Radial solution of the Logarithmic Laplacian system

The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the radial symmetry of the solution of the Logarithmic Laplacian system is obtained.

Prediction of Planing Craft Motion Based on Grey System Theory

In order to minimize the harm caused by the instability of a planing craft, a motion prediction model is essential. This paper analyzed the feasibility of using an MGM（1,N） model in grey system theory to predict planing craft motion and carried out the numerical simulation experiment. According to the characteristics of planing craft motion, a recurrence formula was proposed of the parameter matrix of an MGMfl,N） model. Using this formula, data can be updated in real-time without increasing computational complexity significantly. The results of numerical simulation show that using an MGM（1,N） model to predict planing motion is feasible and useful for prediction. So the method proposed in this study can reflect the planing craft motion mechanism successfully, and has rational and effective functions of forecasting and analyzing trends.

2-D distributed pose estimation of multi-agent systems using bearing measurements

This article studies distributed pose(orientation and position)estimation of leader–follower multi-agent systems over𝜅-layer graphs in 2-D plane.Only the leaders have access to their orientations and positions,while the followers can measure the relative bearings or(angular and linear)velocities in their unknown local coordinate frames.For the orientation estimation,the local relative bearings are used to obtain the relative orientations among the agents,based on which a distributed orientation estimation algorithm is proposed for each follower to estimate its orientation.For the position estimation,the local relative bearings are used to obtain the position constraints among the agents,and a distributed position estimation algorithm is proposed for each follower to estimate its position by solving its position constraints.Both the orientation and position estimation errors converge to zero asymptotically.A simulation example is given to verify the theoretical results.

A novel method for simulating nuclear explosion with chemical explosion to form an approximate plane wave: Field test and numerical simulation

A nuclear explosion in the rock mass medium can produce strong shock waves,seismic shocks,and other destructive effects,which can cause extreme damage to the underground protection infrastructures.With the increase in nuclear explosion power,underground protection engineering enabled by explosion-proof impact theory and technology ushered in a new challenge.This paper proposes to simulate nuclear explosion tests with on-site chemical explosion tests in the form of multi-hole explosions.First,the mechanism of using multi-hole simultaneous blasting to simulate a nuclear explosion to generate approximate plane waves was analyzed.The plane pressure curve at the vault of the underground protective tunnel under the action of the multi-hole simultaneous blasting was then obtained using the impact test in the rock mass at the site.According to the peak pressure at the vault plane,it was divided into three regions:the stress superposition region,the superposition region after surface reflection,and the approximate plane stress wave zone.A numerical simulation approach was developed using PFC and FLAC to study the peak particle velocity in the surrounding rock of the underground protective cave under the action of multi-hole blasting.The time-history curves of pressure and peak pressure partition obtained by the on-site multi-hole simultaneous blasting test and numerical simulation were compared and analyzed,to verify the correctness and rationality of the formation of an approximate plane wave in the simulated nuclear explosion.This comparison and analysis also provided a theoretical foundation and some research ideas for the ensuing study on the impact of a nuclear explosion.

A review of rockburst:Insights from engineering sites to theoretical investigations

Rockburst has perennially posed a formidable challenge to the stability of underground engineering works,particularly under conditions of deep-seated high stress.This paper provides a comprehensive review of recent advancements in on-site research related to rockburst occurrences,covering on-site case analyses,monitoring methodologies,early warning systems,and risk(proneness)evaluation.Initially,the concepts and classifications of rockburst based on on-site understanding were summarized.The influences of structural planes(in various spatial distribution combinations),in-situ stress(particularly magnitude and direction of the principal stress),dynamic disturbances,and excavation profiles on rockburst were thoroughly assessed and discussed through the analysis of published rockburst cases and on-site survey results.Subsequently,a compendium of commonly employed on-site monitoring techniques was outlined,delineating their respective technical attributes.Particular emphasis is accorded to the efficacy of microseismic monitoring technology and its prospective utility in facilitating dynamic rockburst early warning mechanisms.Building upon this foundation,the feasibility of assessing rockburst propensity while considering on-site variables is verified,encompassing the selection and quantitative evaluation of pertinent indicators.Ultimately,a comprehensive synthesis of the paper is presented,alongside the articulation of prospective research goals for the future.

