Fibonacci oscillators

We discuss the properties of oscillators whose spectrum is given by a generalized Fibonacci sequence. The properties include: invariance under the unitary quantum group, generalized angular momentum, coherent states and difference calculus, relativistic interpretation.     

Coherence of acoustic modes propagating through shallow water internal waves

The 1995 Shallow Water Acoustics in a Random Medium (SWARM) experiment [Apel et al., IEEE J. Ocean. Eng. 22, 445-464 (1997)] was conducted off the New Jersey coast. The experiment featured two well-populated vertical receiving arrays, which permitted the measured acoustic field to be decomposed into its normal modes. The decomposition was repeated for successive transmissions allowing the amplitude of each mode to be tracked. The modal amplitudes were observed to decorrelate with time scales on the order of 100 s [Headrick et al., J. Acoust. Soc. Am. 107(1), 201-220 (2000)]. In the present work, a theoretical model is proposed to explain the observed decorrelation. Packets of intense internal waves are modeled as coherent structures moving along the acoustic propagation path without changing shape. The packets cause mode coupling and their motion results in a changing acoustic interference pattern. The model is consistent with the rapid decorrelation observed in SWARM. The model also predicts the observed partial recorrelation of the field at longer time scales. The model is first tested in simple continuous-wave simulations using canonical representations for the internal waves. More detailed time-domain simulations are presented mimicking the situation in SWARM. Modeling results are compared to experimental data.     

Equivariant frame fields on spheres with complementary equivariant complex structures

LetG be a finite group and letM be a unitary representation space ofG. We consider the existence problem of equivariant frame fields on the unit sphereS(M) whose orthogonal complements in the tangent bundleT(S(M)) admitG-equivariant complex structures. Under mild fixed point conditions we give a complete solution for this problem whenG is either ℤ/2ℤ or a finite group of odd order. This article was processed by the author using theLaT_EX style filecljourl from Springer-Verlag.     

Analytical and numerical solutions of mathematical biology models: The Newell-Whitehead-Segel and Allen-Cahn equations

In this paper, we combine the unified and the explicit exponential finite difference methods to obtain both analytical and numerical solutions for the Newell-Whitehead-Segel–type equations which are very important in mathematical biology. The unified method is utilized to obtain various solitary wave solutions for these equations. Numerical solutions of the specific case studies are investigated by using the explicit exponential finite difference method ensures the accuracy and reliability of the proposed scheme. After obtaining the approximate solutions, convergence analysis and error estimation (the error norms and absolute errors) are presented by comparing these results with the analytical obtained solutions and other methods in the literature through tables and graphs. The obtained analytical and numerical results are in good agreement.     

On the Orthogonality of Two Thiol‐Based Modular Ligations

The chemoselectivity of two thiol‐based modular ligations operating under mild conditions is assessed. For this purpose, a macromolecular scaffold possessing allyl and pentafluorophenyl groups in two distinct parts is employed, which enables facile characterization by NMR spectroscopy (¹H and ¹⁹F) and size‐exclusion chromatography. By using appropriate triggers (introduction of a base or light irradiation), it is possible to direct thiols to an arbitrarily chosen part of the scaffold, without any change to the other part and with no involvement of protecting group chemistry. Dual functionalization experiments are achieved by applying these triggers consecutively with no consideration of the reaction sequence order, evidencing full bidirectionality. A set of one‐pot, purification‐free procedures that enable near‐quantitative to full dual functionalization in (very) short reaction times (17–180 min) is also presented.     

AlGaN-based high-performance metal–semiconductor–metal photodetectors

Design, structure growth, fabrication, and characterization of high performance AlGaN-based metal–semiconductor–metal (MSM) photodetectors (PD) are reported. By incorporating AlN nucleation and buffer layers, the leakage current density of GaN MSM PD was reduced to 1.96 × 10⁻¹⁰ A/cm² at a 50 V bias, which is four orders of magnitude lower compared to control devices. A 229 nm cut-off wavelength, a peak responsivity of 0.53 A/W at 222 nm, and seven orders of magnitude visible rejection was obtained from Al_0.75Ga_0.25N MSM PD. Two-color monolithic AlGaN MSM PD with excellent dark current characteristics were demonstrated, where both detectors reject the other detector spectral band with more than three orders of magnitude. High-speed measurements of Al_0.38Ga_0.62N MSM PD resulted in fast responses with greater than gigahertz bandwidths, where the fastest devices had a 3-dB bandwidth of 5.4 GHz.     

An investigation of Zn/ZnO:Al/p-Si/Al heterojunction diode by sol–gel spin coating technique

Present study shows the structural, morphological, optical characterization of sol–gel spin coated ZnO:Al film and investigation of device efficiency of Zn/ZnO:Al/p-Si/Al heterojunction diode structure. X-ray diffraction study indicates that film has hexagonal polycrystalline structure with (002) preferential direction. Atomic force microscope and scanning electron microscope images exhibit that surface of ZnO:Al/p-Si consists of homogenously scattered nanoparticles. The surface roughness of ZnO:Al film is found to be 15.24 nm. The band gap value of ZnO:Al film deposited on glass substrate is calculated to be 3.34 eV. The electrical characterization of Zn/ZnO:Al/p-Si/Al heterojunction structure is made by current–voltage (I–V) and capacitance–voltage (C–V) measurements. From these measurements, the heterojunction structure shows a rectifying behavior under a dark condition. The ideality factor and barrier height of Zn/n-ZnO:Al/p-Si/Al structure are calculated as 3.23 and 0.68 eV. The heterojunction structure have diode characteristic with rectification ratio at 64.4 at +2.0 V in the dark. The results suggest that Zn/ZnO:Al/p-Si/Al heterojunction diode can be successfully used in many optoelectronic applications.     

Dye‐sensitized solar cells based on zinc(II) phthalocyanines bearing 3‐pyridin‐3‐ylpropoxy anchoring groups

In this study, nonperipherally tetra‐substituted ( 2 ), peripherally tetra‐substituted ( 3 ), and peripherally octa‐substituted ( 4 ) zinc(II) phthalocyanines were synthesized as sensitizers for dye‐sensitized solar cells (DSSCs) in which 3‐pyridin‐3‐ylpropoxy substituent acts as anchoring unit to bind TiO₂ surface. The optical results indicated that there is an interaction between the dyes and the TiO₂ surface. The photovoltaic performances of the DSSCs based on these dyes were found to depend on both the position and number of the substituents. Despite the more red‐shifted absorption, the DSSC based on 2 showed the conversion efficiency of 0.68%, which is lower than 1.36% and 0.92% for 3 and 4 , respectively, under one sun (AM 1.5G). The vertical orientation of the dye on TiO₂ surface could be the main reason for the higher photovoltaic performance of complex 3 , which is beneficial for not only injecting the electrons into the conduction band of TiO₂ but also reducing the charge recombination. Overall, these results demonstrate that the peripherally tetra‐substituted 3‐pyridin‐3‐ylpropoxy zinc(II) phthalocyanine complex ( 3 ) as a sensitizer can more efficiently utilize the photons in the red/near‐infrared region with respect to the other complexes studied.