Straight Plane Research Articles

Using Advanced Mathematical Method to find Normal Curvature of the Curve on Regular Surfaces

Curvature, being a crucial geometric parameter in many applications of surface analysis, is the amount of deviation of curve from a straight line or plane. This study's objective is to use Matlab to objectively calculate Normal Curvature on Smooth Surfaces. The following article concerns curvature and normal curvature with the focus on two uses: first for the manufacturing of automobile tire’s inner tubes, and second one to identify the ideal choice degree of normal curvature. The aim of the study is finding the normal curvature numerically and using Matlab, which can carry out complex computational tasks with general commands and is relatively more precise and swifter than the standard numerical calculations.

Prevalence of malocclusion and oral health-related factors among pre-school children in Northern Albania.

The aim of the present study was to investigate prevalence and association between malocclusion and caries among pre-school children aged 4-6 years frequenting public kindergartens in Shkodër, the largest city in North Albania. The sample for this descriptive and cross-sectional study included 389 pre-school children aged 4-6 years frequenting 20 public kindergartens in Shkodër, the largest city in North Albania. The participants were divided into two groups according to their caries experience evaluated, as determined by decayed-missing-filled index dmf (World Health Organization criteria) score. Those with dmf score of zero were considered to be free of caries. The prevalence of children with at least one malocclusion trait was 89%. The prevalence of caries was 66% (mean dmf score: 3.63). Increased overbite (43%), followed by increased overjet, were the most prevalent malocclusion traits observed in children with a dmf of zero. Among children with caries, the most prevalent trait was increased overjet (42%) and increased overbite. Almost half of the entire study population had a straight terminal plane and class I canine relationship. There was a similar prevalence of bilateral crossbite. Significant changes (p = 0.008) were observed between the groups with regards to the absence of spacing in the maxillary anterior region. Regression analysis further revealed that children with an absence of maxillary spacing were 2.564-fold more likely to have caries; those with a deepbite were 0.814-fold more likely to have caries. More than half of the children had caries. Increased overjet, overbite, crossbite and maxillary crowding were malocclusion traits observed in the population included in this study. A positive association was identified between maxillary crowding, deepbite and caries. The association between malocclusion and caries, highlights the necessity for an increased awareness of these two conditions that are commonly found among children of pre-school age.

A NOVEL MACHINE LEARNING STUDY: MAXIMIZING THE EFFICIENCY OF PARABOLIC TROUGH SOLAR COLLECTORS WITH ENGINE OIL-BASED COPPER AND SILVER NANOFLUIDS

Estimating the heat transfer parameters of parabolic trough solar collectors with machine learning is crucial for improving the efficiency and performance of these renewable energy systems, optimizing their design and operation, and reducing costs while increasing the use of solar energy as a sustainable power source. In this study, the heat transfer characteristics of two different nanofluids flowing through the porous media in a straight plane underneath thermal jump conditions were investigated by machine learning methods. For the flow in the parabolic trough solar collector, two different nanofluids obtained from silver- and copper-based motor oil are considered. Flow characteristics were obtained by nonlinear surface tension, thermal radiation, and Cattaneo–Christov heat flow, which was used to calculate the heat flow in the thermal boundary layer. A neural network structure was established to estimate the skin friction and Nusselt number determined for the analysis of the flow characteristic. The data used in the multilayer neural network, which was developed using a total of 30 data sets, were divided into three groups as training, validation, and testing. In the input layer of the network model with 15 neurons in the hidden layer, 10 parameters were defined and four different results were obtained for two different nanofluids in the output layer. The prediction performance of the established neural network model has been comprehensively studied by means of several performance parameters. The study findings presented that the established artificial neural network can predict the heat transfer characteristics of two different nanofluids obtained from silver- and copper-based motor oil with deviation rates less than 0.06%.

