Vertical Axis Research Articles

Optical soliton solutions of complex Ginzburg–Landau equation with triple power law and modulation instability

This paper examines the complex Ginzburg Landau equation, which describes pulse propagation inside a fiber with the triple power law of self-phase modulation. Since the effect of parameter selection has become very important in relevant model studies recently, self-phase modulation has been added to the complex Ginzburg Landau equation, which has been studied in the literature, and it is aimed at investigating the analytical solutions of the presented equation. Adding the triple power law of the self-phase modulation parameter to the model, in addition to existing studies in the literature, emphasizes the innovative aspect and importance of the study. The first aim is to reveal bright and singular solitons using the new Kudryashov method. The new Kudryashov method is a technique that is frequently used in the literature, is effective for generating analytical solutions, provides ease of operation, and can be applied to a wide class of nonlinear partial differential equations. The second goal is to show that the obtained solutions have modulation stability. By using modulation instability analysis, the gain spectrum is formed for different parameter values. Graphic presentations support the findings. Moreover, bright and singular soliton portraits are demonstrated with 3D and 2D graphs. The novelty of the study lies in the fact that the relevant model has not been studied before with an effective method such as the new Kudryashov method, and the modulation instability has been studied for the first time.

Effects of magnetic and Aharonov–Bohm flux fields on information entropy with modified Kratzer plus screened Coulomb potential for selected diatomic molecules

The Shannon information entropy for scandium fluoride (ScF) and hydrogen ( H 2 ) molecules in the presence of magnetic and Aharanov–Bohm (AB) fields with modified Kratzer plus screened Coulomb potential in the position and momentum coordinate is investigated. The wavefunction and probability density are obtained by solving the two-dimensional (2D) Schrödinger wave equation using the Nikiforov–Uvarov functional analysis method and then applied to calculate the Shannon entropy. The graphical behaviour of the 2D wavefunction and probability density is showcased. Our results depict the effects of the external fields on Shannon entropy for ScF and ( H 2 ) , the negative values of the position Shannon entropies obtained imply higher localisation of the particles and molecules indicating more stability of the system. Another interesting part of this work is that Bialynicki–Birula–Mycielski inequality is tested and proven bounded for both diatomic molecules. A few to mention, this research will enhance the apprehension of the dynamics of quantum molecules and systems subjected to external fields, quantum information signal processing and communication.

Mathematics Exploration Extant in The Checker Game: A Mathematics Teaching Contribution

Aversion to mathematics shown by learners belonging to different age stages, worries and challenges mathematicians and/ or mathematics teachers to develop surveys which might improve learners´ mathematics learnings. “Thawing” recondite mathematics in several games may aid to provide a different mathematics vision. The current research article aims to identify and analyze the “concealed” mathematics through checker games played in Angola, mostly in Cuando Cubango province. The survey is placed in ethnomathematics and considering its sorts, qualitative methodology has been used supported by a half-structured interview, direct observation to picture recording.  The research was conducted in the Menongue municipality (Cuando Cubango capital city). The three versions of checkers games were described (12 by 12; 10 by 10 and 8 by 8), some questions were created that guided this investigation (Why does the structure of the checkers game have the same number of rows and columns? Why do players when placing checkers pieces in the middle always leave two empty rows? Why is the sum of rows and columns equal to the even number? Why is each painted square on the checkers board corresponds to an odd number?) and, finally, some mathematical concepts involved in that game were explored (such as, for example, the notion of the Cartesian plane, diagonal lines, distance between two points, median (element of Statistics), numbers even and odd).

Irreducible lateral dislocation of the patella with vertical rotation in a child: A case report

Case A 13-year-old adolescent girl had an irreducible fixed lateral patellar dislocation, with rotation about the vertical axis, following a fall from standing. Open reduction and medial repair were necessary. Follow-up radiographs demonstrated a reduced patella without signs of complication. Conclusion This report details an injury that is exceptionally rare in the pediatric population and is potentially the first to characterize such significant findings following minor trauma in a young girl. The purpose of this report is to highlight this rare condition and provide an outline for physicians to ensure successful identification and management in the clinical setting.

Comparison of the efficacy of the convex side short fusion combined with concave side single growing rod technique and the traditional bilateral growing rod technique in the treatment of early onset scoliosis

ObjectivesThe application of a growing rod technique can retain the growth and development potential of the spine and thorax while controlling the progression of scoliosis deformity. Theoretically, convex side short fusion combined with a concave side single growing rod technique can significantly reduce the asymmetric growth of the spine in the vertex region in most patients. However, the final clinical outcome of various techniques is yet to be clearly determined and compared between studies. Therefore, we compared the efficacy of these two growing rod techniques in treating early onset scoliosis.MethodsIn a retrospective study of 152 EOS patients seen between 2013.1 and 2019.12, 36 cases of EOS patients were selected for inclusion. Among the 36 cases, 11 cases were treated with convex side short fusion combined with a concave side single growing rod technique, group (A) The remaining 25 cases were treated with traditional bilateral growing rod technique, group (B) Age, gender, etiology, follow-up time, Cobb angle of main curve, T1-S1 height, coronal trunk shift, sagittal vertical axis (SVA), Cobb angle of thoracic kyphosis at last follow-up, and Cobb angle at proximal junction kyphosis of the first and last post-operation follow-up were recorded. In addition, internal fixation related complications, infection, nervous system complications were recorded as well.ResultsThere was no statistically significant difference between group A and group B in preoperative age, Cobb angle of main curve, coronal trunk shift, T1-S1 height, SVA, Cobb angle of thoracic kyphosis (p > 0.05). However, at the last follow-up (Group A, mean 4.4 ± 1.01 years; Group B, mean 3.6 ± 0.01 years) the Cobb angle of the main curve was less and T1-S1 height greater in group A compared with group B (p < 0.05). There was no statistically significant difference between group A and group B in the correction rate of the Cobb angle of the main curve or the growth rate of T1-S1 height (p > 0.05). There was no statistically significant difference in the coronal imbalance ratio, thoracic kyphosis abnormality ratio, or the occurrence PJK ratio between group A and group B at the last follow-up (p > 0.05), but the sagittal imbalance ratio and internal fixation abnormality ratio were higher in group A than in the group B (p < 0.05).ConclusionsDuring the treatment of EOS, both the convex side short fusion combined with concave side single growing rod technique and traditional bilateral growing rod technique can correct the Cobb angle of main curve with no significant hindering of the spinal growth observed. The traditional bilateral growing rod technique has advantages in control of the sagittal balance of the spine, and the complications associated with internal fixation were lower.

Comparison of radiological and clinical outcomes of cervical laminoplasty versus lateral mass screw fixation in patients with ossification of the posterior longitudinal ligament

PurposeThis study aimed to compare cervical sagittal parameters and clinical outcomes between patients undergoing cervical laminoplasty(CL) and those undergoing lateral mass screw fixation(LMS).MethodsWe retrospectively studied 67 patients with multilevel ossification of the posterior longitudinal ligament (OPLL) of the cervical spine who underwent lateral mass screw fixation (LMS = 36) and cervical laminoplasty (CL = 31). We analyzed cervical sagittal parameters (C2-7 sagittal vertical axis (C2-7 SVA), C0-2 Cobb angle, C2-7 Cobb angle, C7 slope (C7s), T1 slope (T1s), and spino-cranial angle (SCA)) and clinical outcomes (visual analog scale [VAS], neck disability index [NDI], Japanese Orthopaedic Association [JOA] scores, recovery rate (RR), and minimum clinically significant difference [MCID]). The cervical sagittal parameters at the last follow-up were analyzed by binary logistic regression. Finally, we analyzed the correlation between the cervical sagittal parameters and each clinical outcome at the last follow-up after surgery in both groups.ResultsAt the follow-up after posterior decompression in both groups, the mean values of C2-C7 SVA, C7s, and T1s in the LMS group were more significant than those in the CL group (P ≤ 0.05). Compared with the preoperative period, C2-C7 SVA, T1s, and SCA gradually increased, and the C2-C7 Cobb angle gradually decreased after surgery (P < 0.05). The improvement in the JOA score and the recovery rate was similar between the two groups, while the improvement in the VAS-N score and NDI score was more significant in the CL group (P = 0.001; P = 0.043). More patients reached MCID in the CL group than in the LMS group (P = 0.036). Binary logistic regression analysis showed that SCA was independently associated with whether patients reached MCID at NDI postoperatively. SCA was positively correlated with cervical NDI and negatively correlated with cervical JOA score at postoperative follow-up in both groups (P < 0.05); C2-7 Cobb angle was negatively correlated with cervical JOA score at postoperative follow-up (P < 0.05).ConclusionCL may be superior to LMS in treating cervical spondylotic myelopathy caused by OPLL. In addition, smaller cervical SCA after posterior decompression may suggest better postoperative outcomes.

