Subplanes of PG( 2, q 3 ) and the Ruled Varieties V 2 5 of PG( 6,q )

In this note we study subplanes of order q of the projective plane Π=PG( 2, q 3 ) and the ruled varieties V 2 5 of Σ=PG( 6,q ) using the spatial representation of Π in Σ, by fixing a hyperplane Σ ′ with a regular spread of planes. First are shown some configurations of the affine q-subplanes. Then to prove that a variety V 2 5 of Σ represents a non-affine subplane of order q of Π, after having shown basic incidence properties of it, such a variety V 2 5 is constructed by choosing appropriately the two directrix curves in two complementary subspaces of Σ. The result can be translated into further incidence properties of the affine points of V 2 5 . Then a maximal bundle of varieties V 2 5 having in common one directrix cubic curve is constructed.

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.

Dynamic damage evolution of bank slopes with serrated structural planes considering the deteriorated rock mass and frequent reservoirinduced earthquakes

To investigate the dynamic damage evolution characteristics of bank slopes with serrated structural planes,the shaking table model test and the numerical simulation were utilized.The main findings indicate that under continuous seismic loads,the deformation of the bank slope increased,particularly around the hydro-fluctuation belt,accompanying by the pore water pressure rising.The soil pressure increased and then decreased showed dynamic variation characteristics.As the undulation angle of the serrated structural planes increased(30°, 45°, and 60°),the failure modes were climbing,climbinggnawing,and gnawing respectively.The first-order natural frequency was used to calculate the damage degree(Dd)of the bank slope.During microseisms and small earthquakes,it was discovered that the evolution of Dd followed the“S”shape,which was fitted by a logic function.Additionally,the quadratic function was used to fit the Dd during moderately strong earthquakes.Through the numerical simulation,the variation characteristics of safety factors(Sf)for slopes with serrated structural planes and slopes with straight structural planes were compared.Under continuous seismic loads,the Sf of slopes with straight structural planes reduce stalely,whereas the Sf for slopes with serrated structural planes was greater than the former and the reduction rate was increasing.

Study of beam divergence and thrust vector eccentricity characteristics of the Hall thruster based on dual Faraday probe array planes and its applications

The accurate knowledge of the thrust vector eccentricity and beam divergence characteristics of Hall thrusters are of significant engineering value for the beneficial integration and successful application of Hall thrusters on spacecraft.For the characteristics of the plume bipolar diffusion due to the annular discharge channel of the Hall thruster,a Gaussian-fitted method for thrust vector deviation angle and beam divergence of Hall thrusters based on dual Faraday probe array planes was proposed in respect of the Hall thruster beam characteristics.The results show that the ratios of the deviation between the maximum and minimum values of the beam divergence angle and the thrust vector eccentricity angle using a Gaussian fit to the optimized Faraday probe dual plane to the mean value are 1.4%and 11.5%,respectively.The optimized thrust vector eccentricity angle obtained has been substantially improved,by approximately 20%.The beam divergence angle calculated using a Gaussian fitting to the optimized Faraday probe dual plane is approximately identical to the non-optimized one.The beam divergence and thrust vector eccentricity angles for different anode mass flow rates were obtained by averaging the beam divergence and thrust vector eccentricity angles calculated by the dual-plane,Gaussian-fitted ion current density method for different cross-sections.The study not only allows for an immediate and effective tool for determining the design of thrust vector adjustment mechanisms of spacecraft with different power Hall thrusters but also for characterizing the 3D spatial distribution of the Hall thruster plume.

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.

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.

Remazolam combined with transversus abdominis plane block in gastrointestinal tumor surgery:Have we achieved better anesthetic effects?

Laparoscopic surgery is the main treatment method for patients with gastrointestinal malignant tumors.Although laparoscopic surgery is minimally invasive,its tool stimulation and pneumoperitoneum pressure often cause strong stress reactions in patients.On the other hand,gastrointestinal surgery can cause stronger pain in patients,compared to other surgeries.Transversus abdominis plane block(TAPB)can effectively inhibit the transmission of nerve impulses caused by surgical stimulation,alleviate patient pain,and thus alleviate stress reactions.Remazolam is an acting,safe,and effective sedative,which has little effect on hemodynamics and is suitable for most patients.TAPB combined with remazolam can reduce the dosage of total anesthetic drugs,reduce adverse reactions,reduce stress reactions,and facilitate the rapid postoperative recovery of patients.

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.

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.

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.

