General symmetries in optimal control

In this paper we study general symmetries for optimal control problems making use of the geometric formulation proposed in [7]. This framework allows us to reduce the number of equations associated with optimal control problems with symmetry and compare the solutions of the original system with the solutions of the reduced one. The reconstruction of the optimal controls starting from the reduced problem is also explored.     

Two-flux composite fermion series of the fractional quantum Hall states in strained Si

Magnetotransport properties are investigated in a high-mobility two-dimensional electron system in the strained Si quantum well of a (100) Si(0.75)Ge(0.25)/Si/Si(0.75)Ge0.25 heterostructure, at temperatures down to 30 mK and in magnetic fields up to 45 T. We observe around nu=1/2 the two-flux composite fermion (CF) series of the fractional quantum Hall effect (FQHE) at nu=2/3, 3/5, 4/7, and at nu=4/9, 2/5, 1/3. Among these FQHE states, the nu=1/3, 4/7, and 4/9 states are seen for the first time in the Si/SiGe system. Interestingly, of the CF series, the 3/5 state is weaker than the nearby 4/7 state and the 3/7 state is conspicuously missing, resembling the observation in the IQHE regime that the nu=3 is weaker than the nearby nu=4 state. Our results can be quantitatively understood in the picture of CF's with the valley degree of freedom.     

Wavelet-based ultra-high compression of multidimensional NMR data sets

The application of a lossy data compression algorithm based on wavelet transform to 2D NMR spectra is presented. We show that this algorithm affords rapid and extreme compression ratios (e.g., 800:1), providing high quality reconstructed 2D spectra. The algorithm was evaluated to ensure that qualitative and quantitative information are retained in the compressed NMR spectra. Whilst the maximum compression ratio that can be achieved depends on the number of signals and on the difference between the most and the least intense peaks (dynamic range), a compression ratio of 80:1 is affordable even for the challenging case of homonuclear 2D experiments of large biomolecules.     

Material and device properties of ZnO-based film bulk acoustic resonator for mass sensing applications

Zinc oxide based film bulk acoustic resonator as mass sensor was fabricated by multi-target magnetron sputtering under optimized deposition condition. Each layer of the device was well crystallized and highly textural observed by transmission electron microscopy and X-ray diffraction measurement. Through piezoelectric test, the device vibrated with significant distance. The influence of top electrode on resonant frequency and the bio-specimen of mass loading effect were investigated. Data show that the device has qualified properties as mass biosensor, with a resonant frequency of 3-4 GHz and a high sensitivity of 8-10 kHz cm²/ng.     

A Geometric Approach to Integrability of Abel Differential Equations

A geometric approach is used to study the Abel first-order differential equation of the first kind. The approach is based on the recently developed theory of quasi-Lie systems which allows us to characterise some particular examples of integrable Abel equations. Second order Abel equations will be discussed and the inverse problem of the Lagrangian dynamics is analysed: the existence of two alternative Lagrangian formulations is proved, both Lagrangians being of a non-natural class. The study is carried out by means of the Darboux polynomials and Jacobi multipliers.     

Beam focusing from double subwavelength metallic slits filled with nonlinear material surrounded by dielectric surface gratings

Based on the radiation properties of surface plasmon polaritons (SPPs) can be controlled by adjusting the refractive indexes of dielectric materials in the metallic slits, a novel plasmonic focusing structure formed by two subwavelength metal apertures filled with Kerr nonlinear material surrounded by surface dielectric gratings is proposed and demonstrated numerically. Directions of radiation fields are determined by the phase difference of the surface waves at the exit interface and resonance property of each surface grating. Numerical simulations using two-dimensional (2D) Finite-Difference Time-Domain (FDTD) method verify that the deflection angle and focal length can be controlled easily by changing the intensity of incident light, dynamically tunable on-axis and off-axis focusing effects can be achieved.     

Fluorescent Properties of a Hybrid Cadmium Sulfide-Dendrimer Nanocomposite and its Quenching with Nitromethane

A fluorescent hybrid cadmium sulphide quantum dots (QDs) dendrimer nanocomposite (DAB-CdS) synthesised in water and stable in aqueous solution is described. The dendrimer, DAB-G5 dendrimer (polypropylenimine tetrahexacontaamine) generation 5, a diaminobutene core with 64 amine terminal primary groups. The maximum of the excitation and emission spectra, Stokes’ shift and the emission full width of half maximum of this nanocomposite are, respectively: 351, 535, 204 and 212 nm. The fluorescence time decay was complex and a four component decay time model originated a good fit (χ = 1.20) with the following lifetimes: τ ₁ = 657 ps; τ ₂ = 10.0 ns; τ ₃ = 59.42 ns; and τ ₄ = 265 ns. The fluorescence intensity of the nanocomposite is markedly quenched by the presence of nitromethane with a dynamic Stern-Volmer constant of 25 M⁻¹. The quenching profiles show that about 81% of the CdS QDs are located in the external layer of the dendrimer accessible to the quencher. PARAFAC analysis of the excitation emission matrices (EEM) acquired as function of the nitromethane concentration showed a trilinear data structure with only one linearly independent component describing the quenching which allows robust estimation of the excitation and emission spectra and of the quenching profiles. This water soluble and fluorescent nanocomposite shows a set of favourable properties to its use in sensor applications.     

Morphology–luminescence correlations in europium-doped ZnO nanomaterials

In order to investigate the correlations of morphologies and optical properties, different morphologies of Eu-doped ZnO were synthesized by different methods. Specifically, the structure of SiO₂/ZnO:Eu nanoflower was synthesized for the first time and has not been reported previously. One percent was chosen as the Eu doping concentration. The relations of the morphology, diameter, and uniformity with the PL intensity were examined. The PL intensity of ZOE samples has a close relationship with the morphology. The PL intensity order of the different morphologies of ZnO:Eu is as follows: nanorod arrays > thin film > nanospheres > nanoparticles > nanoflowers > nanorods. The PL intensity of nanomaterials is larger, if the diameter of the nanomaterials is larger. However, the size of diameter is not the most important reason. It was found that the sample uniformity plays a key role on ZnO:Eu PL intensity. ZnO:Eu with small particle diameters may have strong photoluminescence intensity, if the nanoparticles are uniform.     

Edge-enhanced imaging with polyvinyl alcohol/acrylamide photopolymer gratings

We demonstrate edge-enhanced imaging produced by volume phase gratings recorded on a polyvinyl alcohol/acrylamide photopolymer. Bragg diffraction, exhibited by volume gratings, modifies the impulse response of the imaging system, facilitating spatial filtering operations with no need for a physical Fourier plane. We demonstrate that Kogelnik's coupled-wave theory can be used to calculate the transfer function for the transmitted and the diffracted orders. The experimental and simulated results agree, and they demonstrate the feasibility of our proposal.