Rectangular Coordinate System Research Articles

Nano particle distribution in blood via electroosmotic peristaltic flow in a non-uniform wavy membrane base capillaries

ObjectiveThe primary purpose of this article is to undertake a mathematical investigation into the electro osmotically thermally driven transport of solute particles, which are typically on a micro to nano-meter scale, suspended in blood. The study is conducted within a non-uniform porous channel for a Williamson fluid. The main objective of this research is to explore the interactions and consequences of solute particles and nanoparticles in the Esophagus, particularly regarding their potential applications in drug delivery and biomedical engineering, especially in the context of electroosmotic non-Newtonian fluids. SignificanceThis research also has significant implications for microscale physiological phenomena. In this investigation, blood serves as the base fluid, and a nanofluid is created by introducing Nickel and Cobalt nanoparticles into the blood. Both nanoparticles have critical medical applications, especially in drug delivery and cancer treatment. To delve deeper into the study of nanomedicine delivery, Nickel and Cobalt nanoparticles are introduced into the blood alongside other smaller solute particles. MethodologyThe mathematical modeling is conducted in a rectangular coordinate system, and the governing flow equations are linearized using approximations that consider low Reynolds numbers and large wavelengths. The numerical solution is computed for a coupled set of nonlinear equations that describe the profiles of fluid-particle velocity, temperature, and fluid-particle composition. The study explores the influence of various key parameters and presents these effects through graphical representations. FindingsIt is observed that an increase in the suspension concentration and the Williamson fluid parameter leads to higher fluid velocity, while the temperature distribution exhibits the opposite trend. The introduction of nanoparticles into the fluid decelerates the flow and raises the temperature.

Interior solution of azimuthally symmetric case of Laplace equation in orthogonal similar oblate spheroidal coordinates

Curvilinear coordinate systems distinct from the rectangular Cartesian coordinate system are particularly valuable in the field calculations as they facilitate the expression of boundary conditions of differential equations in a reasonably simple way when the coordinate surfaces fit the physical boundaries of the problem. The recently finalized orthogonal similar oblate spheroidal (SOS) coordinate system can be particularly useful for a physical processes description inside or in the vicinity of the bodies or particles with the geometry of an oblate spheroid. The solution of the azimuthally symmetric case of the Laplace equation was found for the interior space in the orthogonal SOS coordinates. In the frame of the derivation of the harmonic functions, the Laplace equation was separated by a special separation procedure. A generalized Legendre equation was introduced as the equation for the angular part of the separated Laplace equation. The harmonic functions were determined as relations involving generalized Legendre functions of the first and of the second kind. Several lower-degree functions are reported. Recursion formula facilitating determination of the higher-degree harmonic functions was found. The general solution of the azimuthally symmetric Laplace equation for the interior space in the SOS coordinates is reported.

THREE-DIMENSIONAL MODEL OF EQUIVALENT ROLL GAP OF CVC MILL UNDER CONDITIONS OF ROLL CROSSING AND NO LOAD

Traditional roll technologies focus solely on the contour of the roll gap at the outlet under ideal conditions. However, upon roll crossing, the three-dimensional distribution of the deformation zone becomes asymmetrical, leading to an adverse impact on the rolling pressure in the deformation zone. To study the screw-down load deviation of plate mills, it is necessary to accurately calculate the equivalent three-dimensional roll gap in the deformation zone under roll-crossing conditions. In this paper a model for calculating the equivalent three-dimensional roll gap under the conditions of roll crossing and no load was established based on the method of the coordinate nonlinear transformation of the spatial rectangular coordinate system. Based on this model, the influences of roll-crossing angles and translation parameters on the symmetry of the equivalent three-dimensional roll gap were analyzed. The distribution of the three-dimensional equivalent roll gap was calculated with different roll lengths, roll radii, and the roll gap’s nominal thickness. The intuitive contour map reveals that under the same condition of crossing angle and translation parameters, the larger the roll length and roll radii and the smaller the roll gap’s nominal thickness are, the greater the influence of the roll crossing on the asymmetrical distribution of roll gap is. It put forward a quantitative calculation method for evaluating the symmetrical distribution of the roll gap, and the calculation results can provide the equivalent roll profile for the roll-deformation model.

