Geometric Analysis of Singularity for Single-Gimbal Control Moment Gyro Systems

This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.

Global Geometric Analysis of Ship Rolling and Capsizing in Random Waves

The nonlinear biased ship rolling motion and capsizing in randoro waves are studied by utilizing a global geometric method. Thompson＇ s α-parameterized family of restoring functions is adopted in the vessel equation of motion for the representation of bias. To take into account the presence of randomness in the excitation and the response, a stochastic Melnikov method is developed and a mean-square criterion is obtained to provide an upper bound on the domain of the potential chaotic rolling motion. This criterion can be used to predict the qualitative nature of the invariant manifolds which represent the boundary botween safe and unsafe initial conditions, and how these depend on system parameters of the specific ship model. Phase space transport theory and lobe dynamics are used to demonstrate how motions starting from initial conditions inside the regions bounded by the intersected manifolds will evolve and how unexpected capsizing can occur.

Computational Geometric Analysis for <i>C. elegans</i>Trajectories on Thermal and Salinity Gradient

Elegans are one of the best model organisms in neural researches, and tropism movement is a typical learning and memorizing activity. Based on one imaging technique called Fast Track-Capturing Microscope (FTCM), we investigated the movement regulation. Two movement patterns are extracted from various trajectories through analysis on turning angle. Then we applied this classification on trajectory regulation on the compound gradient field, and theoretical results corresponded with experiments well, which can initially verify the conclusion. Our breakthrough is performed computational geometric analysis on trajectories. Several independent features were combined to describe movement properties by principal composition analysis (PCA) and support vector machine (SVM). After normalizing all data sets, no-supervising machine learning was processed along with some training under certain supervision. The final classification results performed perfectly, which indicates the further application of such computational analysis in biology researches combining with machine learning.

Optimal linear attitude estimators via geometric analysis

Three optimal linear attitude estimators are proposed for single-point real-time estimation of spacecraft attitude using a geometric approach. The final optimal attitude is represented by modified Rodrigues parameters （MRPs）. After introducing incidental right-hand orthogonal coordinates for each pair of measured values, three error vectors are obtained by the use of dot or/and cross products. Corresponding optimality criteria are rigorously quadratic and unconstrained, which do not coincide with Wahba＇s constrained criterion. The singularity, which occurs when the principal angle is close to n, can be easily avoided by one proper rotation. Numerical simulations show that the proposed three optimal linear estimators can provide a precision comparable with those complying with the Wahba optimality definition, and have faster computational speed than the famous quatemion estimator （QUEST）.

Geometrical-Analysis-Based Algorithm for Stereo Matching of Single-Lens Binocular and Multi-Ocular Stereovision System

A geometrical analysis based algorithm is proposed to achieve the stereo matching of a single-lens prism based stereovision system. By setting the multi- face prism in frontal position of the static CCD （CM-140MCL） camera, equivalent stereo images with different orientations are captured synchronously by virtual cameras which are defined by two boundary lines： the optical axis and CCD camera field of view boundary. Subsequently, the geometrical relationship between the 2D stereo images and corresponding 3D scene is established by employing two fundamentals： ray sketching in which all the pertinent points, lines, and planes are expressed in the 3D camera coordinates and the rule of refraction. Landing on this relationship, the epipolar geometry is thus obtained by fitting a set of corresponding candidate points and thereafter, stereo matching of the prism based stereovision system is obtained. Moreover, the unique geometrical properties of the imaging system allow the proposed method free from the complicated camera calibration procedures and to be easily generalized from binocular and tri-oeular to multi-ocular stereovision systems. The performance of the algorithm is presented through the experiments on the binocular imaging system and the comparison with a conventional projection method demonstrates the efficient assessment of our novel contributions.

