Stretched exponentials and power laws in granular avalanching

We introduce a model for granular avalanching which exhibits both stretched exponential and power law avalanching over its parameter range. Two modes of transport are incorporated, a rolling layer consisting of individual particles and the overdamped, sliding motion of particle clusters. The crossover in behaviour observed in experiments on piles of rice is attributed to a change in the dominant mode of transport. We predict that power law avalanching will be observed whenever surface flow is dominated by clustered motion. Comment: 8 pages, more concise and some points clarified

Rotation of an atomic Bose-Einstein condensate with and without a quantized vortex

We theoretically examine the rotation of an atomic Bose-Einstein condensate in an elliptical trap, both in the absence and presence of a quantized vortex. Two methods of introducing the rotating potential are considered - adiabatically increasing the rotation frequency at fixed ellipticity, and adiabatically increasing the trap ellipticity at fixed rotation frequency. Extensive simulations of the Gross-Pitaevskii equation are employed to map out the points where the condensate becomes unstable and ultimately forms a vortex lattice. We highlight the key features of having a quantized vortex in the initial condensate. In particular, we find that the presence of the vortex causes the instabilities to shift to lower or higher rotation frequencies, depending on the direction of the vortex relative to the trap rotation.Comment: 15 pages, 8 figure

Scale-free network topology and multifractality in weighted planar stochastic lattice

We propose a weighted planar stochastic lattice (WPSL) formed by the random sequential partition of a plane into contiguous and non-overlapping blocks and find that it evolves following several non-trivial conservation laws, namely $\sum_i^N x_i^{n-1} y_i^{4/n-1}$ is independent of time $\forall \ n$, where $x_i$ and $y_i$ are the length and width of the $i$th block. Its dual on the other hand, obtained by replacing each block with a node at its center and common border between blocks with an edge joining the two vertices, emerges as a network with a power-law degree distribution $P(k)\sim k^{-\gamma}$ where $\gamma=5.66$ revealing scale-free coordination number disorder since $P(k)$ also describes the fraction of blocks having $k$ neighbours. To quantify the size disorder, we show that if the $i$th block is populated with $p_i\sim x_i^3$ then its distribution in the WPSL exhibits multifractality.Comment: 7 pages, 8 figures, To appear in New Journal of Physics (NJP

Fractional time random walk subdiffusion and anomalous transport with finite mean residence times: faster, not slower

Continuous time random walk (CTRW) subdiffusion along with the associated fractional Fokker-Planck equation (FFPE) is traditionally based on the premise of random clock with divergent mean period. This work considers an alternative CTRW and FFPE description which is featured by finite mean residence times (MRTs) in any spatial domain of finite size. Transient subdiffusive transport can occur on a very large time scale $\tau_c$ which can greatly exceed mean residence time in any trap, $\tau_c\gg$, and even not being related to it. Asymptotically, on a macroscale transport becomes normal for $t\gg\tau_c$. However, mesoscopic transport is anomalous. Differently from viscoelastic subdiffusion no long-range anti-correlations among position increments are required. Moreover, our study makes it obvious that the transient subdiffusion and transport are faster than one expects from their normal asymptotic limit on a macroscale. This observation has profound implications for anomalous mesoscopic transport processes in biological cells because of macroscopic viscosity of cytoplasm is finite

Void Formation and Roughening in Slow Fracture

Slow crack propagation in ductile, and in certain brittle materials, appears to take place via the nucleation of voids ahead of the crack tip due to plastic yields, followed by the coalescence of these voids. Post mortem analysis of the resulting fracture surfaces of ductile and brittle materials on the $\mu$m-mm and the nm scales respectively, reveals self-affine cracks with anomalous scaling exponent $\zeta\approx 0.8$ in 3-dimensions and $\zeta\approx 0.65$ in 2-dimensions. In this paper we present an analytic theory based on the method of iterated conformal maps aimed at modelling the void formation and the fracture growth, culminating in estimates of the roughening exponents in 2-dimensions. In the simplest realization of the model we allow one void ahead of the crack, and address the robustness of the roughening exponent. Next we develop the theory further, to include two voids ahead of the crack. This development necessitates generalizing the method of iterated conformal maps to include doubly connected regions (maps from the annulus rather than the unit circle). While mathematically and numerically feasible, we find that the employment of the stress field as computed from elasticity theory becomes questionable when more than one void is explicitly inserted into the material. Thus further progress in this line of research calls for improved treatment of the plastic dynamics.Comment: 15 pages, 20 figure

