Diagrammatic Approach for the High-Temperature Regime of Quantum Hall Transitions

We use a general diagrammatic formalism based on a local conductivity approach to compute electronic transport in continuous media with long-range disorder, in the absence of quantum interference effects. The method allows us then to investigate the interplay of dissipative processes and random drifting of electronic trajectories in the high-temperature regime of quantum Hall transitions. We obtain that the longitudinal conductance \sigma_{xx} scales with an exponent {\kappa}=0.767\pm0.002 in agreement with the value {\kappa}=10/13 conjectured from analogies to classical percolation. We also derive a microscopic expression for the temperature-dependent peak value of \sigma_{xx}, useful to extract {\kappa} from experiments.Comment: 4+epsilon pages, 5 figures, attached with Supplementary Material. A discussion and a plot of the temperature-dependent longitudinal conductance was added in the final versio

On calculation of effective galvanomagnetic characteristics of inhomogeneous metals. Exact solution for the longitudinal effective conductivity of polycrystals of metals in high magnetic fields

In the framework of the perturbation theory an expression suitable for calculation of the effective conductivity of 3-D inhomogeneous metals in uniform magnetic field $H$ is derived. For polycrystals of metals with closed Fermi surfaces in high magnetic fields the perturbation series defining the longitudinal and the hall elements of the perturbation series can be summed allowing us to obtain the exact expression for the leading terms of all these elements of the effective conductivity tensor.Comment: 12 page

Planar isotropic two-phase systemsin perpendicular magnetic field: effective conductivity

Three explicit approximate expressions for the effective conductivity sigma_e of various planar isotropic two-phase systems in a magnetic field are obtained using the dual linear fractional transformation, connecting sigma_e of these systems with and without magnetic field. The obtained results are applicable for two-phase systems (regular and nonregular as well as random), satisfying the symmetry and self-duality conditions, and allow to describe sigma_e of various two-dimensional and layered inhomogeneous media at arbitrary phase concentrations and magnetic fields. All these results admit a direct experimental checking.Comment: 10 pages, Latex2e, 3 figure

Internal and surface phenomena in metal combustion

Combustion of metals has been widely studied in the past, primarily because of their high oxidation enthalpies. A general understanding of metal combustion has been developed based on the recognition of the existence of both vapor-phase and surface reactions and involvement of the reaction products in the ensuing heterogeneous combustion. However, distinct features often observed in metal particle combustion, such as brightness oscillations and jumps (spearpoints), disruptive burning, and non-symmetric flames are not currently understood. Recent metal combustion experiments using uniform high-temperature metal droplets produced by a novel micro-arc technique have indicated that oxygen dissolves in the interior of burning particles of certain metals and that the subsequent transformations of the metal-oxygen solutions into stoichiometric oxides are accompanied with sufficient heat release to cause observed brightness and temperature jumps. Similar oxygen dissolution has been observed in recent experiments on bulk iron combustion but has not been associated with such dramatic effects. This research addresses heterogeneous metal droplet combustion, specifically focusing on oxygen penetration into the burning metal droplets, and its influence on the metal combustion rate, temperature history, and disruptive burning. A unique feature of the experimental approach is the combination of the microgravity environment with a novel micro-arc Generator of Monodispersed Metal Droplets (GEMMED), ensuring repeatable formation and ignition of uniform metal droplets with controllable initial temperature and velocity. The droplet initial temperatures can be adjusted within a wide range from just above the metal melting point, which provides means to ignite droplets instantly upon entering an oxygen containing environment. Initial droplet velocity will be set equal to zero allowing one to organize metal combustion microgravity experiments in a fashion similar to usual microgravity liquid fuel droplet combustion studies. In addition, the internal compositions of rapidly quenched metal particles will be analyzed using SEM technique. Such compositions are similar to those existing during the combustion and provide new insight on metal combustion processes. The results of this experimental work will be used to model the fundamental mechanisms of metal combustion. Preliminary experimental results on Al and Zr particle combustion at normal gravity are discussed here