Efficient and accurate worm grinding of spur face gears according to an advanced geometrical analysis and a closed-loop manufacturing process

Worm grinding has been applied to manufacture gears to pursue high accuracy and fine surface finish.When the worm used to grind face gears is manufactured with multi-axis computer numerical control(CNC)machining,the machining accuracy is usually improved by increasing the number of tool paths with more time cost.Differently,this work proposes a generated method to improve the efficiency by dressing the worm surface with only one path,and a closed-loop manufacturing process is applied to ensure the machining accuracy.According to an advanced geometric analysis,the worm surface is practically approximated as a swept surface generated by a planar curve.Meanwhile,this curve is applied as the profile of a dressing wheel,which is used to dress the worm surface.The practical machining is carried out in a CNC machine tool,which was originally used to grind helical gears.Finally,a closed-loop manufacturing process including machining,measurement,and modification is proposed to compensate the machining errors.The proposed method is validated with simulations and practical experiments.

Geometric Scaling Analysis of Deep Inelastic Scattering Data Including Heavy Quarks

An analytic massive total cross section of photon proton scattering is derived, which has geometric scaling. A geometric scaling is used to perform a global analysis of the deep inelastic scattering data on inclusive structure function F2 measured in lepton-hadron scattering experiments at small values of Bjorken x. It is shown that the descriptions of the inclusive structure function F2 and longitudinal structure function FL are improved with the massive analytic structure function, which may imply the gluon saturation effect dominating the parton evolution process at HERA. The inclusion of the heavy quarks prevent the divergence of the lepton-hadron cross section, which plays a significant role in the description of the photoproduction region.

Geometrically Nonlinear Analysis of Structures Using Various Higher Order Solution Methods: A Comparative Analysis for Large Deformation

The suitability of six higher order root solvers is examined for solving the nonlinear equilibrium equations in large deformation analysis of structures.The applied methods have a better convergence rate than the quadratic Newton-Raphson method.These six methods do not require higher order derivatives to achieve a higher convergence rate.Six algorithms are developed to use the higher order methods in place of the Newton-Raphson method to solve the nonlinear equilibrium equations in geometrically nonlinear analysis of structures.The higher order methods are applied to both continuum and discrete problems(spherical shell and dome truss).The computational cost and the sensitivity of the higher order solution methods and the Newton-Raphson method with respect to the load increment size are comparatively investigated.The numerical results reveal that the higher order methods require a lower number of iterations that the Newton-Raphson method to converge.It is also shown that these methods are less sensitive to the variation of the load increment size.As it is indicated in numerical results,the average residual reduces in a lower number of iterations by the application of the higher order methods in the nonlinear analysis of structures.

Relationships between femoral strength evaluated by nonlinear finite element analysis and BMD,material distribution and geometric morphology

Precisely quantifying the strength of the proximal femur and accurately assessing hip fracture risk would enable those at high risk to be identified so that preventive interventions could be taken.Development of better measures of femoral strength using the clinically

Geometric Proof of Riemann Conjecture

This paper proves Riemann conjecture (RH), i.e., that all the zeros in critical region of Riemann ξ -function lie on symmetric line σ =1/2 . Its proof is based on two important properties: the symmetry and alternative oscillation for ξ = u + iv . Denote . Riemann proved that u is real and v ≡ 0 for β =0 (the symmetry). We prove that the zeros of u and v for β > 0 are alternative, so u (t,0) is the single peak. A geometric model was proposed. is called the root-interval of u (t,β) , if |u| > 0 is inside Ij and u = 0 is at its two ends. If |u (t,β)| has only one peak on each Ij, which is called the single peak, else called multiple peaks (it will be proved that the multiple peaks do not exist). The important expressions of u and v for β > 0 were derived. By , the peak u (t,β) will develop toward its convex direction. Besides, ut (t,β) has opposite signs at two ends t = tj , tj+1 of Ij , also does, then there exists some inner point t′ such that v (t′,β) = 0. Therefore {|u|,|v|/β} in Ij form a peak-valley structure such that has positive lower bound independent of t ∈ Ij (i.e. RH holds in Ij ). As u (t,β) does not have the finite condensation point (unless u = const.), any finite t surely falls in some Ij , then holds for any t (RH is proved). Our previous paper “Local geometric proof of Riemann conjecture” (APM, V.10:8, 2020) has two defects, this paper has amended these defects and given a complete proof of RH.

