Splitting Surface Research Articles

On $ H' $-splittings of a handlebody

<p>Let $ M $ be a compact connected orientable 3-manifold and $ F $ be a compact connected orientable surface properly embedded in $ M $. If $ F $ cuts $ M $ into two handlebodies $ X $ and $ Y $ (i.e., $ M = X\cup_FY $), then we say that $ F $ is an $ H' $-splitting surface for $ M $ and call $ X\cup_FY $ an $ H' $-splitting for $ M $. When the $ H' $-splitting surface $ F $ is incompressible in a handlebody $ H $, a characteristic of an $ H' $-splitting $ H_1\cup_F H_2 $ to denote $ H $ is already known. In the present paper, we generalize the above result as follows: Let $ H $ be a handlebody of genus $ g\geq 1 $, $ X\cup_F Y $ an $ H' $-splitting for $ H $. Then, either $ X\cup_F Y $ is stabilized, or there exists a reducing system $ \mathcal{J}_1\cup\mathcal{K}_1 $ of $ F $, such that $ \mathcal{J}_1 $ is quasi-primitive in $ Y $ and $ \mathcal{K}_1 $ is quasi-primitive in $ X $. Combining the result with the known result, we obtain a characteristic of an $ H' $-splitting $ H_1\cup_F H_2 $ to denote a handlebody.</p>

Acoustic emission and splitting surface roughness of sandstone in a Brazilian splitting test under the influence of water saturation

Water weakens rock masses, which induces a series of engineering geological hazards. In this study, Brazilian splitting and acoustic emission (AE) experiments were conducted on sandstone with different saturation levels (0%, 25%, 50%, 75%, and 100%), and the effect of saturation on the AE and fracture characteristics was investigated. Meanwhile, nuclear magnetic resonance (NMR) test was used to analyze the water absorption and distribution characteristics of the samples with different saturation. Three-dimensional (3D) morphological scanning and scanning electron microscopy (SEM) were performed to analyze the roughness of the splitting surface. The tensile strength of rocks decreased from 3.05 MPa to 0.98 MPa with a moisture content from dry to saturated conditions, which obeyed an exponential function. The hardness of the sandstone decreased from dry to saturated by 56.6%, whereas the plasticity of the high-saturation sandstone increased. The AE counts and cumulative energy distribution decreased from 3880 and 39,550 to 1248 and 476, respectively, from dry to saturated conditions. Based on the Ib value, the rock damage process can be divided into three stages: fluctuation, stabilization, and decline. As the saturation increased, the initial Ib value decreased from 0.1047 to 0.0755. The development of large fractures increased during the splitting of the highly saturated rocks. With increasing saturation, the fracture surface joint roughness coefficient (JRC) and fractal dimension increased. The mean JRC increased from 5.98 to 13.6025. The unsaturated JRC showed an obvious dispersion compared with the dry and saturated sandstones. Combined with micro-macro characterization, it was found that an increase in saturation caused the rock to generate a weak structure. The damage gradually evolved from transgranular to intergranular fractures, leading to the macroscopic performance of rougher splitting surfaces and lower AE.

Bond strength theory between rebar and recycled aggregate concrete after freeze-thaw cycles under stress state Ⅰ: Uniaxial lateral compression

In recent years, the utilization of recycled aggregate concrete (RAC) as an environmental-friendly material in the construction industry has been actively promoted. A sufficient bond between rebar and RAC is crucial for the load carrying capacity and long-term durability of RAC structure. However, many connection sections between rebar and RAC may be destructed, especially in cold regions where freeze-thaw cycles can worsen the deterioration of structures, under uniaxial compression. To investigate the coupling effect of freeze-thaw cycles and uniaxial lateral pressure on bonding properties of rebar and RAC, variables, such as number of freeze-thaw cycles (F), uniaxial lateral pressure stress ratio (ξ), and recycled aggregate replacement ratio (R), are considered in this study. 117 specimens were fabricated and divided into 39 groups for pull-out test. Different bond-slip curves were obtained, and corresponding characteristics were analyzed. Moreover, this paper proposed a novel bond strength theory by combining a superposed stress field distribution function with a splitting surface stress analysis. The distribution function consisted of the stress distribution of uniaxial lateral pressure loading state without pullout and pullout process without lateral pressure, while the stress analysis amended the softened sleeve theory with a spatial intensity model. The results show that both bond strength and peak slip are positively correlated with uniaxial lateral compression but negatively correlated with the accumulation of freeze-thaw damage. The recycled aggregate (RA) replacement ratio has a minor effect on bond strength and peak slip. The factor of uniaxial lateral pressure is dominant and mitigates the adverse effects of freeze-thaw damage and RA substitution on bonding properties. Notably, the methods of decomposition and stress synthesis break through the limitations of traditional bond strength theory, resulting in a wider scope of application. The bond strength theory applies not only to elastic sleeve bonding part but also to softened sleeve bonding part in reinforced concrete building structure. This theory can more accurately predict the failure morphology and ultimate bond strength in freeze-thaw conditions under uniaxial lateral pressure load.

