The Convergence of Particle-in-Cell Schemes for Cosmological Dark Matter Simulations

Particle methods are a ubiquitous tool for solving the Vlasov-Poisson equation in comoving coordinates, which is used to model the gravitational evolution of dark matter in an expanding universe. However, these methods are known to produce poor results on idealized test problems, particularly at late times, after the particle trajectories have crossed. To investigate this, we have performed a series of one- and two-dimensional "Zel'dovich Pancake" calculations using the popular Particle-in-Cell (PIC) method. We find that PIC can indeed converge on these problems provided the following modifications are made. The first modification is to regularize the singular initial distribution function by introducing a small but finite artificial velocity dispersion. This process is analogous to artificial viscosity in compressible gas dynamics, and, as with artificial viscosity, the amount of regularization can be tailored so that its effect outside of a well-defined region - in this case, the high-density caustics - is small. The second modification is the introduction of a particle remapping procedure that periodically re-expresses the dark matter distribution function using a new set of particles. We describe a remapping algorithm that is third-order accurate and adaptive in phase space. This procedure prevents the accumulation of numerical errors in integrating the particle trajectories from growing large enough to significantly degrade the solution. Once both of these changes are made, PIC converges at second order on the Zel'dovich Pancake problem, even at late times, after many caustics have formed. Furthermore, the resulting scheme does not suffer from the unphysical, small-scale "clumping" phenomenon known to occur on the Pancake problem when the perturbation wave vector is not aligned with one of the Cartesian coordinate axes.Comment: 29 pages, 29 figures. Accepted for publication in ApJ. The revised version includes a discussion of energy conservation in the remapping procedure, as well as some interpretive differences in the Conclusions made in response to the referee report. Results themselves are unchange

Storage Tank Overfill Vapor Cloud Explosions – Science, Causes, and Prevention

PresentationThe 2009 Puerto Rico incident reminds us that few events are as devastating as a vapor cloud explosion initiated by a tank overfill. Any company that transfers a flammable liquid into a storage tank is vulnerable to the vapor cloud that is generated by a tank overfill. Because the liquid typically pours out from the top of the tank and falls into the secondary containment, the liquid may be contained but the vapor can easily traverse the secondary containment wall and find an ignition sources where either a vapor cloud explosion or a flash fire (deflagration) that may result. In either case, it is important to understand and prevent this type of incident. Although recent gasoline tank overfill vapor cloud explosions (VCEs) have made the news, much larger crude oil volumes are shipped throughout the world. Therefore, it seems reasonable to investigate how the VCA methodology can be applied to crude oil tank overfills. In this paper we build on the Vapor Cloud Analysis (VCA) proposed by the UK Health Safety Executive as documented in Research Report 908 and the FABIG Technical Note 12. We summarize the latest results but we extend the method so that it is applicable to crude oil tank overfills. In addition, we show how to positively eliminate the potential for these incidents without large investments or complex systems

A 4th-Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov-Poisson Equation

Numerical solutions to the Vlasov-Poisson system of equations have important applications to both plasma physics and cosmology. In this paper, we present a new Particle-in-Cell (PIC) method for solving this system that is 4th-order accurate in both space and time. Our method is a high-order extension of one presented previously [B. Wang, G. Miller, and P. Colella, SIAM J. Sci. Comput., 33 (2011), pp. 3509--3537]. It treats all of the stages of the standard PIC update - charge deposition, force interpolation, the field solve, and the particle push - with 4th-order accuracy, and includes a 6th-order accurate phase-space remapping step for controlling particle noise. We demonstrate the convergence of our method on a series of one- and two- dimensional electrostatic plasma test problems, comparing its accuracy to that of a 2nd-order method. As expected, the 4th-order method can achieve comparable accuracy to the 2nd-order method with many fewer resolution elements.Comment: 18 pages, 10 figures, submitted to SIS

Storage Tank Overfill Vapor Cloud Explosions – Science, Causes, and Prevention

PresentationThe 2009 Puerto Rico incident reminds us that few events are as devastating as a vapor cloud explosion initiated by a tank overfill. Any company that transfers a flammable liquid into a storage tank is vulnerable to the vapor cloud that is generated by a tank overfill. Because the liquid typically pours out from the top of the tank and falls into the secondary containment, the liquid may be contained but the vapor can easily traverse the secondary containment wall and find an ignition sources where either a vapor cloud explosion or a flash fire (deflagration) that may result. In either case, it is important to understand and prevent this type of incident. Although recent gasoline tank overfill vapor cloud explosions (VCEs) have made the news, much larger crude oil volumes are shipped throughout the world. Therefore, it seems reasonable to investigate how the VCA methodology can be applied to crude oil tank overfills. In this paper we build on the Vapor Cloud Analysis (VCA) proposed by the UK Health Safety Executive as documented in Research Report 908 and the FABIG Technical Note 12. We summarize the latest results but we extend the method so that it is applicable to crude oil tank overfills. In addition, we show how to positively eliminate the potential for these incidents without large investments or complex systems

