Elliptic problems in a two-dimensional domain containing one or several small holes are studied asymptotically in the limit of small hole radius ". As a result of the perturbation , the asymptotic solution to this class of problems contains an innnite logarithmic expansion in powers of ?1= log ". A hybrid asymptotic-numerical technique is used to sum these innnite logarithmic expansions and to ...

Following Frénod and Sonnendrücker ([12]), we consider the finite Larmor radius regime for a plasma submitted to a large magnetic field and take into account both the quasineutrality and the local thermodynamic equilibrium of the electrons. We then rigorously establish the asymptotic gyrokinetic limit of the rescaled and modified Vlasov-Poisson system in a three-dimensional setting with the hel...

In this paper we introduce the class of Wp scale mixture random vectors with a particular radial decomposition and a independent splitting property specified by some random variable Wp, p ∈ (0,∞). We derive several conditional limit results assuming that the distribution of the random radius is in the max-domain of attraction of a univariate extreme value distribution andWp has a certain tail a...

In nonlinear elastic theory, the inverse bulk modulus K , for example, depends on the compression P: 1yKsPd ­ c0 1 c1P 1 c2P 1 · · · 1 cnP 1 · · · . Elastic materials that allow cracks are unstable at finite temperature with respect to fracture under a stretching load. As a result, the above power series has zero radius of convergence: it is an asymptotic series. For a two-dimensional isotropic...

The classical problem of the interaction of a non-emitting spherical body with a zero meanfree-path continuum plasma is solved numerically in the full range of physically allowed free parameters (electron Debye length to body radius ratio, ion to electron temperature ratio, and body bias), and analytically in rigorously defined asymptotic regimes (weak and strong bias, weak and strong shielding...

In this article, we consider the existence and asymptotic behavior of solutions for the Hénon equation −∆BN u = (d(x)) α|u|p−2u, x ∈ Ω u = 0 x ∈ ∂Ω, where ∆BN denotes the Laplace Beltrami operator on the disc model of the Hyperbolic space BN , d(x) = dBN (0, x), Ω ⊂ BN is geodesic ball with radius 1, α > 0, N ≥ 3. We study the existence of hyperbolic symmetric solutions when 2 < p < 2N+2α N−2 ....

Two-dimensional CP models are investigated byMonte Carlo methods on the lattice, for values of N ranging from 2 to 21. Scaling and rotation invariance are studied by comparing different definitions of correlation length ξ. Several lattice formulations are compared and shown to enjoy scaling for ξ as small as 2.5. Asymptotic scaling is investigated using as bare coupling constant both the usual ...

Radix-rational sequences are solutions of systems of recurrence equations based on the radix representation of the index. For each radix-rational sequence with complex values we provide an asymptotic expansion, essentially in the scale N logN . The precision of the asymptotic expansion depends on the joint spectral radius of the linear representation of the sequence of first-order differences. ...

In this paper we explore the idea that Teichmüller space with the Teichmüller metric is hyperbolic “on average.” We consider several different measures on Teichmüller space and show that with respect to each one, the average distance between points in a ball of radius r is asymptotic to 2r, which is as large as possible.

We detail numerical methods to compute the geometry of static vacuum black holes in 6 dimensional gravity compactified on a circle. We calculate properties of these Kaluza-Klein black holes for varying mass, while keeping the asymptotic compactification radius fixed. For increasing mass the horizon deforms to a prolate ellipsoid, and the geometry near the horizon and axis decompactifies. We are...