Effect of Modulus Heterogeneity on the Equilibrium Shape and Stress Field ofαPrecipitate in Ti-6Al-4V

For media with inclusions(e.g.,precipitates,voids,reinforcements,and others),the difference in lattice parameter and the elastic modulus between the matrix and inclusions cause stress concentration at the interfaces.These stress fields depend on the inclusions’size,shape,and distribution and will respond instantly to the evolving microstructure.This study develops a phase-field model concerningmodulus heterogeneity.The effect of modulus heterogeneity on the growth process and equilibrium state of theαplate in Ti-6Al-4V during precipitation is evaluated.Theαprecipitate exhibits strong anisotropy in shape upon cooling due to the interplay of the elastic strain and interfacial energy.The calculated orientation of the habit plane using the homogeneous modulus ofαphase shows the smallest deviation fromthat of the habit plane observed in the experiment,compared to the case where the homogeneous modulus ofβphase is adopted.In addition,the equilibrium volume ofαphase within the systemusing homogeneousβmodulus exhibits the largest dependency on the applied stresses.The stress fields across theα/βinterface are further calculated under the assumption of modulus heterogeneity and compared to those using homogeneous modulus of eitherαorβphase.This study provides an essential theoretical basis for developing mechanics models concerning systems with heterogeneous structures.

THE NONLINEAR STABILITY OF PLANE PARALLEL SHEAR FLOWS WITH RESPECT TO TILTED PERTURBATIONS

The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods.Tilted perturbation refers to the fact that perturbations form an angleθ∈(0,π/2)with the direction of the basic flows.By defining an energy functional,it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for tilted streamwise perturbation when the Reynolds number is below a certain critical value and the boundary conditions are either rigid or stress-free.In the case of stress-free boundaries,by taking advantage of the poloidal-toroidal decomposition of a solenoidal field to define energy functionals,it can be even shown that plane parallel shear flows are unconditionally nonlinearly exponentially stable for all Reynolds numbers,where the tilted perturbation can be either spanwise or streamwise.

Coupling of quasi-localized and phonon modes in glasses at low frequency

Boson peak of glasses,a THz vibrational excess compared to Debye squared-frequency law,remains mysterious in condensed-matter physics and material science.It appears in many different kinds of glassy matters and is also argued to exist in damped crystals.A consensus is that boson peak originates from the coupling of the(quasi)-localized non-phonon modes and the plane-wave-like phonon modes,but the coupling behavior is still not fully understood.In this paper,by modulating the content of localized modes and the frequencies of phonon modes,the coupling is clearly reflected in the localization and anharmonicity of low-frequency vibrational modes.The coupling enhances with increasing cooling rate and sample size.For finite sample size,phonon modes do not fully intrude into the low frequency to form a dense spectrum and they are not sufficiently coupled to the localized modes,thus there is no Debye level and boson peak is ill-defined.This suggestion remains valid in the presence of thermal motions induced by temperature,even though the anharmonicity comes into play.Our results point to the coupling of quasi-localized and phonon modes and its relation to the boson peak.

