Comments on the Links between su(3) Modular Invariants, Simple Factors in the Jacobian of Fermat Curves, and Rational Triangular Billiards

We examine the proposal made recently that the su(3) modular invariant partition functions could be related to the geometry of the complex Fermat curves. Although a number of coincidences and similarities emerge between them and certain algebraic curves related to triangular billiards, their meaning remains obscure. In an attempt to go beyond the su(3) case, we show that any rational conformal field theory determines canonically a Riemann surface.Comment: 56 pages, 4 eps figures, LaTeX, uses eps

Nonlinear dielectric response of Debye, alpha, and beta relaxation in 1-propanol

We present nonlinear dielectric measurements of glass-forming 1-propanol, a prototypical example for the monohydroxy alcohols that are known to exhibit unusual relaxation dynamics, namely an additional Debye relaxation, slower than the structural alpha relaxation. Applying high ac fields of 468 kV/cm allows for a detailed investigation of the nonlinear properties of all three relaxation processes occurring in 1-propanol, namely the Debye, alpha, and beta relaxation. Both the field-induced variations of dielectric constant and loss are reported. Polarization saturation and the absorption of field energy govern the findings in the Debye-relaxation regime, well consistent with the suggested cluster-like nature of the relaxing entities. The behavior of the alpha relaxation is in good accord with the expectations for a heterogeneous relaxation scenario. Finally, the Johari-Goldstein beta-relaxation in 1-propanol seems to exhibit no or only weak field dependence, in agreement with recent findings for the excess wing of canonical glass formers.Comment: 8 pages, 4 figure

Cooperativity and Heterogeneity in Plastic Crystals Studied by Nonlinear Dielectric Spectroscopy

The glassy dynamics of plastic-crystalline cyclo-octanol and ortho-carborane, where only the molecular reorientational degrees of freedom freeze without long-range order, is investigated by nonlinear dielectric spectroscopy. Marked differences to canonical glass formers show up: While molecular cooperativity governs the glassy freezing, it leads to a much weaker slowing down of molecular dynamics than in supercooled liquids. Moreover, the observed nonlinear effects cannot be explained with the same heterogeneity scenario recently applied to canonical glass formers. This supports ideas that molecular relaxation in plastic crystals may be intrinsically non-exponential. Finally, no nonlinear effects were detected for the secondary processes in cyclo-octanol.Comment: Final version as accepted for publication in Phys. Rev. Lett. 6 pages, 5 figures (including 1 page and figure in Supplemental Material

Nonlinear dielectric response at the excess wing of glass-forming liquids

We present nonlinear dielectric measurements of glass-forming glycerol and propylene carbonate applying electrical fields up to 671 kV/cm. The measurements extend to sufficiently high frequencies to allow for the investigation of the nonlinear behavior in the regime of the so-far mysterious excess wing, showing up in the loss spectra of many glass formers as a second power law at high frequencies. Surprisingly, we find a complete lack of nonlinear behavior in the excess wing, in marked contrast to the alpha-relaxation where, in agreement with previous reports, a strong increase of dielectric constant and loss is found.Comment: 8 pages (including 3 pages Supplementary Information), 4 + 1 figures. Revised according to suggestions of referee

Runtime Verification of Temporal Properties over Out-of-order Data Streams

We present a monitoring approach for verifying systems at runtime. Our approach targets systems whose components communicate with the monitors over unreliable channels, where messages can be delayed or lost. In contrast to prior works, whose property specification languages are limited to propositional temporal logics, our approach handles an extension of the real-time logic MTL with freeze quantifiers for reasoning about data values. We present its underlying theory based on a new three-valued semantics that is well suited to soundly and completely reason online about event streams in the presence of message delay or loss. We also evaluate our approach experimentally. Our prototype implementation processes hundreds of events per second in settings where messages are received out of order.Comment: long version of the CAV 2017 pape

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

Repeated Evolution of Digital Adhesion in Geckos: A Reply to Harrington and Reeder

We published a phylogenetic comparative analysis that found geckos had gained and lost adhesive toepads multiple times over their long evolutionary history (Gamble et al., PLoS One, 7, 2012, e39429). This was consistent with decades of morphological studies showing geckos had evolved adhesive toepads on multiple occasions and that the morphology of geckos with ancestrally padless digits can be distinguished from secondarily padless forms. Recently, Harrington & Reeder (J. Evol. Biol., 30, 2017, 313) reanalysed data from Gamble et al. (PLoS One, 7, 2012, e39429) and found little support for the multiple origins hypothesis. Here, we argue that Harrington and Reeder failed to take morphological evidence into account when devising ancestral state reconstruction models and that these biologically unrealistic models led to erroneous conclusions about the evolution of adhesive toepads in geckos

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

First-principles study of magnetization relaxation enhancement and spin-transfer in thin magnetic films

The interface-induced magnetization damping of thin ferromagnetic films in contact with normal-metal layers is calculated from first principles for clean and disordered Fe/Au and Co/Cu interfaces. Interference effects arising from coherent scattering turn out to be very small, consistent with a very small magnetic coherence length. Because the mixing conductances which govern the spin transfer are to a good approximation real valued, the spin pumping can be described by an increased Gilbert damping factor but an unmodified gyromagnetic ratio. The results also confirm that the spin-current induced magnetization torque is an interface effect.Comment: 10 pages, 8 figures, RevTeX; modified according to Referees' request