Polynomial Relations in the Centre of U_q(sl(N))

When the parameter of deformation q is a m-th root of unity, the centre of U_q(sl(N))$ contains, besides the usual q-deformed Casimirs, a set of new generators, which are basically the m-th powers of all the Cartan generators of U_q(sl(N)). All these central elements are however not independent. In this letter, generalising the well-known case of U_q(sl(2)), we explicitly write polynomial relations satisfied by the generators of the centre. Application to the parametrization of irreducible representations and to fusion rules are sketched.Comment: 8 pages, minor TeXnical revision to allow automatic TeXin

Wavelet entropy of stochastic processes

We compare two different definitions for the wavelet entropy associated to stochastic processes. The first one, the Normalized Total Wavelet Entropy (NTWS) family [Phys. Rev. E 57 (1998) 932; J. Neuroscience Method 105 (2001) 65; Physica A (2005) in press] and a second introduced by Tavares and Lucena [Physica A 357 (2005)~71]. In order to understand their advantages and disadvantages, exact results obtained for fractional Gaussian noise (-1<alpha< 1) and the fractional Brownian motion (1 < alpha < 3) are assessed. We find out that NTWS family performs better as a characterization method for these stochastic processes.Comment: 12 pages, 4 figures, submitted to Physica

Maximum of N Independent Brownian Walkers till the First Exit From the Half Space

We consider the one-dimensional target search process that involves an immobile target located at the origin and $N$ searchers performing independent Brownian motions starting at the initial positions $\vec x = (x_1,x_2,..., x_N)$ all on the positive half space. The process stops when the target is first found by one of the searchers. We compute the probability distribution of the maximum distance $m$ visited by the searchers till the stopping time and show that it has a power law tail: $P_N(m|\vec x)\sim B_N (x_1x_2... x_N)/m^{N+1}$ for large $m$. Thus all moments of $m$ up to the order $(N-1)$ are finite, while the higher moments diverge. The prefactor $B_N$ increases with $N$ faster than exponentially. Our solution gives the exit probability of a set of $N$ particles from a box $[0,L]$ through the left boundary. Incidentally, it also provides an exact solution of the Laplace's equation in an $N$-dimensional hypercube with some prescribed boundary conditions. The analytical results are in excellent agreement with Monte Carlo simulations.Comment: 18 pages, 9 figure

Depinning exponents of the driven long-range elastic string

We perform a high-precision calculation of the critical exponents for the long-range elastic string driven through quenched disorder at the depinning transition, at zero temperature. Large-scale simulations are used to avoid finite-size effects and to enable high precision. The roughness, growth, and velocity exponents are calculated independently, and the dynamic and correlation length exponents are derived. The critical exponents satisfy known scaling relations and agree well with analytical predictions.Comment: 6 pages, 5 figure

Characterization of laser propagation through turbulent media by quantifiers based on the wavelet transform: dynamic study

We analyze, within the wavelet theory framework, the wandering over a screen of the centroid of a laser beam after it has propagated through a time-changing laboratory-generated turbulence. Following a previous work (Fractals 12 (2004) 223) two quantifiers are used, the Hurst parameter, $H$, and the Normalized Total Wavelet Entropy, $\text{NTWS}$. The temporal evolution of both quantifiers, obtained from the laser spot data stream is studied and compared. This allows us to extract information of the stochastic process associated to the turbulence dynamics.Comment: 11 pages, 3 figures, accepted to be published in Physica

Seismic cycles, size of the largest events, and the avalanche size distribution in a model of seismicity

We address several questions on the behavior of a numerical model recently introduced to study seismic phenomena, that includes relaxation in the plates as a key ingredient. We make an analysis of the scaling of the largest events with system size, and show that when parameters are appropriately interpreted, the typical size of the largest events scale as the system size, without the necessity to tune any parameter. Secondly, we show that the temporal activity in the model is inherently non-stationary, and obtain from here justification and support for the concept of a "seismic cycle" in the temporal evolution of seismic activity. Finally, we ask for the reasons that make the model display a realistic value of the decaying exponent $b$ in the Gutenberg-Richter law for the avalanche size distribution. We explain why relaxation induces a systematic increase of $b$ from its value $b\simeq 0.4$ observed in the absence of relaxation. However, we have not been able to justify the actual robustness of the model in displaying a consistent $b$ value around the experimentally observed value $b\simeq 1$.Comment: 11 pages, 10 figure

