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In this paper we show that, under certain generic conditions, billiards on ovals have only a finite number of periodic orbits, for each period N, all nondegenerate. Moreover, the stable and unstable manifolds of hyperbolic points are transversal. We explore these properties to give some dynamical consequences especially about the dynamics in the instability regions.

A velocity feedback control system is evaluated in the active control of vibrations of a smart beam with a pair of surface mounted piezoelectric ceramic patches, and finite element (FE) model results are validated against measured ones. To this end, a three-layered smart beam FE model is utilized, where a partial layerwise theory and a fully coupled electro-mechanical theory are considered for the formulation of the displacement field and electric potential, respectively. Regarding the test rig, it consists of a cantilever smart aluminum beam with two piezoelectric patches mounted close to the clamped end. One of the piezoelectric patches is utilized to excite the beam while the other is utilized as an actuator in the feedback control loop. The control voltage applied to the actuator is proportional to the transverse velocity at the free end, which is measured by a laser vibrometer. First, the quasi-static actuation capacity of the piezoelectric patches is evaluated. Next, the free and forced velocity responses to an initial displacement field and harmonic excitation are analyzed. The capacity to predict instabilities and the accuracy of the FE model are demonstrated and the applicability and functionality of the velocity feedback vibration control system are discussed.

The problem of shape control and correction of small displacements in composite structures using piezoelectric actuators glued or embedded was addressed. A finite element model based on Mindlin plate theory was used to characterize the behaviour of the structure and the one of the actuators. Emphasis was put on the development of an efficient and general methodology, based on genetic algorithms, for the determination of the optimal actuation voltages needed to apply to the piezoelectric actuators in such a way that a pre-defined shape of the structure is achieved. The model was investigated numerically and verified experimentally. Measurements were carried out using electronic speckle pattern interferometry. Good agreement was found between simulation results and the optically measured values.

We apply J Mather's theory (1991) on minimizing measures to the case of positive definite autonomous Lagrangians L:TM to R. We show that the minimal action function beta (h)=min( integral Ld mu mod rho ( mu )=h), has radial derivative, rho ( mu ) in H1(M,R) is the homology vector of the invariant probability mu . As one consequence, for any supporting domain S of beta , the closure of the union of the support of any minimizing measures with homology in S is contained in a fixed energy level. It is also shown that there is a one-to-one correspondence between minimizing measures for Lagrangians associated to mechanical systems (kinetic minus potential energy) and minimizing measures for the geodesic problem on a fixed energy level.

Ferroelectric polymers such as PVDF and its copolymer P(VDF/TrFE) as well as ferroelectric ceramic-polymer composites have to be annealed at a high temperature for an extended period of time after polling, before the measurement of the pyroelectric coefficient by the direct method can be performed, in order to eliminate the high depolarization current which hinders the determination of the true pyroelectric current. Here it is suggested that a periodic temperature oscillation of a ceramic-polymer composite sample would permit measurement of its true pyroelectric coefficient without the need to anneal the sample. The temperature distribution inside the composite sample, the magnitude of the pyroelectric current and their variation with the frequency of temperature oscillation have been simulated with the present theory. Pyroelectric measurements using this technique have been made on a poled composite of calcium-modified lead titanate (PbTiO3) and a copolymer of vinylidene fluoride and trifluoroethylene P(VDF/TrFE) and compared with the results of the direct measurements before and after annealing, in order to test the validity of the method.

The authors obtain a simple solution for the one-dimensional nucleonic diffusion equation in the atmosphere assuming that both the interaction mean free path and inelasticity are energy dependent. They also show that a fairly accurate description of nucleonic fluxes is obtained by using the average inelasticity as an increasing function of energy.

