Ruled Surfaces Research Articles

Timelike Surface Couple with Bertrand Couple as Joint Geodesic Curves in Minkowski 3-Space

A curve on a surface is a geodesic curve if its principal normal vector is anywhere aligned with the surface normal. Using the Serret–Frenet frame, a timelike surface couple (TLSC) with the symmetry of a Bertrand couple (BC) can be specified in terms of linear combinations of the components of the local frames in Minkowski 3-space E13. With these parametric representations, the necessary and sufficient conditions for the specified BC are derived to be the geodesic curves defining these surfaces. Afterward, the definition of a TL ruled surface (RS) is also provided. Furthermore, the application of the method to some significant models is given.

Bertrand Offsets of Spacelike Ruled Surfaces With Blaschke Approach

Dual parametrizaions of the Bertrand offset- spacelike ruled surfaces are assigned and sundry modern outcomes are acquired in view of their integral invariants. A modern characterization of the Bertrand offsets of spacelike developable surfaces is specified. Further, many connections among the striction curves of Bertrand offsets of spacelike ruled surfaces and their integral invariants are gained.

Timelike Ruled Surfaces with Stationary Disteli-Axis

This paper derives the declarations for timelike ruled surfaces with stationary timelike Disteli-axis by the E. Study map. This prepares the ability to determine a set of Lorentzian invariants which explain the local shape of timelike ruled surfaces. As a result, the Hamilton and Mannhiem formulae of surfaces theory are attained at Lorentzian line space and their geometrical explanations are examined. Then, we define and explicate the kinematic geometry of a timelike Plűcker conoid created by the timelike Disteli-axis. Additionally, we provide the relationships through timelike ruled surface and the order of contact with its timelike Disteli-axis.

Characterizations of Unit Darboux Ruled Surface with Quaternions

This paper presents a quaternionic approach to generating and characterizing the ruled surface drawn by the unit Darboux vector. The study derives the Darboux frame of the surface and relates it to the Frenet frame of the base curve. Moreover, it obtains the quaternionic shape operator and its matrix representation using the normal and geodesic curvatures to provide a more detailed analysis. To illustrate the concepts discussed, the paper offers a clear example that will help readers better understand the concepts and showcases the quaternionic shape operator, Gauss curvature, mean curvature, and rotation matrix. Finally, it emphasizes the need for further research on this topic.

The Invariants of Dual Parallel Equidistant Ruled Surfaces

In this paper, we calculate the Gaussian curvatures of the dual spherical indicatrix curves formed on unit dual sphere by the Blaschke vectors and dual instantaneous Pfaff vectors of dual parallel equidistant ruled surfaces (DPERS) and we give the relationships between these curvatures. In addition to—in cases where the base curves of these DPERS are closed—computing the dual integral invariants of the indicatrix curves. Additionally, we show the relationships between them. Finally, we provide an example for each of these indicatrix curves.

Intelligent Gear Decision Method for Automatic Vehicles Based on Data Mining Under Uphill Conditions

Existing gear decision methods are affected by the limiting factors of deviation of numerical models as well as the subjectivity of the designer, which results in poor adaptability to the driving intentions and driving environments. Excellent drivers are able to choose the appropriate gear to satisfy their driving intentions and respond to changes in driving environments when driving manual transmission vehicles. Therefore, an intelligent gear decision method and design methodology of vehicle automatic transmission system that adapts to different driving intentions and complex driving environments are constructed from the massive driving data of excellent drivers by using data mining method. Excellent drivers are employed to drive vehicles with manual transmission to obtain a large amount of driving data. Subsequently, data preprocessing, data cleaning, and outlier removal are performed on the collected driving data to extract the shift boundary points of each gear aiming at constructing the shift rule surface of each gear. Using the uphill condition as an example, a data-mining-based shift control strategy is established, and the comparison results verify that the proposed gear decision design method can mine the shift strategy of excellent drivers from massive driving data, and the constructed strategy can better adapt to the driver’s intention while obtaining better fuel economy and avoiding unreasonable gearshifts compared with the automatic transmission’s default strategy.

