The Orientation of Unsymmetrical Molecules at Interfaces

A function giving the distribution of the angles of orientation of the molecular axes from the normal to the interface can be obtained if one makes use of a number of special assumptions regarding the forces of orientation. This is compared with the distribution calculated on assuming an extreme form of Langmuir's principle of independent surface action. The importance of having such a function is pointed out

Regularization independent of the noise level: an analysis of quasi-optimality

The quasi-optimality criterion chooses the regularization parameter in inverse problems without taking into account the noise level. This rule works remarkably well in practice, although Bakushinskii has shown that there are always counterexamples with very poor performance. We propose an average case analysis of quasi-optimality for spectral cut-off estimators and we prove that the quasi-optimality criterion determines estimators which are rate-optimal {\em on average}. Its practical performance is illustrated with a calibration problem from mathematical finance.Comment: 18 pages, 3 figure

A Tale of Two Theories: Quantum Griffiths Effects in Metallic Systems

We show that two apparently contradictory theories on the existence of Griffiths-McCoy singularities in magnetic metallic systems [1,2] are in fact mathematically equivalent. We discuss the generic phase diagram of the problem and show that there is a non-universal crossover temperature range T* < T < W where power law behavior (Griffiths-McCoy behavior) is expect. For T<T* power law behavior ceases to exist due to the destruction of quantum effects generated by the dissipation in the metallic environment. We show that T* is an analogue of the Kondo temperature and is controlled by non-universal couplings.Comment: 4 pages, 2 figure

Shape analysis on homogeneous spaces: a generalised SRVT framework

Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare curves independently of their parametrisation. One computationally efficient approach to shape analysis is based on the Square Root Velocity Transform (SRVT). In this paper we propose a generalised SRVT framework for shapes on homogeneous manifolds. The method opens up for a variety of possibilities based on different choices of Lie group action and giving rise to different Riemannian metrics.Comment: 28 pages; 4 figures, 30 subfigures; notes for proceedings of the Abel Symposium 2016: "Computation and Combinatorics in Dynamics, Stochastics and Control". v3: amended the text to improve readability and clarify some points; updated and added some references; added pseudocode for the dynamic programming algorithm used. The main results remain unchange

Harmonic Generation from Laser-Irradiated Clusters

The harmonic emission from cluster nanoplasmas subject to short, intense infrared laser pulses is analyzed by means of particle-in-cell simulations. A pronounced resonant enhancement of the low-order harmonic yields is found when the Mie plasma frequency of the ionizing and expanding cluster resonates with the respective harmonic frequency. We show that a strong, nonlinear resonant coupling of the cluster electrons with the laser field inhibits coherent electron motion, suppressing the emitted radiation and restricting the spectrum to only low-order harmonics. A pump-probe scheme is suggested to monitor the ionization dynamics of the expanding clusters.Comment: 4 pages, ReVTeX

Potential and limitations of nucleon transfer experiments with radioactive beams at REX-ISOLDE

As a tool for studying the structure of nuclei far off stability the technique of gamma-ray spectroscopy after low-energy single-nucleon transfer reactions with radioactive nuclear beams in inverse kinematics was investigated. Modules of the MINIBALL germanium array and a thin position-sensitive parallel plate avalanche counter (PPAC) to be employed in future experiments at REX-ISOLDE were used in a test experiment performed with a stable 36S beam on deuteron and 9Be targets. It is demonstrated that the Doppler broadening of gamma lines detected by the MINIBALL modules is considerably reduced by exploiting their segmentation, and that for beam intensities up to 10^6 particles/s the PPAC positioned around zero degrees with respect to the beam axis allows not only to significantly reduce the gamma background by requiring coincidences with the transfer products but also to control the beam and its intensity by single particle counting. The predicted large neutron pickup cross sections of neutron-rich light nuclei on 2H and 9Be targets at REX-ISOLDE energies of 2.2 MeV A are confirmed.Comment: 11 pages, 8 figure

Phase Transitions in a Two-Component Site-Bond Percolation Model

A method to treat a N-component percolation model as effective one component model is presented by introducing a scaled control variable $p_{+}$. In Monte Carlo simulations on $16^{3}$, $32^{3}$, $64^{3}$ and $128^{3}$ simple cubic lattices the percolation threshold in terms of $p_{+}$ is determined for N=2. Phase transitions are reported in two limits for the bond existence probabilities $p_{=}$ and $p_{\neq}$. In the same limits, empirical formulas for the percolation threshold $p_{+}^{c}$ as function of one component-concentration, $f_{b}$, are proposed. In the limit $p_{=} = 0$ a new site percolation threshold, $f_{b}^{c} \simeq 0.145$, is reported.Comment: RevTeX, 5 pages, 5 eps-figure