THE SMOOTHING EFFECT IN SHARP GEVREY SPACE FOR THE SPATIALLY HOMOGENEOUS NON-CUTOFF BOLTZMANN EQUATIONS WITH A HARDPOTENTIAL

In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.

Rational manipulation of electrolyte to induce homogeneous SEI on hard carbon anode for sodium-ion battery

Sodium-ion batteries (SIBs) have great potential to be the next major energy storage devices due to their obvious advantages and developing advanced electrodes and electrolytes is urgently necessary to promote its future industrialization.However,hard carbon as a state-of-the-art anode of SIBs still suffers from the low initial Coulomb efficiency and unsatisfactory rate capability,which could be improved by forming desirable solid electrolyte interphases (SEI) to some extent.Indeed,the chemistry and morphology of these interfacial layers are fundamental parameters affecting the overall battery operation,and optimizing the electrolyte to dictate the quality of SEI on hard carbon is a key strategy.Hence,this review summarizes the recent research on SEI design by electrolyte manipulation from solvents,salts,and additives.It also presents some potential mechanisms of SEI formation in various electrolyte systems.Besides,the current advanced characterization techniques for electrolyte and SEI structure analyses have been comprehensively discussed.Lastly,current challenges and future perspectives of SEI formation on hard carbon anode for SIBs are provided from the viewpoints of its compositions,evolution processes,structures,and characterization techniques,which will promote SEI efficient manipulation and improve the performance of hard carbon,and further contribute to the development of SIBs.

Synthesis strategies of hard carbon anodes for sodium-ion batteries

Sodium-ion battery(SIB)is an ideal candidate for large-scale energy storage due to high abundant sodium sources,relatively high energy density,and potentially low costs.Hard carbons,as one of the most promising anodes,could deliver high plateau capacities at low potentials,which boosts the energy densities of SIBs.Their slope capacities have been demonstrated from the defect adsorption of sodium ions,while the plateau capacity depends highly on intercalation and pore filling.Nevertheless,the specific structures of sodium ions stored in hard carbons have not been clarified,namely active sites of adsorption,intercalation,and pore-filling mechanisms.Therefore,delicate synthesis methods are required to prepare hard carbons with controllable specific structures,along with elucidating the precise active sites for enhancing the Na-ion storage performance.To offer databases for future designs,we summarized the synthesis strategies of hard carbon anodes for constructing active sites of plateau capacities.Synthesis methods were highlighted with corresponding influences on the meticulous structures of hard carbons and Na-ion storage behaviors.Last but not least,perspectives were proposed for developing hard carbon anodes from the points of research and practical applications.

High-efficiently doping nitrogen in kapok fiber-derived hard carbon used as anode materials for boosting rate performance of sodium-ion batteries

The engineering of plant-based precursor for nitrogen doping has become one of the most promising strategies to enhance rate capability of hard carbon materials for sodium-ion batteries;however,the poor rate performance is mainly caused by lack of pyridine nitrogen,which often tends to escape because of high temperature in preparation process of hard carbon.In this paper,a high-rate kapok fiber-derived hard carbon is fabricated by cross-linking carboxyl group in 2,6-pyridinedicarboxylic acid with the exposed hydroxyl group on alkalized kapok with assistance of zinc chloride.Specially,a high nitrogen doping content of 4.24%is achieved,most of which are pyridine nitrogen;this is crucial for improving the defect sites and electronic conductivity of hard carbon.The optimized carbon with feature of high nitrogen content,abundant functional groups,degree of disorder,and large layer spacing exhibits high capacity of 401.7 mAh g^(−1)at a current density of 0.05 A g^(−1),and more importantly,good rate performance,for example,even at the current density of 2 A g^(−1),a specific capacity of 159.5 mAh g^(−1)can be obtained.These findings make plant-based hard carbon a promising candidate for commercial application of sodium-ion batteries,achieving high-rate performance with the enhanced pre-cross-linking interaction between plant precursors and dopants to optimize aromatization process by auxiliary pyrolysis.

