Critical Gradient Research Articles

A non-critical hillslope model: Evidence and topographic implications

Hillslopes constitute the majority of a drainage basin space, and they, together with channelized streams and mountain glaciations, form the most representative exogenic agents sculpting the diverse landforms of the Earth's surface. It is well acknowledged that the hillslope evolution is dominated by a diffusion mechanism. A prominent progress in the last two decades is the proposed non-linearity in hillslope process, suggesting a non-linear relationship between the hillslope transport flux and the hillslope gradient. Existing non-linear hillslope models, by introducing a critical hillslope gradient, are successful in accounting for catastrophic processes, e.g., landslides. However, the present analytical descriptions of hillslope morphology remain complex in mathematical forms, hindering straightforward practical implementation. In this study, we develop a non-critical hillslope model based on the generic hillslope transport equation, which has the advantages of a simple mathematical form and easy practical application. The new hillslope model is compatible with the existing linear and non-linear hillslope models and is capable of emulating topographic evolution under arbitrary hillslope gradients. Using the non-critical hillslope model, we explore the characteristics of steady-state hillslope morphology, its identification, and the general transient response to tectonic uplift by numerical modeling. The proposed non-critical hillslope model is validated and supported by high-resolution topography in southern Tibet and wide basin erosional data compiled from published studies, supporting that the non-linear behavior of hillslopes is universal and might not be unique to steep hillslopes. The non-critical hillslope model provides a new prospective framework for modeling hillslope and landform evolution.

Formation, propagation and conversion of transport barriers triggered by dynamical critical gradient in tokamak plasmas

In this work, we propose a reduced model with a dynamical critical gradient to study the formation, propagation, and conversion of the transport barriers. In contrast to the commonly adopted static critical gradient, an evolving critical gradient self-consistently softens the profile stiffness, so as to facilitate the generation of transport barriers. This is especially crucial to the internal transport barrier (ITB) formation. Numerically, we show that the inhomogeneity of turbulent and neoclassical diffusivities can induce the global wave front propagation of the transport barrier. When the heating power ramps quickly, the ITB propagates unidirectionally to the edge region and converts into an edge transport barrier. For slow power ramping, the propagating ITB will bifurcate into bidirectional wavefronts and finally convert into a steady double transport barrier state. Our model uncovers the vital role of a dynamical ‘profile-stiffness’ in depicting the global dynamics of the transport barrier.

MR-guided stereotactic radiation therapy for head and neck cancers

PurposeMR-guided radiotherapy (MRgRT) has the advantage of utilizing high soft tissue contrast imaging to track daily changes in target and critical organs throughout the entire radiation treatment course. Head and neck (HN) stereotactic body radiation therapy (SBRT) has been increasingly used to treat localized lesions within a shorter timeframe. The purpose of this study is to examine the dosimetric difference between the step-and-shot intensity modulated radiation therapy (IMRT) plans on Elekta Unity and our clinical volumetric modulated arc therapy (VMAT) plans on Varian TrueBeam for HN SBRT. MethodFourteen patients treated on TrueBeam sTx with VMAT treatment plans were re-planned in the Monaco treatment planning system for Elekta Unity MR-Linac (MRL). The plan qualities, including target coverage, conformity, homogeneity, nearby critical organ doses, gradient index and low dose bath volume, were compared between VMAT and Monaco IMRT plans. Additionally, we evaluated the Unity adaptive plans of adapt-to-position (ATP) and adapt-to-shape (ATS) workflows using simulated setup errors for five patients and assessed the outcomes of our treated patients. ResultsMonaco IMRT plans achieved comparable results to VMAT plans in terms of target coverage, uniformity and homogeneity, with slightly higher target maximum and mean doses. The critical organ doses in Monaco IMRT plans all met clinical goals; however, the mean doses and low dose bath volumes were higher than in VMAT plans. The adaptive plans demonstrated that the ATP workflow may result in degraded target coverage and OAR doses for HN SBRT, while the ATS workflow can maintain the plan quality. ConclusionThe use of Monaco treatment planning and online adaptation can achieve dosimetric results comparable to VMAT plans, with the additional benefits of real-time tracking of target volume and nearby critical structures. This offers the potential to treat aggressive and variable tumors in HN SBRT and improve local control and treatment toxicity.

