An Improved Semi-Analytical Spherical Collapse Model for Non-linear Density Evolution

We derive a semi-analytical extension of the spherical collapse model of structure formation that takes account of the effects of deviations from spherical symmetry and shell crossing which are important in the non-linear regime. Our model is designed so that it predicts a relation between the peculiar velocity and density contrast that agrees with the results of N-body simulations in the region where such a comparison can sensibly be made. Prior to turnaround, when the unmodified spherical collapse model is expect to be a good approximation, the predictions of the two models coincide almost exactly. The effects of a late time dominating dark energy component are also taken into account. The improved spherical collapse model is a useful tool when one requires a good approximation not just to the evolution of the density contrast but also its trajectory. Moreover, the analytical fitting formulae presented is simple enough to be used anywhere where the standard spherical collapse might be used but with the advantage that it includes a realistic model of the effects of virialisation.Comment: 6 pages, 3 figures. Matches the version in print at Astrophys.

Electroneutrality and Phase Behavior of Colloidal Suspensions

Several statistical mechanical theories predict that colloidal suspensions of highly charged macroions and monovalent microions can exhibit unusual thermodynamic phase behavior when strongly deionized. Density-functional, extended Debye-H\"uckel, and response theories, within mean-field and linearization approximations, predict a spinodal phase instability of charged colloids below a critical salt concentration. Poisson-Boltzmann cell model studies of suspensions in Donnan equilibrium with a salt reservoir demonstrate that effective interactions and osmotic pressures predicted by such theories can be sensitive to the choice of reference system, e.g., whether the microion density profiles are expanded about the average potential of the suspension or about the reservoir potential. By unifying Poisson-Boltzmann and response theories within a common perturbative framework, it is shown here that the choice of reference system is dictated by the constraint of global electroneutrality. On this basis, bulk suspensions are best modeled by density-dependent effective interactions derived from a closed reference system in which the counterions are confined to the same volume as the macroions. Linearized theories then predict bulk phase separation of deionized suspensions only when expanded about a physically consistent (closed) reference system. Lower-dimensional systems (e.g., monolayers, small clusters), depending on the strength of macroion-counterion correlations, may be governed instead by density-independent effective interactions tied to an open reference system with counterions dispersed throughout the reservoir, possibly explaining observed structural crossover in colloidal monolayers and anomalous metastability of colloidal crystallites.Comment: 12 pages, 5 figures. Discussion clarified, references adde

Valuing spectrum at mm wavelengths for cellular networks

This paper investigates the economic value of spectrum at mm wavelengths. The analysis uses four techniques to value spectrum, namely a benchmarking comparison, a discounted cash flow analysis, a real options approach and a deprival method. The methods to calculate spectrum value presented in this paper can be used for any spectrum band and in any country. However, to determine the value of mm wavelengths for cellular networks, we have used data from New Zealand, specifically for the existing 700 MHz LTE network and for a hypothetical 28 GHz LTE network. These models are based on geographic data, population, cellular traffic analysis and LTE network design from this country. The results from the modelling analysis show that the value of spectrum in this case is bounded by the low value presented by the deprival valuation method and by the high value presented in the real options approach. All results show that as the demand for network capacity increases then mm wavelength spectrum becomes more valuable. This work will be useful to both regulators and operators. To regulators it offers insights into the economic value of mm wavelength spectrum which helps sets fees for spectrum licenses and to set reserve price and expected budgets for future spectrum auctions. To operators this paper offers insights into spectrum valuation techniques and presents data on the value of mm wavelengths for cellular networks

The constrained modified KP hierarchy and the generalized Miura transformations

In this letter, we consider the second Hamiltonian structure of the constrained modified KP hierarchy. After mapping the Lax operator to a pure differential operator the second structure becomes the sum of the second and the third Gelfand-Dickey brackets defined by this differential operator. We simplify this Hamiltonian structure by factorizing the Lax operator into linear terms.Comment: 8 pages, latex, no figure

Nonuniform Self-Organized Dynamical States in Superconductors with Periodic Pinning

We consider magnetic flux moving in superconductors with periodic pinning arrays. We show that sample heating by moving vortices produces negative differential resistivity (NDR) of both N and S type (i.e., N- and S-shaped) in the voltage-current characteristic (VI curve). The uniform flux flow state is unstable in the NDR region of the VI curve. Domain structures appear during the NDR part of the VI curve of an N type, while a filamentary instability is observed for the NDR of an S type. The simultaneous existence of the NDR of both types gives rise to the appearance of striking self-organized (both stationary and non-stationary) two-dimensional dynamical structures.Comment: 4 pages, 2 figure

Evolutionary bi-stability in pathogen transmission mode

Many pathogens transmit to new hosts by both infection (horizontal transmission) and transfer to the infected host's offspring (vertical transmission). These two transmission modes require speci®c adap- tations of the pathogen that can be mutually exclusive, resulting in a trade-off between horizontal and vertical transmission. We show that in mathematical models such trade-offs can lead to the simultaneous existence of two evolutionary stable states (evolutionary bi-stability) of allocation of resources to the two modes of transmission. We also show that jumping between evolutionary stable states can be induced by gradual environmental changes. Using quantitative PCR-based estimates of abundance in seed and vege- tative parts, we show that the pathogen of wheat, Phaeosphaeria nodorum, has jumped between two distinct states of transmission mode twice in the past 160 years, which, based on published evidence, we interpret as adaptation to environmental change. The ®nding of evolutionary bi-stability has impli- cations for human, animal and other plant diseases. An ill-judged change in a disease control programme could cause the pathogen to evolve a new, and possibly more damaging, combination of transmission modes. Similarly, environmental changes can shift the balance between transmission modes, with adverse effects on human, animal and plant health

Epidemiology and integrated control of Potato Late Blight in Europe

Phytophthora infestans, the causal agent of late blight, is a major threat to potato production in northwestern Europe. Before 1980, the worldwide population of P. infestans outside Mexico appeared to be asexual and to consist of a single clonal lineage of A1 mating type characterized by a single genotype. It is widely believed that new strains migrated into Europe in 1976 and that this led to subsequent population changes including the introduction of the A2 mating type. The population characteristics of recently collected isolates in NW Europe show a diverse population including both mating types, sexual reproduction and oospores, although differences are observed between regions. Although it is difficult to find direct evidence that new strains are more aggressive, there are several indications from experiments and field epidemics that the aggressiveness of P. infestans has increased in the past 20 years. The relative importance of the different primary inoculum sources and specific measures for reducing their role, such as covering dumps with plastic and preventing seed tubers from becoming infected, is described for the different regions. In NW Europe, varieties with greater resistance tend not to be grown on a large scale. From the grower’s perspective, the savings in fungicide input that can be achieved with these varieties are not compensated by the higher (perceived) risk of blight. Fungicides play a crucial role in the integrated control of late blight. The spray strategies in NW Europe and a table of the specific attributes of the most important fungicides in Europe are presented. The development and use of decision support systems (DSSs) in NW Europe are described. In The Netherlands, it is estimated that almost 40% of potato growers use recommendations based on commercially available DSS. In the Nordic countries, a new DSS concept with a fixed 7-day spray interval and a variable dose rate is being tested. In the UK, commercially available DSSs are used for c. 8% of the area. The validity of Smith Periods for the new population of P. infestans in the UK is currently being evaluated