Decoupling the cortical power spectrum reveals real-time representation of individual finger movements in humans.

During active movement the electric potentials measured from the surface of the motor cortex exhibit consistent modulation, revealing two distinguishable processes in the power spectrum. At frequencies <40 Hz, narrow-band power decreases occur with movement over widely distributed cortical areas, while at higher frequencies there are spatially more focal power increases. These high-frequency changes have commonly been assumed to reflect synchronous rhythms, analogous to lower-frequency phenomena, but it has recently been proposed that they reflect a broad-band spectral change across the entire spectrum, which could be obscured by synchronous rhythms at low frequencies. In 10 human subjects performing a finger movement task, we demonstrate that a principal component type of decomposition can naively separate low-frequency narrow-band rhythms from an asynchronous, broad-spectral, change at all frequencies between 5 and 200 Hz. This broad-spectral change exhibited spatially discrete representation for individual fingers and reproduced the temporal movement trajectories of different individual fingers.

Effect of a columnar defect on the shape of slow-combustion fronts.

We report experimental results for the behavior of slow-combustion fronts in the presence of a columnar defect with enhanced or reduced driving, and compare them with those of mean-field theory. We also compare them with simulation results for an analogous problem of driven flow of particles with hard-core repulsion (ASEP) and a single defect bond with a different hopping probability. The difference in the shape of the front profiles for enhanced vs reduced driving in the defect clearly demonstrates the existence of a Kardar-Parisi-Zhang-type nonlinear term in the effective evolution equation for the slow-combustion fronts. We also find that slow-combustion fronts display a faceted form for large enough enhanced driving, and that there is a corresponding increase then in the average front speed. This increase in the average front speed disappears at a nonzero enhanced driving in agreement with the simulated behavior of the ASEP model.

Anomalous roughness, localization, and globally constrained random walks.

The scaling properties of a random walker subject to the global constraint that it needs to visit each site an even number of times are determined. Such walks are realized in the equilibrium state of one-dimensional surfaces that are subject to dissociative-dimer-type surface dynamics. Moreover, they can be mapped onto unconstrained random walks on a random surface, and the latter corresponds to a non-Hermitian random free fermion model that describes electron localization near a band edge. We show analytically that the dynamic exponent of this random walk is z=d+2 in spatial dimension d. This explains the anomalous roughness, with exponent alpha=1/3, in one-dimensional equilibrium surfaces with dissociative-dimer-type dynamics.

Reconstructed rough growing interfaces: ridge-line trapping of domain walls.

We investigate whether surface reconstruction order exists in stationary growing states at all length scales or only below a crossover length l(rec). The latter behavior would be similar to surface roughness in growing crystal surfaces; below the equilibrium roughening temperature they evolve in a layer-by-layer mode within a crossover length scale l(R), but are always rough at large length scales. We investigate this issue in the context of Kardar-Parisi-Zhang (KPZ) type dynamics and a checkerboard type reconstruction, using the restricted solid-on-solid model with negative monatomic step energies. This is a topology where surface reconstruction order is compatible with surface roughness and where a so-called reconstructed rough phase exists in equilibrium. We find that during growth reconstruction order is absent in the thermodynamic limit, but exists below a crossover length l(rec)>l(R), and that this local order fluctuates critically. Domain walls become trapped at the ridge lines of the rough surface, and thus the reconstruction order fluctuations are slaved to the KPZ dynamics.

Anomalous roughness in dimer-type surface growth

We point out how geometric features affect the scaling properties of nonequilibrium dynamic processes, by a model for surface growth where particles can deposit and evaporate only in dimer form, but dissociate on the surface. Pinning valleys (hilltops) develop spontaneously and the surface facets for all growth (evaporation) biases. More intriguingly, the scaling properties of the rough one dimensional equilibrium surface are anomalous. Its width, W approximately Lalpha, diverges with system size L as alpha = 1 / 3 instead of the conventional universal value alpha = 1 / 2. This originates from a topological nonlocal evenness constraint on the surface configurations.

Facet ridge end points in crystal shapes

We study equilibrium crystal shapes (ECS) near facet ridge end points (FRE) by means of a numerical study of a body-centered solid-on-solid model on a square lattice with an enhanced uniaxial interaction range. This tests the stability of the so-called stochastic FRE point where the model maps exactly onto one dimensional Kardar-Parisi-Zhang-type growth and where the local ECS is simple. We find that the generic shapes are more complex. They contain first-order faceted to rough boundaries terminating in Pokrovsky-Talapov-type end points, and first-order ridges inside the rounded part of the ECS where two rough surface orientations coexist.

Active width at a slanted active boundary in directed percolation.

The width W of the active region around an active moving wall in a directed percolation process diverges at the percolation threshold p(c) as W approximately Aepsilon(-nu( parallel)) ln(epsilon(0)/epsilon), with epsilon=p(c)-p, epsilon(0) a constant, and nu( parallel)=1.734 the critical exponent of the characteristic time needed to reach the stationary state xi( parallel) approximately epsilon(-nu(parallel)). The logarithmic factor arises from screening the statistically independent needle shaped subclusters in the active region. Numerical data confirm this scaling behavior.