An Upper Bound Energy Formulation of Free-Chip Machining with Flat Chips and an Alternative Method of Determination of Cutting Forces without Using the Merchant’s Circle Diagram

An upper bound analysis of free-chip machining has been carried out, where the tool cutting and friction forces were determined from the deformation energy dissipated during the chip separation process. The method employed was based on the classical upper bound theorem, as formulated by Prager and Hodge, and Drucker, Prager, and Greenberg, and its modification by Collins, to deal with the metal forming processes involving coulomb friction. A straight shear plane and coulomb friction at the chip/tool interface were assumed and the energy required for cutting was calculated from a strain rate/velocity field that was constructed using the method proposed by Collins. Cutting forces, thrust forces, tool/chip contact lengths, and chip thickness ratios were determined for different tool rake angles and friction conditions. The theoretical results were also compared with some experimental results that are available in the published literature. The comparison between the two was not found to be satisfactory. This may be due to the non-unique nature of the machining process, as stated by Hill and demonstrated by other authors. The results calculated from the present method of ”energy balance” were also found to be in agreement with those obtained by Merchant using the principle of ”force balance”.

THEORETICAL FOUNDATIONS OF THE POINT CALCULUS AS A MATHEMATICAL APPARATUS FOR GEOMETRIC AND COMPUTER MODELING

The purpose of the article is to acquaint the reader with the new mathematical apparatus – point calculus, which was developed for solving engineering and scientific problems by the leading scientists of the Melitopol School of Applied Geometry and continues its active development in the works of Russian and Ukrainian scientists-geometers. The article presents the fundamental definitions and terms, basic methods, metrics, fundamental theorems of point calculus, shows the principles of parametrization of a straight line, plane and three-dimensional space in point calculus. Possibilities of point calculus include the definition of continuous and discrete geometric models of objects, processes and phenomena in the form of point equations and computational algorithms based on them. The advantage of the new mathematical apparatus is the representation of geometric objects in the form of a set of projections on the axes of the global coordinate system, which makes it possible to determine the geometric models of objects, processes and phenomena in spaces of any dimension. The use of point calculus in computer graphics and virtual reality, solid modeling of isotropic and anisotropic bodies and computer modeling of objects consisting of nanoparticles is seen as promising. Therefore, the main direction of promising research is seen as the further expansion of theoretical and applied point calculus tools, and its popularization by solving a wide range of important engineering and scientific problems of an applied nature.

Diffusion Laws and Modified Pascal’s Triangles

Four main diffusion laws: 1D diffusion in a planar bulk sample or random walks along a straight line x=α1t1/2; 3D diffusion or random walks from a point source and forming small spherical particle: x=α2t1/3; 1D+1D diffusion or random walks along a straight plane with simultaneous outflow into balk: x=α3t1/4; 1D+2D diffusion or random walks along a straight line with simultaneous outflow into balk: x=α4t1/6 are analysed theoretically using mathematical modelling and appropriate physical models. Convex shape of the diffusion profile near the top along a dislocation pipe with simultaneous outflow into balk is predicted. It is shown that the cone angle near the top is increasing with time. Literature experimental data are used for analysis.

Enhanced mechanical properties in metastable β titanium alloy via ω-assisted nucleation

In this study, we performed heat treatment with different solution cooling routes and aging heating rates were performed on the TB18 alloy (Ti-5.3Cr-4.9Mo-4.9V-4.3Al-0.9Nb-0.3Fe) to enhance its mechanical properties via ω-assisted nucleation. The results showed that the intragranular α plates that precipitated during aging appeared finer under slow heating than under fast heating because the ωiso particles formed during the slow heating process provide abundant ω/β interfaces, which can serve as heterogeneous nucleation sites for α precipitates and reduce the nucleation driving force. The corresponding phase transformation sequence is expected to be β + ωath → β + ωath + ωiso → β + ωiso + α → β + α during continuous heating. Further comparing the microstructures, we found that a faster solution cooling rate is more conducive to ω-assisted nucleation. During ω-assisted nucleation, the three-phase orientation relationship holds for: (112‾0)ω//(0001)α//(110)β, and [0001]ω//[112‾0]α//[11‾1]β. At the atomic scale, the ω/α interface appeared as a relatively straight atomic plane, whereas more defects, termed as disconnections, were observed at the α/β interface. Moreover, appropriate ω-assisted nucleation could enhance the ductility of the TB18 alloy without reducing its strength to obtain the optimal comprehensive mechanical properties, and the corresponding fracture mechanism was a mixed mode dominated by ductile fracture. Excessive ω-assisted nucleation could considerably strengthen the alloy but significantly deteriorated its ductility, and the mixed fracture mode was more inclined to brittle fracture.

