We report an experimental and a theoretical study of the radial elasticity of multiwalled carbon nanotubes as a function of external radius. We use atomic force microscopy and apply small indentation amplitudes in order to stay in the linear elasticity regime. The number of layers for a given tube radius is inferred from transmission electron microscopy, revealing constant ratios of external to...

We consider a continuous, infinitely divisible random field in Rd, d = 1, 2, 3, given as an integral of a kernel function with respect to a Lévy basis with convolution equivalent Lévy measure. For a large class of such random fields we compute the asymptotic probability that the excursion set at level x contains some rotation of an object with fixed radius as x → ∞. Our main result is that the ...

Abstract. The generating series of a radix-rational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radix-rational sequence with complex values we provide an asymptotic expansion for the sequence of its Cesàro means. The precision of the asymptotic depends on the joint spectral radius of the linear representation of...

Abstract. Let (X, Y ) be a bivariate elliptical random vector with associated random radius in the Gumbel maxdomain of attraction. In this paper we obtain a second order asymptotic expansion of the joint survival probability P{X > x, Y > y} for x, y large. Further, based on the asymptotic bounds we discuss some aspects of the statistical modelling of joint survival probabilities and the surviva...

The generating series of a radix-rational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radix-rational sequence with complex values we provide an asymptotic expansion for the sequence of its Cesàro means. The precision of the asymptotic expansion depends on the joint spectral radius of the linear representation of...

We discuss the asymptotic behaviour of weak solutions to the Hele-Shaw and one-phase Stefan problems in exterior domains. We prove that, if the space dimension is greater than one, the asymptotic behaviour is given in both cases by the solution of the Dirichlet exterior problem for the Laplacian in the interior of the positivity set and by a singular, radial and self-similar solution of the Hel...

We examine, with asymptotic analysis and numerical simulation, the iterated stretching dynamics of FENE and Oldroyd-B jets of initial radius r0 , shear viscosity n, Weissenberg number We, retardation number S, and capillary number Ca. The usual Rayleigh instability stretches the local uniaxial extensional flow region near a minimum in jet radius into a primary filament of radius @Ca(12S)/We#r0 ...

Let Γ be a finitely generated group with a given word metric. The asymptotic density of elements in Γ that have a particular property P is the limit, as r → ∞, of the proportion of elements in the ball of radius r which have the property P . We obtain a formula to compute the asymptotic density of finite-order elements in any virtually nilpotent group. Further, we show that the spectrum of numb...

Axisymmetrical stresses in an infinitely long hollow isotropic circular cylinder (plane strain) quickly approach their asymptotic values as the external radius increases. This is not the case if the cylinder is even slightly anisotropic -asymptotic solutions (for an infinitely large external radius) do not exist. We find the mechanical meaning of this disparity by using formulas for radial and ...