Nonlinear constitutive models of rock structural plane and their applications

Structural planes play an important role in controlling the stability of rock engineering,and the influence of structural planes should be considered in the design and construction process of rock engineering.In this paper,mechanical properties,constitutive theory,and numerical application of structural plane are studied by a combination method of laboratory tests,theoretical derivation,and program development.The test results reveal the change laws of various mechanical parameters under different roughness and normal stress.At the pre-peak stage,a non-stationary model of shear stiffness is established,and threedimensional empirical prediction models for initial shear stiffness and residual stage roughness are proposed.The nonlinear constitutive models are established based on elasto-plastic mechanics,and the algorithms of the models are developed based on the return mapping algorithm.According to a large number of statistical analysis results,empirical prediction models are proposed for model parameters expressed by structural plane characteristic parameters.Finally,the discrete element method(DEM)is chosen to embed the constitutive models for practical application.The running programs of the constitutive models have been compiled into the discrete element model library.The comparison results between the proposed model and the Mohr-Coulomb slip model show that the proposed model can better describe nonlinear changes at different stages,and the predicted shear strength,peak strain and shear stiffness are closer to the test results.The research results of the paper are conducive to the accurate evaluation of structural plane in rock engineering.

A monolithic integrated medium wave Mercury Cadmium Telluride polarimetric focal plane array

A medium wave(MW)640×512(25μm)Mercury Cadmium Telluride(HgCdTe)polarimetric focal plane array(FPA)was demonstrated.The micro-polarizer array(MPA)has been carefully designed in terms of line grating structure optimization and crosstalk suppression.A monolithic fabrication process with low damage was explored,which was verified to be compatible well with HgCdTe devices.After monolithic integration of MPA,NETD<9.5 mK was still maintained.Furthermore,to figure out the underlying mechanism that dominat⁃ed the extinction ratio(ER),specialized MPA layouts were designed,and the crosstalk was experimentally vali⁃dated as the major source that impacted ER.By expanding opaque regions at pixel edges to 4μm,crosstalk rates from adjacent pixels could be effectively reduced to approximately 2%,and promising ERs ranging from 17.32 to 27.41 were implemented.

Influence of High-Density Bedding Plane Characteristics on Hydraulic Fracture Propagation in Shale Oil Reservoir

The existence of high-density bedding planes is a typical characteristic of shale oil reservoirs.Understanding the behavior of hydraulic fracturing in high-density laminated rocks is significant for promoting shale oil production.In this study,a hydraulic fracturing model considering tensile failure and frictional slip of the bedding planes is established within the framework of the unified pipe-interface element method(UP-IEM).The model developed for simulating the interaction between the hydraulic fracture and the bedding plane is validated by comparison with experimental results.The hydraulic fracturing patterns in sealed and unsealed bedding planes are compared.Additionally,the effects of differential stress,bedding plane permeability,spacing,and the friction coefficient of the bedding plane are investigated.The results showed that a single main fracture crossing the bedding planes is more likely to form in sealed bedding planes under high differential stress.The decrease in bedding plane permeability and the increase in the friction coefficient also promote the fracture propagating perpendicular to the bedding planes.Shale with high-density bedding planes has a poorer fracturing effect than that with low-density bedding planes,as the hydraulic fracture is prone to initiate and propagate along the bedding planes.Moreover,higher injection pressure is needed to maintain fracture propagation along the bedding.An increase in bedding density will lead to a smaller fracturing area.Fracturing fluid seepage into the bedding planes slows shale fracturing.It is recommended that increasing the injection flow rate,selecting alternative fracturing fluids,and employing multi-well/multi-cluster fracturing may be efficient methods to improve energy production in shale oil reservoirs.

Semi-analytical solution for mechanical analysis of tunnels crossing strike-slip fault zone considering nonuniform fault displacement and uncertain fault plane position

