Subplanes of PG(2,qr), Ruled Varieties V2r-12 in PG( 2r,q), and Related Codes

In this note we consider ruled varieties V22r−1of PG(2r,q), generalizing some results shown for r=2,3in previous papers. By choosing appropriately two directrix curves, a V22r−1represents a non-affine subplane of order qof the projective plane PG(2,qr)represented in PG(2r,q)by a spread of a hyperplane. That proves the conjecture assumed in [1]. Finally, a large family of linear codes dependent on r≥2is associated with projective systems defined both by V22r−1and by a maximal bundle of such varieties with only an r-directrix in common, then are shown their basic parameters.

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.

Tunnel failure in hard rock with multiple weak planes due to excavation unloading of in-situ stress

Natural geological structures in rock(e.g.,joints,weakness planes,defects)play a vital role in the stability of tunnels and underground operations during construction.We investigated the failure characteristics of a deep circular tunnel in a rock mass with multiple weakness planes using a 2D combined finite element method/discrete element method(FEM/DEM).Conventional triaxial compression tests were performed on typical hard rock(marble)specimens under a range of confinement stress conditions to validate the rationale and accuracy of the proposed numerical approach.Parametric analysis was subsequently conducted to investigate the influence of inclination angle,and length on the crack propagation behavior,failure mode,energy evolution,and displacement distribution of the surrounding rock.The results show that the inclination angle strongly affects tunnel stability,and the failure intensity and damage range increase with increasing inclination angle and then decrease.The dynamic disasters are more likely with increasing weak plane length.Shearing and sliding along multiple weak planes are also consistently accompanied by kinetic energy fluctuations and surges after unloading,which implies a potentially violent dynamic response around a deeply-buried tunnel.Interactions between slabbing and shearing near the excavation boundaries are also discussed.The results presented here provide important insight into deep tunnel failure in hard rock influenced by both unloading disturbance and tectonic activation.

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.

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.

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.

In-package P/G planes analysis and optimization based on transmission matrix method

Power integrity (PI) has become a limiting factor for the chip's overall performance, and how to place in-package decoupling capacitors to improve a chip's PI performance has become a hot issue. In this paper, we propose an improved trans- mission matrix method (TMM) for fast decoupling capacitance allocation. An irregular grid partition mechanism is proposed, which helps speed up the impedance computation and complies better with the irregular power/ground (P/G) plane or planes with many vias and decoupling capacitors. Furthermore, we also ameliorate the computation procedure of the impedance matrix whenever decoupling capacitors are inserted or removed at specific ports. With the fast computation of impedance change, in-package decoupling capacitor allocation is done with an efficient change based method in the frequency domain. Experimental results show that our approach can gain about 5× speedup compared with a general TMM, and is efficient in restraining the noise on the P/G plane.

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.

Teaching method for reading views by analyzing lines and planes

This paper deals with the teaching method in reading engineering drawing. It introduces the basic theory and fundamental ideas as well as the approach of reading views by analyzing lines and planes. It gives out the steps for completing the third view based on the other two views. As it is easy and quick for students to read and understand views by this method, it is welcome by students in teaching practice.

Some Symmetry Results for the A-Laplacian Equation via the Moving Planes Method

In this paper, we are concerned with a positive solution of the non-homogeneous A-Laplacian equation in an open bounded connected domain. We use moving planes method to prove that the domain is a ball and the solution is radially symmetric.

On Transposed Translation Planes

This paper is devoted to the study of a translation plane π(C) associated with a t-spread set C and its transposed t-spread set C t. In this paper, an explicit matrix form of the inverse of an isomorphism from a translation plane into another translation plane associated with t-spread sets is derived and proved that two translation planes associated with t-spread sets are isomorphic if and only if their corresponding transposed translation planes are isomorphic. Further, it is shown that the transpose of a flag-transitive plane is flag-transitive and derived a necessary and sufficient condition for a translation plane π(C) to be isomorphic to its transposed translation plane.

China to Open Sky to Private Planes

It is believed that China will promulgate its Regulations Concerning General Aviation Flight Control before the end of this year. This will permit private aircraft to fly at low-altitude (below 600 meters). "China’s sky will become unprecedented-ly open," predicted Cao Jingnan, senior engineer and deputy director of the Chinese Association of Aeronautics

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.

Engineering geological classification of the structural planes for hydroelectric projects in Emeishan Basalts

The scale and characteristics of rock mass are important indexes of the rock mass structural plane classification. This paper firstly analyzes the spatial distribution characteristics, the structural plane types （original structural plane, tectonic structural plane and hypergenic structural plane） and the associated features of the Emeishan basalts and then studies the classification schemes of the built hydropower structure planes of different rock areas （the east district, the central district and the west district） in the Emeishan basalt distribution area, Southwest China. Based on the analysis and comparison of the scale and the engineering geological characteristics of the typical structure planes in the basalt hydroelectric Stations, the types of structural planes are used in the first order classification. The secondary order classification is made by considering the impact factors of rock mass quality, e.g., the state of the structural planes, infilling, joint opening, extending length, the grade of weathering and strength. The engineering geological classification for Emeishan basalt is proposed. Because there are no evidences of a large structure presenting in study area, the first-order （Ⅰ） controlling structural planes do not appear in the classification, there only appear Ⅱ, Ⅲ, Ⅳ and Ⅴ grade structural planes influencing the rock-mass quality. According to the different rock-block types in bedding fault zone, the second-grade （Ⅱ） structural planes consisted of bedding fault zone is further classified into Ⅱ1, Ⅱ2 and Ⅱ3. The third-grade （Ⅲ） structural planes constructed by intraformational faulted zones are not subdivided. According to the different characteristics of intrusion, alteration and weathering unloading structural planes, the Ⅳ grade structure plane is divided into Ⅳ1, Ⅳ2 and Ⅳ3. According to the development characteristics of joints and fractures, the V grade structure plane is divided into fracture Ⅴ1 and columnar joint Ⅴ2. In all, the structural planes are classified into four groups with nine subsets. The research proposes the engineering geological classification of the structural plane for the hydropower project in the Emishan basalts, and the result of the study has a potential application in similar regions.

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.

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.

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.

Hydro-mechanical fault reactivation modeling based on elasto-plasticity with embedded weakness planes

In this paper,an elasto-plastic constitutive model is employed to capture the shear failure that may occur in a rock mass presenting mechanical discontinuities,such as faults,fractures,bedding planes or other planar weak structures.The failure may occur in two modes:a sliding failure on the weak plane or an intrinsic failure of the rock mass.The rock matrix is expected to behave elastically or fail in a brittle manner,being represented by a non-associated Mohr-Coulomb behavior,while the sliding failure is represented by the evaluation of the Coulomb criterion on an explicitly defined plane.Failure may furthermore affect the hydraulic properties of the rock mass:the shearing of the weakness plane may create a transmissive fluid pathway.Verification of the mechanical submodel is conducted by comparison with an analytical solution,while the coupled hydro-mechanical behavior is validated with field data and will be applied within a model and code validation initiative.The work presented here aims at documenting the progress in code development,while accurate match of the field data with the numerical results is current work in progress.

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.