Study on microscopic failure mechanism and numerical simulation of sandstone under different saturated pressure

X-ray diffraction and SEM scanning are conducted to examine the alterations in sandstone under different saturation conditions to reveal the water-rock softening effect on sandstone from the Qilicun tunnels in China under varying saturation pressures. The mechanisms underpinning the strength softening of sandstone are analyzed using uniaxial compression tests. The experimental results demonstrated that after immersion in water, the internal cementing material within the sandstone dissolves, and the mineral particles fragment or disintegrate, increasing porosity. In the presence of water, the macroscopic compressive strength of sandstone exhibits a declining trend. Concurrently, as the saturation pressure escalates, the compressive strength diminishes by approximately 10%, the elastic modulus decreases by about 30%, and Poisson's ratio incrementally falls by about 25%. The sandstone's failure is characterized by both axial multiple splitting surface failure and shear failure surface. Finally, a strain-softening numerical model is employed to simulate the failure behaviors of sandstone under various saturation pressures. The findings indicated that the sandstone sample exhibits plastic failure characteristics under high saturation pressure.

A numerical study on the tensile splitting of concrete with digital image processing

Numerical simulations are performed to investigate the mechanical behavior of concrete in uniaxial compression test and tensile splitting test. Especially, the digital image processing (DIP) techniques are utilized to differentiate the interface types on the fracture surface of the specimen that is already split, which involves transforming the color image of the fracture surface into a binary image through graying, binarization, and opening operation processing. The boundary data obtained from the binary image is further processed by mirrored comparison and contour simplification, and is finally imported into the numerical model to reconstruct the different interface regions on the splitting surface. Different material properties are assigned to the corresponding interface regions through intensive programming with Python, whereby the influence of heterogeneity on the splitting process is analyzed through the established numerical model. Through comparison with homogeneous model, it is found that the heterogeneous model is capable of reproducing a more genuine fracturing process, with respect to the fracture initiation locations and splitting sequence of different interfaces. The proposed modeling schemes are valuable for potential researches exploring the failure process of the materials such as concretes and rocks whose mechanical behavior is influenced by their inherent heterogeneity.

Stellar stability in the presence of reacting interfaces: consequences for hybrid stars

If the surface tension of dense matter is high enough, a hybrid star composed of a quark matter core and a hadronic mantle may display a sharp interface. Perturbations of such a star may lead to conversion reactions occurring in the vicinity of the quark-hadron splitting surface. If the conversion timescale is much larger than the perturbation one (slow reactions), changes of stellar stability do occur at critical points of the M(R) curve. As a consequence, a new class of dynamically stable hybrid stars is possible. Densities tens of times larger than the nuclear saturation density could be attained at the center of these hypothetic objects. We examine possible formation mechanisms for this new class of hybrid configurations and explore potential observational signatures that could serve as evidence for their existence.