Application of dose-gradient function in reducing radiation induced lung injury in breast cancer radiotherapy.

Try to create a dose gradient function (DGF) and test its effectiveness in reducing radiation induced lung injury in breast cancer radiotherapy. Radiotherapy plans of 30 patients after breast-conserving surgery were included in the study. The dose gradient function was defined as DGH=VDVp3, then the area under the DGF curve of each plan was calculated in rectangular coordinate system, and the minimum area was used as the trigger factor, and other plans were triggered to optimize for area reduction. The dosimetric parameters of target area and organs at risk in 30 cases before and after re-optimization were compared. On the premise of ensuring that the target dose met the clinical requirements, the trigger factor obtained based on DGF could further reduce the V5, V10, V20, V30 and mean lung dose (MLD) of the ipsilateral lung in breast cancer radiotherapy, P < 0.01. And the D2cc and mean heart dose (MHD) of the heart were also reduced, P < 0.01. Besides, the NTCPs of the ipsilateral lung and the heart were also reduced, P < 0.01. The trigger factor obtained based on DGF is efficient in reducing radiation induced lung injury in breast cancer radiotherapy.

Asymptotic Solutions of Steady Lamellar Eutectic Growth in Directional Solidification for Small Tangent Values of the Contact Angles

A system of steady lamellar eutectic growth in directional solidification is considered with the case of small tangent values of the contact angles. The mathematical model is given in the non-dimensional rectangular coordinate system and the uniformly valid asymptotic solutions are obtained based on the method of the asymptotic expansions. The necessary condition for existing asymptotic solutions was obtained. The results indicate that the curvature undercooling and the solute undercooling determined the patterns of the solid–liquid interface. The dimensional average undercooling presents a relationship with eutectic spacing and pulling velocity. It can be seen that the dimensional average undercooling in front of both phases is not equal, and the total average undercooling as a function of the lamellar eutectic spacing exhibits a minimum. The minimum undercooling spacing decreases with an increase in the pulling velocity, which is in good agreement with Jackson and Hunt’s results.

Displacement identification of oil storage tank and calibration of tank capacity table model based on indicator function integral.

Based on the indicator function integral, this paper identifies the displacement of oil storage tank and calibrates the tank capacity table model. The displacement parameters of a cylinder oil tank with spherical caps at both ends are deduced by establishing an appropriate rectangular coordinate system while cross-section analysis, coordinate transformation, and the functional relationship between oil reserves and oil level height are used as well. Furthermore, the displacement parameters are determined by the least square method and alternating contraction search method to verify the data, which improves the accuracy of the calculation. This research simplifies the integral operation and can be extended to other types of liquid containers of arbitrary shape as a generally applicable method, which shows significant application value for further research on the integral method of indicator function.

Efficient computation of heat distribution of processed workpiece with coupling to bottom water vapor in water-jet guided laser machining.

In this paper, we present a novel approach for calculating the heat distribution within a processed workpiece subjected to laser irradiation while accounting for the influence of bottom water vapor. A comprehensive mathematical model is introduced and numerical techniques using difference approximation are employed. Initially, the three-dimensional heat equation, originally defined in the rectangular coordinate system, is transformed into a corresponding model within the cylindrical coordinate system, incorporating a nonlinear boundary condition to account for coupling effects. Subsequently, leveraging the axial symmetry of the heat distribution, the three-dimensional model is simplified into a two-dimensional one. This simplified model is solved using the alternating direction implicit scheme coupled with the Crank-Nicolson method. Moreover, we develop a high-precision numerical treatment for the nonlinear boundary condition within the cylindrical coordinate system. To validate our methodology, simulation experiments are conducted on three distinct samples. Our comparative results demonstrate the feasibility and efficiency of the proposed approach in the context of water-jet guided laser processing.