Weakly Interacting Bose-Einstein Condensates Under Rotation: Mean-field versus Exact Solutions

We consider a weakly-interacting, harmonically-trapped Bose-Einstein condensed gas under rotation and investigate the connection between the energies obtained from mean-field calculations and from exact diagonalizations in a subspace of degenerate states. From the latter we derive an approximation scheme valid in the thermodynamic limit of many particles. Mean-field results are shown to emerge as the correct leading-order approximation to exact calculations in the same subspace.Comment: 4 pages, RevTex, submitted to PR

A high-efficiency spin-resolved phototemission spectrometer combining time-of-flight spectroscopy with exchange-scattering polarimetry

We describe a spin-resolved electron spectrometer capable of uniquely efficient and high energy resolution measurements. Spin analysis is obtained through polarimetry based on low-energy exchange scattering from a ferromagnetic thin-film target. This approach can achieve a similar analyzing power (Sherman function) as state-of-the-art Mott scattering polarimeters, but with as much as 100 times improved efficiency due to increased reflectivity. Performance is further enhanced by integrating the polarimeter into a time-of-flight (TOF) based energy analysis scheme with a precise and flexible electrostatic lens system. The parallel acquisition of a range of electron kinetic energies afforded by the TOF approach results in an order of magnitude (or more) increase in efficiency compared to hemispherical analyzers. The lens system additionally features a 90{\deg} bandpass filter, which by removing unwanted parts of the photoelectron distribution allows the TOF technique to be performed at low electron drift energy and high energy resolution within a wide range of experimental parameters. The spectrometer is ideally suited for high-resolution spin- and angle-resolved photoemission spectroscopy (spin-ARPES), and initial results are shown. The TOF approach makes the spectrometer especially ideal for time-resolved spin-ARPES experiments.Comment: 16 pages, 11 figure

Volatility of Linear and Nonlinear Time Series

Previous studies indicate that nonlinear properties of Gaussian time series with long-range correlations, $u_i$, can be detected and quantified by studying the correlations in the magnitude series $|u_i|$, i.e., the ``volatility''. However, the origin for this empirical observation still remains unclear, and the exact relation between the correlations in $u_i$ and the correlations in $|u_i|$ is still unknown. Here we find analytical relations between the scaling exponent of linear series $u_i$ and its magnitude series $|u_i|$. Moreover, we find that nonlinear time series exhibit stronger (or the same) correlations in the magnitude time series compared to linear time series with the same two-point correlations. Based on these results we propose a simple model that generates multifractal time series by explicitly inserting long range correlations in the magnitude series; the nonlinear multifractal time series is generated by multiplying a long-range correlated time series (that represents the magnitude series) with uncorrelated time series [that represents the sign series $sgn(u_i)$]. Our results of magnitude series correlations may help to identify linear and nonlinear processes in experimental records.Comment: 7 pages, 5 figure

Local density of states for the corner geometry interface of d-wave superconductors, within the extended Hubbard model

The spatial variations of the order parameter, and the local density of states (LDOS) on the corner of s-wave or $d_{x^2-y^2}$-wave superconductors, as well as in superconductor-insulator-normal metal interfaces, are calculated self consistently using the Bogoliubov-deGennes formalism within the two dimensional extended Hubbard model. The exact diagonalization method is used. Due to the suppression of the dominant d-wave order parameter, the extended s-wave order parameter is induced near the surface, that alternates its sign for the topmost sites at adjacent edges of the lattice and decays to zero in the bulk. The presence of surface roughness results into the appearance of the zero band conduction peak (ZBCP) near the corner surface which lacks from the predictions of the quasiclassical theory.Comment: 13 pages with 17 figure

Distinguishing cancerous from non-cancerous cells through analysis of electrical noise

Since 1984, electric cell-substrate impedance sensing (ECIS) has been used to monitor cell behavior in tissue culture and has proven sensitive to cell morphological changes and cell motility. We have taken ECIS measurements on several cultures of non-cancerous (HOSE) and cancerous (SKOV) human ovarian surface epithelial cells. By analyzing the noise in real and imaginary electrical impedance, we demonstrate that it is possible to distinguish the two cell types purely from signatures of their electrical noise. Our measures include power-spectral exponents, Hurst and detrended fluctuation analysis, and estimates of correlation time; principal-component analysis combines all the measures. The noise from both cancerous and non-cancerous cultures shows correlations on many time scales, but these correlations are stronger for the non-cancerous cells.Comment: 8 pages, 4 figures; submitted to PR