Differential-geometry-based multi-dimensional joint position-velocity estimation using Crab pulsar profile distortion

The traditional orbit determination method based on pulsar profile distortion can determine the six elements of the orbit.However,the estimation accuracies of these methods are limited and the computational load of a six-dimensional search is huge.To solve this problem,the differential-geometry-based Multi-dimensional Joint Position-Velocity Estimation(MJPVE)using Crab pulsar profile distortion is proposed in this paper.Firstly,through theoretical analysis,it is found that the pulsar profile distortion caused by the initial state error in some joint positionvelocity directions is very small.In other words,the accuracies of estimation in these directions are very low.Namely,the search dimension can be reduced,which in turn greatly reduces the computational load.Then,we construct the chi-squared function of the pulsar profile with respect to the estimation error in joint position-velocity direction and use differential geometry to find the joint position-velocity directions corresponding to different degrees of distortion.Finally,we utilize the grid search based on directory folding in these joint position-velocity directions corresponding to large degrees of distortion to obtain the joint position-velocity estimation.The experimental results show that compared with the grouping bi-chi-squared inversion method,MJPVE has high precision and extensive navigation information.

Discrete Plane Segmentation and Estimation from a Point Cloud Using Local Geometric Patterns

This paper presents a method for segmenting a 3D point cloud into planar surfaces using recently obtained discretegeometry results. In discrete geometry, a discrete plane is defined as a set of grid points lying between two parallel planes with a small distance, called thickness. In contrast to the continuous case, there exist a finite number of local geometric patterns （LGPs） appearing on discrete planes. Moreover, such an LGP does not possess the unique normal vector but a set of normal vectors. By using those LGP properties, we first reject non-linear points from a point cloud, and then classify non-rejected points whose LGPs have common normal vectors into a planar-surface-point set. From each segmented point set, we also estimate the values of parameters of a discrete plane by minimizing its thickness.

Hyperbolic Fibonacci and Lucas Functions, “Golden” Fibonacci Goniometry, Bodnar’s Geometry, and Hilbert’s Fourth Problem—Part II. A New Geometric Theory of Phyllotaxis (Bodnar’s Geometry)

This article refers to the “Mathematics of Harmony” by Alexey Stakhov in 2009, a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries–New Geometric Theory of Phyllotaxis (Bodnar’s Geometry) and Hilbert’s Fourth Problem based on the Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci λ-Goniometry (λ > 0 is a given positive real number). Although these discoveries refer to different areas of science (mathematics and theoretical botany), however they are based on one and the same scientific ideas-the “golden mean,” which had been introduced by Euclid in his Elements, and its generalization—the “metallic means,” which have been studied recently by Argentinian mathematician Vera Spinadel. The article is a confirmation of interdisciplinary character of the “Mathematics of Harmony”, which originates from Euclid’s Elements.

Influence of Wires Properties on Warp-Knitted Loop Geometry in Plane Based on Theory of Elastic Rod

Based on classic theory of elastic rod,the warp-knitted loop geometry in plane is independent of yarn properties,while there is a certain gap between the geometrical model and the actual fabrics.According to this problem,further analysis of loop geometry is done based on the theory of elastic rod with theoretical calculation and experiments.The theoretical analysis found that the distance between the contacted points at the loop root affected the loop geometry,and the distance was affected by the ratio of bending rigidity and the friction between yarns.The experiments,forming simple loop by taking the yarn as an elastic rod,found that the bending rigidity affected the loop geometry.Then the relationships between warp-knitted loop geometry in plane of metallic fabrics and wires properties were studied.The results show that metallic fabrics are more suitable for the theory of elastic rod;the friction and bending rigidity of wire yarns affect the loop geometry in plane.Also,the elongation of yarn affects the loop geometry in the actual warp-knitted fabric.