A method for searching splitting surface considering network splitting adaptation index

AbstractAs an effective control measure to ensure uninterrupted power supply to critical loads under extreme faults, network splitting is of great significance for maintaining system safety and stability. The purpose of this study is to develop a method to accurately and quickly find a reasonable splitting surface and reliably perform network splitting. To address the current problem of poor node classification when splitting, the correlation between nodes is obtained through modal analysis of the system. Node classification criteria are proposed to accurately classify different types of nodes and obtain a suitable splitting space. Based on the node correlation, a splitting adaptation index reflecting the suitability of splitting is proposed. Furthermore, a comprehensive index for the optimisation of the splitting surface is proposed by combining the minimum unbalanced power and the splitting adaptation index, and the splitting surface is quickly determined based on this index. Finally, simulation verification is carried out using the IEEE‐118 standard system, which shows that the method can accurately determine the splitting space and optimise the selection of the splitting surface.

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

By introducing the dimensional splitting (DS) method into the multiscale interpolating element-free Galerkin (VMIEFG) method, a dimension-splitting multiscale interpolating element-free Galerkin (DS-VMIEFG) method is proposed for three-dimensional (3D) singular perturbed convection-diffusion (SPCD) problems. In the DS-VMIEFG method, the 3D problem is decomposed into a series of 2D problems by the DS method, and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method. The improved interpolation-type moving least squares (IIMLS) method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems. The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems. The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes. For extremely small singular diffusion coefficients, the numerical solution will avoid numerical oscillation and has high computational stability.

Effects of water on mechanical behavior and acoustic emission characteristics of coal in Brazilian tests

An in-depth understanding of how water affects mechanical behavior of coal and fracture failure modes is important for evaluating the stability of underground engineering. In this paper, Brazilian splitting tests are carried out on coal samples with different moisture contents (0%, 1.10%, 2.20%, 3.29% and 4.41%), and acoustic emission (AE) signals are collected simultaneously. The fractal dimension of splitting surfaces is calculated by the cubic covering method to quantitatively describe characteristics of specimens. Combined with two microscopic imaging technologies, i.e. computed tomography (CT) technology and scanning electron microscopy (SEM), the mechanism of crack propagation and strength degradation in coal samples under the effect of water is discussed. Experimental results present that moisture contents change the mechanical strength, AE signals and failure mode of coal samples. As moisture contents increase, the tensile strength of coal samples reduces exponentially, the plastic behavior increases, while the wave velocity increases logarithmically. In the perspective of AE signals, the maximum R value (ratio of cumulative AE hits to cumulative AE energy) increases with the increase of moisture contents, indicating that specimens under higher moisture content conditions can induce more low-energy events, and more complicated crack network. After the splitting failure in coal samples, the fractal dimension of splitting surfaces increases logarithmically with the growth of moisture contents. Based on the macroscopic and mesoscopic characterization results such as AE signals, CT and SEM, it is considered that the existence of water reduces the strength of pre-existing weaknesses (beddings and cleats) in coal samples. As a result, the splitting surface develops along pre-existing weaknesses, which increases the fractal dimension of splitting surfaces and reduces the intensity of AE signals.

Change of the Structural Properties of High-Performance Concretes Subjected to Thermal Effects.

The paper refers to studies of the structure of high-performance concrete with polypropylene fibre at different dosages. The authors see a research gap in the study of the effect of adding polypropylene fibre on the parameters of concrete exposed to high temperatures. The study takes into account the thermal effect—groups of samples were heated to 200 °C, 400 °C and 600 °C. The authors carried out basic tests to describe the changes in density, ultrasonic tests, uniaxial compression strength tests and tensile tests by splitting. The positive effect of polypropylene fibres is mainly observed between 20 °C and 200 °C. The melting of polypropylene fibres causes a delay in the development of micro-cracks in the structure of these concretes compared to HPC. Adding polypropylene fibres to the mixtures also increased the speed of ultrasonic wave propagation in the medium. The research was deepened with tomographic imaging. A description of the splitting surface was carried out. The results of tensile by splitting tests clearly show an increase in the relative failure area for unheated concretes in proportion to the number of fibres used. Changes in splitting surfaces under the influence of temperature are graphically illustrated. Furthermore, differences in the samples under the influence of heating at high temperatures are presented. Finally, the porosity development of all sample groups before and after heating at all temperatures is described.

Study of the Mechanical Properties of Alkali-Activated Solid Waste Cementitious Materials at the Interface.