The tunnel subjected to strike-slip fault dislocation exhibits severe and catastrophic damage.The existing analysis models frequently assume uniform fault displacement and fixed fault plane position.In contrast,post-earthquake observations indicate that the displacement near the fault zone is typically nonuniform,and the fault plane position is uncertain.In this study,we first established a series of improved governing equations to analyze the mechanical response of tunnels under strike-slip fault dislocation.The proposed methodology incorporated key factors such as nonuniform fault displacement and uncertain fault plane position into the governing equations,thereby significantly enhancing the applicability range and accuracy of the model.In contrast to previous analytical models,the maximum computational error has decreased from 57.1%to 1.1%.Subsequently,we conducted a rigorous validation of the proposed methodology by undertaking a comparative analysis with a 3D finite element numerical model,and the results from both approaches exhibited a high degree of qualitative and quantitative agreement with a maximum error of 9.9%.Finally,the proposed methodology was utilized to perform a parametric analysis to explore the effects of various parameters,such as fault displacement,fault zone width,fault zone strength,the ratio of maximum fault displacement of the hanging wall to the footwall,and fault plane position,on the response of tunnels subjected to strike-slip fault dislocation.The findings indicate a progressive increase in the peak internal forces of the tunnel with the rise in fault displacement and fault zone strength.Conversely,an augmentation in fault zone width is found to contribute to a decrease in the peak internal forces.For example,for a fault zone width of 10 m,the peak values of bending moment,shear force,and axial force are approximately 46.9%,102.4%,and 28.7% higher,respectively,compared to those observed for a fault zone width of 50 m.Furthermore,the position of the peak internal forces is influenced by variations in the ratio of maximum fault displacement of the hanging wall to footwall and the fault plane location,while the peak values of shear force and axial force always align with the fault plane.The maximum peak internal forces are observed when the footwall exclusively bears the entirety of the fault displacement,corresponding to a ratio of 0:1.The peak values of bending moment,shear force,and axial force for the ratio of 0:1 amount to approximately 123.8%,148.6%,and 111.1% of those for the ratio of 0.5:0.5,respectively.

Testing method of rock structural plane using digital drilling

The rock mass consists of rock blocks and structural planes,which can reduce its integrity and strength.Therefore,accurately obtaining the characteristics of the rock mass structural plane is a prerequisite for evaluating stability and designing supports in underground engineering.Currently,there are no effective testing methods for the characteristic parameters of the rock mass structural plane in underground engineering.The paper presents the digital drilling technology as a new testing method of rock mass structural planes.Flawed rock specimens with cracks of varying widths and angles were used to simulate the rock mass structural planes,and the multifunctional rock mass digital drilling test system was employed to carry out the digital drilling tests.The analysis focuses on the variation laws of drilling parameters,such as drilling pressure and drilling torque,affected by the characteristics of prefabricated cracks,and clarifies the degradation mechanism of rock equivalent compressive strength.Additionally,an identification model for the characteristic parameters of rock mass structural planes during drilling is established.The test results indicate that the average difference of the characteristics of prefabricated cracks identified by the equivalent compressive strength is 2.45°and 0.82 mm,respectively.The identification model while drilling is verified to be correct due to the high identification accuracy.Based on this,a method for testing the characteristic parameters of the surrounding rock structural plane while drilling is proposed.The research offers a theoretical and methodological foundation for precise in situ identification of structural planes of the surrounding rock in underground engineering.

THE RADIAL SYMMETRY OF POSITIVE SOLUTIONS FOR SEMILINEAR PROBLEMS INVOLVING WEIGHTED FRACTIONAL LAPLACIANS

This paper deals with the radial symmetry of positive solutions to the nonlocal problem(-Δ)_(γ)~su=b(x)f(u)in B_(1){0},u=h in R~N B_(1),where b:B_1→R is locally Holder continuous,radially symmetric and decreasing in the|x|direction,F:R→R is a Lipschitz function,h:B_1→R is radially symmetric,decreasing with respect to|x|in R^(N)/B_(1),B_(1) is the unit ball centered at the origin,and(-Δ)_γ~s is the weighted fractional Laplacian with s∈(0,1),γ∈[0,2s)defined by(-△)^(s)_(γ)u(x)=CN,slimδ→0+∫R^(N)/B_(δ)(x)u(x)-u(y)/|x-y|N+2s|y|^(r)dy.We consider the radial symmetry of isolated singular positive solutions to the nonlocal problem in whole space(-Δ)_(γ)^(s)u(x)=b(x)f(u)in R^(N)\{0},under suitable additional assumptions on b and f.Our symmetry results are derived by the method of moving planes,where the main difficulty comes from the weighted fractional Laplacian.Our results could be applied to get a sharp asymptotic for semilinear problems with the fractional Hardy operators(-Δ)^(s)u+μ/(|x|^(2s))u=b(x)f(u)in B_(1)\{0},u=h in R^(N)\B_(1),under suitable additional assumptions on b,f and h.