Full-wave Analyses of Scattering of Electromagnetic Wave from the Weakly Ionized Plasma in Plane Geometry

The purpose of the present work is to present a full-wave analysis of scattering from the weakly ionized plasma in the plane geometry. We have yielded an approximate solution in an analytic form to the electromagnetic wave scattering from the weakly ionized plasma. In the normal and oblique incidence, the analytic solution works well, as compared with the exact solution and the solution based on the Wenzell-Kramers-Brillouin-Jeffreys (WKBJ) approximation to the uniform density profile.

Fractal Geometry:Axioms,Fractal Derivative and Its Geometrical Meaning

Physics success is largely determined by using mathematics.Physics often themselves create the necessary mathematical apparatus.This article shows how you can construct a fractal calculus-mathematics of fractal geometry.In modem scientific literature often write from a firm that"there is no strict definition of fractals",to the more moderate that"objects in a certain sense,fractal and similar."We show that fractal geometry is a strict mathematical theory,defined by their axioms.This methodology allows the geometry of axiomatised naturally define fractal integrals and differentials.Consistent application on your input below the axiom gives the opportunity to develop effective methods of measurement of fractal dimension,geometri-cal interpretation of fractal derivative gain and open dual symmetry.

Ermakov System and Plane Curve Motions in Affine Geometries

It is shown that the Pinney equation, Ermakov systems, and their higher-order generalizations describeself-similar solutions of plane curve motions in centro-affine and affine geometries.

HAMILTONIAN SYSTEM AND SIMPLETIC GEOMETRY IN MECHANICS OF COMPOSITE MATERIALS (Ⅱ)——PLANE STRESS PROBLEM

Fundamental theory presented in Part (I)[8] is used to analyze anisotropic plane stress problems. First we construct the generalized variational principle to enter Hamiltonian system and get Hamiltonian differential operator matrix; then we solve eigen problem; finally, we present the process of obtaining analytical solutions and semi-analytical solutions for anisotropic plane stress porblems on rectangular area.

Investigation of pore geometry influence on fluid flow in heterogeneous porous media:A pore-scale study

Brazilian pre-salt reservoirs are renowned for their intricate pore networks and vuggy nature,posing significant challenges in modeling and simulating fluid flow within these carbonate reservoirs.Despite possessing excellent petrophysical properties,such as high porosity and permeability,these reservoirs typically exhibit a notably low recovery factor,sometimes falling below 10%.Previous research has indicated that various enhanced oil recovery(EOR)methods,such as water alternating gas(WAG),can substantially augment the recovery factor in pre-salt reservoirs,resulting in improvements of up to 20%.Nevertheless,the fluid flow mechanism within Brazilian carbonate reservoirs,characterized by complex pore geometry,remains unclear.Our study examines the behavior of fluid flow in a similar heterogeneous porous material,utilizing a plug sample obtained from a vugular segment of a Brazilian stromatolite outcrop,known to share analogies with certain pre-salt reservoirs.We conducted single-phase and multi-phase core flooding experiments,complemented by medical-CT scanning,to generate flow streamlines and evaluate the efficiency of water flooding.Subsequently,micro-CT scanning of the core sample was performed,and two cross-sections from horizontal and vertical plates were constructed.These cross-sections were then employed as geometries in a numerical simulator,enabling us to investigate the impact of pore geometry on fluid flow.Analysis of the pore-scale modeling and experimental data unveiled that the presence of dead-end pores and vugs results in a significant portion of the fluid remaining stagnant within these regions.Consequently,the injected fluid exhibits channeling-like behavior,leading to rapid breakthrough and low areal swept efficiency.Additionally,the numerical simulation results demonstrated that,irrespective of the size of the dead-end regions,the pressure variation within the dead-end vugs and pores is negligible.Despite the stromatolite's favorable petrophysical properties,including relatively high porosity and permeability,as well as the presence of interconnected large vugs,the recovery factor during water flooding remained low due to early breakthrough.These findings align with field data obtained from pre-salt reservoirs,providing an explanation for the observed low recovery factor during water flooding in such reservoirs.

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.