A Novel Surface Subsidence Prediction Model Based on Stochastic Medium Theory for Inclined Coal Seam Mining

Most coal resources are deposited in the form of inclined coal seams, and surface subsidence basin morphology induced by the mining of inclined coal seams is frequently skewed. The probability integral method with symmetrical distribution characteristics is widely used at present in surface subsidence prediction in coal mining in China. However, this method performs poorly when the inclined coal seam mining subsidence is predicted, and prediction accuracy decreases considerably with an increase in coal seam inclination. To solve this problem, this study first establishes three coordinate systems: a working surface rectangular coordinate system, a working face body-following coordinate system, and a surface rectangular coordinate system. Then, a random medium theory is applied to realize the superposition integral operation of the subsidence influence of unit mining in the working faces body-following coordinate system. Subsequently, the subsidence effect of a certain point on the surface is converted into the surface rectangular coordinate system. Finally, the inclined coal seam mining subsidence prediction model is constructed under the surface rectangular coordinate system. Results show that the surface subsidence caused by the mining of the inclined coal seam units conforms to the Weibull polar distribution law, and the effectiveness of the prediction model is verified through examples. The relative mean squared error of the prediction is less than 10%. The results of the study can provide theoretical and technical support for the subsidence prediction of similar mining areas.

Magnetotelluric Forward Modeling in Spherical Coordinate System Under Non-planar Wave Field Source

In the traditional magnetotelluric forward modeling, the spherical earth model is typically stretched into the rectangular coordinate system using geographical projection, inevitably producing modeling errors especially for cases with large-scale data coverage. In these cases, the earth can not be considered as be flat, and the external source is not laterally uniform. In this paper, we developed a MT modeling algorithm in the spherical coordinate system based on the use of the spherical harmonic function P10 for the source. A model with public solutions is used to verify our algorithm. A more realistic model is designed to show the application of our algorithm.

Research on Measurement of Multi-beam Transducer Based on Analytic Geometry Method

The ocean is inseparable from the survival and development of human beings. It not only provides rich resources for human beings, but also provides a large number of samples for human scientific research. For the efficient development of the ocean, detailed and accurate seabed topography and geomorphology information is needed as a prerequisite. In this paper, aiming at the problem of multi-beam detection system detecting full coverage water depth strip in waterway, the measurement model of multi-beam transducer under different survey lines is established. Based on the combination of numbers and shapes, firstly, this paper considering the special situation that the survey line is perpendicular to the horizontal component of the normal of the seabed slope, it is concluded that the depth of seawater is positively correlated with the width of the survey line. Secondly, when the angle of the survey line is arbitrary, and the spatial rectangular coordinate system model is established, this paper considering the law of the width of the survey line at different angles and distances. Finally, through analytic geometry method, the measuring line equations at different positions and angles are expressed in this paper, and the measuring line width is quantified according to the distance formula between two points. The results show that the coverage width is unchanged at the center of the sea area or when the direction of the survey line is perpendicular to the horizontal component of the normal of the submarine slope. The coverage width is symmetrically distributed at the survey line angle. The results show that the multi-beam transducer measurement model is effective.

Safe surgical corridor for iliosacral screw placement in unstable pelvic fractures: a computed-tomography-guided validation study of the “triangulation method”

