Scaling of the Critical Function for the Standard Map: Some Numerical Results

The behavior of the critical function for the breakdown of the homotopically non-trivial invariant (KAM) curves for the standard map, as the rotation number tends to a rational number, is investigated using a version of Greene's residue criterion. The results are compared to the analogous ones for the radius of convergence of the Lindstedt series, in which case rigorous theorems have been proved. The conjectured interpolation of the critical function in terms of the Bryuno function is discussed.Comment: 26 pages, 3 figures, 13 table

Scaling law in the Standard Map critical function. Interpolating hamiltonian and frequency map analysis

We study the behaviour of the Standard map critical function in a neighbourhood of a fixed resonance, that is the scaling law at the fixed resonance. We prove that for the fundamental resonance the scaling law is linear. We show numerical evidence that for the other resonances $p/q$, $q \geq 2$, $p \neq 0$ and $p$ and $q$ relatively prime, the scaling law follows a power--law with exponent $1/q$.Comment: AMS-LaTeX2e, 29 pages with 8 figures, submitted to Nonlinearit

Stand and coarse woody debris dynamics in subalpine Norway spruce forests withdrawn from regular management

We studied structural characteristics, amount and quality of coarse woody debris (CWD), intensity of competition and mortality in two subalpine Norway spruce stands withdrawn from regular management. The stands, that we measured twice (in 1993 and 2005), have similar age and structure, but a different time has elapsed since the last silvicultural treatments (respectively 22 and about 55 y). The main purposes were to analyze the current stage of development as compared to the old-growth one and to highlight the legacies of past management. Although relatively old, the first plot (Valbona 1) was at the end of the pole stage. CWD was low in volume and was mainly of man-made origin (stumps). A recent thinning from below has reduced density-dependent competition and delayed the development of old-growth characteristics. The second plot (Valbona 2a) was at the beginning of the transition stage, with density-dependent and allogenic mortality both active at the same time. CWD volume was higher in plot Valbona 2a than in Valbona 1, but neither was comparable yet to the reference old-growth sites from Central Europe, both in quantity and in quality (e.g., decay rate continuity). The effects of the past management were: (1) reducing the quality and quantity of the CWD, (2) alleviating competition, (3) increasing resistance to minor disturbances and, as a consequence, (4) delaying the development processes. In mature or overmature subalpine Norway spruce stands withdrawn from regular management many decades are necessary to develop old-growth characteristics and a longer period of time is necessary to reach a true old-growth stage

Computational Speciation Models: A Tool for the Interpretation of Spectroelectrochemistry for Catalytic Layers under Operative Conditions

none7In this study,the first coupled FEXRAV and chemical speciation modelling study of the Pd deactivation is presented. Due to the high brilliance of synchrotron light, FEXRAV can investigat edeeply buried surfaces. More specifically, we directly analyzed the evolution of the Pd/C catalytic layer during a voltammetric cycle, through a specifically designed electrochemical cell. Still, we observed a complex interfacial chemistry of Pd, which impairs a straightforward interpretation of FEXRAV data. Exploiting thermodynamic chemical speciation modelling we were able to overcome this issue. The study leads to three main results: 1) the confirmation of the relationship between the change of the Pd/Pd(II) ratio and the change of the Fluorescence intensity 2) the investigation of the deactivation mechanism 3)the identification of the relevant species leading to the electrodissolution of Pd under operative conditions. This study opens new perspectives for the application of the chemical speciation modelling to the study of the deactivation mechanism of Pd in Pd/C catalytic layers under operative conditions in different electrolytes.mixedMontegrossi, G.; GIACCHERINI, ANDREA; BERRETTI, ENRICO; DI BENEDETTO, FRANCESCO; INNOCENTI, MASSIMO; D'Acapito, F.; LAVACCHI, ALESSANDROMontegrossi, G.; Giaccherini, Andrea; Berretti, Enrico; DI BENEDETTO, Francesco; Innocenti, Massimo; D'Acapito, F.; Lavacchi, Alessandr

Fully Automatic Expression-Invariant Face Correspondence

We consider the problem of computing accurate point-to-point correspondences among a set of human face scans with varying expressions. Our fully automatic approach does not require any manually placed markers on the scan. Instead, the approach learns the locations of a set of landmarks present in a database and uses this knowledge to automatically predict the locations of these landmarks on a newly available scan. The predicted landmarks are then used to compute point-to-point correspondences between a template model and the newly available scan. To accurately fit the expression of the template to the expression of the scan, we use as template a blendshape model. Our algorithm was tested on a database of human faces of different ethnic groups with strongly varying expressions. Experimental results show that the obtained point-to-point correspondence is both highly accurate and consistent for most of the tested 3D face models

Chaotic systems in complex phase space

This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviors of these two PT-symmetric dynamical models in complex phase space exhibit strong qualitative similarities.Comment: 22 page, 16 figure

Perturbative analysis of disordered Ising models close to criticality

We consider a two-dimensional Ising model with random i.i.d. nearest-neighbor ferromagnetic couplings and no external magnetic field. We show that, if the probability of supercritical couplings is small enough, the system admits a convergent cluster expansion with probability one. The associated polymers are defined on a sequence of increasing scales; in particular the convergence of the above expansion implies the infinite differentiability of the free energy but not its analyticity. The basic tools in the proof are a general theory of graded cluster expansions and a stochastic domination of the disorder

Monte Carlo Methods for the Self-Avoiding Walk

This article is a pedagogical review of Monte Carlo methods for the self-avoiding walk, with emphasis on the extraordinarily efficient algorithms developed over the past decade.Comment: 81 pages including lots of figures, 700138 bytes Postscript (NYU-TH-94/05/02) [To appear in Monte Carlo and Molecular Dynamics Simulations in Polymer Science, edited by Kurt Binder, Oxford University Press, expected late 1994