Sobolev Metrics on Diffeomorphism Groups and the Derived Geometry of Spaces of Submanifolds

Given a finite dimensional manifold $N$, the group $\operatorname{Diff}_{\mathcal S}(N)$ of diffeomorphism of $N$ which fall suitably rapidly to the identity, acts on the manifold $B(M,N)$ of submanifolds on $N$ of diffeomorphism type $M$ where $M$ is a compact manifold with $\dim M<\dim N$. For a right invariant weak Riemannian metric on $\operatorname{Diff}_{\mathcal S}(N)$ induced by a quite general operator $L:\frak X_{\mathcal S}(N)\to \Gamma(T^*N\otimes\operatorname{vol}(N))$, we consider the induced weak Riemannian metric on $B(M,N)$ and we compute its geodesics and sectional curvature. For that we derive a covariant formula for curvature in finite and infinite dimensions, we show how it makes O'Neill's formula very transparent, and we use it finally to compute sectional curvature on $B(M,N)$.Comment: 28 pages. In this version some misprints correcte

Individuality in northern lapwing migration and its link to timing of breeding

We tracked eight adult northern lapwings Vanellus vanellus (six females and two males) from a Dutch breeding colony by light-level geolocation year-round, three of them for multiple years. We show that birds breeding virtually next to each other may choose widely separated wintering grounds, stretching from nearby the colony west towards the UK and Ireland, and southwest through France into Iberia and Morocco. However, individual lapwings appeared relatively faithful to a chosen wintering area, and timing of outward and homeward migration can be highly consistent between years. Movements of migratory individuals were usually direct and fast, with some birds covering distances of approximately 2000 km within 2 to 4 days of travel. The two males wintered closest and returned earliest to the breeding colony. The female lapwings returned well before the onset of breeding, spending a pre-laying period of 19 to 54 days in the wider breeding area. Despite the potential for high migration speeds, the duration that birds were absent from the breeding area increased with distance to wintering areas, a pattern which was mainly driven by an earlier outward migration of birds heading for more distant wintering grounds. Moreover, females that overwintered closer to colony bred earlier. A large variation in migration strategies found even within a single breeding colony has likely supported the species’ responsiveness to recent climate change as evidenced by a shortened migration distance and an advanced timing of reproduction in Dutch lapwings since the middle of the 20th century. Migration strategies may vary between species, populations, individuals and between years within an individual. Individuals from a particular breeding population may migrate to the same wintering area or they may spread out over much of the non-breeding range. These connections between breeding and non-breeding areas of a migratory species are called ‘migratory connectivity’, and the strength of migratory connectivity has implications for the species ecology, evolution and conservation (Webster et al. 2002). Furthermore, the choice of a certain wintering area and migratory strategy may affect annual schedules including timing of events at breeding area (Marra et al. 1998), which demonstrates the importance to follow individuals throughout the annual cycle. Knowledge of variation in migratory routines within and between individuals of a population is also important to understanding and predicting the ability of species responses to environmental change, including climate change (Conklin et al. 2013). We employed GLS (Global Location Sensing, also called ‘light-level geolocation’ or just ‘geolocation’) technique based on the analysis of diurnal changes in light levels to track annual movements of northern lapwings (Vanellus vanellus; here synonymously termed ‘lapwing(s)’). Archival tags (‘geolocators’) record light intensities to determine dusk and dawn times from which geographical positions (two fixes daily) are calculated; day (night) length determines the latitude and time of local midday (midnight) the longitude (Hill ). Lapwings have been intensively ringed in many European countries for many years. Imboden (1974) undertook an extensive analysis (nicely summarized in Alerstam ) of ring recoveries collected during 1900 to 1969 from birds ringed as unfledged young and recovered within their first year of life or later. Albeit relying mainly on dead recoveries of hunted individuals, this analysis enabled the reconstruction of average seasonal movement patterns at population(s) level. It also revealed a large overlap in non-breeding locations used by lapwings originating from widely separated breeding colonies. Here, we present results from a first-time tracking study on this species by charting the year-round whereabouts of adult lapwings from a Dutch breeding colony. Some individuals were tracked for multiple years thereby providing first insights into individual consistency of migratory timing and choice of non-breeding locations. Finally, we investigate if spatial variation in non-breeding location relates to temporal variation of events at breeding area

Detection of arabis mosaic virus using the polymerase chain reaction (PCR)

A new method is described for detecting arabis mosaic virus (ArMV) in infected plants. Specific sequences of ArMV-RNA present in total nucleic acid extracts of infected Vitis vinifera or Chenopodium quinoa were initially reverse-transcribed into a complementary DNA (cDNA), then amplified by PCR using specific oligonucleotide-primers. Different primer combinations distinguished between an ArMV infection and an infection with grapevine fanleaf or raspberry ringspot virus. The amount of nucleic acids obtained from 5 mg grapevine leaves resp. 1 mg leaves of Ch. quinoa were sufficient for detecting ArMV

