Cross Product and Partitioned Filtering-Based Graham Convex Hull for Buoy Drifting Area Demarcating

An improved Graham scan convex hull algorithm is designed using the convex hull region shrinkage algorithm and the sample selection decision algorithm. In the sorting of Graham scan convex hull algorithm, the cross-multiplication method is used instead of the operation of finding the polar angle, which avoids the high computational complexity of finding the inverse trigonometric function. When the polar angles are the same, that is, the two points are collinear, the points close to each other are deleted directly. Select the maximal horizontal ordinate point, minimal horizontal ordinate point, maximal longitudinal coordinate point, and minimal longitudinal coordinate point. Connect these points and obtain lines. The whole plane is divided into different regions. The points that are not on the convex hull are deleted, and the redundant points are removed. This can speed up the calculation of approximate convex hull boundary and shorten the time of convex hull calculation. The proposed algorithm is used for buoy drifting area demarcating. The offsets of the geometric center of the high-frequency position point and the distance from geometric center of high-frequency position of buoy to sinking stone are calculated. The experimental results show that the new algorithm can effectively accelerate the convex hull calculation. We use the convex hull process to compute the area of the drifting buoy position and discover that the drift area of the port hand buoy is similar. The drift area of the port hand buoys is similar. The drift area of the port hand buoy is greater than that of the port hand buoy.

Interaction of Viscoelastic Tube with Inner Nonuniform Coating of Variable Thickness and Rigid Cylindrical Insert

This work is devoted to the formulation and search of an analytical solution for the problem of the interaction of a rigid cylindrical body and a pipe with an inner coating in the case when the cylinder is placed inside such a pipe. It is assumed that the pipe coating can have a strong nonuniformity, and its thickness depends on the longitudinal coordinate. A special approach used in this work allows obtaining analytical solutions in which functions related to the properties and profile of the coating are separated by separate terms and factors. This allows us to provide efficient calculations even in cases where coating characteristics are described by complex functions. Other known methods lead to significant calculation errors.

Longitudinal distribution of the field intensity of a circular focused aperture

Microwave and millimeter-wave antennas focused in their Fresnel zone, which are usually named as near-field focused (NFF) antennas, are becoming increasingly popular. Indeed, when compared to conventional far-field focused antennas, they can guarantee performance improvement at a relatively limited implementation cost, in short-range communication systems, wireless power transfer arrangements, remote nondestructive sensing setups, and radiofrequency identification apparatus, among many others. In this paper, analytical expressions are obtained for calculating the main parameters characterizing the longitudinal distribution of the circular focused aperture field intensity with a relatively large diameter (2R/λ≥10) : the displacement of the intensity maximum relative to the focal point, focusing gain and depth of focus. Cases of uniform and decreasing amplitude distributions of the excitation field are considered. The found approximate relations make it possible to determine the values of the above parameters for any values of the longitudinal coordinate of the focal point, lying both in the Fresnel zone and in the far zone. Comparison with numerical calculations showed that the error in the obtained parameter values does not exceed 5%. The results of this paper will be useful when calculating the field of antennas in the form of a circular focused aperture, as well as focused antenna arrays operating in the Fresnel zone.

Simulation of non-isothermal free turbulent gas jets in the process of energy exchange

This article proposes a numerical method for solving the propagation and combustion of a jet of a gas mixture in an axisymmetric satellite air stream. To model the process, the dimensionless equations of the turbulent boundary layer of reacting gases in the Mises coordinates are used. A two-layer four-point nonlinear boundary separation scheme was used to solve the problem in the Mises coordinates, and a second-order along the longitudinal coordinate was given. The iterative process was used because of the nonlinearity of the storage and displacement equations of substations. Individual results of the numerical experiment are presented.

On modeling bodies with delaminating coatings taking into account the fields of prestresses

The paper presents a model of steady-state oscillations of an inhomogeneous body with a prestressed exfoliating coating based on a general linearized statement of the problem of the motion of a prestressed-strained elastic body. On its basis, the statement of the problem of oscillations of an inhomogeneous strip consisting of a substrate and a prestressed coating is formulated, between which there is a delamination in a certain region. Steady oscillations are caused by a load applied to the upper boundary of the coating. To calculate the oscillations of the two-dimensional structure under consideration, the Fourier transform in the longitudinal coordinate was used and the original problem was reduced to solving a number of auxiliary boundary value problems with respect to transformants of the desired functions. From the conditions that the stress functions vanish (the cover is modeled as a mathematical section) of the substrate and the coating, the operator relations are constructed in the area of delamination to calculate the opening functions. The kernels of these operator relations are singular and are integrals over an infinite interval. A study was made of the behavior of their integrands at infinity, on the basis of which special approaches were used to calculate the kernels. As a result of solving the obtained hypersingular equations with difference kernels, for which the collocation method is used, the originals of the disclosure functions are constructed. Using a similar approach for inverting the Fourier transformations, we constructed relations to calculate the originals of the displacement functions at the upper boundary of the coverage. Based on the computational experiments, an analysis is made of the influence of the initial geometric and mechanical parameters of the substrate and coating on the values of the disclosure functions in the delamination region and the displacement functions at the upper boundary of the layer. The influence of the prestress level on the amplitude-frequency characteristics (AFC) was also investigated. It was found that the most significant effect on the frequency response is in the vicinity of the frequencies of the thick resonances. Based on the information on the displacement fields, it is possible to construct schemes for identifying delamination characteristics.