BackgroundThe percutaneous iliosacral screw technique represents a global standard fixation method for unstable fractures of the posterior pelvic ring. However, the inaccurate positioning of iliosacral screws is associated with a significant risk of severe intra-operative complications. Therefore, this study aimed to investigate the relationship between the skin entry point of the transverse iliosacral screw of the first sacral vertebral body and the anterior superior iliac spine and the greater trochanter of the femur using computed-tomography-guided validation.MethodsOverall, 91 consecutive patients admitted to a tertiary referral center in China for posterior pelvic ring fixation via the “triangulation method” using computed-tomography-guided validation between January 1, 2020, and December 31, 2020, were included in this retrospective observational cohort study. Modeling and simulated iliosacral screw placement were performed using the Mimics software. The distance between the three points of interest was measured, and their relationship in a rectangular coordinate system was determined. Patients were categorized according to gender, body mass index, and femoral rotation angle to investigate the factors affecting the positional relationship between the three points.ResultsAn equilateral triangular relationship was observed between the positioning points of the transverse iliosacral screw, anterior iliac spine, and greater trochanter. Additionally, 95% of the entry points were within a circle radius centered 12 mm at the apex of an equilateral triangle comprising the anterior superior iliac spine and the greater trochanter as the base. The entry point in the femoral external rotation was more dorsal than that in the internal femoral rotation. Furthermore, the entry point in females was more rostral than that in males, and the entry point in overweight patients was more dorsal than that in normal-weight patients.ConclusionsThe skin entry point of the percutaneous iliosacral screw can be located by drawing an equilateral triangle from the anterior superior iliac spine and the greater trochanter as the base to the dorsum end of the patient’s head. In summary, this retrospective cohort study validated the safety and efficacy of the “triangulation methods” for percutaneous fixation of unstable posterior pelvic ring injuries.

Research on radial velocity and airspace position calculations of target in airborne active radar simulation

The detection of the target in the airborne active radar simulation is simplified to the calculations of the radial velocity, the maximum detecting range of the airborne active radar corresponding to the RCS, and the airspace position of the target. However, the coordinate transformations related to the calculations of the radial velocity and the airspace position are usually bewildering due to the different referenced coordinate systems. This paper introduces the radial velocity and airspace position calculations of the target in the airborne active radar simulation to illuminate the transformation process containing the specific rotation matrices, suggesting the unifying transformation to the north-up-east (NUE) rectangular coordinate system of the aircraft for both the radial velocity calculation and airspace position calculation of the target.

MABAC method based on cumulative prospect theory for MCGDM with dual probabilistic linguistic term set and applications to sustainable supplier selection

Dual probabilistic linguistic term set (DPLTS) is a new proposed decision-making environment. It uses probabilistic form to represent the appraisal of the alternative from decision makers. There are few methods to deal with DPLTS according to the literature proposed up to now. The purpose of this article is to proposed a new improved Multi-Attribute Border Approximation Area Comparison (MABAC) method extended by cumulative prospect theory (CPT) and combined with DPLTS to address the multi-criteria group decision-making (MCGDM) problem of sustainable supplier selection. In order to make the decision procedure containing more fuzzy information, we also improved the equation of distance between DPLTSs with system of rectangular coordinates. This new improved MABAC method is combined with CPT and it is semi-objective method. Not only in the procedure of calculating distance between alternatives and border approximation area, but also in the procedure of determining the weights of attributes. At the end of this paper, the comparison of this new method with other proposed DPLTS methods, such as Correlation Coefficient Method and DPLTS-TODIM-CRITIC Method, demonstrates the availability and difference.

OppHeatmap: Rendering Various Types of Heatmaps for Omics Data.

Heatmaps are preferred visualization modes for biologists to display high-dimensional information from high-throughput omics data. Many software including website services and R packages are available to generate various types of customized heatmaps. Here, we describe oppHeatmap (omics pilot platform of heatmap), a new tool constructed to render different kinds of heatmaps through MATLAB. oppHeatmap is available for plotting ordinary heatmaps, hierarchical clustering, TreeMaps, microplates graph, sample correlation (full heatmap and upper and lower triangle parts), gene correlation (between columns or tables), and polar heatmaps. oppHeatmap can support the modification of borders, fonts, and colors to customize the final plots. oppHeatmap can not only read data from Microsoft Excel to generate specific heatmaps but also make Excel heatmaps by coloring each cell in Excel. The graphs can be stored in SVG (supported vector graph) format and modified by other SVG recognition software. oppHeatmap is designed by MATLAB AppDesigner with GUI (graphical user interface) operation. The program for oppHeatmap was available at https://github.com/HangZhouSheep/oppHeatmap .are diagramed by.

