Initial Condition for QGP Evolution from NEXUS

We recently proposed a new approach to high energy nuclear scattering, which treats the initial stage of heavy ion collisions in a sophisticated way. We are able to calculate macroscopic quantities like energy density and velocity flow at the end of this initial stage, after the two nuclei having penetrated each other. In other words, we provide the initial conditions for a macroscopic treatment of the second stage of the collision. We address in particular the question of how to incorporate the soft component properly. We find almost perfect "Bjorken scaling": the rapidity coincides with the space-time rapidity, whereas the transverse flow is practically zero. The distribution of the energy density in the transverse plane shows typically a very "bumpy" structure.Comment: 17 pages, 24 figure

Enhanced Perturbative Continuous Unitary Transformations

Unitary transformations are an essential tool for the theoretical understanding of many systems by mapping them to simpler effective models. A systematically controlled variant to perform such a mapping is a perturbative continuous unitary transformation (pCUT) among others. So far, this approach required an equidistant unperturbed spectrum. Here, we pursue two goals: First, we extend its applicability to non-equidistant spectra with the particular focus on an efficient derivation of the differential flow equations, which define the enhanced perturbative continuous unitary transformation (epCUT). Second, we show that the numerical integration of the flow equations yields a robust scheme to extract data from the epCUT. The method is illustrated by the perturbation of the harmonic oscillator with a quartic term and of the two-leg spin ladders in the strong-rung-coupling limit for uniform and alternating rung couplings. The latter case provides an example of perturbation around a non-equidistant spectrum.Comment: 27 pages, 18 figures; separated methodological background from introduction, added perturbed harmonic oscillator for additional illustration, added explicit solution of deepCUT equation

Policy brief, number 11, 2014

[From Introduction] Urbanisation in sub-Saharan Africa: changing the locus of poverty. Urbanisation is a global phenomenon that is changing the face of the Earth, as well as how people earn a living and secure their livelihoods. In 2006 the number of urban people in the world surpassed the number of rural people, and this gap will continue to grow. In only 16 years (by 2030) just under two-thirds of the world's people will be urban dwellers. Whilst most of the developed world and large parts of Latin America already have more than threequarters of their populations living in cities and towns, most countries in Asia and sub-Saharan Africa are still catching up. This means that they are experiencing massive migrations from rural to urban areas as rural people wish to swap the insecurities of rural living for the allure of secure employment and better services for health, education, sanitation and transport in towns and cities. Sub-Saharan Africa (SSA) is the most rapidly urbanising region of the globe. According to UN-Habitat, in 1990, only 28 % of the region's inhabitants lived in towns and cities; that increased to approximately 32 % in 2001 and 41 % in 2010. The size of the urban population is likely to surpass the rural one around 2025. Contrary to popular belief, most urban residents in SSA (and globally) live in small towns rather than massive megacities; with just over half living in towns of less than 200,000 people and 78 % living in towns of less than 500,000 residents. Only 14 % of urban dwellers live in cities of more than one million people. Many new urban households maintain strong links to relatives and clans in rural areas, with circular migration patterns emerging as the urban transition takes place over several decades. The implications of this extremely rapid urbanisation in SSA countries for livelihoods and poverty are widely debated. UN-Habitat highlights a relatively unique aspect of urbanisation in SSA as being the accompanying high rate of growth in informal settlements or slums. In other words, not all rural migrants to towns and cities find secure incomes or shelter. Some slum areas have become permanent features where inter-generational poverty is reproduced. Although urban areas are producing an increasing share of national wealth in SSA countries, some argue that slowly the nexus of poverty is shifting towards urban areas. Rates of poverty are high in rural areas of SSA, but migration and internal population growth means that in some countries the number of urban poor almost matches the number of rural poor, and it is likely to grow. The informal economy contributes an average of 40 – 45 % of total urban GDP, which is higher than any other region of the world