The paper uses alkali-activated slag and fly ash as cementitious materials to pour and repair concrete. Their modification on the bonding surface of new and old concrete is studied. The new and old concrete composite specimens were prepared. The split tensile strength test of the new and old concrete specimens along the interface was carried out, and the test results of different alkali-stimulated slag and fly ash concrete as repair materials were compared and analyzed. The influence of activator modulus and other factors on the bond strength of new and old concrete interfaces was studied, and the law of its strength change was explored. The research results show that with the gradual increase in the amount of fly ash minerals, the splitting tensile strength presents a trend of first increasing and then decreasing. When the amount is 50%, the splitting surface partly occurs on the old concrete. It shows that the bonding effect is the best at this content; the alkali excitation modulus gradually increases, and the splitting tensile strength shows a downward trend. When the activator modulus is 1.3, more gelatinous substances can be observed in the section of the specimen. These overlap each other to form a tight material skeleton structure; a comparative analysis of the bonding strength of the new and old concrete interfaces with different interface agents and without interface agents showed that the alkali-activated solid waste cementitious material has the best repair performance and greater bonding strength when the water-to-binder ratio is 0.3.

Rock Dynamic Fracture Characteristics by Mini‐Linear Shaped Charge Jet Penetration: A Case Study

An insignificant number of studies have focused on employing penetration using mini‐linear shaped charge jets for directionally controlled splitting of massive rocks. In this study, we adopt a numerical calculation method to simulate the penetration and formation of the main splitting surface of a concrete specimen, considering a wedge angle of 45° in both processes. The surface on the principal axial plane is found to split first due to linear jet penetration. In the case of single primary‐plane splitting, cracks appear at both ends of the long axis of the penetration crack and the splitting surface extends diagonally from the center of the penetration. A transverse crack separates the splitting surface and the radial‐fracture surface, and the degree of fracture decreases along the direction of the height of the specimen. Finally, a realistic physical model demonstrating penetration using a mini‐linearshaped charge jet is established. It is a rapid and safe blasting technology to handle hazardous massive rocks during emergency rescuing or mining.

Integrating ferromagnetism and ferroelectricity in an iron chalcogenide monolayer: a first-principles study.

Two-dimensional (2D) ferro-type materials have received great attention owing to the remarkable polarization effect in optoelectronics and spintronics. Using the first-principles method, the coupling between ferromagnetism and ferroelectricity is investigated in a multiferroic Janus 1T-FeSSe monolayer, which has a strong Stoner ferromagnetic ground state. The magnetic anisotropy energy (MAE) is apparently impacted by the out-of-plane asymmetry donated ferroelectricity, which is reflected by the asymmetry of the Z-MAE image. The easy magnetization axis of Janus FeSSe is the +y axis with a large MAE of 0.59 meV, rooting in unpaired d electrons of Fe atoms. The transformation of band splitting and Fermi surface can be effectively engineered by different magnetic polarization directions. The ferromagnetic (FM) coupling of the FeSSe monolayer is very robust under external strain within the range of -6% to 6%, while the strength of magnetic moment of Fe atoms and polarization are easily strain-engineered, the intrinsic mechanism of which can be elaborated by the GKA rules that depend on angles and distances. This multiferroic FeSSe monolayer provides a new platform for exploring the coupling of 2D ferromagnetism and ferroelectricity and designing low-dimensional multiferroic electronics.

Influence of mesoscopic pore characteristics on the splitting-tensile strength of cellular concrete through deep-learning based image segmentation

Properties of cellular concrete are significantly influenced by the mesoscopic pore structures, but the porosity-property relationships are still unclear. This paper tried to understand the pore effect on the splitting-tensile strength of cellular concrete by the specially prepared specimens with controlled additions of porosity. A series of cellular concrete specimens with different mix design were carefully prepared and subjected to splitting-tensile tests at a specified loading rate of 1 mm/min. Then, an integrated framework was developed for recognizing and measuring meso-structure based on the deep-learning model. The meso-characteristics of pores on splitting surfaces directly related to the splitting-tensile strength were captured and quantified automatically, and the relationship between meso-characteristics of pores and splitting-tensile strength was discussed in details. It was found that the splitting-tensile strength decreases as the porosity or pore size increases, accompanied by the variability of other pore characteristics such as uniformity coefficient and fractal dimension. At last, pore size and surface porosity on the splitting surface were identified as the main factors for splitting-tensile strength, and an empirical model was suggested to predict it with the above main factors. The findings in this paper further improve the understanding of the influencing mechanism for pores on the splitting-tensile strength, which can be used to optimal design of cellular concrete.

