Optical signatures of type-II Weyl fermions in the noncentrosymmetric semimetals RAlSi (R=La, Ce, Pr, Nd, Sm)

Weyl semimetals with magnetic ordering provide a promising platform for the investigation of rare topological effects such as the anomalous Hall effect, resulting from the interplay of nontrivial bands with various spin configurations. The materials RAlSi, where R represents a rare-earth element, are prominent representatives of Weyl semimetals, where the Weyl states are induced by space inversion symmetry breaking, and in addition, for several rare-earth elements R, enhanced by time-reversal symmetry breaking through the formation of a magnetic order at low temperature. We report optical signatures of Weyl fermions in the magnetic compounds CeAlSi, PrAlSi, NdAlSi, and SmAlSi as well as the nonmagnetic family member LaAlSi by broad-frequency infrared spectroscopy at room temperature, i.e., in the paramagnetic phase. A similar profile of the optical conductivity spectrum and a metallic character are observed for all compounds, with LaAlSi showing the strongest free charge-carrier contribution. Furthermore, the linear-in-frequency behavior of the optical conductivity of all investigated compounds indicates the presence of Weyl nodes in close proximity to the Fermi energy, resulting from inversion symmetry breaking in noncentrosymmetric structures. According to the characteristics of these linear slopes, the RAlSi compounds are expected to host mainly type-II Weyl states with overtilted Weyl cones. The results are compared to the optical response of the closely related RAlGe materials, which are considered as potential hybridization-driven Weyl-Kondo systems

On the relation between Differential Privacy and Quantitative Information Flow

Differential privacy is a notion that has emerged in the community of statistical databases, as a response to the problem of protecting the privacy of the database's participants when performing statistical queries. The idea is that a randomized query satisfies differential privacy if the likelihood of obtaining a certain answer for a database $x$ is not too different from the likelihood of obtaining the same answer on adjacent databases, i.e. databases which differ from $x$ for only one individual. Information flow is an area of Security concerned with the problem of controlling the leakage of confidential information in programs and protocols. Nowadays, one of the most established approaches to quantify and to reason about leakage is based on the R\'enyi min entropy version of information theory. In this paper, we analyze critically the notion of differential privacy in light of the conceptual framework provided by the R\'enyi min information theory. We show that there is a close relation between differential privacy and leakage, due to the graph symmetries induced by the adjacency relation. Furthermore, we consider the utility of the randomized answer, which measures its expected degree of accuracy. We focus on certain kinds of utility functions called "binary", which have a close correspondence with the R\'enyi min mutual information. Again, it turns out that there can be a tight correspondence between differential privacy and utility, depending on the symmetries induced by the adjacency relation and by the query. Depending on these symmetries we can also build an optimal-utility randomization mechanism while preserving the required level of differential privacy. Our main contribution is a study of the kind of structures that can be induced by the adjacency relation and the query, and how to use them to derive bounds on the leakage and achieve the optimal utility

The Newsvendor problem: analysis of the cost structure under normally distributed demand

We briefly review selected mathematical models that describe the dynamics of pattern formation phenomena in dip-coating and Langmuir-Blodgett transfer experiments, where solutions or suspensions are transferred onto a substrate producing patterned deposit layers with structure length from hundreds of nanometres to tens of micrometres. The models are presented with a focus on their gradient dynamics formulations that clearly shows how the dynamics is governed by particular free energy functionals and facilitates the comparison of the models. In particular, we include a discussion of models based on long-wave hydrodynamics as well as of more phenomenological models that focus on the pattern formation processes in such systems. The models and their relations are elucidated and examples of resulting patterns are discussed before we conclude with a discussion of implications of the gradient dynamics formulation and of some related open issues

Trust in Crowds: probabilistic behaviour in anonymity protocols

The existing analysis of the Crowds anonymity protocol assumes that a participating member is either ‘honest’ or ‘corrupted’. This paper generalises this analysis so that each member is assumed to maliciously disclose the identity of other nodes with a probability determined by her vulnerability to corruption. Within this model, the trust in a principal is defined to be the probability that she behaves honestly. We investigate the effect of such a probabilistic behaviour on the anonymity of the principals participating in the protocol, and formulate the necessary conditions to achieve ‘probable innocence’. Using these conditions, we propose a generalised Crowds-Trust protocol which uses trust information to achieves ‘probable innocence’ for principals exhibiting probabilistic behaviour

Thin film dynamics with surfactant phase transition

A thin liquid film covered with an insoluble surfactant in the vicinity of a first-order phase transition is discussed. Within the lubrication approximation we derive two coupled equations to describe the height profile of the film and the surfactant density. Thermodynamics of the surfactant is incorporated via a Cahn-Hilliard type free-energy functional which can be chosen to describe a transition between two stable phases of different surfactant density. Within this model, a linear stability analysis of stationary homogeneous solutions is performed, and drop formation in a film covered with surfactant in the lower density phase is investigated numerically in one and two spatial dimensions

Continuation for thin film hydrodynamics and related scalar problems

This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues