Constraint-preserving boundary conditions in the 3+1 first-order approach

A set of energy-momentum constraint-preserving boundary conditions is proposed for the first-order Z4 case. The stability of a simple numerical implementation is tested in the linear regime (robust stability test), both with the standard corner and vertex treatment and with a modified finite-differences stencil for boundary points which avoids corners and vertices even in cartesian-like grids. Moreover, the proposed boundary conditions are tested in a strong field scenario, the Gowdy waves metric, showing the expected rate of convergence. The accumulated amount of energy-momentum constraint violations is similar or even smaller than the one generated by either periodic or reflection conditions, which are exact in the Gowdy waves case. As a side theoretical result, a new symmetrizer is explicitly given, which extends the parametric domain of symmetric hyperbolicity for the Z4 formalism. The application of these results to first-order BSSN-like formalisms is also considered.Comment: Revised version, with conclusive numerical evidence. 23 pages, 12 figure

Bethe--Salpeter equation in QCD

We extend to regular QCD the derivation of a confining $q \bar{q}$ Bethe--Salpeter equation previously given for the simplest model of scalar QCD in which quarks are treated as spinless particles. We start from the same assumptions on the Wilson loop integral already adopted in the derivation of a semirelativistic heavy quark potential. We show that, by standard approximations, an effective meson squared mass operator can be obtained from our BS kernel and that, from this, by ${1\over m^2}$ expansion the corresponding Wilson loop potential can be reobtained, spin--dependent and velocity--dependent terms included. We also show that, on the contrary, neglecting spin--dependent terms, relativistic flux tube model is reproduced.Comment: 23 pages, revte

Flux quantization and superfluid weight in doped antiferromagnets

Doped antiferromagnets, described by a t-t'-J model and a suitable 1/N expansion, exhibit a metallic phase-modulated antiferromagnetic ground state close to half-filling. Here we demonstrate that the energy of latter state is an even periodic function of the external magnetic flux threading the square lattice in an Aharonov-Bohm geometry. The period is equal to the flux quantum $\Phi_{0}=2\pi\hbar c/q$ entering the Peierls phase factor of the hopping matrix elements. Thus flux quantization and a concomitant finite value of superfluid weight D_s occur along with metallic antiferromagnetism. We argue that in the context of the present effective model, whereby carriers are treated as hard-core bosons, the charge q in the associated flux quantum might be set equal to 2e. Finally, the superconducting transition temperature T_c is related to D_s linearly, in accordance to the generic Kosterlitz-Thouless type of transition in a two-dimensional system, signaling the coherence of the phase fluctuations of the condensate. The calculated dependence of T_c on hole concentration is qualitatively similar to that observed in the high-temperature superconducting cuprates.Comment: 5 pages, 2 figures, to be published in J. Phys. Condens. Matte

Analytic Quantization of the QCD String

We perform an analytic semi-classical quantization of the straight QCD string with one end fixed and a massless quark on the other, in the limits of orbital and radial dominant motion. We compare our results to the exact numerical semi-classical quantization. We observe that the numerical semi-classical quantization agrees well with our exact numerical canonical quantization.Comment: RevTeX, 10 pages, 9 figure

In Search of the Vortex Loop Blowout Transition for a type-II Superconductor in a Finite Magnetic Field

The 3D uniformly frustrated XY model is simulated to search for a predicted "vortex loop blowout" transition within the vortex line liquid phase of a strongly type-II superconductor in an applied magnetic field. Results are shown to strongly depend on the precise scheme used to trace out vortex line paths. While we find evidence for a transverse vortex path percolation transition, no signal of this transition is found in the specific heat.Comment: 11 pages, 17 figure

Finite-Size-Scaling at the Jamming Transition: Corrections to Scaling and the Correlation Length Critical Exponent

We carry out a finite size scaling analysis of the jamming transition in frictionless bi-disperse soft core disks in two dimensions. We consider two different jamming protocols: (i) quench from random initial positions, and (ii) quasistatic shearing. By considering the fraction of jammed states as a function of packing fraction for systems with different numbers of particles, we determine the spatial correlation length critical exponent $\nu\approx 1$, and show that corrections to scaling are crucial for analyzing the data. We show that earlier numerical results yielding $\nu<1$ are due to the improper neglect of these corrections.Comment: 5 pages, 4 figures -- slightly revised version as accepted for Phys. Rev. E Rapid Communication

