Wannier-based definition of layer polarizations in perovskite superlattices

In insulators, the method of Marzari and Vanderbilt [Phys. Rev. B {\bf 56}, 12847 (1997)] can be used to generate maximally localized Wannier functions whose centers are related to the electronic polarization. In the case of layered insulators, this approach can be adapted to provide a natural definition of the local polarization associated with each layer, based on the locations of the nuclear charges and one-dimensional Wannier centers comprising each layer. Here, we use this approach to compute and analyze layer polarizations of ferroelectric perovskite superlattices, including changes in layer polarizations induced by sublattice displacements (i.e., layer-decomposed Born effective charges) and local symmetry breaking at the interfaces. The method provides a powerful tool for analyzing the polarization-related properties of complex layered oxide systems

Incipient ferroelectricity in 2.3% tensile-strained CaMnO3 films

Epitaxial CaMnO3 films grown with 2.3% tensile strain on (001)-oriented LaAlO3 substrates are found to be incipiently ferroelectric below 25 K. Optical second harmonic generation (SHG) was used for the detection of the incipient polarization. The SHG analysis reveals that CaMnO3 crystallites with in-plane orientation of the orthorhombic b axis contribute to an electric polarization oriented along the orthorhombic a (resp.\ c) axis in agreement with the predictions from density functional calculations

Testing Landau gauge OPE on the Lattice with a <A2><A^2> Condensate

Using the operator product expansion we show that the $O(1/p^2)$ correction to the perturbative expressions for the gluon propagator and the strong coupling constant resulting from lattice simulations in the Landau gauge are due to a non-vanishing vacuum expectation value of the operator $A^\mu A_\mu$. This is done using the recently published Wilson coefficients of the identity operator computed to third order, and the subdominant Wilson coefficient computed in this paper to the leading logarithm. As a test of the applicability of OPE we compare the $$ estimated from the gluon propagator and the one from the coupling constant in the flavourless case. Both agree within the statistical uncertainty: $\sqrt{} \simeq 1.64(15)$ GeV. Simultaneously we fit \Lams = 233(28) MeV in perfect agreement with previous lattice estimates. When the leading coefficients are only expanded to two loops, the two estimates of the condensate differ drastically. As a consequence we insist that OPE can be applied in predicting physical quantities only if the Wilson coefficients are computed to a high enough perturbative order.Comment: 15 pages, LaTex file with 5 figure

Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow

Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding "negligible" terms, so as to obtain a correct analytic answer. Their inferential moves find suitable proxies in the context of modern theories of infinitesimals, and specifically the concept of shadow. We give an application to decreasing rearrangements of real functions.Comment: 35 pages, 2 figures, to appear in Notices of the American Mathematical Society 61 (2014), no.

Spatial variability of microbial indicators and assessment of tillage systems on the soil microbiological functioning on organic farming.

Reduction tillage, in modifying the soil microorganisms’ environment, modifies their potential to supply plants nutrients. This is of primary importance in organic farming as the nutrients availability is mainly dependent on the organic matter degradation by microorganisms. To study the effect of tillage on soil physical and microbiological properties, we compare 4 tillage practises (deep and shallow ploughing, chisel and no tillage) in an experimental field near Lyon. Our objective is to link a structural statement with a microbiological functioning in order to study the microorganisms’ abilities to supply nitrogen and phosphorus. For such studies, it is of primary importance to use a convenient sampling design as the microbiological properties are highly variable in space and time. So, we first studied, before the treatments differentiation, the spatial variability of some microbiological properties. We first present this study briefly and its utilities for the future assessment of the tillage practises on the soil microbiological functioning

Monitoring Sarcomere Structure Changes in Whole Muscle Using Diffuse Light Reflectance

doi:10.1117/1.2234278Normal biomechanical and physiological functions of striated muscles are facilitated by the repeating sarcomere units. Light scattering technique has been used in studying single extracted muscle fibers. However, few studies, if any, have been conducted to investigate the possibility of using optical detection to examine sarcomere structure changes in whole muscles. We conducted a series of experiments to demonstrate that optical scattering properties measured in whole muscle are related to changes in sarcomere structure. These results suggest that photon migration technique has a potential for characterizing in vivo tissue ultrastructure changes in whole muscle

Algebraic-geometrical formulation of two-dimensional quantum gravity

We find a volume form on moduli space of double punctured Riemann surfaces whose integral satisfies the Painlev\'e I recursion relations of the genus expansion of the specific heat of 2D gravity. This allows us to express the asymptotic expansion of the specific heat as an integral on an infinite dimensional moduli space in the spirit of Friedan-Shenker approach. We outline a conjectural derivation of such recursion relations using the Duistermaat-Heckman theorem.Comment: 10 pages, Latex fil