Arithmetic harmonic analysis for smooth quartic Weyl sums: three additive equations

We establish the non-singular Hasse principle for systems of three diagonal quartic equations in 32 or more variables, subject to a certain rank condition. Our methods employ the arithmetic harmonic analysis of smooth quartic Weyl sums and also a new estimate for their tenth moment.Comment: 22 page

Correlation estimates for sums of three cubes

We establish estimates for linear correlation sums involving sums of three positive integral cubes. Under appropriate conditions, the underlying methods permit us to establish the solubility of systems of homogeneous linear equations in sums of three positive cubes whenever these systems have more than twice as many variables as equations.Comment: arXiv admin note: substantial text overlap with arXiv:1304.5165 25pp; Revisions to sections 2 and 3 to address referee comment

Resolving the fine-scale structure in turbulent Rayleigh-Benard convection

We present high-resolution direct numerical simulation studies of turbulent Rayleigh-Benard convection in a closed cylindrical cell with an aspect ratio of one. The focus of our analysis is on the finest scales of convective turbulence, in particular the statistics of the kinetic energy and thermal dissipation rates in the bulk and the whole cell. The fluctuations of the energy dissipation field can directly be translated into a fluctuating local dissipation scale which is found to develop ever finer fluctuations with increasing Rayleigh number. The range of these scales as well as the probability of high-amplitude dissipation events decreases with increasing Prandtl number. In addition, we examine the joint statistics of the two dissipation fields and the consequences of high-amplitude events. We also have investigated the convergence properties of our spectral element method and have found that both dissipation fields are very sensitive to insufficient resolution. We demonstrate that global transport properties, such as the Nusselt number, and the energy balances are partly insensitive to insufficient resolution and yield correct results even when the dissipation fields are under-resolved. Our present numerical framework is also compared with high-resolution simulations which use a finite difference method. For most of the compared quantities the agreement is found to be satisfactory.Comment: 33 pages, 24 figure

Radiative Corrections to Multi-Level Mollow-Type Spectra

This paper is concerned with two rather basic phenomena: the incoherent fluorescence spectrum of an atom driven by an intense laser field and the coupling of the atom to the (empty) modes of the radiation field. The sum of the many-photon processes gives rise to the inelastic part of the atomic fluorescence, which, for a two-level system, has a well-known characteristic three-peak structure known as the Mollow spectrum. From a theoretical point of view, the Mollow spectrum finds a natural interpretation in terms of transitions among laser-dressed states which are the energy eigenstates of a second-quantized two-level system strongly coupled to a driving laser field. As recently shown, the quasi-energies of the laser-dressed states receive radiative corrections which are nontrivially different from the results which one would expect from an investigation of the coupling of the bare states to the vacuum modes. In this article, we briefly review the basic elements required for the analysis of the dynamic radiative corrections, and we generalize the treatment of the radiative corrections to the incoherent part of the steady-state fluorescence to a three-level system consisting of 1S, 3P and 2S states.Comment: Dedicated to Prof. H. Walther on the occasion of his 70th birthda

Clustering of Galaxies in a Hierarchical Universe: III. Mock Redshift Surveys

This is the third paper in a series which combines N-body simulations and semi-analytic modelling to provide a fully spatially resolved simulation of the galaxy formation and clustering processes. Here we extract mock redshift surveys from our simulations: a Cold Dark Matter model with either Omega_0=1 (tauCDM) or Omega_0=0.3 and Lambda=0.7 (LambdaCDM). We compare the mock catalogues with the northern region (CfA2N) of the Center for Astrophysics (CfA) Redshift Surveys. We study the properties of galaxy groups and clusters identified using standard observational techniques and we study the relation of these groups to real virialised systems. Most features of CfA2N groups are reproduced quite well by both models with no obvious dependence on Omega_0. Redshift space correlations and pairwise velocities are also similar in the two cosmologies. The luminosity functions predicted by our galaxy formation models depend sensitively on the treatment of star formation and feedback. For the particular choices of Paper I they agree poorly with the CfA survey. To isolate the effect of this discrepancy on our mock redshift surveys, we modify galaxy luminosities in our simulations to reproduce the CfA luminosity function exactly. This adjustment improves agreement with the observed abundance of groups, which depends primarily on the galaxy luminosity density, but other statistics, connected more closely with the underlying mass distribution, remain unaffected. Regardless of the luminosity function adopted, modest differences with observation remain. These can be attributed to the presence of the ``Great Wall'' in the CfA2N. It is unclear whether the greater coherence of the real structure is a result of cosmic variance, given the relatively small region studied, or reflects a physical deficiency of the models.Comment: 47 pages, LaTex, 17 figures, MNRAS, in press; one figure adde

Harmonising and formalising research administration profiles CASRAI / CERIF

CASRAI and CERIF are international standardisation initiatives in the domain of Research Information Management. CASRAI develops and maintains a standard extensible vocabulary and exchangeable data profiles that reflect the business requirements of involved stakeholders. A data profile specifies the maximal ideal space of its application with compliant data records. CERIF is a data model supplying standard formal syntax and declared semantics to preserve the meaning inherent in identified requirements. It enables the transformation of conceptual descriptions into formal representation thereof and thus their meaningful re-use as well as a semantically compliant and syntactically valid data interchange. With this paper we share the experience, and the lessons learned from the transformation of CASRAI profiles into CERIF XML through the example of an Abridged CV

Renormalization flow of QED

We investigate textbook QED in the framework of the exact renormalization group. In the strong-coupling region, we study the influence of fluctuation-induced photonic and fermionic self-interactions on the nonperturbative running of the gauge coupling. Our findings confirm the triviality hypothesis of complete charge screening if the ultraviolet cutoff is sent to infinity. Though the Landau pole does not belong to the physical coupling domain owing to spontaneous chiral symmetry breaking (chiSB), the theory predicts a scale of maximal UV extension of the same order as the Landau pole scale. In addition, we verify that the chiSB phase of the theory which is characterized by a light fermion and a Goldstone boson also has a trivial Yukawa coupling.Comment: 4 pages, 1 figur