Geometrical nonlinear stability analyses of cable-truss domes

The nonlinear finite element method is used to analyze the geometrical nonlinear stability of cable truss domes with different cable distributions. The results indicate that the critical load increases evidently when cables, especially diagonal cables, are distributed in the structure. The critical loads of the structure at different rise span ratios are also discussed in this paper. It was shown that the effect of the tensional cable is more evident at small rise span ratio. The buckling of the structure is characterized by a global collapse at small rise span ratio; that the torsional buckling of the radial truss occurs at big rise span ratio; and that at proper rise span ratio, the global collapse and the lateral buckling of the truss occur nearly simultaneously.

Analysis of interlaminar stress and nonlinear dynamic response for composite laminated plates with interfacial damage

By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general sixdegrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.

Digital watermarking algorithm based on scale-invariant feature regions in non-subsampled contourlet transform domain

Contraposing the need of the robust digital watermark for the copyright protection field, a new digital watermarking algorithm in the non-subsampled contourlet transform （NSCT） domain is proposed. The largest energy sub-band after NSCT is selected to embed watermark. The watermark is embedded into scaleinvariant feature transform （SIFT） regions. During embedding, the initial region is divided into some cirque sub-regions with the same area, and each watermark bit is embedded into one sub-region. Extensive simulation results and comparisons show that the algorithm gets a good trade-off of invisibility, robustness and capacity, thus obtaining good quality of the image while being able to effectively resist common image processing, and geometric and combo attacks, and normalized similarity is almost all reached.

Revisiting the ionic diffusion mechanism in Li_(3)PS_(4) via the joint usage of geometrical analysis and bond valence method

Inorganic solid electrolytes have obvious advantages on safety and electrochemical stability compared to organic liquid electrolytes,but the advance on high ionic conductivity of typical electrolytes is still undergoing.Although the first-principles calculation in the ion migration simulation is an important strategy to develop high-performance solid electrolyte,the process is very time-consuming.Here,we propose an effective method by combining the geometrical analysis and bond valance sum calculation to obtain an approximate minimum energy path preliminarily,in parallel to pave the way for the interoperability of low-precision and high-precision ion transport calculation.Taking a promising electrolyte Li_(3)PS_(4) as an example,we revisit its Li-ionic transport behavior.Our calculated Li-ion pathways and the activation energies(the corresponding values:1.09 eV vs.0.88 eV vs.0.86 eV)in γ-,β- and α-Li_(3)PS_(4) are consistent with the ones obtained from the first-principles calculations.The variations of the position of P-ions lead the rearrangement of the host PS_(4) tetrahedron,affecting the diffusion positions of Li-ions and further enabling high Li^(+) conductivity in β-Li_(3)PS_(4).

The Derivation of Skeleton Lines for Terrain Features

The geometric and physical analysis methods are conventional methods for the derivation of skeleton lines in the fields of cartography,digital photogrammetry,and related areas.This paper proposes a stepwise approach that uses the physical analysis method in the first stage and the geometric analysis method in the subsequent stage.The physical analysis method analyses the terrain globally to obtain a rough set of skeleton lines for a terrain surface.The rough skeleton lines help to structure the ordering of feature points by the geometric analysis method.

Structural geometrical analysis and simulation of decollement growth folds in piedmont Fauqi Anticline of Zagros Mountains, Iraq

This study carried out detailed structural analyses of the plane structural deformation pattern and sectional structural deformation styles of the Fauqi Anticline by the 3D seismic section with full cover collection, and carried out the kinematical simulation of the Fauqi anticlinal deep decollement coupling shallow growth folds and faults based on the fault decollement fold model and the forward balanced geological section technique. The study subsequently evaluated the differentiated petroleum enrichment mechanism of the Fauqi Anticline by utilizing the results of the structural analysis and combining the spatial-temporal relationship analysis of the source, the reservoir, and the caprock. The results showed that the differentiated plane structural deformation pattern and hierarchical sectional structural deformation style were developed by the superposed coupling of deep decollement, syntectonic sedimentation of shallow growth strata, and the compression of the south-west horizontal tectonic stress from the Zagros Mountains. It was found that the differentiated structural deformation caused the differentiated enrichment of petroleum in the Fauqi Anticline. It was also found that the horizontal slip distance of the Fauqi Anticlinal Folds reached around 3.5 km by the simulation of deep decollement coupling the movement of the shallow growth folds and the faults.

