Non-Linear Periodic and Quasi-Periodic Vibrations in Mechanical Systems - On the use of the Harmonic Balance Methods

Available freely from: http://www.intechopen.com/books/advances-in-vibration-analysis-research/non-linear-periodic-and-quasi-periodic-vibrations-in-mechanical-systems-on-the-use-of-the-harmonic-bInternational audienceIn this chapter, the general formulation and extensions of the harmonic balance method will be presented. The chapter is divided into four parts. Firstly we propose to present the general formulation and the basic concept of the harmonic balance method to find periodic oscillations of non-linear systems. Secondly a generalization of the method is exposed to treat quasi-periodic solutions. Thirdly, a condensation procedure that keeps only the non-linear degrees of freedom of the mechanical system is described. This technique may be of great interest to reduce the original non-linear system and to calculate the dynamical behaviour of non-linear systems with many degrees of freedom. The last part presents the classical continuation procedures that let us follow the evolution of a solution as a system parameter varies

Quasi-classical alternatives in quantum chemistry

The article contains an overview of authors achievements in development of alternative quantum-chemical approaches oriented towards revival of the classical tradition of qualitative chemical thinking instead of obtaining numerical results. The above-mentioned tradition is concluded to be based mainly on principles (rules) of additivity, transferability and locality of molecular properties. Accordingly, model Hamiltonian matrices are used in the approaches under development (called quasi-classical alternatives), wherein algebraic parameters play the role of matrix elements and these are assumed to be transferable for similar atoms and/or atomic orbitals in addition. Further, passing to delocalized descriptions of electronic structures (as usual) is expected to be the main origin of difficulties seeking to formulate quasi-classical alternatives. In the framework of the canonical method of molecular orbitals (MOs), delocalization is shown to be partially avoidable by invoking a recently-suggested approach to secular (eigenvalue) equations for model Hamiltonian matrices, wherein the usual initial imposing of the zero-determinant condition is replaced by a certain reformulation of the problem itself. The most efficient way of achieving the same end, however, is shown to consist in passing to non-canonical one-electron problems. The latter may be exemplified by the block-diagonalization problem for the relevant Hamiltonian matrix following from the Brillouin theorem and yielding non-canonical (localized) MOs and by the commutation equation for the respective one-electron density matrix (charge- bond order matrix). In this connection, most of attention is paid in the article to perturbative solutions of the above-mentioned non-canonical problems and to their implications, including common quantum-chemical descriptions of entire classes of chemical compounds.Comment: 70 page

Geometry-Based Channel Models for Car-to-Car Communication Systems and Applications

In last two decades, intelligent transportation systems (ITS) have received considerable attention due to new road traffic safety applications that significantly improve the efficiency of traffic flow and reduce the number of road accidents. Consequently, there has been an increased interest in studying and developing car-to-car (C2C) communication systems, which play a key role in ITS. C2C communications has also gained the attention of standardization bodies, such as the IEEE1 and 3GPP LTE2, which aim to provide improvements in C2C communication systems. As it follows from the title, in this dissertation, we present the state-of-the-art regarding the modeling and analysis of different C2C channels in C2C communication systems. In C2C communication systems, the underlying radio channel differs from the conventional fixed-to-mobile (F2M) and fixed-to-fixed (F2F) channels in the way that both the mobile transmitter and the mobile receiver are in motion. In this regard, reliable and robust traffic telematic systems have to be designed, developed and tested. This leads to a demand for new radio channel models for C2C communication systems. Therefore, this dissertation is devoted to design, develop and validate new geometry-based channel models for C2C communication systems. In particular, two goals are aimed, which are study and investigation of the propagation characteristics of C2C fading channels and analyzing the performance of C2C communication systems over those fading channels correlated in time and space.publishedVersio

Perfectoid Diamonds and n-Awareness. A Meta-Model of Subjective Experience.

