Real closed exponential fields

In an extended abstract Ressayre considered real closed exponential fields and integer parts that respect the exponential function. He outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we give a detailed account of Ressayre's construction, which becomes canonical once we fix the real closed exponential field, a residue field section, and a well ordering of the field. The procedure is constructible over these objects; each step looks effective, but may require many steps. We produce an example of an exponential field $R$ with a residue field $k$ and a well ordering $<$ such that $D^c(R)$ is low and $k$ and $<$ are $\Delta^0_3$, and Ressayre's construction cannot be completed in $L_{\omega_1^{CK}}$.Comment: 24 page

Valuation theory, generalized IFS attractors and fractals

Using valuation rings and valued fields as examples, we discuss in which ways the notions of “topological IFS attractor” and “fractal space” can be generalized to cover more general settings

Heat Transfer across the Free Surface of a Thermocapillary Liquid Bridge

The heat transfer across the free surface of a millimetric thermocapillary liquid bridge is investigated for two dimensional axisymmetric flows, computed by Newton–Raphson iteration. The coupled multiphase flow in the silicone-oil liquid bridge and in the ambient gas (air) is considered for Marangoni and Prandtl numbers of interest for typical space experiments. Based on the space-resolved heat flux of the two-phase flow for a wide range of parameters, we derive a model for the heat flux in form of Newton’s heat transfer law for a surrogate single phase flow, in which a space-dependent Biot function is considered. A parametric study for a 2 St silicone-oil liquid bridge is conducted for 150 configurations to derive a reliable fit of the Biot function for a wide range of Reynolds numbers and aspect ratios. An explicit form of the parametric fit is provided which takes into account the hot- and cold-wall boundary layers in the liquid

Basic biology and small-scale rearing of Celatoria compressa (Diptera: Tachinidae), a parasitoid of Diabrotica virgifera virgifera (Coleoptera: Chrysomelidae)

The tachinid Celatoria compressa Wulp has been evaluated as a candidate biological control agent for the western corn rootworm, Diabrotica virgifera virgifera LeConte, in Europe, where it is an invasive alien pest of maize. Special emphasis has been placed on understanding aspects of the parasitoid basic biology and on developing a rearing technique for a small-scale production of C. compressa puparia. The age of C. compressa adults was found to be the most crucial factor in achieving mating. Only newly emerged, 1-h-old females, mated successfully with 2- to 5-day-old males, achieving a success rate of 74%. After mating, a prelarviposition period of 4 days occurred. The 5-day-old C. compressa females inserted their eggs containing fully-developed first instars directly into adults of D. v. virgifera. Total larval and pupal developmental time, including a pre-larviposition period of 4 days, was 29 days under quarantine laboratory conditions (25°C daytime, 15°C at night, L:D 14:10, 50% ± 10% r.h). Females of C. compressa were capable of producing on average 30 puparia throughout a female's mean larviposition period of 15 days. A large number of host attacks by C. compressa were unsuccessful, resulting in a mean larviposition success rate of 24% per female. Parasitoid females appear to have difficulties inserting the egg through the intersegmental sutures or membranes around leg openings of the host adults. Although the small-scale rearing technique of C. compressa presented is both time and labour intensive, C. compressa has been reared successfully for at least 20 successive generations without shifting the 1 male: 1 female sex ratio using a non-diapause strain of D. v. virgifer