Triangular Flap Insertion: An Option for Correction of Dog-Ears Deformity in High-Tension Areas.

Dog-ear deformity is a common protrusion defect of skin tissue after the closure of a surgical wound, affecting patients' appearance and quality of life. The common methods for correcting dog ears involve the removal of excess tissue in different directions or shapes after extending the incision along the long axis of the original wound. However, the literature regarding tissue preservation techniques for dog-ear correction is poor, especially for areas with insufficient skin tissue or high tension. The authors modified the original design of direct excisions, which transferred excess tissue from the horizontal axis of the wound to the longitudinal axis, thereby absorbing longitudinal tension and relieving linear scar contracture. This technique provides a way to correct dog ears without removing excess healthy tissue, especially as an option for dog-ear correction in high-tension areas.

A Real-Time Monitoring Method for Selective Laser Melting of TA1 Materials Based on Radiation Detection of a Molten Pool

Selective laser melting (SLM) technology is a promising additive manufacturing technology. However, due to the numerous influencing factors in this complex process, a reliable real-time method is needed to monitor the forming process of SLM. The molten pool is the smallest forming unit in the SLM process, the consistency of which can effectively reflect the quality of the printing process. By using a coaxial optical path structure and a compound amplifier circuit, high-speed acquisition of molten pool radiation can be realized. Next, single factor analysis and orthogonal experimentation were used to investigate the influence levels of key process parameters on the radiation of molten pool. In addition, numerical simulation was carried out with the same parameter setting schemes, the results of which are consistent with those in radiation detection experiments. It is shown that the laser power has the greatest effect on the radiation of the molten pool, while the scanning speed and the hatch spacing have little effect on the radiation. Finally, the positioning experiment involving the small hole structure was carried out, and the experimental results showed that the device could accurately locate the position coordinates of the given hole structure.

3D electromagnetic analytical model for radial-flux eddy-current couplers

Purpose This paper aims to develop a new 3D analytical model in cylindrical coordinates to study radial flux eddy current couplers (RFECC) while considering the magnetic edge and 3D curvature effects, and the field reaction due to the induced currents. Design/methodology/approach The analytical model is developed by combining two formulations. A magnetic scalar potential formulation in the air and the magnets regions and a current density formulation in the conductive region. The magnetic field and eddy currents expressions are obtained by solving the 3D Maxwell equations in 3D cylindrical coordinates with the variable separation method. The torque expression is derived from the field solution using the Maxwell stress tensor. In addition to 3D magnetic edge effects, the proposed model takes into account the reaction field effect due to the induced currents in the conducting part. To show the accuracy of the developed 3D analytical model, its results are compared to those from the 3D finite element simulation. Findings The obtained results prove the accuracy of the new developed 3D analytical model. The comparison of the 3D analytical model with the 2D simulation proves the strong magnetic edge effects impact (in the axial direction) in these devices which must be considered in the modelling. The new analytical model allows the magnetic edge effects consideration without any correction factor and also presents a good compromise between precision and computation time. Practical implications The proposed 3D analytical model presents a considerably reduced computation time compared to 3D finite element simulation which makes it efficient as an accurate design and optimization tool for radial flux eddy current devices. Originality/value A new analytical model in 3D cylindrical coordinates has been developed to find the electromagnetic torque in radial flux eddy current couplers. This model considers the magnetic edge effects, the 3D curvature effects and the field reaction (without correction factors) while improving the computation time.

