Obtaining Potential Field Solution with Spherical Harmonics and Finite Differences

Potential magnetic field solutions can be obtained based on the synoptic magnetograms of the Sun. Traditionally, a spherical harmonics decomposition of the magnetogram is used to construct the current and divergence free magnetic field solution. This method works reasonably well when the order of spherical harmonics is limited to be small relative to the resolution of the magnetogram, although some artifacts, such as ringing, can arise around sharp features. When the number of spherical harmonics is increased, however, using the raw magnetogram data given on a grid that is uniform in the sine of the latitude coordinate can result in inaccurate and unreliable results, especially in the polar regions close to the Sun. We discuss here two approaches that can mitigate or completely avoid these problems: i) Remeshing the magnetogram onto a grid with uniform resolution in latitude, and limiting the highest order of the spherical harmonics to the anti-alias limit; ii) Using an iterative finite difference algorithm to solve for the potential field. The naive and the improved numerical solutions are compared for actual magnetograms, and the differences are found to be rather dramatic. We made our new Finite Difference Iterative Potential-field Solver (FDIPS) a publically available code, so that other researchers can also use it as an alternative to the spherical harmonics approach.Comment: This paper describes the publicly available Finite Difference Iterative Potential field Solver (FDIPS). The code can be obtained from http://csem.engin.umich.edu/FDIP

Simulating radiative shocks in nozzle shock tubes

We use the recently developed Center for Radiative Shock Hydrodynamics (CRASH) code to numerically simulate laser-driven radiative shock experiments. These shocks are launched by an ablated beryllium disk and are driven down xenon-filled plastic tubes. The simulations are initialized by the two-dimensional version of the Lagrangian Hyades code which is used to evaluate the laser energy deposition during the first 1.1ns. The later times are calculated with the CRASH code. This code solves for the multi-material hydrodynamics with separate electron and ion temperatures on an Eulerian block-adaptive-mesh and includes a multi-group flux-limited radiation diffusion and electron thermal heat conduction. The goal of the present paper is to demonstrate the capability to simulate radiative shocks of essentially three-dimensional experimental configurations, such as circular and elliptical nozzles. We show that the compound shock structure of the primary and wall shock is captured and verify that the shock properties are consistent with order-of-magnitude estimates. The produced synthetic radiographs can be used for comparison with future nozzle experiments at high-energy-density laser facilities.Comment: submitted to High Energy Density Physic

On 22-cycles of graphs

Let $G=(V,E)$ be a finite undirected graph. Orient the edges of $G$ in an arbitrary way. A $2$-cycle on $G$ is a function $d : E^2\to \mathbb{Z}$ such for each edge $e$, $d(e, \cdot)$ and $d(\cdot, e)$ are circulations on $G$, and $d(e, f) = 0$ whenever $e$ and $f$ have a common vertex. We show that each $2$-cycle is a sum of three special types of $2$-cycles: cycle-pair $2$-cycles, Kuratowski $2$-cycles, and quad $2$-cycles. In case that the graph is Kuratowski connected, we show that each $2$-cycle is a sum of cycle-pair $2$-cycles and at most one Kuratowski $2$-cycle. Furthermore, if $G$ is Kuratowski connected, we characterize when every Kuratowski $2$-cycle is a sum of cycle-pair $2$-cycles. A $2$-cycles $d$ on $G$ is skew-symmetric if $d(e,f) = -d(f,e)$ for all edges $e,f\in E$. We show that each $2$-cycle is a sum of two special types of skew-symmetric $2$-cycles: skew-symmetric cycle-pair $2$-cycles and skew-symmetric quad $2$-cycles. In case that the graph is Kuratowski connected, we show that each skew-symmetric $2$-cycle is a sum of skew-symmetric cycle-pair $2$-cycles. Similar results like this had previously been obtained by one of the authors for symmetric $2$-cycles. Symmetric $2$-cycles are $2$-cycles $d$ such that $d(e,f)=d(f,e)$ for all edges $e,f\in E$

Global Economic Prospects for Increasing Developing Country Migration into Developed Countries

