Structure of logarithmically divergent one-loop lattice Feynman integrals

For logarithmically divergent one-loop lattice Feynman integrals I(p,a), subject to mild general conditions, we prove the following expected and crucial structural result: I(p,a) = f(p)log(aM)+g(p)+h(p,M) up to terms which vanish for lattice spacing a -> 0. Here p denotes collectively the external momenta and M is a mass scale which may be chosen arbitrarily. The f(p) and h(p,M) are shown to be universal and coincide with analogous quantities in the corresponding continuum integral when the latter is regularized either by momentum cut-off or dimensional regularization. The non-universal term g(p) is shown to be a homogeneous polynomial in p of the same degree as f(p). This structure is essential for consistency between renormalized lattice and continuum formulations of QCD at one loop.Comment: 26 pages (after reformatting using revtex); typos corrected; to appear in Phys.Rev.

The Ultimate Halo Mass in a LCDM Universe

In the far future of an accelerating LCDM cosmology, the cosmic web of large-scale structure consists of a set of increasingly isolated halos in dynamical equilibrium. We examine the approach of collisionless dark matter to hydrostatic equilibrium using a large N-body simulation evolved to scale factor a = 100, well beyond the vacuum--matter equality epoch, a_eq ~ 0.75, and 53/h Gyr into the future for a concordance model universe (Omega_m ~ 0.3, Omega_Lambda ~ 0.7). The radial phase-space structure of halos -- characterized at a < a_eq by a pair of zero-velocity surfaces that bracket a dynamically active accretion region -- simplifies at a > 10 a_eq when these surfaces merge to create a single zero-velocity surface, clearly defining the halo outer boundary, rhalo, and its enclosed mass, mhalo. This boundary approaches a fixed physical size encompassing a mean interior density ~ 5 times the critical density, similar to the turnaround value in a classical Einstein-deSitter model. We relate mhalo to other scales currently used to define halo mass (m200, mvir, m180b) and find that m200 is approximately half of the total asymptotic cluster mass, while m180b follows the evolution of the inner zero velocity surface for a < 2 but becomes much larger than the total bound mass for a > 3. The radial density profile of all bound halo material is well fit by a truncated Hernquist profile. An NFW profile provides a somewhat better fit interior to r200 but is much too shallow in the range r200 < r < rhalo.Comment: 5 pages, 3 figures, submitted to MNRAS letter

Etching of High Purity Zinc

A method of etching high purity zinc to reveal various etch figures on {101¯0} planes is presented in this paper. Etch figures are formed by polishing in a dichromic acid solution after the introduction of mercury to the crystal surface. No measurable aging time is required to form etch figures at newly formed dislocation sites when mercury is on the surface prior to deformation. The mercury concentrates at the sites where etch figures form and may be removed by vacuum distillation and chemical polishing before it appreciably affects the purity of the bulk of the crystal

Dislocations and etch figures in high purity zinc

A method of etching high purity zinc single crystals to reveal various etch figures on {1010} planes is presented in the preceding paper. The procedure involves the introduction of mercury to the crystal surface prior to a chemical polish with dichromic acid. The mercury was found to be concentrated at the etch figures. This paper presents the results of several experiments which support the conclusion that there exists a one-to-one correspondence between etch figures and dislocations. Some observations of slip on (0001) basal planes and {1212} pyramidal planes, and of twinning in zinc are also presented

Orientation Dependence of a Dislocation Etch for Zinc

The dislocation etch for (101-[bar]0] surfaces of zinc reported by Brandt, Adams, and Vreeland have been further explored. Additional surface orientations have been found where dislocation etching takes place. These orientations cover an area located between 3 degrees and 12.2 degrees to the [0001], and the area is symmetric about that axis. Attempts to produce dislocation etching on within 2 degrees of (0001) were generally unsuccessful. This is in contrast to etching of many crystals which takes place only within a few degrees of a low index plane

General bounds on the Wilson-Dirac operator

Lower bounds on the magnitude of the spectrum of the Hermitian Wilson-Dirac operator H(m) have previously been derived for 0<m<2 when the lattice gauge field satisfies a certain smoothness condition. In this paper lower bounds are derived for 2p-2<m<2p for general p=1,2,...,d where d is the spacetime dimension. The bounds can alternatively be viewed as localisation bounds on the real spectrum of the usual Wilson-Dirac operator. They are needed for the rigorous evaluation of the classical continuum limit of the axial anomaly and index of the overlap Dirac operator at general values of m, and provide information on the topological phase structure of overlap fermions. They are also useful for understanding the instanton size-dependence of the real spectrum of the Wilson-Dirac operator in an instanton background.Comment: 26 pages, 2 figures. v3: Completely rewritten with new material and new title; to appear in Phys.Rev.

The Impact of Isospin Breaking on the Distribution of Transition Probabilities

In the present paper we investigate the effect of symmetry breaking in the statistical distributions of reduced transition amplitudes and reduced transition probabilities. These quantities are easier to access experimentally than the components of the eigenvectors and were measured by Adams et al. for the electromagnetic transitions in ^{26}Al. We focus on isospin symmetry breaking described by a matrix model where both, the Hamiltonian and the electromagnetic operator, break the symmetry. The results show that for partial isospin conservation, the statistical distribution of the reduced transition probability can considerably deviate from the Porter-Thomas distribution.Comment: 16 pages, 8 figures, submitted to PR

Physical disruption of intervertebral disc promotes cell clustering and a degenerative phenotype

© 2019, The Author(s). To test the hypothesis that physical disruption of an intervertebral disc disturbs cell-matrix binding, leading to cell clustering and increased expression of matrix degrading enzymes that contribute towards degenerative disc cell phenotype. Lumbar disc tissue was removed at surgery from 21 patients with disc herniation, 11 with disc degeneration, and 8 with adolescent scoliosis. 5 μm sections were examined with histology, and 30-µm sections by confocal microscopy. Antibodies were used against integrin α5beta1, matrix metalloproteinases (MMP) 1, MMP-3, caspase 3, and denatured collagen types I and II. Spatial associations were sought between cell clustering and various degenerative features. An additional, 11 non-herniated human discs were used to examine causality: half of each specimen was cultured in a manner that allowed free ‘unconstrained’ swelling (similar to a herniated disc in vivo), while the other half was cultured within a perspex ring that allowed ‘constrained’ swelling. Changes were monitored over 36 h using live-cell imaging. 1,9-Di-methyl methylene blue (DMMB) assay for glycosaminoglycan loss was carried out from tissue medium. Partially constrained specimens showed little swelling or cell movement in vitro. In contrast, unconstrained swelling significantly increased matrix distortion, glycosaminoglycan loss, exposure of integrin binding sites, expression of MMPs 1 and 3, and collagen denaturation. In the association studies, herniated disc specimens showed changes that resembled unconstrained swelling in vitro. In addition, they exhibited increased cell clustering, apoptosis, MMP expression, and collagen denaturation compared to ‘control’ discs. Results support our hypothesis. Further confirmation will require longitudinal animal experiments