Representing three-dimensional cross fields using 4th order tensors

This paper presents a new way of describing cross fields based on fourth order tensors. We prove that the new formulation is forming a linear space in $\mathbb{R}^9$. The algebraic structure of the tensors and their projections on \mbox{SO}(3) are presented. The relationship of the new formulation with spherical harmonics is exposed. This paper is quite theoretical. Due to pages limitation, few practical aspects related to the computations of cross fields are exposed. Nevetheless, a global smoothing algorithm is briefly presented and computation of cross fields are finally depicted

Airline hub strategies: a tale of two airport

A lot of airlines in the world fly from more than just one airport in a single city. Examples to such airlines may be British Airways (BA), operating from London Heathrow (LHR), London Gatwick (LGW) and London City (LCY) airports; Delta Airlines (DL), operating from John F. Kennedy (JFK), Newark (EWR) and La Guardia (LGA) in New York; Turkish Airlines (THY), operating from Istanbul Ataturk Airport (IST) and Sabiha Gokcen Airport (SAW); Air France (AF), operating from Charles de Gaulle (CDG) and Orly (ORY) airports and Japan Airlines (JAL), operating from Haneda (HND) and Narita (NRT).Dünya’da birçok havayolu şirketi aynı şehirde birden fazla havalimanından operasyon gerçekleştirmektedir. Bu şirketlere örnek olarak Londra’daki London Heathrow (LHR), Gatwick (LGW) ve London City (LCY) havalimanlarından operasyon yapan British Airways (BA); New York’daki John F. Kennedy (JFK), Newark (EWR) ve La Guardia (LGA) havalimanlarından operasyon yapan Delta Havayolları (DL); Istanbul’daki Ataturk (IST) ve Sabiha Gokcen (SAW) havalimanlarından operasyon yapan Türk Hava Yolları (THY); Paris’deki Charles de Gaulle (CDG) ve Orly (ORY) havalimanlarından operasyon yapan Air France; ve Tokyo Haneda (HND) ve Narita (NRT) havalimanlarından operasyon yapan Japan Airlines (JAL) verilebilir

Samuel Fuller

Abstract not availabl

Implementation of discrete PID controller using Atmel AVR 8-bit microcontroller

Бесконтактные двигатели постоянного тока (БДПТ) широко распространены в различныхприложениях, где важны широкий диапазон изменения угловой скорости, отсутствие узлов, которые требуются частое обслуживание, высокая долговечность и надежность. Управление данными двигателями и регулирование их скоростей вращения являются важнейшей научной и инженерной задачей, Космические аппараты и приборы18 решения которой можно достичь при помощи микроконтроллера. На практике оказывается, что при проектировании различных устройств автоматики неоднократно сталкивается задача обеспечения заданной угловой скорости вала двигателя, которая не зависит от действующей нагрузки. В работе представлены теоретический подход и результаты применения дискретного ПИД - регулятора для регулирования угловой скорости бесконтактного двигателя постоянного тока с применением 8-разрядными микроконтроллерами Atmel AVR. На основе полученных данных построены графическиезависимости.Brushless direct current (BLDC) motors are widely distributed in a variety of applications where a wide range of changes in angular velocity is important, the absence of nodes that requires frequent maintenance, is high durability and reliability. BLDC motor control and regulation of their speeds are essential scientific and engineering tasks which can be accomplished by using a microcontroller. In practice the fact is that the task of providing a predetermined angular velocity of the motor shafts, which is independent of the actual load, repeatedly meets in the design of various control devices. The article presents the theoretical approach and the results of application of discrete PID - controller for regulation the rotation speed of brushless direct current motor using Atmel AVR 8-bit microcontroller. Characteristic curves are built on basic of the received data

Design sensitivity analysis for shape optimization based on the Lie derivative

peer reviewedAbstract The paper presents a theoretical framework for the shape sensitivity analysis of systems governed by partial differential equations. The proposed approach, based on geometrical concepts borrowed from differential geometry, shows that sensitivity of a performance function (i.e. any function of the solution of the problem) with respect to a given design variable can be represented mathematically as a Lie derivative, i.e. the derivative of that performance function along a flow representing the continuous shape modification of the geometrical model induced by the variation of the considered design variable. Theoretical formulae to express sensitivity analytically are demonstrated in detail in the paper, and applied to a nonlinear magnetostatic and a linear elastic problem, following both the direct and the adjoint approaches. Following the analytical approach, one linear system of which only the right-hand side needs be evaluated (the system matrix being known already) has to be solved for each of the design variables in the direct approach, or for each performance functions in the adjoint approach. A substantial gain in computation time is obtained this way compared to a finite difference evaluation of sensitivity, which requires solving a second nonlinear system for each design variable. This is the main motivation of the analytical approach. There is some freedom in the definition of the auxiliary flow that represents the shape modification. We present a method that makes benefit of this freedom to express sensitivity locally as a volume integral over a single layer of finite elements connected to both sides of the surfaces undergoing shape modification. All sensitivity calculations are checked with a finite difference in order to validate the analytic approach. Convergence is analyzed in 2D and 3D, with first and second order finite elements