Rural labor migration and farmers’arrangements of rice production systems in Central China:Insight from the intergenerational division of labor

Rice production is crucial for food security in China,and its relationship with rural labor migration has been studied extensively.Labor migration in rural China has taken new forms in recent years.There has been a discernible trend wherein adult children have started migrating to cities while their elderly parents return to villages to re-engage in on-farm work.The phenomenon has notably shaped the intergenerational division of labor(IDL)within households.However,it remains to be seen how farmers adjust their rice production systems in response to the IDL.The age of 60 years for employment injury insurance is the eligibility threshold for off-farm employment and is used to obtain a source of exogenous variation in the IDL.Based on a representative household survey of 1,752 rice farmers in the Hubei Province of Central China,our fuzzy regression discontinuity analysis reveals that farmers in IDL households are more likely to adopt ratoon rice(RR)than single cropping rice(SR)or double cropping rice(DR).The effect of the IDL varies under different levels of operational scales and specialized agricultural service availability.Further analysis suggests that farmers’arrangements are associated with two potential mechanisms of downward intergenerational transfer.Monetary transfer for urban housing purchases increases RR in IDL households,and time transfer for intergenerational childcare significantly promotes SR in IDL households.This study enhances the understanding of the relationship between rural labor migration and rice production in China,providing a reference for adjusting rice production systems to ensure food security.

Can rifaximin for hepatic encephalopathy be discontinued during broad-spectrum antibiotic treatment?

Hepatic encephalopathy(HE)is a formidable complication in patients with decompensated cirrhosis,often necessitating the administration of rifaximin(RFX)for effective management.RFX,is a gut-restricted,poorly-absorbable oral rifamycin derived antibiotic that can be used in addition to lactulose for the secondary prophylaxis of HE.It has shown notable reductions in infection,hospital readmission,duration of hospital stay,and mortality.However,limited data exist about the concurrent use of RFX with broad-spectrum antibiotics,because the patients are typically excluded from studies assessing RFX efficacy in HE.A pharmacist-driven quasi-experimental pilot study was done to address this gap.They argue against the necessity of RFX in HE during broad-spectrum antibiotic treatment,particularly in critically ill patients in intensive care unit(ICU).The potential for safe RFX discontinuation without adverse effects is clearly illuminated and valuable insight into the optimization of therapeutic strategies is offered.The findings also indicate that RFX discontinuation during broadspectrum antibiotic therapy was not associated with higher rates of delirium or coma,and this result remained robust after adjustment in multivariate analysis.Furthermore,rates of other secondary clinical and safety outcomes,including ICU mortality and 48-hour changes in vasopressor requirements,were comparable.However,since the activity of RFX is mainly confined to the modulation of gut microbiota,its potential utility in patients undergoing extensive systemic antibiotic therapy is debatable,given the overlapping antibiotic activity.Further,this suggests that the action of RFX on HE is class-specific(related to its activity on gut microbiota),rather than drug-specific.A recent double-blind randomized controlled(ARiE)trial provided further evidence-based support for RFX withdrawal in critically ill cirrhotic ICU patients receiving broad-spectrum antibiotics.Both studies prompt further discussion about optimal therapeutic strategy for patients facing the dual challenge of HE and systemic infections.Despite these compelling results,both studies have limitations.A prospective,multi-center evaluation of a larger sample,with placebo control,and comprehensive neurologic evaluation of HE is warranted.It should include an exploration of longer-term outcome and the impact of this protocol in non-critically ill liver disease patients.

