Hofer geometry of a subset of a symplectic manifold

To every closed subset X of a symplectic manifold (M, ω) we associate a natural group of Hamiltonian diffeomorphisms Ham(X, ω). We equip this group with a semi-norm · X,ω, generalizing the Hofer norm.We discuss Ham(X, ω) and · X,ω if X is a symplectic or isotropic submanifold. The main result involves the relative Hofer diameter of X in M. Its first part states that for the unit sphere in R2n this diameter is bounded below by π2 , if n ≥ 2. Its second part states that for n ≥ 2 and d ≥ n there exists a compact subset X of the closed unit ball in R2n, such that X has Hausdorff dimension at most d + 1 and relative Hofer diameter bounded below by π/ k(n, d), where k(n, d) is an explicitly defined integer

Theoretical models of planetary system formation: mass vs semi-major axis

Planet formation models have been developed during the last years in order to try to reproduce the observations of both the solar system, and the extrasolar planets. Some of these models have partially succeeded, focussing however on massive planets, and for the sake of simplicity excluding planets belonging to planetary systems. However, more and more planets are now found in planetary systems. This tendency, which is a result of both radial velocity, transit and direct imaging surveys, seems to be even more pronounced for low mass planets. These new observations require the improvement of planet formation models, including new physics, and considering the formation of systems. In a recent series of papers, we have presented some improvements in the physics of our models, focussing in particular on the internal structure of forming planets, and on the computation of the excitation state of planetesimals, and their resulting accretion rate. In this paper, we focus on the concurrent effect of the formation of more than one planet in the same protoplanetary disc, and show the effect, in terms of global architecture and composition of this multiplicity. We use a N-body calculation including collision detection to compute the orbital evolution of a planetary system. Moreover, we describe the effect of competition for accretion of gas and solids, as well as the effect of gravitational interactions between planets. We show that the masses and semi-major axis of planets are modified by both the effect of competition and gravitational interactions. We also present the effect of the assumed number of forming planets in the same system (a free parameter of the model), as well as the effect of the inclination and eccentricity damping.Comment: accepted in Astronomy and Astrophysic

Componentes de la tasa de crecimiento poblacional en el negrón especulado de Saskatchewan, Canadá

Breeding range and abundance of White–winged Scoters (Melanitta fusca deglandi) have declined in northwestern North America. Hypotheses proposed to account for this trend are that survival and/or recruitment of females had declined. Thus, we used a reverse–time capture–recapture approach to directly estimate survival, seniority and capture probabilities for females of breeding age at Redberry Lake, Saskatchewan, Canada for 1975–1980 and 2000–2003. We also estimated population size of breeding females for 1975–1985 and 2000–2003 using capture–recapture data. Initially, this local population was in serious decline [95% CL ( ) = 0.89 ± 0.09], but has since stabilized and may be slowly increasing [95% CL ( ) = 1.07 ± 0.11]. This reversal in trajectory apparently resulted from increased recruitment rather than increased apparent survival. Importantly, recent recruitment of adult females appeared to be driven solely by immigration of adult females with no detectable in situ recruitment, suggesting a hypothesis that the local population is being rescued by females produced elsewhere.El rango reproductivo y la abundancia del negrón especulado (Melanitta fusca deglandi) han disminuido en la zona noroeste de América del Norte. La hipótesis propuesta para explicar esta tendencia es que se ha producido una disminución en la supervivencia y/o el reclutamiento de hembras. Por consiguiente, utilizamos un enfoque de captura–recaptura con el tiempo invertido para estimar directamente la supervivencia, la jerarquía y las probabilidades de captura de las hembras en edad reproductora del lago Redberry, Saskatchewan, Canadá, durante los periodos 1975–1980 y 2000– 2003. También estimamos el tamaño poblacional de las hembras reproductoras durante los periodos 1975–1985 y 2000–2003, mediante el empleo de datos de captura–recaptura. En un principio, esta población local experimentó una importante disminución [95% CL ( ) = 0,89 ± 0,09], pero posteriormente se estabilizó, y es posible que poco a poco vaya aumentando [95% CL ( ) = 1,07 ± 0,11]. Por lo visto, la inversión de esta trayectoria se produjo como consecuencia de un mayor reclutamiento, en lugar de una mayor supervivencia aparente. Es importante destacar que el reclutamiento reciente de hembras adultas parece haber obedecido exclusivamente a la migración de hembras adultas sin un reclutamiento detectable in situ, lo que sugiere la hipótesis de que la población local está siendo rescatada por hembras procedentes de otros lugares

