Water-waves modes trapped in a canal by a body with the rough surface

The problem about a body in a three dimensional infinite channel is considered in the framework of the theory of linear water-waves. The body has a rough surface characterized by a small parameter $\epsilon>0$ while the distance of the body to the water surface is also of order $\epsilon$. Under a certain symmetry assumption, the accumulation effect for trapped mode frequencies is established, namely, it is proved that, for any given $d>0$ and integer $N>0$, there exists $\epsilon(d,N)>0$ such that the problem has at least $N$ eigenvalues in the interval $(0,d)$ of the continuous spectrum in the case $\epsilon\in(0,\epsilon(d,N))$. The corresponding eigenfunctions decay exponentially at infinity, have finite energy, and imply trapped modes.Comment: 25 pages, 8 figure

The localization effect for eigenfunctions of the mixed boundary value problem in a thin cylinder with distorted ends

A simple sufficient condition on curved end of a straight cylinder is found that provides a localization of the principal eigenfunction of the mixed boundary value for the Laplace operator with the Dirichlet conditions on the lateral side. Namely, the eigenfunction concentrates in the vicinity of the ends and decays exponentially in the interior. Similar effects are observed in the Dirichlet and Neumann problems, too.Comment: 25 pages, 10 figure

An interview with Roger Cooke

n/

Permanent Thermohaline Staircases in the Tyrrhenian Sea

n/

Jobseekers Regime and Flexible New Deal, the Six Month Offer and Support for the Newly Unemployed evaluations: An early process study

Not availabl