Five-loop additive renormalization in the phi^4 theory and amplitude functions of the minimally renormalized specific heat in three dimensions

We present an analytic five-loop calculation for the additive renormalization constant A(u,epsilon) and the associated renormalization-group function B(u) of the specific heat of the O(n) symmetric phi^4 theory within the minimal subtraction scheme. We show that this calculation does not require new five-loop integrations but can be performed on the basis of the previous five-loop calculation of the four-point vertex function combined with an appropriate identification of symmetry factors of vacuum diagrams. We also determine the amplitude functions of the specific heat in three dimensions for n=1,2,3 above T_c and for n=1 below T_c up to five-loop order. Accurate results are obtained from Borel resummations of B(u) for n=1,2,3 and of the amplitude functions for n=1. Previous conjectures regarding the smallness of the resummed higher-order contributions are confirmed. Borel resummed universal amplitude ratios A^+/A^- and a_c^+/a_c^- are calculated for n=1.Comment: 30 pages REVTeX, 3 PostScript figures, submitted to Phys. Rev.

Cellular pattern formation during Dictyostelium aggregation

The development of multicellularity in the life cycle of Dictyostelium discoideum provides a paradigm model system for biological pattern formation. Previously, mathematical models have shown how a collective pattern of cell communication by waves of the messenger molecule cyclic adenosine 3′5′-monophosphate (cAMP) arises from excitable local cAMP kinetics and cAMP diffusion. Here we derive a model of the actual cell aggregation process by considering the chemotactic cell response to cAMP and its interplay with the cAMP dynamics. Cell density, which previously has been treated as a spatially homogeneous parameter, is a crucial variable of the aggregation model. We find that the coupled dynamics of cell chemotaxis and cAMP reaction-diffusion lead to the break-up of the initially uniform cell layer and to the formation of the striking cell stream morphology which characterizes the aggregation process in situ. By a combination of stability analysis and two-dimensional simulations of the model equations, we show cell streaming to be the consequence of the growth of a small-amplitude pattern in cell density forced by the large-amplitude cAMP waves, thus representing a novel scenario of spatial patterning in a cell chemotaxis system. The instability mechanism is further analysed by means of an analytic caricature of the model, and the condition for chemotaxis-driven instability is found to be very similar to the one obtained for the standard (non-oscillatory) Keller-Segel system. The growing cell stream pattern feeds back into the cAMP dynamics, which can explain in some detail experimental observations on the time evolution of the cAMP wave pattern, and suggests the characterization of the Dictyostelium aggregation field as a self-organized excitable medium

Climate's Long-term Impact on New Zealand Infrastructure (CLINZI) - A Case Study of Hamilton City, New Zealand

Infrastructure systems and services (ISS) are vulnerable to changes in climate. This paper reports on a study of the impact of gradual climate changes on ISS in Hamilton City, New Zealand. This study is unique in that it is the first of its kind to be applied to New Zealand ISS. This study also considers a broader range of ISS than most other climate change studies recently conducted. Using historical climate data and four climate change scenarios, we modelled the impact of climate change on water supply and quality, transport, energy demand, public health and air quality. Our analysis reveals that many of Hamilton City's infrastructure sectors demonstrated greater responsiveness to population changes than changes in gradual climate change. Any future planning decisions should be sensitive to climate change, but not driven by it (even though that may be fashionable to do so). We find there is considerable scope for extending this analysis. First, there is a need for local infrastructure managers to improve the coverage of the data needed for this kind of study. Second, any future study of this kind must focus on daily (rather than monthly) time steps and extreme (as well as gradual) climate changes.Climate change, infrastructure, integrated assessment, adaptation, Agricultural and Food Policy, Community/Rural/Urban Development, Crop Production/Industries, Environmental Economics and Policy, Farm Management, International Relations/Trade, Land Economics/Use, Livestock Production/Industries, Political Economy,

Venting of fission products and shielding in thermionic nuclear reactor systems

Most thermionic reactors are designed to allow the fission gases to escape out of the emitter. A scheme to allow the fission gases to escape is proposed. Because of the low activity of the fission products, this method should pose no radiation hazards

Refining of atmospheric transport model entries by the globally observed passive tracer distributions of 85krypton and sulfur hexafluoride (SF6)

Our high precision data base of the global distribution of SF6 in the troposphere [Maiss et al., 1996] is used in a two-dimensional atmospheric transport model (2D-HD model) to study the behaviour of this new tracer in comparison to the classical global atmospheric transport tracer 85Krypton. The 2D-HD model grid has been deduced from the 3D Hamburg TM2 model with the same resolution in the vertical and meridional direction, and was designed to run on any standard personal computer. The same vertical convection scheme and wind field as in the TM2 model, reduced to two dimensions, were used in the calculations. In addition, the horizontal diffusion parameter of the model was fine-tuned by matching the model estimated mean meridional 85Krypton distribution with observations over the Atlantic ocean. For simulating global tropospheric SF6 concentrations, an almost linearly increasing SF6 source strength was applied since 1970. The latitudinal distribution of the SF6 source was assumed to be similar to the global electrical power production. Excellent agreement between SF6 model results and observations is achieved with the 85Krypton-tuned 2D-HD transport model with respect to the global meridional concentration distribution and particularly in mid to high northern latitudes. In the southern hemisphere, at the German Antarctic Neumayer station, a significant seasonal cycle of SF6 has been observed which is reproduced by the model, however with a smaller ampitude. This finding may point to possible shortcomings of the model's transport scheme when simulating the seasonality of stratosphere-troposphere exchange in high southern latitudes

Limits of Random Trees

Local convergence of bounded degree graphs was introduced by Benjamini and Schramm. This result was extended further by Lyons to bounded average degree graphs. In this paper, we study the convergence of a random tree sequence where the probability of a given tree is proportional to $\prod_{v_i\in V(T)}d(v_i)!$. We show that this sequence is convergent and describe the limit object, which is a random infinite rooted tree