2D Ship-Like Section Slamming Pressure Numerical Analysis by Conformal Mapping

In this paper, a method to predict slamming pressures and pressure distribution at the time of water entry for 2D sections is presented. The mathematical model is based on the Schwarz-Christoffel conformal mapping method. This conformal mapping technique has been used to calculate slamming loads during water entry. The pile-up of water during motion is also considered and an alternative pile-up coefficient is assumed against Wagner’s generalized method. A simplified and accurate method is presented, which does not include non-linear terms and jet flow in the calculated pressure distribution on monotonically increasing 2D sections like wedge shapes. Comparison with real ship sections has been done to show accuracy of the results. Finally, a simple yet powerful method is obtained to aid the initial design stage of ships.

Dynamic performance for piezoelectric bi-materials with an interfacial crack near an eccentric elliptical hole under anti-plane shearing

The purpose of this paper is to evaluate the stress concentration at the tip of a permeable interfacial crack near an eccentric elliptical hole in piezoelectric bi-materials under anti-plane shearing. Fracture analysis is performed by Green’s function method and the conformal mapping method, which are used to solve the boundary conditions problem. The mechanical model of the interfacial crack is constructed by interface-conjunction and crack-deviation techniques so that the crack problem is simplified as solving a series of the first kind of Fredholm’s integral equations, from which the dynamic stress intensity factors (DSIFs) at the inner and the outer crack-tips can be derived. The validity of the present method is verified by comparing with a crack emerging from the edge of a circular hole as a reference. Numerical cases reveal parametric dependence of DSIFs on the geometry of eccentric elliptical holes and interfacial cracks, the characteristics of the incident wave, the equivalent piezoelectric elastic modulus and piezoelectric parameters. The results illustrate that the eccentric distance has a great effect on the stress concentration at the crack tip, which may be harmful to the normal service of piezoelectric devices and materials. In addition, the method proposed in this paper can also deal with non-eccentric problems and has wider applicability.

PULSE SIGNAL LOSS ESTIMATION TECHNIQUE IN SWITCHING EQUIPMENT AUTHENTICATION SUBSYSTEM

Для аутентификации коммутаторов второго уровня можно использовать код аутентификации, переданный отправителем информации получателю с помощью модуля аутентификации, встроенного в коммутатор. Для формирования кода аутентификации используется оптический импульс, энергия которого равна энергии фотона. При передаче оптического импульса актуальной является оценка потерь энергии в оптических устройствах модуля аутентификации. Разработана методика оценки потерь оптического импульса на изгибах интегрально-оптических волноводов. Новая методика получена в результате модификации расчета потерь оптической энергии на изгибах волноводов для непрерывного лазерного излучения. Используется классическое моделирование распространения оптического импульса гауссовой формы, при этом для замены изогнутого волновода эквивалентным прямолинейным волноводом применяется метод конформного отображения. С помощью метода конформного отображения изменен профиль показателя преломления прямолинейного волновода и преобразовано волновое уравнение для электрического поля. В результате применения новой методики выведена формула для расчета отношения энергетической мощности оптического импульса к мощности постоянного оптического сигнала. На основе графика полученной зависимости сделан вывод, что для импульсов длительностью 10 фс потери оптического импульса сильно отличаются от потерь непрерывного лазерного излучения, для импульсов длительностью 100 фс это отличие несущественно. Таким образом, для коротких импульсов при расчете потерь оптического сигнала в устройствах подсистем аутентификации необходимо использовать методику решения волнового уравнения с процедурой конформного отображения To authenticate L2 switches, you can use the authentication code transmitted by the sender of information to the recipient using the authentication module built into the switch. To generate the authentication code, an optical pulse is used, the energy of which is equal to the photon energy. When transmitting an optical pulse, it is important to estimate the energy losses in the optical devices of the authentication module. A technique was developed for assessing the loss of an optical pulse at bends in integrated optical waveguides. The new technique was obtained as a result of a modification of the calculation of optical energy losses at bends of waveguides for continuous laser radiation. The classical simulation of the propagation of a Gaussian optical pulse was used, while the conformal mapping method was used to replace a curved waveguide with an equivalent rectilinear waveguide. Using the conformal mapping method, the profile of the refractive index of a rectilinear waveguide was changed and the wave equation for the electric field was transformed. As a result of applying the new technique, a formula was derived for calculating the ratio of the energy power of an optical pulse to the power of a constant optical signal. On the basis of the plot of the obtained dependence, it was concluded that for pulses with a duration of 10 fs, the loss of an optical pulse differs greatly from the loss of continuous laser radiation; for pulses with a duration of 100 fs, this difference is insignificant. Thus, for short pulses, when calculating the loss of an optical signal in devices of authentication subsystems, it is necessary to use the method for solving the wave equation with the conformal mapping procedure