Discontinuity development patterns and the challenges for 3D discrete fracture network modeling on complicated exposed rock surfaces

Natural slopes usually display complicated exposed rock surfaces that are characterized by complex and substantial terrain undulation and ubiquitous undesirable phenomena such as vegetation cover and rockfalls.This study presents a systematic outcrop research of fracture pattern variations in a complicated rock slope,and the qualitative and quantitative study of the complex phenomena impact on threedimensional(3D)discrete fracture network(DFN)modeling.As the studies of the outcrop fracture pattern have been so far focused on local variations,thus,we put forward a statistical analysis of global variations.The entire outcrop is partitioned into several subzones,and the subzone-scale variability of fracture geometric properties is analyzed(including the orientation,the density,and the trace length).The results reveal significant variations in fracture characteristics(such as the concentrative degree,the average orientation,the density,and the trace length)among different subzones.Moreover,the density of fracture sets,which is approximately parallel to the slope surface,exhibits a notably higher value compared to other fracture sets across all subzones.To improve the accuracy of the DFN modeling,the effects of three common phenomena resulting from vegetation and rockfalls are qualitatively analyzed and the corresponding quantitative data processing solutions are proposed.Subsequently,the 3D fracture geometric parameters are determined for different areas of the high-steep rock slope in terms of the subzone dimensions.The results show significant variations in the same set of 3D fracture parameters across different regions with density differing by up to tenfold and mean trace length exhibiting differences of 3e4 times.The study results present precise geological structural information,improve modeling accuracy,and provide practical solutions for addressing complex outcrop issues.

Experimental investigation on shear strength deterioration at the interface between different rock types under cyclic loading

The shear strength deterioration of bedding planes between different rock types induced by cyclic loading is vital to reasonably evaluate the stability of soft and hard interbedded bedding rock slopes under earthquake;however,rare work has been devoted to this subject due to lack of attention.In this study,experimental investigations on shear strength weakening of discontinuities with different joint wall material(DDJM)under cyclic loading were conducted by taking the interface between siltstone and mudstone in the Shaba slope of Yunnan Province,China as research objects.A total of 99 pairs of similar material samples of DDJM(81 pairs)and discontinuities with identical joint wall material(DIJM)(18 pairs)were fabricated by inserting plates,engraved with typical surface morphology obtained by performing three-dimensional laser scanning on natural DDJMs sampled from field,into mold boxes.Cyclic shear tests were conducted on these samples to study their shear strength changes with the cyclic number considering the effects of normal stress,joint surface morphology,shear displacement amplitude and shear rate.The results indicate that the shear stress vs.shear displacement curves under each shear cycle and the peak shear strength vs.cyclic number curves of the studied DDJMs are between those of DIJMs with siltstone and mudstone,while closer to those of DIJMs with mudstone.The peak shear strengths of DDJMs exhibit an initial rapid decline followed by a gradual decrease with the cyclic number and the decrease rate varies from 6%to 55.9%for samples with varied surface morphology under different testing conditions.The normal stress,joint surface morphology,shear displacement amplitude and shear rate collectively influence the shear strength deterioration of DDJM under cyclic shear loading,with the degree of influence being greater for larger normal stress,rougher surface morphology,larger shear displacement amplitude and faster shear rate.

Production induced fracture closure of deep shale gas well under thermo-hydro-mechanical conditions

Deep shale gas reservoirs have geological characteristics of high temperature,high pressure,high stress,and inferior ability to pass through fluids.The multi-stage fractured horizontal well is the key to exploiting the deep shale gas reservoir.However,during the production process,the effectiveness of the hydraulic fracture network decreases with the closure of fractures,which accelerates the decline of shale gas production.In this paper,we addressed the problems of unclear fracture closure mechanisms and low accuracy of shale gas production prediction during deep shale gas production.Then we established the fluid—solid—heat coupled model coupling the deformation and fluid flow among the fracture surface,proppant and the shale matrix.When the fluid—solid—heat coupled model was applied to the fracture network,it was well solved by our numerical method named discontinuous discrete fracture method.Compared with the conventional discrete fracture method,the discontinuous discrete fracture method can describe the three-dimensional morphology of the fracture while considering the effect of the change of fracture surface permeation coefficient on the coupled fracture—matrix flow and describing the displacement discontinuity across the fracture.Numerical simulations revealed that the degree of fracture closure increases as the production time proceeds,and the degree of closure of the secondary fractures is higher than that of the primary fractures.Shale creep and proppant embedment both increase the degree of fracture closure.The reduction in fracture surface permeability due to proppant embedment reduces the rate of fluid transfer between matrix and fracture,which has often been overlooked in the past.However,it significantly impacts shale gas production,with calculations showing a 24.7%cumulative three-year yield reduction.This study is helpful to understand the mechanism of hydraulic fracture closure.Therefore,it provides the theoretical guidance for maintaining the long-term effectiveness of hydraulic fractures.

