Asymptotic solutions to a class of nonlinear oscillation systems

In this paper, we present an asymptotic method for the analysis of a class of strongly nonlinear oscillators, derive second-order approximate solutions to them expressed in terms of their amplitudes and phases, and obtain the equations governing the amplitudes and phases, by which the amplitudes of the corresponding limit cycles and their behaviour can be determined. As an example, we investigate the modified van der Pol oscillator and give the second-order approximate analytical solution of its limit cycle. The comparison with the numerical solutions shows that the two results agree well with each other.

Lock-in and quasiperiodicity in a forced hydrodynamically self-excited jet

The ability of hydrodynamically self-excited jets to lock into strong external forcing is well known. Their dynamics before lock-in and the specific bifurcations through which they lock in, however, are less well known. In this experimental study, we acoustically force a low-density jet around its natural global frequency. We examine its response leading up to lock-in and compare this to that of a forced van der Pol oscillator. We find that, when forced at increasing amplitudes, the jet undergoes a sequence of two nonlinear transitions: (i) from periodicity to T{double-struck}2 quasiperiodicity via a torus-birth bifurcation; and then (ii) from T{double-struck}2 quasiperiodicity to 1:1 lock-in via either a saddle-node bifurcation with frequency pulling, if the forcing and natural frequencies are close together, or a torus-death bifurcation without frequency pulling, but with a gradual suppression of the natural mode, if the two frequencies are far apart. We also find that the jet locks in most readily when forced close to its natural frequency, but that the details contain two asymmetries: the jet (i) locks in more readily and (ii) oscillates more strongly when it is forced below its natural frequency than when it is forced above it. Except for the second asymmetry, all of these transitions, bifurcations and dynamics are accurately reproduced by the forced van der Pol oscillator. This shows that this complex (infinite-dimensional) forced self-excited jet can be modelled reasonably well as a simple (three-dimensional) forced self-excited oscillator. This result adds to the growing evidence that open self-excited flows behave essentially like low-dimensional nonlinear dynamical systems. It also strengthens the universality of such flows, raising the possibility that more of them, including some industrially relevant flames, can be similarly modelled. © 2013 Cambridge University Press.

Aceleração de Fermi em bilhares com fronteiras dependentes do tempo descritas por osciladores não lineares: caso conservativo e dissipativo

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Um estudo da dinâmica fracamente não-linear de um sistema nanomecânico

Pós-graduação em Matemática - IBILCE

A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators

Future sensor arrays will be composed of interacting nonlinear components with complex behaviours with no known analytic solutions. This paper provides a preliminary insight into the expected behaviour through numerical and analytical analysis. Specically, the complex behaviour of a periodically driven nonlinear Duffing resonator coupled elastically to a van der Pol oscillator is investigated as a building block in a 2D lattice of such units with local connectivity. An analytic treatment of the 2-device unit is provided through a two-time-scales approach and the stability of the complex dynamic motion is analysed. The pattern formation characteristics of a 2D lattice composed of these units coupled together through nearest neighbour interactions is analysed numerically for parameters appropriate to a physical realisation through MEMS devices. The emergent patterns of global and cluster synchronisation are investigated with respect to system parameters and lattice size.

Bifurcation and dynamic response analysis of a rotating blade excited by upstream vortices

Acknowledgements The authors acknowledge the projects supported by the National Basic Research Program of China (973 Project)(No. 2015CB057405) and the National Natural Science Foundation of China (No. 11372082) and the State Scholarship Fund of CSC. DW thanks for the hospitality of the University of Aberdeen.

High Aspect Ratio (L/D) Riser Viv Prediction Using Wake Oscillator Model

A two-dimensional (2-D) vortex-induced vibration (VIV) prediction model for high aspect ratio (LID) riser subjected to uniform and sheared flow is studied in this paper. The nonlinear structure equations are considered. The near wake dynamics describing the fluctuating nature of vortex shedding is modeled using classical van der Pol equation. A new approach was applied to calibrate the empirical parameters in the wake oscillator model. Compared the predicted results with the experimental data and computational fluid dynamic (CFD) results. Good agreements are observed. It can be concluded that the present model can be used as simple computational tool in predicting some aspects of VIV of long flexible structures. (C) 2008 Elsevier Ltd. All rights reserved.

A NEW WAKE OSCILLATOR MODEL FOR PREDICTING VORTEX INDUCED VIBRATION OF A CIRCULAR CYLINDER

This article proposes a new wake oscillator model for vortex induced vibrations of an elastically supported rigid circular cylinder in a uniform current. The near wake dynamics related with the fluctuating nature of vortex shedding is modeled based on the classical van der Pol equation, combined with the equation for the oscillatory motion of the body. An appropriate approach is developed to estimate the empirical parameters in the wake oscillator model. The present predicted results are compared to the experimental data and previous wake oscillator Model results. Good agreement with experimental results is found.

