Multiple boundary peak solutions for some singularly perturbed Neumann problems

We consider the problem \left \{ \begin{array}{rcl} \varepsilon^2 \Delta u - u + f(u) = 0 & \mbox{ in }& \ \Omega\\ u > 0 \ \mbox{ in} \ \Omega, \ \frac{\partial u}{\partial \nu} = 0 & \mbox{ on }& \ \partial\Omega, \end{array} \right. where \Omega is a bounded smooth domain in R^N, \varepsilon>$is a small parameter and f is a superlinear, subcritical nonlinearity. It is known that this equation possesses boundary spike solutions such that the spike concentrates, as \varepsilon approaches zero, at a critical point of the mean curvature function H(P), P \in \partial \Omega . It is also known that this equation has multiple boundary spike solutions at multiple nondegenerate critical points of H(P) or multiple local maximum points of H(P). In this paper, we prove that for any fixed positive integer$K$there exist boundary$K-peak$solutions at a local minimum point of$H(P)$. This implies that for any smooth and bounded domain there always exist boundary$K-peak$ solutions. We first use the Liapunov-Schmidt method to reduce the problem to finite dimensions. Then we use a maximizing procedure to obtain multiple boundary spikes

Experimental performance of the regenerator for the Chrysler upgraded automotive gas turbine engine

Automobile gas turbine engine regenerator performance was studied in a regenerator test facility that provided a satisfactory simulation of the actual engine operating environment but with independent control of airflow and gas flow. Velocity and temperature distributions were measured immediately downstream of both the core high-pressure-side outlet and the core low-pressure-side outlet. For the original engine housing, the regenerator temperature effectiveness was 1 to 2 percent higher than the design value, and the heat transfer effectiveness was 2 to 4 percent lower than the design value over the range of test conditions simulating 50 to 100 percent of gas generator speed. Recalculating the design values to account for seal leakage decreased the design heat transfer effectiveness to values consistent with those measured herein. A baffle installed in the engine housing high-pressure-side inlet provided more uniform velocities out of the regenerator but did not improve the effectiveness. A housing designed to provide more uniform axial flow to the regenerator was also tested. Although temperature uniformity was improved, the effectiveness values were not improved. Neither did 50-percent flow blockage (90 degree segment) applied to the high-pressure-side inlet change the effectiveness significantly

Localization and its consequences for quantum walk algorithms and quantum communication

The exponential speed-up of quantum walks on certain graphs, relative to classical particles diffusing on the same graph, is a striking observation. It has suggested the possibility of new fast quantum algorithms. We point out here that quantum mechanics can also lead, through the phenomenon of localization, to exponential suppression of motion on these graphs (even in the absence of decoherence). In fact, for physical embodiments of graphs, this will be the generic behaviour. It also has implications for proposals for using spin networks, including spin chains, as quantum communication channels.Comment: 4 pages, 1 eps figure. Updated references and cosmetic changes for v

A Radio--Optical Reference Frame VIII. CCD observations from KPNO and CTIO: internal calibration and first results

In this pilot investigation, precise optical positions in the FK5 system are presented for a set of 16 compact extragalactic radio sources, which will be part of the future radio--optical reference frame. The 0.9 m KPNO and CTIO telescopes equipped with 2K CCD's have been used for this project. The astrometric properties of these instruments are investigated in detail. New techniques of using wide field CCD observations for astrometry in general are developed. An internal precision of 5 to 31 mas in position per single exposure is found, depending on the brightness of the object. The tie to the primary optical reference system is established by photographic astrometry using dedicated astrographs on both hemispheres. An accuracy of $\approx 30$ mas per source is estimated for the multi--step reduction procedure when based on the future Hipparcos catalog, while the FK5--based positions suffer from system errors of 100 to 200 mas as compared to the radio positions. This work provides a contribution to the international effort to link the Hipparcos instrumental coordinate system to the quasi--inertial VLBI radio reference frame. Precise radio and optical astrometry of a large sample of compact extragalactic sources will also contribute to the astrophysics of these objects by comparing the respective centers of emission at the optical and radio wavelengths.Comment: AAS v.4 LaTeX, 2 parts on 1 file (main text + deluxetable), accepted by AJ, Dec.95, fig. with reprint