Combination of linguistic Z-numbers and IF-THEN rules based on rectangular coordinate system

There is a growing body of literature that recognises the importance of Z-numbers proposed by Prof Zadeh. However, due to the complicated structure and short presentation time, many unknowns about Z-numbers still exist. To fill these gaps, this study aims to make use of rectangular coordinate system to express linguistic Z-numbers. Simultaneously, this study sets out to design a score function to quantify the information contained in different Z-numbers. Subsequently, distance measure and similarity measure are also presented from the perspective of coordinate system. Besides, linguistic discrete Z-numbers and belief rule base (BRB) model are combined to construct a novel reasoning model on the basis of implication operators. To verify the validity of the proposed method, three representative examples of epidemic level assessment, multicriteria group decision-making (MCGDM), and network security assessment are employed. The comparison with other widely used methods are performed to further demonstrate the superiority of the proposed method.

Analysis of increasing channel capacity of MIMO communication system by vortex electromagnetic wave

Multiple-input and multiple-output (MIMO) communication technology which depends on multipath reflection can bring more efficient use of spectrum and higher channel capacity without expanding the bandwidth. This technology has been widely used in 5G communication system these days. However, under some circumstances which are lack of multipath reflection, the performance of traditional MIMO communication is not satisfying. Therefore, some researchers have pointed out that the technology of vortex electromagnetic wave can improve this situation efficiently. This article has done some researches on analyzing the channel capacity in traditional MIMO system and the MIMO system with vortex electromagnetic wave. Firstly, the spatial channel geometry model has been established with a 4-antenna transmit array and a 25-antenna receiving array in a three-dimensional rectangular coordinate system. In order to obtain the total channel capacity, the Los channel fading matrix should be calculated through calculating the distances between each two transmit and receiving antennas. After that the water filling algorithm has been used to decide the power allocation method to each subchannel to get the maximum capacity of the system. Finally, the relationship between maximum channel capacities and the signal-noise ratio (SNR) can be plotted as a line chart. The experiment first compared the capacities with and without the vortex electromagnetic wave of MIMO communication system under different SNR and found that the adding of vortex electromagnetic wave can increase the capacity efficiently. Next the influences of some variables to the channel capacity include the height of transmit antenna array, the distance between each two nearby transmit antenna elements and the variable Q which can change the phase complexity of wavefront have been discussed.

Traffic Path Recommendation Model based on a Weighted Sum of Extracted Parameter

A path recommendation for vehicular traffic is important task of traffic analysis. It is a challenging problem for researchers to extract all paths and recommend the shortest path between Origin and Destination (OD) pairs. This paper comes up with a model which is established on the weighted sum of selected link references to recommend a path for OD pairs. First, to maintain spatial dependence between link references, a vehicular traffic network of roads is proposed as a rectangular coordinate system. The algorithm based on K-means and smoothing is introduced to select link references across OD pairs. A distance aggregation algorithm is proposed to evaluate all possible paths across an OD pair. Finally, out of overwhelming paths, the algorithm recommends the shortest distance path across an OD pair. Our proposed model effectively selects the link references and gets an overall shortest path recommendation. The proposed model analyzes the non-Euclidean distance of selected link references. Our experimental analysis shows that on an average, the first four link predictions lead to 77.37% distance coverage for the recommended path.

