Wedge Angle Research Articles

Study on the characteristics of cavitation and COD removal of an addendum rotational hydrodynamic cavitation reactors

AbstractThis paper presented an addendum rotational hydrodynamic cavitation reactors (ARHCR) that enabled circumferential shear cavitation, axial cavitation, and the Venturi effect, thus increasing cavitation efficiency. The experiments on hydroxyl (·OH) release and chemical oxygen demand (COD) removal demonstrate the feasibility of cavitation performance characterization and COD removal rate. The findings indicate that the COD removal rate can reach a maximum value of 28% or 30% with an increase in flow rate or rotating speed, respectively. Specifically, the maximum values were achieved at a rotation speed of 2,500 rpm or a flow rate of 1.0 m3·h−1. Based on the mechanism of the addendum cavitation, the wedge angles, and the crucial structural parameters, were examined for optimizing cavitation performance. The results revealed that the cavitation number and cavitation bubble were significantly influenced by wedge angles, as well as the efficiency of cavitation energy. The mechanical shear of fluid was enhanced by wedge angles, resulting in constant compression and release of fluid with increased kinetic energy. This led to stronger effects on bulge blocks, and the formation of vortexes that rebounded constantly, resulting in lower pressure areas and expanded regions of cavitation. Among the wedge angles tested, the wedge angle of 15° exhibited the highest cavitation bubbles with a maximum value of 46%. This was 31% higher than the grooves‐type cavitator reported. Furthermore, the cavitation performance was extremely improved with a wedge angle of 15°, as corresponding with the maximum efficiency of cavitation energy. These explorations provide references for the removal of COD in industrial and agricultural wastewater, as well as the development of novel reactors for wastewater treatment.

Is it safe to treat osteoporotic burst thoracolumbar fracture using percutaneous vertebroplasty? A minimum of five-year follow-up study

Percutaneous vertebroplasty for the treatment of osteoporotic burst fractures remains controversial. A previous study has shown that an osteoporotic burst fracture with asymptomatic spinal canal compromise is not a contraindication for percutaneous vertebroplasty. To determine whether these outcomes persist over a long term, we continued to observe patients in their short-term study over a long-term period. Prospective study. Patients with osteoporotic vertebral fractures were classified as Dennis type I and II and AO type A1-A4, and no neurological deficits were observed. Oswestry disability index and visual analog scale (VAS1) for pain were outcome measures. Radiological outcomes were vertebral body height and kyphotic angle. Complications included cement leakage, adjacent fractures, and transition to instrumented fusion. Between June 2015 and December 2016, 96 patients with osteoporotic vertebral fractures who met the inclusion criteria were prospectively enrolled. Preoperative, postoperative, and latest follow-up clinical outcomes were assessed using the Oswestry disability index and VAS. The radiological outcomes included vertebral body height, kyphotic angle, and adjacent fractures. Patients with intractable pain and neurological deficits during the follow-up were indicated for surgical treatment using decompression and instrumented fusion. Fifty-one patients with osteoporotic compression fractures and 45 with osteoporotic burst fractures were included in this study. Mean follow-up duration was 74 months, and posterior vertebral body height, kyphotic wedge angle, and VAS score were not altered during the follow-up period. Three (5.9%) patients in an osteoporotic compression fracture group and three (6.7%) in a osteoporotic burst fracture group developed persistent pain, further collapse, and neurological deficits, and were indicated for surgical treatment. No significant differences were observed in the rates of adjacent fractures. Percentage of patients who required surgical treatment was not significantly different between the groups. Osteoporotic burst fractures with asymptomatic spinal canal compromise treated with percutaneous vertebroplasty are safe and effective for pain management during long-term follow-up.