A numerical technique to solve a problem of the fluid motion in a straight plane rigid duct with two axisymmetric rectangular constrictions. An alternative approach

A numerical technique is devised to solve a problem of the steady laminar fluid motion in a straight plane hard-walled duct with two local axisymmetric rectangular constrictions. It uses the stream function, the vorticity and the pressure as the basic variables, has the second order of accuracy in the spatial and the first order of accuracy in the temporal coordinates, provides high stability of a solution, and needs significantly less computational time to obtain a result compared to appropriate techniques available in a scientific literature. The technique consists in: a) introducing the stream function and the vorticity, and subsequent transiting from the non-dimensional governing relations for the fluid velocity and the pressure to the corresponding non-dimensional relations for the stream function, the vorticity and the pressure; b) deriving their discrete counterparts in the nodes of the chosen space-time computational grid; c) integrating the systems of linear algebraic equations obtained after making the discretization. The discretization is based on applying appropriate differencing schemes to the terms of the equations for the basic variables. These are the two-point temporal onward difference for the unsteady term of the vorticity equation, as well as the two-point backward differences (for its convective term) and the five-point approximations (for its diffusive term and for the Poisson’s equations for the stream function and the pressure) in the axial and cross-flow coordinates. As for the velocity components, the appropriate central differences are applied to discretize their expressions. The above-mentioned systems of linear algebraic equations for the stream function and the pressure are integrated by the iterative successive over-relaxation method. The algebraic relation for the vorticity does not need application of any method to be solved, because it is a computational scheme to find this quantity based on the known magnitudes computed at the previous instant of time.

Water flow modeling in bounded gas-bearing fractured geological strata: A semi-analytical and experimental study

Underground water disposal is a technique for wastewater management, enhanced oil recovery (EOR), or artificial groundwater/aquifer recharge. Host layers might be naturally or even hydraulically fractured which can significantly increase the permeability of the medium where a linear flow geometry around the vertical fractures intersecting the wells is expected. In fact, each of flow from wellbore (injection point) to fracture as well as fracture-matrix flow may be linear in different conditions of fracture conductivity. When both are linear it is named “bilinear flow” in hydraulic fracture appications equivalent to “fully linear flow” in this study. In this paper, a semi-analytical solution is presented for transient saturation of injected water in naturally/hydraulically fractured gas-bearing rocks with linear flow in both wellbore-fracture and fracture-matrix spacings. The solution is general and can be used for either unsaturated soils or depleted reservoirs which are defined with no-flow boundaries. To do so, proposed semi-analytical model was validated with experimental results, based on waterflood testing apparatus in an artificially fractured core-plug which showed a very good matching. In addition to introducing new sets of type curves to delineate water saturation in both matrix and fracture in both constant terminal rate and saturation (CTR and CTS) inner boundary conditions, we defined the average water velocity ratio (AWVR), a conceptual criterion, to assess if CTS and CTR water storage can be logically compared. Results derived based on this concept are: 1) more speedy movement of water front along the last four-fifth of the fracture length by CTR and 2) higher matrix blocks storativity neighboring the first half of the straight fracture plane by CTS. Solutions from our model can directly simulate the unsteady behavior of saturation variations along the fracture and across the rock matrix versus time for an underground water injection problem. Ultimately, this can assist engineers to have an easy spatiotemporal estimation of water storage in the matrix of the host formation.