A parallel construction method based on linear hierarchical bounding box without stack

The intersect operation of geometry is a common method of collision detection. To achieve a fast intersect operation, a hierarchical bounding box must be quickly constructed. This paper proposes an effective space division method for constructing high-quality linear hierarchical bounding boxes through ray tracing. This method can generate more regular axial bounding boxes into a complete binary tree. This structure can be completely parallel on the GPU, and effective parallelization can ensure the fastest tree-building time. The algorithm in this paper uses a non-stack ray tracing method to increase the frame rate of the 3D model rendering in the graphics processing unit and reduce the construction time of the bounding box. The experimental analysis of construction time, frame rate, average number of intersections and other performance indicators, the experimental results show that the use of stack-free midpoint splitting method and surface heuristic splitting method to ensure rapid construction time and efficient ray traversal performance, improve the object’s light traversal efficiency.

Enhanced Terahertz Radiation by Efficient Spin-to-Charge Conversion in Rashba-Mediated Dirac Surface States.

The enhancement of terahertz (THz) radiation is of extreme significance for the realization of the THz probe and imaging. However, present THz technologies are far from being enough to realize high-performance and room-temperature THz sources. Fortunately, topological insulators (TIs), with spin-momentum-locked Dirac surface states, are expected to exhibit a high terahertz emission efficiency. In this work, the novel concept of a Rashba-state-enhanced spintronic THz emitter is demonstrated on the basis of ferromagnet/heavy metal/topological insulator (FM/HM/TI) heterostructure. We find that the THz emission intensity changes as a function of HM interlayer thickness, and a 1.98 times higher intensity compared to that of FM/TI can be achieved when a meticulously designed thickness of the HM layer is inserted. The improvement of terahertz radiation is ascribed to the additive effect of Rashba splitting and topological surface states at the HM/TI interface. These results offer new possibilities for realizing spintronic THz emitters in TI-based magnetic heterostructures.

Dynamic splitting tensile behaviours of distilled-water and river-water ice using a modified SHPB setup

The tensile strength of ice subjected to dynamic loading constitutes many ice engineering applications such as ice blasting and hail-aircraft impact. In this study, the dynamic tensile behaviours of distilled-water and river-water ice were firstly investigated using the flattened Brazilian disc method with a modified split Hopkinson pressure bar system. Columnar freshwater ice samples were tested at strain rates ranging from 20 to 135 s−1 and temperatures ranging from −5 to −45 °C. The effects of impact velocity, loading rate, and ice sample thickness on the dynamic splitting tensile strength were also explored. Distilled-water ice specimens exhibited a higher indirect tensile strength than their river-water counterparts. The lower the temperature, the greater is the tensile strength, particularly in the case of distilled-water ice in the strain rate range of 89–135 s−1. The temperature had less effect on the dynamic tensile strength of distilled-water ice compared to the loading rate, and the specimen thickness had little effect on the dynamic indirect tensile strength. A large number of non-penetrating cracks were observed on the disc surface, indicating the inhomogeneous distribution of the tensile stress interpreted based on the 3D Brazilian disc theory. The closer the two end faces in the central cross section, the greater the tensile stress. The presence of single and multiple strip cracks on the splitting surface were discovered, possibly because of the instant expansion of the ice specimen and subsequent formation of mode-I cracks in the thickness direction.