Regular reflection to Mach reflection (RR–MR) transition in short wedges

Regular reflection (RR) to Mach reflection (MR) transitions ( ${\rm RR}\leftrightarrow {\rm MR}$ ) on long wedges in steady supersonic flows have been well studied and documented. However, in a short wedge where the wedge length is small, the transition prediction becomes really challenging owing to the interaction of the expansion fan emanating from the trailing edge of the wedge with the incident shock and the triple/reflection point. The extent of this interaction depends on the distance between the wedge trailing edge and the symmetry line (Ht). This distance is a geometric combination of the distance of the wedge leading edge from the symmetry line $(H)$ , the wedge angle ( $\theta$ ) and the wedge length $(w)$ . In the present study, we used the method of characteristics to model the complete wave interactions which accurately predicted shock curvatures and the reflection configurations for all ranges of the incoming flow Mach number. In the case of short wedges, the transition criterion strongly depends on the wedge length, which can be so adjusted even to eliminate the ${\rm RR}\rightarrow {\rm MR}$ transitions till the wedge angle reaches the no-reflection domain. Transition lines for both the detachment criterion and von Neumann criterion are also drawn to investigate the dual solution domain, and the reflection configurations were verified experimentally for the first time on short wedges. By using proper input configuration parameter ( $w/H$ ), various types of shifts in the dual solution domain for short wedges are studied and categorised into three types, namely Type I, Type II and Type III.

Tool–Branch Interaction Mechanism of Impact-Pruning Process Based on Finite Element Method

This study addresses the necessity for a more profound comprehension of the mechanical behavior and fracture mechanisms of tree branches during impact pruning. The methodologies of the research are to develop a failure model of impact-cutting mechanics and a tool–branch interaction model using the finite element method (FEM). The validation of the model was conducted through the measurement of cutting forces and cross-sectional morphology in the field. A comparative analysis between experimental and simulation data revealed an average relative error below 15% for cutting force and below 10% for the cross-sectional ratio, thereby confirming the accuracy of the model. The findings indicate the presence of plastic deformation within the cutting zone, with elastic deformation prevailing in the surrounding region. As the branch approaches the yield point, the phenomenon of plastic deformation intensifies, resulting in a notable increase in internal energy demands, particularly in larger branches. The optimal pruning diameter was identified as 15 mm. An increase in cutting velocity raises the peak cutting force by 460.9 N per m/s, while a 1° increase in the blade wedge angle adds 34.9 N. A reduction in normal stress by increasing the tool back angle improves energy efficiency. This study provides insights to optimize pruning practices, enhancing efficiency and precision.

Thermal transportation of radiative cathode nanotube‐based nanofluid on a stretching/shrinking wedge with varying magnetism and heat source

AbstractThe complex heat transfer processes occurring in a magnetized water‐based hybrid nanofluid flowing past a stretching or shrinking wedge are investigated in this work. The research highlights the significant influence of the wedge angle on fluid flow patterns and temperature gradients, emphasizing how larger angles cause changes in pressure, flow separation, and temperature profiles. Additionally, the study emphasizes the importance of radiation effects near surfaces, where increased radiation often leads to cooling due to thermal energy emission. The findings have implications in industries such as aerospace, electronics, thermal management, and groundwater resources management where precise temperature control is critical for safe and efficient operations. The numerical method applied to solve the governing equations in the study is the fourth‐order Runge–Kutta technique with shooting technique. This method efficiently solves the boundary value problem by converting it into a system of first‐order initial value problems. Then shooting technique is used to solve the system, starting with an adequate initial guess. The study's results are presented in tabular and graphical forms, providing valuable insights into the complex fluid dynamics and thermal behavior in the given setting, enabling more informed decision‐making and optimization in relevant engineering applications. Increased radiation frequently results in a cooling effect owing to thermal energy output. Heat sinks/heat sources are crucial in temperature regulation and are effective in lowering temperatures via processes. We also emphasize the importance of radiation impacts near surfaces, where increased radiation frequently leads to cooling owing to thermal energy emission. The numerical values of skin friction and Nusselt number for various parameters in the cases of shrinking and stretching provide crucial insights into the heat transmission and frictional properties of the system under examination. These quantitative results contribute to a better understanding of the complex fluid dynamics and thermal behavior in the given setting, emphasizing the significance of the research findings.

