One-dimensional potential for image-potential states on graphene

In the framework of dielectric theory, the static non-local self-energy of an electron near an ultra-thin polarizable layer has been calculated and applied to study binding energies of image-potential states near free-standing graphene. The corresponding series of eigenvalues and eigenfunctions have been obtained by numerically solving the one-dimensional Schrodinger equation. The imagepotential state wave functions accumulate most of their probability outside the slab. We find that the random phase approximation (RPA) for the nonlocal dielectric function yields a superior description for the potential inside the slab, but a simple Fermi-Thomas theory can be used to get a reasonable quasi-analytical approximation to the full RPA result that can be computed very economically. Binding energies of the image-potential states follow a pattern close to the Rydberg series for a perfect metal with the addition of intermediate states due to the added symmetry of the potential. The formalism only requires a minimal set of free parameters: the slab width and the electronic density. The theoretical calculations are compared with experimental results for the work function and image-potential states obtained by two-photon photoemission.

From the Cajal alumni Achucarro and Rio-Hortega to the rediscovery of never-resting microglia

Under the guidance of Ramon y Cajal, a plethora of students flourished and began to apply his silver impregnation methods to study brain cells other than neurons: the neuroglia. In the first decades of the twentieth century, Nicolas Achucarro was one of the first researchers to visualize the brain cells with phagocytic capacity that we know today as microglia. Later, his pupil Pio del Rio-Hortega developed modifications of Achucarro's methods and was able to specifically observe the fine morphological intricacies of microglia. These findings contradicted Cajal's own views on cells that he thought belonged to the same class as oligodendroglia (the so called "third element" of the nervous system), leading to a long-standing discussion. It was only in 1924 that Rio-Hortega's observations prevailed worldwide, thus recognizing microglia as a unique cell type. This late landing in the Neuroscience arena still has repercussions in the twenty first century, as microglia remain one of the least understood cell populations of the healthy brain. For decades, microglia in normal, physiological conditions in the adult brain were considered to be merely "resting," and their contribution as "activated" cells to the neuroinflammatory response in pathological conditions mostly detrimental. It was not until microglia were imaged in real time in the intact brain using two-photon in vivo imaging that the extreme motility of their fine processes was revealed. These findings led to a conceptual revolution in the field: "resting" microglia are constantly surveying the brain parenchyma in normal physiological conditions. Today, following Cajal's school of thought, structural and functional investigations of microglial morphology, dynamics, and relationships with neurons and other glial cells are experiencing a renaissance and we stand at the brink of discovering new roles for these unique immune cells in the healthy brain, an essential step to understand their causal relationship to diseases.

Crank-Nicholson method for rate equations in powder random lasers

3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE 2014)