On the predictive power of Local Scale Invariance

Local Scale Invariance (LSI) is a theory for anisotropic critical phenomena designed in the spirit of conformal invariance. For a given representation of its generators it makes non-trivial predictions about the form of universal scaling functions. In the past decade several representations have been identified and the corresponding predictions were confirmed for various anisotropic critical systems. Such tests are usually based on a comparison of two-point quantities such as autocorrelation and response functions. The present work highlights a potential problem of the theory in the sense that it may predict any type of two-point function. More specifically, it is argued that for a given two-point correlator it is possible to construct a representation of the generators which exactly reproduces this particular correlator. This observation calls for a critical examination of the predictive content of the theory.Comment: 17 pages, 2 eps figure

A possible signature of terrestrial planet formation in the chemical composition of solar analogs

Recent studies have shown that the elemental abundances in the Sun are anomalous when compared to most (about 85%) nearby solar twin stars. Compared to its twins, the Sun exhibits a deficiency of refractory elements (those with condensation temperatures Tc>900K) relative to volatiles (Tc<900K). This finding is speculated to be a signature of the planet formation that occurred more efficiently around the Sun compared with the majority of solar twins. Furthermore, within this scenario, it seems more likely that the abundance patterns found are specifically related to the formation of terrestrial planets. In this work we analyze abundance results from six large independent stellar abundance surveys to determine whether they confirm or reject this observational finding. We show that the elemental abundances derived for solar analogs in these six studies are consistent with the Tc trend suggested as a planet formation signature. The same conclusion is reached when those results are averaged heterogeneously. We also investigate the dependency of the abundances with first ionization potential (FIP), which correlates well with Tc. A trend with FIP would suggest a different origin for the abundance patterns found, but we show that the correlation with Tc is statistically more significant. We encourage similar investigations of metal-rich solar analogs and late F-type dwarf stars, for which the hypothesis of a planet formation signature in the elemental abundances makes very specific predictions. Finally, we examine a recent paper that claims that the abundance patterns of two stars hosting super-Earth like planets contradict the planet formation signature hypothesis. Instead, we find that the chemical compositions of these two stars are fully compatible with our hypothesis.Comment: To appear in Astronomy and Astrophysic

Ageing without detailed balance: local scale invariance applied to two exactly solvable models

I consider ageing behaviour in two exactly solvable reaction-diffusion systems. Ageing exponents and scaling functions are determined. I discuss in particular a case in which the equality of two critical exponents, known from systems with detailed balance, does not hold any more. Secondly it is shown that the form of the scaling functions can be understood by symmetry considerations.Comment: 6 pages, contribution to the summer school "Ageing and the Glass Transition" held in Luxemburg in September 05. Published versio

Kinetics of the long-range spherical model

The kinetic spherical model with long-range interactions is studied after a quench to $T < T_c$ or to $T = T_c$. For the two-time response and correlation functions of the order-parameter as well as for composite fields such as the energy density, the ageing exponents and the corresponding scaling functions are derived. The results are compared to the predictions which follow from local scale-invariance.Comment: added "fluctuation-dissipation ratios"; fixed typo

Desensitizing Inflation from the Planck Scale

A new mechanism to control Planck-scale corrections to the inflationary eta parameter is proposed. A common approach to the eta problem is to impose a shift symmetry on the inflaton field. However, this symmetry has to remain unbroken by Planck-scale effects, which is a rather strong requirement on possible ultraviolet completions of the theory. In this paper, we show that the breaking of the shift symmetry by Planck-scale corrections can be systematically suppressed if the inflaton field interacts with a conformal sector. The inflaton then receives an anomalous dimension in the conformal field theory, which leads to sequestering of all dangerous high-energy corrections. We analyze a number of models where the mechanism can be seen in action. In our most detailed example we compute the exact anomalous dimensions via a-maximization and show that the eta problem can be solved using only weakly-coupled physics.Comment: 34 pages, 3 figures

A matheuristic for a customer assignment problem in direct marketing

In direct marketing, companies use sales campaigns to target their customers with personalized product offers. The effectiveness of direct marketing greatly depends on the assignment of customers to campaigns. In this paper, we consider a real-world planning problem of a major telecommunications company that assigns its customers to individual activities of its direct marketing campaigns. Various side constraints, such as budgets and sales targets, must be met. Conflict constraints ensure that individual customers are not assigned too frequently to similar activities. Related problems have been addressed in the literature; however, none of the existing approaches cover all the side constraints considered here. To close this gap, we develop a matheuristic that employs a new decomposition strategy to cope with the large number of conflict constraints in typical problem instances. In a computational experiment, we compare the performance of the proposed matheuristic to the performance of two mixed-binary linear programs on a test set that includes large-scale real-world instances. The matheuristic derives near-optimal solutions in short running times for small- to medium-sized instances and scales to instances of practical size comprising millions of customers and hundreds of activities. The deployment of the matheuristic at the company has considerably increased the overall effectiveness of its direct marketing campaigns

Magnetic order in double-layer manganites (La(1-z)Pr(z))1.2Sr1.8Mn2O7: intrinsic properties and role of the intergrowths

We report on an investigation of the double-layer manganite series (La(1-z)Pr(z))1.2Sr1.8Mn2O7 (0 <= z <= 1), carried out on single crystals by means of both macroscopic magnetometry and local probes of magnetism (muSR, 55Mn NMR). Muons and NMR demonstrate an antiferromagnetically ordered ground state at non-ferromagnetic compositions (z >= 0.6), while more moderate Pr substitutions (0.2 <= z <= 0.4) induce a spin reorientation transition within the ferromagnetic phase. A large magnetic susceptibility is detected at {Tc,TN} < T < 250K at all compositions. From 55Mn NMR spectroscopy, such a response is unambiguously assigned to the intergrowth of a ferromagnetic pseudocubic phase (La(1-z)Pr(z))(1-x)Sr(x)MnO3, with an overall volume fraction estimated as 0.5-0.7% from magnetometry. Evidence is provided for the coupling of the magnetic moments of these inclusions with the magnetic moments of the surrounding (La(1-z)Pr(z))1.2Sr1.8Mn2O7 phase, as in the case of finely dispersed impurities. We argue that the ubiquitous intergrowth phase may play a role in the marked first-order character of the magnetic transition and the metamagnetic properties above Tc reported for double-layer manganites.Comment: 11 pages, 9 figures. Submitted to Phys. Rev.