Error analysis based on a tunable wave plate polarization interferometric imaging spectrometer

Interference imaging spectroscopy combines modern imaging technology with spectral technology, holding significant importance for object imaging and spectral detection. This article introduces the principle of an adjustable wave plate polarization interferometric imaging spectrometer. The example design specifications are set for an observation wavelength range of 450–780 nm and a maximum resolution of 2 nm at 450 nm, with a 0.5 in detector as the base for calculating the specific dimensions of the Soleil–Babinet compensator. An investigation was conducted on the issues of nonuniform sampling, as well as three types of mechanical errors: flatness, wedge angle tolerance, and optical axis orientation accuracy. Emphasis was placed on discussing the impact of these errors on the instrument’s optical path difference and spectral reconstruction accuracy. This research provides theoretical guidance for the design and engineering of this miniaturized imaging spectrometer.

Effect of screw insertion depth into fractured vertebrae in the treatment of thoracolumbar fractures

PurposeThe study’s objective was to assess the effect of the screw insertion depth into fractured vertebrae in treating thoracolumbar fractures.Materials and methodsThis was a retrospective analysis of 92 patients with thoracolumbar fractures from December 2018 to February 2020. Patients had AO type A2, A3 thoracolumbar fractures. The patients were divided into two groups according to the screw insertion depth. The vertebral wedge angle (VWA), Cobb angle (CA), anterior vertebral body height (AVBH), middle vertebral body height (MVBH), visual analog scale (VAS) score, and Oswestry Disability Index (ODI) were compared preoperatively and at one week and 12 months postoperatively. The correlation between Vertebral height loss and potential risk factors, such as sex, age, BMD and BMI was evaluated.ResultsCompared with the preoperative data, the postoperative clinical and radiographic findings were significantly different in both groups, But no significant difference between the two groups at 1 week. At 1 year postoperatively, there was a significant difference in the CA (p < 0.0001), VWA (p = 0.047), AVBH (p < 0.0001), MVBH (p < 0.0001), VAS score (p < 0.0001), and ODI (p < 0.0001) between the two groups, Except for age, bone density and other influencing factors the long screw group had better treatment results than the short screw group.ConclusionA longer screw provides greater grip on the fractured vertebral body and stronger support to the vertebral plate. The optimal screw placement depth exceeds 60% of the vertebral body length on the lateral view.

Overloaded Vertebral Body Following Consecutive Three-Level Hybrid Surgery Comparing with Anterior Cervical Discectomy and Fusion.

Based on the varying number and relative positions of cervical disc replacement (CDR) and anterior cervical discectomy and fusion (ACDF) procedures, three-segment hybrid surgery (HS) presents a diverse structural approach. Currently, the potential differential effects of HS with different segment combinations and surgical procedures on overloaded vertebral body (OVB) occurrence remain unexplored. The purpose of this retrospective study is to compare the clinical and radiological outcomes of HS and ACDF in treating cervical degenerative disc disease (CDDD), aiming to provide further insights into OVB. This study included patients with three-level CDDD who underwent ACDF or HS at our institution. Eligible patients were divided into three groups: Type I (one-level CDR and two-level ACDF), Type II (two-level CDR and one-level ACDF), and ACDF (three-level ACDF). For radiographic analysis, patients were further divided into the Replacement Segment Group and the Nonreplacement Segment Group based on the presence of replacement segments above and below the OVB. Clinical outcomes were evaluated using visual analog scale (VAS) scores for neck and arm pain, Japanese Orthopedic Association (JOA) scores, and neck disability index (NDI) scores. The cervical radiological parameters assessed included (1) vertebral cross-sectional area (CSA), (2) wedge angle (WA), (3) anterior vertebral height (AH), (4) posterior vertebral height (PH), and (5) Hounsfield unit (HU) values. Statistical methods included paired t-test, ANOVA test, and chi-square test. Independent samples t-test, Mann-Whitney U test, and Wilcoxon signed-rank test were used to compare the differences between two groups according to the results of normal distribution test. A total of 123 patients, evenly distributed among three groups, were included and were well matched in terms of demographic characteristics. The likelihood of vertebral body collapse (VBC) was notably higher in the ACDF group (41.5%) compared with the Type I (17.9%) and Type II (8.9%) groups (p < 0.01). Following surgery, both at 3 and 6 months, the ACDF group demonstrated higher VAS neck scores and NDI scores compared with the Type I and Type II groups (p < 0.01). Additionally, the WA and AH values of the upper and lower adjacent OVB were consistently lower in the ACDF group than in the Type I and Type II groups at 6 and 12 months and at the final follow-up (p < 0.01). Notably, in the Nonreplacement Segment Group, WA significantly decreased at 12 months postoperatively and at the final follow-up compared with the Replacement Segment Group (p < 0.01). Three levels of HS appear to reduce stress concentrations and alleviate morphological changes in OVB. The occurrence of more VBC patients with OVB was associated with the use of Zero-P or Zero-P VA implants.

