Stability of a fermionic N+1N+1 particle system with point interactions

We prove that a system of $N$ fermions interacting with an additional particle via point interactions is stable if the ratio of the mass of the additional particle to the one of the fermions is larger than some critical $m^*$. The value of $m^*$ is independent of $N$ and turns out to be less than $1$. This fact has important implications for the stability of the unitary Fermi gas. We also characterize the domain of the Hamiltonian of this model, and establish the validity of the Tan relations for all wave functions in the domain.Comment: LaTeX, 29 pages, 2 figures; typos corrected, explanations and references added; to appear in Commun. Math. Phy

Stability of the 2+2 fermionic system with point interactions

We give a lower bound on the ground state energy of a system of two fermions of one species interacting with two fermions of another species via point interactions. We show that there is a critical mass ratio m_c \approx 0.58 such that the system is stable, i.e., the energy is bounded from below, for m \in [m_c, m_c^{-1}]. So far it was not known whether this 2+2 system exhibits a stable region at all or whether the formation of four-body bound states causes an unbounded spectrum for all mass ratios, similar to the Thomas effect. Our result gives further evidence for the stability of the more general N+M system.Comment: LaTeX, 12 pages; typos corrected, references and 2 figures added; to appear in Math. Phys. Anal. Geo

Triviality of a model of particles with point interactions in the thermodynamic limit

We consider a model of fermions interacting via point interactions, defined via a certain weighted Dirichlet form. While for two particles the interaction corresponds to infinite scattering length, the presence of further particles effectively decreases the interaction strength. We show that the model becomes trivial in the thermodynamic limit, in the sense that the free energy density at any given particle density and temperature agrees with the corresponding expression for non-interacting particles.Comment: LaTeX, 20 pages; final version, to appear in Lett. Math. Phy

Synthesis, characterization and evaluation of CO-oxidation catalysts for high repetition rate CO2 TEA lasers

An extremely active class of noble metal catalysts supported on titania was developed and fabricated at Hughes for the recombination of oxygen (O2) and carbon monoxide (CO) in closed-cycle CO2 TEA lasers. The incipient wetness technique was used to impregnate titania and alumina pellets with precious metals including platinum and palladium. In particular, the addition of cerium (used as an oxygen storage promoter) produced an extremely active Pt/Ce/TiO2 catalyst. By comparison, the complementary Pt/Ce/ gamma-Al2O3 catalyst was considerably less active. In general, chloride-free catalyst precursors proved critical in obtaining an active catalyst while also providing uniform metal distributions throughout the support structure. Detailed characterization of the Pt/Ce/TiO2 catalyst demonstrated uniform dendritic crystal growth of the metals throughout the support. Electron spectroscopy for Chemical Analysis (ESCA) analysis was used to characterize the oxidation states of Pt, Ce and Ti. The performance of the catalysts was evaluated with an integral flow reactor system incorporating real time analysis of O2 and CO. With this system, the transient and steady-state behavior of the catalysts were evaluated. The kinetic evaluation was complemented by tests in a compact, closed-cycle Hughes CO2 TEA laser operating at a pulse repetition rate of 100 Hz with a catalyst temperature of 75 to 95 C. The Pt/Ce/TiO2 catalyst was compatible with a C(13)O(16)2 gas fill

Der Einfluss von Feld- und Landschaftsparameter auf die Abundanzen wichtiger Rapsschädlinge

