Control of the 1-d wave equation from an interior moving point

We consider the one-dimensional linear wave equation with Dirichlet boundary conditions in a bounded interval, and with a control acting on a single point which moves following a regular trajectory in time. We analyze the exact controllability problem

Numerical approximation of the boundary control for the wave equation with mixed finite elements in a square

This paper studies the numerical approximation of the boundary control for the wave equation in a square domain. It is known that the discrete and semi-discrete models ob- tained by discretizing the wave equation with the usual ¯nite di®erence or ¯nite element methods do not provide convergent sequences of approximations to the boundary control of the continuous wave equation, as the mesh size goes to zero (see [7, 15]). Here we introduce and analyze a new semi-discrete model based on the space discretization of the wave equa- tion using a mixed ¯nite element method with two di®erent basis functions for the position and velocity. The main theoretical result is a uniform observability inequality which allows us to construct a sequence of approximations converging to the minimal L2¡norm control of the continuous wave equation. We also introduce a fully-discrete system, obtained from our semi-discrete scheme, for which we conjecture that it provides a convergent sequence of discrete approximations as both h and ¢t, the time discretization parameter, go to zero. We illustrate this fact with several numerical experiments

Numerical approximation of a one-dimensional elliptic optimal design problem

We address the numerical approximation by finite-element methods of an optimal design problem for a two phase material in one space dimension. This problem, in the continuous setting, due to high frequency oscillations, often does not have a classical solution, and a relaxed formulation is needed to ensure existence. On the contrary, the discrete versions obtained by numerical approximation have a solution. In this article we prove the convergence of the discretizations and obtain convergence rates. We also show a faster convergence when the relaxed version of the continuous problem is taken into account when building the discretization strategy. In particular it is worth emphasizing that, even when the original problem has a classical solution so that relaxation is not necessary, numerical algorithms converge faster when implemented on the relaxed version.Ministerio de Ciencia e InnovaciónJunta de Andalucí

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements