Titles of the Posters

s of the Posters Ngoc Do, Some graph models in nano-science and solid state Abstract: Graph model is proven in many cases to be much simpler to study than other approaches and yet preserves all essential ingredients of the dispersion relation. We study some spectral problems for periodic operators originating from mathematical physics. Using quantum graph model, we analyze the dispersion relation, and thus spectra, of periodic Schrödinger operators on a particular graphyne structure and its nanotubes. We found highly directional Dirac cones, which makes graphynes fascinating. We also study a conjecture, which has been widely assumed in solid state physics, for a class of periodic differential operators on graphs. Namely, we prove that extrema of dispersion relations of generic periodic differential operators on a class of discrete graphs are non-degenerate. (Here by non-degeneracy we mean extrema having non-degenerate Hessian.) Silvia Gazzola, Arnoldi-Tikhonov methods for sparse reconstruction Abstract: Hybrid Krylov subspace methods for inverse problems apply a standard regularization method, such as Tikhonov, to projected least squares problems at each iteration. In this poster we focus on methods based on the Arnoldi algorithm and we describe some new preconditioning approaches that can be used to enforce sparsity constraints into the approximate solution. This is a joint work with James Nagy (Emory University, USA) and Paolo Novati (University of Padova, Italy). Rim Gouia-Zarrad, Reconstructing a function from its conical Radon transform Abstract: In recent years, Radon type transforms that integrate functions along families of curves or surfaces, have been intensively studied due to their applications to inverse scattering, synthetic aperture radar, imaging science, nuclear industry, etc. In this presentation, we consider the transform that integrates a function f over a family of cones invariant to translation. A new exact inversion formula is presented in the case of fixed opening angle and vertical central axis. In addition, the results of numerical simulations are presented to demonstrate the efficiency of the suggested algorithm in 2D.