In this paper, we propose a mathematical model of subjective experience in terms of classes of hierarchical geometries of representations (“n-awareness”). We first outline a general framework by recalling concepts from higher category theory, homotopy theory, and the theory of (infinity,1)-topoi. We then state three conjectures that enrich this framework. We first propose that the (infinity,1)-category of a geometric structure known as perfectoid diamond is an (infinity,1)-topos. In order to construct a topology on the (infinity,1)-category of diamonds we then propose that topological localization, in the sense of Grothendieck-Rezk-Lurie (infinity,1)-topoi, extends to the (infinity,1)-category of diamonds. We provide a small-scale model using triangulated categories. Finally, our meta-model takes the form of Efimov K-theory of the (infinity,1)-category of perfectoid diamonds, which illustrates structural equivalences between the category of diamonds and subjective experience (i.e.its privacy, self-containedness, and self-reflexivity). Based on this, we investigate implications of the model. We posit a grammar (“n-declension”) for a novel language to express n-awareness, accompanied by a new temporal scheme (“n-time”). Our framework allows us to revisit old problems in the philosophy of time: how is change possible and what do we mean by simultaneity and coincidence? We also examine the notion of “self” within our framework. A new model of personal identity is introduced which resembles a categorical version of the “bundle theory”: selves are not substances in which properties inhere but (weakly) persistent moduli spaces in the K-theory of perfectoid diamonds

Characterisation of silicon photonics devices

Silicon based integrated circuits has been dominating the electronics technology industry in the last few decades. As the telecommunications and the computing industry slowly converges together, the need for a material to build photonics integrated circuits (PIC) that can be cost-effective and be produced in mass market has become very important. This thesis describes and outlines the characteristics of high index contrast waveguides as a building blocks that can be designed, fabricated and employed on devices in silicon photonics. Initially in this work, a fully vectorial H-field based finite element method has been used to obtain the modal characteristics of high index contrast bent waveguide to get a better understanding of the curved section. Through the beam propagation method, the propagation losses and the spot-size along the propagation distance are obtained when a mode from the straight guide is launched into a bent guide. It is also learnt that mode beating exists at the junction of a straight-to-bent waveguide, in which higher order modes will also be generated. It will be shown in this work that power do exchange between the two polarization states, therefore the polarization conversion, the power losses and the bending losses will be investigated. It will also shown in here that by applying lateral offsets with coupled waveguides of unequal widths, the insertion loss can be reduced. Secondly, for a high index contrast waveguide such as the silicon strip waveguide with a nanoscale cross-section, modes in such waveguide are not purely TE or TM but hybrid in nature, with all the six components of their E and H-fields being present. Therefore a detail analysis of the modal field profiles along with the Poynting vector profile will be shown. The effects of waveguide's width and height on the effective indices, the hybridness, the modal effective area and the power confinement in the core or cladding has been studied. Furthermore the modal birefringence of such strip waveguide will be shown. It will be presented that for a strip waveguide with height of 260 nm, single mode exists in the region of the width being 200 nm to 400 nm and that the modal effective is at its minimum when width is around 320 nm for both polarization states. Thirdly, a compact polarization rotator with an asymmetric waveguide structure design, suitable for fabrication that does not require a slanted side wall or curved waveguide is considered in this work. It will be shown in here that due to the hybrid nature of the asymmetric waveguide design, maximum polarization rotation (from TE to TM) will be achieve by enhancing the non-dominant field profile of both polarized fundamental mode. As the modal hybridness and the propagation constants of both polarized modes will be obtained, the half-beat length, polarization conversion and polarization cross-talk will be calculated by using the FEM and the least squares residual boundary method (LSBR). It is learnt that a compact single stage polarization rotator with a device length of 48 μm with more than 99% of polarization conversion is achieved in this work. Finally, a study of vertical and horizontal slot waveguide will be shown. Based on silicon strip waveguide, a detail modal characteristics of E and H-fields along with the Poynting vectors are presented. It will be shown that for slot waveguide, high power confinement and power density will be achieved in the slot area. It will be presented that by optimising the waveguide and slot dimension, the performance of the power confinement and power density in the slot region can be improved.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015

This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politècnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: ● Formulations and Numerical Methods ● Efficient Methods and Real-Time Applications ● Flexible Multibody Dynamics ● Contact Dynamics and Constraints ● Multiphysics and Coupled Problems ● Control and Optimization ● Software Development and Computer Technology ● Aerospace and Maritime Applications ● Biomechanics ● Railroad Vehicle Dynamics ● Road Vehicle Dynamics ● Robotics ● Benchmark ProblemsPostprint (published version