Scale-space effect and scale hybridization in image intelligent recognition of geological discontinuities on rock slopes

Geological discontinuity(GD)plays a pivotal role in determining the catastrophic mechanical failure of jointed rock masses.Accurate and efficient acquisition of GD networks is essential for characterizing and understanding the progressive damage mechanisms of slopes based on monitoring image data.Inspired by recent advances in computer vision,deep learning(DL)models have been widely utilized for image-based fracture identification.The multi-scale characteristics,image resolution and annotation quality of images will cause a scale-space effect(SSE)that makes features indistinguishable from noise,directly affecting the accuracy.However,this effect has not received adequate attention.Herein,we try to address this gap by collecting slope images at various proportional scales and constructing multi-scale datasets using image processing techniques.Next,we quantify the intensity of feature signals using metrics such as peak signal-to-noise ratio(PSNR)and structural similarity(SSIM).Combining these metrics with the scale-space theory,we investigate the influence of the SSE on the differentiation of multi-scale features and the accuracy of recognition.It is found that augmenting the image's detail capacity does not always yield benefits for vision-based recognition models.In light of these observations,we propose a scale hybridization approach based on the diffusion mechanism of scale-space representation.The results show that scale hybridization strengthens the tolerance of multi-scale feature recognition under complex environmental noise interference and significantly enhances the recognition accuracy of GD.It also facilitates the objective understanding,description and analysis of the rock behavior and stability of slopes from the perspective of image data.

Review on the plastic instability of medium -Mn steels for identifying the formation mechanisms of Lüders and Portevin -Le Chatelier bands

Plastic instability,including both the discontinuous yielding and stress serrations,has been frequently observed during the tensile deformation of medium-Mn steels(MMnS)and has been intensively studied in recent years.Unfortunately,research results are controversial,and no consensus has been achieved regarding the topic.Here,we first summarize all the possible factors that affect the yielding and flow stress serrations in MMnS,including the morphology and stability of austenite,the feature of the phase interface,and the deformation parameters.Then,we propose a universal mechanism to explain the conflicting experimental results.We conclude that the discontinuous yielding can be attributed to the lack of mobile dislocation before deformation and the rapid dislocation multiplication at the beginning of plastic deformation.Meanwhile,the results show that the stress serrations are formed due to the pinning and depinning between dislocations and interstitial atoms in austenite.Strain-induced martensitic transformation,influenced by the mechanical stability of austenite grain and deformation parameters,should not be the intrinsic cause of plastic instability.However,it can intensify or weaken the discontinuous yielding and the stress serrations by affecting the mobility and density of dislocations,as well as the interaction between the interstitial atoms and dislocations in austenite grains.

THE RIEMANN PROBLEM FOR ISENTROPIC COMPRESSIBLE EULER EQUATIONS WITH DISCONTINUOUS FLUX

We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separated by a discontinuity x=x(t).We prove that this problem admits global Radon measure solutions for all kinds of initial data.The over-compressing condition on the discontinuity x=x(t)is not enough to ensure the uniqueness of the solution.However,there is a unique piecewise smooth solution if one proposes a slip condition on the right-side of the curve x=x(t)+0,in addition to the full adhesion condition on its left-side.As an application,we study a free piston problem with the piston in a tube surrounded initially by uniform pressureless flow and a polytropic gas.In particular,we obtain the existence of a piecewise smooth solution for the motion of the piston between a vacuum and a polytropic gas.This indicates that the singular Riemann problem looks like a control problem in the sense that one could adjust the condition on the discontinuity of the flux to obtain the desired flow field.

