First Passage Time in a Two-Layer System

As a first step in the first passage problem for passive tracer in stratified porous media, we consider the case of a two-dimensional system consisting of two layers with different convection velocities. Using a lattice generating function formalism and a variety of analytic and numerical techniques, we calculate the asymptotic behavior of the first passage time probability distribution. We show analytically that the asymptotic distribution is a simple exponential in time for any choice of the velocities. The decay constant is given in terms of the largest eigenvalue of an operator related to a half-space Green's function. For the anti-symmetric case of opposite velocities in the layers, we show that the decay constant for system length $L$ crosses over from $L^{-2}$ behavior in diffusive limit to $L^{-1}$ behavior in the convective regime, where the crossover length $L^*$ is given in terms of the velocities. We also have formulated a general self-consistency relation, from which we have developed a recursive approach which is useful for studying the short time behavior.Comment: LaTeX, 28 pages, 7 figures not include

Sliding blocks with random friction and absorbing random walks

With the purpose of explaining recent experimental findings, we study the distribution $A(\lambda)$ of distances $\lambda$ traversed by a block that slides on an inclined plane and stops due to friction. A simple model in which the friction coefficient $\mu$ is a random function of position is considered. The problem of finding $A(\lambda)$ is equivalent to a First-Passage-Time problem for a one-dimensional random walk with nonzero drift, whose exact solution is well-known. From the exact solution of this problem we conclude that: a) for inclination angles $\theta$ less than \theta_c=\tan(\av{\mu}) the average traversed distance \av{\lambda} is finite, and diverges when $\theta \to \theta_c^{-}$ as \av{\lambda} \sim (\theta_c-\theta)^{-1}; b) at the critical angle a power-law distribution of slidings is obtained: $A(\lambda) \sim \lambda^{-3/2}$. Our analytical results are confirmed by numerical simulation, and are in partial agreement with the reported experimental results. We discuss the possible reasons for the remaining discrepancies.Comment: 8 pages, 8 figures, submitted to Phys. Rev.

Diffusion and Trapping on a one-dimensional lattice

The properties of a particle diffusing on a one-dimensional lattice where at each site a random barrier and a random trap act simultaneously on the particle are investigated by numerical and analytical techniques. The combined effect of disorder and traps yields a decreasing survival probability with broad distribution (log-normal). Exact enumerations, effective-medium approximation and spectral analysis are employed. This one-dimensional model shows rather rich behaviours which were previously believed to exist only in higher dimensionality. The possibility of a trapping-dominated super universal class is suggested.Comment: 20 pages, Revtex 3.0, 13 figures in compressed format using uufiles command, to appear in Phys. Rev. E, for an hard copy or problems e-mail to: [email protected]

Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"

We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states $g(\omega)$ are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states $g(\omega)/\omega^2$ as a precursor of the instability. We argue that this peak is the analogon of the "boson peak", observed in structural glasses. By means of the level distance statistics we show that the peak is not associated with localized states

Hole-doping dependence of percolative phase separation in Pr_(0.5-delta)Ca_(0.2+delta)Sr_(0.3)MnO_(3) around half doping

We address the problem of the percolative phase separation in polycrystalline samples of Pr$_{0.5-\delta}$Ca$_{0.2+\delta}$Sr$_{0.3}$MnO$_3$ for $-0.04\leq \delta \leq 0.04$ (hole doping $n$ between 0.46 and 0.54). We perform measurements of X-ray diffraction, dc magnetization, ESR, and electrical resistivity. These samples show at $T_C$ a paramagnetic (PM) to ferromagnetic (FM) transition, however, we found that for $n>0.50$ there is a coexistence of both of these phases below $T_C$. On lowering $T$ below the charge-ordering (CO) temperature $T_{CO}$ all the samples exhibit a coexistence between the FM metallic and CO (antiferromagnetic) phases. In the whole $T$ range the FM phase fraction ($X$) decreases with increasing $n$. Furthermore, we show that only for $n\leq 0.50$ the metallic fraction is above the critical percolation threshold $X_C\simeq 15.5$. As a consequence, these samples show very different magnetoresistance properties. In addition, for $n\leq 0.50$ we observe a percolative metal-insulator transition at $T_{MI}$, and for $T_{MI}<T<T_{CO}$ the insulating-like behavior generated by the enlargement of $X$ with increasing $T$ is well described by the percolation law $\rho ^{-1}=\sigma \sim (X-X_C)^t$, where $t$ is a critical exponent. On the basis of the values obtained for this exponent we discuss different possible percolation mechanisms, and suggest that a more deep understanding of geometric and dimensionality effects is needed in phase separated manganites. We present a complete $T$ vs $n$ phase diagram showing the magnetic and electric properties of the studied compound around half doping.Comment: 9 text pages + 12 figures, submitted to Phys. Rev.

Effective one-dimensionality of AC hopping conduction in the extreme disorder limit

It is argued that in the limit of extreme disorder AC hopping is dominated by "percolation paths". Modelling a percolation path as a one-dimensional path with a sharp jump rate cut-off leads to an expression for the universal AC conductivity, that fits computer simulations in two and three dimensions better than the effective medium approximation.Comment: 6 postscript figure

Magnetic relaxation in La0.250Pr0.375Ca0.375MnO3 with varying phase separation

We have studied the magnetic relaxation properties of the phase-separated manganite compound La0.250Pr0.375Ca0.375MnO3 . A series of polycrystalline samples was prepared with different sintering temperatures, resulting in a continuous variation of phase fraction between metallic (ferromagnetic) and charge-ordered phases at low temperatures. Measurements of the magnetic viscosity show a temperature and field dependence which can be correlated to the static properties. Common to all the samples, there appears to be two types of relaxation processes - at low fields associated with the reorientation of ferromagnetic domains and at higher fields associated with the transformation between ferromagnetic and non-ferromagnetic phases.Comment: 30 pages with figures, PDF, accepted to be published in Physical Review