Existence of positive solutions of a superlinear boundary value problem with indefinite weight

We deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change its sign. We assume that the function $g\colon\mathopen{[}0,+\infty\mathclose{[}\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, so as the case $g(s)=s^{p}$, with $p>1$, is covered. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.Comment: 12 pages, 4 PNG figure

Phonon quarticity induced by changes in phonon-tracked hybridization during lattice expansion and its stabilization of rutile TiO2_2

Although the rutile structure of TiO$_2$ is stable at high temperatures, the conventional quasiharmonic approximation predicts that several acoustic phonons decrease anomalously to zero frequency with thermal expansion, incorrectly predicting a structural collapse at temperatures well below 1000\,K. Inelastic neutron scattering was used to measure the temperature dependence of the phonon density of states (DOS) of rutile TiO$_2$ from 300 to 1373\,K. Surprisingly, these anomalous acoustic phonons were found to increase in frequency with temperature. First-principles calculations showed that with lattice expansion, the potentials for the anomalous acoustic phonons transform from quadratic to quartic, stabilizing the rutile phase at high temperatures. In these modes, the vibrational displacements of adjacent Ti and O atoms cause variations in hybridization of $3d$ electrons of Ti and $2p$ electrons of O atoms. With thermal expansion, the energy variation in this "phonon-tracked hybridization" flattens the bottom of the interatomic potential well between Ti and O atoms, and induces a quarticity in the phonon potential.Comment: 7 pages, 6 figures, supplemental material (3 figures

Inherent Mach-Zehnder interference with "which-way" detection for single particle scattering in one dimension

We study the coherent transport of single photon in a one-dimensional coupled-resonator-array, "non-locally" coupled to a two-level system. Since its inherent structure is a Mach-Zehnder interferometer, we explain the destructive interference phenomenon of the transmission spectrums according to the effect of which-way detection. The quantum realization of the present model is a nano-electromechanical resonator arrays with two nearest resonators coupled to a single spin via their attached magnetic tips. Its classical simulation is a waveguide of coupled defected cavity array with double couplings to a side defected cavity.Comment: 5 papges, 4 figure

Progress in reducing vibration levels on the Naval Postgraduate School Cube-Sat launcher

The Operationally Unique Technologies Satellite (OUTSat), the Government Experimental Multi-Satellite (GEMSat), and the Unique Lightweight Technology and Research Auxiliary Satellite (ULTRASat) missions, launched in 2012, 2013, and May 2015, successfully deployed a total of 33 CubeSats from Poly-Picosatellite Orbital Deployers (P-PODS) mounted to the Naval Postgraduate School (NPS) CubeSat Launcher (NPSCuL) on the aft end of the Atlas V Centaur upper stage. An additional 13 CubeSats are scheduled to launch on the Government Rideshare Advanced Concepts Experiment (GRACE) in September 2015. Force-limited vibration testing (FLVT) has been effective on all four missions in reducing the low-frequency vibration test environment at the P-POD interface on NPSCuL; however, the CubeSats were still subjected to high-frequency amplifications from the NPSCuL structure. Implementing commercial-off-the-shelf (COTS) isolators at the base of the NPSCuL structure has recently been shown to significantly reduce the high-frequency amplifications. This paper discusses the testing and the resulting 35-85% drop in overall G(RMS) vibration test levels, a welcome reduction in the CubeSat vibration test envirionment on NPSCuL. This reduction should allow more sensitive payloads to fly on future NPSCuL missions, and the implementation of low-cost, COTS isolators could possibly be useful for other small satellites and CubeSat launch applications.NRO Office of Space Launch and Cube Sat Program Office.Approved for public release; distribution is unlimited

Blunt-end vectors generated by polymerase chain reaction (PCR) for direct cloning of blunt-end DNA fragments

Blunt-end cloning is a convenient way to clone polymerase chain reaction (PCR) products generated by proof-reading DNA polymerase. However, it is a time consuming procedure to prepare the linearized blunt-end vector, which usually involves plasmid extraction and restriction enzyme digestion. Moreover, 5’ dephosporylation of the vector is usually required to avoid vector self-ligation. Here, we reported a method for generating linearized blunt-end vector pBSK-blunt by PCR. Vector generated in this way has no 5’-phosphate groups, hence completely avoiding vector self-ligation and yielding almost 100% positive clones.Key words: Blunt-end cloning, phosphorylated DNA fragment, dephosphorylated blunt-end vector