Global labor markets have evolved dramatically in the last several decades and will continue to so for some time to come, driven by changing population demographics, economic globalization, dramatic changes in transportation technology, and accelerating institutional change. All these characteristics of migration make it an essential policy issue for the human development agenda. The United Nations Human Development Report for 2009 intends to provide a forward-looking assessment of global labor market dynamics, with particular reference to the effects of increased labor mobility on global patterns of employment and output. To date, the most rigorous analysis of this subject is the World Bank Global Prospect Group’s forecasts with their Global Economic Prospects Linkage model. This report describes how an update of the GEP model captures more detailed information on global labor movements and heterogeneity, and reports new projections on global migration patterns. These results suggest complex market interactions between migrants and resident workers, whether native or migrant, and between labor and other factors of production. For example reducing migration raises the premium on migrant labor in the destination countries, while lowering the relative return to capital. The first effect makes for higher real income, consumption, and remittances for migrants of both types. For native populations in high income countries, the negative capital income effect dominates the wage effect of reduced competition from migrants. It is perhaps ironic that reducing labor competition is more beneficial to migrants, who lack the capital income and thereby gain absolutely from rising relative wages. Of course one of the primary demand drivers for migrants is the desire to profit from using capital resources more fully within high income economies. In OECD economies, pension schemes guarantee that a significant part of these profits accrue indirectly to native workers. Taken together, these results strongly support the argument that migration has beneficial growth effects on global real economic activity, improving the efficiency of international resource allocation for the benefit of both sending and receiving countries. However, these reassuring aggregate results mask more complex interactions in domestic labor markets, and there will inevitably be both winners and losers from the ensuing structural adjustments. Having said this, the existence of substantial aggregate gains, particularly new fiscal resources for the public sector, suggests the prospect of adjustment assistance to offset adverse impacts.Migration, globalization, North-South

Global Economic Prospects for Increasing Developing Country Migration into Developed Countries

Global labor markets have evolved dramatically in the last several decades and will continue to so for some time to come, driven by changing population demographics, economic globalization, dramatic changes in transportation technology, and accelerating institutional change. All these characteristics of migration make it an essential policy issue for the human development agenda. The United Nations Human Development Report for 2009 intends to provide a forward-looking assessment of global labor market dynamics, with particular reference to the effects of increased labor mobility on global patterns of employment and output. To date, the most rigorous analysis of this subject is the World Bank Global Prospect Group’s forecasts with their Global Economic Prospects Linkage model. This report describes how an update of the GEP model captures more detailed information on global labor movements and heterogeneity, and reports new projections on global migration patterns. These results suggest complex market interactions between migrants and resident workers, whether native or migrant, and between labor and other factors of production. For example reducing migration raises the premium on migrant labor in the destination countries, while lowering the relative return to capital. The first effect makes for higher real income, consumption, and remittances for migrants of both types. For native populations in high income countries, the negative capital income effect dominates the wage effect of reduced competition from migrants. It is perhaps ironic that reducing labor competition is more beneficial to migrants, who lack the capital income and thereby gain absolutely from rising relative wages. Of course one of the primary demand drivers for migrants is the desire to profit from using capital resources more fully within high income economies. In OECD economies, pension schemes guarantee that a significant part of these profits accrue indirectly to native workers. Taken together, these results strongly support the argument that migration has beneficial growth effects on global real economic activity, improving the efficiency of international resource allocation for the benefit of both sending and receiving countries. However, these reassuring aggregate results mask more complex interactions in domestic labor markets, and there will inevitably be both winners and losers from the ensuing structural adjustments. Having said this, the existence of substantial aggregate gains, particularly new fiscal resources for the public sector, suggests the prospect of adjustment assistance to offset adverse impacts.Migration, globalization, North-South

A short proof of the planarity characterization of Colin de Verdière

AbstractColin de Verdière introduced an interesting new invariant μ(G) for graphs G, based on algebraic and analytic properties of matrices associated with G. He showed that the invariant is monotone under taking miners and moreover, that μ(G) ≤ 3 if only if G is planar. In this paper we give a short proof of Colin de Verdière′s result that μ(G) ≤ 3 if G is planar

Three-dimensional modeling of charge transport, injection and recombination in organic light-emitting diodes

