On the generalized eigenvalue method for energies and matrix elements in lattice field theory

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E(N+1) - E(n))t). The gap E(N+1) - E(n) can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m(b) in HQET.

Linear covariant gauges on the lattice

Linear covariant gauges, such as Feynman gauge, are very useful in perturbative calculations. Their non-perturbative formulation is, however, highly non-trivial. In particular, it is a challenge to define linear covariant gauges on a lattice. We consider a class of gauges in lattice gauge theory that coincides with the perturbative definition of linear covariant gauges in the formal continuum limit. The corresponding gauge-fixing procedure is described and analyzed in detail, with an application to the pure SU(2) case. In addition, results for the gluon propagator in the two-dimensional case are given. (C) 2008 Elsevier B.V. All rights reserved.

Energy of bond defects in quantum spin chains obtained from local approximations and from exact diagonalization

We study the influence of ferromagnetic and antiferromagnetic bond defects on the ground-state energy of antiferromagnetic spin chains. In the absence of translational invariance, the energy spectrum of the full Hamiltonian is obtained numerically, by an iterative modi. cation of the power algorithm. In parallel, approximate analytical energies are obtained from a local-bond approximation, proposed here. This approximation results in significant improvement upon the mean-field approximation, at negligible extra computational effort. (C) 2008 Published by Elsevier B.V.

An application of lattice basis reduction to polynomial identities for algebraic structures

The authors` recent classification of trilinear operations includes, among other cases, a fourth family of operations with parameter q epsilon Q boolean OR {infinity}, and weakly commutative and weakly anticommutative operations. These operations satisfy polynomial identities in degree 3 and further identities in degree 5. For each operation, using the row canonical form of the expansion matrix E to find the identities in degree 5 gives extremely complicated results. We use lattice basis reduction to simplify these identities: we compute the Hermite normal form H of E(t), obtain a basis of the nullspace lattice from the last rows of a matrix U for which UE(t) = H, and then use the LLL algorithm to reduce the basis. (C) 2008 Elsevier Inc. All rights reserved.

Histological evaluation of chitosan-based biomaterials used for the correction of critical size defects in rat`s calvaria

Chitosan, a biopolymer obtained from chitin, and its derivates, such as chitosan hydrochloride, has been reported as wound healing accelerators and as possible bone substitutes for tissue engineering, and therefore these Substances could be relevant in dentistry and periodontology. The purpose of this investigation was to make a histological evaluation of chitosan and chitosan hydrochloride biomaterials (gels) used in the correction of critical size bone defects made in rat`s calvaria. Bone defects of 8 mm in diameter were surgically created in the calviria of 50 Holtzman (Rattus norvegicus) rats and filled with blood clot (control), low molecular weight chitosan, high molecular weight chitosan, low molecular weight chitosan hydrochloride, and high molecular weight chitosan hydrochloride, numbering 10 animals, divided into two experimental periods (15 and 60 days), for each biomaterial. The histological evaluation was made based on the morphology of the new-formed tissues in defect`s region, and the results indicated that there was no statistical difference between the groups when the new bone formation in the entire defect`s area were compared (p > 0.05) and, except in the control groups, assorted degrees of inflammation Could be Seen. In Conclusion, chitosan and chitosan hydrochloride biomaterials used in this study were not able to promote new bone formation in critical size defects made in rat`s calvaria. (C) 2009 Wiley Periodicals, Inc. J Biomed Mater Res 93A: 107-114, 2016

Implants of polyanionic collagen matrix in bone defects of ovariectomized rats

In recent years, there has been a great interest in the development of biomaterials that could be used in the repair of bone defects. Collagen matrix (CM) has the advantage that it can be modified chemically to improve its mechanical properties. The aim of the present study was to evaluate the effect of three-dimensional membranes of native or anionic (submitted to alkaline treatment for 48 or 96 h) collagen matrix on the consolidation of osteoporosis bone fractures resulting from the gonadal hormone alterations caused by ovariectomy in rats subjected to hormone replacement therapy. The animals received the implants 4 months after ovariectomy and were sacrificed 8 weeks after implantation of the membranes into 4-mm wide bone defects created in the distal third of the femur with a surgical bur. Macroscopic analysis revealed the absence of pathological alterations in the implanted areas, suggesting that the material was biocompatible. Microscopic analysis showed a lower amount of bone ingrowth in the areas receiving the native membrane compared to the bone defects filled with the anionic membranes. In ovariectomized animals receiving anionic membranes, a delay in bone regeneration was observed mainly in animals not subjected to hormone replacement therapy. We conclude that anionic membranes treated with alkaline solution for 48 and 96 h presented better results in terms of bone ingrowth.