Assessment and control of the mine tremor disaster induced by the energy accumulation and dispersion of thick-hard roofs

In order to solve the problem that current theory models cannot accurately describe thick-hard roof(THR)elastic energy and assess the mine tremor disasters,a theoretical method,a Timoshenko beam theory on Winkler foundation was adopted to establish the THR’s periodic breaking model.The superposition principle was used for this complex model to derive the calculation formulas of the elastic energy and impact load on hydraulic supports.Then,the influence of roof thickness h,cantilever length L_(1),and load q on THR’s elastic energy and impact load was analyzed.And,the effect of mine tremor disasters was assessed.Finally,it is revealed that:(1)The THR’s elastic energy U exhibits power-law variations,with the fitted relationships U=0.0096L_(1)^(3.5866^),U=5943.9h^(-1.935),and U=21.049q^(2).(2)The impact load on hydraulic supports F_(ZJ) increases linearly with an increase in the cantilever length,thickness,and applied load.The fitted relationships are F_(ZJ)=1067.3L_(1)+6361.1,F_(ZJ)=125.89h+15100,and F_(ZJ)=10420q+3912.6.(3)Ground hydraulic fracturing and liquid explosive deep-hole blasting techniques effectively reduce the THR’s cantilever length at periodic breakages,thus eliminating mine tremor disasters.

Influencing factors analysis of hard limestone reformation and strength weakening under acidic effect

Roof disaster has always been an important factor restricting coal mine safety production.Acidic effect can reform the rock mass structure to weaken the macroscopic strength characteristics,which is an effective way to control the hard limestone roof.In this study,the effects of various factors on the reaction characteristics and mechanical properties of limestone were analyzed.The results show that the acid with stronger hydrogen production capacity after ionization(pK_(a)<0)has more prominent damage to the mineral grains of limestone.When pKa increases from−8.00 to 15.70,uniaxial compressive strength and elastic modulus of limestone increase by 117.22%and 75.98%.The influence of acid concentration is manifested in the dissolution behavior of mineral crystals,the crystal defects caused by large-scale acid action will lead to the deterioration of limestone strength,and the strength after 15%concentration reformation can be reduced by 59.42%.The effect of acidification time on limestone has stages and is the most obvious in the initial metathesis reaction stage(within 60 min).The key to the strength damage of acidified limestone is the participation of hydrogen ions in the reaction system.Based on the analytic hierarchy process method,the influence weights of acid type,acid concentration and acidification time on strength are 24.30%,59.54% and 16.16%,respectively.The research results provide theoretical support for the acidification control of hard limestone roofs in coal mines.

Regulating solid electrolyte interphase film on fluorinedoped hard carbon anode for sodium-ion battery

For the performance optimization strategies of hard carbon,heteroatom doping is an effective way to enhance the intrinsic transfer properties of sodium ions and electrons for accelerating the reaction kinetics.However,the previous work focuses mainly on the intrinsic physicochemical property changes of the material,but little attention has been paid to the resulting interfacial regulation of the electrode surface,namely the formation of solid electrolyte interphase(SEI)film.In this work,element F,which has the highest electronegativity,was chosen as the doping source to,more effectively,tune the electronic structure of the hard carbon.The effect of F-doping on the physicochemical properties of hard carbon was not only systematically analyzed but also investigated with spectroscopy,optics,and in situ characterization techniques to further verify that appropriate F-doping plays a positive role in constructing a homogenous and inorganic-rich SEI film.The experimentally demonstrated link between the electronic structure of the electrode and the SEI film properties can reframe the doping optimization strategy as well as provide a new idea for the design of electrode materials with low reduction kinetics to the electrolyte.As a result,the optimized sample with the appropriate F-doping content exhibits the best electrochemical performance with high capacity(434.53 mA h g^(-1)at 20mA g^(-1))and excellent rate capability(141 mAh g^(-1)at 400 mA g^(-1)).