Finite Element Simulations of the Localized Failure and Fracture Propagation in Cohesive Materials with Friction

Strain localization frequently occurs in cohesive materials with friction(e.g.,composites,soils,rocks)and is widely recognized as a fundamental cause of progressive structural failure.Nonetheless,achieving high-fidelity simulation for this issue,particularly concerning strong discontinuities and tension-compression-shear behaviors within localized zones,remains significantly constrained.In response,this study introduces an integrated algorithmwithin the finite element framework,merging a coupled cohesive zone model(CZM)with the nonlinear augmented finite elementmethod(N-AFEM).The coupledCZMcomprehensively describes tension-compression and compressionshear failure behaviors in cohesive,frictional materials,while the N-AFEM allows nonlinear coupled intraelement discontinuities without necessitating extra nodes or nodal DoFs.Following CZM validation using existing experimental data,this integrated algorithm was utilized to analyze soil slope failure mechanisms involving a specific tensile strength and to assess the impact of mechanical parameters(e.g.,tensile strength,weighting factor,modulus)in soils.

Particle Discontinuous Deformation Analysis of Static and Dynamic Crack Propagation in Brittle Material

Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.

Application of modified discontinuous deformation analysis to dynamic modelling of the Baige landslide in the Jinsha River

Accurate dynamic modeling of landslides could help understand the movement mechanisms and guide disaster mitigation and prevention.Discontinuous deformation analysis(DDA)is an effective approach for investigating landslides.However,DDA fails to accurately capture the degradation in shear strength of rock joints commonly observed in high-speed landslides.In this study,DDA is modified by incorporating simplified joint shear strength degradation.Based on the modified DDA,the kinematics of the Baige landslide that occurred along the Jinsha River in China on 10 October 2018 are reproduced.The violent starting velocity of the landslide is considered explicitly.Three cases with different violent starting velocities are investigated to show their effect on the landslide movement process.Subsequently,the landslide movement process and the final accumulation characteristics are analyzed from multiple perspectives.The results show that the violent starting velocity affects the landslide motion characteristics,which is found to be about 4 m/s in the Baige landslide.The movement process of the Baige landslide involves four stages:initiation,high-speed sliding,impact-climbing,low-speed motion and accumulation.The accumulation states of sliding masses in different zones are different,which essentially corresponds to reality.The research results suggest that the modified DDA is applicable to similar high-level rock landslides.

Dissolution mechanism and kinetics ofβ(Mg_(17)Al_(12))phases in AZ91 magnesium alloy

In this study,the phase transformations,crystallization kinetics and dissolution mechanism ofβphase(Mg_(17)Al_(12))in magnesium alloy AZ91 were investigated by optical microscopy,X-ray diffraction,differential scanning calorimetry and differential dilatometry.The results indicate that this AZ91 alloy undergoes a phase transformation during aging,a discontinuous precipitation of theβphase(Mg_(17)Al_(12))at 150℃at the grain boundaries and another continuous at 350℃within the grains.The activation energy of the dissolution reaction of theβphase(Mg_(17)Al_(12))under non-isothermal conditions is 116.781 kJ/mol,while it is 129.7383 kJ/mol under isothermal conditions.The Avrami coefficient,n,relevant for the dissolution kinetics of theβphase(Mg_(17)Al_(12))is 1.152 and 1.211 in the non-isothermal and isothermal conditions respectively.The numerical coefficients m and Avrami n are 0.993 and 1.152.

No basalt accumulation and segregation atop the 660-km discontinuity beneath the Sea of Okhotsk

Recent seismic evidence shows that basalt accumulation is widespread in the mantle transition zone(MTZ),yet its ubiquity or sporadic nature remains uncertain.To investigate this phenomenon further,we characterized the velocity structure across the 660-km discontinuity that separates the upper mantle from the lower mantle beneath the Sea of Okhotsk by modeling the waveform of the S660P phase,a downgoing S wave converting into a P wave at the 660-km interface.These waves were excited by two regional>410-km-deep events and were recorded by stations in central Asia.Our findings showed no need to introduce velocity anomalies at the base of the MTZ to explain the S660P waveforms because the IASP91 model adequately reproduced the waveforms.This finding indicates that the basalt accumulation has not affected the bottom of the MTZ in the study area.Instead,this discontinuity is primarily controlled by temperature or water content variations,or both.Thus,we argue that the basalt accumulation at the base of the MTZ is sporadic,not ubiquitous,reflecting its heterogeneous distribution.