Quaternionic Approach of Slant Ruled Surfaces

Quaternionic Approach of Slant Ruled Surfaces

Estimation of tool–chip contact length using optimized machine learning in orthogonal cutting

Tool–chip contact length has a significant effect on the various characteristics of metal cutting, including cutting pressures, chip formation, tool wear, tool life, and cutting temperatures. It should be added that there is a direct relationship between the tool–chip contact length and secondary shear zone thickness in the metal cutting process. The cutting force and shear zone temperature decrease by the reduction of tool–chip contact length. In addition, the tool–chip contact length affects the tool life and workpiece surface roughness. Lots of researchers have conducted extensive research to calculate the tool–chip contact length using mathematical or machine learning methods. The main objective of this study is to calculate the tool–chip contact length using a highly advanced machine learning method without any time-consuming and expensive experiments. However, an adaptive network-based fuzzy inference system (ANFIS) is not used yet in the prediction of the tool–chip contact length. In this study, we proposed the ANFIS to predict the tool–chip contact length for the first time in orthogonal cutting using depth of cut, feed-rate, and cutting speed as inputs of the proposed model. As the second contribution of this study, three evolutionary-based optimization techniques, including genetic algorithm, particle swarm optimization, and grey wolf optimization, as well as global-based Bayesian optimization, are employed to select the optimal hyperparameters of the proposed ANFIS model known as GA-ANFIS, PSO-ANFIS, GWO-ANFIS, and B-ANFIS, respectively. The proposed methods are designed and developed in MATLAB software to be compared with the previous method using genetic programming (GP). The outcomes of this research demonstrate that the GWO-ANFIS can decrease the mean square error between the actual and predicted tool–chip contact length of 15.60%, 3.67%, 89.75%, and 92.17% in comparison with those of GA-ANFIS, PSO-ANFIS, B-ANFIS, and GP, respectively. In addition, the fuzzy logic rule surface of the GWO-ANFIS shows 57.20%, 30.95%, and 11.85% dependency of tool–chip contact length to cutting speed, feed-rate, and depth of cut as the inputs of the orthogonal cutting process, respectively.

The Dual Expression of Parallel Equidistant Ruled Surfaces in Euclidean 3-Space

In this study, we examine the dual expression of Valeontis’ concept of parallel p-equidistant ruled surfaces well known in Euclidean 3-space, according to the Study mapping. Furthermore, we show that the dual part of the dual angle on the unit dual sphere corresponds to the p-distance. We call these ruled surfaces we obtained “dual parallel equidistant ruled surfaces” and we briefly denote them with “DPERS”. Furthermore, we find the Blaschke vectors, the Blaschke invariants and the striction curves of these DPERS and we give the relationships between these elements. Moreover, we show the relationships between the Darboux screws, the instantaneous screw axes, the instantaneous dual Pfaff vectors and dual Steiner rotation vectors of these surfaces. Finally, we give an example, which we reinforce this article, and we explain all of these features with the figures on the example. Furthermore, we see that the corresponding dual curves on the dual unit sphere to these DPERS are such that one of them is symmetric with respect to the imaginary symmetry axis of the other.

Kinematic Geometry of Timelike Ruled Surfaces in Minkowski 3-Space E13

Symmetry is a frequently recurring theme in mathematics, nature, science, etc. In mathematics, its most familiar manifestation appears in geometry, most notably line geometry, and in other closely related areas. In this study, we take advantage of the symmetry properties of both dual space and original space in order to transfer problems in original space to dual space. We use E. Study Mappingas a direct method for analyzing the kinematic geometry of timelike ruled and developable surfaces. Then, the invariants for a spacelike line trajectory are studied and the well-known formulae of Hamilton and Mannheim on the theory of surfaces are provenfor the line space. Meanwhile, a timelike Plücker conoid generated by the Disteli-axis is derived and its kinematic geometry is discussed. Finally, some equations for particular timelike ruled surfaces, such as the general timelike helicoid, the Lorentzian sphere, and the timelike cone, are derived and plotted.

