Polyamide-rubber blends: micrscopic studies of the deformation zone

The morphology of injection moulded samples of polyamide—polybutadiene blends (85.15) with an average particle size of 0.3 μm was studied. The samples were fractured in a notched tensile test at crosshead speeds of 10−4 and 1 ms −1 and the structure of the deformation zone was studied using various techniques: polarized light microscopy, scanning electron microscopy, transmission electron microscopy on stained cut samples and carbon replicas, and selected area electron diffraction transmission electron microscopy. The deformation zone of samples tested at 10−4 ms−1 was found to consist of two layers. Far from the fracture surface a layer was observed with more or less round cavities and with cavities in the rubber particles, while near the fracture surface a layer with strongly deformed cavities (length/diameter ratio of 5–10) could be seen. In the samples tested at 1 ms−1 the deformation zone was found to have three layers. In addition to the two previous layers an extra layer next to the fracture plane was found. This layer was 2–3 μm thick with round rubber particles and no orientation of the matrix material. This indicates that, at the high deformation speed of the test, relaxation in the melt took place, suggesting that the material around the crack tip was molten during fracture.\u

Direct solution of the hard pomeron problem for arbitrary conformal weight

A new method is applied to solve the Baxter equation for the one dimensional system of noncompact spins. Dynamics of such an ensemble is equivalent to that of a set of reggeized gluons exchanged in the high energy limit of QCD amplitudes. The technique offers more insight into the old calculation of the intercept of hard Pomeron, and provides new results in the odderon channel.Comment: Contribution to the ICHEP96 Conference, July 1996, Warsaw, Poland. LaTeX, 4 pages, 3 epsf figures, includes modified stwol.sty file. Some references were revise

Finite Conductivity Minimum in Bilayer Graphene without Charge Inhomogeneities

Boltzmann transport theory fails near the linear band-crossing of single-layer graphene and near the quadratic band-crossing of bilayer graphene. We report on a numerical study which assesses the role of inter-band coherence in transport when the Fermi level lies near the band-crossing energy of bilayer graphene. We find that interband coherence enhances conduction, and that it plays an essential role in graphene's minimum conductivity phenomena. This behavior is qualitatively captured by an approximate theory which treats inter-band coherence in a relaxation-time approximation. On the basis of this short-range-disorder model study, we conclude that electron-hole puddle formation is not a necessary condition for finite conductivity in graphene at zero average carrier density.Comment: revised version as published in Phys. Rev.

Summing free unitary random matrices

I use quaternion free probability calculus - an extension of free probability to non-Hermitian matrices (which is introduced in a succinct but self-contained way) - to derive in the large-size limit the mean densities of the eigenvalues and singular values of sums of independent unitary random matrices, weighted by complex numbers. In the case of CUE summands, I write them in terms of two "master equations," which I then solve and numerically test in four specific cases. I conjecture a finite-size extension of these results, exploiting the complementary error function. I prove a central limit theorem, and its first sub-leading correction, for independent identically-distributed zero-drift unitary random matrices.Comment: 17 pages, 15 figure

Dirac eigenvalues and eigenvectors at finite temperature

We investigate the eigenvalues and eigenvectors of the staggered Dirac operator in the vicinity of the chiral phase transition of quenched SU(3) lattice gauge theory. We consider both the global features of the spectrum and the local correlations. In the chirally symmetric phase, the local correlations in the bulk of the spectrum are still described by random matrix theory, and we investigate the dependence of the bulk Thouless energy on the simulation parameters. At and above the critical point, the properties of the low-lying Dirac eigenvalues depend on the $Z_3$-phase of the Polyakov loop. In the real phase, they are no longer described by chiral random matrix theory. We also investigate the localization properties of the Dirac eigenvectors in the different $Z_3$-phases.Comment: Lattice 2000 (Finite Temperature), 5 page

Universal eigenvector statistics in a quantum scattering ensemble

We calculate eigenvector statistics in an ensemble of non-Hermitian matrices describing open quantum systems [F. Haake et al., Z. Phys. B 88, 359 (1992)] in the limit of large matrix size. We show that ensemble-averaged eigenvector correlations corresponding to eigenvalues in the center of the support of the density of states in the complex plane are described by an expression recently derived for Ginibre's ensemble of random non-Hermitian matrices.Comment: 4 pages, 5 figure

Lectures on Chiral Disorder in QCD

I explain the concept that light quarks diffuse in the QCD vacuum following the spontaneous breakdown of chiral symmetry. I exploit the striking analogy to disordered electrons in metals, identifying, among others, the universal regime described by random matrix theory, diffusive regime described by chiral perturbation theory and the crossover between these two domains.Comment: Lectures given at the Cargese Summer School, August 6-18, 200