A more direct representation for complex relativity

An alternative to the representation of complex relativity by self‐dual complex 2‐forms on the spacetime manifold is presented by assuming that the bundle of real 2‐forms is given an almost‐complex structure. From this, one can define a complex orthogonal structure on the bundle of 2‐forms, which results in a more direct representation of the complex orthogonal group in three complex dimensions. The geometrical foundations of general relativity are then presented in terms of the bundle of oriented complex orthogonal 3‐frames on the bundle of 2‐forms in a manner that essentially parallels their construction in terms of self‐dual complex 2‐forms. It is shown that one can still discuss the Debever‐Penrose classification of the Riemannian curvature tensor in terms of the representation presented here.     

On the axioms of topological electromagnetism

The axioms of topological electromagnetism that were given by Hehl, Obukhov, and Rubilar are refined by the use of geometrical and topological notions that are found on orientable manifolds. The central problem of defining the spacetime electromagnetic constitutive law in terms of the geometrical and topological structure of the spacetime manifold is elaborated upon in the linear and nonlinear cases. The manner by which the spacetime metric might follow from the electromagnetic constitutive law is examined in the linear case. The possibility that the intersection form of the spacetime manifold might play a role in defining a topological basis for a nonlinear electromagnetic constitutive law is explored. The manner by which electromagnetic wave motion relates to the geometric structure is also discussed.     

Multiscale electromagnetic SERS enhancement on self‐assembled micropatterned gold nanoparticle films

In this work, we demonstrate a cascaded, multiplicative electromagnetic enhancement effect in surface‐enhanced Raman scattering (SERS) on periodically micropatterned films made of colloidal gold nanoparticles, prepared by a self‐assembly approach, without implying lithography procedures. The multiplicative enhancement effect is obtained by combining surface plasmon near‐field enhancement due to nanoscale features with far‐field photonic coupling by periodic microscale features. The effect is observed for both internal Raman reporters (molecules attached to the Au colloids before their assembly) and external Raman probes (molecules adsorbed on the samples after film assembly). The ability of the patterned films for far‐field light coupling is supported by reflectivity spectra, which present minima/maxima in the visible spectral range. Finite‐difference time‐domain computer simulations of the electric field distribution also support this interpretation. The fabricated dual‐scale SERS substrates exhibit a good spot‐to‐spot reproducibility and time stability, as proved by the SERS response over a time scale longer than 1 month. The experimental demonstration of this cascaded electromagnetic enhancement effect contributes to a better understanding of SERS and can affect future design of SERS substrates. Moreover, such dual‐scale colloidal films prepared by convective self‐assembly can be of general interest for the broader field of nanoparticle‐based devices. Copyright © 2014 John Wiley & Sons, Ltd.     

Transmission X‐ray scattering as a probe for complex liquid‐surface structures

The need for functional materials calls for increasing complexity in self‐assembly systems. As a result, the ability to probe both local structure and heterogeneities, such as phase‐coexistence and domain morphologies, has become increasingly important to controlling self‐assembly processes, including those at liquid surfaces. The traditional X‐ray scattering methods for liquid surfaces, such as specular reflectivity and grazing‐incidence diffraction, are not well suited to spatially resolving lateral heterogeneities due to large illuminated footprint. A possible alternative approach is to use scanning transmission X‐ray scattering to simultaneously probe local intermolecular structures and heterogeneous domain morphologies on liquid surfaces. To test the feasibility of this approach, transmission small‐ and wide‐angle X‐ray scattering (TSAXS/TWAXS) studies of Langmuir films formed on water meniscus against a vertically immersed hydrophilic Si substrate were recently carried out. First‐order diffraction rings were observed in TSAXS patterns from a monolayer of hexagonally packed gold nanoparticles and in TWAXS patterns from a monolayer of fluorinated fatty acids, both as a Langmuir monolayer on water meniscus and as a Langmuir–Blodgett monolayer on the substrate. The patterns taken at multiple spots have been analyzed to extract the shape of the meniscus surface and the ordered‐monolayer coverage as a function of spot position. These results, together with continual improvement in the brightness and spot size of X‐ray beams available at synchrotron facilities, support the possibility of using scanning‐probe TSAXS/TWAXS to characterize heterogeneous structures at liquid surfaces.     

