Null controllability results for parabolic equations in unbounded domains

In this talk we present some results concerning the null controllability for a heat equation in unbounded domains. We characterize the conditions that must satisfy the weight function, introduced by Fursikov and Imanuvilov, in order to prove a global Carleman inequality for the adjoint problem and then to get a null controllability result. We give some examples of unbounded domains (Ω, ω) that satisfy these sufficient conditions. Finally, when Ω \ ω is bounded, we prove the null controllability of the semi-linear heat equation when the nonlinearity is slightly superlinear

Controllability results for cascade systems of m coupled parabolic PDEs by one control force

In this paper we will analyze the controllability properties of a linear coupled parabolic system of m equations when a unique distributed control is exerted on the system. We will see that, when a cascade system is considered, we can prove a global Carleman inequality for the adjoint system which bounds the global integrals of the variable ϕ = (ϕ1, . . . , ϕm)∗ in terms of a unique localized variable. As a consequence, we will obtain the null controllability property for the system with one control force.Dirección General de InvestigaciónConsejo Nacional de Ciencia y Tecnología (México)Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológico (Universidad Nacional Autónoma de México

Effect of fluorination on the molecule–substrate interactions of pentacene/Cu(1 0 0) interfaces

4 páginas, 3 figuras.-- et al.-- El pdf es la versión post-print del artículo.By means of scanning tunneling microscopy (STM), X-ray photoelectron spectroscopy (XPS) and nearedge X-ray absorption fine structure (NEXAFS), we study and compare the crystalline and electronic structure of fluorinated and non-fluorinated pentacene fims on Cu(1 0 0). Pentacene perfluorination strongly affects its electronic structure both in the bulk and at the metal–organic interface. While the azimuthal anisotropy of the molecule–substrate interactions on Cu(1 0 0) remains unaffected by the fluorination, the interaction mechanisms, as concluded from their effect on the core-levels and on the conduction band of the respective molecules, show a completely disparate behaviour.Peer reviewe

Reversible Graphene decoupling by NaCl photo-dissociation

We describe the reversible intercalation of Na under graphene on Ir(111) by photo-dissociation of a previously adsorbed NaCl overlayer. After room temperature evaporation, NaCl adsorbs on top of graphene forming a bilayer. With a combination of electron diffraction and photoemission techniques we demonstrate that the NaCl overlayer dissociates upon a short exposure to an X-ray beam. As a result, chlorine desorbs while sodium intercalates under the graphene, inducing an electronic decoupling from the underlying metal. Low energy electron diffraction shows the disappearance of the moir\'e pattern when Na intercalates between graphene and iridium. Analysis of the Na 2p core-level by X-ray photoelectron spectroscopy shows a chemical change from NaCl to metallic buried Na at the graphene/Ir interface. The intercalation-decoupling process leads to a n-doped graphene due to the charge transfer from the Na, as revealed by constant energy angle resolved X-ray photoemission maps. Moreover, the process is reversible by a mild annealing of the samples without damaging the graphene

Bottom-up fabrication of atomically precise graphene nanoribbons

Graphene nanoribbons (GNRs) make up an extremely interesting class of materials. On the one hand GNRs share many of the superlative properties of graphene, while on the other hand they display an exceptional degree of tunability of their optoelectronic properties. The presence or absence of correlated low-dimensional magnetism, or of a widely tunable band gap, is determined by the boundary conditions imposed by the width, crystallographic symmetry and edge structure of the nanoribbons. In combination with additional controllable parame-ters like the presence of heteroatoms, tailored strain, or the formation of hetero-structures, the possibilities to shape the electronic properties of GNRs according to our needs are fantastic. However, to really benefit from that tunability and harness the opportunities offered by GNRs, atomic precision is strictly required in their synthesis. This can be achieved through an on-surface synthesis approach, in which one lets appropriately designed precursor molecules to react in a selective way that ends up forming GNRs. In this chapter we review the structure-property relations inherent to GNRs, the synthesis approach and the ways in which the var-ied properties of the resulting ribbons have been probed, finalizing with selected examples of demonstrated GNR applications

Dielectric properties of thin insulating layers measured by Electrostatic Force Microscopy

In order to measure the dielectric permittivity of thin insulting layers, we developed a method based on electrostatic force microscopy (EFM) experiments coupled with numerical simulations. This method allows to characterize the dielectric properties of materials without any restrictions of film thickness, tip radius and tip-sample distance. The EFM experiments consist in the detection of the electric force gradient by means of a double pass method. The numerical simulations, based on the equivalent charge method (ECM), model the electric force gradient between an EFM tip and a sample, and thus, determine from the EFM experiments the relative dielectric permittivity by an inverse approach. This method was validated on a thin SiO2 sample and was used to characterize the dielectric permittivity of ultrathin poly(vinyl acetate) and polystyrene films at two temperatures