Review on dynamic analysis of road pavements under moving vehicles and plane strain conditions

This paper reviews works on the dynamic analysis of flexible and rigid pavements under moving vehicles on the basis of continuum-based plane strain models and linear theories.The purpose of this review is to provide in-formation about the existing works on the subject,critically discuss them and make suggestions for further research.The reviewed papers are presented on the basis of the various models for pavement-vehicle systems and the various methods for dynamically analyzing these systems.Flexible pavements are modeled by a homogeneous or layered half-plane with isotropic or anisotropic and linear elastic,viscoelastic or poroelastic material behavior.Rigid pavements are modeled by a beam or plate on a homogeneous or layered half-plane with material properties like the ones for flexible pavements.The vehicles are modeled as concentrated or distributed over a finite area loads moving with constant or time dependent speed.The above pavement-vehicle models are dynamically analyzed by analytical,analytical/numerical or purely numerical methods working in the time or frequency domain.Representative examples are presented to illustrate the models and methods of analysis,demonstrate their merits and assess the effects of the various parameters on pavement response.The paper closes with con-clusions and suggestions for further research in the area.The significance of this research effort has to do with the presentation of the existing literature on the subject in a critical and easy to understand way with the aid of representative examples and the identification of new research areas.

Study on the Evolution of Plane Shape of Guangfu Ancestral Hall Buildings and the Construction of Type Genealogy in the Ming and Qing Dynasties

This paper studies the clan temples in four periods,namely,the development period(early Ming Dynasty and before),the shaping period(mid-Ming Dynasty to early Qing Dynasty),the maturity period(mid-Qing Dynasty),and the programmed period(late Qing Dynasty),analyzes and summarizes their prototypical planform features and attempts to summarize and construct a genealogy of the architectural characteristics of the plane shape of clan temples.During the Ming and Qing dynasties,Guangfu ancestral halls in general showed a journey of development from a centripetal-single-linear-multi-linear-grid pattern,forming the unique Guangsanlu classic pattern in the Guangfu area.

Symplectic eigenfunction expansion theorem for elasticity of rectangular planes with two simply-supported opposite sides

The eigenvalue problem of the Hamiltonian operator associated with plane elasticity problems is investigated.The eigenfunctions of the operator are directly solved with mixed boundary conditions for the displacement and stress in a rectangular region.The completeness of the eigenfunctions is then proved,providing the feasibility of using separation of variables to solve the problems.A general solution is obtained with the symplectic eigenfunction expansion theorem.

Modeling shale with consideration of bedding planes by cohesive finite element method

Shale contains distributed directional bedding planes,which make the shale transverse isotropic.To model shale with consideration of the bedding planes,a cohesive finite element method(CFEM)is developed based on the randomized triangular mesh.The interface orientation generated from such mesh tends to be uniformly distributed with the element number increasing.To represent the bedding plane,the interfaces aligned with the bedding plane are assigned the cohesive law that characterizes the bedding plane while the other interfaces are assigned the cohesive law that characterizes the matrix.By this means,the anisotropy characteristics of the stiffness and the strength of shale are well represented.The simulation examples demonstrate that the bedding plane has a significant influence on the fracture trajectory,which is consistent with the observation in the experiment.It is suggested that this modeling method of shale is feasible.It provides an alternative approach to fracture simulation in shale.

Stability analysis of concrete gravity dam on complicated foundation with multiple slide planes

A key problem in gravity dam design is providing enough stability to prevent slide, and the difficulty increases if there are several weak structural planes in the dam foundation. Overload and material weakening were taken into account, and a .finite difference strength reserve method with partial safety factors based on the reliability method was developed and used to study the anti-slide stability of a concrete gravity dam on a complicated foundation with multiple slide planes. Possible slide paths were obtained, and the stability of the foundation with possible failure planes was evaluated through analysis of the stress distribution characteristics. The results reveal the mechanism and process of sliding due to weak structural planes and their deformations, and provide a reference for anti-slide stability analysis of gravity dams in complicated geological conditions.

Application of fuzzy clustering method to determining sub-fault planes of earthquake from aftershocks sequence

Earthquake rupture process generally involves several faults activities instead of a single fault A new method using both fuzzy clustering and principal component analysis makes it possible to reconstruct three dimensional structure of involved faults in earthquake if the aftershocks around the active fault planes distribute uniformly. When seismic events are given, the optimal faults structures can be determined by our new method. Each of sub-fault planes is fully characterized by its central location, length, width, strike and dip. The resolution determines the number of fault segments needed to describe the earthquake catalog. The higher the resolution, the finer the structure of the reconstructed fault segments. The new method successfully reconstructs the fault segments using synthetic earthquake catalogs. By taking the 28 June 1992 Landers earthquake oceured in southern California as an example, the reconstructed fault segments are consistent with the faults already known on geological maps or blind faults that appeared quite frequently in longer-term catalogs.