Experimental and numerical results of active flow control on a highly loaded stator cascade

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.This article presents experimental and numerical results for a compressor cascade with active flow control. Steady and pulsed blowing has been used to control the secondary flow and separation characteristics of a highly loaded controlled diffusion airfoil. Investigations were performed at the design incidence for blowing ratios from approximately 0.7 to 3.0 (jet-to-inlet velocity) and a Reynolds number of 840 000 (based on axial chord and inlet velocity). Detailed flow field data were collected using a five-hole pressure probe, pressure taps on the blade surfaces, and time-resolved Particle Image Velocimetry. Unsteady Reynolds-averaged Navier–Stokes simulations were performed for a wide range of flow control parameters. The experimental and numerical results are used to understand the interaction between the jet and the passage flow. The benefit of the flow control on the cascade performance is weighted against the costs of the actuation by introducing an efficiency which takes the presence of the jets into account.DFG, SFB 557, Beeinflussung komplexer turbulenter Scherströmunge

Design of an Enhanced Throughput Catalytic Test System Capable of Rapid Heating and Cooling

Introduction High-throughput techniques are used in combinatorial chemistry, for example to per-mit preparation and screening of hundreds of catalysts simultaneously [1]. The prin-ciple of conducting more than one experiment at the same time is generally desir-able. Here we present a system allowing three concurrent fixed bed reactor tests, to be conducted on the laboratory scale (2 ml bed volume). This enhancement in throughput is achieved without loss of reaction analysis information. System Requirements The system is designed to investigate low temperature alkane isomerization (butane, pentane) on sulfated zirconia catalysts and therefore must fulfill the following condi-tions: (I) Isothermal over a wide temperature range, from 0°C (n-pentane isomerization) to 650°C (in situ calcination of the catalyst material [2]) (II) Rapid heating and cooling to reduce time loss (III) Fast and quantitative gas phase analysis Design and Test Results The requirements led to the construction of a reaction vessel in which three U-shaped tubular quartz reactors (inlet Ø 12 mm, outlet Ø 6 mm) are positioned sym-metrically. These tubular reactors each contain a quartz frit in the inlet tube to hold the catalyst powders. They are fixed at the top by seals made of polytetrafluorethyl-ene. Cooling the lid by an air flow avoids thermolysis of the PTFE. Isothermal heating is possible using a fluidized sand bed. The bottom of the vessel is heated electrically. It contains a frit of metal wire that supports the sand (50-70 mesh, ca. 500 ml). The sand is fluidized by air flowing through the frit (ca. 12 l/min). A 25 K/min heating ramp is possible. For experiments below room temperature the air can be cooled, e.g. by liquid nitrogen. The reaction vessel is enclosed by a cylindrical shell that can be purged by air for cooling. Thus a fast return to lower temperatures after activa-tion/calcination is guaranteed (from 450°C to 50°C in ca. 45 min). The temperature of the reactor is monitored by a thermocouple positioned in the center of the vessel and controlled by a second thermocouple close to the heating wire. A four position valve selects the outlet of either one of the three reactors, or the bypass, for analysis. Analysis of the gas phase is performed using a Micro GC (Varian CP 4900) equipped with a thermal conductivity detector, which allows separation of n-butane and isobu-tane within ca. 1 min. Cross section through the reaction vessel containing the U-shaped reactors Reaction vessel without cylindrical shell References [1] A. Hagemeyer, B. Jandeleit, Y. Liu, D.M. Poojary, H.W. Turner, A.F. Volpe Jr, W.H. Weinberg, Appl. Catal. A, 2001, 221, 23-43. [2] A. Hahn, T. Ressler, R.E. Jentoft, F.C. Jentoft, Chem. Comm., 2001, 537-538

Attosecond electron spectroscopy using a novel interferometric pump-probe technique

We present an interferometric pump-probe technique for the characterization of attosecond electron wave packets (WPs) that uses a free WP as a reference to measure a bound WP. We demonstrate our method by exciting helium atoms using an attosecond pulse with a bandwidth centered near the ionization threshold, thus creating both a bound and a free WP simultaneously. After a variable delay, the bound WP is ionized by a few-cycle infrared laser precisely synchronized to the original attosecond pulse. By measuring the delay-dependent photoelectron spectrum we obtain an interferogram that contains both quantum beats as well as multi-path interference. Analysis of the interferogram allows us to determine the bound WP components with a spectral resolution much better than the inverse of the attosecond pulse duration.Comment: 5 pages, 4 figure