Geometrical Modeling of Crystal Structures with Use of Space of Elliptic Riemannian Geometry

The space of internal geometry of a model of a real crystal is supposed to be finite, closed, and with a constant Gaussian curvature equal to unity, permitting the realization of lattice systems in accordance with Fedorov groups of transformations. For visualizing computations, the interpretation of geometrical objects on a Clifford surface (SK) in Riemannian geometry with the help of a 2D torus in a Euclidean space is used. The F-algorithm ensures a computation of 2D sections of models of point systems arranged perpendicularly to the symmetry axes l3, l4, and l6. The results of modeling can be used for calculations of geometrical sizes of crystal structures, nanostructures, parameters of the cluster organization of oxides, as well as for the development of practical applications connected with improving the structural characteristics of crystalline materials.

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.

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.

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.

Theoretical model of current propagation in a helical coil with varying geometry and screen tube

An analytical model of current propagation in a helical coil with varying geometry is developed.It can be used for post-acceleration and post-focusing of ions produced via laser-driven target normal sheath acceleration and generation of electromagnetic pulses.We calculate the current that propagates in a helical coil and suggest a method for improving its dispersion properties using a screening tube and with pitch and radius variation.The electromagnetic fields calculated with the analytical model are in agreement with particle-in-cell simulations.The model provides insights into the physics of current propagation in helical coils with varying geometries and enables a numerical implementation for rapid proton spectrum computations,which facilitate the design of such coils for future experiments.

A Generalized Array Factor for Time-Modulated Hexagonal Based Antenna Array Geometry With Novel Trapezoidal Switching

The concept of the time-modulated array has been emerging as an alternative to the complex phase shifters,which lowers the cost of the array feeding network due to the utilization of radio frequency(RF)switches.The various forms of hexagonal antenna array geometries can be used for applications like surveillance tracking in phased array radar and wireless communication systems.This work proposes the generalized array factor(AF)for the hexagonal antenna array geometry based on time modulation.The time modulation in generalized hexagonal geometry can maintain the fixed static amplitude excitation,giving more flexibility over time.Furthermore,a novel trapezoidal switching function is also proposed and applied to the generalized array factor to enable future researchers to use this array factor in the field of advancement to observe how switching schemes like trapezoidal and rectangular affect the array pattern's side lobe level(SLL).The generalized equation can be utilized for the analysis and synthesis of radiation characteristics of the time-modulated hexagonal array(TMHA),time-modulated concentric hexagonal array(TMCHA),time-modulated hexagonal cylindrical array(TMHCA),and time-modulated hexagonal concentric cylindrical array(TMHCCA).The numerical result illustrates the generation of AF of time-modulated hexagonal structures and also shows that the trapezoidal switching sequence outperforms the rectangular switch using the cat swarm optimization(CSO)approach.

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.

A photogrammetric approach for quantifying the evolution of rock joint void geometry under varying contact states

Accurate measurement of the evolution of rock joint void geometry is essential for comprehending the distribution characteristics of asperities responsible for shear and seepage behaviors.However,existing techniques often require specialized equipment and skilled operators,posing practical challenges.In this study,a cost-effective photogrammetric approach is proposed.Particularly,local coordinate systems are established to facilitate the alignment and precise quantification of the relative position between two halves of a rock joint.Push/pull tests are conducted on rock joints with varying roughness levels to induce different contact states.A high-precision laser scanner serves as a benchmark for evaluating the photogrammetry method.Despite certain deviations exist,the measured evolution of void geometry is generally consistent with the qualitative findings of previous studies.The photogrammetric measurements yield comparable accuracy to laser scanning,with maximum errors of 13.2%for aperture and 14.4%for void volume.Most joint matching coefficient(JMC)measurement errors are below 20%.Larger measurement errors occur primarily in highly mismatched rock joints with JMC values below 0.2,but even in cases where measurement errors exceed 80%,the maximum JMC error is only 0.0434.Thus,the proposed photogrammetric approach holds promise for widespread application in void geometry measurements in rock joints.