An efficient algorithm for nucleolus and prekernel computation in some classes of TU-games

We consider classes of TU-games. We show that we can efficiently compute an allocation in the intersection of the prekernel and the least core of the game if we can efficiently compute the minimum excess for any given allocation. In the case where the prekernel of the game contains exactly one core vector, our algorithm computes the nucleolus of the game. This generalizes both a recent result by Kuipers on the computation of the nucleolus for convex games and a classical result by Megiddo on the nucleolus of standard tree games to classes of more general minimum cost spanning tree games. Our algorithm is based on the ellipsoid method and Maschler's scheme for approximating the prekernel. \u

Theoretical and experimental bubble formation at a single orifice in a two-dimensional gas-fluidized bed

An earlier developed, first principles hydrodynamic model of gas-fluidized beds has been employed to study theoretically bubble formation at a single orifice in a two-dimensional bed. For several orifice discharge rates, theoretically predicted bubble sizes, formation times and shapes have been compared with experimental data obtained from triggered photographs. Besides, the present experimental and theoretical results were compared with predictions from two approximate models reported in the literature which are based on an idealized picture of the process of bubble formation. The advanced hydrodynamic model appears to predict the experimentally observed diameters, formation times and shapes of bubbles quite satisfactorily. The observed and calculated bubble diameters fall between the predictions from the two approximate models. Both the experimental and theoretical results clearly indicate that a strong leakage of bubble gas into the surrounding porous emulsion phase occurs, especially during the initial stage of bubble formatio

Direct numerical simulation of the drag force in bubble swarms

This paper studies the swarm effect on the drag force in bubbly flows. From literature it is well-known that for relatively small bubbles, the drag force increases with the bubble hold-up due to additional hindrance experienced by the bubbles caused by the modified flow field. Very large (spherical cap) bubbles on the other hand may rise cooperatively. The unique capabilities of a 3D Front Tracking model were used to investigate the influence of important parameters like the gas fraction, Reynolds number and the bubble size independently. It was found that the relative drag force increases for bubbles in the range of 2 to 5 mm when the gas fraction is increased up to 13%, while the bubbles become more spherical. Also the influence of the Reynolds number and the bubble aspect ratio on the increased drag force has been determined. It can be concluded that there is only a very weak effect over several decades of the Reynolds number, while there is a strong effect of the bubble aspect ratio.\ud This also helps explaining why the increase in drag is smaller for larger bubbles: when the gas fraction is increased deformable bubbles become more spherical, thus reducing the drag force

Experimental and theoretical porosity profiles in a two-dimensional gas-fluidized bed with a central jet

A light transmission technique has been developed for measurement of the local porosity in two-dimensional gas-fluidized beds. The principles of liquid-solid fluidization and vibrofluidization were employed to perform the necessary calibration. Time-averaged porosity profiles have been measured in a thin two-dimensional gas-fluidized bed with a central rectangular jet. These profiles were predicted satisfactorily with a previously developed first principles hydrodynamic model, without the use of any fitted parameters. The hydrodynamic model is based on a two-fluid model approach in which both phases are considered to be continuous and fully interpenetratin

Adiabatic reactor simulations of the reverse flow catalytic membrane reactor concept with Perovskite membranes

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Azimuth axis optical alignment system Final report

Azimuth axis optical alignment system to monitor and measure attitude or angular position of remote object about azimuth axis using phase information imposed on returning beam of ligh

Validation of the granular temperature prediction of the kinetic theory of granular flow by particle image velocimetry and discrete particle model

In order to give a detailed description of the hydrodynamics in large industrial scale fluidized beds, continuum models are required. Continuum models often use the kinetic theory of granular flow (KTGF) to provide closure equations for the internal momentum transport in the particulate phase. In this work the outcome of the continuum model is compared with both an experimental technique and detailed simulations, i.e. particle image velocimetry (PIV) and the discrete particle model (DPM).\ud PIV is used for the measurement of an instantaneous velocity field of the flow in the front plane of a fluid bed. The classical PIV analysis is extended to enable the measurement of the local velocity fluctuations in the interrogation area, i.e. the granular temperature. In the DPM, each particle is tracked individually. In this model detailed collision models can be incorporated, rendering the DPM a valuable research tool to validate the underlying assumptions in the KTGF concerning the particle-particle interactions and the particle velocity distribution functions.\ud The aforementioned experimental and numerical techniques are used to measure the granular temperature distribution around a single bubble rising in a gas-fluidized bed. It was found that the results of PIV and the DPM are very similar. Although the initial bubble shape and size are well predicted by the continuum model, it fails once the bubble has detached from the bottom plate. Further research in the area of KTGF closures is needed to improve the predictions of the TFM

Computing an element in the lexicographic kernel of a game

The lexicographic kernel of a game lexicographically maximizes the surplusses $s_{ij}$ (rather than the excesses as would the nucleolus). We show that an element in the lexicographic kernel can be computed efficiently, provided we can efficiently compute the surplusses $s_{ij}(x)$ corresponding to a given allocation $x$. This approach improves previously obtained results and allows us to determine a kernel element without appealing to Maschler transfers in the execution of the algorithm. \u

Description of the fluctuating colloid-polymer interface

To describe the full spectrum of surface fluctuations of the interface between phase-separated colloid-polymer mixtures from low scattering vector q (classical capillary wave theory) to high q (bulk-like fluctuations), one must take account of the interface's bending rigidity. We find that the bending rigidity is negative and that on approach to the critical point it vanishes proportionally to the interfacial tension. Both features are in agreement with Monte Carlo simulations.Comment: 5 pages, 3 figures, 1 table. Accepted for publication in Phys. Rev. Let