Three-dimensional reconstruction of porous polymer films from FIB-SEM nanotomography data using random forests

Combined focused ion beam and scanning electron microscope (FIB-SEM) tomography is a well-established technique for high resolution imaging and reconstruction of the microstructure of a wide range of materials. Segmentation of FIB-SEM data is complicated due to a number of factors; the most prominent is that for porous materials, the scanning electron microscope image slices contain information not only from the planar cross-section of the material but also from underlying, exposed subsurface pores. In this work, we develop a segmentation method for FIB-SEM data from ethyl cellulose porous films made from ethyl cellulose and hydroxypropyl cellulose (EC/HPC) polymer blends. These materials are used for coating pharmaceutical oral dosage forms (tablets or pellets) to control drug release. We study three samples of ethyl cellulose and hydroxypropyl cellulose with different volume fractions where the hydroxypropyl cellulose phase has been leached out, resulting in a porous material. The data are segmented using scale-space features and a random forest classifier. We demonstrate good agreement with manual segmentations. The method enables quantitative characterization and subsequent optimization of material structure for controlled release applications. Although the methodology is demonstrated on porous polymer films, it is applicable to other soft porous materials imaged by FIB-SEM. We make the data and software used publicly available to facilitate further development of FIB-SEM segmentation methods. Lay Description For imaging of very fine structures in materials, the resolution limits of, e.g. X-ray computed tomography quickly become a bottleneck. Scanning electron microscopy (SEM) provides a way out, but it is essentially a two-dimensional imaging technique. One manner in which to extend it to three dimensions is to use a focused ion beam (FIB) combined with a scanning electron microscopy and acquire tomography data. In FIB-SEM tomography, ions are used to perform serial sectioning and the electron beam is used to image the cross section surface. This is a well-established method for a wide range of materials. However, image analysis of FIB-SEM data is complicated for a variety of reasons, in particular for porous media. In this work, we analyse FIB-SEM data from ethyl cellulose porous films made from ethyl cellulose and hydroxypropyl cellulose (EC/HPC) polymer blends. These films are used as coatings for controlled drug release. The aim is to perform image segmentation, i.e. to identify which parts of the image data constitute the pores and the solid, respectively. Manual segmentation, i.e. when a trained operator manually identifies areas constituting pores and solid, is too time-consuming to do in full for our very large data sets. However, by performing manual segmentation on a set of small, random regions of the data, we can train a machine learning algorithm to perform automatic segmentation on the entire data sets. The method yields good agreement with the manual segmentations and yields porosities of the entire data sets in very good agreement with expected values. The method facilitates understanding and quantitative characterization of the geometrical structure of the materials, and ultimately understanding of how to tailor the drug release

Semi-leptonic B decays into higher charmed resonances

We apply HQET to semi-leptonic $B$ meson decays into a variety of excited charm states. Using three realistic meson models with fermionic light degrees of freedom, we examine the extent that the sum of exclusive single charmed states account for the inclusive semi-leptonic $B$ decay rate. The consistency of form factors with the Bjorken and Voloshin sum rules is also investigated.Comment: Latex, 27 pages. A few references and errors corrected, to appear in Phys. Rev.

On the validity of the reduced Salpeter equation

We adapt a general method to solve both the full and reduced Salpeter equations and systematically explore the conditions under which these two equations give equivalent results in meson dynamics. The effects of constituent mass, angular momentum state, type of interaction, and the nature of confinement are all considered in an effort to clearly delineate the range of validity of the reduced Salpeter approximations. We find that for $J\not{\hspace*{-1.0mm}=}0$ the solutions are strikingly similar for all constituent masses. For zero angular momentum states the full and reduced Salpeter equations give different results for small quark mass especially with a large additive constant coordinate space potential. We also show that $\frac{1}{m}$ corrections to heavy-light energy levels can be accurately computed with the reduced equation.Comment: Latex (uses epsf macro), 24 pages of text, 12 postscript figures included. Slightly revised version, to appear in Phys. Rev.