Distinguished non-Archimedean representations

For a symmetric space (G,H), one is interested in understanding the vector space of H-invariant linear forms on a representation \pi of G. In particular an important question is whether or not the dimension of this space is bounded by one. We cover the known results for the pair (G=R_{E/F}GL(n),H=GL(n)), and then discuss the corresponding SL(n) case. In this paper, we show that (G=R_{E/F}SL(n),H=SL(n)) is a Gelfand pair when n is odd. When $n$ is even, the space of H-invariant forms on \pi can have dimension more than one even when \pi is supercuspidal. The latter work is joint with Dipendra Prasad

Mid-infrared sub-wavelength grating mirror design: tolerance and influence of technological constraints

High polarization selective Si/SiO2 mid-infrared sub-wavelength grating mirrors with large bandwidth adapted to VCSEL integration are compared. These mirrors have been automatically designed for operation at \lambda = 2.3 $\mu$m by an optimization algorithm which maximizes a specially defined quality factor. Several technological constraints in relation with the grating manufacturing process have been imposed within the optimization algorithm and their impact on the optical properties of the mirror have been evaluated. Furthermore, through the tolerance computation of the different dimensions of the structure, the robustness with respect to fabrication errors has been tested. Finally, it appears that the increase of the optical performances of the mirror imposes a less tolerant design with severer technological constraints resulting in a more stringent control of the manufacturing process.Comment: The final publication is available at http://iopscience.iop.org/2040-8986/13/12/125502

Measurement of energy and angular distributions of secondary ions in the sputtering of gold by swift Au-n clusters: Study of emission mechanisms

Energy and angular distributions of negative ions (Au–, Au2-, Au3-, and Au5-) emitted from gold target bombarded by Au, Au4, and Au9 projectiles at 200 keV/atom were measured with a multipixel position sensitive detector. The angular distributions are symmetrical with respect to the normal to the target surface and forward peaked. They depend on the type of emitted ions, on the emission energy, and on the projectile size. More forward directed emission is observed with Au9 projectiles. The secondary ion energy distributions obtained with Au and Au4 projectiles are well reproduced by a sum of linear collision cascades and thermal spike processes. However, in the case of Au9 projectiles the energy distributions are better described by using a simple spike model with two different average temperature regimes: the first one corresponds to high emission energy occurring in the early stage of the whole process, and the second to the low energy component

Dichotomy for generic supercuspidal representations of G2G_2

The local Langlands conjectures imply that to every generic supercuspidal irreducible representation of $G_2$ over a $p$-adic field, one can associate a generic supercuspidal irreducible representation of either $PGSp_6$ or$PGL_3$. We prove this conjectural dichotomy, demonstrating a precise correspondence between certain representations of $G_2$ and other representations of $PGSp_6$ and $PGL_3$. This correspondence arises from theta correspondences in $E_6$ and $E_7$, analysis of Shalika functionals, and spin L-functions. Our main result reduces the conjectural Langlands parameterization of generic supercuspidal irreducible representations of $G_2$ to a single conjecture about the parameterization for $PGSp_6$.Comment: Version 2: Mistakes in Prop 3.2 and 3.5 corrected. Results strengthened in case p=2. Changes made throughout for consistency with stronger results and reformulatio

Gene Expression of Tissue-Engineered Distal Phalanx Models Utilizing Polymer Scaffolds with Hydroxyapatite and Beta-Tricalcium Phosphate

Tissue engineering is a scientific methodology that provides the means for fabrication of vital tissues in a laboratory with the ultimate goal of translating the tissue to a patient in a clinic. It is a desirable technique in clinical medicine because it eliminates the need for patient tissue grafts and transplants, which have the potential for donor site morbidity and rejection. In tissue engineering, the scaffolding material, typically a polymer upon which tissue is grown, is important. The goal of this research is to investigate optimization of tissue-engineered polymer scaffold constructs for cell proliferation and gene expression. This work includes an analysis of scaffold type to determine the appropriate engineered materials for growing human periosteum. Many scaffolding materials have been investigated for tissue-engineering purposes; however, the present study will be examining novel scaffolds for growing periosteum, those scaffolds being composed of hydroxyapatite (HA) or beta-tricalcium phosphate (β-TCP) with polylactic acid/polycaprolinic acid [P(LA/CL)]. To conduct this analysis, histology of tissue-engineered constructs will be utilized to determine cell proliferation, and reverse transcription-quantitative polymerase chain reaction (RT-qPCR) will be applied to determine gene expression of construct cells. Results will be compared to determine differences in fold-change expression levels of several genes of interest that may be affected by the two different scaffolds. The initial findings of the study showed that there were few significant differences in gene expression between the scaffolds composed of HA or β-TCP

Towards two-dimensional metallic behavior at LaAlO3/SrTiO3 interfaces

Using a low-temperature conductive-tip atomic force microscope in cross-section geometry we have characterized the local transport properties of the metallic electron gas that forms at the interface between LaAlO3 and SrTiO3. At low temperature, we find that the carriers do not spread away from the interface but are confined within ~10 nm, just like at room temperature. Simulations taking into account both the large temperature and electric-field dependence of the permittivity of SrTiO3 predict a confinement over a few nm for sheet carrier densities larger than ~6 10^13 cm-2. We discuss the experimental and simulations results in terms of a multi-band carrier system. Remarkably, the Fermi wavelength estimated from Hall measurements is ~16 nm, indicating that the electron gas in on the verge of two-dimensionality.Comment: Accepted for publication in Physical Review Letter

Even Galois Representations and the Fontaine--Mazur conjecture II

We prove, under mild hypotheses, that there are no irreducible two-dimensional_even_ Galois representations of \Gal(\Qbar/\Q) which are de Rham with distinct Hodge--Tate weights. This removes the "ordinary" hypothesis required in previous work of the author. We construct examples of irreducible two-dimensional residual representations that have no characteristic zero geometric (= de Rham) deformations.Comment: Updated to take into account suggestions of the referee; the main theorems remain unchange