VARIATIONAL PERSPECTIVE TO (2+1)-DIMENSIONAL KADOMTSEV–PETVIASHVILI MODEL AND ITS FRACTAL MODEL

In this work, the [Formula: see text]-dimensional Kadomtsev–Petviashvili model is investigated. A novel variational scheme, namely, the variational transform wave method (VTWM), is successfully established to seek the solitary wave solution of the Kadomtsev–Petviashvili model. Furthermore, the fractal solitary solution of fractal Kadomtsev–Petviashvili model is also studied based on the local fractional derivative. Numerical examples are given to fully demonstrate that the VTWM is straightforward, efficient and attractive. Finally, the physical properties of solitary wave solutions are demonstrated by some 3D graphs.

Efficient Target Classification Based on Vehicle Volume Estimation in High-Resolution Radar Systems

In this paper, we propose a method for efficient target classification based on the spatial features of the point cloud generated by using a high-resolution radar sensor. The frequency-modulated continuous wave radar sensor can estimate the distance and velocity of a target. In addition, the azimuth and elevation angle of the target can be estimated by using a multiple-input and multiple-output antenna system. Using the estimated distance, velocity, and angle, the 3D point cloud of target can be generated. From the generated point cloud, we extract the point cloud for each individual target using the density-based spatial clustering of application with noise method and a camera mounted on the radar sensor. Then, we define the convex hull boundaries that enclose these point clouds in both 3D and 2D spaces obtained by orthogonally projecting onto the xy, yz, and zx planes. Using the vertices of convex hull, we calculate the volume of the targets and the areas in 2D spaces. Several feature points, including the calculated spatial information, are numerized and configured into feature vectors. We design an uncomplicated deep neural network classifier based on minimal input information to achieve fast and efficient classification performance. As a result, the proposed method achieved an average accuracy of 97.1%, and the time required for training was reduced compared to the method using only point cloud data and the convolutional neural network-based method.

Automated 3D Perioral Landmark Detection Using High-Resolution Network: Artificial Intelligence-Based Anthropometric Analysis.

3D facial stereophotogrammetry, as a convenient, non-invasive and highly reliable evaluation tool, has shown great potential in pre-operative planning and treatment efficacy evaluation of plastic surgery in recent years. However, it requires manual identification of facial landmarks by trained evaluators to obtain anthropometric data, which consumes large amount of time and effort. Automatic 3D facial landmark localization may facilitate fast data acquisition and eliminate evaluator error. In this paper, we propose a novel deep-learning method based on dimension-transformation and key-point detection for automated 3D perioral landmark annotation. The 3D facial model is transformed into 2D images on which High-Resolution Network is implemented for key point detection. The 2D coordinates of key points are then mapped back to the 3D model using mathematical methods to obtain the 3D landmark coordinates. This program was trained with 120 facial models and validated in 50 facial models. Our approach achieved satisfactory accuracy of 1.30 ± 0.68 mm error in landmark detection with an average processing time of 5.2 ± 0.21 seconds per model. And subsequent analysis based on these landmarks showed an error of 0.87 ± 1.02 mm for linear measurements and 5.62 ± 6.61° for angular measurements. This automated 3D perioral landmarking method could serve as an effective tool that enables fast and accurate anthropometric analysis of lip morphology for plastic surgery and aesthetic procedures.