In agroecological research it has been appreciated only fairly recently that plant-insect interactions and other ecological processes depend on scales much larger than a single habitat (Wiens et al. 1997). Crop-pest interactions have mainly been studied on single pest species by focusing either on the impact of field parameters or on landscape structure but only rarely included both factors (Östman et al. 2001). Here we investigated how the abundances of three major insect pest species in oilseed rape (OSR) responded to field parameters and landscape characteristics at various spatial scales. Pest species considered in the current study include (i) ceutorhynchid stem weevils that lay eggs in leaf petioles or midribs of OSR plants while the larvae tunnel in the stems; (ii) pollen beetles that feed on pollen and destroy flower buds and (iii) brassica pod midge that lay eggs into OSR pods where the hatched larvae consume the seeds as well as tissue of the pod walls and cause the pods to split prematurely (Alford et al. 2003). Studying these different groups of pests is especially important because they attack different parts of the crop, use different habitats as overwintering sites and also differ in their mobility; with the exception of pollen beetles these pest species have never been studied in a landscape context. The specific objectives of this study were to determine (i) whether the major OSR pest species differ in their relation to field and landscape characteristics and (ii) at which spatial scales landscape variables are effective.Der Einfluss von Feld- und Landschaftsparameter auf die Abundanzen wichtiger Rapsschädlinge (Rapsglanzkäfer - Meligethes aeneus und M. viridescens, Nitidulidae, Coleoptera; Gefleckter Kohltriebrüssler und Großer Rapsstängelrüssler - Ceutorhynchus pallidactylus und C. napi, Curculionidae, Coleoptera; Kohlschotenmücke - Dasineura brassicae, Cecidomyiidae, Diptera) wurde untersucht. In Raps-Untersuchungsfeldern wurden die Beziehungen zwischen Schädlingsabundanzen und Feld-/Landschaftsparametern in 29 von strukturarm bis komplex reichenden Landschaftssektoren auf acht räumlichen Skalen (Radien 250 - 2000 m) untersucht. Die Abundanzen der Stängelrüssler waren signifikant positiv korreliert mit der Bestandesdichte des Raps und der Bodenqualität. Die Abundanzen der Rapsglanzkäfer reagierten auf allen Radien signifikant negativ mit dem Anteil an Rapsfläche und positiv mit der Bestandesdichte. Die Dichte der Kohlschotenmücke war jeweils auf dem kleinsten Radius signifikant positiv mit dem Anteil an Gehölzen korreliert, negativ mit dem Anteil an Rapsfläch

Skalenabhängiger Einfluss der Landschaft auf die Diversität epigäischer Spinnen in Winterrapsfeldern

Agricultural intensification is a major threat to biological diversity worldwide. Land management activities enhancing landscape diversity are therefore regarded as a key strategy to halt species loss in cultural landscapes. Diverse and abundant communities of predatory arthropods, e.g. spiders (Araneae), have a high potential to suppress pest populations (Symondson et al. 2002) and could therefore contribute to allow reductions of pesticide use. Crop fields alone are usually not able to sustain diverse and individual-rich populations of predatory arthropods, because agricultural management results in disturbances and habitat deteriorations (harvest, soil cultivation, pesticide application) that kill or drive away large parts of the populations. Therefore semi-natural and perennial habitats in agricultural landscapes are considered to be of great importance for beneficial arthropods. On the one hand they offer refuge habitats in times when arable fields are hostile, e.g. fields with bare grounds during winter (Schmidt & Tscharntke 2005). On the other hand, viable populations of predatory arthropods in semi-natural habitats can serve as sources for (re-) colonisation of arable fields (Schmidt & Tscharntke 2005). Because of these exchanges between crop and non-crop areas it is important to include the surrounding landscape when investigating field-scale processes. We investigated the relations between spider assemblages in arable fields and the surrounding landscape in 29 fields of winter oilseed rape (OSR) in an agricultural landscape in eastern Austria. The objectives of this study were to estimate (1) how much spider assemblages in oilseed rape fields are influenced by the surrounding landscape, (2) the relative influence of landscape variables compared to field-scale variables and (3) at which spatial scales landscape variables are effective.Die Intensivierung der Landwirtschaft stellt weltweit eine der bedeutendsten Bedrohungen der Biodiversität dar. Maßnahmen, die die Diversität der Landschaft erhöhen werden daher als eine zentrale Möglichkeit gesehen, den Verlust von Arten in Kulturlandschaften zu stoppen und durch die Förderung von Nützlingen einen Betrag zu einer Reduktion des Pestizideinsatzes zu leisten. Wir untersuchten den Einfluss der Landschaft auf epigäische Spinnen (Araneae) in 29 Winterrapsfelder in einer durch landwirtschaftliche Nutzung dominierten Region östlich von Wien (Österreich). Spinnen – generalistische Prädatoren, die ein bedeutsames Potenzial in der natürlichen Schädlingskontrolle aufweisen – wurden während der Feldsaison 2005 mit Barberfallen erfasst. Die umgebenden Landschaften wurden hinsichtlich Zusammensetzung, Diversität und Komplexität charakterisiert (Landschaftsausschnitte mit 250 bis 2000 m Radius). Zusätzlich wurden Feldparameter, vor allem die Bewirtschaftung betreffend, in die Analyse einbezogen. Die Datenanalyse erfolgte mit Generalized Linear Models. Unsere Ergebnisse zeigten, dass die Spinnengemeinschaften hinsichtlich Diversität und Individuenzahlen auf unterschiedliche Landschaftvariablen auf unterschiedlichen Skalenebenen reagieren. Für die Gesamtartenzahl war der Anteil an gehölzdominierten Habitaten in der näheren Umgebung der Felder der wichtigste, fördernde Faktor. Die Anzahl der häufigen Arten und die Gesamtindividuenzahlen hingegen nahmen mit dem Anteil an Brachen bzw. der Lauflänge an Wegrainen in größerem Umkreis der Felder zu. Diese Ergebnisse unterstreichen die Bedeutung von naturnahe Landschaftselementen, v.a. Brachen, für epigäische Spinnen als eine Gruppe von räuberischen Arthropoden in Agrarsystemen

