Multifractal Dimensions for Branched Growth

A recently proposed theory for diffusion-limited aggregation (DLA), which models this system as a random branched growth process, is reviewed. Like DLA, this process is stochastic, and ensemble averaging is needed in order to define multifractal dimensions. In an earlier work [T. C. Halsey and M. Leibig, Phys. Rev. A46, 7793 (1992)], annealed average dimensions were computed for this model. In this paper, we compute the quenched average dimensions, which are expected to apply to typical members of the ensemble. We develop a perturbative expansion for the average of the logarithm of the multifractal partition function; the leading and sub-leading divergent terms in this expansion are then resummed to all orders. The result is that in the limit where the number of particles n -> \infty, the quenched and annealed dimensions are {\it identical}; however, the attainment of this limit requires enormous values of n. At smaller, more realistic values of n, the apparent quenched dimensions differ from the annealed dimensions. We interpret these results to mean that while multifractality as an ensemble property of random branched growth (and hence of DLA) is quite robust, it subtly fails for typical members of the ensemble.Comment: 82 pages, 24 included figures in 16 files, 1 included tabl

Diffusion-Reorganized Aggregates: Attractors in Diffusion Processes?

A process based on particle evaporation, diffusion and redeposition is applied iteratively to a two-dimensional object of arbitrary shape. The evolution spontaneously transforms the object morphology, converging to branched structures. Independently of initial geometry, the structures found after long time present fractal geometry with a fractal dimension around 1.75. The final morphology, which constantly evolves in time, can be considered as the dynamic attractor of this evaporation-diffusion-redeposition operator. The ensemble of these fractal shapes can be considered to be the {\em dynamical equilibrium} geometry of a diffusion controlled self-transformation process.Comment: 4 pages, 5 figure

Velocity Correlations in Dense Gravity Driven Granular Chute Flow

We report numerical results for velocity correlations in dense, gravity-driven granular flow down an inclined plane. For the grains on the surface layer, our results are consistent with experimental measurements reported by Pouliquen. We show that the correlation structure within planes parallel to the surface persists in the bulk. The two-point velocity correlation function exhibits exponential decay for small to intermediate values of the separation between spheres. The correlation lengths identified by exponential fits to the data show nontrivial dependence on the averaging time \dt used to determine grain velocities. We discuss the correlation length dependence on averaging time, incline angle, pile height, depth of the layer, system size and grain stiffness, and relate the results to other length scales associated with the rheology of the system. We find that correlation lengths are typically quite small, of the order of a particle diameter, and increase approximately logarithmically with a minimum pile height for which flow is possible, \hstop, contrary to the theoretical expectation of a proportional relationship between the two length scales.Comment: 21 pages, 16 figure

Two scenarios for avalanche dynamics in inclined granular layers

We report experimental measurements of avalanche behavior of thin granular layers on an inclined plane for low volume flow rate. The dynamical properties of avalanches were quantitatively and qualitatively different for smooth glass beads compared to irregular granular materials such as sand. Two scenarios for granular avalanches on an incline are identified and a theoretical explanation for these different scenarios is developed based on a depth-averaged approach that takes into account the differing rheologies of the granular materials.Comment: 4 pages, 4 figures, accepted to Phys. Rev. Let

Technology needs assessment of an atmospheric observation system for tropospheric research missions, part 1

The technology advancements needed to implement the atmospheric observation satellite systems for air quality research were identified. Tropospheric measurements are considered. The measurements and sensors are based on a model of knowledge objectives in atmospheric science. A set of potential missions and attendant spacecraft and sensors is postulated. The results show that the predominant technology needs will be in passive and active sensors for accurate and frequent global measurements of trace gas concentration profiles

Synapse at CAp 2017 NER challenge: Fasttext CRF

We present our system for the CAp 2017 NER challenge which is about named entity recognition on French tweets. Our system leverages unsupervised learning on a larger dataset of French tweets to learn features feeding a CRF model. It was ranked first without using any gazetteer or structured external data, with an F-measure of 58.89\%. To the best of our knowledge, it is the first system to use fasttext embeddings (which include subword representations) and an embedding-based sentence representation for NER

Current-voltage scaling of a Josephson-junction array at irrational frustration

Numerical simulations of the current-voltage characteristics of an ordered two-dimensional Josephson junction array at an irrational flux quantum per plaquette are presented. The results are consistent with an scaling analysis which assumes a zero temperature vortex glass transition. The thermal correlation length exponent characterizing this transition is found to be significantly different from the corresponding value for vortex-glass models in disordered two-dimensional superconductors. This leads to a current scale where nonlinearities appear in the current-voltage characteristics decreasing with temperature $T$ roughly as $T^2$ in contrast with the $T^3$ behavior expected for disordered models.Comment: RevTex 3.0, 12 pages with Latex figures, to appear in Phys. Rev. B 54, Rapid. Com

Kinetic Inductance of Josephson Junction Arrays: Dynamic and Equilibrium Calculations

We show analytically that the inverse kinetic inductance $L^{-1}$ of an overdamped junction array at low frequencies is proportional to the admittance of an inhomogeneous equivalent impedance network. The $ij^{th}$ bond in this equivalent network has an inverse inductance $J_{ij}\cos(\theta_i^0-\theta_j^0-A_{ij})$, where $J_{ij}$ is the Josephson coupling energy of the $ij^{th}$ bond, $\theta_i^0$ is the ground-state phase of the grain $i$, and $A_{ij}$ is the usual magnetic phase factor. We use this theorem to calculate $L^{-1}$ for square arrays as large as $180\times 180$. The calculated $L^{-1}$ is in very good agreement with the low-temperature limit of the helicity modulus $\gamma$ calculated by conventional equilibrium Monte Carlo techniques. However, the finite temperature structure of $\gamma$, as a function of magnetic field, is \underline{sharper} than the zero-temperature $L^{-1}$, which shows surprisingly weak structure. In triangular arrays, the equilibrium calculation of $\gamma$ yields a series of peaks at frustrations $f = \frac{1}{2}(1-1/N)$, where $N$ is an integer $\geq 2$, consistent with experiment.Comment: 14 pages + 6 postscript figures, 3.0 REVTe

A Ball in a Groove

We study the static equilibrium of an elastic sphere held in a rigid groove by gravity and frictional contacts, as determined by contact mechanics. As a function of the opening angle of the groove and the tilt of the groove with respect to the vertical, we identify two regimes of static equilibrium for the ball. In the first of these, at large opening angle or low tilt, the ball rolls at both contacts as it is loaded. This is an analog of the "elastic" regime in the mechanics of granular media. At smaller opening angles or larger tilts, the ball rolls at one contact and slides at the other as it is loaded, analogously with the "plastic" regime in the mechanics of granular media. In the elastic regime, the stress indeterminacy is resolved by the underlying kinetics of the ball response to loading.Comment: RevTeX 3.0, 4 pages, 2 eps figures included with eps

Conformal Mapping on Rough Boundaries I: Applications to harmonic problems

The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this boundary. We introduce a conformal mapping technique that is tailored to this problem in two dimensions. An efficient algorithm is introduced to compute the conformal map for arbitrarily chosen boundaries. Harmonic fields can then simply be read from the conformal map. We discuss applications to "equivalent" smooth interfaces. We study the correlations between the topography and the field at the surface. Finally we apply the conformal map to the computation of inhomogeneous harmonic fields such as the derivation of Green function for localized flux on the surface of a rough boundary