Effect of movability of water on the low-velocity pre-Darcy flow in clay soil

Water seepage in soil is a fundamental problem involving various scientific and engineering fields. According to the literature, low-velocity water seepage in low-permeability porous media, such as clay, does not follow Darcy's law, also known as pre-Darcy flow. The formation of immovable water due to water adsorption on the pore wall is believed to be responsible for the formation of pre-Darcy flow. However, this view lacks direct solid evidence. To investigate the pre-Darcy water flow in clay, head permeability experiments are conducted on six clay samples with different densities. The results indicate that water seepage in clay at low hydraulic gradients does not follow Darcy's law. A clear nonlinear relationship between flow velocity and hydraulic gradient is observed. Water flow in clay can be divided into the pre-Darcy flow and Darcy flow regions by the critical hydraulic gradient, which is 10–12 for the Albic soil with dry density between 1.3 g/cm3 and 1.8 g/cm3. According to the disjoining pressure theory, immovable water due to water adsorption on the pore wall is the primary reason for water flow deviating from Darcy's law in clay. The results indicate that the percentage of movable water ranges from 39.7% to 59.3% for the six samples at a hydraulic gradient of 1. As the hydraulic gradient increases, the percentage of moveable water also increases. Additionally, there is a strong correlation between the percentage of movable water and the variation in hydraulic conductivity with the hydraulic gradient. Furthermore, a quantitative relationship between the percentage of movable water and the hydraulic conductivity has been established. The results of this study suggest that water adsorption on the pore wall not only affects the water movability, but is also closely related to the pre-Darcy flow phenomenon in clay.

Catheter-tissue contact optimizes pulsed electric field ablation with a large area focal catheter.

Pulsed electric field (PEF) ablation relies on the intersection of a critical voltage gradient with tissue to cause cell death. Field-based lesion formation with PEF technologies may still depend on catheter-tissue contact (CTC). The purpose of this study was to assess the impact of CTC on PEF lesion formation with an investigational large area focal (LAF) catheter in a preclinical model. PEF ablation via a 10-spline LAF catheter was used to create discrete right ventricle (RV)lesions and atrial lesion sets in 10 swine (eight acute, two chronic). Local impedance (LI) was used to assess CTC. Lesions were assigned to three cohorts using LI above baseline: no tissue contact (NTC: ≤∆10 Ω, close proximity to tissue), low tissue contact (LTC: ∆11-29 Ω), and high tissue contact (HTC: ≥∆30 Ω). Acute animals were infused with triphenyl tetrazolium chloride (TTC) and killed ≥2 hpost-treatment. Chronic animals were remapped 30 days post-index procedure and stained with infused TTC. Mean (± SD) RV treatment sizes between LTC (n = 14) and HTC (n = 17) lesions were not significantly different (depth: 5.65 ± 1.96vs. 5.68 ± 2.05 mm, p = .999; width: 15.68 ± 5.22vs. 16.98 ± 4.45 mm, p = .737), while mean treatment size for NTC lesions (n = 6) was significantly smaller (1.67 ± 1.16 mm depth, 5.97 ± 4.48 mm width, p < .05). For atrial lesion sets, acute and chronic conduction block were achieved with both LTC (N = 7) and HTC (N = 6), and NTC resulted in gaps. PEF ablation with a specialized LAF catheter in a swine model is dependent on CTC. LI as an indicator of CTC may aid in the creation of consistent transmural lesions in PEF ablation.

Numerical simulation of the critical hydraulic gradient of granular soils at seepage failure by discrete element method and computational fluid dynamics

Seepage failure is a common problem in engineering, and the calculation and analysis of critical hydraulic gradient are of great significance for the safety and protection of engineering. Based on the principle of discrete element method and computational fluid dynamics, the fluid–solid coupled models were established to study the critical hydraulic gradient and particle loss rate of granular soils at seepage failure. The evolution of seepage failure was divided into four stages: seepage development stage, local damage stage, volume expansion stage and overall damage stage. The validity of numerical simulation was demonstrated by comparing the critical hydraulic gradient obtained by numerical simulation and by Terzaghi’s formula. According to the fabric damage and flow velocity variation of the models at seepage failure, the influences of model size and particle size on the critical hydraulic gradient and particle loss rate were analyzed. The results indicate that critical hydraulic gradient and particle loss rate were not sensitive to changes in model size. A wide particle size distribution range resulted in large critical hydraulic gradient and small particle loss rate at seepage failure. The discrete element numerical simulation can not only be used to determine the critical hydraulic gradient of geotechnical and hydraulic engineering, but also offer a visual portrayal of the evolution of seepage failure, serving as an important complement to comprehend the intricate microscopic mechanisms underlying soil seepage failure.