IST Austria Thesis

In this thesis we will discuss systems of point interacting fermions, their stability and other spectral properties. Whereas for bosons a point interacting system is always unstable this ques- tion is more subtle for a gas of two species of fermions. In particular the answer depends on the mass ratio between these two species. Most of this work will be focused on the N + M model which consists of two species of fermions with N, M particles respectively which interact via point interactions. We will introduce this model using a formal limit and discuss the N + 1 system in more detail. In particular, we will show that for mass ratios above a critical one, which does not depend on the particle number, the N + 1 system is stable. In the context of this model we will prove rigorous versions of Tan relations which relate various quantities of the point-interacting model. By restricting the N + 1 system to a box we define a finite density model with point in- teractions. In the context of this system we will discuss the energy change when introducing a point-interacting impurity into a system of non-interacting fermions. We will see that this change in energy is bounded independently of the particle number and in particular the bound only depends on the density and the scattering length. As another special case of the N + M model we will show stability of the 2 + 2 model for mass ratios in an interval around one. Further we will investigate a different model of point interactions which was discussed before in the literature and which is, contrary to the N + M model, not given by a limiting procedure but is based on a Dirichlet form. We will show that this system behaves trivially in the thermodynamic limit, i.e. the free energy per particle is the same as the one of the non-interacting system

Model vanadium-phosphorous-oxygen catalysts for the selective oxidation of C4 hydrocarbons to maleic anhydride

Two model vanadium-phosphorus-oxygen catalysts, (beta)-VOPO(,4) and (VO)(,2)P(,2)O(,7), were investigated for the selective oxidation of C(,4) hydrocarbons to maleic anhydride. Particular emphasis was given to the characterization of the functioning model catalysts using in situ laser Raman spectroscopy. Complementary techniques including X-ray powder diffraction and X-ray photoelectron spectroscopy were used for characterization of the fresh and used catalytic materials. The in situ Raman technique was particularly valuable since it made possible the characterization of catalyst features during C(,4) hydrocarbon oxidation which were otherwise undetectable by post-catalytic characterization. The direct observation of phase stability and the participation of lattice oxygen during catalysis was possible using the in situ Raman technique. In particular, (beta)-VOPO(,4) and (VO)(,2)P(,2)O(,7) demonstrated bulk structural integrity during n-butane oxidation. The relatively greater reducing capacity of 1-butene induced the (beta)-VOPO(,4) to (VO)(,2)P(,2)O(,7) phase transformation. Direct structural identification of catalytically active centers for paraffin and olefin oxidation were investigated using an (\u2718)O-enriched (beta)-VOPO(,4) phase catalyst. Active sites responsible for complete combustion (Site I) and selective oxidation (Site II) were identified. The selective route for 1-butene oxidation involved predominantly Site II centers, while Site I centers were associated with complete combustion. In contrast, n-butane oxidation required the highly active Site I centers for initial activation and for the formation of an intermediate containing two oxygen atoms. Raman band assignments indicated these oxygen sites were associated with PO(,4) units in the (beta)-VOPO(,4) lattice;Maleic anhydride conversion was particularly sensitive to the catalytic phase present. Significant combustion activity was observed when maleic anhydride was fed directly to an integral flow reactor charged with model catalysts. The combustion activity was least for (VO)(,2)P(,2)O(,7), nominally a V(IV) phase. The (beta)-VOPO(,4)catalyst, nominally a V(V) phase, resulted in increased conversions of maleic anhydride