The hard X-ray nanoprobe beamline at the SSRF

The hard X-ray nanoprobe beamline BL13U is a phase-Ⅱ beamline project at the Shanghai Synchrotron Radiation Facility.The beamline aims to enable comprehensive experiments at high spatial resolutions ranging from 50 to 10 nm. The X-ray energy range of the beamline, 5–25 keV, can detect most elements in the periodic table. Two operating modes were designed to accommodate the experimental requirements of high-energy resolution or high photon flux, respectively. X-ray nanofluorescence, nanodiffraction, and coherent diffraction imaging are developed as the main experimental techniques for BL13U. This paper describes the beamline optics, end station configurations, experimental methods under development, and preliminary test results. This comprehensive overview aims to provide a clear understanding of the beamline capabilities and potential applications.

Hybrid hard carbon framework derived from polystyrene bearing distinct molecular crosslinking for enhanced sodium storage

Exploiting high-performance yet low-cost hard carbon anodes is crucial to advancing the state-of-the-art sodium-ion batteries.However,the achievement of superior initial Coulombic efficiency(ICE)and high Na-storage capacity via low-temperature carbonization remains challenging due to the presence of tremendous defects with few closed pores.Here,a facile hybrid carbon framework design is proposed from the polystyrene precursor bearing distinct molecular bridges at a low pyrolysis temperature of 800℃ via in situ fusion and embedding strategy.This is realized by integrating triazine-and carbonylcrosslinked polystyrene nanospheres during carbonization.The triazine crosslinking allows in situ fusion of spheres into layered carbon with low defects and abundant closed pores,which serves as a matrix for embedding the well-retained carbon spheres with nanopores/defects derived from carbonyl crosslinking.Therefore,the hybrid hard carbon with intimate interface showcases synergistic Na ions storage behavior,showing an ICE of 70.2%,a high capacity of 279.3 mAh g^(-1),and long-term 500 cycles,superior to carbons from the respective precursor and other reported carbons fabricated under the low carbonization temperature.The present protocol opens new avenues toward low-cost hard carbon anode materials for high-performance sodiumion batteries.

Gravel hardness effect on compaction characteristics of gravelly soil

The compaction characteristics of gravelly soil are affected by gravel hardness.To investigate the evolution and influencing mechanism of different gravel hardness on the compaction characteristics of gravelly soil,heavy compaction tests and crushing tests were conducted on gravelly soils with gravels originated from hard,soft and extremely soft rocks.According to orthogonal experiments and variance analysis,it was found that hardness has a significant impact on the maximum dry density of gravelly soil,followed by gravel content,and lastly,moisture content.For gravel compositions with an average saturated uniaxial compressive strength less than 60 MPa,the order of compacted maximum dry density is soft gravels>hard gravels>extremely soft gravels.Each type of gravelly soil has a threshold for gravel content,with 60%for hard and soft gravels and 50%for extremely soft gravels.Beyond these thresholds,the compacted dry density decreases significantly.There is a certain interaction between hardness,gravel content,and moisture content.Higher hardness increases the influence of gravel content,whereas lower hardness increases the influence of moisture content.Gravelly soils with the coarse aggregate(CA)between 0.7 and 0.8 typically achieve higher dry densities after compaction.In addition,the prediction equations for the particle breakage rate and CA ratio in the Bailey method were proposed to estimate the compaction performance of gravelly soil preliminarily.The results further revealed the compaction mechanism of different gravelly soils and can provide reference for subgrade filling construction.

Failure mechanism and infrared radiation characteristic of hard siltstone induced by stratification effect

The deformation in sedimentary rock induced by train loads has potential threat to the safe operation of tunnels. This study investigated the influence of stratification structure on the infrared radiation and temporal damage mechanism of hard siltstone. The uniaxial compression tests, coupled with acoustic emission(AE) and infrared radiation temperature(IRT) were conducted on siltstones with different stratification effects. The results revealed that the stratigraphic structure significantly affects the stress-strain response and strength degradation characteristics. The mechanical parameters exhibit anisotropy characteristics, and the stratification effect exhibits a negative correlation with the cracking stress and peak stress. The failure modes caused by the stratification effect show remarkable anisotropic features, including splitting failure(Ⅰ: 0°-22.50°, Ⅱ: 90°), composite failure(45°), and shearing failure(67.50°). The AE temporal sequences demonstrate a stepwise response characteristic to the loading stress level. The AE intensity indicates that the stress sensitivity of shearing failure and composite failure is generally greater than that of splitting failure. The IRT field has spatiotemporal migration and progressive dissimilation with stress loading and its dissimilation degree increases under higher stress levels. The stronger the stratification effect, the greater the dissimilation degree of the IRT field. The abnormal characteristic points of average infrared radiation temperature(AIRT) variance at local stress drop and peak stress can be used as early and late precursors to identify fracture instability. Theoretical analysis shows that the competitive relationship between compaction strengthening and fracturing damage intensifies the dissimilation of the infrared thermal field for an increasing stress level. The present study provides a theoretical reference for disaster warnings in hard sedimentary rock mass.