Study on Voids and Seepage Characteristics within Rock Fracture after Shear Dislocation Viewing from CT Test and Numerical Modeling

In rock mass engineering, stress balance changes often cause the relative slip of fractures along a wall surface, impacting the seepage behavior of fluid in the fractures. Using computer tomography (CT) scanning, spatial models of fractures with dislocations ranging from 0 to 10 mm were created to explore the relationship between changes in fracture dislocation and changes in fluid flow behavior, respectively. The spatial fractal dimension of cavity distribution within the fractures was calculated using a thin-plate filling approach to characterize the complexity of the fracture cavity distribution. The fluid flow within the dislocation fractures was then simulated using COMSOL, and the effect of cavity alterations in the form of dislocation on the fluid seepage behavior was analyzed using the spatial fractal. The results show that the values of mechanical aperture after dislocation of the fracture obtained by a CT test are normally distributed, the distribution range of mechanical aperture gradually widens with an increase in the dislocation distance, and the average mechanical aperture increases on a logarithmic curve. The relative spatial fractal dimension decreases gradually with an increase in dislocation distance, and the interconnected pathways within the fracture decrease; in addition, it is observed that the change in the relative spatial fractal dimension is closely correlated with the change in the mean mechanical aperture. Numerical simulations of dislocation fracture seepage found that the permeability increases nonlinearly with increasing dislocation distance. When the dislocation distance reaches 5 mm, nonlinear behaviors such as eddy currents occur, and the influence range of eddy currents gradually expands with the increase in dislocation distance under the influence of the boundary. Moreover, the inertia coefficient B in the Forchheimer equation and the critical hydraulic gradient Jc, which can describe the nonlinear seepage characteristics, show a power function decreasing trend with increasing dislocation distance, and the fluid in the fracture is more likely to produce nonlinear flow.

Pilot test and consolidation theory of marine dredged slurry using the membrane-free horizontal-vacuum method

Laboratory tests and theoretical analyses were conducted to investigate the membrane-free horizontal-vacuum (MFHV) method for inducing seepage consolidation in dredged marine fills. First, six well-designed tests with dredged marine slurry were conducted to simulate the consolidation behaviour with a prefabricated horizontal drain (PHD). The dewatering features under MFHV conditions were studied with respect to the drainage rate, settlement, water content, and permeability. The dewatering rate saltation (DRS) problem was systematically investigated by observing the changes in the supernatant water. The results indicated that the DRS problem existed in the case of the thin slurry layer rather than the thick slurry layer. Furthermore, a modified consolidation model was proposed considering the vacuum boundary and critical gradient. An explicit solution was provided to calculate the average consolidation degree and settlement. The settlement and DRS points obtained from the model tests and analytical solutions were compared. The results showed that the proposed analytical method could reasonably predict the consolidation behaviour of the MFHV method. In addition, a parameter study was conducted to investigate the influence of the critical gradient, void ratio, and compression index on seepage consolidation. Finally, an equation to design the optimum drain space for the MFHV-treated slurry was presented for direct engineering practice.

Gyro-Landau-fluid simulations of impurity effects on ion temperature gradient driven turbulence transport

The effects of impurities on ion temperature gradient (ITG) driven turbulence transport in tokamak core plasmas are investigated numerically via global simulations of microturbulence with carbon impurities and adiabatic electrons. The simulations use an extended fluid code (ExFC) based on a four-field gyro-Landau-fluid (GLF) model. The multispecies form of the normalized GLF equations is presented, which guarantees the self-consistent evolution of both bulk ions and impurities. With parametric profiles of the cyclone base case, well-benchmarked ExFC is employed to perform simulations focusing on different impurity density profiles. For a fixed temperature profile, it is found that the turbulent heat diffusivity of bulk ions in a quasi-steady state is usually lower than that without impurities, which is contrary to the linear and quasi-linear predictions. The evolutions of the temperature gradient and heat diffusivity exhibit a fast relaxation process, indicating that the destabilization of the outwardly peaked impurity profile is a transient state response. Furthermore, the impurity effects from different profiles can obviously influence the nonlinear critical temperature gradient, which is likely to be dominated by linear effects. These results suggest that the improvement in plasma confinement could be attributed to the impurities, most likely through adjusting both heat diffusivity and the critical temperature gradient.

