The dynamics of dislocation-free crystal facets is examined in the context of grain boundary grooves at the junction between two crystallites of a solid and the liquid phase. The geometry and thermal conditions of grain boundary grooves allow a detailed analysis of facet morphology during solidification in terms of the nucleation and spreading rates of elementary crystal planes. Observations on...

In 1981, J. Hawkes conjectured the exact form of the Hausdorff gauge function for the boundary of supercritical Galton-Watson trees under a certain assumption on the tail at infinity of the total mass of the branching measure. Hawkes’s conjecture has been proved by T. Watanabe in 2007 as well as other precise results on fractal properties of the boundary of Galton-Watson trees. The goal of this...

We show that the aspherical manifolds produced via the relative strict hyperbolization of polyhedra enjoy many group-theoretic and topological properties of open finite volume negatively pinched manifolds, including relative hyperbolicity, nonvanishing of simplicial volume, co-Hopf property, finiteness of outer automorphism group, absence of splitting over elementary subgroups, acylindricity, a...

There are many approaches to conventional Euclidian scattering theory. In this exposition an essentially microlocal view is adopted. Apart from its intrinsic interest this is intended as preparation for later generalization, to more complicated geometric settings. In fact, the treatment given here extends beyond the usual confines of scattering theory in that the spectral and scattering theory,...

Salva and Tarzia, [N.N. Salva, D.A. Tarzia, J. Math. Anal. Appl. 379 (2011) 240 244], gave explicit solutions of a similarity type for a class of free boundary problem for a semi-infinite material. In this paper, through an elementary approach and less stringent assumption on data, we obtain more general results than those given by their central result, and thereby construct explicit solutions ...

We present a new numerical method, based on a coupling of finite elements and boundary elements, to solve a fluid–solid interaction problem posed in the plane. The boundary unknowns involved in our formulation are approximated by a spectral method. We provide error estimates for the Galerkin method, propose fully discrete schemes based on elementary quadrature formulas and show that the perturb...

ABSTRACT An exact formulation of the problem of imaging a 2D object through a Köhler illumination system is presented; the accurate simulation of a real layout is then not time-limited, but memory-limited. The main idea behind the algorithm is that the boundary of the region that comprise a typical TCC is made up of circular arcs, and therefore the area – which determines the value of the TCC –...

Recently, investigation into shot boundary detection schemes has gathered much momentum [20-29]. Cut detection is seemingly easily solved by an elementary statistical examination of inter-frame characteristics; however a truly accurate and generalized cut detection algorithm still eludes researchers. Reliable shot boundary detection forms the cornerstone for video segmentation applications as s...

We write down and solve a closed set of Schwinger-Dyson equations for the twomatrix model in the large N limit. Our elementary method yields exact solutions for correlation functions involving angular degrees of freedom whose calculation was impossible with previously known techniques. The result sustains the hope that more complicated matrix models important for lattice string theory and QCD m...

The inflow problem of full compressible Navier-Stokes equations is considered on the half line (0,+∞). Firstly, we give the existence (or non-existence) of the boundary layer solution to the inflow problem when the right end state (ρ+, u+, θ+) belongs to the subsonic, transonic and supersonic regions respectively. Then the asymptotic stability of not only the single contact wave but also the su...