Ultrasonography-guided canal decompression combined with vertebroplasty and cement-augmented pedicle screw fixation for stage III Kümmell’s disease with neurological deficits: a retrospective cohort study

BackgroundPercutaneous vertebroplasty or kyphoplasty is the preferred procedure for stage I and II Kümmell’s diseases (KDs), but there exist controversies on the operative option of stage III KD. This study aimed at exploring the safety and efficacy of ultrasonography-guided canal decompression (UG-CD) combined with vertebroplasty and cement-augmented pedicle screw fixation (CA-PSF) for treating stage III KD with neurological deficit (ND).MethodsBetween September 2017 and December 2023, all patients who received the UG-CD combined with vertebroplasty and CA-PSF for managing stage III KD with NDs were reviewed retrospectively with their demographic and operation data, and complications recorded. Besides, the scores of Visual Analogue Scale (VAS) and Oswestry Disability Index (ODI), together with imaging data including the kyphotic Cobb angle (KCA), wedge angle (WA), spinal canal area (SCA) at the narrowest level as well as anterior (AHR) and middle (MHR) height ratios were measured and compared between pre- and post-operation.ResultsA total of eleven patients with a mean age of 70.09 ± 2.98 years old were included in our study with their surgical time, hospitalization length, blood loss, and follow-up time being 150.91 ± 17.94 min, 202.09 ± 39.95 ml, 8.18 ± 1.17 days, and 16.91 ± 4.09 months, respectively. During the final follow-up, the KCA, WA, VAS scores, ODI scores, AHR, MHR, and SCA were significantly improved (P < 0.01). Intraoperatively, one case suffered a transient decrease in the motor evoked potential. Another case experienced a cerebrospinal fluid leakage postoperatively that was then successfully treated.ConclusionUG-CD combined with vertebroplasty and CA-PSF could be a feasible procedure for safely and effectively handling stage III KD with NDs.

Bone density as a risk of early loss of correction after percutaneous posterior spinal fixation for traumatic thoracolumbar fracture: a study on the usefulness of Hounsfield unit values on computed tomography scan.

Vertebral Hounsfield unit values on computed tomography scan (CT values) have been found to be correlated with bone density measured using dual-energy X-ray absorptiometry. We hypothesized that low preoperative CT values are risk factors for early loss of correction after percutaneous posterior spinal fixation (PPSF). This study aimed to evaluate the usefulness of measuring preoperative CT values. In total, 104 patients underwent PPSF due to traumatic thoracolumbar fracture. Among them, 53 with a range of fixation that was within two vertebrae above and below the fractured vertebra were selected. CT values were measured preoperatively from the most cephalad vertebrae on the fixed vertebrae. Vertebral wedge angle (VWA) and local kyphosis angle (LKA) were measured before and after surgery. participants were classified into progression (P) and nonprogression (NP) groups. The P group comprised patients with LKA progressing > 10° from the immediate postoperative period to 3months postoperatively. Meanwhile, the NP group included patients without progression. Eight (15.1%) patients were included in the P group. The vertebral CT values were 102.2 ± 36.7 in the P group and 162.4 ± 59.7 in the NP group (p < 0.01). The pedicle CT values were 114.4 ± 45.9 in the P group and 170.8 ± 72.3 in the NP group (p < 0.05). At 2weeks postoperatively, VWA and LKA of the P group progressed to 9.8° ± 7.0° and 10.9° ± 7.6°, respectively. CT values can predict progressive loss of correction after PPSF.