Free radicals trigger the closure of open pores in lignin-derived hard carbons toward improved sodium-storage capacity

The chemical activation of various precursors is effective for creating additional closed pores in hard carbons for sodium storage.However,the formation mechanism of closed pores under the influence of pore-forming agents is not well understood.Herein,an effective chemical activation followed by a high-temperature self-healing strategy is employed to generate interconnected closed pores in lignin-derived hard carbon(HCs).By systematic experimental design combined with electron paramagnetic res-onance spectroscopy,it can be found that the content of free radicals in the carbon matrix influences the closure of open pores at high temperatures.Excessively high activation temperature(>700 C)leads to a low free radical concentration,making it difficult to achieve self-healing of open pores at high tempera-tures.By activation at 700°C,a balance between pore making and self-healing is achieved in the final hard carbon.A large number of free radicals triggers rapid growth and aggregation of carbon microcrys-tals,blocking pre-formed open micropores and creating additional interconnected closed pores in as-obtained hard carbons.As a result,the optimized carbon anode(LK-700-1300)delivers a high reversible capacity of 330.8 mA h g^(-1) at 0.03 A g^(-1),which is an increase of 86 mA h g^(-1) compared to the pristine lignin-derived carbon anode(L-700-1300),and exhibits a good rate performance(202.1 mA h g^(-1) at 1 A g^(-1)).This work provides a universal and effective guidance for tuning closed pores of hard carbons from otherprecursors.

Influence of heat input on microhardness and microstructure across the welding interface between stainless steel and low alloy steel

The welding interface is crucial to the service safety of dissimilar metal weld(DMW)joints between stainless steel(SS)and low alloy(LA)steel.Different status of welding interfaces was prepared by cladding SS consumables to LA steel substrates with different heat inputs via tungsten inert gas arc welding(TIG),followed by a series of microstructural characterizations and hardness tests.Results showed that a hardening and transition layer(TL)would be generated along the welding interface,and the width and hardening degree of the TL would increase with the heat input.Meanwhile,heavy load hardness tests showed that highly severe inhomogeneous plastic deformation and the microcrack would be generated in the interfacial region and the welding interface respectively in the highest heat input sample(1.03 kJ/mm).These results indicate that the increase in heat input would deteriorate the bonding performance of DMW joints.Further microstructural observations showed that the higher hardening degree of the highest heat input sample was mainly attributed to the stronger grain boundary,solution,and dislocation strengthening effects.

Physical and numerical investigations of target stratum selection for ground hydraulic fracturing of multiple hard roofs

Ground hydraulic fracturing plays a crucial role in controlling the far-field hard roof,making it imperative to identify the most suitable target stratum for effective control.Physical experiments are conducted based on engineering properties to simulate the gradual collapse of the roof during longwall top coal caving(LTCC).A numerical model is established using the material point method(MPM)and the strain-softening damage constitutive model according to the structure of the physical model.Numerical simulations are conducted to analyze the LTCC process under different hard roofs for ground hydraulic fracturing.The results show that ground hydraulic fracturing releases the energy and stress of the target stratum,resulting in a substantial lag in the fracturing of the overburden before collapse occurs in the hydraulic fracturing stratum.Ground hydraulic fracturing of a low hard roof reduces the lag effect of hydraulic fractures,dissipates the energy consumed by the fracture of the hard roof,and reduces the abutment stress.Therefore,it is advisable to prioritize the selection of the lower hard roof as the target stratum.

