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

A group theoretic characterization of Buekenhout–Metz unitalsin PG(2, q2) containing conics

Let U be a unital in PG(2, q^2), q = p^h and let G be the group of projectivities of PG(2, q2) stabilizing U. In this paper we prove that U is a Buekenhout–Metz unital containing conics and q is odd if, and only if, there exists a point A of U such that the stabilizer of A in G contains an elementary Abelian p-group of order q^2 with no non-identity elations

Asymptotic analysis of a planar waveguide perturbed by a non periodic perforation

We consider a general second order elliptic operator in a planar waveguide perforated by small holes distributed along a curve and subject to classical boundary conditions on the holes. Under weak assumptions on the perforation, we describe all possible homogenized problems

Performances analysis of a semi-displacement hull by numerical simulations

The flow field generated by the towing of a semi-displacement hull, free to heave and pitch, is numerically investigated in the velocity range 18 34 Kn. The numerical code adopted is the in-house developed Xnavis, which is a general purpose unsteady RANS based solver; the solver is based on a Finite Volume approach together with a Chimera technique for overlapping grids and a Level Set approach to handle the air/water interface. The generated wave pattern shows many interesting features with an evident wave plunging near the hull bow, while the stern remains completely dry for velocities over 30 Kn. The numerical outcomes are discussed in terms of total resistance, sinkage and trim

Scalable computation of predictive probabilities in probit models with Gaussian process priors

Predictive models for binary data are fundamental in various fields, and the growing complexity of modern applications has motivated several flexible specifications for modeling the relationship between the observed predictors and the binary responses. A widely-implemented solution is to express the probability parameter via a probit mapping of a Gaussian process indexed by predictors. However, unlike for continuous settings, there is a lack of closed-form results for predictive distributions in binary models with Gaussian process priors. Markov chain Monte Carlo methods and approximation strategies provide common solutions to this problem, but state-of-the-art algorithms are either computationally intractable or inaccurate in moderate-to-high dimensions. In this article, we aim to cover this gap by deriving closed-form expressions for the predictive probabilities in probit Gaussian processes that rely either on cumulative distribution functions of multivariate Gaussians or on functionals of multivariate truncated normals. To evaluate these quantities we develop novel scalable solutions based on tile-low-rank Monte Carlo methods for computing multivariate Gaussian probabilities, and on mean-field variational approximations of multivariate truncated normals. Closed-form expressions for the marginal likelihood and for the posterior distribution of the Gaussian process are also discussed. As shown in simulated and real-world empirical studies, the proposed methods scale to dimensions where state-of-the-art solutions are impractical.Comment: 21 pages, 4 figure