Theory of Double-Sided Flux Decorations

A novel two-sided Bitter decoration technique was recently employed by Yao et al. to study the structure of the magnetic vortex array in high-temperature superconductors. Here we discuss the analysis of such experiments. We show that two-sided decorations can be used to infer {\it quantitative} information about the bulk properties of flux arrays, and discuss how a least squares analysis of the local density differences can be used to bring the two sides into registry. Information about the tilt, compressional and shear moduli of bulk vortex configurations can be extracted from these measurements.Comment: 17 pages, 3 figures not included (to request send email to [email protected]

Preliminary Studies of Magnetic NDE Techniques for Identifying Neutron Embrittlement of Pressure Vessel Steel

In operating nuclear reactors, the steel pressure vessel is exposed to neutron irradiation. The high energy part (\u3e1 MeV) of this irradiation, over a long period, makes the steel brittle and susceptible to rupture

The Weakly Pushed Nature of "Pulled" Fronts with a Cutoff

The concept of pulled fronts with a cutoff $\epsilon$ has been introduced to model the effects of discrete nature of the constituent particles on the asymptotic front speed in models with continuum variables (Pulled fronts are the fronts which propagate into an unstable state, and have an asymptotic front speed equal to the linear spreading speed $v^*$ of small linear perturbations around the unstable state). In this paper, we demonstrate that the introduction of a cutoff actually makes such pulled fronts weakly pushed. For the nonlinear diffusion equation with a cutoff, we show that the longest relaxation times $\tau_m$ that govern the convergence to the asymptotic front speed and profile, are given by $\tau_m^{-1} \simeq [(m+1)^2-1] \pi^2 / \ln^2 \epsilon$, for $m=1,2,...$.Comment: 4 pages, 2 figures, submitted to Brief Reports, Phys. Rev.

Minimal speed of fronts of reaction-convection-diffusion equations

We study the minimal speed of propagating fronts of convection reaction diffusion equations of the form $u_t + \mu \phi(u) u_x = u_{xx} +f(u)$ for positive reaction terms with $f'(0 >0$. The function $\phi(u)$ is continuous and vanishes at $u=0$. A variational principle for the minimal speed of the waves is constructed from which upper and lower bounds are obtained. This permits the a priori assesment of the effect of the convective term on the minimal speed of the traveling fronts. If the convective term is not strong enough, it produces no effect on the minimal speed of the fronts. We show that if $f''(u)/\sqrt{f'(0)} + \mu \phi'(u) < 0$, then the minimal speed is given by the linear value $2 \sqrt{f'(0)}$, and the convective term has no effect on the minimal speed. The results are illustrated by applying them to the exactly solvable case $u_t + \mu u u_x = u_{xx} + u (1 -u)$. Results are also given for the density dependent diffusion case $u_t + \mu \phi(u) u_x = (D(u)u_x)_x +f(u)$.Comment: revised, new results adde

Emergence of pulled fronts in fermionic microscopic particle models

We study the emergence and dynamics of pulled fronts described by the Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation in the microscopic reaction-diffusion process A + A A$ on the lattice when only a particle is allowed per site. To this end we identify the parameter that controls the strength of internal fluctuations in this model, namely, the number of particles per correlated volume. When internal fluctuations are suppressed, we explictly see the matching between the deterministic FKPP description and the microscopic particle model.Comment: 4 pages, 4 figures. Accepted for publication in Phys. Rev. E as a Rapid Communicatio

Universality of Frequency and Field Scaling of the Conductivity Measured by Ac-Susceptibility of a Ybco-Film

Utilizing a novel and exact inversion scheme, we determine the complex linear conductivity $\sigma (\omega )$ from the linear magnetic ac-susceptibility which has been measured from 3\,mHz to 50\,MHz in fields between 0.4\,T and 4\,T applied parallel to the c-axis of a 250\,nm thin disk. The frequency derivative of the phase $\sigma ''/\sigma '$ and the dynamical scaling of $\sigma (\omega)$ above and below $T_g(B)$ provide clear evidence for a continuous phase transition at $T_g$ to a generic superconducting state. Based on the vortex-glass scaling model, the resulting critical exponents $\nu$ and $z$ are close to those frequently obtained on films by other means and associated with an 'isotropic' vortex glass. The field effect on $\sigma(\omega)$ can be related to the increase of the glass coherence length, $\xi_g\sim B$.Comment: 8 pages (5 figures upon request), revtex 3.0, APK.94.01.0

Short-Range Interactions and Scaling Near Integer Quantum Hall Transitions

We study the influence of short-range electron-electron interactions on scaling behavior near the integer quantum Hall plateau transitions. Short-range interactions are known to be irrelevant at the renormalization group fixed point which represents the transition in the non-interacting system. We find, nevertheless, that transport properties change discontinuously when interactions are introduced. Most importantly, in the thermodynamic limit the conductivity at finite temperature is zero without interactions, but non-zero in the presence of arbitrarily weak interactions. In addition, scaling as a function of frequency, $\omega$, and temperature, $T$, is determined by the scaling variable $\omega/T^p$ (where $p$ is the exponent for the temperature dependence of the inelastic scattering rate) and not by $\omega/T$, as it would be at a conventional quantum phase transition described by an interacting fixed point. We express the inelastic exponent, $p$, and the thermal exponent, $z_T$, in terms of the scaling dimension, $-\alpha < 0$, of the interaction strength and the dynamical exponent $z$ (which has the value $z=2$), obtaining $p=1+2\alpha/z$ and $z_T=2/p$.Comment: 9 pages, 4 figures, submitted to Physical Review

Random Mass Dirac Fermions in Doped Spin-Peierls and Spin-Ladder systems: One-Particle Properties and Boundary Effects

Quasi-one-dimensional spin-Peierls and spin-ladder systems are characterized by a gap in the spin-excitation spectrum, which can be modeled at low energies by that of Dirac fermions with a mass. In the presence of disorder these systems can still be described by a Dirac fermion model, but with a random mass. Some peculiar properties, like the Dyson singularity in the density of states, are well known and attributed to creation of low-energy states due to the disorder. We take one step further and study single-particle correlations by means of Berezinskii's diagram technique. We find that, at low energy $\epsilon$, the single-particle Green function decays in real space like $G(x,\epsilon) \propto (1/x)^{3/2}$. It follows that at these energies the correlations in the disordered system are strong -- even stronger than in the pure system without the gap. Additionally, we study the effects of boundaries on the local density of states. We find that the latter is logarithmically (in the energy) enhanced close to the boundary. This enhancement decays into the bulk as $1/\sqrt{x}$ and the density of states saturates to its bulk value on the scale $L_\epsilon \propto \ln^2 (1/\epsilon)$. This scale is different from the Thouless localization length $\lambda_\epsilon\propto\ln (1/\epsilon)$. We also discuss some implications of these results for the spin systems and their relation to the investigations based on real-space renormalization group approach.Comment: 26 pages, LaTex, 9 PS figures include

Microwave conductivity of a d-wave superconductor disordered by extended impurities: a real-space renormalization group approach

Using a real-space renormalization group (RSRG) technique, we compute the microwave conductivity of a d-wave superconductor disordered by extended impurities. To do this, we invoke a semiclassical approximation which naturally accesses the Andreev bound states localized near each impurity. Tunneling corrections (which are captured using the RSRG) lead to a delocalization of these quasiparticles and an associated contribution to the microwave conductivity.Comment: 8 pages, 4 figures. 2 figures added to previous versio