Localised systems

In the first place, we have been studying those parts of the theory of the electronic structure of molecules which bear on a theory of valence. That is we are not attempting to present a theory of molecular electronic structure, but an approximate theory of valence. The latter is but a small part of the former. In particular we are (in the main) concerned with localised systems of electrons in their ground states the theory... 

Y. E. Perlin and M. H. L. Wagner, The Dynamical John—Teller Effect in Localised Systems, North Holland, Amsterdam, 1984. 

On the other hand, the localised system must use simplified models, because the localised system uses a small-scale computer or minicomputer from the viewpoint of cost-effectiveness. Therefore, the major characteristics of the localised system are the low cost and the high-speed response. 

In this cavity model the atom is confined at the centre of a spherical box, of finite radius R, with an impenetrable wall. This is, of course, a highly idealised model and its limitations were clearly recognised [3]. However, as pointed out in Fowler s extensive work on confined 1-electron problems [6], it does serve as a framework for discussing properties of localised systems. 

The Accident Localisation System was designed around most of the primary circuit... 

In most European national jurisdictions (including Sweden, France, and the Netherlands), occupational health and safety standards are enforced by unitary labour inspectorates that fall within the responsibilities of State Departments of Employment or their equivalent (Cunningham and Johnstone 1999 378-379 Walters 1996 302-303 Walters et al. 2011). Some jurisdictions, such as Spain and Italy, utilise localised systems of regulation, while Cermany divides this... 

LDA Location Dependent Addressing)—voice communication with railway employees fulfilling certain operational functions which is changing in relation to train localisation or dedicated calling area. Location is mainly defined by cellular identity however to ensure better location dependent addressing additional information can be used as on-board localisation systems, trackside information e.g. from ETCS balises or other fixed installation,... 

The eombination in a compact system of an infrared sensor and a laser as excitation source is called a photothermal camera. The surface heating is aehieved by the absorption of the focused beam of a laser. This localisation of the heating permits a three-dimensional heat diffusion in the sample to be examined. The infrared (IR) emission of the surface in the neighbourhood of the heating spot is measured by an infrared detector. A full surface inspection is possible through a video scanning of the excitation and detection spots on the piece to test (figure 1). 

Figure 4c illustrates interfacial polymerisation encapsulation processes in which the reactant(s) that polymerise to form the capsule shell is transported exclusively from the continuous phase of the system to the dispersed phase—continuous phase interface where polymerisation occurs and a capsule shell is produced. This type of encapsulation process has been carried out at Hquid—Hquid and soHd—Hquid interfaces. An example of the Hquid—Hquid case is the spontaneous polymerisation reaction of cyanoacrylate monomers at the water—solvent interface formed by dispersing water in a continuous solvent phase (14). The poly(alkyl cyanoacrylate) produced by this spontaneous reaction encapsulates the dispersed water droplets. An example of the soHd—Hquid process is where a core material is dispersed in aqueous media that contains a water-immiscible surfactant along with a controUed amount of surfactant. A water-immiscible monomer that polymerises by free-radical polymerisation is added to the system and free-radical polymerisation localised at the core material—aqueous phase interface is initiated thereby generating a capsule sheU (15). 

The activity of antioxidants in food [ 1 ] emulsions and in some biological systems [2] is depends on a multitude of factors including the localisation of the antioxidant in the different phases of the system. The aim of this study is determining antioxidant distributions in model food emulsions. For the purpose, we measured electrochemically the rate constant of hexadecylbenzenediazonium tetrafluorborate (16-ArN,BF ) with the antioxidant, and applied the pseudophase kinetic model to interpret the results. 

After each strong collision the system, having been localised in the left or right well, resumes free tunneling from the diagonal state. Thus, after N collisions the probability to survive in the left well is... 

The ohmic case is the most complex. A particular result is that the system is localised in one of the wells at T = 0, for sufficiently strong friction, viz. rj > nhjlQo. At higher temperatures there is an exponential relaxation with the rate Ink oc (4riQllnh — l)ln T. Of special interest is the special case t] = nhl4Ql. It turns out that the system exhibits exponential decay with a rate constant which does not depend at all on temperature, and equals k = nAl/2co. Comparing this with (2.37), one sees that the collision frequency turns out to be precisely equal to the cutoff vibration frequency Vo = cojln. 

So, despite the very small diameter of the MWCNT with respeet to the de Broglie wavelengths of the charge carriers, the cylindrical structure of the honeycomb lattice gives rise to a 2D electron gas for both weak localisation and UCF effects. Indeed, both the amplitude and the temperature dependence of the conductance fluctuations were found to be consistent with the universal conductance fluctuations models for mesoscopic 2D systems applied to the particular cylindrical structure of MWCNTs [10]. 

In conclusion, wc have shown the interesting information which one can get from electrical resistivity measurements on SWCNT and MWCNT and the exciting applications which can be derived. MWCNTs behave as an ultimate carbon fibre revealing specific 2D quantum transport features at low temperatures weak localisation and universal conductance fluctuations. SWCNTs behave as pure quantum wires which, if limited in length, reduce to quantum dots. Thus, each type of CNT has its own features which are strongly dependent on the dimensionality of the electronic gas. We have also briefly discussed the very recent experimental results obtained on the thermopower of SWCNT bundles and the effect of intercalation on the electrical resistivity of these systems. 

The SSW form an ideal expansion set as their shape is determined by the crystal structure. Hence only a few are required. This expansion can be formulated in both real and reciprocal space, which should make the method applicable to non periodic systems. When formulated in real space all the matrix multiplications and inversions become 0(N). This makes the method comparably fast for cells large than the localisation length of the SSW. In addition once the expansion is made, Poisson s equation can be solved exactly, and the integrals over the intersitital region can be calculated exactly. 

Although corrosion is due to the thermodynamic instability of a metal in a specific environment, and although in many metal/environment systems attack will tend to be uniform, there are a variety of factors associated with the metal, the environment and the geometry of the system that may result in the attack being localised. 

Unfortunately, there is no general theory that will explain all the forms of localised attack that occur with the variety of metal/environment systems encountered in practice, e.g. the mechanism of the pitting of stainless steels in Cl -containing solutions is quite different from the dezincification of brass in a fresh natural water. Nevertheless, many of the following factors play an important part in most forms of localised attack ... 

A similar effect can be produced if a crevice is present in the steel, since the geometry of the system is such that whereas oxygen can diffuse readily to the metal surface outside the crevice it can only gain access to the metal within the crevice through its very narrow mouth (Fig. 1 A6d), and the large cathode anode area ratio leads to localised attack of the metal within the crevice. 

The majority of the different types of localised attack dealt with in this section occur in near-neutral solutions containing dissolved oxygen, and the pH changes that occur at the anodic and cathodic sites are of fundamental importance when the reaction products are prevented from mixing by the geometry of the system. 

This form of attack, especially as affecting copper alloys in sea water, has been widely studied since the pioneer work of Bengough and May . Impingement attack of sea water pipe and heat exchanger systems is considered in Sections 1.6 and 4.2. In such engineering systems the water flow is invariably turbulent and the thickness of the laminar boundary layer is an important factor in controlling localised corrosion. 

---