Material, espacio y color en Mies van der Rohe. Café Samt & Seide: Hacia una Propuesta Estructural

La aparición de varias fotografías del Café Samt & Seide no publicadas hasta 2008 en las que se observaba la luz natural de la exposición; los planos a escala de la nave donde se realizó la exposición textil; y los croquis inéditos de la instalación de la seda localizados durante el transcurso de la Tesis Doctoral por el doctorando en el plano de la Sala de Cristal, han sido las principales aportaciones de la búsqueda documental que ha tenido por objeto el conocimiento espacial e interpretación gráfica del proyecto expositivo realizada durante el transcurso de la Tesis Doctoral para poder profundizar en el alcance de la propuesta protoarquitectónica y, a través de ella, en la obra y pensamiento de Mies van der Rohe. Material, espacio y color son elementos propuestos como capítulos que estructuran la disertación y que son empleados por Mies van der Rohe como factores de una nueva expresión espacial en la exposiciones como ensayos identificados con su idea de arquitectura. En el Café Samt & Seide, Mies van der Rohe y Lilly Reich proponen una sensibilidad en el empleo del material y color trasladada al espacio mediante una atmósfera rítmica y en movimiento de superficies abstraídas e iluminadas. La estructura visual de opuestos nace del doble material textil de la exposición desplegándose en un orden espacial y constructivo de elementos independientes iniciado en los apartamentos de la Colonia Weissenhof y Sala de Cristal de Stuttgart 1926-1927, y que será trasladado desde los espacios experimentales de 1927 a las series de mármoles y cristales del Pabellón Alemán 1928-1929. La síntesis intelectual (arte-ciencia-filosofía) guía el proceso de formalización y la técnica en una intención que será trasladada a su arquitectura en el empleo de la tecnología. La creatividad y repercusión de las vanguardias en la instalación muestra la voluntad integradora de la exposición y arquitectura como arte total. Los aspectos interpretativos de las artes plásticas, visuales y musicales se integran como criterios y sensibilidades aplicadas a las estructuras yuxtapuestas material, espacial y de color. Modernidad y tradición tectónica convergen en este espacio construido cuyas superficies cubren un armazón metálico oculto. La construcción mínima textil será incorporada como idea de forma en la futura construcción del pilar metálico, la pared flotante de sus viviendas y pabellones abiertos a la naturaleza, y la gran fachada tecnológica del espacio público de sus agrupaciones en la ciudad. El espacio total del Café Samt & Seide dentro de la gran nave de Berlín anticipa las exposiciones artísticas e industriales realizadas junto a Lilly Reich en el interior de las espaciosas salas de estructura metálica como instalaciones conceptuales de gravedad y luz antecedentes de los pabellones de grandes dimensiones y espacio universal. Arquitectura, construcción y lugar son integrados en la instalación por el principio estructural como propuesta de una idea de arquitectura que es desarrollada en las exposiciones. Oscilador y bastidor son construcciones escaladas dentro de la gran nave iluminada, expresando el conjunto un orden de partes que reflejan un todo integrado en la naturaleza y lo universal. Las múltiples relaciones espaciales, constructivas y conceptuales de la exposición con su arquitectura desvelan al Café Samt & Seide como un exponente y antecedente de su obra e idea a la que definió como una propuesta estructural. La estructura, entendida como un conjunto de valores culturales y medios técnicos, es el concepto con el que Mies van der Rohe identifica la síntesis intelectualtecnológica de su tiempo, constituyendo la finalidad de su expresión material, espacial y de color. ABSTRACT The unpublished pictures of the Café Samt & Seide appeared in 2008 in which the natural light in the exhibition can be seen; the scaled plan of the nave where the textile exhibition was held; and the unpublished sketches of the silk exhibition located by the doctoral candidate while preparing his dissertation have been the main input of the data search aiming at a better understanding of the space and a graphic interpretation of the exhibition project made by the doctoral candidate during the dissertation as a basic requirement to deepen in the scope of this protoarchitectural proposal and, though it, into Mies van der Rohe’s work and thinking. Material, space and colour are the elements put forward as the chapters structuring this dissertation and were used by Mies van der Rohe as factors of a new spatial expression in expositions as tests identified with his idea of architecture. In Café Samt & Seide, Mies van der Rohe and Lilly Reich present material and colour sensitivity transferred to space though a rhythmic and moving atmosphere made up by abstracted and lit surfaces. Such a visual grammar and oppositions unfolds into a space and constructive order of independent elements originated with the apartments of the Weissenhof Colony and Glass Room in Stuttgart 1926-1927, and which were transferred these test spaces 1927 to the series of marble and glass in the German Pavilion 1928-1929. The intellectual and formal will (art-science-philosophy) guides the technical expression, which is transferred to architecture through technology. The creativity and impact of avant-gardes in the installation reflects exhibition and architecture’s will to integrate as a Total Art. The interpretative aspects of plastic, visual and musical arts are part of a sensitivity applied to the overlapped structures of material, space and colour. Tectonic modernity and tradition converge in this space built with surfaces covering a hidden metal framework. The minimal textile construction is integrated as a shape idea in his subsequent construction of the metal pillar, floating wall in his housing and pavilions open to nature, and the great technological façade of the public space of his urban clusters. The total space of the exhibition inside the great nave in Berlin anticipates the artistic and industrial exhibitions done together with Lilly Reich inside the spacious Halls built with exposed metal structures as conceptual installation of gravity and light prior to the big-dimensioned pavilions and universal space. Architecture, construction and place are integrated by the structural principle. Oscillator and framework are scaled constructions integrated inside the great, lit nave, and the whole conveys order of its parts reflecting a whole integrated in nature and the universal. The many conceptual, space and constructive link of the textile exhibition to his European and American architecture add a greater knowledge of the time when Mies van der Rohe stated he gained a “new awareness” 1926, revealing Café Samt & Seide as a valuable example and the experimental precursor of his work and idea defined by himself as a “structural proposal”. The structure, understood as a set of cultural and material values expressed by architecture, is the notion used by Mies van der Rohe to identify the intellectual-technological synthesis as the idea of a time and which is the goal of its material, space and colour expression.