A study on the spectral characteristics of surface enhanced Raman scattering based on far‐field extinction and near‐field electromagnetic field intensity of 2D nanostructures

A new solid‐state electrochemical patterning technique was applied to fabrication of high‐resolution silver bowtie antennas and hexagonal arrays. These silver nanofeatures were used to investigate the relation among surface enhanced Raman scattering (SERS) enhancement factor (EF), extinction, local electromagnetic (EM) field maxima of the features. It is found that spectral extinction property or the plasmonic resonance of a given SERS substrate alone is not sufficient for determining optimal EF; the number of points of high local EM field, or ‘hot spots’, and the distribution of those high‐field spots, too, play a role. Copyright © 2014 John Wiley & Sons, Ltd.     

Kinetics of pi‐complex isomerization during AlCl3‐catalyzed Friedel–Crafts reactions between linear olefins and p‐xylene

Rapid isomerization of pi‐complex intermediates results in the formation of multiple isomers of alkyl aromatics during AlCl₃‐catalyzed reactions between linear olefins and aromatic rings. The authors present results of a kinetic study of reactions between p‐xylene, 1‐dodecene, and linear tetradecenes. Product distributions are well predicted based on a model of reversible pi‐complex isomerization. Surprisingly, no double bond isomerization was observed in the linear olefins: All isomerization occurred in the pi‐complexes. Copyright © 2014 John Wiley & Sons, Ltd.     

Eigen electromagnetic waves of a coaxial waveguiding structure filled by a non‐uniform dissipative plasma with azimuthal magnetic field

This paper studies the propagation and spatial attenuation of high‐frequency eigen‐symmetric and dipolar electromagnetic waves along a coaxial plasma–metal waveguiding structure that contains a slightly axial and strong radial non‐uniform cylindrical plasma slab in an external azimuthal non‐uniform magnetic field. The influence of such parameters as the effective electron collision frequency, the direct current value producing the external azimuthal magnetic field, parameters that characterize plasma density radial profile, and waveguide geometric parameters on the dispersion, spatial attenuation, and radial field structure of the waves is considered. The regions of waveguiding structure parameters where the electromagnetic wave properties can be effectively controlled are studied and analyzed.     

On the pre‐metric foundations of wave mechanics I: massless waves

The mechanics of wave motion in a medium are founded in conservation laws for the physical quantities that the waves carry, combined with the constitutive laws of the medium, and define Lorentzian structures only in degenerate cases of the dispersion laws that follow from the field equations. It is suggested that the transition from wave motion to point motion is best factored into an intermediate step of extended matter motion, which then makes the dimension‐codimension duality of waves and trajectories a natural consequence of the bicharacteristic (geodesic) foliation associated with the dispersion law. This process is illustrated in the conventional case of quadratic dispersion laws, as well as quartic ones, which include the Heisenberg–Euler dispersion law. It is suggested that the contributions to geodesic motion from the non‐quadratic nature of a dispersion law might represent another source of quantum fluctuations about classical extremals, in addition to the diffraction effects that are left out by the geometrical optics approximation.     

Stereochemical control in the structures of linear δ,α‐hybrid tripeptides containing tetrahydrofuran amino acids

Structural and electronic properties of diastereomers of tetrahydrofuran amino acids (TAA) derived tripeptide, Boc‐TAA‐Leu‐Val‐OMe, are studied using density functional theory. Predicted secondary folding patterns with hydrogen bonded pseudocycles of different sizes in peptides containing (2R,5S)‐cis‐TAA and (2S,5R)‐cis‐TAA are confirmed by detailed NMR studies of both, and single crystal X‐ray analysis of the former. A novel unusual folding pattern emanating from three‐centered hydrogen bond is found in peptide with (2R,5S)‐cis relationship. Stereochemical control on the orientation of interacting sites is substantiated by structural analysis of the peptides. Using natural bonding orbital and atoms in molecules analyses, charge transfer interactions are analyzed. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of the non‐linear screening on a modification of the Debye–Hückel plus hole approximation in complex plasma

The authors analyse two‐component electroneutral systems of classical macroions of finite size and point‐like oppositely charged microions. This article deals with the modification of the Debye–Hückel plus hole approximation when a non‐linear screening effect is taken into account in a complex plasma. Parameters of non‐linear screening of the macroions by surrounding microions are calculated within the framework of the Poisson–Boltzmann approximation. Two effects are found as a result of such calculations: (a) subdivision of all microions into two subclasses, free microions and bound microions and (b) a significant reduction of an effective charge Z^* of the macroion in comparison with its true value Z due to the non‐linear screening by a thin high‐density envelope of the bound microions. We show that the value of a non‐ideal portion of an internal energy differs considerably in the case when the non‐linear screening effect is taken into account in the vicinity of the macroion.