On the role of shear in cosmological averaging

Using the spherically symmetric inhomogeneous Lemaitre-Tolman-Bondi dust solution, we study how the shear and the backreaction depend on the sharpness of the spatial transition between voids and walls and on the size of the voids. The voids considered here are regions with matter density Omega ~ 0 and expansion rate Ht ~ 1, while the walls are regions with matter density Omega ~ 1 and expansion rate Ht ~ 2/3. The results indicate that both the volume-average shear and the variance of the expansion rate grow proportional to the sharpness of the transition and diverge in the limit of a step function, but, for realistic-sized voids, are virtually independent of the size of the void. However, the backreaction, given by the difference of the variance and the shear, has a finite value in the step-function limit. By comparing the exact result for the backreaction to the case where the shear is neglected by treating the voids and walls as separate Friedmann-Robertson-Walker models, we find that the shear suppresses the backreaction by a factor of (r_0/t_0)^2, the squared ratio of the void size to the horizon size. This exemplifies the importance of using the exact solution for the interface between the regions of different expansion rates and densities. The suppression is justified to hold also for a network of compensated voids, but may not hold if the universe is dominated by uncompensated voids.Comment: 17 pages, 3 figure

Modelling dust processing and the evolution of grain sizes in the ISM using the method of moments

Interstellar dust grains do not have a single well-defined origin. Stars are demonstrably dust producers, but also efficient destroyers of cosmic dust. Dust destruction in the ISM is believed to be the result of SN shocks hitting the ambient ISM gas (and dust) and lead to an increased rate of ion sputtering, which reduces the dust mass. Grains located in cold molecular clouds can on the other hand grow by condensation, thus providing a replenishment mechanism or even a dominant channel of dust formation. In dense environments grains may coagulate and form large composite grains and aggregates and if grains collide with large enough energies they may be shattered, forming a range of smaller debris grains. The present paper presents a statistical modelling approach using the method of moments, which is computationally very inexpensive and may therefore be an attractive option when combining dust processing with, e.g., detailed simulations of interstellar gas dynamics. A solar-neighbourhood-like toy model of interstellar dust evolution is presented as an example.Comment: 21 pages, 8 figures and 2 tables. To appear in the special issue in P&SS on cosmic dust ("Cosmic Dust VIII"

On the role of shear in cosmological averaging II: large voids, non-empty voids and a network of different voids

We study the effect of shear on the cosmological backreaction in the context of matching voids and walls together using the exact inhomogeneous Lemaitre-Tolman-Bondi solution. Generalizing JCAP 1010 (2010) 021, we allow the size of the voids to be arbitrary and the densities of the voids and walls to vary in the range 0 < Omega_v < Omega_w < 1. We derive the exact analytic result for the backreaction and consider its series expansion in powers of the ratio of the void size to the horizon size, r_0/t_0. In addition, we deduce a very simple fitting formula for the backreaction with error less than 1% for voids up to sizes r_0 = t_0. We also construct an exact solution for a network of voids with different sizes and densities, leading to a non-zero relative variance of the expansion rate between the voids. While the leading order term of the backreaction for a single void-wall pair is of order (r_0/t_0)^2, the relative variance between the different voids in the network is found to be of order (r_0/t_0)^4 and thus very small for voids of the observed size. Furthermore, we show that even for very large voids, the backreaction is suppressed by an order of magnitude relative to the estimate obtained by treating the walls and voids as disjoint Friedmann solutions. Whether the suppression of the backreaction due to the shear is just a consequence of the restrictions of the used exact models, or a generic feature, has to be addressed with more sophisticated solutions.Comment: 19 pages, 5 figure

Thresholds for the Dust Driven Mass Loss from C-rich AGB Stars

It is well established that mass loss from AGB stars due to dust driven winds cannot be arbitrarily low. We model the mass loss from carbon rich AGB stars using detailed frequency-dependent radiation hydrodynamics including dust formation. We present a study of the thresholds for the mass loss rate as a function of stellar parameters based on a subset of a larger grid of such models and compare these results to previous observational and theoretical work. Furthermore, we demonstrate the impact of the pulsation mechanism and dust formation for the creation of a stellar wind and how it affects these thresholds and briefly discuss the consequences for stellar evolution.Comment: 2 pages, 1 figure. To be published in the proceedings of IAU Symp. 241 on Stellar Populations as Building Blocks of Galaxies, ed. A. Vazdekis et al. (2007). Replaced to match edited versio

Closed Loop Feedback Control of Injection and Production Wells in the SPE Brugge Model

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Transport and location effects of a ring road with or without road pricing

Many city authorities consider how to develop long-tem strategies to achieve sustainable transport and land use systems. One of the key issues is the balance between policy measures to increase transport supply and measures to reduce transport demand or to reduce its adverse environmental impact. Some cities grow rapidly. They are often facing increasing congestion problems in their road transport systems. This leads to demand from the citizens or trade and industry for increased road capacity to improve accessibility and to facilitate mobility of people and goods. Such investments alone would not solve the problems, some analysts argue, but would rather induce new car traffic that would keep the congestion more or less at the same level as before. The solution is rather, they claim, to introduce economic instruments such as congestion pricing. Cities are very complex systems. Investments in the road network, or the introduction of congestion pricing, will not only affect the demand for different modes of transport but will also, in the long run, change the location of activities and hence the land use structure of the city. To be able to evaluate such policies appropriately, city and traffic planners need tools that could help them to clarify transport as well as land use effects of different actions. In a long-run perspective they need to be able to analyse the interaction between the transport and land use markets. Will the effects of a policy instrument in the transport market be counteracted or amplified by the relocation of households and workplaces in the land use market? Eliasson and Mattsson (2001) developed a stylised model of a "generic" symmetric city for the simulation of this kind of policies. In the model there are four groups of actors: households, employers, shops and service establish-ments. The households commute to the workplaces and make shopping and service trips by car, public transport or slow mode. In addition, there are road-based goods transport from the workplaces to the shops and service establishments. The different actors locate in the city in response to accessibility factors that are specific to each group of actor. Eliasson and Mattsson (2001) used the model to evaluate transport and land use effects of congestion pricing or a toll ring in the road network. In the present study we extend this analysis to the effects of the introduction of a ring road connecting the innermost suburbs, combined with or without optimal (i.e., marginal cost-based) congestion pricing or a toll ring. The analysis includes the effects on travel time and travel distance by purpose and mode of transport and the effects on the location of households, workplaces, shops and service establishments. A ring road, which is not combined with any economic instrument, will attract activities to the innermost suburbs. Travel by car will increase both in time and distance, while public transport will loose market shares. If the ring road is combined with optimal congestion pricing, this will not change the location pattern very much. The transport effects will be considerable, however. Car traffic volumes will be reduced, and hence congestion and then also car travel times. Part of the car demand will be transferred to public transport and to slow mode that both will increase their shares. If the ring road instead is combined with a toll ring, the location effect depends in an expected way on whether the toll ring is located inside or outside of the ring road. In general, a toll ring has lower car travel reducing effect, and leads to less toll revenues, than an optimal congestion pricing policy. References Eliasson, J. and Mattsson, L.-G. (2001), "Transport and location effects of road pricing: A simulation approach", Journal of Transport Economics and Policy 35: 417-456