Van der Waals-corrected density functional theory : benchmarking for hydrogen–nanotube and nanotube–nanotube interactions

Density functional theory (DFT) is a powerful approach to electronic structure calculations in extended systems, but suffers currently from inadequate incorporation of long-range dispersion, or Van der Waals (VdW) interactions. VdW-corrected DFT is tested for interactions involving molecular hydrogen, graphite, single-walled carbon nanotubes (SWCNTs), and SWCNT bundles. The energy correction, based on an empirical London dispersion term with a damping function at short range, allows a reasonable physisorption energy and equilibrium distance to be obtained for H2 on a model graphite surface. The VdW-corrected DFT calculation for an (8, 8) nanotube bundle reproduces accurately the experimental lattice constant. For H2 inside or outside an (8, 8) SWCNT, we find the binding energies are respectively higher and lower than that on a graphite surface, correctly predicting the well known curvature effect. We conclude that the VdW correction is a very effective method for implementing DFT calculations, allowing a reliable description of both short-range chemical bonding and long-range dispersive interactions. The method will find powerful applications in areas of SWCNT research where empirical potential functions either have not been developed, or do not capture the necessary range of both dispersion and bonding interactions.

Interface of graphane with copper : a van der Waals density-functional study

Various forms of hydrogenated graphene have been produced to date by several groups, while the synthesis of pure graphane has not been achieved yet. The study of the interface between graphane, in all its possible hydrogenation configurations, and catalyst metal surfaces can be pivotal to assess the feasibility of direct CVD growth methods for this material. We investigated the adhesion of graphane to a Cu(111) surface by adopting the vdW-DF2-C09 exchange-correlation functional, which is able to describe dispersion forces. The results are further compared with the PBE and the LDA exchange-correlation functionals. We calculated the most stable geometrical configurations of the slab/graphane interface and evaluated how graphane's geometrical parameters are modified. We show that dispersion forces play an important role in the slab/graphane adhesion. Band structure calculations demonstrated that in the presence of the interaction with copper, the band gap of graphane is not only preserved, but also enlarged, and this increase can be attributed to the electronic charge accumulated at the interface. We calculated a substantial energy barrier at the interface, suggesting that CVD graphane films might act as reliable and stable insulating thin coatings, or also be used to form compound layers in conjunction with metals and semiconductors.

Author's reply to: Ankylosing spondylitis: evidence for a non-HLA-B*27 protective effect, Sjef Van Der Linden, Desieree Van Der Heijde

As mentioned in the letter by van der Linden and van der Heijde, Jurgen Braun’s excellent recent paper describing a survey of blood donors by questionnaire, clinical, and magnetic resonance imaging examinations revealed a prevalence of ankylosing spondylitis in B27 positive blood donors (6.4%)1-1 very similar to that reported by Gran et al(6.7%).1-2 It is probable that some of the differences in reported prevalence of ankylosing spondylitis by the various studies are because of methodological differences.

Applicability of the van der Pauw-Hall measurement technique to implanted samples

The application of the van der Pauw-Hall measurement technique to implanted samples in which the mobility varies with depth has still not been fully justified. A proof that the technique is in fact applicable in this situation is given. Journal of Applied Physics is copyrighted by The American Institute of Physics.