Fractal Generalization of the Scher–Montroll Model for Anomalous Transit-Time Dispersion in Disordered Solids

The Scher–Montroll model successfully describes subdiffusive photocurrents in homogeneously disordered semiconductors. The present paper generalizes this model to the case of fractal spatial disorder (self-similar random distribution of localized states) under the conditions of the time-of-flight experiment. Within the fractal model, we calculate charge carrier densities and transient current for different cases, solving the corresponding fractional-order equations of dispersive transport. Photocurrent response after injection of non-equilibrium carriers by the short laser pulse is expressed via fractional stable distributions. For the simplest case of one-sided instantaneous jumps (tunneling) between neighboring localized states, the dispersive transport equation contains fractional Riemann–Liouville derivatives on time and longitudinal coordinate. We discuss the role of back-scattering, spatial correlations induced by quenching of disorder, and spatiotemporal non-locality produced by the fractal trap distribution and the finite velocity of motion between localized states. We derive expressions for the photocurrent and transit time that allow us to determine the fractal dimension of the distribution of traps and the dispersion parameter from the time-of-flight measurements.

Group Analysis of the Boundary Layer Equations in the Models of Polymer Solutions

The famous Toms effect (1948) consists of a substantial increase of the critical Reynolds number when a small amount of soluble polymer is introduced into water. The most noticeable influence of polymer additives is manifested in the boundary layer near solid surfaces. The task includes the ratio of two characteristic length scales, one of which is the Prandtl scale, and the other is defined as the square root of the normalized coefficient of relaxation viscosity (Frolovskaya and Pukhnachev, 2018) and does not depend on the characteristics of the motion. In the limit case, when the ratio of these two scales tends to zero, the equations of the boundary layer are exactly integrated. One of the goals of the present paper is group analysis of the boundary layer equations in two mathematical models of the flow of aqueous polymer solutions: the second grade fluid (Rivlin and Ericksen, 1955) and the Pavlovskii model (1971). The equations of the plane non-stationary boundary layer in the Pavlovskii model are studied in more details. The equations contain an arbitrary function depending on the longitudinal coordinate and time. This function sets the pressure gradient of the external flow. The problem of group classification with respect to this function is analyzed. All functions for which there is an extension of the kernels of admitted Lie groups are found. Among the invariant solutions of the new model of the boundary layer, a special place is taken by the solution of the stationary problem of flow around a rectilinear plate.

Experimental and Numerical Investigation of the Thermal Transition Area at the Heated Bottom-Wall of a Horizontal Rectangular Channel

This article represents a part of an ongoing work on the preparation of an experimental rectangular channel for the PIV and LIF measurements of vortex structures and temperature field in a non-isothermal water flow. The main aim of the current study is to develop a sufficiently accurate simplified numerical model of the real problem. The basic requirements for thermal properties of heated bottom-wall are specified. In the computational model, there are several simplifications such as 2D case and a constant temperature of a heated surface along the longitudinal coordinate. Results of the numerical simulation of the fluid flow and heat transfer are verified on the experimental data obtained in a laboratory channel with the same geometry and similar flow conditions. The presented results helped to define additional requirements on the design of a new experimental channel intended for investigation of the flow instabilities in a non-isothermal liquid flow.

Dynamic Bending of an Infinite Electromagnetoelastic Rod

The problem of non-stationary bending of an infinite electromagnetoelastic rod is considered. It is assumed that the material of the rod is a homogeneous isotropic conductor. The closed-form system of process equations is constructed under the assumption that the desired functions depend only on the longitudinal coordinate and time using the corresponding relations for shells which take into account the initial electromagnetic field, the Lorentz force, Maxwell’s equations, and the generalized Ohm’s law. The desired functions are assumed to be bounded, and the initial conditions are assumed to be null. The solution of the problem is constructed in an integral form with kernels in the form of influence functions. Images of kernel are found in the space of Laplace transformations in time and Fourier transformations in spatial coordinates. It is noted that the images are rational functions of the Laplace transform parameter, which makes it quite easy to find the originals. However, for a general model that takes into account shear deformations, the subsequent inversion of the Fourier transform can be carried out only numerically, which leads to computational problems associated with the presence of rapidly oscillating integrals. Therefore, the transition to simplified equations corresponding to the Bernoulli – Euler rod and the quasistationary electromagnetic field is carried out. The method of a small parameter is used for which a coefficient is selected that relates the mechanical and electromagnetic fields. In the linear approximation, influence functions are found for which images and originals are constructed. In this case, the zeroth approximation corresponds to a purely elastic solution. Originals are found explicitly using transform properties and tables. Examples of calculations are given for an aluminum rod with a square cross section. It is shown that for the selected material the quantitative difference from the elastic solution is insignificant. At the same time, taking into account the connectedness of the process leads to additional significant qualitative effects.