Abelian deterministic self organized criticality model: Complex dynamics of avalanche waves

The aim of this study is to investigate a wave dynamics and size scaling of avalanches which were created by the mathematical model {[}J. \v{C}ern\'ak Phys. Rev. E \textbf{65}, 046141 (2002)]. Numerical simulations were carried out on a two dimensional lattice $L\times L$ in which two constant thresholds $E_{c}^{I}=4$ and $E_{c}^{II}>E_{c}^{I}$ were randomly distributed. A density of sites $c$ with the threshold $E_{c}^{II}$ and threshold $E_{c}^{II}$ are parameters of the model. I have determined autocorrelations of avalanche size waves, Hurst exponents, avalanche structures and avalanche size moments for several densities $c$ and thresholds $E_{c}^{II}$. I found correlated avalanche size waves and multifractal scaling of avalanche sizes not only for specific conditions, densities $c=0.0$, 1.0 and thresholds $8\leq E_{c}^{II}\leq32$, in which relaxation rules were precisely balanced, but also for more general conditions, densities $0.0<c<1.0$ and thresholds $8\leq E_{c}^{II}\leq3 in which relaxation rules were unbalanced. The results suggest that the hypothesis of a precise relaxation balance could be a specific case of a more general rule

Voltage-Current curves for small Josephson junction arrays

We compute the current voltage characteristic of a chain of identical Josephson circuits characterized by a large ratio of Josephson to charging energy that are envisioned as the implementation of topologically protected qubits. We show that in the limit of small coupling to the environment it exhibits a non-monotonous behavior with a maximum voltage followed by a parametrically large region where $V\propto 1/I$. We argue that its experimental measurement provides a direct probe of the amplitude of the quantum transitions in constituting Josephson circuits and thus allows their full characterization.Comment: 12 pages, 4 figure

Variational solution of the Gross-Neveu model at finite temperature in the large N limit

We use a nonperturbative variational method to investigate the phase transition of the Gross-Neveu model. It is shown that the variational procedure can be generalized to the finite temperature case. The large N result for the phase transition is correctly reproduced.Comment: 12 p., 1 fig, this is the version which will appear in the Phys Lett B, it differs from the previous one in what concerns the introduction and conclusions (re written), several references have been adde

1/fα1/f^\alpha spectra in elementary cellular automata and fractal signals

We systematically compute the power spectra of the one-dimensional elementary cellular automata introduced by Wolfram. On the one hand our analysis reveals that one automaton displays $1/f$ spectra though considered as trivial, and on the other hand that various automata classified as chaotic/complex display no $1/f$ spectra. We model the results generalizing the recently investigated Sierpinski signal to a class of fractal signals that are tailored to produce $1/f^{\alpha}$ spectra. From the widespread occurrence of (elementary) cellular automata patterns in chemistry, physics and computer sciences, there are various candidates to show spectra similar to our results.Comment: 4 pages (3 figs included

Matrix Product State description of the Halperin States

Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact Matrix Product States (MPS) that was extensively studied for the systems without any spin or any other internal degrees of freedom. In that case, the correlators are built from a single electronic operator, which is primary with respect to the underlying conformal field theory. We generalize this construction to the archetype of Abelian multicomponent fractional quantum Hall wavefunctions, the Halperin states. These latest can be written as conformal blocks involving multiple electronic operators and we explicitly derive their exact MPS representation. In particular, we deal with the caveat of the full wavefunction symmetry and show that any additional SU(2) symmetry is preserved by the natural MPS truncation scheme provided by the conformal dimension. We use our method to characterize the topological order of the Halperin states by extracting the topological entanglement entropy. We also evaluate their bulk correlation length which are compared to plasma analogy arguments.Comment: 23 pages, 16 figure

Stable fractal sums of pulses: the cylindrical case

A class of α-stable, 0\textlessα\textless2, processes is obtained as a sum of ’up-and-down’ pulses determined by an appropriate Poisson random measure. Processes are H-self-affine (also frequently called ’self-similar’) with H\textless1/α and have stationary increments. Their two-dimensional dependence structure resembles that of the fractional Brownian motion (for H\textless1/2), but their sample paths are highly irregular (nowhere bounded with probability 1). Generalizations using different shapes of pulses are also discussed

Cross correlation surveys with the Square Kilometre Array

By the time that the first phase of the Square Kilometre Array is deployed it will be able to perform state of the art Large Scale Structure (LSS) as well as Weak Gravitational Lensing (WGL) measurements of the distribution of matter in the Universe. In this chapter we concentrate on the synergies that result from cross-correlating these different SKA data products as well as external correlation with the weak lensing measurements available from CMB missions. We show that the Dark Energy figures of merit obtained individually from WGL/LSS measurements and their independent combination is significantly increased when their full cross-correlations are taken into account. This is due to the increased knowledge of galaxy bias as a function of redshift as well as the extra information from the different cosmological dependences of the cross-correlations. We show that the cross-correlation between a spectroscopic LSS sample and a weak lensing sample with photometric redshifts can calibrate these same photometric redshifts, and their scatter, to high accuracy by modelling them as nuisance parameters and fitting them simultaneously cosmology. Finally we show that Modified Gravity parameters are greatly constrained by this cross-correlations because weak lensing and redshift space distortions (from the LSS survey) break strong degeneracies in common parameterisations of modified gravity.Comment: 12 pages, 3 figures. This article is part of the 'Cosmology Chapter, Advancing Astrophysics with the SKA (AASKA14) Conference, Giardini Naxos (Italy), June 9th-13th 2014

Educational Motivation in Heritage Speakers of Spanish

This study examined the themes associated with the lack of motivation for school in middle school students, specifically among Heritage Speakers of Spanish. The researcher used two methods to examine student and parent attitudes and beliefs about school and education, as attitudes and beliefs are strongly linked to motivation. The researcher did face-to-face interviews of Mexican parents with direct questions about education and school, and asked middle school students of Mexican descent to read the first part of a short selection about a Mexican immigrant boy in school, then complete the story using their imagination. The researcher compiled the parents\u27 responses, and used content analysis to identify eight themes in the students \u27 narratives. Four findings emerged from the data: Mexican immigrant parents are perceived by their children as ineffective adults, parental expectations regarding school and the future are in conflict with student expectations, students have more extrinsic motivation (rewards) than intrinsic motivation (learning for itself), and students perceive many obstacles to school success