Bounded imaginary powers of differential operators on manifolds with conical singularities

 We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted L _p -spaces over B, 1<p<∞. Under suitable ellipticity assumptions we can define a family of complex powers A ^z , zℂ. We also obtain sufficient information on the resolvent of A to show the boundedness of the purely imaginary powers. Examples concern unique solvability and maximal regularity for the solution of the Cauchy problem for the Laplacian on conical manifolds as well as certain quasilinear diffusion equations. Received: 12 June 2001; in final form: 3 June 2002 / Published online: 1 April 2003 Mathematics Subject Classification (2000): 35J70, 47A10, 35K57     

Complex morphology of melt-spun nylon-6 fibres investigated by 1H double-quantum-filtered NMR spin-diffusion experiments.

The complex morphology of high-speed melt-spun nylon-6 fibres hydrated with D2O was investigated using 1H double-quantum-filtered spin-diffusion NMR experiments. The magnetisation exchange from selected crystalline domains along the fibrils and interfibrils was simulated with the help of a three-dimensional solution of a spin-diffusion equation approximated by a product of one-dimensional analytical NMR signals, which correspond to a lamellar morphology. This allows to measure the sizes of crystalline and less-mobile amorphous domains along the fibrils, as well as the diameter of the fibrils and interfibril distances. A series of nylon-6 fibres with extreme values of winding speed and draw ratio was investigated. The changes detected in the domain size along the fibrils and interfibrils show the same trend in the data obtained from wide-angle X-ray diffraction and small-angle X-ray scattering.     

Inside Front Cover: Three‐Dimensionally Ordered Gold Nanocrystal/Silica Superlattice Thin Films Synthesized via Sol–Gel Self‐Assembly (Adv. Funct. Mater. 7/2006)

The synthesis of three‐dimensionally ordered, transparent gold‐nanocrystal (NC)/silica superlattice thin films using the self‐assembly (by spin‐coating) of water‐soluble gold nanocrystal micelles and soluble silica is reported by Fan and co‐workers on p. 891. The robust, 3D NC/silica superlattice films are of interest for the development of collective optical and electronic phenomena, and, importantly, for the integration of NC arrays into device architectures. Nanocrystals and their ordered arrays hold many important applications in fields such as catalysis, surface‐enhanced Raman spectroscopy based sensors, memory storage, and electronic and optical nanodevices. Herein, a simple and general method to synthesize ordered, three‐dimensional, transparent gold nanocrystal/silica superlattice thin films by self‐assembly of gold nanocrystal micelles with silica or organosilsesquioxane by spin‐coating is reported. The self‐assembly process is conducted under acidic sol–gel conditions (ca. pH 2), ensuring spin‐solution homogeneity and stability and facilitating the formation of ordered and transparent gold nanocrystal/silica films. The monodisperse nanocrystals are organized within inorganic host matrices as a face‐centered cubic mesostructure, and characterized by transmission electron spectroscopy and X‐ray diffraction.     

Immune-Inspired Adaptable Error Detection for Automated Teller Machines

This paper presents an immune-inspired adaptable error detection (AED) framework for automated teller machines (ATMs). This framework has two levels: one is local to a single ATM, while the other is network-wide. The framework employs vaccination and adaptability analogies of the immune system. For discriminating between normal and erroneous states, an immune-inspired one-class supervised algorithm was employed, which supports continual learning and adaptation. The effectiveness of the proposed approach was confirmed in terms of classification performance and impact on availability. The overall results are encouraging as the downtime of ATMs can de reduced by anticipating the occurrence of failures before they actually occur.     

Secure vehicular communication systems: implementation, performance, and research challenges

Vehicular communication systems are on the verge of practical deployment. Nonetheless, their security and privacy protection is one of the problems that have been addressed only recently. In order to show the feasibility of secure VC, certain implementations are required. In [1] we discuss the design of a VC security system that has emerged as a result of the European SeVe- Com project. In this second article we discuss various issues related to the implementation and deployment aspects of secure VC systems. Moreover, we provide an outlook on open security research issues that will arise as VC systems develop from today?s simple prototypes to fullfledged systems.     

Dense amorphous packing of binary hard sphere mixtures with chemical order: The stability of a solute ordered approximant

Recently, Miracle proposed that the intermediate structure in metallic glasses could be usefully characterized as an ordered face centered cubic packing of solute-centered coordination clusters. In this paper we examine the stability of such solute ordered arrangements in binary hard sphere mixtures subject to density maximization through local particle moves.     

MgO films grown on yttria-stabilized zirconia by molecular beam epitaxy

MgO films were grown on (0 0 1) yttria-stabilized zirconia (YSZ) substrates by molecular beam epitaxy (MBE). The crystalline structures of these films were investigated using X-ray diffraction and transmission electron microscopy. Growth temperature was varied from 350 to 550 °C, with crystalline quality being improved at higher temperatures. The MgO films had a domain structure: (1 1 1)[1 1 2¯]_MgO(0 0 1)[1 0 0]_YSZ with four twin variants related by a 90° in-plane rotation about the [1 1 1]_MgO axis. The observed epitaxial orientation was compared to previous reports of films grown by pulsed laser deposition and sputtering and explained as resulting in the lowest interface energy.     

Predicting the onset of DNA supercoiling using a non-linear hemitropic elastic rod

Elastic rod models provide a means to interpret single molecule DNA experiments as well as predict DNA behavior under physiological conditions. Here we use an elastic rod model to predict the stability boundary (critical torque vs. applied tension) for single molecule DNA experiments in which the molecule is subjected to applied tension and twist. We discuss the shortcomings of the usual isotropic rod model. We then derive a consistent non-linear material law from the general representation for a hemitropic (chiral) rod. Finally, we present results of a standard bifurcation analysis predicting the stability boundary. We find results from the non-linear hemitropic rod to match the data closely.     

Ductile–brittle transitions in the fracture of plastically deforming,adhesively bonded structures. Part II: Numerical studies

To enable the effective and reliable use of structural adhesive bonding in automotive applications, the cohesive properties of a joint need to be determined over a wide range of loading rates. In this paper, a strategy for determining these properties has been described and used to analyze a set of experimental results presented in a companion paper. In the particular system studied, a crack growing in a toughened quasi-static mode could make a catastrophic transition to a brittle mode of fracture. The cohesive parameters for both the toughened and brittle modes of crack growth were determined by comparing numerical predictions from cohesive-zone simulations to the results of experimental tests performed using double-cantilever beam specimens and tensile tests. The cohesive parameters were found to be essentially rate-independent for the toughened mode, but the toughness dropped by a factor of four upon a transition to the brittle mode. The results of wedge tests were used as an independent verification of the cohesive parameters, and to verify that the quasi-static properties remained rate-independent to very high crack velocities corresponding to conditions of low-velocity impact. The effects of friction, and the use of the wedge test to determine cohesive parameters, were also explored.     

Approximation of transient temperatures in complex geometries using fractional derivatives

It is shown that time-dependent temperatures in a transient, conductive system can be approximately modeled by a fractional-order differential equation, the order of which depends on the Biot number. This approximation is particularly suitable for complex shapes for which a first-principles approach is too difficult or computationally time-consuming. Analytical solutions of these equations can be written in terms of the Mittag-Leffler function. The approximation is especially useful if a suitable fractional-order controller is to be designed for the system.