CMGC: a CAD to Monte Carlo geometry conversion code

Automatic conversion from a computer-aided design (CAD) model to Monte Carlo geometry is one of the most effective methods for large-scale and detailed Monte Carlo modeling. The CAD to Monte Carlo geometry converter (CMGC) is a newly developed conversion code based on the boundary representation to constructive solid geometry (BRep → CSG) conversion method. The goal of the conversion process in the CMGC is to generate an appropriate CSG representation to achieve highly efficient Monte Carlo simulations. We designed a complete solid decomposition scheme to split a complex solid into as few nonoverlapping simple sub-solids as possible. In the complete solid decomposition scheme, the complex solid is successively split by so-called direct, indirect, and auxiliary splitting surfaces. We defined the splitting edge and designed a method for determining the direct splitting surface based on the splitting edge, then provided a method for determining indirect and auxiliary splitting surfaces based on solid vertices. Only the sub-solids that contain concave boundary faces need to be supplemented with auxiliary surfaces because the solid is completely decomposed, which will reduce the redundancy in the CSG expression. After decomposition, these sub-solids are located on only one side of their natural and auxiliary surfaces; thus, each sub-solid can be described by the intersections of a series of half-spaces or geometrical primitives. The CMGC has a friendly graphical user interface and can convert a CAD model into geometry input files for several Monte Carlo codes. The reliability of the CMGC was evaluated by converting several complex models and calculating the relative volume errors. Moreover, JMCT was used to test the efficiency of the Monte Carlo simulation. The results showed that the converted models performed well in particle transport calculations.

Preparation of a Flexible Superhydrophobic Surface and Its Wetting Mechanism Based on Fractal Theory

Substrates of superhydrophobic surface are important for their application. Preparation of a flexible superhydrophobic surface has drawn more and more attention. In this work, a flexible substrate was made using a semi-curing spray method to obtain a flexible superhydrophobic surface with excellent abrasion resistance on the surface of a room temperature vulcanized silicone rubber. Results show that under a bending condition, excellent superhydrophobic properties are still maintained. The Cassie-Baxter model and Wenzel model can be used to estimate the static water contact angle for regular roughness surfaces. There are few numerical theoretical models to predict contact angle or wetting mode for irregular micro-nanostructures superhydrophobic surfaces. The fractal theory can be used to transform the equation of Wenzel model and obtained the fractal wetting theory suitable for fractal structures on irregular rough surfaces. However, this fractal-wetting model cannot be applied to Cassie-Baxter state, which is always suitable for superhydrophobic surfaces. A new method was developed to calculate the static water contact angle of water droplets in the Cassie-Baxter model state. Using image identification and split surface method, a new model is constructed based on the fractal theory. Experimental data for water contact angles on flexible superhydrophobic surface with SiC/CNTs micro-nanostructures is agreement with the simulated values.

Mechanical behavior of different sedimentary rocks in the Brazilian test

Mechanical behavior of the rock in tensile stress environment remains an unresolved problem in the underground mining, where surrounding rocks commonly experience tensile failure. In the present study, tensile failure behavior of three types of sedimentary rocks is investigated experimentally and numerically. The deformation response, fracture propagation, and splitting pattern as well as energy conversion of the rocks are examined in the Brazilian test with a testing machine, high-speed camera, and image scanning system. The tested rocks tend to show elastic-brittle-plastic deformation behavior in the biaxial stress state. Tensile strengths of the coal, mudstone, and sandstone are 1.2, 3.9, and 13.4 MPa, respectively. The coal and mudstone split in a static mode while the sandstone in dynamic mode. The splitting fracture initiates at the disk center in the coal and sandstone, and it emerges at the loading point in the mudstone. The fracture propagates more quickly in the rock with larger strength. It uses 1200.0, 5.8, and 0.4 ms, to break out sample surface of the coal, mudstone, and sandstone, respectively. The joint roughness coefficient (JRC) of the splitting fracture is largest (20.1) in the mudstone, followed by that in the coal (17.7), and it is smallest in the sandstone (15.3). A continuous-discontinuous coupling model, which is capable of analyzing the stress distribution and fracture propagation synergistically, is developed and calibrated against the experimental data. The numerical model accurately reproduces mechanical behavior of the tested rocks observed in the Brazilian test. The splitting fracture propagates along the maximum tensile stress plane in the sandstone. The propagation direction is locally influenced by the grain boundary with small tensile strength in the coal while, in the mudstone, the fracture is mainly formed along the grain boundary. Such differences in the fracture propagation path lead to the increasing trend from the JRC of the splitting surface in the sandstone to that in the coal and finally to that in the mudstone.