Retrospective and prospective review of the generalized nonlinear strength theory for geomaterials

Strength theory is the basic theory for calculating and designing the strength of engineering materials in civil,hydraulic,mechanical,aerospace,military,and other engineering disciplines.Therefore,the comprehensive study of the generalized nonlinear strength theory(GNST)of geomaterials has significance for the construction of engineering rock strength.This paper reviews the GNST of geomaterials to demonstrate the research status of nonlinear strength characteristics of geomaterials under complex stress paths.First,it systematically summarizes the research progress of GNST(classical and empirical criteria).Then,the latest research the authors conducted over the past five years on the GNST is introduced,and a generalized three-dimensional(3D)nonlinear Hoek‒Brown(HB)criterion(NGHB criterion)is proposed for practical applications.This criterion can be degenerated into the existing three modified HB criteria and has a better prediction performance.The strength prediction errors for six rocks and two in-situ rock masses are 2.0724%-3.5091%and 1.0144%-3.2321%,respectively.Finally,the development and outlook of the GNST are expounded,and a new topic about the building strength index of rock mass and determining the strength of in-situ engineering rock mass is proposed.The summarization of the GNST provides theoretical traceability and optimization for constructing in-situ engineering rock mass strength.

Regulating the inner Helmholtz plane structure at the electrolyte-electrode interface for highly reversible aqueous Zn batteries

The development of aqueous Zn batteries is limited by parasitic water reactions,corrosion,and dendrite growth.To address these challenges,an inner Helmholtz plane(IHP)regulation method is proposed by employing low-cost,non-toxic maltitol as the electrolyte additive.The preferential adsorption behavior of maltitol can expel the water from the inner Helmholtz plane,and thus hinder the immediate contact between Zn metal and H_(2)O.Meanwhile,strong interaction between maltitol and H_(2)O molecules can restrain the activity of H_(2)O.Besides,the"IHP adsorption effect"along with the low LUMO energy level of maltitol-CF_(3)SO_(3)^(-)can promote the in-situ formation of an organic-inorganic complex solid electrolyte interface(SEI)layer.As a result,the hydrogen/oxygen evolution side reaction,corrosion,and dendrites issues are effectively suppressed,thereby leading to highly reversible and dendrite-free Zn plating/stripping.The Zn‖I_(2)battery with hybrid electrolytes also demonstrates high electrochemical performance and ultralong cycling stability,showing a capacity retention of 75%over 20000 charge-discharge cycles at a large current density of 5 A g^(-1).In addition,the capacity of the device has almost no obvious decay over20000 cycles even at-30℃.This work offers a successful electrolyte regulation strategy via the IHP adsorption effect to design electrolytes for high-performance rechargeable Zn-ion batteries.

Source parameters and aftershock pattern of the October 7,2021,M5.9 Harnai earthquake,Pakistan

On October 7,2021,a magnitude 5.9 earthquake struck the Harnai(Baluchistan)region of Pakistan,causing several fatalities and injuries within the epicentral area.First-order tectonic deformation in this region is caused by the convergence of the Indian Plate with respect to the Eurasian Plate.The Katwaz Block hinders the motion of the Indian Plate,resulting in the formation of strike-slip faults.In this study,the P-wave first-motion polarity technique was used to determine the mainshock faulting style.Cyclic scanning of the polarity solutions was applied to determine the most suitable focal mechanism solution among the available solutions generated by the FOCMEC(focal mechanism)software.The nodal planes correspond to different faulting styles(i.e.,thrust and strike-slip faulting).A nodal plane oriented in the NW-SE direction corresponded to a strike-slip mechanism,which was considered to be the fault plane.Tectonically,this earthquake was associated with the Harnai-Karahi strike-slip fault zone owing to the fault strike and direction of slip.The apparent stress drop,fault length,and moment magnitude of the Harnai earthquake were 35.4 bar,6.1 km,and 5.9,respectively.A lower b-value for the Gutenberg-Richter law was observed prior to the earthquake.Higherα-than b-values(α>b)indicate that this earthquake was governed by large events as opposed to small-magnitude events.The Harnai sequence had a decay exponent close to unity,lasted for 145 days,and produced few aftershocks.The study will help the future hazard mitigation in the region.

