Construction of an Effective Preconditioner for the Even-odd Splitting of Cubic Spline Wavelets

In this study, the method for decomposing splines of degree m and smoothness C^m-1 into a series of wavelets with zero moments is investigated. The system of linear algebraic equations connecting the coefficients of the spline expansion on the initial scale with the spline coefficients and wavelet coefficients on the embedded scale is obtained. The originality consists in the application of some preconditioner that reduces the system to a simpler band system of equations. Examples of applying the method to the cases of first-degree spline wavelets with two first zero moments and cubic spline wavelets with six first zero moments are presented. For the cubic case after splitting the system into even and odd rows, the resulting matrix acquires a seven-diagonals form with strict diagonal dominance, which makes it possible to apply an effective sweep method to its solution

On Characterization of Optimal Control Model of Whooping Cough

Whooping cough is a vaccine avoidable public health problem which is caused by bacterium Bordetella Pertussis and it is a highly contagious disease of the respiratory system. In this paper, an SIR epidemiological model of whooping cough with optimal control strategy was formulated to control the transmission. The model was characterized to obtain the disease free and the endemic equilibrium points. Finally, the simulation was carried out using the Forward-backward sweep method by incorporating the Runge Kutta method to check the validity and the result obtained was an improvement over the existing results.

Method of lines for solving linear equations of mathematical physics with the third and first types boundary conditions

The use of the method of lines in solving multidimensional problems of mathematical physics makes it possible to eliminate the discrepancies caused by the use of the sweep method in certain coordinates. As a result, the solution of the Poisson equation, for example, is obtained without using the relaxation method. In the article, the problem on the eigenvalues and vectors of the transition matrix is solved for boundary conditions of the third and first types, used to solve a one-dimensional equation of parabolic type by the method of lines. Due to the features of boundary conditions of the third type for determining the eigenvalues, a mixed method was proposed based on the Vieta theorem and the representation of the characteristic equation in trigonometric form typical for the method of lines. To solve the eigenvector problem, a simple sweep method was used with the algebraic compliments to the transition matrix. Discontinuous solutions of a one-dimensional parabolic equation were presented for various values of complex 1 -αl; the method for solving the characteristic equation was selected based on these values. The calculation results are in good agreement with the analytical solution.

Optimal Control of an HIV Model with Gene Therapy and Latency Reversing Agents

In this paper, we study the dynamics of HIV under gene therapy and latency reversing agents. While previous works modeled either the use of gene therapy or latency reversing agents, we consider the effects of a combination treatment strategy. For constant treatment controls, we establish global stability of the disease-free equilibrium and endemic equilibrium based on the value of R0. We then consider time-dependent controls and formulate an associated optimal control problem that emphasizes reduction of the latent reservoir. Characterizations for the optimal control profiles are found using Pontryagin’s Maximum Principle. We perform numerical simulations of the optimal control model using the fourth-order Runge–Kutta forward-backward sweep method. We find that a combination treatment of gene therapy with latency reversing agents provides better remission times than gene therapy alone. We conclude with a discussion of our findings and future work.

Characteristics of HEMP Radiation Field on Typical Transport Aircraft with Frequency Sweep Method

This paper presents characteristics of the HEMP radiation field on a typical transport aircraft using the frequency sweep method. Firstly, the characteristics of the HEMP field are analyzed. Then, various parameters including the electric field strength and magnetic field strength distribution are calculated using Altair FEKO software. Afterwards, the electric field strength distributions of three layers (top layer, inner layer and bottom layer) are calculated and analyzed. The results indicate that the HEMP induced field is affected by the aircraft body. The induced electric field strength E(t) varies greatly at different positions. Nevertheless, the peak value of E(t) is usually greater than the initial peak value of electric field strength E0. Such a study can provide guidance and insight into the protection design of the HEMP of the aircraft.

Novel Focal Sweep Strategy for Optical Aerothermal Measurements of Film-Cooled Gas Turbine Blades With Highly Inclined Viewing Angle

The viewing angle for optical aerothermal measurements on turbine surfaces is often limited by the turbine structure, requiring the optical system to have a large depth of field (DoF). Although the DoF can be increased by decreasing the lens aperture, this approach is impractical as a large aperture is essential to maintain an acceptable signal-to-noise ratio (SNR). To solve these problems in the optical aerothermal measurements of film-cooled gas turbine blades, an approach combining the focal-sweep method and three-dimensional (3D) reconstruction is proposed. The focal-sweep method is used to obtain all-in-focus images at an inclined viewing angle, following which the two-dimensional image is restored through 3D reconstruction. Thus, 3D point clouds with both a large DoF and high SNR can be produced. The developed method was validated via flat-plate film cooling experiments using pressure-sensitive paint at three blowing ratios of 0.4, 0.8, and 1.2, as well as three viewing angles. The measured adiabatic effectiveness contours demonstrate that the proposed method can produce all-in-focus measurements at highly inclined viewing angles, albeit at the price of slightly higher noise. In flat-plate experiments, the maximum relative difference is measured to be 6% between results obtained by conventional method at normal view and the proposed method at highly inclined view. Furthermore, the proposed method was applied to the turbine blade cascade film cooling experiment at a highly inclined viewing angle, and successfully reconstructed the 3D point cloud of the cooling effectiveness at the curved turbine blade surface.

Characterization of Modal Frequencies and Orientation of Axisymmetric Resonators in Coriolis Vibratory Gyroscopes

This paper presents the characterization of the modal frequencies and the modal orientation of the axisymmetric resonators in Coriolis vibratory gyroscopes based on the approaches of the frequency sweep and the ring down. The modal frequencies and the orientation of the stiffness axis are the key parameters for the mechanical correction of the stiffness imperfections. The frequency sweep method utilizes the zero and the poles in the magnitude-frequency responses of the two-dimensional transfer function to extract the modal orientation information within the frequency domain. The ring down method makes use of the peak and the valley values of the beat signals at the readout electrodes to obtain the modal orientation and the coefficient of the nonlinear stiffness directly within the time domain. The proposed approaches were verified via a silicon ring resonator designed for gyroscopic sensing and the modal information from the experiments exhibited a good agreement between the methods of the frequency sweep and the ring down.