Experimental investigation and modeling of boundary layer flashback for non-swirling premixed prevaporized n-propanol/air and /isopropanol/air flames

The idea of utilizing lean, premixed and prevaporized (LPP) combustion could be a step towards sustainable aviation in the future, with the absolute absence of soot particles and very low nitrogen oxide emissions. However, premixing with compressed hot air presents a challenge for both conventional jet fuel and synthetically produced sustainable aviation fuel (SAF) due to self-ignition and flashbacks. Our group is thus seeking LPP-compatible advanced sustainable aviation fuels, which are evaluated based on their flashback propensity. Preliminary studies indicate that short-chain alcohols, with their higher ignition delay times and lower flame velocities, may be appropriate for LPP combustion concepts. In this study, the isomers of propanol, n-propanol, and isopropanol, are the first representatives of the short-chain alcohols to be investigated experimentally and numerically with respect to their flame stability limits. The experimental determination of stability limits for n- and isopropanol/air premixed flames was conducted on a generic, non-swirled atmospheric burner for an equivalence ratio range of 0.82 to 1.11. A fully automated measurement procedure was used to generate 119 measurement points with Reynolds numbers in the range from 1430 to 2750. The influence of the positional isomerism and of the preheat temperature (422 K, 446 K and 466 K) of the unburned mixture are investigated. A clear influence of the isomeric fuel structure is found. A theoretical analysis shows that it can be related to the different laminar flame speed and laminar flame thickness of the isomers. Moreover, a detailed analysis shows that the critical velocity gradient concept to describe boundary layer flashback is well usable with a Péclet number model.

Методология влияния свободной порозности и водоотдачи на процессы, происходящие в почвогрунтах оросительных каналов с земляным руслом

Purpose of the research: to consider the influence of free porosity and water loss on the filtration of water from channels with an earthen bed. Explore existing calculation methods taking into account the parameters of free porosity and fluid loss. Collect calculation material that can form the basis of a program for calculating the filtration of channels with an earthen bed, taking into account the factors influencing the first and second stages of filtration in the channels. Materials and research methods: The work used theoretical methods for calculating filtration in channels with an earthen bed, presented the calculation of the loss of flow rate Qf for filtration per 1 km of length with a steady free surface for different types of channel cross-sections, considered the basic formulas proving that water supply changes with changes in transverse cross-section of the canal, the change in the stability of the canal slopes is shown, a test calculation of the canal for filtration strength according to the maximum pressure gradients is presented, the need to compare the excess of the critical filtration pressure gradient with the permissible pressure gradient is considered. Results and its discussion. The relationship between the total, capillary and minimum moisture capacity and water yield in the thickness of soils is presented, the dependence of free porosity on the groundwater level, and the change in water permeability of soils over time are considered. As a result of the research, material was collected on the influence of free porosity and water loss on the movement of water in soils and the influence on the increase in groundwater levels in the zone of influence of canals, a methodology was presented for the influence of free porosity and water loss on the processes occurring in the soils of irrigation canals in an earthen channel, which will allow its use for modeling these processes on a computer.

