Random graph asymptotics on high-dimensional tori. II. Volume, diameter and mixing time

For critical bond-percolation on high-dimensional torus, this paper proves sharp lower bounds on the size of the largest cluster, removing a logarithmic correction in the lower bound in Heydenreich and van der Hofstad (2007). This improvement finally settles a conjecture by Aizenman (1997) about the role of boundary conditions in critical high-dimensional percolation, and it is a key step in deriving further properties of critical percolation on the torus. Indeed, a criterion of Nachmias and Peres (2008) implies appropriate bounds on diameter and mixing time of the largest clusters. We further prove that the volume bounds apply also to any finite number of the largest clusters. The main conclusion of the paper is that the behavior of critical percolation on the high-dimensional torus is the same as for critical Erdos-Renyi random graphs. In this updated version we incorporate an erratum to be published in a forthcoming issue of Probab. Theory Relat. Fields. This results in a modification of Theorem 1.2 as well as Proposition 3.1.Comment: 16 pages. v4 incorporates an erratum to be published in a forthcoming issue of Probab. Theory Relat. Field

Anomalous Crossing Frequency in Odd Proton Nuclei

A generic explanation for the recently observed anomalous crossing frequencies in odd proton rare earth nuclei is given. As an example, the proton ${1\over 2} [541]$ band in $^{175}$Ta is discussed in detail by using the angular momentum projection theory. It is shown that the quadrupole pairing interaction is decisive in delaying the crossing point and the changes in crossing frequency along the isotope chain are due to the different neutron shell fillings

Nuclear pairing and Coriolis effects in proton emitters

We introduce a Hartree-Fock-Bogoliubov mean-field approach to treat the problem of proton emission from a deformed nucleus. By substituting a rigid rotor in a particle-rotor-model with a mean-field we obtain a better description of experimental data in $^{141}$Ho. The approach also elucidates the softening of kinematic coupling between particle and collective rotation, the Coriolis attenuation problem.Comment: 2 pages, 1 figur

The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion

For independent nearest-neighbour bond percolation on Z^d with d >> 6, we prove that the incipient infinite cluster's two-point function and three-point function converge to those of integrated super-Brownian excursion (ISE) in the scaling limit. The proof is based on an extension of the new expansion for percolation derived in a previous paper, and involves treating the magnetic field as a complex variable. A special case of our result for the two-point function implies that the probability that the cluster of the origin consists of n sites, at the critical point, is given by a multiple of n^{-3/2}, plus an error term of order n^{-3/2-\epsilon} with \epsilon >0. This is a strong statement that the critical exponent delta is given by delta =2.Comment: 56 pages, 3 Postscript figures, in AMS-LaTeX, with graphicx, epic, and xr package

Feeding behaviour and appetite in young children with non-organic failure to thrive

The study reported in this thesis was aimed at investigating taste preferences and caloric compensation in one to two year old children with non-organic failure to thrive (FTT) as compared to normally developing children of the same age. The sample studied included 28 cases with non-organic FTT, and 28 controls with normal growth. The study comprised two experiments. The first tested the child's relative preference for sucrose sweetened solutions versus water. The test session included six 60 second presentations of tastant at three levels of concentration n i.e. water, 0.2 Mol sucrose solution, and 0.4 Mol sucrose solution, with at least 30 second intervals between presentations. The second experiment measured caloric compensation, by testing the child's intake from a standard meal on two occasions, after a pre-load of no-calorie or high-calorie drink. In addition meal time behavioural observations were made, and information about the child’s feeding history was obtained from parent reports. All children regardless of whether they were failing to thrive or not preferred 0.2 Mol sucrose solution to 0.4 Mol sucrose and to water. The energy intake of children with FTT was lower than that of controls, and meal-time behaviours showed some differences between groups in both the child and parent behaviours. Unlike the controls the FTT children showed no caloric compensation, but showed a trend towards the opposite of compensation. Analysis of growth data showed that FTT in the sample studied was present from birth

Angular dependence of Josephson currents in unconventional superconducting junctions

Josephson effect in junctions between unconventional superconductors is studied theoretically within the model describing the effects of interface roughness. The particularly important issue of applicability of the frequently used Sigrist-Rice formula for Josephson current in d-wave superconductor / insulator / d-wave superconductor junctions is addressed. We show that although the SR formula is not applicable in the ballistic case, it works well for rough interfaces when the diffusive normal metal regions exist between the d-wave superconductor and the insulator. It is shown that the SR approach only takes into account the component of the d-wave pair potential symmetric with respect to an inversion around the plane perpendicular to the interface. Similar formula can be derived for general unconventional superconductors with arbitrary angular momentum l.Comment: 4 pages, 4 figure

Strong optical force induced by morphology dependent resonances

We consider the resonant optical force acting on a pair of transparent microspheres by the excitation of the Morphology Dependent Resonance (MDR). The bonding and anti-bonding modes of the MDR correspond to strong attractions and repulsions respectively. The dependence of the force on separation and the role of absorption are discussed. At resonance, the force can be enhanced by orders of magnitude so that it will dominate over other relevant forces. We find that a stable binding configuration can be induced by the resonant optical force.Comment: 4 pages, 4 figure