A Functional LIL for <Emphasis Type="Italic">d</Emphasis>-Dimensional Stable Processes; Invariance for Lévy- and Other Weakly Convergent Processes

We establish a functional LIL for the maximal process M(t) :=sup _0≤s≤t ‖X(s)‖ of an ℝ ^d -valued α-stable Lévy process X, provided X(1) has density bounded away from zero over some neighborhood of the origin. We also provide a broad invariance result governing a class independent-increment processes related to the domain of attraction of X(1). This breadth is particularly notable for two types of processes captured: First, it not only describes any partial sum process built from iid summands in the domain of normal attraction of X(1), but also addresses those with arbitrary iid summands in the full domain of attraction (here we give a technical condition necessary and sufficient for the partial sum process to share the exact LIL we prove for X). Second, it reveals that any Lévy process L such that L(1) satisfies the technical condition just mentioned will also share the LIL of X. Supported in part by NSF Grant DMS 02-05034.     

Demand sensitivity to space-price competition with Manhattan and Euclidean representations of distance

This paper provides extensive evidence from a simulation model supporting our claim that it is not appropriate to use the Euclidean metric in a competitive system where the Manhattan metric would provide a more accurate representation of distances. The Euclidean metric has the property of biasing firms' demands by a distortion of their sensitivity to competitive strategies and, therefore, generates an excessive level of competition.     

Applications of location models

The degree to which locational complexity and geographical complexity is represented in a location model is a critical decision that influences the quality of the application. Criteria which can be used to guide these decisions are presented and research that would better inform these decisions is described.     

Predicted structure,thermo-mechanical properties and Li ion transport in LiAlF4 glass

Materials with the LiAlF₄ composition are of interest as protective electrode coatings in Li ion battery applications due to their high cationic conductivity. Here classical molecular dynamics calculations are used to produce amorphous model structures by simulating a quench from the molten state. These are analysed in terms of their individual pair correlation functions and atomic coordination environments. This indicates that amorphous LiAlF₄ is formed of a network of corner sharing AlF₆ octahedra. Li ions are distributed within this network, primarily associated with non-bridging fluorine atoms. The nature of the octahedral network is further analysed through intra‐ and interpolyhedral bond angle distributions and the relative populations of bridging and non-bridging fluorine ions are calculated. Network topology is considered through the use of ring statistics, which indicates that, although topologically well connected, LiAlF₄ contains an appreciable number of corner‐linked branch‐like AlF₆ chains. Thermal expansion values are determined above and below the predicted glass transition temperature of 1340 K. Finally, movement of Li ions within the network is examined with predictions of the mean squared displacements, diffusion coefficients and Li ion activation energy. Different regimes for lithium ion movement are identified, with both diffusive and sessile Li ions observed. For migrating ions, a typical trajectory is illustrated and discussed in terms of a hopping mechanism for Li transport.     

Palladium-mediated fragmentation reactions of meta photocycloadducts to afford arylated or oxidatively cyclised products

Whilst seeking to improve the yield of a Heck-style arylation/fragmentation reaction using a silyloxy substituted meta photocycloadduct, an alternative reaction pathway was discovered that led to the formation of the unique oxidatively cyclised compound 8. This tricyclic ether is believed to form as the result of the meta photocycloadduct structure fragmenting to give a π-allyl palladium species and then subsequently being displaced by a neighbouring hydroxyl group. An attempt to develop an enantioselective version of this reaction via the desymmetrisation of a meso π-allyl palladium intermediate was made using the meta photocycloadduct derived from anisole and Z-but-2-ene-1,4-diol, however no enantioenrichment of the products could be detected.     

The slow motion of two spherical particles along their line of centres

The motion of spherical, solid particles, liquid droplets or gas bubbles along their line of centres is considered. Conditions are limited to quasi-steady creeping flow and results are presented for drag coefficients and streamlines in these systems. Various interactions between two particles are reviewed and applications to gravity settling and droplet coalescence discussed.     

Partial ordering of glass networks adjacent to simulated glass–crystal interfaces

Interfaces between sodium lithium borosilicate glasses and the (100) and (110) surfaces of MgO and CaO crystals were simulated using a melt-quench procedure, employing classical pair potentials and molecular dynamics. The density of network forming species within the glass at these interfaces was considered as a function of distance from the plane of the interface and the positions of network formers were calculated in relation to sites in the crystal surface.For each interface, a strong correlation was found between the position and orientation of borate and silicate coordination polyhedra within the glass and particular positions of ions in the crystal surface, indicating that different partial ordering of the glass had occurred. In addition, examination of oxygen density profiles revealed a sequence of consistently spaced layers of increased density extending into the glass for all interfacial systems.