Energy Stable Nodal DG Methods for Maxwell’s Equations of Mixed-Order Form in Nonlinear Optical Media

In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic Kerr response,and the nonlinear delayed Raman molecular vibrational response.Unlike the first-order PDE-ODE governing equations considered previously in Bokil et al.(J Comput Phys 350:420–452,2017)and Lyu et al.(J Sci Comput 89:1–42,2021),a model of mixed-order form is adopted here that consists of the first-order PDE part for Maxwell’s equations coupled with the second-order ODE part(i.e.,the auxiliary differential equations)modeling the linear and nonlinear dispersion in the material.The main contribution is a new numerical strategy to treat the Kerr and Raman nonlinearities to achieve provable energy stability property within a second-order temporal discretization.A nodal discontinuous Galerkin(DG)method is further applied in space for efficiently handling nonlinear terms at the algebraic level,while preserving the energy stability and achieving high-order accuracy.Indeed with d_(E)as the number of the components of the electric field,only a d_(E)×d_(E)nonlinear algebraic system needs to be solved at each interpolation node,and more importantly,all these small nonlinear systems are completely decoupled over one time step,rendering very high parallel efficiency.We evaluate the proposed schemes by comparing them with the methods in Bokil et al.(2017)and Lyu et al.(2021)(implemented in nodal form)regarding the accuracy,computational efficiency,and energy stability,by a parallel scalability study,and also through the simulations of the soliton-like wave propagation in one dimension,as well as the spatial-soliton propagation and two-beam interactions modeled by the two-dimensional transverse electric(TE)mode of the equations.

Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.

Adaptive Sparse Grid Discontinuous Galerkin Method:Review and Software Implementation

This paper reviews the adaptive sparse grid discontinuous Galerkin(aSG-DG)method for computing high dimensional partial differential equations(PDEs)and its software implementation.The C++software package called AdaM-DG,implementing the aSG-DG method,is available on GitHub at https://github.com/JuntaoHuang/adaptive-multiresolution-DG.The package is capable of treating a large class of high dimensional linear and nonlinear PDEs.We review the essential components of the algorithm and the functionality of the software,including the multiwavelets used,assembling of bilinear operators,fast matrix-vector product for data with hierarchical structures.We further demonstrate the performance of the package by reporting the numerical error and the CPU cost for several benchmark tests,including linear transport equations,wave equations,and Hamilton-Jacobi(HJ)equations.

Electroacupuncture with different waveforms for primary dysmenorrhea:A randomized controlled trial

Objective To observe and compare the clinical effects of different electroacupuncture waveforms on primary dysmenorrhea.Methods This was a prospective,randomized,three-group,parallel-controlled trial.Participants with primary dysmenorrhea were randomly divided into dense-sparse wave,continuous wave,and discontinuous wave groups in a 1:1:1 ratio.Two lateral Ciliao(BL 32)points were used.All three groups started treatment 3–5 days before menstruation,once a day for six sessions per course of treatment,one course of treatment per menstrual cycle,and three menstrual cycles.The primary outcome measure was the proportion with an average visual analog scale(VAS)score reduction of≥50%from baseline for dysmenorrhea in the third menstrual cycle during treatment.The secondary outcome measures included changes in dysmenorrhea VAS scores,Cox Menstrual Symptom Scale scores and the proportion of patients taking analgesic drugs.Results The proportion of cases where the average VAS score for dysmenorrhea decreased by≥50%from baseline in the third menstrual cycle was not statistically significant(P>.05).Precisely 30 min after acupuncture and regarding immediate analgesia on the most severe day of dysmenorrhea,there was a statistically significant difference in the dense-sparse wave group compared with the other two groups during the third menstrual cycle(P<.05).Additionally,there was a statistically significant difference between the dense-sparse wave and discontinuous wave groups 24 h after acupuncture(P<.05).Conclusions Waveform electroacupuncture can alleviate primary dysmenorrhea and its related symptoms in patients.The three groups showed similar results in terms of short-and long-term analgesic efficacy and a reduction in the number of patients taking analgesic drugs.Regarding achieving immediate analgesia,the dense-sparse wave group was slightly better than the other two groups.

