Mixed-dimensional coupling in finite element models

In many finite element analysis models it would be desirable to combine reduced- or lower-dimensional element types with higher-dimensional element types in a single model. In order to achieve compatibility of displacements and stress equilibrium at the junction or interface between the differing element types, it is important in such cases to integrate into the analysis some scheme for coupling the element types. A novel and effective scheme for establishing compatibility and equilibrium at the dimensional interface is described and its merits and capabilities are demonstrated. Copyright (C) 2000 John Wiley & Sons, Ltd.

Nonlinear frequency coupling in dual radio-frequency driven atmospheric pressure plasmas

Plasma ionization, and associated mode transitions, in dual radio-frequency driven atmospheric pressure plasmas are governed through nonlinear frequency coupling in the dynamics of the plasma boundary sheath. Ionization in low-power mode is determined by the nonlinear coupling of electron heating and the momentary local plasma density. Ionization in high-power mode is driven by electron avalanches during phases of transient high electric fields within the boundary sheath. The transition between these distinctly different modes is controlled by the total voltage of both frequency components.

Palladium-mediated reductive coupling, a stereoselective approach to the 8-dehydropumiliotoxin skeleton

Reductive cyclisation of ail E-vinyl bromide with ail allylic acetate proceeds under palladium catalysis 10 give the 8-dehydropumiliotoxin skeleton, a potential advanced precursor to 8-deoxypumiliotoxin alkaloids. Control of the stereochemistry of the E-vinyl bromide precursor is achieved readily using the Kogen or Bruckner bromophosphonate reagents and the reductive cyclisation proceeds with retention of the vinyl bromide stereochemistry. The mechanism for the cyclisation involves an in situ conversion of the allylic acetate to ail allyl stannane followed by ail intramolecular Stille-type coupling.

Multi component coupling reactions of N-acetyl-2-azetine

N-Acetyl-2-azetine undergoes Lewis acid catalysed formal [4+2]-cycloaddition with imines derived from aromatic amines to initially give an approximately 1: 1 mixture of exo-endo-diastereoisomeric 1-(2a,3,4,8b-tetrahydro-2H-1,4-diaza-cyclobuta[a]naphthalen-1-yl)-ethanone cycloadducts which were detected by proton NMR spectroscopy. These products, which were too unstable to isolate, and characterise, reacted further with aromatic amines to give 2,3,4-trisubstituted tetrahydroquinolines in good to excellent yield, predominantly as a single diastereoisomer, with the minor diastereoisomer converting to the major diastereoisomer on silica. The cycloaddition was irreversible and a mechanism is presented for the formation of the major diastereoisomer from the mixture of diastereoisomeric intermediates. A range of conditions is described for converting the 2,3,4-trisubsitituted tetrahydroquinolines into 2,3-disubstituted quinolines.

Three component coupling reactions of N-acetyl-2-azetine-rapid stereoselective entry to 2,3,4-trisubstituted tetrahydroquinolines

N-Acetyl-2-azetine undergoes Lewis acid catalysed [4 + 2]-cycloaddition with imines derived from aromatic amines and gave a 1:1 mixture of exo-endo diastereoisomeric azetidine cycloadducts which reacted further with aromatic amine, to give 2,3,4-trisubsitituted tetrahydroquinolines in good to excellent yield, predominantly as one diastereoisomer.

Prism coupler with variable coupling gap

The construction and operation of a prism/variable-gap/sample system (or variable-gap Otto coupler) for the excitation of surface electromagnetic modes is reported. This system has been used for the observation and characterization of surface plasmon polaritons on thin film structures. The initial alignment of prism and sample is performed under gravity and the subsequent gap variation is performed by means of a single actuator operating a flexure stage on which the prism is mounted. The flexure stage ensures the maintenance of good parallelism between sample and prism as the gap dimension is varied. The coupler has also served as a prototype, in terms of design principle, for the construction of a more sophisticated, variable-gap Otto coupler that can operate in vacuum at temperatures from ambient to 85 K. (C) 2000 American Institute of Physics. [S0034-6748(00)02311-X].

Nonlinear modulation of transverse dust lattice waves in complex plasma crystals

The occurrence of the modulational instability in transverse dust lattice waves propagating in a one-dimensional dusty plasma crystal is investigated. The amplitude modulation mechanism, which is related to the intrinsic nonlinearity of the sheath electric field, is shown to destabilize the carrier wave under certain conditions, possibly leading to the formation of localized envelope excitations. Explicit expressions for the instability growth rate and threshold are presented and discussed. (C) 2004 American Institute of Physics.

Weakly nonlinear effects associated with transverse oscillations in dusty plasma crystals

We study the amplitude modulation of transverse dust lattice waves (TDLW) propagating in a single- and double-layer dusty plasma (DP) crystal. It is shown that a modulational instability mechanism, which is related to an intrinsic nonlinearity of the sheath electric field, may occur under certain conditions. Possibility of the formation of localized excitations (envelope solitons) in the dusty plasma crystal is discussed.

Modulated transverse off-plane dust-lattice wave packets in hexagonal two-dimensional dusty plasma crystals

The propagation of nonlinear dust-lattice waves in a two-dimensional hexagonal crystal is investigated. Transverse (off-plane) dust grain oscillatory motion is considered in the form of a backward propagating wave packet whose linear and nonlinear characteristics are investigated. An evolution equation is obtained for the slowly varying amplitude of the first (fundamental) harmonic by making use of a two-dimensional lattice multiple scales technique. An analysis based on the continuum approximation (spatially extended excitations compared to the lattice spacing) shows that wave packets will be modulationally stable and that dark-type envelope solitons (density holes) may occur in the long wavelength region. Evidence is provided of modulational instability and of the occurrence of bright-type envelopes (pulses) at shorter wavelengths. The role of second neighbor interactions is also investigated and is shown to be rather weak in determining the modulational stability region. The effect of dissipation, assumed negligible in the algebra throughout the article, is briefly discussed.