Duality and exact results for conductivity of 2D isotropic heterophase systems in magnetic field

Using a fact that the effective conductivity sigma_{e} of 2D random heterophase systems in the orthogonal magnetic field is transformed under some subgroup of the linear fractional group, connected with a group of linear transformations of two conserved currents, the exact values for sigma_{e} of isotropic heterophase systems are found. As known, for binary (N=2) systems a determination of exact values of both conductivities (diagonal sigma_{ed} and transverse Hall sigma_{et}) is possible only at equal phase concentrations and arbitrary values of partial conductivities. For heterophase (N > 2) systems this method gives exact values of effective conductivities, when their partial conductivities belong to some hypersurfaces in the space of these partial conductivities and the phase concentrations are pairwise equal. In all these cases sigma_e does not depend on phase concentrations. The complete, 3-parametric, explicit transformation, connecting sigma_e in binary systems with a magnetic field and without it, is constructedComment: 15 pages, 3 figures, Latex2

Extraordinary magnetoresistance in graphite: experimental evidence for the time-reversal symmetry breaking

The ordinary magnetoresistance (MR) of doped semiconductors is positive and quadratic in a low magnetic field, B, as it should be in the framework of the Boltzmann kinetic theory or in the conventional hopping regime. We observe an unusual highly-anisotropic in-plane MR in graphite, which is neither quadratic nor always positive. In a certain current direction MR is negative and linear in B in fields below a few tens of mT with a crossover to a positive MR at higher fields, while in a perpendicular current direction we observe a giant super-linear and positive MR. These extraordinary MRs are respectively explained by a hopping magneto-conductance via non-zero angular momentum orbitals, and by the magneto-conductance of inhomogeneous media. The linear orbital NMR is a unique signature of the broken time-reversal symmetry (TRS) in graphite. While some local paramagnetic centers could be responsible for the broken TRS, the observed large diamagnetism suggests a more intriguing mechanism of this breaking, involving superconducting clusters with unconventional (chiral) order parameters and spontaneously generated normal-state current loops in graphite.Comment: 4 pages, 5 figure

Non-saturating magnetoresistance of inhomogeneous conductors: comparison of experiment and simulation

The silver chalcogenides provide a striking example of the benefits of imperfection. Nanothreads of excess silver cause distortions in the current flow that yield a linear and non-saturating transverse magnetoresistance (MR). Associated with the large and positive MR is a negative longitudinal MR. The longitudinal MR only occurs in the three-dimensional limit and thereby permits the determination of a characteristic length scale set by the spatial inhomogeneity. We find that this fundamental inhomogeneity length can be as large as ten microns. Systematic measurements of the diagonal and off-diagonal components of the resistivity tensor in various sample geometries show clear evidence of the distorted current paths posited in theoretical simulations. We use a random resistor network model to fit the linear MR, and expand it from two to three dimensions to depict current distortions in the third (thickness) dimension. When compared directly to experiments on Ag$_{2\pm\delta}$Se and Ag$_{2\pm\delta}$Te, in magnetic fields up to 55 T, the model identifies conductivity fluctuations due to macroscopic inhomogeneities as the underlying physical mechanism. It also accounts reasonably quantitatively for the various components of the resistivity tensor observed in the experiments.Comment: 10 pages, 7 figure

Effective conductivity of 2D isotropic two-phase systems in magnetic field

Using the linear fractional transformation, connecting effective conductivities sigma_{e} of isotropic two-phase systems with and without magnetic field, explicit approximate expressions for sigma_{e} in a magnetic field are obtained. They allow to describe sigma_{e} of various inhomogeneous media at arbitrary phase concentrations x and magnetic fields. the x-dependence plots of sigma_e at some values of inhomogeneity and magnetic field are constructed. Their behaviour is qualitatively compatible with the existing experimental data. The obtained results are applicable for different two-phase systems (regular and nonregular as well as random), satisfying the symmetry and self-duality conditions, and admit a direct experimental checking.Comment: 9 pages, 2 figures, Latex2e, small corrections and new figure