Current-voltage characteristics of diluted Josephson-junction arrays: scaling behavior at current and percolation threshold

Dynamical simulations and scaling arguments are used to study the current-voltage (IV) characteristics of a two-dimensional model of resistively shunted Josephson-junction arrays in presence of percolative disorder, at zero external field. Two different limits of the Josephson-coupling concentration $p$ are considered, where $p_c$ is the percolation threshold. For $p$ $>$ $p_c$ and zero temperature, the IV curves show power-law behavior above a disorder dependent critical current. The power-law behavior and critical exponents are consistent with a simple scaling analysis. At $p_c$ and finite temperature $T$, the results show the scaling behavior of a T=0 superconducting transition. The resistance is linear but vanishes for decreasing $T$ with an apparent exponential behavior. Crossover to non-linearity appears at currents proportional to $$, with a thermal-correlation length exponent $\nu_T$ consistent with the corresponding value for the diluted XY model at $p_c$.Comment: Revtex, 9 postscript pages, to appear in Phys. Rev.

Infinite-cluster geometry in central-force networks

We show that the infinite percolating cluster (with density P_inf) of central-force networks is composed of: a fractal stress-bearing backbone (Pb) and; rigid but unstressed ``dangling ends'' which occupy a finite volume-fraction of the lattice (Pd). Near the rigidity threshold pc, there is then a first-order transition in P_inf = Pd + Pb, while Pb is second-order with exponent Beta'. A new mean field theory shows Beta'(mf)=1/2, while simulations of triangular lattices give Beta'_tr = 0.255 +/- 0.03.Comment: 6 pages, 4 figures, uses epsfig. Accepted for publication in Physical Review Letter

Towards a first principles description of phonons in Ni50_{50}Pt50_{50} disordered alloys: the role of relaxation

Using a combination of density-functional perturbation theory and the itinerant coherent potential approximation, we study the effects of atomic relaxation on the inelastic incoherent neutron scattering cross sections of disordered Ni$_{50}$Pt$_{50}$ alloys. We build on previous work, where empirical force constants were adjusted {\it ad hoc} to agree with experiment. After first relaxing all structural parameters within the local-density approximation for ordered NiPt compounds, density-functional perturbation theory is then used to compute phonon spectra, densities of states, and the force constants. The resulting nearest-neighbor force constants are first compared to those of other ordered structures of different stoichiometry, and then used to generate the inelastic scattering cross sections within the itinerant coherent potential approximation. We find that structural relaxation substantially affects the computed force constants and resulting inelastic cross sections, and that the effect is much more pronounced in random alloys than in ordered alloys.Comment: 8 pages, 3 eps figures, uses revtex

Experimental evidence of a fractal dissipative regime in high-T_c superconductors

We report on our experimental evidence of a substantial geometrical ingredient characterizing the problem of incipient dissipation in high-T_c superconductors(HTS): high-resolution studies of differential resistance-current characteristics in absence of magnetic field enabled us to identify and quantify the fractal dissipative regime inside which the actual current-carrying medium is an object of fractal geometry. The discovery of a fractal regime proves the reality and consistency of critical-phenomena scenario as a model for dissipation in inhomogeneous and disordered HTS, gives the experimentally-based value of the relevant finite-size scaling exponent and offers some interesting new guidelines to the problem of pairing mechanisms in HTS.Comment: 5 pages, 3 figures, RevTex; Accepted for publication in Physical Review B; (figures enlarged

Gradient Clogging in Depth Filtration

We investigate clogging in depth filtration, in which a dirty fluid is ``cleaned'' by the trapping of dirt particles within the pore space during flow through a porous medium. This leads to a gradient percolation process which exhibits a power law distribution for the density of trapped particles at downstream distance x from the input. To achieve a non-pathological clogging (percolation) threshold, the system length L should scale no faster than a power of ln w, where w is the width. Non-trivial behavior for the permeability arises only in this extreme anisotropic geometry.Comment: 4 pages, 3 figures, RevTe

Phonons in random alloys: the itinerant coherent-potential approximation

We present the itinerant coherent-potential approximation(ICPA), an analytic, translationally invariant and tractable form of augmented-space-based, multiple-scattering theory in a single-site approximation for harmonic phonons in realistic random binary alloys with mass and force-constant disorder. We provide expressions for quantities needed for comparison with experimental structure factors such as partial and average spectral functions and derive the sum rules associated with them. Numerical results are presented for Ni_{55} Pd_{45} and Ni_{50} Pt_{50} alloys which serve as test cases, the former for weak force-constant disorder and the latter for strong. We present results on dispersion curves and disorder-induced widths. Direct comparisons with the single-site coherent potential approximation(CPA) and experiment are made which provide insight into the physics of force-constant changes in random alloys. The CPA accounts well for the weak force-constant disorder case but fails for strong force-constant disorder where the ICPA succeeds.Comment: 19 pages, 12 eps figures, uses RevTex

Thermodynamics of Mesoscopic Vortex Systems in 1+1 Dimensions

The thermodynamics of a disordered planar vortex array is studied numerically using a new polynomial algorithm which circumvents slow glassy dynamics. Close to the glass transition, the anomalous vortex displacement is found to agree well with the prediction of the renormalization-group theory. Interesting behaviors such as the universal statistics of magnetic susceptibility variations are observed in both the dense and dilute regimes of this mesoscopic vortex system.Comment: 4 pages, REVTEX, 6 figures included. Comments and suggestions can be sent to [email protected]

Statistics of self-avoiding walks on randomly diluted lattice

A comprehensive numerical study of self-avoiding walks (SAW's) on randomly diluted lattices in two and three dimensions is carried out. The critical exponents $\nu$ and $\chi$ are calculated for various different occupation probabilities, disorder configuration ensembles, and walk weighting schemes. These results are analyzed and compared with those previously available. Various subtleties in the calculation and definition of these exponents are discussed. Precise numerical values are given for these exponents in most cases, and many new properties are recognized for them.Comment: 34 pages (+ 12 figures), REVTEX 3.

Using Nonlinear Response to Estimate the Strength of an Elastic Network

Disordered networks of fragile elastic elements have been proposed as a model of inner porous regions of large bones [Gunaratne et.al., cond-mat/0009221, http://xyz.lanl.gov]. It is shown that the ratio $\Gamma$ of responses of such a network to static and periodic strain can be used to estimate its ultimate (or breaking) stress. Since bone fracture in older adults results from the weakening of porous bone, we discuss the possibility of using $\Gamma$ as a non-invasive diagnostic of osteoporotic bone.Comment: 4 pages, 4 figure

Absence of Two-Dimensional Bragg Glasses

The stability to dislocations of the elastic phase, or ``Bragg glass'', of a randomly pinned elastic medium in two dimensions is studied using the minimum-cost-flow algorithm for a disordered fully-packed loop model. The elastic phase is found to be unstable to dislocations due to the quenched disorder. The energetics of dislocations are discussed within the framework of renormalization group predictions as well as in terms of a domain wall picture.Comment: 5 pages, REVTEX, 3 figures included. Further information can be obtained from [email protected]