Seungoh Ryu

DYNAMICAL PHASE TRANSITION IN A DRIVEN DISORDERED VORTEX LATTICE

Using Langevin dynamics, we have investigated the dynamics of vortices in a disordered two-dimensional superconductor subjected to a uniform driving current. The results provide direct numerical evidence for a dynamical phase transition between a plastic flow regime and a moving {open_quote}{open_quote}hexatic glass.{close_quote}{close_quote} The simulated current-voltage characteristics are in excellent agreement with recent transport measurements on amorphous Mo{sub 77}Ge{sub 23} thin film superconductors. {copyright} {ital 1996 The American Physical Society.}

Field-Driven Topological Glass Transition in a Model Flux Line Lattice.

We show that the flux line lattice in a model layered high temperature superconductor becomes unstable above a critical magnetic field with respect to a plastic deformation via penetration of pairs of point-like disclination defects. The instability is characterized by the competition between the elastic and the pinning energies and is essentially assisted by softening of the lattice induced by a dimensional crossover of the fluctuations as field increases. We propose that this mechanism provides a model of the low temperature field-driven disordering transition observed in neutron diffraction experiments on Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8} single crystals. {copyright} {ital 1996 The American Physical Society.}

Vortex decoupling crossover in Bi2Sr2CaCu2O8

Abstract We present measurements of c -axis transport in single-crystal Bi 2 Sr 2 CaCu 2 O 8 which suggest that decoupling of the superconducting CuO 2 layers occurs via a continuous crossover in this material. We discuss the process of decoupling and supplement our arguments with Monte Carlo simulations of the vortex fluctuations. Our data suggest two regimes in the coupling process. The first is the establishment of a macroscopic correlation length in the c -direction associated with a sharp drop in the c -axis resistivity. The second stage is the establishment of a finite critical current in the c -axis direction which spans the rest of the temperature range down to the irreversibility/melting line.

Aspects of diffusive-relaxation dynamics with a nonuniform, partially absorbing boundary in general porous media.

We consider the Helmholtz problem in the context of the evolution of uniform initial distribution of a physical attribute in general porous media subject to a partially absorbing boundary condition. Its spectral property as a reflection of the boundary geometry has been widely exploited, such as in biological and geophysical applications. We consider the situation where the critical assumptions which enable such applications break down. Specifically, what are the consequences of an inhomogeneous absorption strength? Using perturbation theory, exact theoretical results, and numerical simulations on random sphere packs, we identify the regions of parameter space in which such inhomogeneity is important and those in which it is not. Our findings shed light on the issue that limits the mapping between the diffusion or relaxation spectrum and the underlying boundary geometry.

Anomalous relaxation in the XY gauge glass

To study relaxation dynamics of the two-dimensional XY gauge glass, we integrate directly the equations of motion and investigate the energy function. As usual, it decays exponentially at high temperatures; at low but nonzero temperatures, it is found to exhibit an algebraic relaxation. We compute the relaxation time {tau} as a function of the temperature T and find that the rapid increase of {tau} at low temperatures is well described by {tau}{approximately}(T{minus}T{sub g}){sup {minus}b} with T{sub g}=0.22{plus_minus}0.02 and b=0.76{plus_minus}0.05, which strongly suggests a finite-temperature glass transition. The decay of vorticity is also examined and explained in terms of a simple heuristic model, which attributes the fast relaxation at high temperatures to annihilation of unpinned vortices. {copyright} {ital 1997} {ital The American Physical Society}

Effects of inhomogeneous partial absorption and the geometry of the boundary on population evolution of molecules diffusing in general porous media.

We consider aspects of the population dynamics, inside a bound domain, of diffusing agents carrying an attribute which is stochastically destroyed upon contact with the boundary. The normal mode analysis of the relevant Helmholtz equation under the partially absorbing, but uniform, boundary condition provides a starting framework in understanding detailed evolution dynamics of the attribute in the time domain. In particular, the boundary-localized depletion has been widely employed in practical applications that depend on geometry of various porous media such as rocks, cement, bones, and cheese. While direct relationship between the pore geometry and the diffusion-relaxation spectrum forms the basis for such applications and has been extensively studied, relatively less attention has been paid to the spatial variation in the boundary condition. In this work, we focus on the way the pore geometry and the inhomogeneous depletion strength of the boundary become intertwined and thus obscure the direct relationship between the spectrum and the geometry. It is often impossible to gauge experimentally the degree to which such interference occurs. We fill this gap by perturbatively incorporating classes of spatially varying boundary conditions and derive their consequences that are observable through numerical simulations or controlled experiments on glass bead packs and artificially fabricated porous media. We identify features of the spectrum that are most sensitive to the inhomogeneity, apply the method to the spherical pore with a simple hemispherical binary distribution of the depletion strength, and obtain bounds for the induced change in the slowest relaxation mode.

Effects of columnar pins on flux line dynamics.

The effects of columnar pins on the flux lines in a model high-T c superconductor in an applied field are studied through Monte Carlo simulations. An analytic solution for a single line case is obtained and compared with the simulation results. By introducing a tilted potential, we study simulated «I-V» characteristics and the results indicate a distinct scaling behavior above and below the depinning temperature. We introduce a diverging length scale measured in terms of a «retrapping length» to analyze self-similar behavior across the sharp depinning crossover

Magnetization Jump in a Model for Flux Lattice Melting at Low Magnetic Fields

Using a frustrated XY model on a lattice with open boundary conditions, we numerically study the magnetization change near a flux lattice melting transition at low fields. In both two and three dimensions, we find that the melting transition is followed at a higher temperature by the onset of large dissipation associated with the zero-field XY transition. It is characterized by the proliferation of vortex-antivortex pairs (in 2D) or vortex loops (in 3D). At the upper transition, there is a sharp increase in magnetization, in qualitative agreement with recent local Hall probe experiments.

DYNAMICS OF AN UNDERDAMPED JOSEPHSON-JUNCTION LADDER

We show analytically that the dynamical equations for an underdamped ladder of coupled small Josephson junctions can be approximately reduced to the discrete sine-Gordon equation. As numerical confirmation, we solve the coupled Josephson equations for such a ladder in a magnetic field. We obtain discrete-sine-Gordon-like {ital IV} characteristics, including a flux flow and a {open_quote}{open_quote}whirling{close_quote}{close_quote} regime at low and high currents, and voltage steps that represent a lock-in between the vortex motion and linear {open_quote}{open_quote}phasons,{close_quote}{close_quote} and which are quantitatively predicted by a simple formula. At sufficiently high anisotropy, the fluxons on the steps propagate ballistically. {copyright} {ital 1996 The American Physical Society.}

Nature of the low-field transition in the mixed state of high-temperature superconductors

We have numerically studied the statics and dynamics of a model three-dimensional (3D) vortex lattice at low magnetic fields. For the statics we use a frustrated 3D XY model on a stacked triangular lattice. We model the dynamics as a coupled network of overdamped resistively shunted Josephson junctions with Langevin noise. At low fields, there is a weakly first-order phase transition, at which the vortex lattice melts into a line liquid. Phase coherence parallel to the field persists until a sharp crossover, conceivably a phase transition, near T{sub scr(l)}{gt}T{sub m} which develops at the same temperature as an {ital infinite} vortex tangle. The calculated flux flow resistivity in various geometries near T=T{sub scr(l)} closely resembles experiment. The local density of field induced vortices increases sharply near T{sub scr(l)}, corresponding to the experimentally observed magnetization jump. We discuss the nature of a possible transition or crossover at T{sub scr(l)}(B) which is distinct from flux lattice melting. {copyright} {ital 1998} {ital The American Physical Society}