THE OPTIMIZATION OF THE SHAPE AND SIZE OF THE INJECTION CONTACTS OF THE INTEGRATED P-I-N-STRUCTURES ON THE BASE OF USING THE CONFORMAL MAPPING METHOD

Context. P-i-n-diodes are widely used in a microwave technology to control the electromagnetic field. The field is controlled by the formation of an electron-hole plasma in the region of an intrinsic semiconductor (i-region) under the influence of a control current. The development of control devices on p-i-n-diodes has led to the emergence of integral p-i-n-structures of various types, the characteristics of which (for example, switching speed, switched power level, etc.) exceed the similar characteristics of volume diodes. The properties of p-i-n-structures are determined by a number of processes: the diffusion-drift charge transfer process, the recombination-generation, thermal, injection, and the so on. Obviously, these processes should be taken into account (are displayed) in the mathematical model of the computer-aided design system for control devices of a microwave systems. Integrated process accounting leads to the formulation of complex tasks. One of them is the task of optimizing the shape, geometric dimensions and placement of the injected contacts (an active region). Objective. The goal of the work is the development of a mathematical model and the corresponding software of the process of a microwave waves interaction with electron-hole plasma in an active region of the surface-oriented integral p-i-n-structures with ribbon-type freeform contacts to optimize an active region shape and its geometric dimensions. Method. The main idea of the developed algorithm is to use the conformal mapping method to bring the physical domain of the problem to canonical form, followed by solving internal boundary value problems in this area for the ambipolar diffusion equation and the wave equation using numerical-analytical methods (the finite difference method; partial domains method using projection boundary conditions similar to the Galerkin method). The optimization algorithm is based on a phased solution of the following problems (the shape and geometric dimensions of the active region are specified at each stage): a computational grid of nodes for the physical regions of the problem is being found, in an active region the carriers concentration distribution is being determined and the energy transmitted coefficient in the system under study is being calculated, which is used in the proposed optimization functional. The extreme values of the functional are found by the uniform search method. Results. The proposed mathematical model and the corresponding algorithm for optimizing the shape and geometric dimensions of the active region (i-region) of integrated surface-oriented p-i-n-structures expands the tool base for the design of semiconductor circuits of microwave frequencies (for example, similar to CST MICROWAVE STUDIO). Conclusions. An algorithm has been developed to optimize the shape and geometrical dimensions of the active region of integrated surface-oriented p-i-n-structures with in-depth contacts intended for switching millimeter-wave electromagnetic signals. The universality of the algorithm is ensured by applying the method of conformal transformations of spatial domains. The example of the application of the proposed algorithm to search for the optimal sizes of wedge-shaped (in cross-section) contacts of silicon structures is considered.

Application of the Schwarz-Christoffel Transformation to the Solution of Harmonic Dirichlet Problems in Electrostatics

In this paper, a purely conformal mapping method for efficiently solving harmonic Dirichlet problems of electrostatic in domains free of charge and with charge whose boundaries have inconvenient geometries consisting of straight-line segments is presented. The method which uses the inverse of an appropriately determined Schwarz-Christoffel transformation as the mapping function, was applied to harmonic Dirichlet problems in an infinite strip and infinite sector and the solution or electrostatic potential for the problem obtained for each case. Furthermore, the equipotential lines of the electric field were also obtained in order to show the features of the solution and the field analysed accordingly. The electric field intensity was also analysed to show its variation in the field. This method could therefore be a suitable alternative method for solving Laplace's equation in two dimensional electrostatic problems.

Thermal Wave Scattering and Temperature Concentration around the Opening in Platinum–Rhodium Leaky Plates

Based on the non-Fourier heat conduction wave model, the thermal wave scattering near the opening in the platinum–rhodium glass fiber leaky plate structure is studied by using complex function method and conformal mapping method, and the general solution of the thermal wave scattering problem is given. The boundary condition of the open surface is adiabatic. The influence of the geometrical and physical parameters of the leaky plate on the temperature distribution in the plate is analyzed, and the numerical results of the temperature concentration are given. This study can provide theoretical basis and reference data for the design and optimization of the opening structure of platinum–rhodium glass fiber leaky plate.