Solid--on--Solid Model for Adsorption on Self--Affine Substrate: A Transfer Matrix Approach

We study a $d=2$ discrete solid--on--solid model of complete wetting of a rough substrate with random self--affine boundary, having roughness exponent $\zeta_s$. A suitable transfer matrix approach allows to discuss adsorption isotherms, as well as geometrical and thermal fluctuations of the interface. For $\zeta_s\leq 1/2$ the same wetting exponent $\psi=1/3$ as for flat substrate is obtained for the dependence of the coverage, $\theta$, on the chemical potential, $h$ ($\theta\sim h^{-\psi}$ for $h\to 0$). The expected existence of a zero temperature fixed point, leading to $\psi=\zeta_s /(2-\zeta_s)$ for $\zeta_s>1/2$, is verified numerically in spite of an unexpected, very slow convergence to asymptotics.Comment: Standard TeX, 13 pages. 5 PostScript figures available on request. Preprint UDPHIR 94/04/G

Site Percolation and Phase Transitions in Two Dimensions

The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters undergo a percolation transition exactly at the critical point. We show that this result is valid for a wide class of bidimensional systems undergoing a continuous magnetization transition. We provide numerical evidence for discrete as well as for continuous spin models, including SU(N) lattice gauge theories. The critical percolation exponents do not coincide with the ones of the thermal transition, but they are the same for models belonging to the same universality class.Comment: 8 pages, 6 figures, 2 tables. Numerical part developed; figures, references and comments adde

Modeling the non-Markovian, non-stationary scaling dynamics of financial markets

A central problem of Quantitative Finance is that of formulating a probabilistic model of the time evolution of asset prices allowing reliable predictions on their future volatility. As in several natural phenomena, the predictions of such a model must be compared with the data of a single process realization in our records. In order to give statistical significance to such a comparison, assumptions of stationarity for some quantities extracted from the single historical time series, like the distribution of the returns over a given time interval, cannot be avoided. Such assumptions entail the risk of masking or misrepresenting non-stationarities of the underlying process, and of giving an incorrect account of its correlations. Here we overcome this difficulty by showing that five years of daily Euro/US-Dollar trading records in the about three hours following the New York market opening, provide a rich enough ensemble of histories. The statistics of this ensemble allows to propose and test an adequate model of the stochastic process driving the exchange rate. This turns out to be a non-Markovian, self-similar process with non-stationary returns. The empirical ensemble correlators are in agreement with the predictions of this model, which is constructed on the basis of the time-inhomogeneous, anomalous scaling obeyed by the return distribution.Comment: Throughout revision. 15 pages, 6 figures. Presented by A.L. Stella in a Talk at the "Econophysics - Kolkata V'' International Workshop, March 2010, Saha Institute of Nuclear Physics, Kolkata, Indi

Evolution of white matter damage in amyotrophic lateral sclerosis

Objective To characterize disease evolution in amyotrophic lateral sclerosis using an event‐based model designed to extract temporal information from cross‐sectional data. Conventional methods for understanding mechanisms of rapidly progressive neurodegenerative disorders are limited by the subjectivity inherent in the selection of a limited range of measurements, and the need to acquire longitudinal data. Methods The event‐based model characterizes a disease as a series of events, each comprising a significant change in subject state. The model was applied to data from 154 patients and 128 healthy controls selected from five independent diffusion MRI datasets acquired in four different imaging laboratories between 1999 and 2016. The biomarkers modeled were mean fractional anisotropy values of white matter tracts implicated in amyotrophic lateral sclerosis. The cerebral portion of the corticospinal tract was divided into three segments. Results Application of the model to the pooled datasets revealed that the corticospinal tracts were involved before other white matter tracts. Distal corticospinal tract segments were involved earlier than more proximal (i.e., cephalad) segments. In addition, the model revealed early ordering of fractional anisotropy change in the corpus callosum and subsequently in long association fibers. Interpretation These findings represent data‐driven evidence for early involvement of the corticospinal tracts and body of the corpus callosum in keeping with conventional approaches to image analysis, while providing new evidence to inform directional degeneration of the corticospinal tracts. This data‐driven model provides new insight into the dynamics of neuronal damage in amyotrophic lateral sclerosis

Dynamically Driven Renormalization Group Applied to Sandpile Models

The general framework for the renormalization group analysis of self-organized critical sandpile models is formulated. The usual real space renormalization scheme for lattice models when applied to nonequilibrium dynamical models must be supplemented by feedback relations coming from the stationarity conditions. On the basis of these ideas the Dynamically Driven Renormalization Group is applied to describe the boundary and bulk critical behavior of sandpile models. A detailed description of the branching nature of sandpile avalanches is given in terms of the generating functions of the underlying branching process.Comment: 18 RevTeX pages, 5 figure

An overview of jets and outflows in stellar mass black holes

In this book chapter, we will briefly review the current empirical understanding of the relation between accretion state and and outflows in accreting stellar mass black holes. The focus will be on the empirical connections between X-ray states and relativistic (`radio') jets, although we are now also able to draw accretion disc winds into the picture in a systematic way. We will furthermore consider the latest attempts to measure/order jet power, and to compare it to other (potentially) measurable quantities, most importantly black hole spin.Comment: Accepted for publication in Space Science Reviews. Also to appear in the Space Sciences Series of ISSI - The Physics of Accretion on to Black Holes (Springer Publisher