Extra plasticity governed by shear band deflection in gradient metallic glasses

Inspired by gradient materials in nature, advanced engineering components with controlled structural gradients have attracted substantial research interests due to their exceptional combinations of properties. However, it remains challenging to generate structural gradients that penetrate through bulk materials, which is essential for achieving enhanced mechanical properties in metallic materials. Here, we report practical strategies to design controllable structural gradients in bulk metallic glasses (BMGs). By adjusting processing conditions, including holding time and/or controlling temperatures, of cryogenic thermal cycling and fast cooling, two different types of gradient metallic glasses (GMGs) with spatially gradient-distributed free volume contents can be synthesized. Both mechanical testing and atomistic simulations demonstrate that the spatial gradient can endow GMGs with extra plasticity. Such an enhanced mechanical property is governed by the gradient-induced deflection of shear deformation that fundamentally suppresses the unlimited shear localization on a straight plane that would be expected in BMGs without such a gradient.

A numerical technique to solve a problem of the fluid motion in a straight plane rigid duct with two axisymmetric rectangular constrictions

A second-order numerical technique is developed to study the steady laminar fluid motion in a straight two-dimensional hard-walled duct with two axisymmetric rectangular constrictions. In this technique, the governing relations are solved via deriving their integral analogs, performing a discretization of these analogs, simplifying the obtained (after making the discretization) coupled nonlinear algebraic equations, and the final solution of the resulting (after making the simplification) uncoupled linear ones. The discretization consists of the spatial and temporal parts. The first of them is performed with the use of the TVD-scheme and a two-point scheme of discretization of the spatial derivatives, whereas the second one is made on the basis of the implicit three-point asymmetric backward differencing scheme. The above-noted uncoupled linear algebraic equations are solved by an appropriate iterative method, which uses the deferred correction implementation technique and the technique of conjugate gradients, as well as the solvers ICCG and Bi-CGSTAB.

Mixing length correlation for laminar liquid mixing in wall-bounded flows

The aim of this paper is twofold. Firstly, to examine the relationship between mixing length with respect to mixing index for two streams of liquid mixing in a two-dimensional (2D) straight plane channel. Secondly, to propose a new correlation for mixing length for a given mixing index. Although the existing analytical mixing length using LM=1 = PeH could yield accurate prediction, it is, however, restricted to only at a fully mixed condition (i.e., at mixing index M = 1). To accommodate a broad spectrum of mixing indices, a new correlation that would accurately predict the mixing length for a specific mixing index, in the range of 0.5 ≤ M ≤ 1, is proposed. As revealed in this study, this correlation is applicable to the practical range of Péclet number, for 10 ≤ Pe ≤ 1000 and would hold valid, as long as the laminar mixing flow prevails. In addition, the new correlation is applicable to liquid mixing in the mixers with different channel inlet designs (i.e., 2D Y-mixer and 2D T-mixer), and also relevant for three-dimensional (3D) straight mixers with different mixing channel aspect ratios.

Modified surgical method of supra- and infratentorial epidural hematoma and the related anatomical study of the squamous part of the occipital bone.