Organic light-emitting diodes (OLEDs) are ideally suited for lighting and display applications. Commercial OLED displays as well as OLED white-light sources are presently being introduced to the market. Essential electronic processes in OLEDs are the injection of electrons and holes into an organic semiconductor, their transport through the semiconductor, and their radiative recombination. In these processes an important role is played by the energetic disorder present in the organic semiconductor. This disorder leads to the localization of electronic states to specific sites. Charges move via a hopping process from one site to another. This hopping process involves quantum-mechanical tunneling assisted by a coupling to lattice vibrations. The energies of the sites are often taken to be distributed according to a Gaussian density of states (DOS). With these ingredients, the electronic processes taking place in OLEDs have been intensively investigated in the last two decades. However, this has not yet led to a satisfactory and complete OLED model that includes these processes in a consistent way, taking into account three-dimensional effects at the microscopic level. The goal of this thesis was to make an important step into this direction. In this thesis, the motion of charge carriers is evaluated by means of calculations based on the Pauli master equation and by means of Monte-Carlo simulations, which are both introduced in Chapter 2. The Pauli master equation describes the time-averaged occupational probabilities of a three-dimensional assembly of sites. This equation can be solved by means of an iterative calculation scheme, after which relevant quantities like the current and the charge-carrier mobility can be obtained. In the Monte-Carlo approach, the actual motion of the charges is simulated in time. The advantage of Monte-Carlo simulations over master-equation calculations is that Coulomb interactions between the charges can be taken into account in a consistent manner. In Chapter 3 it is shown that Coulomb interactions only influence the mobility in the case of high carrier densities and low electric field strengths. In this regime, taking into Coulomb interactions significantly decreases the mobility. This decrease is attributed to the trapping of charge carriers by the Coulomb potential well formed by the surrounding charges. For high electric field strengths and low charge-carrier densities, the mobility with Coulomb interactions agrees quite well with the mobility obtained without taking into account Coulomb interactions. In Chapter 4 the charge-carrier transport in single-carrier single-layer devices consisting of a disordered organic semiconductor sandwiched in between two metallic electrodes is studied by means of master-equation calculations. The effects of space charge, image-charge potentials close to the electrodes, finite injection barriers, and the complete dependence of the charge-carrier mobility on the temperature, the carrier density and the electric field are taken into account. The obtained three-dimensional current density is very inhomogeneous, showing filamentary regions that carry most of the current. Nevertheless, the total current agrees quite well with that of a one-dimensional continuum drift-diffusion model. For very thin devices with a high injection barrier and a high disorder strength (large width of the Gaussian DOS), the one-dimensional continuum drift-diffusion model underestimates the current. In this regime, the current can be described very well by a model assuming injection and transport over one-dimensional straight filaments. In the master-equation approach followed in Chapter 4, Coulomb interactions between charges were only taken into account in a layer-averaged way, because the approach cannot account explicitly for Coulomb interactions in a consistent way. To study the influence of explicitly taking into account Coulomb interactions between charges, the studies of the single-carrier single-layer devices were repeated with Monte-Carlo in Chapter 5. It was found that in the absence of an injection barrier taking into account Coulomb interactions explicitly leads to a decrease in the current as compared to master-equation calculations. This decrease can be rationalized by studying the three-dimensional current density distributions. Taking into account explicit Coulomb interactions leads to a change in the pattern of the filamentary current pathways, which in turn leads to a decrease of the total current. The case of spatial correlations in the energetic disorder was also studied. For this case the filamentary current pathways are broader and the effects of taking into account explicit Coulomb interactions are smaller. Traditionally, the rate of recombination between electrons and holes is described by the Langevin formula, which contains the sum of the electron and hole mobilities as a factor. In Chapter 6 the question of the validity of this formula for electron-hole recombination in disordered organic semiconductors is addressed. One of the main assumptions made in deriving the Langevin formula is that charge-carrier transport occurs homogeneously throughout the semiconductor. As shown in Chapters 4 and 5, however, this is generally not the case in organic semiconductors. Nonetheless, it is found from double-carrier MonteCarlo simulations of recombining electrons and holes that the recombination rate can be very well described by the classical Langevin formula, provided that a change in the chargecarrier mobilities due to the presence of carriers of the opposite type is taken into account. Deviations from the Langevin formula at finite electric field are found to be small at the field scale typical for OLEDs. In Chapter 7, the time-dependent relaxational properties of charge transport are studied. When a charge is injected in a disordered organic semiconductor, its mobility will gradually decrease because of energetic relaxation of the charge into the tail of the DOS. This relaxation process was studied by inserting charges randomly in an assembly of sites with a Gaussian DOS and following the time dependence of their mobility. For short simulation times the mobility was found to be almost independent of the carrier density. However, when the mobility has decreased to a value somewhat higher than the steady-state mobility, the time-dependent mobility branches off and relaxes to the carrier-density dependent steady-state mobility. The obtained results can be used in studying the response of organic devices to a small additional ac voltage. Finally, in Chapter 8 overall conclusions and outlook for the three-dimensional modeling of OLEDs are presented. The results presented in this thesis should be considered as a first step towards the development of a predictive model for state-of-the-art OLEDs