Recursive Process for Constructing the Refinement Rules of New Combined Subdivision Schemes and Its Extended Form

In this article, we present a new method to construct a family of 2 N + 2 -point binary subdivision schemes with one tension parameter. The construction of the family of schemes is based on repeated local translation of points by certain displacement vectors. Therefore, refinement rules of the 2 N + 2 -point schemes are recursively obtained from refinement rules of the 2 N -point schemes. Thus, we get a new subdivision scheme at each iteration. Moreover, the complexity, polynomial reproduction, and polynomial generation of the schemes are increased by two at each iteration. Furthermore, a family of interproximate subdivision schemes with tension parameters is also introduced which is the extended form of the proposed family of schemes. This family of schemes allows a different tension value for each edge and vertex of the initial control polygon. These schemes generate curves and surfaces such that some initial control points are interpolated and others are approximated.

Optical Response Analysis at Various Pb2+ Concentration by Using Fiber Optic Displacement Sensor

A simple and low-cost Fiber Optic Displacement Sensor (FODS) using reflective intensity modulation technique was developed to analyze various concentrations of Pb2+, a compound classified under heavy metal ions. Lead is harmful to the environment including to human but is used in the cosmetic field for beauty without realizing and considering the hazardousness of lead as it would cause a long-term effect. Therefore, a feasible way has been identified in this study to demonstrate the level of Pb2+ concentration in cosmetics field by employing the theory of modulation of intensity as a function of displacement sensor. The permissible limit according to Malaysian Cosmetics Guidelines and ASEAN Cosmetic Directive was 20 ppm. The concentration sensor’s system exhibits 0.0018 V/ppm sensitivity with a linearity of 96% and 94% respectively, for both peaks. Meanwhile, the sensitivity was 0.034 V/ppm for the first peak and 27.72 V/ppm for the second peak, with slope linearity of more than 96% for surface tension parameter. The credibility of these optical response curves data might be useful, especially in the cosmetic’s industrial application.

Primordial monopoles and strings, inflation, and gravity waves

We consider magnetic monopoles and strings that appear in non-supersymmetric SO(10) and E6 grand unified models paying attention to gauge coupling unification and proton decay in a variety of symmetry breaking schemes. The dimensionless string tension parameter Gμ spans the range 10−6− 10−30, where G is Newton’s constant and μ is the string tension. We show how intermediate scale monopoles with mass ∼ 1013− 1014 GeV and flux ≲ 2.8 × 10−16 cm−2s−1sr−1, and cosmic strings with Gμ ∼ 10−11− 10−10 survive inflation and are present in the universe at an observable level. We estimate the gravity wave spectrum emitted from cosmic strings taking into account inflation driven by a Coleman-Weinberg potential. The tensor-to-scalar ratio r lies between 0.06 and 0.003 depending on the details of the inflationary scenario.

Construction and analysis of unified 4-point interpolating nonstationary subdivision surfaces

Subdivision schemes (SSs) have been the heart of computer-aided geometric design almost from its origin, and several unifications of SSs have been established. SSs are commonly used in computer graphics, and several ways were discovered to connect smooth curves/surfaces generated by SSs to applied geometry. To construct the link between nonstationary SSs and applied geometry, in this paper, we unify the interpolating nonstationary subdivision scheme (INSS) with a tension control parameter, which is considered as a generalization of 4-point binary nonstationary SSs. The proposed scheme produces a limit surface having $C^{1}$ C 1 smoothness. It generates circular images, spirals, or parts of conics, which are important requirements for practical applications in computer graphics and geometric modeling. We also establish the rules for arbitrary topology for extraordinary vertices (valence ≥3). The well-known subdivision Kobbelt scheme (Kobbelt in Comput. Graph. Forum 15(3):409–420, 1996) is a particular case. We can visualize the performance of the unified scheme by taking different values of the tension parameter. It provides an exact reproduction of parametric surfaces and is used in the processing of free-form surfaces in engineering.

A Nonstationary Ternary 4-Point Shape-Preserving Subdivision Scheme

This paper uses the continued fraction technique to construct a nonstationary 4-point ternary interpolatory subdivision scheme, which provides the user with a tension parameter that effectively handles cusps compared with a stationary 4-point ternary interpolatory subdivision scheme. Then, the continuous nonstationary 4-point ternary scheme is analyzed, and the limit curve is at least C 2 -continuous. Furthermore, the monotonicity preservation and convexity preservation are proved.

Numerical Simulation of the Instability of a Non-Isothermal Liquid Film in Film Devices

This work presents results of numerical simulation of the instability of vertical liquid film flow at moderate Reynolds numbers in the framework of partial differential equation of the state of the free surface of the liquid film. Equation coefficients include different physicochemical factors such as surface tension parameter and Marangoni parameter. Python scripts are used for computation of wave characteristics, instability regions of liquid films and liquid films free surface state. Computational experiments were carried out for the vertical water and alcohol films. Results could be used in the design or modernization of existing equipment and in the design of technological processes in liquid films.

A nonlinear generalized subdivision scheme of arbitrary degree with a tension parameter

In this paper, a nonlinear generalized subdivision scheme of arbitrary degree with a tension parameter is presented, which refines 2D point-normal pairs. The construction of the scheme is built upon the stationary linear generalized subdivision scheme of arbitrary degree with a tension parameter, by replacing the weighted binary arithmetic average in the linear scheme with the circle average. For such a nonlinear scheme, we investigate its smoothness and get that it can reach $C^{1}$ C 1 with suitable choices of the tension parameter when degree $m\geq 3$ m ≥ 3 . Besides, the nonlinear scheme can reconstruct the circle and the selection of parameters and initial normal vectors can effectively control the shape of the limit curves.

Quality factor of circular microdiaphragm with surface effects in contact with liquids

This paper reports an investigation of the influences of surface effects and residual stress on the quality factor of a circular microdiaphragm in contact with liquids on one side. Acoustic radiation, as the main source of energy dissipation, can decrease the quality factor of a circular microdiaphragm. An approximate solution for the natural frequency can be obtained based on the Rayleigh–Ritz energy method. The results show that the influence of surface effects on the quality factor is obvious, in particular for thinner microdiaphragms. A stiffened surface decreases the quality factor, while a softened surface increases it. Furthermore, the quality factor increases with increases in the normalized tension parameter k for both stiffened and softened surfaces. If k is greater than 30, the influence of the surface effects on the quality factor must be considered. The results can provide effective guidance for the determination of dimensions and selection of material parameters in designing microdiaphragm resonant sensors.

Smoothing and Interpolating Noisy GPS Data with Smoothing Splines

A comprehensive method is provided for smoothing noisy, irregularly sampled data with non-Gaussian noise using smoothing splines. We demonstrate how the spline order and tension parameter can be chosen a priori from physical reasoning. We also show how to allow for non-Gaussian noise and outliers that are typical in global positioning system (GPS) signals. We demonstrate the effectiveness of our methods on GPS trajectory data obtained from oceanographic floating instruments known as drifters.

Shape Preserving Properties with Constraints on the Tension Parameter of Binary Three-Point Approximating Subdivision Scheme

The paper analyzes conditions for preserving the shape properties from the initial data to the limit curves of the binary three-point approximating subdivision scheme. We provide suitable conditions on the initial data utilizing the tension parameter [Formula: see text], thus the scheme can maintain three important shape properties, namely positivity, monotonicity and convexity in the limit curves. The use of derived conditions is illustrated in few examples, which offers more flexibility in the generation of smooth limit curves endowed with shape preserving properties.