Development of systems and techniques for landing an aircraft using onboard television

A flight program was conducted to develop a landing technique with which a pilot could consistently and safely land a remotely piloted research vehicle (RPRV) without outside visual reference except through television. Otherwise, instrumentation was standard. Such factors as the selection of video parameters, the pilot's understanding of the television presentation, the pilot's ground cockpit environment, and the operational procedures for landing were considered. About 30 landings were necessary for a pilot to become sufficiently familiar and competent with the test aircraft to make powered approaches and landings with outside visual references only through television. When steep approaches and landings were made by remote control, the pilot's workload was extremely high. The test aircraft was used as a simulator for the F-15 RPRV, and as such was considered to be essential to the success of landing the F-15 RPRV

Re-entrant magnetic field induced charge and spin gaps in the coupled dual-chain quasi-one dimensional organic conductor Perylene2_2[Pt(mnt)2_2]

An inductive method is used to follow the magnetic field-dependent susceptibility of the coupled charge density wave (CDW) and spin-Peierls (SP) ordered state behavior in the dual chain organic conductor Perylene$_2$[Pt(mnt)$_2$]. In addition to the coexisting SP-CDW state phase below 8 K and 20 T, the measurements show that a second spin-gapped phase appears above 20 T that coincides with a field-induced insulating phase. The results support a strong coupling of the CDW and SP order parameters even in high magnetic fields, and provide new insight into the nature of the magnetic susceptibility of dual-chain spin and charge systems.Comment: 6 pages, 6 figure

Unusual hyperfine interaction of Dirac electrons and NMR spectroscopy in graphene

Theory of nuclear magnetic resonance (NMR) in graphene is presented. The canonical form of the electron-nucleus hyperfine interaction is strongly modified by the linear electronic dispersion. The NMR shift and spin-lattice relaxation time are calculated as function of temperature, chemical potential, and magnetic field and three distinct regimes are identified: Fermi-, Dirac-gas, and extreme quantum limit behaviors. A critical spectrometer assessment shows that NMR is within reach for fully 13C enriched graphene of reasonable size.Comment: 5 pages, 3 figure

On the Distributed Compression of Quantum Information

The problem of distributed compression for correlated quantum sources is considered. The classical version of this problem was solved by Slepian and Wolf, who showed that distributed compression could take full advantage of redundancy in the local sources created by the presence of correlations. Here it is shown that, in general, this is not the case for quantum sources, by proving a lower bound on the rate sum for irreducible sources of product states which is stronger than the one given by a naive application of Slepian–Wolf. Nonetheless, strategies taking advantage of correlation do exist for some special classes of quantum sources. For example, Devetak and Winter demonstrated the existence of such a strategy when one of the sources is classical. Optimal nontrivial strategies for a different extreme, sources of Bell states, are presented here. In addition, it is explained how distributed compression is connected to other problems in quantum information theory, including information-disturbance questions, entanglement distillation and quantum error correction

Bullying and Victimization in Elementary Schools: A Comparison of Bullies, Victims, Bully/Victims, and Uninvolved Preadolescents

Research on bullying and victimization largely rests on univariate analyses and on reports from a single informant. Researchers may thus know too little about the simultaneous effects of various independent and dependent variables, and their research may be biased by shared method variance. The database for this Dutch study was large (N = 1,065) and rich enough to allow multivariate analysis and multisource information. In addition, the effect of familial vulnerability for internalizing and externalizing disorders was studied. Gender, aggressiveness, isolation, and dislikability were most strongly related to bullying and victimization. Among the many findings that deviated from or enhanced the univariate knowledge base were that not only victims and bully/victims but bullies as well were disliked and that parenting was unrelated to bullying and victimization once other factors were controlled.