Quantum Transport. Introduction to Nanoscience,by Y.V. Nazarov and Y.M. Blanter

A brief review of the interstellar medium and its instabilities is given with particular emphasis to recent results on its “two-phase” nature. The existing models (both numerical and analytic) of the collapse of gas clouds to form stars are discussed; this discussion is divided into the optically thin and thick phases. Finally some aspects of the observations of young stars are considered.     

ESR and Theoretical Studies of Bis-Benzene-1, 2-Diselenolate Nickel and Related Complexes

Abstract

ESR and theoretical studies of the transition metal complexes of [Co and Ni (Se₂C₆H₄)₂]^? (n-C₄H₉)₄N⁺ are reported and compared with closely related systems. Room temperature single crystal X-ray studies reveal the Nickel complex is orthorhombic. ESR studies of the polycrystalline powders of the Ni complex as a function of temperature from 108 K to room temperature show a series of spectral envelopes which can arise only from a paramagnetic site which possesses axial symmetry. At ca 160 K, there is an abrupt change in the value of the principal components of the anisotropic g-tensor of the Ni complex which is discussed. Low temperature ESR studies of polycrystalline samples of the ground state triplet Cobalt complex which is isomorphous with the Nickel complex reveal an orthorhombic g-tensor. From the field position of the half-field resonance, it is possible to calculate a mean separation, of the two electrons which make up the triplet state, of 4.3 (±0.5) A.     

Conductivity and Optical Properties of a Polyiodine Canal Complex (Benzophenone)9(KI)2I7, CHCl3

Abstract

(Benzophenone)₉(KI)₂I₇, CHCl₃ single crystals have a golden metallic reflection on the surfaces parallel to the polyiodine chain axis. The compound is a member of a large class of channel-like inclusion compounds in which isolated iodine atom chains are the only possible conducting strands in an otherwise insulating matrix. The (contactless) microwave conductivity is ～ 10 Ω^?1 cm^?1 at room temperature with an activation energy of ～0.03 eV down to 70°K, while the dc conductivity is ～10^?-⁶. Conductivity is strongly frequency dependent and contact problems are severe.     

Nematic Liquid Crystals with a Trifluoromethyl Group

Abstract

We have synthesised a new class of compounds incorporating a trifluoromethyl group in the terminal alkoxy or alkenyloxy chain. Compounds containing several aromatic rings were synthesised with a view to producing compounds of high birefringence. This also included the synthesis of compounds containing a carbon-carbon triple bond. Compounds with three 1,4-disubstituted rings were synthesised in order to produce materials with a high nematic clearing point and as low a melting point as possible. Laterally fluoro-substituted compounds were prepared to generate a high positive value of the dielectric anisotropy, a low melting point and no smectic mesophases. Substances containing a cyclohexyl ring, which tend to induce a lower viscosity and compounds incorporating a bicyclo[2.2.2]octane ring were also synthesised in order to produce a high nematic clearing point and to influence the elastic constants. The (E)-trifluorobut-2-enyloxy-compounds were prepared in attempts to produce compounds with appropriate elastic constants and a high birefringence.     

On lattices of varieties of restriction semigroups

The left restriction semigroups have arisen in a number of contexts, one being as the abstract characterization of semigroups of partial maps, another as the ‘weakly left E-ample’ semigroups of the ‘York school’, and, more recently as a variety of unary semigroups defined by a set of simple identities. We initiate a study of the lattice of varieties of such semigroups and, in parallel, of their two-sided versions, the restriction semigroups. Although at the very bottom of the respective lattices the behaviour is akin to that of varieties of inverse semigroups, more interesting features are soon found in the minimal varieties that do not consist of semilattices of monoids, associated with certain ‘forbidden’ semigroups. There are two such in the one-sided case, three in the two-sided case. Also of interest in the one-sided case are the varieties consisting of unions of monoids, far indeed from any analogue for inverse semigroups. In a sequel, the author will show, in the two-sided case, that some rather surprising behavior is observed at the next ‘level’ of the lattice of varieties.     

A diagrammatic view of the equals sign: arithmetical equivalence as a means,not an end

It is recommended in the mathematics education literature that pupils be presented with equality statements that can be assessed for numerical balance by attending to notational structure rather than computation. I describe an alternative, diagrammatic approach in which pupils do not assess statements but instead use them to make substitutions of notation. I report on two trials of a computer-based task conducted with pairs of pupils and highlight two findings. First, the pupils found it useful to articulate the distinct substitutive effects of commutative (‘swap’, ‘switch’) and partitional (‘split’, ‘separate’) statements when working on the task. Secondly, the pupils did not notice that some of the statements presented were in fact false, which suggests their substituting activities were independent of numerical equivalence conceptions. This demonstrates that making substitutions offers task designers a mathematical utility for equality statements that is distinct from, but complementary to, assessing numerical balance.     

On Modular Edge-Graceful Graphs

Let G be a connected graph of order \({n\ge 3}\) and size m and \({f:E(G)\to \mathbb{Z}_n}\) an edge labeling of G. Define a vertex labeling \({f': V(G)\to \mathbb{Z}_n}\) by \({f'(v)= \sum_{u\in N(v)}f(uv)}\) where the sum is computed in \({\mathbb{Z}_n}\) . If f′ is one-to-one, then f is called a modular edge-graceful labeling and G is a modular edge-graceful graph. A graph G is modular edge-graceful if G contains a modular edge-graceful spanning tree. Several classes of modular edge-graceful trees are determined. For a tree T of order n where \({n\not\equiv 2 \pmod 4}\) , it is shown that if T contains at most two even vertices or the set of even vertices of T induces a path, then T is modular edge-graceful. It is also shown that every tree of order n where \({n\not\equiv 2\pmod 4}\) having diameter at most 5 is modular edge-graceful.     

Electron channelling contrast imaging of dislocations in a conventional SEM

Abstract

Dislocations in shock loaded tantalum single crystals were imaged using both transmission electron microscope (TEM) and electron channelling contrast image (ECCI) in a scanning electron microscope with a conventional backscattered electron detector. The results were compared with backscattered electron intensity profiles across dislocations calculated via the dynamic theory of electron diffraction. A one-to-one correspondence between ECCI and TEM is established. High voltage and low index reflections should be used to obtain the highest dislocation contrast and greatest imaging depth.     

Intermediate temperature creep mechanisms in Ni 3 Al

The intermediate-temperature creep response of single-crystal Ni 3 Al(Ta) has been investigated along both [ ] and [001] axial orientations. The effect of the existing deformation structure (i.e. pre-straining) on the [ ] creep response was reported. The creep responses of virgin specimens and specimens prestrained at room temperature (RT) and 520°C are compared. In order to compare the dislocation structures prior to creep, the microstructure of specimens which had been deformed at a constant strain rate at RT and 520°C, but not subjected to creep, was also examined. Creep curves show that the temperature of pre-strain influences the subsequent creep properties. The primary creep response, like the yielding response, appears to be controlled by the kink size distribution, while the secondary creep response is thought to be controlled by the kink separation (or the length of the Kear-Wilsdorf locks). Specimens crept along [ ] display steady state creep properties and rectangularly oriented [ ](010) dislocations, while a virgin specimen crept along [001] displays an increasing secondary creep rate (inverse creep) and d110 ¢{100}-type dislocations. Inverse creep along [001] is thought to be the result of an increasing density of edge kink octahedral sources where there is little resolved shear stress on the cube planes.