A novel parameter similarity measure between interval-valued picture fuzzy sets with its app-lication in pattern recognition

As an extension of picture fuzzy sets (PFSs), interval-valued picture fuzzy sets (IVPFSs) can better model and handle incomplete, indeterminate and inconsistent information in some practical applications. One of the important topics in IVPFSs is the similarity measure of IVPFSs, for which few studies have been proposed within the literature. Moreover, some existing similarity measures cannot adequately meet the conditions of similarity measure with some counterintuitive cases. In this work, we devise a novel similarity measure between IVPFSs based on the effect of the margin of the degree of refusal membership. First, the interval-valued picture fuzzy numbers will be transformed into two right-angled triangular-based pyramids in a spatial rectangular coordinate system. Then, a new parameter distance measure for IVPFSs is defined to assess the similarity between IVPFNs according to the centers of gravity of their corresponding right-angled triangular-based pyramids. Meanwhile, a comparison between different similarity measures is performed to illustrate that the proposed similarity measure can overcome the deficiencies of other extant measures. Finally, we apply it to handle pattern recognition problems. The comparison results indicate that the proposed algorithm can adequately meet the conditions of similarity measure, produce more reasonable and creditable results and perform well in complex contexts.

Developing a Model for Curve-Fitting a Tree Stem’s Cross-Sectional Shape and Sapwood–Heartwood Transition in a Polar Diagram System Using Nonlinear Regression

A function from the domain (x-set) to the codomain (y-set) connects each x element to precisely one y element. Since each x-point originating from the domain corresponds to two y-points on the graph of a closed curve (i.e., circle, ellipse, superellipse, or ovoid) in a rectangular (Cartesian) diagram, it does not fulfil the function’s requirements. This non-function phenomenon obstructs the nonlinear regression application for fitting observed data resembling a closed curve; thus, it requires transforming the rectangular coordinate system into a polar coordinate system. This study discusses nonlinear regression to fit the circumference of a tree stem’s cross-section and its sapwood–heartwood transition by transforming rectangular coordinates (x, y) of the observed data points’ positions into polar coordinates (r, θ). Following a polar coordinate model, circular curve fitting fits a log’s cross-sectional shape and sapwood–heartwood transition. Ellipse models result in better goodness of fit than circular ones, while the rotated ellipse is the best-fit one. Deviation from the circular shape indicates environmental effects on vascular cambium differentiation. Foresters have good choices: (1) continuing using the circular model as the simplest one or (2) changing to the rotated ellipse model because it gives the best fit to estimate a tree stem’s cross-sectional shape; therefore, it is more reliable to determine basal area, tree volume, and tree trunk biomass. Computer modelling transforms the best-fit model’s formulas of the rotated ellipse using Python scripts provided by Wolfram engine libraries.

Thermally progressive Particle-Cu/Blood peristaltic transport with mass transfer in a Non-Uniform Wavy Channel: Closed-form exact solutions

The motivation behind writing the current article is to mathematically study the thermally driven transport of solute particles (measured in micro to nano meters) suspended in blood in an Esophagus mathematically taken as a non-uniform channel. The aim of the present study is to see the effects of solute particles with blood and nanoparticles in Esophagus to see its application in drug delivery and biomedical engineering etc. It also has many applications in microscale phenomena in physiology. Here blood is taken as a base fluid and nanofluid is prepared by the suspension of copper oxide nanoparticles in blood. Copper oxide is extremely useful in the medical domain for drug delivery and cancer treatment. To further study the impact of nanomedicine delivery we considered copper nanoparticles embedded in blood along other small sized solute particles. The mathematical formulation is performed in a rectangular coordinate system and constitutive flow equations are linearized by the implementation of approximations of low Reynolds number and large wavelength. The exact solution of reduced coupled and nonlinear set of equations for fluid particle velocity, temperature and fluid-particle composition profiles is computed through Mathematica while pressure rise is calculated by applying numerical integration. The effect of notable emerging parameters is discussed through graphs. It is observed that velocity rises with an increase in suspension and Casson fluid parameter, whereas opposite results are observed for temperature distribution. Nanoparticles volumetric fraction contribute to decelerating fluid flow and upsurge temperature. Schmidt number influences the fluid-particle composition by lessening it. PACS number: 47.10. A−; 47.35.Pq; 47.85.-g.