Relative Periodic Solutions of the Complex Ginzburg-Landau Equation

A method of finding relative periodic orbits for differential equations with continuous symmetries is described and its utility demonstrated by computing relative periodic solutions for the one-dimensional complex Ginzburg-Landau equation (CGLE) with periodic boundary conditions. A relative periodic solution is a solution that is periodic in time, up to a transformation by an element of the equation's symmetry group. With the method used, relative periodic solutions are represented by a space-time Fourier series modified to include the symmetry group element and are sought as solutions to a system of nonlinear algebraic equations for the Fourier coefficients, group element, and time period. The 77 relative periodic solutions found for the CGLE exhibit a wide variety of temporal dynamics, with the sum of their positive Lyapunov exponents varying from 5.19 to 60.35 and their unstable dimensions from 3 to 8. Preliminary work indicates that weighted averages over the collection of relative periodic solutions accurately approximate the value of several functionals on typical trajectories.Comment: 32 pages, 12 figure

Mode Shape Description and Model Updating of Axisymmetric Structures Using Radial Tchebichef Moment Descriptors

A novel approach for mode shape feature extraction and model updating of axisymmetric structures based on radial Tchebichef moment (RTM) descriptors is proposed in this study. The mode shape features extracted by RTM descriptors can effectively compress the full-field modal vibration data and retain the most important information. The reconstruction of mode shapes using RTM descriptors can accurately describe the mode shapes, and the simulation shows that the RTM function is superior to Zernike moment function in terms of its mathematical properties and its shape reconstruction ability. In addition, the proposed modal correlation coefficient of the RTM amplitude can overcome the main disadvantage of using the modal assurance criterion (MAC), which has difficulty in identifying double or close modes of symmetric structures. Furthermore, the model updating of axisymmetric structures based on RTM descriptors appears to be more efficient and effective than the normal model updating method directly using modal vibration data, avoids manipulating large amounts of mode shape data, and speeds up the convergence of updating parameters. The RTM descriptors used in correlation analysis and model updating are demonstrated with a cover of an aeroengine rig. The frequency deviation between the test and the FE model was reduced from 17.13% to 1.23% for the first 13 modes via the model updating process. It verified the potential to industrial application with the proposed method

Self-interacting dark matter and Higgs bosons in the SU(3)_C x SU(3)_L x U(1)_N model with right-handed neutrinos

We investigate the possibility that dark matter could be made from CP-even and CP- odd Higgs bosons in the SU(3)_C X SU(3)_L X U(1)_N (3-3-1) model with right-handed neutrinos. This self-interacting dark matters are stable without imposing of new symmetry and should be weak-interacting.Comment: 7 pages, Latex, To appear in Europhys. Let

Terahertz Imaging for Space Applications

The Sensor Research Laboratory (SRL) at the Naval Postgraduate School (NPS) is conducting research on terahertz (THz) imaging for space applications. The approach is two-fold: a commercial-off-the-shelf long-wave infrared (LWIR) camera using uncooled microbolometer technology has been modified with THz optics; and THz-to-IR band converter focal plane arrays have been developed to work as an attachment to the IR cameras. The small form factor of these technologies has enabled the Space System Academic Group at NPS to develop a CubeSat payload based on the THz imaging camera (TIC). The objective of this technology demonstrator is to examine the potential imaging capability in the THz range in the space environment, as THz radiation can penetrate many common gases, non-polar liquids, and non-metallic solids. In preparation for an upcoming launch opportunity in 2022, confidence testing has been performed on an engineering development unit of the TIC, and a concept of operations has been developed to capture low-resolution images in both the IR and THz ranges. There is unexplored potential for THz imaging, and this mission is a first step towards enabling additional imaging capabilities for applications such as submillimeter astronomy, space situational awareness, rendezvous and proximity operations, and possibly satellite inspection