Wavelet entropy and fractional Brownian motion time series

We study the functional link between the Hurst parameter and the Normalized Total Wavelet Entropy when analyzing fractional Brownian motion (fBm) time series--these series are synthetically generated. Both quantifiers are mainly used to identify fractional Brownian motion processes (Fractals 12 (2004) 223). The aim of this work is understand the differences in the information obtained from them, if any.Comment: 10 pages, 2 figures, submitted to Physica A for considering its publicatio

Flower, a Model for the Analysis of Hydraulic Networks and Processes

We have developed in the past years a model that describes hydraulic networks that are typical of the cryogenic interconnection of superconducting magnets. The original model, called Flower, was used mostly to provide consistent boundary conditions for the operation of a magnet. The main limitations were associated with the number and nature of modelling elements available, and to the maximum size of the model that could be solved. Here we present an improvement of the model largely relaxing the above limitations by the addition of new modelling elements, such as parallel flow heat exchangers, and by a significant improvement in the numerics of the solver, using sparse matrix storage and solution techniques. We finally show a typical application to the case of a magnet quench in the LHC string

Analysis of ischaemic crisis using the informational causal entropy-complexity plane

In the present work, an ischaemic process, mainly focused on the reperfusion stage, is studied using the informational causal entropy-complexity plane. Ischaemic wall behavior under this condition was analyzed through wall thickness and ventricular pressure variations, acquired during an obstructive flow maneuver performed on left coronary arteries of surgically instrumented animals. Basically, the induction of ischaemia depends on the temporary occlusion of left circumflex coronary artery (which supplies blood to the posterior left ventricular wall) that lasts for a few seconds. Normal perfusion of the wall was then reestablished while the anterior ventricular wall remained adequately perfused during the entire maneuver. The obtained results showed that system dynamics could be effectively described by entropy-complexity loops, in both abnormally and well perfused walls. These results could contribute to making an objective indicator of the recovery heart tissues after an ischaemic process, in a way to quantify the restoration of myocardial behavior after the supply of oxygen to the ventricular wall was suppressed for a brief period.Fil: Legnani, Walter. Universidad Tecnológica Nacional. Facultad Regional Buenos Aires; Argentina. Universidad Nacional de Lanús; ArgentinaFil: Traversaro Varela, Francisco. Instituto Tecnológico de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Redelico, Francisco Oscar. Hospital Italiano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes; ArgentinaFil: Cymberknop, Leandro Javier. Instituto Tecnologico de Buenos Aires. Departamento de Bioingenieria; Argentina. Universidad Tecnológica Nacional. Facultad Regional Buenos Aires; ArgentinaFil: Armentano, Ricardo Luis. Universidad Tecnológica Nacional. Facultad Regional Buenos Aires; Argentina. Instituto Tecnologico de Buenos Aires. Departamento de Bioingenieria; ArgentinaFil: Rosso, Osvaldo Aníbal. Universidad de los Andes; Chile. Universidade Federal de Alagoas; Brasil. Hospital Italiano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Depinning of elastic manifolds

We compute roughness exponents of elastic d-dimensional manifolds in (d+1)-dimensional embedding spaces at the depinning transition for d=1,...,4. Our numerical method is rigorously based on a Hamiltonian formulation; it allows to determine the critical manifold in finite samples for an arbitrary convex elastic energy. For a harmonic elastic energy, we find values of the roughness exponent between the one-loop and the two-loop functional renormalization group result, in good agreement with earlier cellular automata simulations. We find that the harmonic model is unstable with respect both to slight stiffening and to weakening of the elastic potential. Anharmonic corrections to the elastic energy allow us to obtain the critical exponents of the quenched KPZ class.Comment: 4 pages, 4 figure