Multistability in an electrically actuated carbon nanotube: a dynamical integrity perspective

This study deals with a slacked carbon nanotube, which is electrostatically and electrodynamically actuated. After introducing a reduced-order model, we investigate the overall scenario of the device response when both the frequency and the electrodynamic voltage are varied. Extensive numerical simulations are performed. The nanostructure exhibits several competing attractors with different characteristics. We examine the multistability in detail, based on numerical integration of the equation of motion in time, since it leads to a considerable versatility of behavior, which may be desirable in applications. Nevertheless, these results do not take into account the presence of disturbances, which are unavoidable under realistic conditions. To extend them to the practical case where disturbances exist, we develop a dynamical integrity analysis. This is performed via the combined use of several dynamical integrity tools. Analyzing the potential well, we observe that the device may be vulnerable to pull-in considerably before the theoretical inevitable escape. Focusing on the safe range, the main attractors are examined to investigate the practical probability to catch them and the practical disappearance of the main ones. Special attention is devoted to the practical final response, to detect where the safe jump to another attractor may be ensured and where instead dynamic pull-in may arise. We build the integrity charts, which are able to illustrate if and in which parameter range the theoretical predictions can be guaranteed in practice. They may be used to establish safety factors to effectively operate the device according to the desired outcome, depending on the expected disturbances.     

Measurements of turbulent mixing due to Kelvin–Helmholtz instability in high-energy-density plasmas

Kelvin–Helmholtz (KH) turbulent mixing measurements were performed in experiments on the OMEGA Laser Facility [T.R. Boehly et al., Opt. Commun. 133 (1997) 495]. In these experiments, laser-driven shock waves propagated through low-density plastic foam placed on top of a higher-density plastic foil. Behind the shock front, lower-density foam plasma flowed over the higher-density plastic plasma. The interface between the foam and plastic was KH unstable. The experiments were performed with pre-imposed, sinusoidal 2D perturbations, and broadband 3D perturbations due to surface roughness at the interface between the plastic and foam. KH instability growth was measured using X-ray, point-projection radiography. The mixing layer caused by the KH instability with layer width up to ～100 μm was observed at a location ～1 mm behind the shock front. The measured mixing layer width was in good agreement with simulations using a K–L turbulent mixing model in the two-dimensional ARES hydrodynamics code. In the definition of the K–L model K stands for the specific turbulent kinetic (K) energy, and L for the scale length (L) of the turbulence.     

Spiky nanostructured metal particles as filler of polymeric composites showing tunable electrical conductivity

This work presents a comprehensive investigation of the piezoresistive response of a composite material based on conductive nickel filler in a silicone‐insulating matrix. In the absence of a deformation, the prepared composite shows no electric conductivity, even though the metal particle content is well above the expected percolation threshold. Upon samples deformation (compressive or tensile stress), the composite exploits a variation of electrical resistance up to nine orders of magnitude. This huge variation can be explained with the quantum tunnelling mechanism where the probability of an electron to tunnel from a particle to the next one is exponentially proportional to the thickness of the insulating layer between them and strongly enhanced by the morphology of the nickel particles, showing spiky nanostructured tips. Two different conduction theoretical models are proposed and compared with the experimental results. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Global Comparison Principles for the <Emphasis Type="Italic">p</Emphasis>-Laplace Operator on Riemannian Manifolds

We prove global comparison results for the p-Laplacian on a p-parabolic manifold. These involve both real-valued and vector-valued maps with finite p-energy. Further L ^q comparison principles in the non-parabolic setting are also discussed.     

Uniform decay estimates for finite-energy solutions of semi-linear elliptic inequalities and geometric applications

We prove uniform decay estimates at infinity for solutions 0?u∈Lp of the semilinear elliptic inequality Δu+auσ+bu?0, a,b?0, σ?1, in the presence of a Sobolev inequality (with potential term). This gives a unified point of view in the investigation of different geometric questions. In particular, we present applications to the study of the topology at infinity of parallel mean curvature submanifolds, to the non-compact Yamabe problem, and to estimate the decay rate of the traceless Ricci tensor of conformally flat manifolds.     

Blaschke-decomposable convex bodies

For a given centred convex bodyK of ℝ,n≥3, let be the class of all convex bodies with the same projection body asK. The question whetherK can be expressed as a Blaschke average of two non-homothetic bodies from is considered. Necessary and sufficient conditions onK to be Blaschke decomposable in are given. The paper provides also a characterization of the bodiesK such that the Blaschke indecomposable bodies in are dense in itself.     

Cut problems in graphs with a budget constraint

We study budgeted variants of classical cut problems: the Multiway Cut problem, the Multicut problem, and the k-Cut problem, and provide approximation algorithms for these problems. Specifically, for the budgeted multiway cut and the k-cut problems we provide constant factor approximation algorithms. We show that the budgeted multicut problem is at least as hard to approximate as the sparsest cut problem, and we provide a bi-criteria approximation algorithm for it.