T-TDR) probes have been developed in previous studies, but have not been applied in the field. In this study, we applied T-TDR probes to the simultaneous monitoring of soil water content (θ) and soil water potential (ψ) on a profile beneath a tree in a forest stand, and analyzed the temporal and spatial variations in soil water dynamics in a root-containing environment. The results showed different features in the relationships between the mean and standard deviation of spatial θ and ψ, which exhibited convex-upward shapes and negative curvilinear shapes, respectively. High spatial variability was observed at intermediate values of θ and small values of ψ. Matrix flow and preferential flow accounted for 75% and 25% of the area beneath the tree. Although the infiltration processes were dominated by matrix flow, preferential flow acting for a short time could cause an average θ or ψ to reach their maximum values at all of the locations. Preferential flow primarily occurred at a “hot spot” around a coarse root. Small changes in θ and ψ were generally observed at a “cold spot” beneath a lateral root. Integrated information from multiple sources of θ and ψ could help to evaluate soil water dynamics when one exhibited large spatial variation during the wetting or drying processes, and greatly help to improve the accuracy for detecting the presence of preferential flow in a short measurement period.

Effects of Grass and Forests and the Infiltration Amount on Preferential Flow in Karst Regions of China

Preferential flow is an important water infiltration phenomenon in karst regions. The response of preferential flow to vegetation restoration requires urgent investigation due to the special soil structure of karst regions. In order to study the effect of vegetation restoration on water movement in karst regions, four kinds of ponded water infiltration experiments were carried out in Pinus Yunnanensis plantation forestland, secondary forestland, and natural grassland. A brilliant blue dyeing experiment was conducted to visualize the distribution of water infiltration in soil (a total of 150 stained images from vertical soil slices). Results showed that the average depth of matrix flow in natural grassland was approximately six times those in plantation and secondary forestlands. An increase in matrix flow will have a negative effect on the development of preferential flow. Water transported in preferential flow paths affects the distribution of nutrients and organic matter in the soil. However, preferential flow in grassland can promote the accumulation of available nutrients, and preferential flow in plantations can inhibit the loss of organic matter. Preferential flow in grasslands and forest plantations is less than that in native forests soils. Preferential flow increases the percolation of water in soils. The effect is that preferential flow can obstructs water uptake by the roots under low rainfall conditions, and decreases surface runoff before soil saturation under high rainfall conditions. In the process of nutrient element migration, preferential flow has a good contribution, which is conducive to the migration and accumulation of elements required for surface vegetation growth. The contribution of preferential flow needs to be considered in studies on vegetation restoration planning and land degradation.

Dimensional-Invariance Principles in Coupled Dynamical Systems: A Unified Analysis and Applications

In this paper we study coupled dynamical systems and investigate dimension properties of the subspace spanned by solutions of each individual system. Relevant problems on \textit{collinear dynamical systems} and their variations are discussed recently by Montenbruck et. al. in \cite{collinear2017SCL}, while in this paper we aim to provide a unified analysis to derive the dimensional-invariance principles for networked coupled systems, and to generalize the invariance principles for networked systems with more general forms of coupling terms. To be specific, we consider two types of coupled systems, one with scalar couplings and the other with matrix couplings. Via the \textit{rank-preserving flow theory}, we show that any scalar-coupled dynamical system (with constant, time-varying or state-dependent couplings) possesses the dimensional-invariance principles, in that the dimension of the subspace spanned by the individual systems' solutions remains invariant. For coupled dynamical systems with matrix coefficients/couplings, necessary and sufficient conditions (for constant, time-varying and state-dependent couplings) are given to characterize dimensional-invariance principles. The proofs via a rank-preserving matrix flow theory in this paper simplify the analysis in \cite{collinear2017SCL}, and we also extend the invariance principles to the cases of time-varying couplings and state-dependent couplings. Furthermore, subspace-preserving property and signature-preserving flows are also developed for coupled networked systems with particular coupling terms. These invariance principles provide insightful characterizations to analyze transient behaviors and solution evolutions for a large family of coupled systems, such as multi-agent consensus dynamics, distributed coordination systems, formation control systems, among others.