Formation of property gradient in coarse-grained niobium using a wedge tool: Experiment and analysis

We introduce a novel severe plastic deformation process for coarse-grained niobium, which employs a tool with an inclined (wedge) surface for deforming the material by a reverse shear scheme. The process increases the intensity of shear deformations and the depth of plastic deformation in the body of the workpiece when a wedge tool acts on its surface. The essence of the process is in the repeated displacement of the workpiece material in opposite directions during the asymmetrical introduction of a wedge tool until the required degree of deformation is accumulated in the tool-affected volume. This deformation scheme applies a 15° angle wedge tool to a 21-mm high workpiece. After nine cycles of plastic deformation, a gradient of the accumulated degree of deformation in the range of true strain e = 0.3–4.5 was created. At maximum deformation, the microhardness of the workpieces increased by 1.86 times and the tensile strength by 1.6 times. Fractograms show a significant influence of the accumulated degree of deformation on the nature of the fracture. The finite element method simulation of the deformation process showed that creating a uniformly strengthened layer requires at least five deforming operations. For example, the proposed reverse shear process with a wedge tool can be applied to improve the structure of the surface layers of niobium ingots for subsequent forming. Due to the creation of a significant gradient of properties, the reverse shear process can be used as an express method for determining the mechanical characteristics of different materials in a wide range of accumulated degree of deformation.

Analysis of Wedge Angle Variations in the Treatment Planning System Based on Dose Volume Histogram on Ca Mammae Sinistra

Breast cancer ranks first in terms of the highest number of cancers in Indonesia and is one of the first contributors to cancer deaths. According to IARC, radiotherapy is one of the most important modalities in the treatment of breast cancer. Radiotherapy is a type of treatment that uses ionizing radiation to kill cancer cells without damaging surrounding healthy tissue. To obtain an even or homogeneous dose distribution on an uneven skin surface, a wedge is used so that the radiation given to the tumor area is truly optimal and the surrounding healthy tissue receives a minimum dose. This research was carried out by evaluating the Planning Target Volume (PTV) value based on ICRU-83 and dose distribution in Organs at Risk (OAR) based on QUANTEC standards at four different wedge angles, namely 15°, 30°, 45°, and 60°, used the 3D-CRT technique of tangential radiation with a dose of 50 Gy in 25 fractions on 5 left-sided breast cancer patients. The research results showed that the average Homogeneity Index (HI) values for the 15°, 30°, 45° and 60° wedges were 0.286, 0.346, 0.436 and 0.578, respectively. In the left and right lung dose distribution, the results obtained for the 15°, 30°, 45°, and 60° wedge were respectively 2231.4 and 116.2 cGy, 2257.8 and 114.6 cGy, 2141 and 100 cGy, and 2059.4 and 88.8 cGy. For the average dose distribution to the heart, the values obtained at the 15°, 30°, 45°, and 60° wedges were 2005.6 cGy, 2040.4 cGy, 1930.6 cGy, and 1844.4 cGy, respectively. where the average dose received by OAR is still below the limit allowed by QUANTEC. Using a wedge angle of 15° provides a homogeneous dose distribution for the PTV and a wedge angle of 60° provides the lowest dose distribution for the OAR.

Development of a Disc Blade Cutting System for Sesame Harvesting: Determination of Operating Criteria and Energy Requirements

This study aimed to explore the use of rotary disc blades in cutting, since the mowing units used in sesame harvesting contain many parts, require frequent lubrication, and have vibration problems. An experimental setup with a disc blade working on a cut-mowing system based from harvesting methods of sesame plants was designed and fabricated. The most suitable cutting criteria which are blade edge types (30°-30°, 30°-Flat, 45°-45°, 45°-Flat) and disc blade diameters (150, 180, and 210 mm) were determined for shearing and disc cutting action. The lowest cutting energy was consumed by the disc blade with a 30°-wedge angle at all stem thicknesses and by the disc blade with a diameter of 180 mm for large stem thicknesses. In all pairs of edge, as the disc diameter increased, the energy spent for cutting the stems decreased. There was a significant difference between the two methods in terms of energy consumption only when cutting stems with a diameter of 10 mm. These results show that disc cutting can be recommended as a method for sesame harvesting.