Research on wind-induced responses of a large-scale membrane structure

The wind-induced responses of a large-scale membrane structure, Expo Boulevard, are evaluated in this study. To obtain the wind pressure distribution on the roof surface, a wind tunnel test is performed. A brief analysis of wind pressure on the membrane roof is conducted first and then an analysis of the wind-induced responses of the structure is carried out using a numerical integral method in the time domain. In the process of calculation, the geometrical nonlinearity is taken into account. Results indicate that mean, RSM and peak values of the structure responses increase nonlinearly while the approaching flow velocity increases. Strong nonlinear characteristics are observed in the displacement responses, whereas the responses of nodal stress and cable axial force show minimal nonlinear properties when the membrane structure is subjected to wind loads. Different values of the damping ratio only have a minimal impact on the RSM response of the structure because the background component is a dominant part of the total dynamic response and the resonant component is too small. As the damping ratio increases from 0.02 to 0.05, the RMS responses of vertical displacement, nodal stress and cable axial force decrease by 8.1%, 6.7% and 17.9%, respectively. Since the mean component plays a significant role in the wind-induced response, the values of the gust response factor are not high for Expo Boulevard.

Mapping Microscale Strain Fields Around a Crack Tip in Molybdenum Via Geometric Phase Analysis and Digital Image Correlation

Uniaxial tension tests were conducted on single-edge-notched tensile specimens of pure molybdenum with a mesh grid pattern in front of the notch. A series of images of crack initialization and propagation with a distorted mesh grid pattern were obtained by means of in situ scanning electron microscopy. Strain fields around the crack tip were mapped successively using geometric phase analysis and digital image correlation techniques, and then compared with the predictions obtained through linear elastic fracture mechanics （LEFM）. The comparison shows that the measured strain distribution ahead of the crack tip is consistent with the LEFM predictions of up to 25 μm from the crack tip.

A study on characteristics of tectonic block motion and tectonic setting of strong earthquakes in northern part of the Shanxi fault depression zone

This paper makes a systematical study on characteristics of structure and motion of the tectonic blocks in northern part of the Shanxi fault depression zone by means of geometrical and kinematical analysis of the blocks. The ki-netic behavior of the blocks is discussed by comparing associated geomorphic features of fault movement. All analyses and studies are based on a Domino model. The block movement, fault basin extension and their regional distribution are systematically investigated. The result shows: (a) The studied region is divided into sub-regions by NW striking faults: the western, middle and eastern sub-region with crustal extension being 4.46 km, 2.80 km and 1.86 km, respectively. The extensional amount of each block in the region is estimated being generally about 1 km. The calculated result using the block motion model approximately fits the data of geologic survey. (b) Block kin-ematical features are obviously different between the northern and southern part, with the Hengshan block in be-tween, of the studied region. Moreover, the magnitude of the largest historical earthquake in the northern part is about 6, while that in the southern is 7. The faulted blocks in the northern sub-region show northwestward exten-sion, indicating a feature of extensional graben, while the blocks in the southern part manifest tilt motion, extend-ing southeastward, in the opposite sense of fault dipping. Additional tectonic stress generated by block rotation may be one of major factors affecting seismogenic process in the region. It is responsible for the difference in the movement of the block boundary faults and seismic activities between the two sub-regions.

General coupled-mode analysis of a geometrically symmetric waveguide array with nonuniform gain and loss

The exceptional point(EP)is one of the typical properties of parity–time-symmetric systems,arising from modes coupling with identical resonant frequencies or propagation constants in optics.Here we show that in addition to two different modes coupling,a nonuniform distribution of gain and loss leads to an offset from the original propagation constants,including both real and imaginary parts,resulting in the absence of EP.These behaviors are examined by the general coupled-mode theory from the first principle of the Maxwell equations,which yields results that are more accurate than those from the classical coupled-mode theory.Numerical verification via the finite element method is provided.In the end,we present an approach to achieve lossless propagation in a geometrically symmetric waveguide array.