Gyrokinetic turbulence modeling of a high performance scenario in JT-60SA

Local gyrokinetic simulations are used to model turbulent transport for the first time in a representative high-performance plasma discharge projected for the new JT-60SA tokamak. The discharge features a double-null separatrix, 41 MW of combined neutral beam heating and electron cyclotron heating, and a high predicted ratio of the normalized plasma kinetic to magnetic pressure β. When considering input parameters computed from reduced transport models, gyrokinetic simulations predict a turbulent heat flux well below the injected 41 MW. Increasing the background gradients, on the other hand, can trigger a non-zonal transition (NZT), causing heat fluxes to no longer saturate. Furthermore, when considering fast ions in the simulations, a high-frequency mode is destabilized that substantially impacts the turbulence. The NZT is avoided by reducing the electron pressure by 10% below its nominal value, and the fast-ion resonance is removed by reducing the fast-ion temperature. The thus-obtained simulation features broadband frequency spectra and density and temperature fluctuation levels δn/n≈1% –2%, δT/T≈1% –6% that should be measurable with fluctuation diagnostics planned for JT-60SA. The temperature profile is fixed by the critical main-ion temperature gradient as a consequence of the high stiffness; heat fluxes increase by a factor of ten when increasing the main ion temperature gradient by 17%. Despite large gradients, it is demonstrated that, due to the large β, retaining compressional magnetic field fluctuations and in particular, the contribution of the pressure gradient in the ∇B drifts, is crucial to achieving non-zero heat fluxes.

Internal instability of cohesionless soils in upward and downward flow: an experimental verification of theory

Rigid-wall permeameter testing of two potentially unstable gradations established that the critical hydraulic gradient to trigger instability is smaller for upward flow than for downward flow. The experimental finding is explained with reference to the Skempton-Brogan stress reduction factor α in the finer fraction content of the soil. Theory uses the α-factor to define a hydro-mechanical envelope in gradient-stress space that is independent of flow direction, and the experimental results are found to be in good agreement with the theory. Testing with upward flow is recommended to determine the value of α for an internally unstable gradation because, in contrast to downward flow, there is no requirement for an outflow boundary.

The Criteria for Transition of Fluid to Nonlinear Flow for Fractured Rocks: The Role of Fracture Intersection and Aperture

Understanding the fluid pattern is of special significance for estimating the hydraulic conductivity of fractured rock masses. The nonlinearity of fluid flow in discrete fracture networks (DFNs) originates from inertial effects and is enhanced by complex geometric topologies, which produces additional viscous friction and is subject to inertia effects, consequently transitioning the fluid to the nonlinear flow regime. Therefore, it is important to obtain the critical conditions for the transition of a fluid from laminar to turbulent flow. To investigate the role of fracture aperture and fracture intersection on the onset of the transition of a fluid to nonlinear flow in fractured rocks, the fluid dynamic computation was performed by solving Navier–Stokes (N–S) equations in DFN models. The results show that the flow flux initially linearly correlates with the hydraulic gradient (J) and the permeability of DFNs initially remains constant. As the hydraulic gradient increases, the flow flux presents a strong nonlinear relationship with the hydraulic gradient, and the permeability decreases dramatically. In particular, significant inertial effects appear earlier with a large fracture aperture or a dense fracture intersection. A critical hydraulic gradient (Jc) is proposed to judge the onset of nonlinear flow. The mathematical expression of Jc and Forchheimer coefficients A and B involving the fracture aperture and fracture intersection density is established through a multiple regression algorithm. Finally, the reliability of the predictive model was verified by comparing the results of the prediction and fluid dynamic computation of a series of DFN models with well-known geometric distributions. The consistency of the fitted equations and a correlation coefficient greater than 0.9 between them indicate that the predictive model proposed in this study is reliable.

Observation of pedestal quasi-coherent mode in Type-I ELMy H-mode of HL-2A tokamak

High confinement mode plasma experiments with Type-I edge localized modes (ELMs) have been carried out on HL-2A tokamak. With neutral beam injection and lower hybrid current drive heating, a quasi-coherent mode (QCM) located at pedestal region has been observed, which exists during the ELM-free stage till the first ELM burst. Analysis based on density and magnetic fluctuations has revealed that the QCM propagating radially outward is electrostatic in nature whose radial wavenumber is kr∼0.5 cm−1 as well as the poloidal wavenumber around kθ∼1.4 cm−1, rotating in electron diamagnetic drift direction. The central frequency of the mode gradually decreases from 50 to 20 kHz, which varies almost linearly with toroidal rotation. Experimental findings indicate that the QCM is excited above a critical electron density gradient in the ELM-free phase during which the latter gradually increases due to the confinement transition. The disappearance of QCM is closely associated with the onset of ELMy H-mode, suggesting that the presence of QCM could potentially delay the occurrence of ELM bursts, consequently supporting the maintenance of an ELM-free operational regime. Moreover, the pedestal region locates more radially outside where the density gradient shows a more spanned region with QCM. A quantitative comparison between experimental measurements and linear GENE gyrokinetic simulations suggests that the dissipative trapped electron mode might be the candidate interpretation of the QCM.

