Quenched Free Energy and Large Deviations for Random Walks in Random Potentials

We study quenched distributions on random walks in a random potential on integer lattices of arbitrary dimension and with an arbitrary finite set of admissible steps. The potential can be unbounded and can depend on a few steps of the walk. Directed, undirected, and stretched polymers, as well as random walk in random environment, are covered. The restriction needed is on the moment of the potential, in relation to the degree of mixing of the ergodic environment. We derive two variational formulas for the limiting quenched free energy and prove a process‐level quenched large deviation principle (LDP) for the empirical measure. As a corollary we obtain LDPs for types of random walks in random environments not covered by earlier results. © 2012 Wiley Periodicals, Inc.     

An easy way to prepare pressurized glass inserts for MAS rotors

A novel technique to prepare pressurized glass insert samples for MAS rotors is described. In this technique, a small drop of epoxy is added to the tip of a piston and the gas is squeezed into the insert by pressing the piston. The amount of gas, i.e., pressure, in the sample can be controlled by the overall length of an insert test tube. As examples, (129)Xe NMR spectra taken from samples containing xenon gas, xenon gas and liquid crystal, and xenon gas, liquid crystal and porous solid, are shown. In principle, the method is feasible for making any kind of samples into glass inserts.     

An empirical constitutive model for complex glass-forming liquids using bitumen as a model material

While extensive research efforts have been devoted to understand the dynamics of chemically and structurally simple glass-forming liquids (SGFLs), the viscoelasticity of chemically and structurally complex glass-forming liquids (CGFLs) has received only little attention. This study explores the rheological properties of CGFLs in the vicinity of the glass transition. Bitumen is selected as the model material for CGFLs due to its extremely complex chemical composition and microstructure, fast physical aging and thermorheological simplicity, and abundant availability. A comprehensive rheological analysis reveals a significant broadening of the glass transition dynamics in bitumen as compared to SGFLs. In particular, the relaxation time spectrum of bitumen is characterized by a broad distribution of long relaxation modes. This observation leads to the development of a new constitutive equation, named the broadened power-law spectrum model. In this model, the wide distribution of long relaxation times is described by a power-law with positive exponent and a stretched exponential cut-off, with parameter β serving as a measure of the broadness of the distribution. This characteristic shape of the bitumen spectrum is attributed to the heterogeneous freezing of different molecular components of bitumen, i.e., to the coexistence of liquid and glassy micro-phases. Furthermore, as this type of heterogeneous glass transition behavior can be considered as a general feature of complex glass-forming systems, the broadened power-law spectrum model is expected to be valid for all types of CGFLs. Examples of the applicability of this model in various complex glass-forming systems are given.     

Violation of the Wiedemann-Franz law in a single-electron transistor

We study the influence of Coulomb interaction on the thermoelectric transport coefficients for a metallic single-electron transistor. By performing a perturbation expansion up to second order in the tunnel-barrier conductance, we include sequential and cotunneling processes as well as quantum fluctuations that renormalize the charging energy and the tunnel conductance. We find that Coulomb interaction leads to a strong violation of the Wiedemann-Franz law: the Lorenz ratio becomes gate-voltage dependent for sequential tunneling, and is increased by a factor 9/5 in the cotunneling regime. Finally, we suggest a measurement scheme for an experimental realization.     

Copolymerisation properties of siloxy‐substituted bis(indenyl)zirconocene catalysts: modified rheological behaviour

The combination of the copolymerisation ability and vinyl end group selectivity of siloxy substitution of ethylene‐bridged bis(indenyl)zirconium dichlorides suggest these catalyst as potential ones for the production of polyethylene containing small amounts of long chain branching. The role of the polymerisation conditions with these highly active catalysts can clearly be seen. Furthermore low contents of multiple branches may occur, even though the probability of attaching several macromonomers into one chain is low. The effect on melt rheological behaviour depends on both the amount of long chain branching and the length of the branch. Moreover the position of the siloxy group is very important. Polymers synthesized with catalysts, where the siloxy group is in position 1, give peculiar rheological behaviour resembling cross‐linked networks although the polymers are completely soluble.     

On the Significance of the Initial Solution in Travelling Salesman Heuristics

The quality requirements set by edge exchange heuristics on their initial solutions are evaluated in connection with the travelling salesman problem. The performance of the heuristics is measured using the expected value of the best solution achievable in a certain computing time. The computational results show that the use of initial solutions generated by applying a construction heuristic, instead of random initial solutions, typically improves the performance of edge exchange heuristics. The improvement, however, is dependent on the edge exchange heuristic to be used, the properties of the problem, and the computing time available.     

Comparison between measured and simulated magnetocardiograms in a case of anterolateral myocardial infarction

Summary The MCGs measured in a case of an anterolateral myocardial infarction were compared with the corresponding simulated MCGs. The most distinctive changes in the measured MCGs were observed in the upper and lower parts of the thorax as predicted by the simulation. Paper presented at the ?IV International Workshop on Biomagnetism?, held in Rome, September 14–16, 1982.