Normal Bundles to Laufer Rational Curves in Local Calabi–Yau Threefolds

We prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank two holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections. Then the normal bundle to such sections is computed in terms of the rank of the Hessian of a suitably defined superpotential at its critical points.     

Molecular dynamics and conformational behaviour of mesogenic resorcinarenes

The dynamic and conformational behaviour of four mesogenic resorcinarenes exhibiting columnar mesophases have been studied by a combination of broadband dielectric spectroscopy and deuterium solid state NMR. Broadband dielectric spectroscopy provided evidence for two relaxation processes present both in the mesophase and in the isotropic liquid. The high frequency process II, common to all mesogens, has been assigned to the libration of the carbonyl groups of the ester junctions between the core and the side chains. The low frequency process I, present in conformationally mobile mesogens 1 and 2, has been attributed to the ring inversion process of the macrocyclic core associated with dipole inversion along the columnar axis. Deuterium solid state NMR performed on 4, the deuteriated analogue of 1, confirmed the molecular dynamics attribution for process I, assigning the ring inversion to the interconversion of the two equivalent crown conformations.     

Use of floating electrodes in transient isotachophoresis to increase the sensitivity of detection

We report a protocol for on-chip electrophoretic sample loading and sample component separation in which each operation requires simultaneous control of the potential of only two electrodes: during the sample-loading phase, the potentials at the ends of the separation channel are electrically floating; during electrophoresis of the sample mixture down the separation channel, the potentials at the ends of the sample-introduction channel are floating. This method, which we call "floating-stacking," avoids the dispersion/distortion of the sample plug that is commonly associated with simultaneous electrical control of only two electrodes in a crossed-channel or offset-double-tee injection system. Further, when this floating loading/separation is done in the presence of back-transient-isotachophoresis, sample loss from the plug of material being injected is minimal and a significant concentration increase--up to 13x--of the sample components in the separated bands occurs relative to the commonly used "pinch-and-pull-back" technique (which requires simultaneous electrical control of four electrodes).     

The surface layers dual to hydrodynamic boundaries

The AdS/hydrodynamics correspondence provides a 1–1 map between large wavelength features of AdS black branes and conformal fluid flows. In this note we consider boundaries between nonrelativistic flows, applying the usual boundary conditions for viscous fluids. We find that a naive application of the correspondence to these boundaries yields a surface layer in the gravity theory whose stress tensor is not equal to that given by the Israel matching conditions. In particular, while neither stress tensor satisfies the null energy condition and both have nonvanishing momentum, only Israel's tensor has stress. The disagreement arises entirely from corrections to the metric due to multiple derivatives of the flow velocity, which violate Israel's finiteness assumption in the thin wall limit.     

An energy-independent nonlocal potential model for bound and scattering states

The general expression of the nucleon-nucleus optical potential has been obtained using Watson's multiple scattering theory and Wolfenstein's parametrization of the nucleon-nucleon scattering amplitude. The resulting theoretical potential is nonlocal and consists of an energy-independent central volume plus surface real and imaginary potential and of a Thomas-like spin-orbit term. The analysis has been restricted to N = Z spherical nuclei, so that neither isospin-isospin nor spin-spin interactions have been included. The widely used Perey-Buck, Greenlees, and Watson expressions of the optical potential are easily obtained as particular cases. For practical purposes, the nonlocal potential has been parametrized in the Frahn-Lemmer form, using Woods-Saxon radial form factors, and the equivalent local potential (ELP) has been calculated by a Perey-Buck-like transformation.The ELP has a radial behavior very similar to the original nonlocal one, but the potential depths and radii are energy dependent. The six free parameters in the ELP have been adjusted to fit the available experimental data in the ?70 to + 150 MeV range of interest in nuclear reactions, namely, energies of single hole and single particle states, charge distributions, proton elastic scattering cross sections, and polarizations. The fitted potential depths show an energy dependence in remarkable agreement with the model predictions with a central nonlocality range β ? 1 F and a spin-orbit nonlocality range β₃ ? 0.8 F. The relative importance of surface and volume dependence in the real central potential in also discussed.     

Synthetic infrared spectra

We have designed, microfabricated, and characterized a diffractive optical element that reproduces the infrared spectrum of HF from 3600 to 4300 cm(-1) . The reflection-mode diffractive optic consists of 4096 lines, each 4.5mum wide, at 16 discrete depths relative to the substrate from 0 to 1.2 mum and was fabricated upon a silicon wafer by anisotropic reactive ion-beam etching in a four-mask-level process. We envisage the use of diffractive optical elements of this type as the basis for a new class of miniaturized, remote chemical sensor systems based on correlation spectroscopy.