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

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

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

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

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

Late Decaying Dark Matter, Bulk Viscosity and the Cosmic Acceleration

We discuss a cosmology in which cold dark matter begins to decay into relativistic particles at a recent epoch (z < 1). We show that the large entropy production and associated bulk viscosity from such decays leads to an accelerating cosmology as required by observations. We investigate the effects of decaying cold dark matter in a Lambda = 0, flat, initially matter dominated cosmology. We show that this model satisfies the cosmological constraint from the redshift-distance relation for type Ia supernovae. The age in such models is also consistent with the constraints from the oldest stars and globular clusters. Possible candidates for this late decaying dark matter are suggested along with additional observational tests of this cosmological paradigm.Comment: 8 pages, 3 figures, 1 tabl

Specifying angular momentum and center of mass for vacuum initial data sets

We show that it is possible to perturb arbitrary vacuum asymptotically flat spacetimes to new ones having exactly the same energy and linear momentum, but with center of mass and angular momentum equal to any preassigned values measured with respect to a fixed affine frame at infinity. This is in contrast to the axisymmetric situation where a bound on the angular momentum by the mass has been shown to hold for black hole solutions. Our construction involves changing the solution at the linear level in a shell near infinity, and perturbing to impose the vacuum constraint equations. The procedure involves the perturbation correction of an approximate solution which is given explicitly.Comment: (v2) a minor change in the introduction and a remark added after Theorem 2.1; (v3) final version, appeared in Comm. Math. Phy

Towards granular hydrodynamics in two-dimensions

We study steady-state properties of inelastic gases in two-dimensions in the presence of an energy source. We generalize previous hydrodynamic treatments to situations where high and low density regions coexist. The theoretical predictions compare well with numerical simulations in the nearly elastic limit. It is also seen that the system can achieve a nonequilibrium steady-state with asymmetric velocity distributions, and we discuss the conditions under which such situations occur.Comment: 8 pages, 9 figures, revtex, references added, also available from http://arnold.uchicago.edu/?ebn