Bound-Preserving Discontinuous Galerkin Methods with Modified Patankar Time Integrations for Chemical Reacting Flows

In this paper,we develop bound-preserving discontinuous Galerkin(DG)methods for chemical reactive flows.There are several difficulties in constructing suitable numerical schemes.First of all,the density and internal energy are positive,and the mass fraction of each species is between 0 and 1.Second,due to the rapid reaction rate,the system may contain stiff sources,and the strong-stability-preserving explicit Runge-Kutta method may result in limited time-step sizes.To obtain physically relevant numerical approximations,we apply the bound-preserving technique to the DG methods.Though traditional positivity-preserving techniques can successfully yield positive density,internal energy,and mass fractions,they may not enforce the upper bound 1 of the mass fractions.To solve this problem,we need to(i)make sure the numerical fluxes in the equations of the mass fractions are consistent with that in the equation of the density;(ii)choose conservative time integrations,such that the summation of the mass fractions is preserved.With the above two conditions,the positive mass fractions have summation 1,and then,they are all between 0 and 1.For time discretization,we apply the modified Runge-Kutta/multi-step Patankar methods,which are explicit for the flux while implicit for the source.Such methods can handle stiff sources with relatively large time steps,preserve the positivity of the target variables,and keep the summation of the mass fractions to be 1.Finally,it is not straightforward to combine the bound-preserving DG methods and the Patankar time integrations.The positivity-preserving technique for DG methods requires positive numerical approximations at the cell interfaces,while Patankar methods can keep the positivity of the pre-selected point values of the target variables.To match the degree of freedom,we use polynomials on rectangular meshes for problems in two space dimensions.To evolve in time,we first read the polynomials at the Gaussian points.Then,suitable slope limiters can be applied to enforce the positivity of the solutions at those points,which can be preserved by the Patankar methods,leading to positive updated numerical cell averages.In addition,we use another slope limiter to get positive solutions used for the bound-preserving technique for the flux.Numerical examples are given to demonstrate the good performance of the proposed schemes.

A Provable Positivity-Preserving Local Discontinuous Galerkin Method for the Viscous and Resistive MHD Equations

In this paper,we construct a high-order discontinuous Galerkin(DG)method which can preserve the positivity of the density and the pressure for the viscous and resistive magnetohydrodynamics(VRMHD).To control the divergence error in the magnetic field,both the local divergence-free basis and the Godunov source term would be employed for the multi-dimensional VRMHD.Rigorous theoretical analyses are presented for one-dimensional and multi-dimensional DG schemes,respectively,showing that the scheme can maintain the positivity-preserving(PP)property under some CFL conditions when combined with the strong-stability-preserving time discretization.Then,general frameworks are established to construct the PP limiter for arbitrary order of accuracy DG schemes.Numerical tests demonstrate the effectiveness of the proposed schemes.

HetNets Under Decoupled Uplink and Downlink Access with UE Random Discontinuous Transmission: Local Delay and Energy Efficiency

Due to the limited uplink capability in heterogeneousnetworks (HetNets), the decoupled uplinkand downlink access (DUDA) mode has recently beenproposed to improve the uplink performance. In thispaper, the random discontinuous transmission (DTX)at user equipment (UE) is adopted to reduce the interferencecorrelation across different time slots. By utilizingstochastic geometry, we analytically derive themean local delay and energy efficiency (EE) of an uplinkHetNet with UE random DTX scheme under theDUDA mode. These expressions are further approximatedas closed forms under reasonable assumptions.Our results reveal that under the DUDA mode, there isan optimal EE with respect to mute probability underthe finite local delay constraint. In addition, with thesame finite mean local delay as under the coupled uplinkand downlink access (CUDA) mode, the HetNetsunder the DUDA mode can achieve a higher EE witha lower mute probability.