BACKGROUNDSupra- and infratentorial acute epidural hematoma (SIEDH) is a common posterior cranial fossa epidural hematoma located at the inner surface of the squamous part of the occipital bone (SOB). Traditionally, surgical treatment of the SIEDH requires a combined supra-infratentorial craniotomy.AIMTo analyze the morphological characteristics of the SOB and introduce a single supratentorial craniotomy for SIEDH.METHODSSkull computed tomography (CT) scan data from 32 adult patients were collected from January 1, 2019 to January 31, 2020. On the median sagittal plane of the CT scan, the angle of the SOB (ASOB) was defined by two lines: Line A was defined from the lambdoid suture (LambS) to the external occipital protuberance (EOP), while line B was defined from the EOP to the posterior edge of the foramen magnum (poFM). The operative angle for the SIEDH (OAS) from the supra- to infratentorial epidural space was determined by two lines: The first line passes from the midpoint between the EOP and the LambS to the poFM, while the second line passes from the EOP to the poFM. The ASOB and OAS were measured and analyzed.RESULTSBased on the anatomical study, a single supratentorial craniotomy was performed in 8 patients with SIEDH. The procedure and the results of the modified surgical method were demonstrated in detail. For males, the ASOB was 118.4 ± 4.7 and the OAS was 15.1 ± 1.8; for females, the ASOB was 130.4 ± 5.1 and the OAS was 12.8 ± 2.0. There were significant differences between males and females both in ASOB and OAS. The smaller the ASOB was, the larger the OAS was. The bone flaps in 8 patients were designed above the transverse sinus intraoperatively, and the SIEDH was completely removed without suboccipital craniotomy. The SOB does not present as a single straight plane but bends at an angle around the EOP and the superior nuchal lines. The OAS was negatively correlated with the ASOB. CONCLUSIONThe single supratentorial craniotomy for SIEDH is reliable and effective.

Fast Positioning Method of Truck Compartment Based on Plane Segmentation

To improve the loading efficiency and shorten the loading time, a method based on LIDAR point cloud segmentation for fast positioning of trucks is proposed for the scenario of level-push automatic loading, in which the truck position and attitude are random. The point cloud data are collected by LIDAR and pre-processed by traditional methods in the order of straight pass filtering, voxel filtering, and plane segmentation. Four planar regions are segmented using the region growth algorithm, and then planar fitting is performed for each of these four regions, which requires a large number of iterations and complex calculations by the traditional planar segmentation method. Focusing on these drawbacks this paper first uses the region growing algorithm to cluster and group the matching points, then combines the least squares and RANSAC algorithms for plane fitting optimization to calculate the intercept of each plane, and finally uses these intercept values to perform spatial geometry calculations to obtain the exact position and locus of the carriage. Experiments show that the method reduces the number of iterations and improves the computational efficiency compared with the traditional RANSAC algorithm, thus improving the efficiency and accuracy of the plane fitting algorithm.

Treatment after anterior cruciate ligament injury: Panther Symposium ACL Treatment Consensus Group

Treatment strategies for anterior cruciate ligament (ACL) injuries continue to evolve. Evidence supporting best practice guidelines for the management of ACL injury is to a large extent based on studies with low-level evidence. An international consensus group of experts was convened to collaboratively advance towards consensus opinions regarding the best available evidence on operative versus non-operative treatment for ACL injury.The purpose of this study was to report the consensus statements on operative versus non-operative treatment of ACL injuries developed at the ACL Consensus Meeting Panther Symposium 2019. Sixty-six international experts on the management of ACL injuries, representing 18 countries, convened and participated in a process based on the Delphi method of achieving consensus. Proposed consensus statements were drafted by the Scientific Organising Committee and Session Chairs for the three working groups. Panel participants reviewed preliminary statements prior to the meeting and provided initial agreement and comments on the statement via online survey. During the meeting, discussion and debate occurred for each statement, after which a final vote was then held. Eighty per cent agreement was defined a priori as consensus. A total of 11 of 13 statements on operative veresus non-operative treatment of ACL injury reached consensus during the symposium. Nine statements achieved unanimous support; two reached strong consensus; one did not achieve consensus; and one was removed due to redundancy in the information provided.In highly active patients engaged in jumping, cutting and pivoting sports, early anatomical anterior cruciate ligament reconstruction (ACLR) is recommended due to the high risk of secondary meniscus and cartilage injuries with delayed surgery, although a period of progressive rehabilitation to resolve impairments and improve neuromuscular function is recommended. For patients who seek to return to straight plane activities, non-operative treatment with structured, progressive rehabilitation is an acceptable treatment option. However, with persistent functional instability or when episodes of giving way occur, anatomical ACLR is indicated. The consensus statements derived from international leaders in the field will assist clinicians in deciding between operative and non-operative treatment with patients after an ACL injury.Level of evidence: V