On parallel p-equidistant ruled surfaces by using mofied orthogonal frame with curvature in E³

In this paper, it is investigated Ruled surfaces according to modified orthogonal frame with curvature in 3-dimensional Euclidean space. Firstly, we give apex angle, pitch and drall of closed ruled surface in E³. Then, it characterized the relationship between these invariant of parallel p-equidistant ruled surfaces.

On the Determination of Spacelike Ruled and Developable Surfaces in Minkowski 3-Space

On the Determination of Spacelike Ruled and Developable Surfaces in Minkowski 3-Space

On the Correlation Between Spanwise Inducer Incidence and Impeller Diffusion for Ruled Surface and Barreled Sweep-Bow Impeller Design at Inlet Guide Vane-Off-Design

AbstractIn the present paper, three centrifugal stages of high volume flow coefficient are compared to each-other regarding their aerodynamic performance in design point and off-design point conditions at different speed and inlet guide vane (IGV)-setting angle: two stages with full-blade design (no splitter blades) have been numerically designed with different design geometry methodology. One geometry is based on a classical ruling surface design with a linear leading edge, the second geometry based on a fully-three-dimensional surface including a blade bow at the trailing edge and a barreled sweep at the leading edge. According to impeller test rig measurements and computational fluid dynamics (CFD) calculation, the classical ruling surface designed impeller outperforms the more sophisticated centrifugal stage with fully 3D-blade at fully axially guided IGV-flow. In the contrary, at closing IGV-off-design setting angles, toward surge operation, the fully 3D-blade impeller performs with higher efficiency and steeper negative pressure slope. On the search of the geometrical causes for the different aerodynamic performance (especially at IGV-off-design conditions), focus is set on the analysis of IGV-flow-interaction with the inducer flow and impeller diffusion. The one-dimensional analysis of the spanwise flow at the impeller leading edge reveals that, compared with the ruling surface impeller, the fully 3D-blade performs with lower flow incidence losses in favor to IGV-off-design operation than at IGV-neutral position. The streamwise flow analysis confirms the improved flow incidence characteristics of the 3D-blade impeller due to reduction of aerodynamic blockage and entropy production in the vicinity of the impeller leading edge. Based on CFD calculations, a new correlation of secondary flow and flow incidence is proposed, to be used for one-dimensional modeling.

RULED SURFACE WITH CONSTANT SLOPE ACCORDING TO OSCULATING PLANE OF BASE CURVE IN GALILEAN 3- SPACE

The object of this paper is to investigate the properties of the ruled surface which direction vector has a constant slope with osculator plane of the base curve in Galiean $3-$space. We obtain some properties of this kind of ruled surface by calculating the geometric invariants. Also, we give an application on the example and their graphs are visualized by using the Mathematica program.

Quaternionic and Dual Quaternionic Darboux Ruled Surfaces

In this paper, firstly the ruled surface drawn by the Darboux vector is expressed as a quaternion. Then, the spatial quaternionic definition of the striction curve is given and the integral invariants of the surface are calculated. Finally, the ruled surface which corresponds to a dual curve drawn by a dual Darboux vector is derived with the help of dual spatial quaternions and dual integral invariants of the ruled surface are obtained.

On the Developability and Distribution Parameters of the Involute Trajectory Ruled Surfaces

On the Developability and Distribution Parameters of the Involute Trajectory Ruled Surfaces

Conformational Transitions upon Maturation Rule Surface and pH-Responsiveness of α-Lactalbumin Microparticulates.

