Spikes for the gierer-meinhardt system with many segments of different diffusivities

We rigorously prove results on spiky patterns for the Gierer-Meinhardt system with a large number of jump discontinuities in the diffusion coefficient of the inhibitor. Using numerical computations in combination with a Turing-type instability analysis, this system has been investigated by Benson, Maini and Sherratt

A Higher-Order Energy Expansion to Two-Dimensional Singularly Neumann Problems

Of concern is the following singularly perturbed semilinear elliptic problem \begin{equation*} \left\{ \begin{array}{c} \mbox{${\epsilon}^2\Delta u -u+u^p =0$ in $\Omega$}\\ \mbox{$u>0$ in $\Omega$ and $\frac{\partial u}{\partial \nu}=0$ on $\partial \Omega$}, \end{array} \right. \end{equation*} where $\Omega$ is a bounded domain in ${\mathbf{R}}^N$ with smooth boundary $\partial \Omega$, $\epsilon>0$ is a small constant and $1< p<\left(\frac{N+2}{N-2}\right)_+$. Associated with the above problem is the energy functional $J_{\epsilon}$ defined by \begin{equation*} J_{\epsilon}[u]:=\int_{\Omega}\left(\frac{\epsilon^2}{2}{|\nabla u|}^2 +\frac{1}{2}u^2 -F(u)\right)dx \end{equation*} for $u\in H^1(\Omega)$, where $F(u)=\int_{0}^{u}s^p ds$. Ni and Takagi (\cite{nt1}, \cite{nt2}) proved that for a single boundary spike solution $u_{\epsilon}$, the following asymptotic expansion holds: \begin{equation*} (1) \ \ \ \ \ \ \ \ J_{\epsilon}[u_{\epsilon}]=\epsilon^{N} \left[\frac{1}{2}I[w]-c_1 \epsilon H(P_{\epsilon})+o(\epsilon)\right], \end{equation*} where $I[w]$ is the energy of the ground state, $c_1 >0$ is a generic constant, $P_{\epsilon}$ is the unique local maximum point of $u_{\epsilon}$ and $H(P_{\epsilon})$ is the boundary mean curvature function at $P_{\epsilon}\in \partial \Omega$. Later, Wei and Winter (\cite{ww3}, \cite{ww4}) improved the result and obtained a higher-order expansion of $J_{\epsilon}[u_{\epsilon}]$: \begin{equation*} (2) \ \ \ \ \ \ J_{\epsilon}[u_{\epsilon}]=\epsilon^{N} \left[\frac{1}{2}I[\omega]-c_{1} \epsilon H(P_{\epsilon})+\epsilon^2 [c_2(H(P_\epsilon))^2 +c_{3} R(P_\epsilon)]+o(\epsilon^2)\right], \end{equation*} where $c_2$ and $c_3>0$ are generic constants and $R(P_\epsilon)$ is the scalar curvature at $P_\epsilon$. However, if $N=2$, the scalar curvature is always zero. The expansion (2) is no longer sufficient to distinguish spike locations with same mean curvature. In this paper, we consider this case and assume that $2 \leq p <+\infty$. Without loss of generality, we may assume that the boundary near P\in\partial\Om is represented by the graph $\{ x_2 = \rho_{P} (x_1) \}$. Then we have the following higher order expansion of $J_\epsilon[u_\epsilon]:$ \begin{equation*} (3) \ \ \ \ \ J_\epsilon [u_\epsilon] =\epsilon^N \left[\frac{1}{2}I[w]-c_1 \epsilon H({P_\epsilon})+c_2 \epsilon^2(H({P_\epsilon}))^2 ] +\epsilon^3 [P(H({P_\epsilon}))+c_3S({P_\epsilon})]+o(\epsilon^3)\right], \end{equation*} where H(P_\ep)= \rho_{P_\ep}^{''} (0) is the curvature, $P(t)=A_1 t+A_2 t^2+A_3 t^3$ is a polynomial, $c_1$, $c_2$, $c_3$ and $A_1$, $A_2$,$A_3$ are generic real constants and S(P_\epsilon)= \rho_{P_\ep}^{(4)} (0). In particular $c_3<0$. Some applications of this expansion are given

