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.     

The rate of convergence of Toeplitz based PCG methods for second order nonlinear boundary value problems

Summary. In previous works [21–23] we proposed the use of [5] and band Toeplitz based preconditioners for the solution of 1D and 2D boundary value problems (BVP) by means of the preconditioned conjugate gradient (PCG) methods. As and band Toeplitz linear systems can be solved [4] by using fast sine transforms [8], these methods become especially attractive in a parallel environment of computation. In this paper we extend this technique to the nonlinear, nonsymmetric case and, in addition, we prove some clustering properties for the spectra of the preconditioned matrices showing why these methods exhibit a convergence speed which results to be more than linear. Therefore these methods work much finer than those based on separable preconditioners [18,45], on incomplete LU factorizations [36,13,27], and on circulant preconditioners [9,30,35] since the latter two techniques do not assure a linear rate of convergence. On the other hand, the proposed technique has a wider range of application since it can be naturally used for nonlinear, nonsymmetric problems and for BVP in which the coefficients of the differential operator are not strictly positive and only piecewise smooth. Finally the several numerical experiments performed here and in [22,23] confirm the effectiveness of the theoretical analysis. Received December 19, 1995 / Revised version received September 15, 1997     

Superlinear PCG methods for symmetric Toeplitz systems

In this paper we deal with the solution, by means of preconditioned conjugate gradient (PCG) methods, of symmetric Toeplitz systems with nonnegative generating function . Here the function is assumed to be continuous and strictly positive, or is assumed to have isolated zeros of even order. In the first case we use as preconditioner the natural and the optimal approximation of proposed by Bini and Di Benedetto, and we prove that the related PCG method has a superlinear rate of convergence and a total arithmetic cost of ops. Under the second hypothesis we cannot guarantee that the natural matrix is positive definite, while for the optimal we show that, in the ill-conditioned case, this can be really a bad choice. Consequently, we define a new matrix for preconditioning the given system; then, by applying the Sherman-Morrison-Woodbury inversion formula to the preconditioned system, we introduce a small, constant number of subsidiary systems which can be solved again by means of the previous PCG method. Finally, we perform some numerical experiments that show the effectiveness of the devised technique and the adherence with the theoretical analysis.

     

Validation of a Monte Carlo simulation of the plane Couette flow of a rarefied gas

We report and discuss the results of a direct Monte Carlo simulation of the flow of a rarefied gas flowing between two parallel plates when one of them moves in its own plane. The boundary conditions are assumed to be of the bounceback type and the molecules to be Maxwell's. Under this condition the moments can be computed exactly, following a method used by Ikenberry and Truesdell in the unbounded case. This allows a comparison of the Monte Carlo methods with the exact solution and an evaluation of its accuracy.