The landscape of nonlinear structural dynamics: an introduction.

Nonlinear behaviour is ever-present in vibrations and other dynamical motions of engineering structures. Manifestations of nonlinearity include amplitude-dependent natural frequencies, buzz, squeak and rattle, self-excited oscillation and non-repeatability. This article primarily serves as an extended introduction to a theme issue in which such nonlinear phenomena are highlighted through diverse case studies. More ambitiously though, there is another goal. Both the engineering context and the mathematical techniques that can be used to identify, analyse, control or exploit these phenomena in practice are placed in the context of a mind-map, which has been created through expert elicitation. This map, which is available in software through the electronic supplementary material, attempts to provide a practitioner's guide to what hitherto might seem like a vast and complex research landscape.This project has arisen from a collaboration between the five UK universities and eight industrial collaborators on the EPSRC ‘Engineering Nonlinearity’ Programme Grant (EPSRC grant no. EP/K003836/1). T.B. is funded by an RAEng/EPSRC Research Fellowship.This is the final version of the article. It was first available from Royal Society Publishing via http://dx.doi.org/10.1098/rsta.2014.040

Coexistence of Ferroelectric Triclinic Phases and Origin of Large Piezoelectric Responses in Highly Strained BiFeO3 films

The structural evolution of the strain-driven morphotropic phase boundary (MPB) in BiFeO3 films has been investigated using synchrotron x-ray diffractometry in conjunction with scanning probe microscopy. Our results demonstrate the existence of mixed-phase regions that are mainly made up of two heavily tilted ferroelectric triclinic phases. Analysis of first-principles computations suggests that these two triclinic phases originate from a phase separation of a single monoclinic state accompanied by elastic matching between the phase-separated states. These first-principle calculations further reveal that the intrinsic piezoelectric response of these two low-symmetry triclinic phases is not significantly large, which thus implies that the ease of phase transition between these two energetically close triclinic phases is likely responsible for the large piezoelectric response found in the BiFeO3 films near its MPB. These findings not only enrich the understandings of the lattice and domain structure of epitaxial BiFeO3 films but may also shed some light on the origin of enhanced piezoelectric response near MPB.Comment: 19 pages, 3 figures and 1 tabl

Inverse Anticipating Synchronization

We report a new type of chaos synchronization:inverse anticipating synchronization, where a time delay chaotic system can drive another system in such a way that the driven system anticipates the driver by synchronizing with its inverse future state. We extend the concept of inverse anticipating chaos synchronization to cascaded systems. We propose means for the experimental observation of inverse anticipating chaos synchronization in external cavity lasers.Comment: LaTex 6 pages, resubmitted to PR

Fibrations on four-folds with trivial canonical bundles

Four-folds with trivial canonical bundles are divided into six classes according to their holonomy group. We consider examples that are fibred by abelian surfaces over the projective plane. We construct such fibrations in five of the six classes, and prove that there is no such fibration in the sixth class. We classify all such fibrations whose generic fibre is the Jacobian of a genus two curve.Comment: 28 page

Lag time and parameter mismatches in synchronization of unidirectionally coupled chaotic external cavity semiconductor lasers

We report an analysis of synchronization between two unidirectionally coupled chaotic external cavity master/slave semiconductor lasers with two characteristic delay times, where the delay time in the coupling is different from the delay time in the coupled systems themselves. We demonstrate for the first time that parameter mismatches in photon decay rates for the master and slave lasers can explain the experimental observation that the lag time is equal to the coupling delay time.Comment: LaTex, 5 pages, submitted to PRE(R

Combinatorial discovery of a lead-free morphotropic phase boundary in a thin-film piezoelectric perovskite

We report on the discovery of a lead-free morphotropic phase boundary in Sm doped BiFeO3 with a simple perovskite structure using the combinatorial thin film strategy. The boundary is a rhombohedral to pseudo-orthorhombic structural transition which exhibits a ferroelectric (FE) to antiferroelectric (AFE) transition at approximately Bi0.86Sm0.14FeO3 with dielectric constant and out-of-plane piezoelectric coefficient comparable to those of epitaxial (001) oriented Pb(Zr,Ti)O3 (PZT) thin films at the MPB. The discovered composition may be a strong candidate of a Pb-free piezoelectric replacement of PZT.Comment: 16 pages, 5 figures, submitted to Applied Physics Letter

The effect of substrate clamping on the paraelectric to antiferroelectric phase transition in Nd-doped BiFeO₃ thin films

Thin films were deposited on Pt/Ti/SiO₂/Si substrates using pulsed laser deposition from a target with a composition (Bi₀.₈₂₅Nd₀.₁₇₅Fe₀.₉₇Ti₀.₀₃O₃) with 5 mol% excess Bi₂O₃ within the antiferroelectric (AFE) region of the NdFeO₃-BiFeO₃ phase diagram. However, Raman spectroscopy and transmission electron microscopy (TEM) revealed that films consisted of a mosaic microstructure in which (AFE), ferroelectric (FE) and paraelectric (PE) phases coexisted. Variation in the spatial distribution of Nd is typically greater in bulk ceramics than in thin films and therefore, the absence of single phase AFE cannot be attributed to local changes in composition. Instead, it is proposed that clamping due to mismatch in thermal expansion coefficient with the substrate suppresses the large volume change associated with the PE-FE and PE-AFE transition in bulk and its absence in the thin film prevents an avalanche-like transition throughout grains, which in bulk sustains single phase AFE, irrespective of local deviations in the Nd concentration

The Kahler Cone as Cosmic Censor

M-theory effects prevent five-dimensional domain-wall and black-hole solutions from developing curvature singularities. While so far this analysis was performed for particular models, we now present a model-independent proof that these solutions do not have naked singularities as long as the Kahler moduli take values inside the extended Kahler cone. As a by-product we obtain information on the regularity of the Kahler-cone metric at boundaries of the Kahler cone and derive relations between the geometry of moduli space and space-time.Comment: 21 pages, 1 figure. Improved discussion of the relation between Kahler moduli and five-dimensional scalars. No changes in the conclusion