Synthesis of optically active 6-substituted 2-(aminomethyl)chromans

Three novel, optically active, 6-substituted 2-(aminomethyl)chromans were synthesized from readily available chroman 2-carboxylic acid precursors. These chroman-containing primary amines are useful building blocks for the synthesis of chroman-derived pharmaceutical agents.     

Nonlinear normal modes and band zones in granular chains with no pre-compression

We study standing waves (nonlinear normal modes—NNMs) and band zones in finite granular chains composed of spherical granular beads in Hertzian contact, with fixed boundary conditions. Although these are homogeneous dynamical systems in the notation of Rosenberg (Adv. Appl. Mech. 9:155–242, 1966), we show that the discontinuous nature of the dynamics leads to interesting effects such as separation between beads, NNMs that appear as traveling waves (these are characterized as pseudo-waves), and localization phenomena. In the limit of infinite extent, we study band zones, i.e., pass and stop bands in the frequency–energy plane of these dynamical systems, and classify the essentially nonlinear responses that occur in these bands. Moreover, we show how the topologies of these bands significantly affect the forced dynamics of these granular media subject to narrowband excitations. This work provides a classification of the coherent (regular) intrinsic dynamics of one-dimensional homogeneous granular chains with no pre-compression, and provides a rigorous theoretical foundation for further systematic study of the dynamics of granular systems, e.g., the effects of disorders or clearances, discrete breathers, nonlinear localized modes, and high-frequency scattering by local disorders. Moreover, it contributes toward the design of granular media as shock protectors, and in the passive mitigation of transmission of unwanted disturbances.     

On the right-angle X-junction diffraction model

We review the important features of the right-angle X-junction diffraction model and discuss both its theoretical framework and its validity range. In addition, we present explicit new results from BPM calculations that show that the analytical model aptly describes the dominant physical processes involved and provides bounds on the numerical results. We also address some misinterpretations of the model that have recently appeared in the literature.     

Energy Transfers in a System of Two Coupled Oscillators with Essential Nonlinearity: 1:1 Resonance Manifold and Transient Bridging Orbits

The purpose of this study is to highlight and explain the vigorous energy transfers that may take place in a linear oscillator weakly coupled to an essentially nonlinear attachment, termed a nonlinear energy sink. Although these energy exchanges are encountered during the transient dynamics of the damped system, it is shown that the dynamics can be interpreted mainly in terms of the periodic orbits of the underlying Hamiltonian system. To this end, a frequency-energy plot gathering the periodic orbits of the system is constructed which demonstrates that, thanks to a 1:1 resonance capture, energy can be irreversibly and almost completely transferred from the linear oscillator to the nonlinear attachment. Furthermore, it is observed that this nonlinear energy pumping is triggered by the excitation of transient bridging orbits compatible with the nonlinear attachment being initially at rest, a common feature in most practical applications. A parametric study of the energy exchanges is also performed to understand the influence of the parameters of the nonlinear energy sink. Finally, the results of experimental measurements supporting the theoretical developments are discussed. This study was carried out while the author was a postdoctoral fellow at the National Technical University of Athens and at the University of Illinois at Urbana-Champaign.     

Computing the endomorphism ring of an ordinary elliptic curve over a finite field

We present two algorithms to compute the endomorphism ring of an ordinary elliptic curve E defined over a finite field Fq. Under suitable heuristic assumptions, both have subexponential complexity. We bound the complexity of the first algorithm in terms of , while our bound for the second algorithm depends primarily on log|DE|, where DE is the discriminant of the order isomorphic to End(E). As a byproduct, our method yields a short certificate that may be used to verify that the endomorphism ring is as claimed.     

Fast electro-optical mode in photo-aligned reflective deformed helix ferroelectric liquid crystal cells

The electro-optical behavior of deformed helix ferroelectric liquid crystal in reflective mode is described in this paper. The electrically controlled reflectance has been measured at subkilohertz driving voltage frequency for different polarizations of the incident light and compared quite successfully with the simulation results.     

Isolated resonances and nonlinear damping

We analyze isolated resonance curves (IRCs) in single-degree-of-freedom systems possessing nonlinear damping. Through the combination of singularity theory and the averaging method, the onset and merging of IRCs, which coincide to isola and simple bifurcation singularities, respectively, can be analytically predicted. Numerical simulations confirm the accuracy of the analytical developments. Another important finding of this paper is that we unveil a geometrical connection between the topology of the damping force and IRCs. Specifically, we demonstrate that extremas and zeros of the damping force correspond to the appearance and merging of IRCs. Considering a damping force possessing several minima and maxima confirms the general validity of the analytical result. It also evidences a very complex scenario for which different IRCs are created, co-exist and then merge together to form a super IRC which eventually merges with the main resonance peak.     

X-junctions in buried channel waveguides

The excess loss across an acute-angle symmetric X-junction composed of two weakly guiding single-mode buried channel waveguides of square core cross-section is shown to be very small provided the junction angle is greater than a few degrees. Numerical and approximate analytical results are presented, as well as a simple criterion for the onset of cross-talk as the junction angle decreases.     

Tuning the electrical and optical properties of dinuclear ruthenium complexes for near infrared optical sensing

[reaction: see text] Redox-active dinuclear ruthenium complexes with various 1,2-dicarbonylhydrazido (DCH) ligands are designed and prepared to have intense absorption in the near-infrared region for potential optical sensing in aqueous media, as demonstrated for sensing hydrogen peroxide in this study.     

Enhanced luminescent iridium(III) complexes bearing aryltriazole cyclometallated ligands

Herein we report the synthesis of 4-aryl-1-benzyl-1H-1,2,3-triazoles (atl), made via "Click chemistry" and their incorporation as cyclometallating ligands into new heteroleptic iridium(III) complexes containing diimine (N(^)N) ancillary ligands 2,2'-bipyridine (bpy) and 4,4'-di-tert-butyl-2,2'-bipyridine (dtBubpy). Depending on decoration, these complexes emit from the yellow to sky blue in acetonitrile (ACN) solution at room temperature (RT). Their emission energies are slightly blue-shifted and their photoluminescent quantum efficiencies are markedly higher (between 25 and 80%) than analogous (C(^)N)(2)Ir(N(^)N)(+) type complexes, where C(^)N is a decorated 2-phenylpyridinato ligand. This increased brilliance is in part due to the presence of the benzyl groups, which act to sterically shield the iridium metal center. X-ray crystallographic analyses of two of the atl complexes corroborate this assertion. Their electrochemistry is reversible, thus making these complexes amenable for inclusion in light-emitting electrochemical cells (LEECs). A parallel computational investigation supports the experimental findings and demonstrates that for all complexes included in this study, the highest occupied molecular orbital (HOMO) is located on both the aryl fragment of the atl ligands and the iridium metal while the lowest unoccupied molecular orbital (LUMO) is located essentially exclusively on the ancillary ligand.