Microstructural Shear Localization in Plastic Deformation of Amorphous Solids

The shear-transformation-zone (STZ) theory of plastic deformation predicts that sufficiently soft, non-crystalline solids are linearly unstable against forming periodic arrays of microstructural shear bands. A limited nonlinear analysis indicates that this instability may be the mechanism responsible for strain softening in both constant-stress and constant-strain-rate experiments. The analysis presented here pertains only to one-dimensional banding patterns in two-dimensional systems, and only to very low temperatures. It uses the rudimentary form of the STZ theory in which there is only a single kind of zone rather than a distribution of them with a range of transformation rates. Nevertheless, the results are in qualitative agreement with essential features of the available experimental data. The nonlinear theory also implies that harder materials, which do not undergo a microstructural instability, may form isolated shear bands in weak regions or, perhaps, at points of concentrated stress.Comment: 32 pages, 6 figure

Onset of Vortices in Thin Superconducting Strips and Wires

Spontaneous nucleation and the consequent penetration of vortices into thin superconducting films and wires, subjected to a magnetic field, can be considered as a nonlinear stage of primary instability of the current-carrying superconducting state. The development of the instability leads to the formation of a chain of vortices in strips and helicoidal vortex lines in wires. The boundary of instability was obtained analytically. The nonlinear stage was investigated by simulations of the time-dependent generalized Ginzburg-Landau equation.Comment: REVTeX 3.0, 12 pages, 5Postscript figures (uuencoded). Accepted for Phys. Rev.

Ordering and finite-size effects in the dynamics of one-dimensional transient patterns

We introduce and analyze a general one-dimensional model for the description of transient patterns which occur in the evolution between two spatially homogeneous states. This phenomenon occurs, for example, during the Freedericksz transition in nematic liquid crystals.The dynamics leads to the emergence of finite domains which are locally periodic and independent of each other. This picture is substantiated by a finite-size scaling law for the structure factor. The mechanism of evolution towards the final homogeneous state is by local roll destruction and associated reduction of local wavenumber. The scaling law breaks down for systems of size comparable to the size of the locally periodic domains. For systems of this size or smaller, an apparent nonlinear selection of a global wavelength holds, giving rise to long lived periodic configurations which do not occur for large systems. We also make explicit the unsuitability of a description of transient pattern dynamics in terms of a few Fourier mode amplitudes, even for small systems with a few linearly unstable modes.Comment: 18 pages (REVTEX) + 10 postscript figures appende

Energy migration in Rhodobacter sphaeroides mutants altered by mutagenesis of the peripheral LH2 complex or by removal of the core LH1 complex

AbstractThe photosynthetic apparatus of the purple bacterium Rhodobacter sphaeroides is organised so that light energy absorbed by the peripheral antenna (LH2) complexes migrates towards the core (LH1) complex, before being trapped by the reaction centre (RC). This migration and trapping process has been studied in mutants where the energy levels of the LH2 BChls have been raised by mutagenesis of the C-terminal aromatic residues (Fowler, G.J.S., Visschers, R.W., Grief, G.G., Van Grondelle, R. and Hunter, C.N. (1992) Nature 355, 848–850), and in a mutant which lacks the core complex. In the former case, the alterations to the LH2 complexes did not prevent efficient energy transfer to the LHI-RC complex, but fluorescence emission spectra indicated that the equilibrium of energy within the system was affected so that back transfer from the LH1-RC core is minimised. This mimics the situation found in some other bacteria such as Rhodopseudomonas acidophila and Rps. cryptolactis. In the mutant lacking LH1, energy is transferred from LH2 directly to the RC, despite the absence of the core antenna. Energy transfer efficiencies for carotenoids and LH2 to LH1 were measured for the blue-shifted LH2 mutants, and were found to be high (70%) in each case. These data, together with measurements of excitation annihilation as a function of incident excitation energy, were used to estimate the domain sizes for energy transfer in these mutants. In the LH2 mutants, domains of about 50 to 170 core BChls were found, depending on the type of mutation. One effect of the removal of LH1 appears to be the reorganisation of the peripheral LH2 antenna to form domains of at least 250 BChls

Regulator constants and the parity conjecture

The p-parity conjecture for twists of elliptic curves relates multiplicities of Artin representations in p-infinity Selmer groups to root numbers. In this paper we prove this conjecture for a class of such twists. For example, if E/Q is semistable at 2 and 3, K/Q is abelian and K^\infty is its maximal pro-p extension, then the p-parity conjecture holds for twists of E by all orthogonal Artin representations of Gal(K^\infty/Q). We also give analogous results when K/Q is non-abelian, the base field is not Q and E is replaced by an abelian variety. The heart of the paper is a study of relations between permutation representations of finite groups, their "regulator constants", and compatibility between local root numbers and local Tamagawa numbers of abelian varieties in such relations.Comment: 50 pages; minor corrections; final version, to appear in Invent. Mat

Nickel on Lead, Magnetically Dead or Alive?

Two atomic layers of Ni condensed onto Pb films behave, according to anomalous Hall effect measurements, as magnetic dead layers. However, the Ni lowers the superconducting T_{c} of the Pb film. This has lead to the conclusion that the Ni layers are still very weakly magnetic. In the present paper the electron dephasing due to the Ni has been measured by weak localization. The dephasing is smaller by a factor 100 than the pair-breaking. This proves that the T_{c}-reduction in the PbNi films is not due magnetic Ni moments

Current-density functional for disordered systems

The effective action for the current and density is shown to satisfy an evolution equation, the functional generalization of Callan-Symanzik equation. The solution describes the dependence of the one-particle irreducible vertex functions on the strength of the quenched disorder and the annealed Coulomb interaction. The result is non-perturbative, no small parameter is assumed. The a.c. conductivity is obtained by the numerical solution of the evolution equation on finite lattices in the absence of the Coulomb interaction. The static limit is performed and the conductivity is found to be vanishing beyond a certain threshold of the impurity strength.Comment: final version, 28 pages, 17 figures, to appear in Phys. Rev.

Quantum railroads and directed localization at the juncture of quantum Hall systems

The integer quantum Hall effect (QHE) and one-dimensional Anderson localization (AL) are limiting special cases of a more general phenomenon, directed localization (DL), predicted to occur in disordered one-dimensional wave guides called "quantum railroads" (QRR). Here we explain the surprising results of recent measurements by Kang et al. [Nature 403, 59 (2000)] of electron transfer between edges of two-dimensional electron systems and identify experimental evidence of QRR's in the general, but until now entirely theoretical, DL regime that unifies the QHE and AL. We propose direct experimental tests of our theory.Comment: 11 pages revtex + 3 jpeg figures, to appear in Phys. Rev.