Construction of MnS/MoS_(2) heterostructure on two-dimensional MoS_(2) surface to regulate the reaction pathways for high-performance Li-O_(2) batteries

The inherent catalytic anisotropy of two-dimensional(2D) materials has limited the enhancement of LiO_(2) batteries(LOBs) performance due to the significantly different adsorption energies on 2D and edge surfaces.Tuning the adsorption strength in 2D materials to the reaction intermediates is essential for achieving high-performance LOBs.Herein,a MnS/MoS_(2) heterostructure is designed as a cathode catalyst by adjusting the adsorption behavior at the surface.Different from the toroidal-like discharge products on the MoS_(2) cathode,the MnS/MoS_(2) surface displays an improved adsorption energy to reaction species,thereby promoting the growth of the film-like discharge products.MnS can disturb the layer growth of MoS_(2),in which the stack edge plane features a strong interaction with the intermediates and limits the growth of the discharge products.Experimental and theoretical results confirm that the MnS/MoS_(2) heterostructure possesses improved electron transfer kinetics at the interface and plays an important role in the adsorption process for reaction species,which finally affects the morphology of Li_2O_(2),In consequence,the MnS/MoS_(2) heterostructure exhibits a high specific capacity of 11696.0 mA h g^(-1) and good cycle stability over 1800 h with a fixed specific capacity of 600 mA h g^(-1) at current density of100 mA g^(-1) This work provides a novel interfacial engineering strategy to enhance the performance of LOBs by tuning the adsorption properties of 2D materials.

An 8-Node Plane Hybrid Element for StructuralMechanics Problems Based on the Hellinger-Reissner Variational Principle

The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurate andunstable when applied. Therefore, developing new elements within the framework of the generalized variationalprinciple is of great significance. In this paper, an 8-node plane hybrid finite element with 15 parameters (PHQ8-15β) is developed for structural mechanics problems based on the Hellinger-Reissner variational principle.According to the design principle of Pian, 15 unknown parameters are adopted in the selection of stress modes toavoid the zero energy modes.Meanwhile, the stress functions within each element satisfy both the equilibrium andthe compatibility relations of plane stress problems. Subsequently, numerical examples are presented to illustrate theeffectiveness and robustness of the proposed finite element. Numerical results show that various common lockingbehaviors of plane elements can be overcome. The PH-Q8-15β element has excellent performance in all benchmarkproblems, especially for structures with varying cross sections. Furthermore, in bending problems, the reasonablemesh shape of the new element for curved edge structures is analyzed in detail, which can be a useful means toimprove numerical accuracy.

Rapid hologram generation through backward ray tracing and adaptive-resolution wavefront recording plane

An advanced method for rapidly computing holograms of large three-dimensional(3D)objects combines backward ray tracing with adaptive resolution wavefront recording plane(WRP)and adaptive angular spectrum propagation.In the initial phase,a WRP with adjustable resolution and sampling interval based on the object’s size is defined to capture detailed information from large 3D objects.The second phase employs an adaptive angular spectrum method(ASM)to efficiently compute the propagation from the large-sized WRP to the small-sized computer-generated hologram(CGH).The computation process is accelerated using CUDA and OptiX.Optical experiments confirm that the algorithm can generate high-quality holograms with shadow and occlusion effects at a resolution of 1024×1024 in 29 ms.