De novo designed protein supramolecular structures are nowadays attracting much interest as highly performing biomaterials. While a clear advantage is provided by the intrinsic biocompatibility and biodegradability of protein and peptide building blocks, developing sustainable and green bottom up approaches for finely tuning the material properties still remains a challenge. Here, we present an experimental study on the formation of protein microparticles in the form of particulates from the protein α-lactalbumin using bulk mixing in water solution and high temperature. Once formed, the structure and stability of these spherical protein condensates change upon further thermal incubation while the size of aggregates does not significantly increase. Combining advanced microscopy and spectroscopy methods, we prove that this process, named maturation, is characterized by a gradual increase of amyloid-like structure in protein particulates, an enhancement in surface roughness and in molecular compactness, providing a higher stability and resistance of the structure in acidic environments. When dissolved at pH 2, early stage particulates disassemble into a homogeneous population of small oligomers, while the late stage particulates remain unaffected. Particulates at the intermediate stage of maturation partially disassemble into a heterogeneous population of fragments. Importantly, differently matured microparticles show different features when loading a model lipophilic molecule. Our findings suggest conformational transitions localized at the interface as a key step in the maturation of amyloid protein condensates, promoting this phenomenon as an intrinsic knob to tailor the properties of protein microparticles formed via bulk mixing in aqueous solution. This provides a simple and sustainable platform for the design and realization of protein microparticles for tailored applications.

Ruled surfaces constructed by quaternions

In this paper, we define a quaternionic operator whose scalar part is a real parameter and vector part is a curve in three dimensional real vector space R3. We prove that quaternion product of this operator and a spherical curve represents a ruled surface in R3 if the vector part of the quaternionic operator is perpendicular to the position vector of the spherical curve. We express this surface as 2-parameter homothetic motion using the matrix representation of the operator. Furthermore, we define another quaternionic operator and show that each ruled surface in R3 can be obtained by this operator. Finally, we give the geometric interpretations of these operators with some examples.

Impact of urban evolution on local temperature trends of Rawalpindi and Islamabad

Rawalpindi and Islamabad commonly known as twin cities of Pakistan have 3.2 million population. Twin cities have rapidly urbanized in the last three decades. The objective of the present study is to compute the urban growth and its effect on evolution of local temperature trends of twin cities. To compute the land-cover change such as built-up area, vegetation cover, water and barren land, Landsat images of 1980, 1992, 2000 and 2013 are classified by using the supervised image classification with maximum likelihood rule and probability surface method. To evaluate the change in temperature trends, homogenized time series data of daily averaged monthly minimum (Tmin) and maximum (Tmax) temperatures for the period of 1983 to 2013 is analyzed by using the linear regression. The results show that built-up area of twin cities increased from 66 km2 in 1983 to 148 km2 in 2013 with an increase of 120 per cent within 31 years. Due to resulted urbanization, Tmin and Tmax of twin cities have been increasing. Tmin is increased more in Rawalpindi than Islamabad and Tmax is increased more in Islamabad than Rawalpindi. The highest increase in Tmin and Tmax at both stations is observed during spring season.

Prediction of lisinopril pediatric dose from the reference adult dose by employing a physiologically based pharmacokinetic model

BackgroundThis study aimed to assess the pediatric lisinopril doses using an adult physiological based pharmacokinetic (PBPK) model. As the empirical rules of dose calculation cannot calculate gender-specific pediatric doses and ignores the age-related physiological differences.MethodsA PBPK model of lisinopril for the healthy adult population was developed for oral (fed and fasting) and IV administration using PK-Sim MoBI® and was scaled down to a virtual pediatric population for prediction of lisinopril doses in neonates to infants, infants to toddler, children at pre-school age, children at school age and the adolescents. The pharmacokinetic parameters were predicted for the above groups at decremental doses of 20 mg, 10 mg, 5 mg, 2.5 mg, and 1.5 mg in order to accomplish doses producing the pharmacokinetic parameters, similar (or comparable) to that of the adult population. The above simulated pediatric doses were compared to the doses computed using the conventional four methods, such as Young’s rule, Clark’s rule, and weight-based and body surface area-based equations and the dose reported in different studies.ResultsThough the doses predicted for all subpopulations of children were comparable to those calculated by Young’s rule, yet the conventional methods overestimated the pediatric doses when compared to the respective PBPK-predicted doses. The findings of previous real time pharmacokinetic studies in pediatric patients supported the present simulated dose.ConclusionThus, PBPK seems to have predictability potential for pediatric dose since it takes into consideration the physiological changes related to age and gender.