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

Examining the link between social media uses and gratifications, and political tolerance and dogmatism

The ability of social media to enable new uses and gratifications, and to shape political behavior, has not been discussed adequately in the social media literature. Drawing on a previous study by the authors that converts a framework by Sundar and Limperos (2013) into a social media uses and gratifications scale, this article examines the association between social media uses and gratifications, and political dogmatism and tolerance. A sample of 313 American citizens was used to develop two discriminant models. The models showed that social media uses and gratifications can be used to classify users with high or low levels of political dogmatism and tolerance with more than 70 percent accuracy. The results also indicate that while some gratifications, such as filtering, are common to individuals with high dogmatism as well as users with high tolerance, there were differences in the perception of uses and gratifications between these two groups. This shows that social media are open platforms that do not gratify only positive, open‐minded users

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

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

A methodology for the decomposition of discrete event models for parallel simulation

Parallel simulation has presented the possibility of performing high-speed simulation. However, when attempting to make a link between the requirements of parallel simulation and discrete event simulation used in commercial areas such as manufacturing, a major problem arises. This lies in the decomposition of the simulation into a series of concurrently executing objects. Using the activity cycle diagram simulation technique as an illustrative example, this paper suggests a solution to this decomposition problem. This is discussed within the context of providing a conceptually seamless methodology for translating simulation models into a form which can exploit the benefits of parallel computing

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

Deep brain stimulation in schizophrenia

Deep brain stimulation (DBS) has successfully advanced treatment options of putative therapy-resistant neuropsychiatric diseases. Building on this strong foundation more and more mental disorders in the stadium of therapy-resistance are considered as possible indications for DBS. Especially schizophrenia with its associated severe and difficult to treat symptoms is gaining attention. This attention demands critical questions regarding the assumed mechanisms of DBS and its possible influence on the supposed pathophysiology of schizophrenia. Here we synoptically compare current approaches and theories of DBS and discuss the feasibility of DBS in schizophrenia as well as the transferability from other psychiatric disorders successfully treated with DBS. For this we consider recent advances in animal models of schizophrenic symptoms, results regarding the influence of DBS on dopaminergic transmission as well as data concerning neural oscillation and synchronization. In conclusion the use of DBS for some symptoms of schizophrenia seems to be a promising approach, but the lack of a comprehensive theory of the mechanisms of DBS as well as its impact on schizophrenia might void the use of DBS in schizophrenia at this point