Sulfur doped iron-nitrogen-hard carbon nanosheets as efficient and robust noble metal-free catalysts for oxygen reduction reaction in PEMFC

Transition metal-nitrogen-carbon(M-N-C)as a promising substitute for the conventional noble metalbased catalyst still suffers from low activity and durability for oxygen reduction reaction(ORR)in proton exchange membrane fuel cells(PEMFCs).To tackle the issue,herein,a new type of sulfur-doped ironnitrogen-hard carbon(S-Fe-N-HC)nanosheets with high activity and durability in acid media were developed by using a newly synthesized precursor of amide-based polymer with Fe ions based on copolymerizing two monomers of 2,5-thiophene dicarboxylic acid(TDA)as S source and 1,8-diaminonaphthalene(DAN)as N source via an amination reaction.The as-synthesized S-Fe-N-HC features highly dispersed atomic Fe Nxmoieties embedded into rich thiophene-S doped hard carbon nanosheets filled with highly twisted graphite-like microcrystals,which is distinguished from the majority of M-N-C with soft or graphitic carbon structures.These unique characteristics endow S-Fe-N-HC with high ORR activity and outstanding durability in 0.5 M H_(2)SO_(4).Its initial half-wave potential is 0.80 V and the corresponding loss is only 21 m V after 30,000 cycles.Meanwhile,its practical PEMFC performance is a maximum power output of 628.0 mW cm^(-2)and a slight power density loss is 83.0 m W cm^(-2)after 200-cycle practical operation.Additionally,theoretical calculation shows that the activity of Fe Nxmoieties on ORR can be further enhanced by sulfur doping at meta-site near FeN_(4)C.These results evidently demonstrate that the dual effect of hard carbon substrate and S doping derived from the precursor platform of amid-polymers can effectively enhance the activity and durability of Fe-N-C catalysts,providing a new guidance for developing advanced M-N-C catalysts for ORR.

Combined blasting for protection of gob-side roadway with thick and hard roof

The deformation control of surrounding rock in gobside roadway with thick and hard roof poses a significant challenge to the safety and efficiency of coal mining.To address this issue,a novel approach combining directional and non-directional blasting techniques,known as combined blasting,was proposed.This study focuses on the experimental investigation of the proposed method in the 122108 working face in Caojiatan Coal Mine as the engineering background.The initial phase of the study involves physical model experiments to reveal the underlying mechanisms of combined blasting for protecting gob-side roadway with thick and hard roof.The results demonstrate that this approach effectively accelerates the collapse of thick and hard roofs,enhances the fragmentation and expansion coefficient of gangue,facilitates the filling of the goaf with gangue,and provides support to the overlying strata,thus reducing the subsidence of the overlying strata above the goaf.Additionally,the method involves cutting the main roof into shorter beams to decrease the stress and disrupt stress transmission pathways.Subsequent numerical simulations were conducted to corroborate the findings of the physical model experiments,thus validating the accuracy of the experimental results.Furthermore,field engineering experiments were performed,affirming the efficacy of the combined blasting method in mitigating the deformation of surrounding rock and achieving the desired protection of the gob-side roadway.

A novel nano-grade organosilicon polymer:Improving airtightness of compressed air energy storage in hard rock formations

Enhancing cavern sealing is crucial for improving the efficiency of compressed air energy storage(CAES)in hard rock formations.This study introduced a novel approach using a nano-grade organosilicon polymer(NOSP)as a sealant,coupled with an air seepage evaluation model that incorporates Knudsen diffusion.Moreover,the initial coating application methods were outlined,and the advantages of using NOSP compared to other sealing materials,particularly regarding cost and construction techniques,were also examined and discussed.Experimental results indicated a significant reduction in permeability of rock specimens coated with a 7–10μm thick NOSP layer.Specifically,under a 0.5 MPa pulse pressure,the permeability decreased to less than 1 n D,and under a 4 MPa pulse pressure,it ranged between4.5×10^(-6)–5.5×10^(-6)m D,marking a 75%–80%decrease in granite permeability.The sealing efficacy of NOSP surpasses concrete and is comparable to rubber materials.The optimal viscosity for application lies between 95 and 105 KU,and the coating thickness should ideally range from 7 to 10μm,applied to substrates with less than 3%porosity.This study provides new insights into air transport and sealing mechanisms at the pore level,proposing NOSP as a cost-effective and simplified solution for CAES applications.

