Gate‐Induced Modification of Water Adsorption on Dielectrics Probed by EFM and Carbon Nanotube FETs

Humidity plays an important role in molecular electronics. It facilitates charge movement on top of dielectric layers and modifies the device transfer characteristics. Using two different methods to probe temporal charge redistribution on the surface of dielectrics, we were able to extract the surface humidity for the first time. The first method is based on the relaxation time constants of the current through carbon nanotube field‐effect transistors (CNTFETs), and the second is based on electric force microscopy (EFM) measurements. Moreover, we found that applying external gate biases modifies the surface humidity. A theoretical model based on dielectrophoretic attraction between the water molecules and the substrate is introduced to explain this observation, and the results support our hypothesis. Furthermore, it is found that upon the adsorption of two to three layers of water the surface conductivity saturates.     

Chelating alkylidene ligands as pacifiers for ruthenium catalysed olefin metathesis

Olefin metathesis catalysed by ruthenium has emerged at the frontier of modern synthetic chemistry. The desire to enhance catalyst stability, gain control over the catalytic process and deepen the understanding of the mechanisms of metathesis has yielded a class of latent ruthenium precatalysts of delayed initiation and with switchable activity. One of the main methodologies developed for this purpose has been the introduction of tethered carbene ligands. Herein we track the evolution of ruthenium based metathesis catalysts bearing chelated alkylidenes, from the early oxygen Hoveyda type benzylidenes to the latent sulphur containing complexes.     

Convolutions of cantor measures without resonance

Denote by µ _a the distribution of the random sum \((1 - a)\sum\nolimits_{j = 0}^\infty {{w_j}{a^j}} \), where P(ω _j = 0) = P(ω _j = 1) = 1/2 and all the choices are independent. For 0 < a < 1/2, the measure µ _a is supported on C _a , the central Cantor set obtained by starting with the closed united interval, removing an open central interval of length (1 ? 2a), and iterating this process inductively on each of the remaining intervals. We investigate the convolutions µ _a * (µ _b ° S _λ ^?1 ), where S _λ (x) = λx is a rescaling map. We prove that if the ratio log b/ log a is irrational and λ ≠ 0, then

$D({\mu _a} * ({\mu _b} \circ S_\lambda ^{ - 1})) = \min ({\dim _H}({C_a}) + {\dim _H}({C_b}),1)$

, where D denotes any of correlation, Hausdorff or packing dimension of a measure.

We also show that, perhaps surprisingly, for uncountably many values of λ the convolution µ_1/4* (µ_1/3 ° S _λ ^?1 ) is a singular measure, although dim _H (C _1/4) + dim _H (C _1/3) > 1 and log(1/3)/ log(1/4) is irrational.     

On the transformation toughening of a crack along an interface between a shape memory alloy and an isotropic medium

In this study, a bilinear cohesive zone model is employed to describe the transformation toughening behavior of a slowly propagating crack along an interface between a shape memory alloy and a linear elastic or elasto-plastic isotropic material. Small scale transformation zones and plane strain conditions are assumed. The crack growth is numerically simulated within a finite element scheme and its transformation toughening is obtained by means of resistance curves. It is found that the choice of the cohesive strength t₀ and the stress intensity factor phase angle φ greatly influence the toughening behavior of the bimaterial. The presented methodology is generalized for the case of an interface crack between a fiber reinforced shape memory alloy composite and a linear elastic, isotropic material. The effect of the cohesive strength t₀, as well as the fiber volume fraction are examined.     

A dimension gap for continued fractions with independent digits

Kinney and Pitcher (1966) determined the dimension of measures on [0, 1] which make the digits in the continued fraction expansion i.i.d. variables. From their formula it is not clear that these dimensions are less than 1, but this follows from the thermodynamic formalism for the Gauss map developed by Walters (1978). We prove that, in fact, these dimensions are bounded by 1−10⁻⁷. More generally, we considerf-expansions with a corresponding absolutely continuous measureμ under which the digits form a stationary process. Denote byE _δ the set of reals where the asymptotic frequency of some digit in thef-expansion differs by at leastδ from the frequency prescribed byμ. ThenE _δ has Hausdorff dimension less than 1 for anyδ>0.     

Elimination of infinities in equivalent edge currents, part I: Fringe current components

New expressions are derived for the fringe current components of the equivalent edge currents. They are obtained by asymptotic endpoint evaluation of the fringe current radiation integral over the "ray coordinate" measured along the diffracted ray grazing the surface of the local wedge. The resulting expressions, unlike the previous ones, are finite for all aspects of illumination and observation, except for the special case where the direction of observation is the continuation of a glancing incident ray propagating "inwards" with respect to the wedge surface (the Ufimtsev singularity).     

The number of infinite clusters in dynamical percolation

Summary. Dynamical percolation is a Markov process on the space of subgraphs of a given graph, that has the usual percolation measure as its stationary distribution. In previous work with O. H?ggstr?m, we found conditions for existence of infinite clusters at exceptional times. Here we show that for ℤ ^d , with p>p _c , a.s. simultaneously for all times there is a unique infinite cluster, and the density of this cluster is θ(p). For dynamical percolation on a general tree Γ, we show that for p>p _c , a.s. there are infinitely many infinite clusters at all times. At the critical value p=p _c , the number of infinite clusters may vary, and exhibits surprisingly rich behaviour. For spherically symmetric trees, we find the Hausdorff dimension of the set T ^k of times where the number of infinite clusters is k, and obtain sharp capacity criteria for a given time set to intersect T ^k . The proof of this capacity criterion is based on a new kernel truncation technique. Received: 5 May 1997 / In revised form: 24 November 1997     

On the Hausdorff dimension of fibres

It is well known that there are planar sets of Hausdorff dimension greater than 1 which are graphs of functions, i.e., all their vertical fibres consist of 1 point. We show this phenomenon does not occur for sets constructed in a certain “regular” fashion. Specifically, we consider sets obtained by partitioning a square into 4 subsquares, discarding 1 of them and repeating this on each of the 3 remaining squares, etc.; then almost all vertical fibres of a set so obtained have Hausdorff dimension at least 1/2. Sharp bounds on the dimensions of sets of exceptional fibres are presented. Partially supported by a grant from the Landau Centre for Mathematical Analysis.     

Contribution of a single face to the wedge diffracted field

In certain wedge diffraction problems, it is advantageous to know the part of the diffracted field created by the currents induced on a single face of the wedge. The rigorous solution to the corresponding canonical problem is derived. This solution indicates which part of the uniform theory of diffraction (UTD) solution for the wedge-diffracted field should be taken to describe its single-face component.