Impact of Uncertainties in Hadron Production on Air-Shower Predictions

At high energy, cosmic rays can only be studied by measuring the extensive air showers they produce in the atmosphere of the Earth. Although the main features of air showers can be understood within a simple model of successive interactions, detailed simulations and a realistic description of particle production are needed to calculate observables relevant to air shower experiments. Currently hadronic interaction models are the main source of uncertainty of such simulations. We will study the effect of using different hadronic models available in CORSIKA and CONEX on extensive air shower predictions.Comment: 12 pages, 6 figures, to appear in the proceedings of International Conference on Interconnection between High Energy Physics and Astroparticle Physics: From Colliders to Cosmic Rays, Prague, Czech Republic, 7-13 Sep 200

Vector lattice model for stresses in granular materials

A vector lattice model for stresses in granular materials is proposed. A two dimensional pile built by pouring from a point is constructed numerically according to this model. Remarkably, the pile violates the Mohr Coulomb stability criterion for granular matter, probably because of the inherent anisotropy of such poured piles. The numerical results are also compared to the earlier continuum FPA model and the (scalar) lattice $q$-model

A stochastic flow rule for granular materials

There have been many attempts to derive continuum models for dense granular flow, but a general theory is still lacking. Here, we start with Mohr-Coulomb plasticity for quasi-2D granular materials to calculate (average) stresses and slip planes, but we propose a "stochastic flow rule" (SFR) to replace the principle of coaxiality in classical plasticity. The SFR takes into account two crucial features of granular materials - discreteness and randomness - via diffusing "spots" of local fluidization, which act as carriers of plasticity. We postulate that spots perform random walks biased along slip-lines with a drift direction determined by the stress imbalance upon a local switch from static to dynamic friction. In the continuum limit (based on a Fokker-Planck equation for the spot concentration), this simple model is able to predict a variety of granular flow profiles in flat-bottom silos, annular Couette cells, flowing heaps, and plate-dragging experiments -- with essentially no fitting parameters -- although it is only expected to function where material is at incipient failure and slip-lines are inadmissible. For special cases of admissible slip-lines, such as plate dragging under a heavy load or flow down an inclined plane, we postulate a transition to rate-dependent Bagnold rheology, where flow occurs by sliding shear planes. With different yield criteria, the SFR provides a general framework for multiscale modeling of plasticity in amorphous materials, cycling between continuum limit-state stress calculations, meso-scale spot random walks, and microscopic particle relaxation

Fluctuations of the Initial Conditions and the Continuous Emission in Hydrodynamic Description of Two-Pion Interferometry

Within hydrodynamic approach, we study the Bose-Einstein correlation of identical pions by taking into account both event-by-event fluctuating initial conditions and continuous pion emission during the whole development of the hot and dense matter formed in high-energy collisions. Considerable deviations occur, compared to the usual hydro calculations with smooth initial conditions and a sudden freeze-out on a well defined hypersurface. Comparison with data at RHIC shows that, despite rather rough approximation we used here, this description can give account of the $m_T$ dependence of $R_L$ and $R_s$ and improves considerably the one for $R_o$ with respect to the usual version.Comment: 5 pages, 4 figure

High-order harmonic generation with a strong laser field and an attosecond-pulse train: the Dirac Delta comb and monochromatic limits

In recent publications, it has been shown that high-order harmonic generation can be manipulated by employing a time-delayed attosecond pulse train superposed to a strong, near-infrared laser field. It is an open question, however, which is the most adequate way to approximate the attosecond pulse train in a semi-analytic framework. Employing the Strong-Field Approximation and saddle-point methods, we make a detailed assessment of the spectra obtained by modeling the attosecond pulse train by either a monochromatic wave or a Dirac-Delta comb. These are the two extreme limits of a real train, which is composed by a finite set of harmonics. Specifically, in the monochromatic limit, we find the downhill and uphill sets of orbits reported in the literature, and analyze their influence on the high-harmonic spectra. We show that, in principle, the downhill trajectories lead to stronger harmonics, and pronounced enhancements in the low-plateau region. These features are analyzed in terms of quantum interference effects between pairs of quantum orbits, and compared to those obtained in the Dirac-Delta limit.Comment: 10 pages, 7 figures (eps files). To appear in Laser Physic