Experimental and theoretical analysis of finely bedded porous rock models with internal cracks

The behavior of ultrasonic waves in synthetic rocks consisting of alternating layers of sand-based (porous and permeable) and acrylic (unporous) materials is investigated. Two synthetic layered media are created, one without cracks and the other with parallel cracks in one of the layers, to increase anisotropy and simulate a heterogeneous transversely isotropic medium with a vertical axis of symmetry. Microcomputed tomography is used to obtain images of the samples, which indicate that there are no bubbles present and that the layers are well connected without any gaps or breaks. The experiment uses ultrasonic measurements to determine the propagation of P and S waves, with transducers at frequencies of 100 kHz, 500 kHz, and 1 MHz for traveltime and waveform measurements. These three sources are chosen to verify the effective behavior of the samples, which depends on the relationship between the dominant wavelength of investigation and the layer thickness ([Formula: see text]). The measured velocities are compared with theoretical models based on Backus, Kennett (traditional models), and Backus (modified for cracked media by Schoenberg and Muir’s theory). The main finding is that the cracked medium exhibits at least twice as large a difference in behavior for P- and S-wave vertical velocities as a function of the number of layers compared with the uncracked medium.

Wind Velocity Effect on the Aerodynamic and Acoustic Behavior of a Vertical Axis Wind Turbine

In this work we present a numerical study on the effect of wind velocity on the aerodynamic and acoustic behavior of a Savonius-type vertical axis wind turbine (VAWT). The study focuses on the prediction of the torque coefficient for different flow velocities and rotational velocities of the wind turbine. We also present the triggering of the wake zone near the wind turbine blades to see the dynamic effect on the behavior of the wind turbine. The study of the numerical simulation is carried out using a fluent CFD calculation code using the finite volume method for the discretization of the differential equations. The equations governing the flow are solved by the SIMPLE algorithm using two K-epsilon turbulence models.

The Influence of Radiographic Parameter on the S2 Alar-Iliac Screw Virtual Trajectory in Degenerative Lumbar Scoliosis Patients: A Computed Tomography Study.

S2 alar-iliac (S2AI) screw had been widely used in the pelvic fusion for degenerative lumbar scoliosis (DLS) patients. However, whether S2AI screw trajectory was influenced by sagittal profile in DLS patients had not been comprehensively investigated. The objective of this study was to evaluate the associations between the optimal S2 alar-iliac (S2AI) screw trajectory and sagittal spinopelvic parameters in DLS patients. Computed tomography (CT) scans of pelvis were performed in 47 DLS patients for three-dimensional reconstruction of S2AI screw trajectory from September 2019 to November 2021. Five S2AI screw trajectory parameters were measured in CT reconstruction images, including: 1) angle in the transverse plane (Tsv angle); 2) angle in the sagittal plane (Sag angle); 3) maximal screw length; 4) screw width; and 5) skin distance. The lumbar Cobb angle, lumbar apical vertebral translation (AVT); global kyphosis (GK); thoracic kyphosis (TK); lumbar lordosis (LL); sagittal vertical axis (SVA); sacral slope (SS); pelvic tilt (PT); and pelvic incidence (PI) were measured in standing X-ray films of the whole spine and pelvis. Both Tsv angle and Sag angle had significant positive associations with SS (p < 0.05) but negative associations with both PT (p < 0.05) and LL (p < 0.05) in all cases. Patients with SS less than 15° had both smaller Tsv angle and Sag angle than those with SS equal to or more than 15° (p < 0.05). The decreased LL would lead to the backward rotation of the pelvis, resulting in a more cephalic and less divergent trajectory of S2AI screw in DLS patients. For DLS patients with lumbar kyphosis, spine surgeons should avoid both excessive Tsv and Sag angles for S2AI screw insertion, especially when using free-hand technique.

Line structure light calibration based on a freely placed single cylindrical object

The traditional Zhang calibration method takes multiple checkerboard images at different positions, but in practical applications, surface measurement is usually required, in which case the planar target is not suitable. Thus, a calibration method is needed, using curved surface targets. In this paper, a line-structured light calibration method is presented based on a freely placed cylindrical object. The calibration process is as follows: the cylindrical target is placed freely and irradiated with a laser; The camera captures the target image and then the light strips of the cylindrical target and its two bus bars are extracted; The translation relation between the cylinder and the images is calculated according to the imaging principle and geometric relation; The center points of the light strip are converted to 3D coordinates according to the internal parameters of the camera for fitting the light plane. Two experiments are designed to verify the advantages of the method. The needle gauge experiment shows that 0.001 mm accuracy can be achieved in a single frame measurement, and the ring gauge experiment shows that the measurement accuracy of the system is increased by 20 %. This method is more applicable and more suitable than the traditional method for high-precision industrial 3D measurement.

