Optimization of perturbative similarity renormalization group for Hamiltonians with asymptotic freedom and bound states

A model Hamiltonian that exhibits asymptotic freedom and a bound state, is used to show on example that similarity renormalization group procedure can be tuned to improve convergence of perturbative derivation of effective Hamiltonians, through adjustment of the generator of the similarity transformation. The improvement is measured by comparing the eigenvalues of perturbatively calculated renormalized Hamiltonians that couple only a relatively small number of effective basis states, with the exact bound state energy in the model. The improved perturbative calculus leads to a few-percent accuracy in a systematic expansion.Comment: 6 pages of latex, 4 eps figure

Modulational-instability-free pulse compression in anti-resonant hollow-core photonic crystal fiber

Gas-filled hollow-core photonic crystal fiber (PCF) is used for efficient nonlinear temporal compression of femtosecond laser pulses, two main schemes being direct soliton-effect self-compression, and spectral broadening followed by phase compensation. To obtain stable compressed pulses, it is crucial to avoid decoherence through modulational instability (MI) during spectral broadening. Here we show that changes in dispersion due to spectral anti-crossings between the fundamental core mode and core wall resonances in anti-resonant-guiding hollow-core PCF can strongly alter the MI gain spectrum, enabling MI-free pulse compression for optimized fiber designs. In addition, higher-order dispersion can introduce MI even when the pump pulses lie in the normal dispersion region

Apparent Scarcity of Low-Density Polymorphs of Inorganic Solids

For most inorganic solids, very few dense polymorphs and no low-density polymorphs are observed. Taking a wide range of tetrahedrally-coordinated binary solids (e.g., ZnO, GaN) as a prototypical system, we show that the apparent scarcity of low-density polymorphs is not due to significant structural or energetic limitations. Using databases of periodic networks as sources of novel crystal structures, followed by ab initio energy minimization, we predict a dense spectrum of low-density low-energy polymorphs. The diverse range of materials considered indicates that this is likely to be a general phenomenon

Polarimetric modeling of corotating interaction regions (CIRs) threading massive-star winds

Massive star winds are complex radiation-hydrodynamic (sometimes magnetohydrodynamic) outflows that are propelled by their enormously strong luminosities. The winds are often found to be structured and variable, but can also display periodic or quasi-periodic behavior in a variety of wind diagnostics. The regular variations observed in putatively single stars, especially in UV wind lines, have often been attributed to corotating interaction regions (CIRs) like those seen in the solar wind. We present light curves for variable polarization from winds with CIR structures. We develop a model for a time-independent CIR based on a kinematical description. Assuming optically thin electron scattering, we explore the range of polarimetric light curves that result as the curvature, latitude, and number of CIRs are varied. We find that a diverse array of variable polarizations result from an exploration of cases. The net polarization from an unresolved source is weighted more toward the inner radii of the wind. Given that most massive stars have relatively fast winds compared to their rotation speeds, CIRs tend to be conical at inner radii, transitioning to a spiral shape at a few to several stellar radii in the wind. Winds with a single CIR structure lead to easily identifiable polarization signatures. By contrast allowing for multiple CIRs, all emerging from a range of azimuth and latitude positions at the star, can yield complex polarimetric behavior. Although our model is based on some simplifying assumptions, it produces qualitative behavior that we expect to be robust, and this has allowed us to explore a wide range of CIR configurations that will prove useful for interpreting polarimetric data.Comment: accepted to A&

Chromodynamic Weibel instabilities in relativistic nuclear collisions

Employing a previously derived formulation, and extending the treatment from purely transverse modes to wave vectors having a longitudinal component, we discuss the prospects for the occurrence of Weibel-type color-current filamentation in high-energy nuclear collisions. Numerical solutions of the dispersion equation for a number of scenarios relevant to RHIC and LHC suggest that modes with (predominantly transverse) wave numbers of several hundred MeV may become moderately agitated during the early collision stage. The emergence of filamentation helps to speed up the equilibration of the parton plasma and it may lead to non-statistical azimuthal patterns in the hadron final state.Comment: 11 pages, RevTex, 13 (e)ps files (revised for PRC

A construction of integer-valued polynomials with prescribed sets of lengths of factorizations

For an arbitrary finite set S of natural numbers greater 1, we construct an integer-valued polynomial f, whose set of lengths in Int(Z) is S. The set of lengths of f is the set of all natural numbers n, such that f has a factorization as a product of n irreducibles in Int(Z)={g in Q[x] | g(Z) contained in Z}.Comment: To appear in Monatshefte f\"ur Mathematik; 11 page

When the Future is not what it used to be: Lessons from the Western European Experience to Forecasting Education and Training in Transition Economies

In an era of rapid technological change, information exchange, and emergence of knowledge-intensive industries it is critical to be able to identify the future skill needs of the labour market. Growing unemployment in EU member states and pre-accession countries in Eastern Europe combined with technological changes which make the skills of a significant number of workers obsolescent each year demand adequate knowledge of medium- and long-term demand for specific skills. Some EU members states have developed employment forecasting methods to identify future skill requirements which take account of the sectoral, occupational, and educational and training factors which influence supply and demand in the labour market for skills. A number of countries in Eastern Europe which are preparing to join the EU are interested in developing employment forecasting models that would provide them with similar information relating to skills. Taking account of the requirements of the Single European Market and increasing international mobility, it is desirable that the pre-accession countries should develop models which, if possible, are comparable with existing methods of forecasting training and qualification needs in existing member states of the EU. This task requires regular medium-term forecasts which will extend the time horizon of decision makers beyond the current economic cycle, be applicable to the whole economy, allow speedy adjustment to changing circumstances, and which will take account of relevant factors such as investment plans, output and labour productivity forecasts, and technological change. The objective of this paper is to provide a summary of existing methods and data sets used to forecast education and training needs in four members of the European Union, in order to motivate similar work in three pre-accession countries. We first provide a detailed account of the different approaches to forecast education and training needs in France, Germany, Ireland and The Netherlands. For each of these countries, we consider the labour market data on which employment forecasts are based and the current methods in use, examine how data reliability and accuracy of forecasts are dealt with, and discuss the dissemination and usage of forecast information generated by those systems. We then look at the same range of issues for three pre-accession Central European countries (Czech Republic, Poland and Slovenia.) The paper concludes by suggesting a number of needed actions in preparation for developing an approach to forecasting education and training needs in the three pre-accession countries.employment forecasting, education and training needs forecasting, labor market, transition