Hexagonal Boron Nitride (h-BN) is a promising insulating material to complement and enable graphene electronics. Given the good lattice match to graphite, graphene/h-BN heterostructures may be grown with negligible amounts of strain and defect states, resulting in high carrier mobilities approaching values for suspended graphene. Chemical vapour deposition (CVD) has emerged as one of the preferred routes for the synthesis of 2D materials for electronic applications. Here we report on the growth of h-BN by low pressure CVD, using borazine as a precursor. Electron backscattered diffraction (EBSD) in conjunction with topographic imaging in the scanning electron microscope are used to investigate the change in crystal structure and orientation of three metallic catalyst substrates: Co, Ni and Cu, by high temperature processing and the growth of nanoscale h-BN domains. The behaviour of the metal foils is interpreted in light of the prevalent growth models. EBSD and imaging conditions are optimized to allow efficient acquisitions for these composite and nanostructured specimens.

Electron beam-induced deposition (EBID) is a direct write process where an electron beam locally decomposes a precursor gas leaving behind non-volatile deposits. It is a fast and relatively in-expensive method designed to develop conductive (metal) or isolating (oxide) nanostructures. Unfortunately the EBID process results in deposition of metal nanostructures with relatively high resistivity because the gas precursors employed are hydrocarbon based. We have developed deposition protocols using novel gas-injector system (GIS) with a carbon free Pt precursor. Interconnect type structures were deposited on preformed metal architectures. The obtained structures were analysed by cross-sectional TEM and their electrical properties were analysed ex-situ using four point probe electrical tests. The results suggest that both the structural and electrical characteristics differ significantly from those of Pt interconnects deposited by conventional hydrocarbon based precursors, and show great promise for the development of low resistivity electrical contacts.

The electrical methods used to study the molecular movements in dielectric materials are based on the movement of the dipoles, which are parts of the component molecules, under a convenient external applied DC or AC electric field. We have proposed recently a combined isothermal and non-isothermal measuring protocol to analyze charge injection/extraction, transport, trapping and de-trapping in low mobility materials. During an electric polarization process or an electric charging process, besides the polarization process, electric charge is injected into the material. This charge is partially transported and partially trapped in the material, depending on the material properties and on the experimental conditions. As a consequence of the charge trapping process, the structure is decorated with space charge and during the subsequent thermally stimulated discharge current experiment we are observing an apparent peak and the genuine peaks that are related to dipole randomization and charge de-trapping determined by the molecular movements. The aim of this paper is to present a combined measuring protocol that allows to separate the apparent peak and the genuine peaks in polar and non-polar dielectric materials. The method is very sensitive, very selective and allows to reveal, in a single run, details that are not observed when other electrical and non-electrical techniques are used.

The unitary equation in the dual approach can be written as a sum over reggeon loop diagrams. We assume that in some definite regions in energy, only one diagram, with a definite number of loops dominates the sum. As consequences we obtain SU(M) symmetry for coupling constants, Gell-Mann Okubo formulae for mass breaking and exchange degeneracy for reggeon trajectories. We also derive relations connecting the Pomeron and reggeon intercepts with quantities referring to production of clusters. Predictions are given for the breaking of Pomeron couplings in reactions involving strange and charmed particles.

We show that asymptotically dσ/du(180°) π/16 |f'(0)|21/k6, where k is the centre-of-mass momentum and f'(0) the derivative with respect to the impact parameter b of the elastic amplitude at b = 0. A comparison with recent p backward scattering data gives an upper bound for |f'(0)| ≤ 0.12 GeV.

Starting from the Pomeron equation in the dual unitarity scheme, we derive a bootstrap equation for the single particle distribution. The solution exhibits a rapidity distribution with a rising, non-flat contribution in the central region, corresponding to a power-law behavior of the average multiplicity.

Models for high-energy elastic scattering can be easily discriminated at the CERN pp collider. In particular, the recent measurement of the pp total cross section, sigma ( square root s=540)=66+or-7 mb, combined with the dispersion relation estimates of the ratio rho identical to ReF(s, 0)/ImF(s, 0) approximately=0.15, already strongly constrains the predictions of geometrical scaling for the differential elastic cross section.

The scaling function for the asymptotic p → ∞ behaviour of periods-p windows useful to describe the phenomenology of periodic windows in one-dimensional maps is calculated. The window size δμ(p) in parameter space and the width δx(p) at the window crisis are accurately estimated even for small periods. We show that the size of periodic-p windows approaching the final aperiodic regime decreases asymptotically with a geometric rate.