Molecular differentiation between osteophytic and articular cartilage – clues for a transient and permanent chondrocyte phenotype

SummaryObjectiveTo identify the molecular differences between the transient and permanent chondrocyte phenotype in osteophytic and articular cartilage.MethodsTotal RNA was isolated from the cartilaginous layer of osteophytes and from intact articular cartilage from knee joints of 15 adult human donors and subjected to cDNA microarray analysis. The differential expression of relevant genes between these two cartilaginous tissues was additionally validated by quantitative reverse transcriptase polymerase chain reaction (RT-PCR) and by immunohistochemistry.ResultsAmong 47,000 screened transcripts, 600 transcripts were differentially expressed between osteophytic and articular chondrocytes. Osteophytic chondrocytes were characterized by increased expression of genes involved in the endochondral ossification process [bone gamma-carboxyglutamate protein/osteocalcin (BGLAP), bone morphogenetic protein-8B (BMP8B), collagen type I, alpha 2 (COL1A2), sclerostin (SOST), growth arrest and DNA damage-induced gene 45ß (GADD45ß), runt-related transcription factor 2 (RUNX2)], and genes encoding tissue remodeling enzymes [matrix metallopeptidase (MMP)9, 13, hyaluronan synthase 1 (HAS1)]. Articular chondrocytes expressed increased transcript levels of antagonists and inhibitors of the BMP- and Wnt-signaling pathways [Gremlin-1 (GREM1), frizzled-related protein (FRZB), WNT1 inducible signaling pathway protein-3 (WISP3)], as well as factors that inhibit terminal chondrocyte differentiation and endochondral bone formation [parathyroid hormone-like hormone (PTHLH), sex-determining region Y-box 9 (SOX9), stanniocalcin-2 (STC2), S100 calcium binding protein A1 (S100A1), S100 calcium binding protein B (S100B)].Immunohistochemistry of tissue sections for GREM1 and BGLAP, the two most prominent differentially expressed genes, confirmed selective detection of GREM1 in articular chondrocytes and that of BGLAP in osteophytic chondrocytes and bone.ConclusionsOsteophytic and articular chondrocytes significantly differ in their gene expression pattern. In articular cartilage, a prominent expression of antagonists inhibiting the BMP- and Wnt-pathway may serve to lock and stabilize the permanent chondrocyte phenotype and thus prevent their terminal differentiation. In contrast, osteophytic chondrocytes express genes with roles in the endochondral ossification process, which may account for their transient phenotype

Chondrogenic differentiation of growth factor-stimulated precursor cells in cartilage repair tissue is associated with increased HIF-1α activity

SummaryObjectiveTo investigate the chondrogenic potential of growth factor-stimulated periosteal cells with respect to the activity of Hypoxia-inducible Factor 1α (HIF-1α).MethodsScaffold-bound autologous periosteal cells, which had been activated by Insulin-like Growth Factor 1 (IGF-1) or Bone Morphogenetic Protein 2 (BMP-2) gene transfer using both adeno-associated virus (AAV) and adenoviral (Ad) vectors, were applied to chondral lesions in the knee joints of miniature pigs. Six weeks after transplantation, the repair tissues were investigated for collagen type I and type II content as well as for HIF-1α expression. The functional role of phosphatidylinositol 3-kinase (PI3K)/mammalian target of rapamycin (mTOR) and mitogen-activated protein kinase (MEK)/extracellular signal-regulated kinase (ERK) signaling on BMP-2/IGF-1-induced HIF-1α expression was assessed in vitro by employing specific inhibitors.ResultsUnstimulated periosteal cells formed a fibrous extracellular matrix in the superficial zone and a fibrocartilaginous matrix in deep zones of the repair tissue. This zonal difference was reflected by the absence of HIF-1α staining in superficial areas, but moderate HIF-1α expression in deep zones. In contrast, Ad/AAVBMP-2-stimulated periosteal cells, and to a lesser degree Ad/AAVIGF-1-infected cells, adopted a chondrocyte-like phenotype with strong intracellular HIF-1α staining throughout all zones of the repair tissue and formed a hyaline-like matrix. In vitro, BMP-2 and IGF-1 supplementation increased HIF-1α protein levels in periosteal cells, which was based on posttranscriptional mechanisms rather than de novo mRNA synthesis, involving predominantly the MEK/ERK pathway.ConclusionThis pilot experimental study on a relatively small number of animals indicated that chondrogenesis by precursor cells is facilitated in deeper hypoxic zones of cartilage repair tissue and is stimulated by growth factors which enhance HIF-1α activity