Competing reduction induced homogeneous oxygen doping to unlock MoS_(2)basal planes for faster polysulfides conversion

The parasitic polysulfides shuttle effect greatly hinders the practical application of lithium sulfur batteries,and this issue can be addressed by promoting polysulfides conversion with catalytic materials such as Mo S_(2).However,the catalytic activity of Mo S_(2)mainly relies on edge sites,but is limited by inert basal planes.We herein report a novel,facile,ethylene glycol enabled competing reduction strategy to dope Mo S_(2)homogeneously with oxygen atoms so that its inert basal planes can be unlocked.Ethylene glycol works as a reducing agent and competes with thiourea to react with ammonium molybdate,leading to insufficient sulfuration of Mo,and consequent formation of O-Mo S_(2).Our theoretical and experimental investigations indicate that the homogeneously distributed O dopants can create abundant adsorption/-catalytic sites in the Mo S_(2)basal planes,enlarge the inter-plane distance to promote ion transport,and thus enhance the catalytic conversion of polysulfides.The oxygen doped Mo S_(2)(O-Mo S_(2))is supported on carbon nanosheets(CNS)and the composite(O-Mo S_(2)/CNS)is employed to modify the separator of Li-S battery.It gives the battery an initial discharge capacity of 1537 m Ah g-1at 0.2 C,and the battery retains a discharge capacity of 545 m Ah g-1after ultra-long 2000 cycles at 1 C,corresponding to a very small cyclic decay rate of 0.0237%.Even under a raising sulfur loading of 8.2 mg cm^(-2),the Li-S battery also delivers a high discharge capacity(554 m Ah g^(-1))with outstanding cycle stability(84.6%capacity retention)after 100 cycles at 0.5 C.Our work provides a novel,facile approach to fabricate highly catalytically active oxygen-doped Mo S_(2)for advanced Li-S batteries.

Photoluminescence of SiV centers in CVD diamond particles with specific crystallographic planes

We prepared the isolated micrometer-sized diamond particles without seeding on the substrate in hot filament chemical vapor deposition. The diamond particles with specific crystallographic planes and strong silicon-vacancy(SiV) photoluminescence(PL) have been prepared by adjusting the growth pressure. As the growth pressure increases from 2.5 to 3.5 kPa,the diamond particles transit from composite planes of {100} and {111} to only smooth {111} planes. The {111}-faceted diamond particles present better crystal quality and stronger normalized intensity of SiV PL with a narrower bandwidth of 5 nm. Raman depth profiles show that the SiV centers are more likely to be formed on the near-surface areas of the diamond particles, which have poorer crystal quality and greater lattice stress than the inner areas. Complex lattice stress environment in the near-surface areas broadens the bandwidth of SiV PL peak. These results provide a feasible method to prepare diamond particles with specific crystallographic planes and stronger SiV PL.

Erector Spinae Plane Block Combined with Serratus Anterior Plane Block Versus Thoracic Paravertebral Block for Postoperative Analgesia and Recovery After Thoracoscopic Surgery:A Randomized Controlled Non-inferiority Clinical Trial

Objective This study aimed to compare the postoperative analgesia and recovery of ultrasound-guided erector spinae plane block combined with serratus anterior plane block(ESPB combined with SAPB)versus thoracic paravertebral block(PVB)after thoracoscopic surgery.Methods Ninety-two patients who underwent video-assisted thoracoscopic surgery(VATS)were randomly divided into group S(n=46)and group P(n=46).After anesthesia induction,the same anesthesiologist performed ultrasound-guided ESPB at T5 and T7 levels combined with SAPB at the level of the fifth rib in the midaxillary line in group S and ultrasound-guided PVB at T5 and T7 levels in group P.Patients in both groups were given 40 mL of 0.4%ropivacaine.Eighty-six patients completed the study(group S,n=44;group P,n=42).The morphine consumption,visual analogue scale(VAS)scores at rest and coughing,and frequency of remedial analgesia were recorded at 1,2,4,8,and 24 h postoperatively.Pulmonary function parameters were recorded at 1,4,and 24 h postoperatively,and the quality of recovery(QoR)-15 score at 24 h postoperatively.The adverse effects,duration of chest tube drainage and length of stay were also recorded.Results The morphine consumption at postoperative 4 and 8 h and the incidence of ipsilateral shoulder pain(ISP)were significantly lower in group S than in group P.The QoR-15 questionnaire score at postoperative 24 h was significantly lower in group P than in group S(P<0.05).The morphine consumption was lower at 24 h postoperatively in group S than in group P,with no significant difference found yet.The morphine consumption at other observed times,VAS scores,pulmonary function parameters,frequency of remedial analgesia,duration of chest tube drainage,length of stay,and incidence of other adverse events were comparable between group S and group P.Conclusion Ultrasound-guided ESPB combined with SAPB is non-inferior to PVB in terms of morphine consumption at postoperative 24 h and postoperative recovery.But,this approach can significantly reduce morphine consumption in the early postoperative period(0–8 h)after thoracoscopy with lower incidence of ISP.It is a simpler and safer operation.

THE WELDING PROBLEM OF TWO HALF-PLANES WITH ANISOTROPIC MEDIA

In this paper, the welding problem of two half-planes with anisotropic media is considered. By means of the complex variable method, the stress distribution is given in closed forms.