Applying Magnetized Accretion-Ejection Models to Microquasars: a preliminary step

We present in this proceeding some aspects of a model that should explain the spectral state changes observed in microquasars. In this model, ejection is assumed to take place only in the innermost disc region where a large scale magnetic field is anchored. Then, in opposite to conventional ADAF models, the accretion energy can be efficiently converted in ejection and not advected inside the horizon. We propose that changes of the disc physical state (e.g. transition from optically thick to optically thin states) can strongly modify the magnetic accretion-ejection structure resulting in the spectral variability. After a short description of our scenario, we give some details concerning the dynamically self-consistent magnetized accretion-ejection model used in our computation. We also present some preliminary results of spectral energy distribution.Comment: Proceeding of the fith Microquasar Workshop, June 7 - 13, 2004, Beijing, China. Accepted for publication in the Chinese Journal of Astronomy and Astrophysic

Fractal dimension of transport coefficients in a deterministic dynamical system

In many low-dimensional dynamical systems transport coefficients are very irregular, perhaps even fractal functions of control parameters. To analyse this phenomenon we study a dynamical system defined by a piece-wise linear map and investigate the dependence of transport coefficients on the slope of the map. We present analytical arguments, supported by numerical calculations, showing that both the Minkowski-Bouligand and Hausdorff fractal dimension of the graphs of these functions is 1 with a logarithmic correction, and find that the exponent $\gamma$ controlling this correction is bounded from above by 1 or 2, depending on some detailed properties of the system. Using numerical techniques we show local self-similarity of the graphs. The local self-similarity scaling transformations turn out to depend (irregularly) on the values of the system control parameters.Comment: 17 pages, 6 figures; ver.2: 18 pages, 7 figures (added section 5.2, corrected typos, etc.

Universal fluctuations in subdiffusive transport

Subdiffusive transport in tilted washboard potentials is studied within the fractional Fokker-Planck equation approach, using the associated continuous time random walk (CTRW) framework. The scaled subvelocity is shown to obey a universal law, assuming the form of a stationary Levy-stable distribution. The latter is defined by the index of subdiffusion alpha and the mean subvelocity only, but interestingly depends neither on the bias strength nor on the specific form of the potential. These scaled, universal subvelocity fluctuations emerge due to the weak ergodicity breaking and are vanishing in the limit of normal diffusion. The results of the analytical heuristic theory are corroborated by Monte Carlo simulations of the underlying CTRW

Level Sets of the Takagi Function: Local Level Sets

The Takagi function \tau : [0, 1] \to [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. The level sets L(y) = {x : \tau(x) = y} of the Takagi function \tau(x) are studied by introducing a notion of local level set into which level sets are partitioned. Local level sets are simple to analyze, reducing questions to understanding the relation of level sets to local level sets, which is more complicated. It is known that for a "generic" full Lebesgue measure set of ordinates y, the level sets are finite sets. Here it is shown for a "generic" full Lebesgue measure set of abscissas x, the level set L(\tau(x)) is uncountable. An interesting singular monotone function is constructed, associated to local level sets, and is used to show the expected number of local level sets at a random level y is exactly 3/2.Comment: 32 pages, 2 figures, 1 table. Latest version has updated equation numbering. The final publication will soon be available at springerlink.co

Analisis Hidrolika Bangunan Krib Permeabel pada Saluran Tanah (Uji Model Laboratorium)

One of the structures to protect river bank erosion is groyne. Groyne can serve and control water flow, reducing flow velocity and scour of river bank. The purposes of this study is to analyze the changes in the river bed elevation (morphology) and the depth of scour in the upstream groyne caused by the permeable groyne installed at the river meanders. The experiment was conducted at Fluid Mechanics and Hydraulics Laboratory, Sriwijaya University. The study tested the hydraulics models, a trapezoidal channel, meanders angle of 90˚, five permeable groynes at meanders, and the water flowing in the channels was clear water. The observations were carried out with a flow rate was 63,32 Lt / min, three variations of permeable groynes angle were 45˚, 90˚ and 135˚ to the upstream within 1 hour, 2,5 hours and 4 hours for each angle variations . The results of this study showed that the flow velocity of meanders was decreasing to the end of the meanders, and the changes of channel only occurred at the riverbed. Maximum riverbed changes (Bt / Bo) for permeable groyne angle of 45˚, 90˚ and 135 ˚ were 1,376 cm, 1,346 cm dan 1,452 cm. The maximum depth of scour (ds/y) for permeable groyne angle of 45˚, 90˚ and 135˚ were 1,05 cm, 0,95 cm dan 1,17 cm. Thus, permeable groyne with angle of 90 proved to be the best with the smallest riverbed changes (Bt /Bo) was 1,346 cm and the coefficient of determination (R2) was 0,9384, and also the smallest scour depth (ds/y) was 0,95 cm and the coefficient of determination (R2) was 0,8317 compared to other groyne permeable angles

Piecewise Linear Models for the Quasiperiodic Transition to Chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request

Dynamical percolation on general trees

H\"aggstr\"om, Peres, and Steif (1997) have introduced a dynamical version of percolation on a graph $G$. When $G$ is a tree they derived a necessary and sufficient condition for percolation to exist at some time $t$. In the case that $G$ is a spherically symmetric tree, H\"aggstr\"om, Peres, and Steif (1997) derived a necessary and sufficient condition for percolation to exist at some time $t$ in a given target set $D$. The main result of the present paper is a necessary and sufficient condition for the existence of percolation, at some time $t\in D$, in the case that the underlying tree is not necessary spherically symmetric. This answers a question of Yuval Peres (personal communication). We present also a formula for the Hausdorff dimension of the set of exceptional times of percolation.Comment: 24 pages; to appear in Probability Theory and Related Field

Wavelets techniques for pointwise anti-Holderian irregularity

In this paper, we introduce a notion of weak pointwise Holder regularity, starting from the de nition of the pointwise anti-Holder irregularity. Using this concept, a weak spectrum of singularities can be de ned as for the usual pointwise Holder regularity. We build a class of wavelet series satisfying the multifractal formalism and thus show the optimality of the upper bound. We also show that the weak spectrum of singularities is disconnected from the casual one (denoted here strong spectrum of singularities) by exhibiting a multifractal function made of Davenport series whose weak spectrum di ers from the strong one

Sixty Years of Fractal Projections

Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand's projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.Comment: Submitted to proceedings of Fractals and Stochastics