PA-LCR: A flexible ultrasonic characterization method

Abstract Critically refracted longitudinal (LCR) wave is demonstrated to be prominent in the characterization sensitivity of stress or surface/sub-surface defects. According to Snell’s law, however, its excitation seriously relies on the inclined angle of wedge, i.e., the first critical angle (θ CR). From this, it shows poor adaptability to the variations of wave velocity, especially for elastic anisotropic materials, e.g., carbon fibre reinforced plastic (CFRP) composites. An enhanced strategy based on the phased array ultrasonic, termed PA-LCR, is introduced here. It applies a wide angular distribution of energy to achieve beam steering, and then the beam is targeted at θ CR. LCR wave is successfully excited both in isotropic steel and anisotropic laminate, and the signal-to-noise ratio (SNR) is as high as 19.0-34.6 dB. With the same delay law, the wave can be excited within a wide wave velocity range about 6000 m/s for the steel, and about 3600 m/s for the CFRP laminate, for -6 dB amplitude. The performance of the LCR technique is strengthened by the proposed PA-LCR method.

Significances of melting heat transfer and bioconvection phenomena in nanofluid flow over a three different geometries

This study addresses the numerical investigation of the steady and two-dimensional flow of magnetohydrodynamic nanofluid containing motile microorganisms over three distinct configurations: a wedge, a plate, and the stagnation point of a flat plate. The impacts of activation energy, melting phenomena, thermophoresis, and Brownian motion are taken into account. The dimensionless form of the governing coupled nonlinear partial differential equations is obtained by using similarity transformations. The system of ordinary differential equations is numerically solved using the “bvp4c” solver in MATLAB, and obtained results are also validated with an analytical approach Optimal Auxiliary Function Method (OAFM). Skin friction, heat, mass and motile microorganisms transfer rates are discussed through graphs and tables. Findings indicate that profile for Nusselt number enhances for higher inputs of melting parameter while Sherwood number lowers with increasing inputs of activation energy parameter. An improving pattern of velocity profiles is magnificent for stagnation point flow [f(η = 1) = 0.943711] compared to wedge [f(η = 1) = 0.915698]and horizontal plate [f(η = 1) = 0.868617]with respect to wedge angle parameter keeping velocity ratio parameter A < 1. For the wedge surface, the temperature profiles decrease [θ(η = 1.5) = 0.933075, 0.895245, 0.858931] for increasing inputs of radiation parameter (2.5 ≤ Nr ≤ 4.5) while motile microorganism profiles enhance [χ(η = 1.3) = 0.532505, 0.621569, 0.690635] with bioconvection Schmidtt number (0.3 ≤ Sb ≤ 0.7) respectively. Furthermore, it was found that, as velocity slip parameter increases then velocity of fluid also improves over a plate, wedge, and stagnation point of a flat plate considering velocity ratio parameter A < 1 .

Employing reflection and diffraction signals around a wedge to determine the wedge angle.

In the present study the acoustic field around rigid wedges is investigated. The acoustic field consists of diffraction contributions (from the edge) and of geometrical acoustics contributions (the incident signal and signals reflected on the wedge faces). A new depiction, called the polarity plot, is proposed that depicts the polarity of the diffracted impulse response, as well as the number of the geometrical acoustics contributions around a given wedge. Based on the observed patterns of the polarity plots, a set of measurements around a wedge is described which (if experimentally feasible) could be used in order to determine the wedge angle.

Load transfer model and failure prevention measures of a mechanical-type anchorage for anchor cable in deep roadway

In this paper, the load transfer mechanism of a mechanical-type anchorage is analyzed and studied. The stress distribution on the surface of the anchor cable is clarified, and the means of mechanical analysis and Abaqus finite element method are used. Results indicated there is no stress concentration, and the peak value indicated by the anchor cable appears near the loading end, and the peak value is about 60 MPa larger than the tensile strength. The results of the tensile test show that the failure mode of the anchor cable is the necking fracture of the steel wires, which indicates that the steel reaches the yield limit stress. The anchor efficiency of mechanical-type anchorage is high, which can effectively exert the tensile strength of anchor cable. In deep mine roadway, two failure modes of anchor cable are summarized when mechanical-type anchorage is used. Including shear failure and slippage failure under dynamic action. Aiming at the shear failure behavior, a new type of anchorage was invented, including the self-aligning and shear resistance functions of the anchor cable, and an experiment was carried out. Results indicated anti-shear anchorage can effectively solve the problem of anchor cable failure caused by shear. For the problem of anchor cable slippage failure under dynamic action. The parameters affecting the stability of mechanical-type anchorage are analyzed by means of theoretical analysis and numerical simulation. Results indicated reducing the bevel angle of wedge and barrel, the difference angle between them, and increasing the friction coefficient μ between wedge and barrel can increase the stability of mechanical-type anchorage. The research content of this paper can provide reference for the design of mechanical-type anchorage in similar underground engineering.

