A wavelet-based method for multifractal image analysis. I. Methodology and test applications on isotropic and anisotropic random rough surfaces

We generalize the so-called wavelet transform modulus maxima (WTMM) method to multifractal image analysis. We show that the implementation of this method provides very efficient numerical techniques to characterize statistically the roughness fluctuations of fractal surfaces. We emphasize the wide range of potential applications of this wavelet-based image processing method in fundamental as well as applied sciences. This paper is the first one of a series of three articles. It is mainly devoted to the methodology and to test applications on random self-affine surfaces (e.g., isotropic fractional Brownian surfaces and anisotropic monofractal rough surfaces). Besides its ability to characterize point-wise regularity, the WTMM method is definitely a multiscale edge detection method which can be equally used for pattern recognition, detection of contours and image denoising. Paper II (N. Decoster, S.G. Roux, A. Arnéodo, to be published in Eur. Phys. J. B 15 (2000)) will be devoted to some applications of the WTMM method to synthetic multifractal rough surfaces. In paper III (S.G. Roux, A. Arnéodo, N. Decoster, to be published in Eur. Phys. J. 15 (2000)), we will report the results of a comparative experimental analysis of high-resolution satellite images of cloudy scenes. Received 8 July 1999     

Prospects of ion-mobility measurements in superheavy element research

The element specific electron configuration of ions directly reflects the two quantum mechanical observables 〈r²〉 and r_max, which denote the r² expectation value of the electron density and the principle maximum of the wave function of the outermost electron orbital, respectively. Thus, the determination of these observables may present a new access to element identification of single superheavy nuclides. In this paper, we discuss how these observables are related to ionic radii deduced from ion-mobility data using the most simple hard sphere model and semi-empirical (n,6,4) model potentials for the interaction of heavy ions with noble gases. A concept for a high resolution ion-mobility spectrometer is presented. Optimum extraction efficiency of the ions will be achieved by decoupling the ion motion from the electric field drift by the friction force of the suitably shaped gas flow at the exit nozzle.     

Extraction of thermalized projectile fragments from gas

The NSCL gas cell and quadrupole ion-guide system has been used to study the thermalization of fast nuclear reaction products in a buffer gas. The fraction of radioactive ions that can be extracted from the gas cell is dramatically suppressed by space charge created by the stopping ions. The results of a review of the ion yields from the NSCL and from other gas cells from the literature with different sizes and different incident particle energies shows an overall consistency with a dramatic decline in extraction efficiency at high ionization rates.     

Determination of the Li/Nb ratio in lithium niobate by means of birefringence and Raman measurements

Two optical methods for the determination of the Li/Nb ratio in lithium niobate (LiNbO₃) are discussed. Data for the optical birefringence method are presented, they cover the entire composition range in which LiNbO₃ can be fabricated and a wide spectral region. The line-widths of lattice modes have been measured by means of Raman scattering as a function of the Li/Nb ratio for single crystals with polished and rough surfaces.     

Fractal axicons

Cantor rings are rotational symmetric pupils that are generated from a Cantor set of a given level of growth. These pupils have certain fractal properties. For example, it is known that when illuminated by a general spherical wavefront they provide self-similar patterns at transverse planes in the Fraunhofer region. In this paper, we study the response of Cantor rings when illuminated by a Bessel light beam conforming what we call fractal axicons. It is shown that, with this kind of illumination a close replica of the radial profile of the pupil is obtained along the optical axis, i.e., we show that the axial behaviour of these pupils has self-similarity properties that can be correlated to those of the diffracting aperture. The influence of several construction parameters is numerically investigated.     

Stable massive particles at colliders

We review the theoretical motivations and experimental status of searches for stable massive particles (SMPs) which could be sufficiently long-lived as to be directly detected at collider experiments. The discovery of such particles would address a number of important questions in modern physics including the origin and composition of dark matter in the universe and the unification of the fundamental forces. This review describes the techniques used in SMP-searches at collider experiments and the limits so far obtained on the production of SMPs which possess various colour, electric and magnetic charge quantum numbers. We also describe theoretical scenarios which predict SMPs along with the phenomenology needed to model their production at colliders and interactions with matter. In addition, the interplay between collider searches and open questions in cosmology such as dark matter composition is addressed.     

Structural properties and scaling of the radius of gyration of two-dimensional star-branched polymers grown by diffusion

We built up star-branched polymers, whose morphology is fully determined by diffusion, with p=1,3,6 and 12 branches with a total of 30,000 monomer units. We investigated their structural properties by calculating the monomer-monomer correlation functions. A detailed finite size scaling analysis of the radius of gyration was also performed to determine the exponent and the corrections to scaling. From these results we calculated the fractal dimension of the branched aggregates and obtained: d_f=1.222(7), for the linear chain, d_f=1.2305(8), d_f=1.247(8) and d_f=1.261(8) for the three, six and twelve branches polymer, respectively.     

On singularity of energy measures on self-similar sets

We provide general criteria for energy measures of regular Dirichlet forms on self-similar sets to be singular to Bernoulli type measures. In particular, every energy measure is proved to be singular to the Hausdorff measure for canonical Dirichlet forms on 2-dimensional Sierpinski carpets.Partially supported by Ministry of Education, Culture, Sports, Science and Technology, Grant-in-Aid for Encouragement of Young Scientists, 15740089.Mathematics Subject Classification (2000): 28A80 (60G30, 31C25, 60J60)     

Viscoelasticity of polydimethylsiloxane at the sol-gel threshold: structural effects

Five model polydimethylsiloxane (PDMS) networks were obtained by hydrosilation of a difunctional vinyl-terminated PDMS prepolymer with a SiH containing crosslinker. Viscoelastic experiments were performed in order to study the influence of molecular parameters on the dynamic properties at the sol-gel threshold. Critical parameters were determined close to and above the sol-gel threshold. The results obtained suggest that the critical exponents depend on the chemical structure of the incipient networks.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, September 11-13, 2003.