Influence of surface tension on the conical miniscus of a magnetic fluid in the field of a current-carrying wire

We study the influence of surface tension on the shape of the conical miniscus built up by a magnetic fluid surrounding a current-carrying wire. Minimization of the total energy of the system leads to a singular second order boundary value problem for the function $\zeta(r)$ describing the axially symmetric shape of the free surface. An appropriate transformation regularizes the problem and allows a straightforward numerical solution. We also study the effects a superimposed second liquid, a nonlinear magnetization law of the magnetic fluid, and the influence of the diameter of the wire on the free surface profile

Coefficient of restitution for viscoelastic disks

The dissipative collision of two identical viscoelastic disks is studied. By using a known law for the elastic part of the interaction force and the viscoelastic damping model an analytical solution for the coefficient of restitution shall be given. The coefficient of restitution depends significantly on the impact velocity. It approaches one for small velocities and decreases for increasing velocities.Comment: 11 pages, 3 figure

Heavy hydrogen in the stratosphere

We report measurements of the deuterium content of molecular hydrogen (H2) obtained from a suite of air samples that were collected during a stratospheric balloon flight between 12 and 33 km at 40º N in October 2002. Strong deuterium enrichments of up to 400 permil versus Vienna Standard Mean Ocean Water (VSMOW) are observed, while the H2 mixing ratio remains virtually constant. Thus, as hydrogen is processed through the H2 reservoir in the stratosphere, deuterium is accumulated in H2 . Using box model calculations we investigated the effects of H2 sources and sinks on the stratospheric enrichments. Results show that considerable isotope enrichments in the production of H2 from CH4 must take place, i.e., deuterium is transferred preferentially to H2 during the CH4 oxidation sequence. This supports recent conclusions from tropospheric H2 isotope measurements which show that H2 produced photochemically from CH4 and non-methane hydrocarbons must be enriched in deuterium to balance the tropospheric hydrogen isotope budget. In the absence of further data on isotope fractionations in the individual reaction steps of the CH4 oxidation sequence, this effect cannot be investigated further at present. Our measurements imply that molecular hydrogen has to be taken into account when the hydrogen isotope budget in the stratosphere is investigated

The isotopic composition of methane in the stratosphere : high-altitude balloon sample measurements

The isotopic composition of stratospheric methane has been determined on a large suite of air samples from stratospheric balloon flights covering subtropical to polar latitudes and a time period of 16 yr. 154 samples were analyzed for δC and 119 samples for δD, increasing the previously published dataset for balloon borne samples by an order of magnitude, and more than doubling the total available stratospheric data (including aircraft samples) published to date. The samples also cover a large range in mixing ratio from tropospheric values near 1800 ppb down to only 250 ppb, and the strong isotope fractionation processes accordingly increase the isotopic composition up to δ13C=−14‰ and δD= +190‰, the largest enrichments observed for atmospheric CH4 so far. When analyzing and comparing kinetic isotope effects (KIEs) derived from single balloon profiles, it is necessary to take into account the residence time in the stratosphere in combination with the observed mixing ratio and isotope trends in the troposphere, and the range of isotope values covered by the individual profile. Temporal isotope trends can also be determined in the stratosphere and compare reasonably well with the tropospheric trends. The effects of chemical and dynamical processes on the isotopic composition of CH4 in the stratosphere are discussed in detail. Different ways to interpret the data in terms of the relative fractions of the three important sink mechanisms (reaction with OH, O(1D)) and Cl, respectively), and their limitations, are investigated. The classical approach of using global mean KIE values can be strongly biased when profiles with different minimum mixing ratios are compared. Approaches for more local KIE investigations are suggested. It is shown that any approach for a formal sink partitioning from the measured data severely underestimates the fraction removed by OH, which is likely due to the insensitivity of the measurements to the kinetic fractionation in the lower stratosphere. Attempts can be made to correct for the lower stratospheric sink bias, but full quantitative interpretation of the CH4 isotope data in terms of the three sink reactions requires a global model

Incremental Network Design with Minimum Spanning Trees

Given an edge-weighted graph $G=(V,E)$ and a set $E_0\subset E$, the incremental network design problem with minimum spanning trees asks for a sequence of edges $e'_1,\ldots,e'_T\in E\setminus E_0$ minimizing $\sum_{t=1}^Tw(X_t)$ where $w(X_t)$ is the weight of a minimum spanning tree $X_t$ for the subgraph $(V,E_0\cup\{e'_1,\ldots,e'_t\})$ and $T=\lvert E\setminus E_0\rvert$. We prove that this problem can be solved by a greedy algorithm.Comment: 9 pages, minor revision based on reviewer comment

Petiolar Anatomy of North American Astragalus Species (Fabaceae) with Persistent Petioles

The petiole and rachis anatomy of 11 North American Astragalus species that show a tendency towards persistent petioles is described and illustrated by line drawings of representative transections. The results are compared with those of a spine anatomical survey of 200 Old World Astragalus and Astracantha species. Attention was given to the anatomical characters previously determined to be taxon-specific such as the amount and position of sclerenchyma and distribution patterns of vascular bundles. Character evolution and the classification of species into sections are discussed. A fundamental difference between New World and Old World Astragalus s.1. species was found. Most of the sclerenchyma contributes to the stability of the persistent petiole by the inner vascular bundle sheath—primarily the median bundle—in North American Astragalus species. In the Old World species, however, the outer sclerenchymatous bundle sheaths form most of the sclerenchyma of the spine. In American as well as in Asian species, the persistence of petioles (and rachises) evolved several times in different sections by convergence. Species representing distinct stages of the evolution towards a spinelike organ occur in the three sections Jejuni, Humillimi and Neonix. Thus, unlike in the Old World species in which the petiolar anatomy of each section reached more or less the same evolutionary level, in the New World the sections investigated contain species with different levels of spine development