Diffuse LEED intensities of disordered crystal surfaces : II. Multiple scattering on disordered overlayers

The diffraction of low energy electrons from disordered overlayers adsorbed on ordered substrates is treated theoretically by an extension of Beeby's multiple scattering method. A lattice gas model is assumed for the disordered adsorbate layer. Multiple scattering within a certain area around each atom — each atom of the overlayer and within the ordered substrate — is treated self-consistently, the remaining contributions to the total scattering amplitude being averaged. The theory can be used in the limiting cases of random distribution and of long range order within the adsorbate layer

Vertical shear instability in accretion disc models with radiation transport

The origin of turbulence in accretion discs is still not fully understood. While the magneto-rotational instability is considered to operate in sufficiently ionized discs, its role in the poorly ionized protoplanetary disc is questionable. Recently, the vertical shear instability (VSI) has been suggested as a possible alternative. Our goal is to study the characteristics of this instability and the efficiency of angular momentum transport, in extended discs, under the influence of radiative transport and irradiation from the central star. We use multi-dimensional hydrodynamic simulations to model a larger section of an accretion disc. First we study inviscid and weakly viscous discs using a fixed radial temperature profile in two and three spatial dimensions. The simulations are then extended to include radiative transport and irradiation from the central star. In agreement with previous studies we find for the isothermal disc a sustained unstable state with a weak positive angular momentum transport of the order of $\alpha \approx 10^{-4}$. Under the inclusion of radiative transport the disc cools off and the turbulence terminates. For discs irradiated from the central star we find again a persistent instability with a similar $\alpha$ value as for the isothermal case. We find that the VSI can indeed generate sustained turbulence in discs albeit at a relatively low level with $\alpha$ about few times $10^{-4}$Comment: 12 pages, 24 figures, accepted for publication in Astronomy & Astrophysic

Diffuse LEED intensities of disordered crystal surfaces : IV. Application of the disorder theory

The principles of the statistical disorder theory are discussed briefly. The theory is applied to a model of the disordered (101)Au surface with the characteristic (1 × 2) supersstructure. A fit procedure is described, by which the experimental angular intensity profiles are used directly to determine the disorder parameters and the interaction energies between the chains of surface atoms

Diffuse LEED intensities of disordered crystal surfaces : I. Correlations between statistics and multiple diffraction

It is shown that the diffraction of slow electrons from disordered crystal surfaces is correlated with the problem of thermodynamical statistics. The correlation functions are completely determined by the self-energies and interaction energies of neighboring complexes. These quantities solve the problem of a-priori probabilities and the cooperative phenomenon of correlation functions of these complexes. If the calculation of a certain set of multiple scattering amplitudes is possible, the remaining problem of determining the diffuse LEED pattern becomes solvable. The calculation of angular beam profiles follows the same lines as already described for the kinematic theory of X-ray diffraction

On the Light Massive Flavor Dependence of the Large Order Asymptotic Behavior and the Ambiguity of the Pole Mass

We provide a systematic renormalization group formalism for the mass effects in the relation of the pole mass $m_Q^{\rm pole}$ and short-distance masses such as the $\overline{\rm MS}$ mass $\overline{m}_Q$ of a heavy quark $Q$, coming from virtual loop insertions of massive quarks lighter than $Q$. The formalism reflects the constraints from heavy quark symmetry and entails a combined matching and evolution procedure that allows to disentangle and successively integrate out the corrections coming from the lighter massive quarks and the momentum regions between them and to precisely control the large order asymptotic behavior. With the formalism we systematically sum logarithms of ratios of the lighter quark masses and $m_Q$, relate the QCD corrections for different external heavy quarks to each other, predict the ${\cal O}(\alpha_s^4)$ virtual quark mass corrections in the pole-$\overline{\rm MS}$ mass relation, calculate the pole mass differences for the top, bottom and charm quarks with a precision of around $20$ MeV and analyze the decoupling of the lighter massive quark flavors at large orders. The summation of logarithms is most relevant for the top quark pole mass $m_t^{\rm pole}$, where the hierarchy to the bottom and charm quarks is large. We determine the ambiguity of the pole mass for top, bottom and charm quarks in different scenarios with massive or massless bottom and charm quarks in a way consistent with heavy quark symmetry, and we find that it is $250$ MeV. The ambiguity is larger than current projections for the precision of top quark mass measurements in the high-luminosity phase of the LHC.Comment: 45 pages + appendix, 6 figures, v2: journal versio

Diffuse LEED intensities of disordered crystal surfaces : III. LEED investigation of the disordered (110) surface of gold

The LEED pattern of clean (101) surfaces of Au show a characteristic (1 × 2) superstructure. The diffuseness of reflections in the reciprocal [010] direction is caused by one-dimensional disorder of chains, strictly ordered into spatial [10 ] direction. There is a transition from this disordered superstructure to the normal (1 × 1) structure at 420 + 15°C. The angular profiles of the and (01) beam are measured at various temperatures and with constant energy and angles of incidence of the primary beam. The beam profiles are deconvoluted approximately with the instrument response function

Effects of a radially varying electrical conductivity on 3D numerical dynamos

The transition from liquid metal to silicate rock in the cores of the terrestrial planets is likely to be accompanied by a gradient in the composition of the outer core liquid. The electrical conductivity of a volatile enriched liquid alloy can be substantially lower than a light-element-depleted fluid found close to the inner core boundary. In this paper, we investigate the effect of radially variable electrical conductivity on planetary dynamo action using an electrical conductivity that decreases exponentially as a function of radius. We find that numerical solutions with continuous, radially outward decreasing electrical conductivity profiles result in strongly modified flow and magnetic field dynamics, compared to solutions with homogeneous electrical conductivity. The force balances at the top of the simulated fluid determine the overall character of the flow. The relationship between Coriolis and Lorentz forces near the outer boundary controls the flow and magnetic field intensity and morphology of the system. Our results imply that a low conductivity layer near the top of Mercury's liquid outer core is consistent with its weak magnetic field.Comment: 30 pages, 11 figures, 2 tables. To be published in Physics of Earth and Planetary Interiors (PEPI)

Learning Mixtures of Gaussians in High Dimensions

Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the covariance matrices of these Gaussians. This learning problem arises in many areas ranging from the natural sciences to the social sciences, and has also found many machine learning applications. Unfortunately, learning mixture of Gaussians is an information theoretically hard problem: in order to learn the parameters up to a reasonable accuracy, the number of samples required is exponential in the number of Gaussian components in the worst case. In this work, we show that provided we are in high enough dimensions, the class of Gaussian mixtures is learnable in its most general form under a smoothed analysis framework, where the parameters are randomly perturbed from an adversarial starting point. In particular, given samples from a mixture of Gaussians with randomly perturbed parameters, when n > {\Omega}(k^2), we give an algorithm that learns the parameters with polynomial running time and using polynomial number of samples. The central algorithmic ideas consist of new ways to decompose the moment tensor of the Gaussian mixture by exploiting its structural properties. The symmetries of this tensor are derived from the combinatorial structure of higher order moments of Gaussian distributions (sometimes referred to as Isserlis' theorem or Wick's theorem). We also develop new tools for bounding smallest singular values of structured random matrices, which could be useful in other smoothed analysis settings

A LEED structural analysis of the Co(100) surface

The structure of the clean Co(1010) surface has been analysed by LEED. Application of a recently developed computational scheme reveals the prevalence of the termination A in which the two topmost layers exhibit a narrow spacing of 0.62 Å, corresponding to a 12.8(±0.5)% contraction with respect to the bulk value, while the spacing between the second and third layer is slightly expanded by 0.8(±0.2)%