A Fixed Point Theorem for Time-Fractional Fornberg-Whitham Equation Arising in Atmospheric Science

In this paper, we apply the Homotopy perturbation transform method of the time-fractional Fornberg-Whitham equation with Caputo-Fabrizio fractional derivative. We establish the existence and uniqueness solutions of the time-fractional Fornberg-Whitham equation using fixed point theory. The physical interpretation of the nonlinear models are also discussed through the semi analytical solutions, which demonstrate the effectiveness of the proposed method. Finally, 2D and 3D graphs of some derived solutions are depicted through suitable parameter values.

A Laboratory-Scale Evaluation of Smart Pebble Sensors Embedded in Geomaterials.

This paper introduces a novel approach to measure deformations in geomaterials using the recently developed 'Smart Pebble' sensors. Smart Pebbles were included in triaxial test specimens of unbound aggregates stabilized with geogrids. The sensors are equipped with an aggregate particle/position tracking algorithm that can manage uncertainty arising due to signal noise and random walk effects. Two Smart Pebbles were placed in each test specimen, one at specimen's mid-height, where a geogrid was installed in the mechanically stabilized specimen, and one towards the top of the specimen. Even with simple raw data processing, the trends on linear vertical acceleration indicated the ability of Smart Pebbles to assess the geomaterial configuration and applied stress states. Employing a Kalman filter-based algorithm, the Smart Pebble position coordinates were tracked during testing. The specimen's resilient deformations were simultaneously recorded. bender element shear wave transducer pairs were also installed on the specimens to further validate the Smart Pebble small-strain responses. The results indicate a close agreement between the BE sensors and Smart Pebbles estimates towards local stiffness enhancement quantification in the geogrid specimen. The study findings confirm the viability of using the Smart Pebbles in describing the resilient behavior of an aggregate material under repeated loading.

Optical solitons retrieval for an extension of novel dual-mode of a dispersive non-linear Schrödinger equation

In this study, we rearrange the non-linear Schrödinger equation (NLSE) into a dual-mode structure, which expands it, and then we investigate the geometrical evaluation and representation of this novel model. Explicit, exact solutions are obtained by implementing the improved modified extended tanh-function (IMETF) approach. The study’s findings have important ramifications for how solitons propagate in nonlinear optics. The resultant solutions can be found in several forms: singular, bright, rational, exponential, Jacobi elliptic function (JEF), Weierstrass elliptic doubly periodic solution, and singular periodic solutions. By comparing our obtained traveling wave solutions with existing literature, we demonstrate their novelty and substantive contribution to current research. The success of our approach suggests its potential applicability to address various nonlinear challenges in different fields, particularly within soliton theory, since the analyzed model appears in a multitude of applications. Besides, in order to better comprehend some of these found solutions behaviors, we showed their outlines in 3D and 2D graphs.

Relaxation oscillations in the Darie wind power plant model

The article discusses the mathematical model of the Daria small wind power plant. This installation is a type of vertical axis wind turbine named after its inventor, Georges Jean Marie Darrieux. The design consists of a vertically oriented shaft with curved blades or airfoils attached to it, forming a shape similar to an egg whisk. In today’s world, against the backdrop of climate change and steadily increasing energy demand, wind energy acts as a critical pillar of the transition to renewable energy sources. This technology helps reduce carbon emissions and mitigate humanity’s impact on the environment. In this context, wind energy is emerging not only as a means of supplying electricity, but also as a powerful catalyst for building a more sustainable and energy-efficient future. The equation of stationary modes is studied at the value of the external resistance of the dynamic model specified by the simplest equation. Conditions have been found under which relaxation oscillations are observed in the system.