117,356 research outputs found
A method for solving the factorized vorticity‐stream function equations by finite elements
No full textA new finite element method for solving the time‐dependent incompressible Navier‐Stokes equations with general boundary conditions is presented. The two second‐order partial differential equations for the vorticity and the stream function are factorized, apart from the non‐linear advection term, by eliminating the coupling due to the double specification on the stream function at (a part of) the boundary. This is achieved by reducing the no‐slip boundary conditions to projection integral conditions for the vorticity field and by evaluating the relevant quantities involved according to an extension of the method of Glowinski and Pironneau for the biharmonic problem. Time integration schemes and iterative algorithms are introduced which require the solution only of banded linear systems of symmetric type. The proposed finite element formulation is compared with its finite difference equivalent by means of a few numerical examples. The results obtained using 4‐noded bilinear elements provide an illustration of the superiority of the finite element based spatial discretization
Integral conditions for the pressure in the computation of incompressible viscous flows
No full textThe problem of finding the correct conditions for the pressure in the time discretized Navier-Stokes equations when the incompressibility constraint is replaced by a Poisson equation for the pressure is critically examined. It is shown that the pressure conditions required in a nonfractional-step scheme to formulate the problem as a system of split second-order equations are of an integral character and similar to the previously discovered integral conditions for the vorticity. The novel integral conditions for the pressure are used to derive a finite element method which is very similar to that developed by Glowinski and Pironneau and is the finite element counterpart of the influence matrix method of Kleiser and Schumann
Are lions democrats? The impact of democratization on economic growth in Africa, 1980-2010
No full textIf we look back at the past two decades, timing seems to point to a close connection between democratic reforms and economic growth in sub- Saharan states. Most countries in the area introduced multiparty politics and made dramatic – if incomplete – democratic progress between 1990 and 1994. Quite strikingly, it is exactly from 1994 to 1995 (and particularly from 2000) that the region began to undergo a period of significant economic progress. Because of the undeniable temporal sequence experienced in the region – that is, first political reforms, then economic growth – some observers pointed to a nexus between democratic progress and economic performance. But is there evidence in support of a causal relationship? As of today, no empirical research has been conducted on the democracy–growth nexus in the early twenty-first century’s so-called “emerging Africa”. To fill this gap, we discuss the different arguments claiming an economic advantage of democracies, we present our theoretical framework and carry out an empirical analysis of the growth impact of political regimes in 43 sub-Saharan states for the entire 1980–2010 period. Our findings confirm that African countries, many of which had long suffered the combination of authoritarian rule and predatory practices, derived some economic dividends from democratic progress
A review of vorticity conditions in the numerical solution of the ζ–ψ equations
No full textIn this review the conditions to be imposed on the vorticity in the calculation of two-dimensional incompressible viscous flows are discussed. Existing boundary vorticity formulas, commonly regarded as a surrogate Dirichlet boundary condition for the vorticity, are more properly interpreted as the discrete counterpart of the Neumann boundary condition for the stream function. This viewpoint helps to elucidate the algebraic equivalence of coupled numerical methods with uncoupled methods based on conditions of integral type for the vorticity. A unified understanding of several available treatments for determining correct vorticity boundary values is achieved by including in the present analysis spatial discretizations by finite differences and finite elements, coupled and uncoupled formulations of the problem as well as steady and unsteady equations. Results of some test calculations are presented to illustrate the numerical consequences of the analysis
Photoluminescent and crystal structure properties of the yellow and orange forms of [Re2(m-Cl)2(CO)6(m- 4,5-trimethyl-silyl-pyridazine]
