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

Boron Nitride Nanotubes Are Noncytotoxic and Can Be Functionalized for Interaction with Proteins and Cells

We report the discovery that boron nitride nanotubes (BNNTs), isosteres of CNTs with unique physical properties, are inherently noncytotoxic. Furthermore, we developed a biomemetic coating strategy to interface BNNTs with proteins and cells. Finally, we showed that BNNTs can deliver DNA oligomers to the interior of cells with no apparent toxicity. This work suggests that BNNTs may be superior to CNTs for use as biological probes and in biomaterials

Atomic-scale Interaction Dynamics in Few-layer Hexagonal Boron Nitride (h-BN)

Extended abstract of a paper presented at Microscopy and Microanalysis 2011 in Nashville, Tennessee, USA, August 7-August 11, 201

High Li+ and Na+ Conductivity in New Hybrid Solid Electrolytes based on the Porous MIL-121 Metal Organic Framework

Solid-state electrolytes (SSEs) can leapfrog the development of all-solid-state batteries (ASSBs), enabling them to power electric vehicles and to store renewable energy from intermittent sources. Here, a new hybrid Li+ and Na+ conducting SSE based on the MIL-121 metal-organic framework (MOF) structure is reported. Following synthesis and activation of the MOF, the free carboxylic units along the 1D pores are functionalized with Li+ or Na+ ions by ion exchange. Ion dynamics are investigated by broadband impedance spectroscopy and by Li-7 and Na-23 NMR spin-lattice relaxation. A crossover at 50 degrees C (Li+) and at 10 degrees C (Na+) from correlated to almost uncorrelated motion at higher temperature is observed, which is in line with Ngai\u27s coupling model. Alternatively, in accordance to the jump relaxation model of Funke, at low temperature only a fraction of the jump processes are successful as lattice rearrangement in the direct vicinity of Li+ (Na+) is slow. H-1 NMR unambiguously shows that Li+ is the main charge carrier. Conductivities reach 0.1 mS cm(-1) (298 K, Na+) while the activation energies are 0.28 eV (Li+) and 0.36 eV (Na+). The findings pave the way towards development of easily tunable and rationally adjustable high-performance MOF-based hybrid SSEs for ASSBs

Density-potential mappings in quantum dynamics

In a recent letter [Europhys. Lett. 95, 13001 (2011)] the question of whether the density of a time-dependent quantum system determines its external potential was reformulated as a fixed point problem. This idea was used to generalize the existence and uniqueness theorems underlying time-dependent density functional theory. In this work we extend this proof to allow for more general norms and provide a numerical implementation of the fixed-point iteration scheme. We focus on the one-dimensional case as it allows for a more in-depth analysis using singular Sturm-Liouville theory and at the same time provides an easy visualization of the numerical applications in space and time. We give an explicit relation between the boundary conditions on the density and the convergence properties of the fixed-point procedure via the spectral properties of the associated Sturm-Liouville operator. We show precisely under which conditions discrete and continuous spectra arise and give explicit examples. These conditions are then used to show that in the most physically relevant cases the fixed point procedure converges. This is further demonstrated with an example.Comment: 20 pages, 8 figures, 3 table

Defects, order, and hysteresis in driven charge-density waves

We model driven two-dimensional charge-density waves in random media via a modified Swift-Hohenberg equation, which includes both amplitude and phase fluctuations of the condensate. As the driving force is increased, we find that the defect density first increases and then decreases. Furthermore, we find switching phenomena, due to the formation of channels of dislocations. These results are in qualitative accord with recent dynamical x-ray scattering experiments by Ringlandet al. and transport experiments by Lemay et al.Comment: Accepted to Phys. Rev. Lett. Click here for "http://www-theory.mpip-mainz.mpg.de/~karttune/CDW/", movies of driven CDW