High frequency homogenisation for elastic lattices

A complete methodology, based on a two-scale asymptotic approach, that enables the homogenisation of elastic lattices at non-zero frequencies is developed. Elastic lattices are distinguished from scalar lattices in that two or more types of coupled waves exist, even at low frequencies. Such a theory enables the determination of effective material properties at both low and high frequencies. The theoretical framework is developed for the propagation of waves through lattices of arbitrary geometry and dimension. The asymptotic approach provides a method through which the dispersive properties of lattices at frequencies near standing waves can be described; the theory accurately describes both the dispersion curves and the response of the lattice near the edges of the Brillouin zone. The leading order solution is expressed as a product between the standing wave solution and long-scale envelope functions that are eigensolutions of the homogenised partial differential equation. The general theory is supplemented by a pair of illustrative examples for two archetypal classes of two-dimensional elastic lattices. The efficiency of the asymptotic approach in accurately describing several interesting phenomena is demonstrated, including dynamic anisotropy and Dirac cones.Comment: 24 pages, 7 figure

Modified discrete Fourier transform algorithm for protection of shunt compensated distribution line

Introduction. The response time of the relay plays vital role when fault occurs on the line. Various algorithms are adopted to increase the sampling rate of the relay which, in turn, improves the response time. Methods. Discrete Fourier transform and modified discrete Fourier transform are the two algorithms used to calculate the fundamental frequency phasor of the signal required by the relay to initiate trip command. It is known that discrete Fourier transform takes four to five cycles to produce the fundamental frequency phasor but it fails to deal with the decaying DC component. On the other hand, modified discrete Fourier transform improves the response time by removing the decaying DC component along with the other harmonics in just one cycle and a few samples. The aim of this paper is to cover discrete Fourier transform and modified discrete Fourier transform algorithms to analyze the performance of the three overcurrent and one earth fault relaying scheme for different types of faults occurring in the distribution system. Methodology. The concept of three overcurrent and one earth fault scheme is also explained in this paper for protection of shunt-compensated distribution system. The scheme is designed for variable power factor. MATLAB/Simulink is used as the software tool to validate the results obtained for various types of faults occurring in the system. The results are represented graphically to illustrate the time of response of the protection scheme when shunt compensators are connected at the receiving end of distribution network.Вступ. Час спрацювання реле відіграє життєво важливу роль при виникненні несправності на лінії. Для збільшення частоти дискретизації реле застосовуються різні алгоритми, що, своєю чергою, покращує час спрацювання. Методи. Дискретне перетворення Фур’є та модифіковане дискретне перетворення Фур’є – це два алгоритми, які використовуються для розрахунку вектора основної частоти сигналу, необхідного для реле подачі команди на відключення. Відомо, що для отримання вектора основної частоти дискретного перетворення Фур’є потрібно від чотирьох до п'яти циклів, але воно не справляється з постійною складовою струму, що згасає. З іншого боку, модифіковане дискретне перетворення Фур’є покращує час спрацювання, видаляючи постійну складову струму, що згасає, разом з іншими гармоніками всього за один цикл і кілька вибірок. Мета цієї статті полягає в тому, щоб охопити алгоритми дискретного перетворення Фур’є та модифікованого дискретного перетворення Фур’є для аналізу характеристик трьох схем реле максимального струму та однієї схеми захисту від замикань на землю для різних типів несправностей, що виникають у розподільчій системі. Методологія. У статті  пояснюється також концепція трьох схем перевантаження по струму і однієї схеми замикання на землю для захисту розподільчої системи з паралельною компенсацією. Схема розрахована на змінний коефіцієнт потужності. MATLAB/Simulink використовується як програмний інструмент для перевірки результатів, отриманих для різних типів відмов, що виникають у системі. Результати представлені графічно, щоб проілюструвати час спрацьовування схеми захисту, коли шунтуючі компенсатори підключені на приймальному кінці розподільної мережі

A case report: a very rarely occurring snakebite

Snake bite is one of the most neglected public health issues in poor rural communities living in the tropics. The venomous bites and stings during pregnancy are very rare and it cause significant adverse effects on fetus and mother. Multiple snake bites to two different individuals by a same snake at the same time are rarely reported in literatures. In present case report, husband and wife with two and half month of pregnancy were bitten with multiple bites by same snake at the same time. This unusual and interesting case occurred in a rural area of Ahmedabad, Gujarat. It is also believed that snake discharges maximum of venom on first bite, which may be fatal compared to subsequent bites. The uniqueness of this case lies in the fact that second bite was more serious than the first bite. Woman with two and half month of pregnancy who was bitten first and hade minor effect, and no negative effects on fetus. Man bitten latter with multiple bites and was affected seriously. Both the patients were successfully treated at our hospital.

Field Pattern computation using 2 - D FFT for Microstrip Reflectarray Antenna

A Microstrip Reflectarray antenna as a planar array antenna is examined in this study effort. The basic original design requires that the phase of the field reflected from a Microstrip Reflectarray element be set so that the overall phase delay from the feed to a fixed aperture plane in front of the Reflectarray is constant for all elements. The array factor and element pattern product are displayed in the overall electric field pattern expression. The arrangement of Microstrip Reflectarray antenna and feed has been placed in prime focal axis. Amplitude tapering is used to improve the main beam's field strength by lowering the side lobe levels. The comparative numerical analysis of computing field pattern normally as well as using 2-D FFT of n x n elements of the Microstrip reflectarray antenna is carried out using MATLAB codes. It is shown that MATLAB simulation time with FFT is much shorter than simulation time without FFT