No full textA series of neutral, dinuclear, luminescent rhenium(I) complexes suitable for phosphorescent organic light emitting devices (OLEDs) has been recently reported1,2. These compounds, of general formula [Re2(μ-Cl)2(CO)6(μ-1,2-diazine)], contain diazines bearing alkyl groups in one or in both the b positions. The complexes show intense green/yellow emissions in toluene solution and in the solid state and some of the complexes possess, in solution, high emission quantum yields (F 0.18-0.22 for the derivatives with disubstituted diazines). The excited state responsible for this emission can be confidentially described as a triplet metal-to-ligand charge transfer (3MLCT) level3. Following the DFT computational suggestions we have now synthetized a new complex of this family using the 4,5-bis(trimetylsilyl)-1,2-diazine ligand namely [Re2(m-Cl)2(CO)6(m- 4,5-trimethyl-silyl-pyridazine] (1, see Scheme). This complex has been completely carachterized in solution and it shows an emission maximum batochromically shifted respect to those of the analogous Re(I) compounds with alkyl-substituted diazine, with a lower quantum yield. Slow evaporation at room temperature of a CH2Cl2 solution containing (1) induces the concomitant formation of orange and yellow single crystals (Figure 1, top). X-ray crystal structure determinations performed at room temperature as well as at 100 K, show that they are two different polymorphs of the same compound. The emission spectra recorded on crystalline samples of the two polymorph (Figure 1, bottom) are hypsochromically shifted respect to the solution one and present higher quantum yields (lem = 537 nm and F = 0.30 for the yellow phase, lem = 575 nm and F = 0.50, for the orange one). References
(1) Mauro, M, Quartapelle Procopio, E., Sun,Y., Chien, C-H., Donghi, D., Panicati, M., Mercandelli, P., Mussini, P., D’Alfonso, G., De Cola, L. Adv. Func. Mat. 2009, in press
(2) Donghi, D., D’Alfonso, G., Mauro, M, Panigati, M., Mercandelli, P., Sironi, A., Mussini, P., D’Alfonso, L., Inorg. Chem. 2008, 47, 4243.
(3) Wrighton, M., Morse, D. L., J. Am. Chem. Soc., 1974, 96, 998
A simple thermodynamic model of diluted hydrogen gas/plasma for CFD applications
No full textThis work describes a simple thermodynamic model of the hydrogen gas at low densities and for temperatures going from those involving quantum rotations of ortho- and para-hydrogen up to the fully ionized state. The closed-form energy levels of Morse rotating oscillator given [D.C. Harris, M.D. Bertolucci, Symmetry and Spectroscopy (Dover, New York, 1989)] (but not those in Morse’s original paper) are shown to provide an internal partition function of H2 that is a sufficiently accurate representation of that exploiting the state-of-the-art spectrum of roto-vibrational levels calculated by Pachucki and Komasa [K. Pachucki, J. Komasa, J. Chem. Phys. 130, 164113 (2009)]. A system of two coupled quadratic equations for molecular dissociation and atomic ionization at thermodynamical and chemical equilibrium is derived according to the statistical mechanics by assuming that the system is an ideal mixture containing molecules, neutral atoms and noninteracting protons and electrons. The system of two equations reduces to a single quartic equation for the ionization unknown, with the coefficients dependent on the temperature and the specific volume. Explicit relations for specific energy and entropy of the hydrogen ideal gas/plasma model are derived. These fully compatible equations of state provide a complete thermodynamic description of the system, uniformly valid from low temperatures up to a fully ionized state, with electrons and ions relaxed to one and the same temperature. The comparison with results of other models developed in the framework of the physical and chemical pictures shows that the proposed elementary model is adequate for computational fluid dynamics purposes, in applications with the hydrogen gas under diluted conditions and when the dissociation and ionization can be assumed at thermodynamical and chemical equilibrium
Calculation of Impulsively Started Incompressible Viscous Flows
No full textThe paper's focus is the calculation of unsteady incompressible 2D flows past airfoils. In the framework of the primitive variable Navier–Stokes equations, the initial and boundary conditions must be assigned so as to be compatible, to assure the correct prediction of the flow evolution. This requirement, typical of all incompressible flows, viscous or inviscid, is often violated when modelling the flow past immersed bodies impulsively started from rest. Its fulfillment can however be restored by means of a procedure enforcing compatibility, consisting in a pre-processing of the initial velocity field, here described in detail. Numerical solutions for an impulsively started multiple airfoil have been obtained using a finite element incremental projection method. The spatial discretization chosen for the velocity and pressure are of different order to satisfy the inf–sup condition and obtain a smooth pressure field. Results are provided to illustrate the effect of employing or not the compatibility procedure, and are found in good agreement with those obtained with a non-primitive variable solver. In addition, we introduce a post-processing procedure to evaluate an alternative pressure field which is found to be more accurate than the one resulting from the projection method. This is achieved by considering an appropriate ‘unsplit’ version of the momentum equation, where the velocity solution of the projection method is substituted
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