Stress transfer in microfibrillated cellulose reinforced poly(vinyl alcohol) composites

Copyright © 2014 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Composites Part A: Applied Science and Manufacturing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Composites Part A: Applied Science and Manufacturing Vol. 65 (2014), DOI: 10.1016/j.compositesa.2014.06.014Combined homogenisation and sonication treatments of micron-sized lyocell fibres were used to generate microfibrillated cellulose (MFC) with fibril diameters of ∼350 nm. No further reduction in fibril diameter was observed after 30 min treatment. Poly(vinyl alcohol) (PVA) composites reinforced with these fibrils were fabricated using solvent casting and physical and mechanical properties were investigated. The presence of MFC in PVA increased the thermal degradation of the polymer. An increase in both the tensile strength and modulus of the composites was observed for up to 3 wt.% of fibrils; beyond this point no significant increases were observed. An estimate of ∼39 GPa is made for the fibril modulus based on this increase. Stress-transfer between the polymer resin and the fibrils was investigated using Raman spectroscopy. Stress transfer in the composite is shown to be greater than that of a pure network of fibres, indicating a good fibre–matrix bond.Royal Thai Governmen

Quantum-gravity-induced matter self-interactions in the asymptotic-safety scenario

We investigate the high-energy properties of matter theories coupled to quantum gravity. Specifically, we show that quantum gravity fluctuations generically induce matter self-interactions in a scalar theory. Our calculations apply within asymptotically safe quantum gravity, where our results indicate that the UV is dominated by an interacting fixed point, with non-vanishing gravitational as well as matter couplings. In particular, momentum-dependent scalar self-interactions are non-zero and induce a non-vanishing momentum-independent scalar potential. Furthermore we point out that terms of this type can have observable consequences in the context of scalar-field driven inflation, where they can induce potentially observable non-Gaussianities in the CMB.Comment: 15 + 8 pages, 8 figures, extended truncation, version to be published in PR

Amplification of different marker sequences for identification of Agrobacterium vitis strains

Research Not

Modeling for the performance of navigation, control and data post-processing of underwater gliders

Underwater gliders allow efficient monitoring in oceanography. In contrast to buoys, which log oceanographic data at individual depths at only one location, gliders can log data over a period of up to one year by following predetermined routes. In addition to the logged data from the available sensors, usually a conductivity-temperature-depth (CTD) sensor, the depth-average velocity can also be estimated using the horizontal glider velocity and the GPS update in a dead-reckoning algorithm. The horizontal velocity is also used for navigation or planning a long-term glider mission. This paper presents an investigation to determine the horizontal glider velocity as accurately as possible. For this, Slocum glider flight models used in practice will be presented and compared. A glider model for a steady-state gliding motion based on this analysis is described in detail. The approach for estimating the individual model parameters using nonlinear regression will be presented. In this context, a robust method to accurately detect the angle of attack is presented and the requirements of the logged vehicle data for statistically verified model parameters are discussed. The approaches are verified using logged data from glider missions in the Indian Ocean from 2016 to 2018. It is shown that a good match between the logged and the modeled data requires a time-varying model, where the model parameters change with respect to time. A reason for the changes is biofouling, where organisms settle and grow on the glider. The proposed method for deciphering an accurate horizontal glider velocity could serve to improve the dead-reckoning algorithm used by the glider for calculating depth-average velocity and for understanding its errors. The depth-average velocity is used to compare ocean current models from CMEMS and HYCOM with the glider logged data

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group

We study Sobolev-type metrics of fractional order $s\geq0$ on the group \Diff_c(M) of compactly supported diffeomorphisms of a manifold $M$. We show that for the important special case $M=S^1$ the geodesic distance on \Diff_c(S^1) vanishes if and only if $s\leq\frac12$. For other manifolds we obtain a partial characterization: the geodesic distance on \Diff_c(M) vanishes for $M=\R\times N, s<\frac12$ and for $M=S^1\times N, s\leq\frac12$, with $N$ being a compact Riemannian manifold. On the other hand the geodesic distance on \Diff_c(M) is positive for $\dim(M)=1, s>\frac12$ and $\dim(M)\geq2, s\geq1$. For $M=\R^n$ we discuss the geodesic equations for these metrics. For $n=1$ we obtain some well known PDEs of hydrodynamics: Burgers' equation for $s=0$, the modified Constantin-Lax-Majda equation for $s=\frac 12$ and the Camassa-Holm equation for $s=1$.Comment: 16 pages. Final versio