Analytical solution for two-dimensional displacement flow in a curved down-sloping duct

Exact solution of the Navier–Stokes equations is used in this study to get a closed form equation for the transient and the steady state displacement flow of two Newtonian iso-viscous fluids in a two-dimensional curved plane channel. First, the displacement flow in a straight plane channel is considered. An available analysis is adapted in order to enhance its capability in explaining more details of the flow as well as prepare an appropriate frame to study the flow in curved channels. The behavior of the interface is predicted qualitatively both immediately and a while after the gate valve separating the fluids opens. It is shown that with the aid of the derivative of the flux of the heavier fluid, the viscous dominated flow regime may be analyzed with less difficulty compared to the available explanations in the literature and can also describe the behavior of the interface over a wider range of variations of the imposed flow. For the case of curved channels, the evolution of the interface at different rates of the imposed flow is analyzed again by considering the rate of change of the flux of the heavier displacing fluid in the viscous dominated regime. The results of the current study suggest that introducing the curvature in a displacement channel flow can facilitate the removal of the lighter fluid.

Treatment after ACL injury: Panther Symposium ACL Treatment Consensus Group

Treatment strategies for ACL injuries continue to evolve. Evidence supporting best practice guidelines to manage ACL injury is largely based on studies with low-level evidence. An international consensus group of...

Effect of the stress field on crack branching in brittle material

To research the effect of the stress field on brittle fracture surface roughness, two types of experiments with different stress fields around the crack tip, bending and tensile fracture tests, were performed with resin materials, PMMA and polycarbonate. Macro-crack branching in PMMA started when the crack speed was over 0.81 cr (cr: Rayleigh wave speed) in bending specimens and only 0.59 cr in tensile specimens. It was experimentally confirmed that the stress field affected fracture surface roughness, and it may be inappropriate to think that dissipated energy is dominated by crack speed only, as some conventional discussions suggest. We presumed that the promotion of macro-crack branching and the increase in fracture surface roughness were caused by a high T-stress. T-stress might act to open microbranches in the mist region because they are tilted to align with the ideally straight crack plane.

Tractor plough designing with specified tillage quality

The required quality of the soil layer crumbling can be obtained by providing a certain movement of soil along the plough-bottom surface. The paper presents a technique for constructing a mathematical pattern for optimal soil movement, characterized by a smooth transition from the straight plane of the mouldboard to the curved surface of the plough-share. A distinctive feature of the experimental mouldboard sample is its capability to regulate three angles of the plough-bottom surface: the angle of the ploughshare position to the furrow bottom, the angle of the ploughshare position to the furrow wall and the angle of the plough-bottom surface bending.

Front dynamics in exchange flow of two immiscible iso-viscous fluids in two-dimensional straight and curved plane channels

Exchange flow of two immiscible fluids at a low Atwood number in a straight and curved plane channel is considered in this analytical study. The fluids are considered immiscible, but practically, the results can be applied to miscible fluids for short times and in nearly horizontal channels where mixing is negligible due to strong segregation. The exchange flow and displacement flow in pipes at different inclinations with respect to vertical have been extensively studied and have many applications in industry or environmental settings. For the case of plane two-dimensional channels, however, because of the simpler geometry, it is more convenient to understand the physics of the problem and formulate the physical phenomena mathematically. An equation has been derived that describes the transient front velocity in exchange flow in a straight plane channel. The steady state front velocity in straight channels is estimated. The exchange flow in curved channels demonstrates an unstable front or a separated trail because of the curvature of the path. In the case of curved channels, some of the general behavior of the interface is predicted and validated against some experimental observations in curved pipes but quantitative analysis of the interface and the flow requires more advanced mathematical formulation and more detailed experiments for validation.