Ground response and failure mechanism of gob-side entry by roof cutting with hard main roof

This study is the result of long-term efforts of the authors’team to assess ground response of gob-side entry by roof cutting(GSERC)with hard main roof,aiming at scientific control for GSERC deformation.A comprehensive field measurement program was conducted to determine entry deformation,roof fracture zone,and anchor bolt(cable)loading.The results indicate that GSERC deformation presents asymmetric characteristics.The maximum convergence near roof cutting side is 458 mm during the primary use process and 1120 mm during the secondary reuse process.The entry deformation is closely associated with the primary development stage,primary use stage,and secondary reuse stage.The key block movement of roof cutting structure,a complex stress environment,and a mismatch in the supporting design scheme are the failure mechanism of GSERC.A controlling ideology for mining states,including regional and stage divisions,was proposed.Both dynamic and permanent support schemes have been implemented in the field.Engineering practice results indicate that the new support scheme can efficiently ensure long-term entry safety and could be a reliable approach for other engineering practices.

Hard-carbon hybrid Li-ion/metal anode enabled by preferred mesoporous uniform lithium growth mechanism

To achieve high energy density in lithium batteries,the construction of lithium-ion/metal hybrid anodes is a promising strategy.In particular,because of the anisotropy of graphite,hybrid anode formed by graphite/Li metal has low transport kinetics and is easy to causes the growth of lithium dendrites and accumulation of dead Li,which seriously affects the cycle life of batteries and even causes safety problems.Here,by comparing graphite with two types of hard carbon,it was found that hybrid anode formed by hard carbon and lithium metal,possessing more disordered mesoporous structure and lithophilic groups,presents better performance.Results indicate that the mesoporous structure provides abundant active site and storage space for dead lithium.With the synergistic effect of this structure and lithophilic functional groups(–COOH),the reversibility of hard carbon/lithium metal hybrid anode is maintained,promoting uniform deposition of lithium metal and alleviating formation of lithium dendrites.The hybrid anode maintains a 99.5%Coulombic efficiency(CE)after 260 cycles at a specific capacity of 500 m Ah/g.This work provides new insights into the hybrid anodes formed by carbon-based materials and lithium metal with high specific energy and fast charging ability.

Deformation characteristics and damage ontologies of soft and hard composite rock masses under impact loading

As one of the most common occurring geological landforms in deep rock formations, the dynamic mechanical properties of layered composite rock bodies under impact loading have been widely studied by scholars. To study the dynamic properties of soft and hard composite rocks with different thickness ratios, this paper utilizes cement, quartz sand and gypsum powder to construct soft and hard composite rock specimens and utilizes a combination of indoor tests, numerical calculations, and theoretical analyses to investigate the mechanical properties of soft and hard composite rock bodies. The test results reveal that:(1) When the proportion of hard rock increases from 20% to 50%, the strength of the combined rock body increases by 69.14 MPa and 87 MPa when the hard rock face and soft rock face are loaded, respectively;however, when the proportion of hard rock is the same, the compressive strength of the hard rock face impact is 9%-17% greater than that of the soft rock face impact;(2) When a specimen of soft and hard combined rock body is subjected to impact loading, the damage mode involves mixed tension and shear damage, and the cracks generally first appear at the ends of the specimen, then develop on the laminar surface from the impact surface, and finally end in the overall damage of the soft rock part. The development rate and the total number of cracks in the same specimen when the hard rock face is impacted are significantly greater than those when the soft rock face is impacted;(3) By introducing Weibull’s statistical strength theory to establish the damage variables of soft-hard combined rock bodies, combined with the DP strength criterion, the damage model and the Kelvin body are concatenated to obtain a statistical damage constitutive model, which can better fit the full stress-strain curve of soft-hard combined rock body specimens under a single impact load.