Exact results for the Kardar--Parisi--Zhang equation with spatially correlated noise

We investigate the Kardar--Parisi--Zhang (KPZ) equation in $d$ spatial dimensions with Gaussian spatially long--range correlated noise --- characterized by its second moment $R(\vec{x}-\vec{x}') \propto |\vec{x}-\vec{x}'|^{2\rho-d}$ --- by means of dynamic field theory and the renormalization group. Using a stochastic Cole--Hopf transformation we derive {\em exact} exponents and scaling functions for the roughening transition and the smooth phase above the lower critical dimension $d_c = 2 (1+\rho)$. Below the lower critical dimension, there is a line $\rho_*(d)$ marking the stability boundary between the short-range and long-range noise fixed points. For $\rho \geq \rho_*(d)$, the general structure of the renormalization-group equations fixes the values of the dynamic and roughness exponents exactly, whereas above $\rho_*(d)$, one has to rely on some perturbational techniques. We discuss the location of this stability boundary $\rho_* (d)$ in light of the exact results derived in this paper, and from results known in the literature. In particular, we conjecture that there might be two qualitatively different strong-coupling phases above and below the lower critical dimension, respectively.Comment: 21 pages, 15 figure

Stability borders of feedback control of delayed measured systems

When stabilization of unstable periodic orbits or fixed points by the method given by Ott, Grebogi and Yorke (OGY) has to be based on a measurement delayed by $\tau$ orbit lengths, the performance of unmodified OGY method is expected to decline. For experimental considerations, it is desired to know the range of stability with minimal knowledge of the system. We find that unmodified OGY control fails beyond a maximal Ljapunov number of $\lambda_{max}=1+\frac{1}{\tau}$. In this paper the area of stability is investigated both for OGY control of known fixed points and for difference control of unknown or inaccurately known fixed points. An estimated value of the control gain is given. Finally we outline what extensions have to be considered if one wants to stabilize fixed points with Ljapunov numbers above $\lambda_{max}$.Comment: 5 pages LaTeX using revtex and epsfig (4 figs included). Revised versio

Half moons are pinch points with dispersion

"Pinch points," singular features observed in (quasi-)elastic neutron scattering, are a widely discussed hallmark of spin liquids with an emergent gauge symmetry. Much less attention has been paid to "half moons," distinctive crescent patterns at finite energy, which have been observed in experiments on a number of pyrochlore magnets, and in a wide range of model calculations. Here we unify these two phenomena within a single framework, paying particular attention to the case of ordered, or field-saturated states, where pinch points and half moons can be found in bands of excitations above a gap. We find that half moons are nothing other than pinch points inscribed on a dispersing band. Molecular dynamics simulations of the kagome lattice antiferromagnet are used to explore how these bands evolve into the ground state and excitations of a classical spin liquid. We explicitly demonstrate that this theory can reproduce the pinch points and half moons observed in Nd$_2$Zr$_2$O$_7$.Comment: 6 pages, 4 figures. Supplementary material: 10 pages, 3 figure

The "Horizon-T" Experiment: Extensive Air Showers Detection

Horizon-T is an innovative detector system constructed to study Extensive Air Showers (EAS) in the energy range above 10^16 eV coming from a wide range of zenith angles (0 - 85 degrees). The system is located at Tien Shan high-altitude Science Station of Lebedev Physical Institute of the Russian Academy of Sciences at approximately 3340 meters above the sea level. It consists of eight charged particle detection points separated by the distance up to one kilometer as well as optical detector subsystem to view the Vavilov-Cerenkov light from the EAS. The time resolution of charged particles and Vavilov-Cerenkov light photons passage of the detector system is a few ns. This level of resolution allows conducting research of atmospheric development of individual EAS.Comment: Initial technical note for Horizon-T experiment, updated with recent detector upgrades, 11/2016. Updated 12/2017 with minor edits. Large upgrade will be in another articl

The role of attitudes and behaviours in explaining socio-economic differences in attainment at age 11

This paper explores the correlates of the socio-economic gradient in children’s educational performance through the primary school years. Thus it sits between the companion papers on pre-school cognitive outcomes and attainment in the secondary school years in this Special Issue. The poorest 20% of children score, on average 14 percentile points lower than the middle 20% in Key Stage 2 tests at age 11, and 31 percentile points lower than the richest 20%. Overall around one third of the attainment gaps by socio-economic background at age 11 are found to emerge after age 7. The evolution of attainment gaps over this period is found to be related a range of attitudes to education and behavioural patterns of the study children. Low maternal aspirations for the child’s final educational attainment are strongly linked to the widening socio-economic gap during these years, over and above their influence on the child’s own measured attitudes and behaviours.This paper explores the correlates of the socio-economic gradient in children’s educational performance through the primary school years. Thus it sits between the companion papers on pre-school cognitive outcomes and attainment in the secondary school years in this Special Issue. The poorest 20% of children score, on average 14 percentile points lower than the middle 20% in Key Stage 2 tests at age 11, and 31 percentile points lower than the richest 20%. Overall around one third of the attainment gaps by socio-economic background at age 11 are found to emerge after age 7. The evolution of attainment gaps over this period is found to be related a range of attitudes to education and behavioural patterns of the study children. Low maternal aspirations for the child’s final educational attainment are strongly linked to the widening socio-economic gap during these years, over and above their influence on the child’s own measured attitudes and behaviours

Low vapor pressure braze alloys for thermionic energy converters

The evaluation of cesium diode electrode materials called for braze fillers with very low vapor pressures and a wide range of melting points. Binary alloys of low vapor pressure refractory metals were chosen to fill this need. These alloys of Th, Zr, Hf, Ru, Nb, Ir, Mo, Ta, Os, Re, and W have reported melting point minima or eutectics from 1,510 K to above 3,000 K. Preliminary data are compiled on the use of several of these braze alloys. Melting points and surface wetting on a Ta base are given. Results of brazing Ir, LaB6, Nb, Re, W, and Zr-22 wt % ZrO2 materials into Ta and Nb-1% Zr bases are presented. Current braze usage is summarized