Critical Hydraulic Gradient of Piping Erosion Under Free Flow and Seepage Flow Coupling Model

Critical Hydraulic Gradient of Piping Erosion Under Free Flow and Seepage Flow Coupling Model

Energetic particle marginal stability profile for HL-2M integrated simulation based on neural network module

A critical gradient model is employed to develop a module of energetic particle (EP) marginal stability profiles in OMFIT integrated simulations for studying EP transport. Currently, each iteration of transport evolution is approximately 10 min in the integrated simulation, whereas, the EP marginal stability profile, which serves as an input in the integrated simulation could take much longer; the reason being a combination of the TGLFEP and EPtran codes is employed in our previous investigation. To reduce the simulation time, the critical gradient is predicted by a neural network instead of the TGLFEP code, and the EPtran code is revised with parallel computing, so that the running time of this module can be controlled to within 5 min. The predictions are in good agreement with previous approaches. The integrated simulation of HL-2M with Alfven eigenmodes transported by neutral beam EP profiles indicates that EP transport reduces the total pressure and current as expected, but could also under some conditions raise the safety factor in the core, which is favorable for reversed magnetic shear and high-performance plasmas.

Seepage safety evaluation of high earth-rockfill dams considering spatial variability of hydraulic parameters via subset simulation

Seepage failure of high earth-rockfill dams have devastating consequences, and its safety analysis is of great importance in the design phase. However, the highest safety standards in high dams pose a challenge to the calculated efficiency of safety assessment. To address this problem, a random seepage safety assessment method which can consider the spatial variability of hydraulic parameters is proposed. Firstly, the spatial variability of the hydraulic parameters in the impervious materials is simulated using the covariance matrix decomposition under the framework of the non-intrusive finite element method. Then, according to the safety index of critical hydraulic gradient, the seepage stability formula is established to evaluate the safety state. Finally, considering that the highest safety standards in high dams make the probability of seepage hazard small (low failure probability event), it may require more than 10,000 deterministic calculations to complete the assessment process. Therefore, an efficient method based on subset simulation is proposed to optimize the computational efficiency. After the seepage safety evaluation of a 315 m high dam, the results show that the hydraulic conductivity of the core wall has the greatest influence on the seepage safety of the dam, and even under the influence of strong parameter spatial variability, its seepage failure probability is lower than 10-3. Compared with Monte Carlo simulation, the proposed method requires only 1/11 of the computation time at the 10-3 failure level. In addition, the results of grey relational analysis show that the coefficient of variation and correlation distance have obvious effects on seepage safety, and the autocorrelation distance has a greater effect.

Different bacterial and fungal community patterns in restored habitats in coal-mining subsidence areas.

Soil microbiota, which plays a fundamental role in ecosystem functioning, is sensitive to environmental changes. Studying soil microbial ecological patterns can help to understand the consequences of environmental disturbances on soil microbiota and hence ecosystem services. The different habitats with critical environmental gradients generated through the restoration of coal-mining subsidence areas provide an ideal area to explore the response of soil microbiota to environmental changes. Here, based on high-throughput sequencing, we revealed the patterns of soil bacterial and fungal communities in habitats with different land-use types (wetland, farmland, and grassland) and with different restored times which were generated during the ecological restoration of a typical coal-mining subsidence area in Jining City, China. The α-diversity of bacterial was higher in wetland than in farmland and grassland, while that of fungi had no discrepancy among the three habitats. The β-diversity of bacterial community in the grassland was lower than in the farmland, and fungal community was significant different in all three habitats, showing wetland, grassland, and farmland from high to low. The β-diversity of the bacterial community decreased with restoration time while that of the fungal community had no significant change in the longer-restoration-time area. Furthermore, soil electrical conductivity was the most important driver for both bacterial and fungal communities. Based on the taxonomic difference among different habitats, we identified a group of biomarkers for each habitat. The study contributes to understand the microbial patterns during the ecological restoration of coal-mining subsidence areas, which has implications for the efficient ecological restoration of subsidence areas.

Critical gradient turbulence optimization toward a compact stellarator reactor concept

Critical gradient turbulence optimization toward a compact stellarator reactor concept