Optimization of a neutrino factory oscillation experiment

We discuss the optimization of a neutrino factory experiment for neutrino oscillation physics in terms of muon energy, baselines, and oscillation channels (gold, silver, platinum). In addition, we study the impact and requirements for detector technology improvements, and we compare the results to beta beams. We find that the optimized neutrino factory has two baselines, one at about 3000 to 5000km, the other at about 7500km (``magic'' baseline). The threshold and energy resolution of the golden channel detector have the most promising optimization potential. This, in turn, could be used to lower the muon energy from about 50GeV to about 20GeV. Furthermore, the inclusion of electron neutrino appearance with charge identification (platinum channel) could help for large values of \sin^2 2 \theta_{13}. Though tau neutrino appearance with charge identification (silver channel) helps, in principle, to resolve degeneracies for intermediate \sin^2 2 \theta_{13}, we find that alternative strategies may be more feasible in this parameter range. As far as matter density uncertainties are concerned, we demonstrate that their impact can be reduced by the combination of different baselines and channels. Finally, in comparison to beta beams and other alternative technologies, we clearly can establish a superior performance for a neutrino factory in the case \sin^2 2 \theta_{13} < 0.01.Comment: 51 pages, 25 figures, 6 tables, references corrected, final version to appear in Phys. Rev.

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

On the quantum chromatic number of a graph

We investigate the notion of quantum chromatic number of a graph, which is the minimal number of colours necessary in a protocol in which two separated provers can convince an interrogator with certainty that they have a colouring of the graph. After discussing this notion from first principles, we go on to establish relations with the clique number and orthogonal representations of the graph. We also prove several general facts about this graph parameter and find large separations between the clique number and the quantum chromatic number by looking at random graphs. Finally, we show that there can be no separation between classical and quantum chromatic number if the latter is 2, nor if it is 3 in a restricted quantum model; on the other hand, we exhibit a graph on 18 vertices and 44 edges with chromatic number 5 and quantum chromatic number 4.Comment: 7 pages, 1 eps figure; revtex4. v2 has some new references; v3 furthe small improvement

Literature review and experimental investigation of heat pipes

Tests on heat pipes determine operational limits, external boundary conditions, noncondensable gas effects, startup behavior, and geometric configurations. Experiment consists of design, construction, and testing of an apparatus for measuring wick properties, conventional heat pipes and coplanar heat pipes

Ethanol Marketing and Input Procurement Practices of U.S. Ethanol Producers: 2008 Survey Results

A mail survey was used to collect information about input procurement and ethanol and co-product marketing practices from 60 U.S. ethanol production facilities. Data were used to answer questions about the conduct or behavior of ethanol producers. It was anticipated that firm conduct or behavior would be fairly homogeneous because the ethanol industry was in Stage II of the industry life-cycle, and societal support for ethanol production resulted in large volumes of publicly available information about technology and markets. Age of facility, size of facility, and type of ownership jointly explained a limited number of differences in responses across ethanol facilities, thus supporting the concept of fairly homogeneous conduct or behavior.entry timing, ethanol, farmer-owned cooperatives, industry life-cycle, Agribusiness, Resource /Energy Economics and Policy, Q11, Q42,

Half-Life of 14^{14}O

We have measured the half-life of $^{14}$O, a superallowed $(0^{+} \to 0^{+})$ $\beta$ decay isotope. The $^{14}$O was produced by the $^{12}$C($^{3}$He,n)$^{14}$O reaction using a carbon aerogel target. A low-energy ion beam of $^{14}$O was mass separated and implanted in a thin beryllium foil. The beta particles were counted with plastic scintillator detectors. We find $t_{1/2} = 70.696\pm 0.052$ s. This result is $1.5\sigma$ higher than an average value from six earlier experiments, but agrees more closely with the most recent previous measurement.Comment: 10 pages, 5 figure

Flight test evaluation of an RAF high altitude partial pressure protective assembly

A partial pressure suit was evaluated during tests in an F-104 and F-15 as a protective garment for emergency descents. The garment is an pressure jerkin and modified anti-g suit combined with an oronasal mask. The garment can be donned and doffed at the aircraft to minimize thermal buildup. The oronasal mask was favored by the pilots due to its immobility on the face during high g-loading. The garment was chosen to provide optimum dexterity for the pilot, which is not available in a full pressure suit, while protecting the pilot at altitudes up to 18,288 meters, during a cabin decompression, and subsequent aircraft descent. During cabin decompressions in the F-104 and F-15, cabin pressure altitude was measured at various aircraft angles of attack, Mach numbers, and altitudes to determine the effect of the aerodynamic slipstream on the cabin altitude