Relaxation of curvature induced elastic stress by the Asaro-Tiller-Grinfeld instability

A two-dimensional crystal on the surface of a sphere experiences elastic stress due to the incompatibility of the crystal axes and the curvature. A common mechanism to relax elastic stress is the Asaro-Tiller-Grinfeld (ATG) instability. With a combined numerical and analytical approach we demonstrate, that also curvature induced stress in surface crystals can be relaxed by the long wave length ATG instability. The numerical results are obtained using a surface phase-field crystal (PFC) model, from which we determine the characteristic wave numbers of the ATG instability for various surface coverages corresponding to different curvature induced compressions. The results are compared with an analytic expression for the characteristic wave number, obtained from a continuum approach which accounts for hexagonal crystals and intrinsic PFC symmetries. We find our numerical results in accordance with the analytical predictions.Comment: 6 pages, 5 figure

On the Expressivity and Applicability of Model Representation Formalisms

A number of first-order calculi employ an explicit model representation formalism for automated reasoning and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of monadic, shallow, linear, Horn (MSLH) clauses, is such a formalism used in the approximation refinement calculus. Our first result is a finite model property for MSLH clause sets. Therefore, MSLH clause sets cannot represent models of clause sets with inherently infinite models. Through a translation to tree automata, we further show that this limitation also applies to the linear fragments of implicit generalizations, which is the formalism used in the model-evolution calculus, to atoms with disequality constraints, the formalisms used in the non-redundant clause learning calculus (NRCL), and to atoms with membership constraints, a formalism used for example in decision procedures for algebraic data types. Although these formalisms cannot represent models of clause sets with inherently infinite models, through an additional approximation step they can. This is our second main result. For clause sets including the definition of an equivalence relation with the help of an additional, novel approximation, called reflexive relation splitting, the approximation refinement calculus can automatically show satisfiability through the MSLH clause set formalism

A simple stochastic model for the evolution of protein lengths

We analyse a simple discrete-time stochastic process for the theoretical modeling of the evolution of protein lengths. At every step of the process a new protein is produced as a modification of one of the proteins already existing and its length is assumed to be random variable which depends only on the length of the originating protein. Thus a Random Recursive Trees (RRT) is produced over the natural integers. If (quasi) scale invariance is assumed, the length distribution in a single history tends to a lognormal form with a specific signature of the deviations from exact gaussianity. Comparison with the very large SIMAP protein database shows good agreement.Comment: 12 pages, 4 figure

On the temporal Wilson loop in the Hamiltonian approach in Coulomb gauge

We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in (1+1) dimensions, the known results can be reproduced using unitary transformations to take care of time evolution. We show how Coulomb gauge can be used for an alternative solution if the exact ground state wave functional is known. In the most interesting case of Yang-Mills theory in (3+1) dimensions, the vacuum wave functional is not known, but recent variational approaches in Coulomb gauge give a decent approximation. We use this formulation to compute the temporal Wilson loop and find that the Wilson and Coulomb string tension agree within our approximation scheme. Possible improvements of these findings are briefly discussed.Comment: 24 pages, 4 eps-figures; new version matches published on

Thermal conduction and reduced cooling flows in galaxy clusters

Conduction may play an important role in reducing cooling flows in galaxy clusters. We analyse a sample of sixteen objects using Chandra data and find that a balance between conduction and cooling can exist in the hotter clusters (T > 5 keV), provided the plasma conductivity is close to the unhindered Spitzer value. In the absence of any additional heat sources, a reduced mass inflow must develop in the cooler objects in the sample. We fit cooling flow models to deprojected data and compare the spectral mass deposition rates found to the values required to account for the excess luminosity, assuming Spitzer-rate heat transfer over the observed temperature gradients. The mass inflow rates found are lower than is necessary to maintain energy balance in at least five clusters. However, emission from cooling gas may be partially absorbed. We also compute the flux supplied by turbulent heat transport (Cho et al. 2003) and find conductivity profiles which follow a strikingly similar temperature dependence to the conductivity values required to prevent cooling. Finally, we show that the cluster radio luminosities vary by over five orders of magnitude in objects with X-ray luminosities differing by no more than a factor of a few. This suggests that there is unlikely to be a straightforward correlation between the mechanical power provided by the radio lobes and the rate of energy loss in cooling flow clusters.Comment: Submitted to MNRA

Galaxy cluster mass profiles

Accurate measurements of the mass distribution in galaxy and cluster halos are essential to test the cold dark matter (CDM) paradigm. The cosmological model predicts a universal shape for the density profile in all halos, independent of halo mass. Its profile has a `cuspy' centre, with no evidence for the constant density core. In this paper we carry out a careful analysis of twelve galaxy clusters, using Chandra data to compute the mass distribution in each system under the assumption of hydrostatic equilibrium. Due to their low concentration, clusters provide ideal objects for studying the central cusps in dark matter halos. The majority of the systems are consistent with the CDM model, but 4 objects exhibit flat inner density profiles. We suggest that the flat inner profile found for these clusters is due to an underestimation of the mass in the cluster centre (rather than any problem with the CDM model), since these objects also have a centrally peaked gas mass fraction. We discuss possible causes for erroneously low mass measurements in the cores of some systems.Comment: 16 pages, 10 figures, 4 tables, accepted for publication in MNRA

A Lagrangian Perspective of Microphysical Impact on Ice Cloud Evolution and Radiative Heating

We generate trajectories in storm-resolving simulations in order to quantify the effect of ice microphysics on tropical upper-tropospheric cloud-radiative heating. The pressure and flow field tracked along the trajectories are used to run different ice microphysical schemes, both one- and two-moment formulations within the Icosahedral Non-hydrostatic Model model and a separate offline box microphysics model (CLaMS-Ice). This computational approach allows us to isolate purely microphysical differences in a variant of “microphysical piggybacking;” feedbacks of microphysics onto pressure and the flow field, for example, via latent heating, are suppressed. Despite these constraints, we find about a 5-fold difference in median cloud ice mass mixing ratios (q$_i$) and ice crystal number (N$_i$) between the microphysical schemes and very distinct q$_i$ distributions versus temperature and relative humidity with respect to ice along the trajectories. After investigating microphysical formulations for nucleation, depositional growth, and sedimentation, we propose three cirrus lifecycles: a weak source-strong sink lifecycle whose longwave and shortwave heating are smallest due to short lifetime and low optical depth, a strong source-weak sink lifecycle whose longwave and shortwave heating are largest due to long lifetime and high optical depth, and a strong source-strong sink lifecycle with intermediate radiative properties

High pressure Ca-VI phase between 158-180 GPa: Stability, electronic structure and superconductivity

We have performed ab initio calculations for new high-pressure phase of Ca-VI between 158-180 GPa. The study includes elastic parameters of mono- and poly-crystalline aggregates, electronic band structure, lattice dynamics and superconductivity. The calculations show that the orthorhombic Pnma structure is mechanically and dynamically stable in the pressure range studied. The structure is superconducting in the entire pressure range and the calculated Tc (~25K) is maximum at ~172 GPa, where the transfer of charges from 4s to 3d may be thought to be completed.Comment: 8 pages, 4 figures; PACS number(s): 74.70.Ad, 62.20.de, 71.20.-b, 74.20.Pq, 74.25.Kc, 74.62.Fj; Keywords: Calcium; High pressure; Electronic band structure; Phonon spectrum; Elastic constants; Superconducto