IT Industry Success in Small Developed Countries

While much research has focused on the reasons for information systems success, little research has focused on reasons for the success of U industries. This study investigates IT industry success in three small developed countries: Israel, New Zeahid and Singapore. All three countries have seen the rapid development of their IT industries in recent years. This is despite the fact that they are considerably different in many geographic, cultural, and political aspects and are widely dispersed around the globe

Developing identities within Roman Iberia: hybridity, urbanism, and economics in southern Iberia in the second and first centuries BC

This thesis examines the development of identities within Iberia during the Roman conquest of the peninsula through the lens of cultural hybridism, urbanism and economic changes. The aim is to explore how local Iberian communities evolved culturally through centuries of pre-Roman contact, and how these interactions fuelled later adaptations to Roman rule. Iberian communities, within this context, did not simply ‘become Roman’ but many acculturation theories have struggled to create alternatives to the ‘Romanization’ model successfully. While ‘Romanization’ is clearly problematic, this thesis will challenge and adapt several acculturation models to explore the visibility of cultural hybridity within ‘Roman’ and Iberian communities, and alternatively suggest the emergence of a pan-Mediterranean cultural background. These theories will then be applied in four case studies of prominent cities in southern Iberia: Italica (Santiponce), Hispalis (Sevilla), Corduba (Cordoba), and Augusta Emerita (Merida). In each of these case studies the thesis will address aspects of acculturation seen in the urban and economic evidence at those sites. The conclusion of this thesis will indicate that, while further study should be conducted, a more flexible approach to cultural identity should be considered in light of the evidence presented in the case of the evidence seen in these four towns

The Spitzer c2d Survey Of Nearby Dense Cores. X. Star Formation In L673 And Cb188

L673 and CB188 are two low-mass clouds isolated from large star-forming regions that were observed as part of the Spitzer Legacy Project "From Molecular Clouds to Planet Forming disks" (c2d). We identified and characterized all the young stellar objects (YSOs) of these two regions and modeled their spectral energy distributions (SEDs) to examine whether their physical properties are consistent with values predicted from the theoretical models and with the YSO properties in the c2d survey of larger clouds. Overall, 30 YSO candidates were identified by the c2d photometric criteria, 27 in L673 and 3 in CB188. We confirm the YSO nature of 29 of them and remove a false Class III candidate in L673. We further present the discovery of two new YSO candidates, one Class 0 and another possible Class I candidate in L673, therefore bringing the total number of YSO candidates to 31. Multiple sites of star formation are present within L673, closely resembling other well-studied c2d clouds containing small groups such as B59 and L1251B, whereas CB188 seems to consist of only one isolated globule-like core. We measure a star formation efficiency (SFE) of 4.6%, which resembles the SFE of the larger c2d clouds. From the SED modeling of our YSO sample we obtain envelope masses for Class I and Flat spectrum sources of 0.01-1.0 M-circle dot. The majority of Class II YSOs show disk accretion rates from 3.3 x 10(-10) to 3 x 10(-8) M-circle dot yr(-1) and disk masses that peak at 10(-4) to 10(-3) M-circle dot. Finally, we examined the possibility of thermal fragmentation in L673 as the main star-forming process. We find that the mean density of the regions where significant YSO clustering occurs is of the order of similar to 10(5) cm(-3) using 850 mu m observations and measure a Jeans Length that is greater than the near-neighbor YSO separations by approximately a factor of 3-4. We therefore suggest that other processes, such as turbulence and shock waves, may have had a significant effect on the cloud's filamentary structure and YSO clustering.University of SouthamptonNASA 1279198, 1288806, 1365763Jet Propulsion Laboratory, California Institute of TechnologyAstronom

Resolved Depletion Zones and Spatial Differentiation of N2H+ and N2D+

We present a study on the spatial distribution of N2D+ and N2H+ in thirteen protostellar systems. Eight of thirteen objects observed with the IRAM 30m telescope show relative offsets between the peak N2D+ (J=2-1) and N2H+ (J=1-0) emission. We highlight the case of L1157 using interferometric observations from the Submillimeter Array and Plateau de Bure Interferometer of the N2D+ (J=3-2) and N2H+ (J=1-0) transitions respectively. Depletion of N2D+ in L1157 is clearly observed inside a radius of ~2000 AU (7") and the N2H+ emission is resolved into two peaks at radii of ~1000 AU (3.5"), inside the depletion region of N2D+. Chemical models predict a depletion zone in N2H+ and N2D+ due to destruction of H2D+ at T ~ 20 K and the evaporation of CO off dust grains at the same temperature. However, the abundance offsets of 1000 AU between the two species are not reproduced by chemical models, including a model that follows the infall of the protostellar envelope. The average abundance ratios of N2D+ to N2H+ have been shown to decrease as protostars evolve by Emprechtinger et al., but this is the first time depletion zones of N2D+ have been spatially resolved. We suggest that the difference in depletion zone radii for N2H+ and N2D+ is caused by either the CO evaporation temperature being above 20 K or an H2 ortho-to-para ratio gradient in the inner envelope.Comment: Accepted to ApJ. 44 pages 13 Figure