Exploring joint orientation effects on rock wedge stability: Experimental and discrete element analysis

The primary objective of this study was to examine and analyze the sliding behavior of rock wedge slopes with the interaction of three joint sets, considering the influence of plunge angles, included wedge angles between joints, and gravity conditions. The discontinuity planes with varying dip directions relative to the wedge's plunge direction were analyzed. The stability assessment of wedge failure was initially reviewed, explicitly focusing on limit equilibrium (LE) analysis and in-house physical tests. Centrifuge tests and discrete element analysis using the 3DEC software were then performed to explore the factors influencing the failure characteristics of the slopes. Additionally, two mitigation strategies were proposed to enhance the stability of the rock wedge slopes. The key findings include the significant impact of plunge angle on wedge slope stability compared to the included wedge angle between joints, the strong effect of gravitational conditions on the collapsing ratio of wedge units, and the higher risk posed by wedge slopes with discontinuity planes dipping out of the slope. The numerical simulation results highlighted the importance of considering joint spacing in slope stability assessments. Mitigation methods such as fixing key wedge blocks were found to effectively reduce the wedge collapsing ratio and improve rock slope stability under more realistic stress levels. This study provides valuable insights for formulating prevention and mitigation strategies, useful for enhancing safety and reducing the potential damage caused by rock wedge failure events.

Numerical simulation of heat transport mechanism in chemically influenced ternary hybrid nanofluid flow over a wedge geometry

Ternary hybrid nanofluid flow over a wedge surface facilitates optimization, promotes industrial processes such as heat transfer, temperature regulation, material compatibility, energy efficiency and is very useful in equipment design. Due to this attention the current study focalizes the heat diffusion and mass transportation in ternary hybrid (TiO2-AL2O3-SiO2) nanofluid flow over a stretching/shrinking wedge geometry. Additionally, Ternary hybrid flow is examined under the impact of activation energy together with chemical reactions. The nanofluid flow process is structured using Modified Boungiorno Model together with framed set of partial differential equation (PDEs). The resulting systems is altered into non dimensional form of ordinary differential equation (ODEs) using transform functions and linearization is obtained through shooting technique. MATLAB bvp4c solver scheme is utilized for numerical findings of the problem. Influence of key parameters are analyzed on velocity, temperature, and concentration field. Fluid concentration intensifies via augmentation in activation rate whereas wedge stretching due to larger values of wedge angle, lessens velocity of fluid. Heat transportation escalate with higher values of fluid index, whereas negative trend is seen in case of higher value of Brownian parameter.

Curvature Estimates for Stable Free Boundary Minimal Hypersurfaces in Locally Wedge-Shaped Manifolds

Abstract In this paper, we consider locally wedge-shaped manifolds, which are Riemannian manifolds that are allowed to have both boundary and certain types of edges. We define and study the properties of free boundary minimal hypersurfaces inside locally wedge-shaped manifolds. In particular, we show a compactness theorem for free boundary minimal hypersurfaces with curvature and area bounds in a locally wedge-shaped manifold. Additionally, using Schoen–Simon–Yau’s estimates, we also prove a Bernstein-type theorem indicating that, under certain conditions, a stable free boundary minimal hypersurface inside a Euclidean wedge must be a portion of a hyperplane. As our main application, we establish a curvature estimate for sufficiently regular free boundary minimal hypersurfaces in a locally wedge-shaped manifold with certain wedge angle assumptions. We expect this curvature estimate will be useful for establishing a min-max theory for the area functional in wedge-shaped spaces.