When a fiber is brought into contact with a soft etching liquid, a conical tip is generally shaped. We show here that the use of corrosive liquids which release gases during the etching reaction may lead to original self-similar shapes, because of successive pinning and detachment of the meniscus. The conditions for the formation of this shape and its evolution are described. In particular, we ...

I present a technique for constructing self-similar curves from smooth base curves. The technique is similar to that used in Iterated Function Systems like the Koch curve, except that it does not require a piecewise linear path in order to induce a set of similarities. I explain the mathematical machinery behind the technique, describe a practical numerical approximation that can be implemented...

We introduce a probabilistic model that is meant to describe an object that falls apart randomly as time passes and fulfills a certain scaling property. We show that the distribution of such a process is determined by its index of self-similarity , a rate of erosion c�0, and a so-called Lévy measure that accounts for sudden dislocations. The key of the analysis is provided by a transformation o...

Network testing presents different challenges from software testing. One challenge is that only a small number of networks, at best, can actually be tested, even when the goal is to test a class of networks. One solution is to select a representative network, which will display any faults present in any network of the class. This paper introduces the use of “self-similarity” to select such a ne...

We introduce the self-similar sketch, a new method for the extraction of intermediate image features that combines three principles: detection of self-similarity structures, nonaccidental alignment, and instance-specific modelling. The method searches for self-similar image structures that form nonaccidental patterns, for example collinear arrangements. We demonstrate a simple implementation of...

Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Papers published in Hydrology and Earth System Sciences Discussions are under open-access review for the journal Hydrology and Earth System Sciences Abstract Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion EGU Abstract In many cases, the...

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approxima...

A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather delicate questions: What can be said about the convergence of the calculational procedure when only a few its terms are available and how to decide which of ...

We propose statistically self-similar and rotation-invariant models for vector fields, study some of the more significant properties of these models, and suggest algorithms and methods for reconstructing vector fields from numerical observations, using the same notions of self-similarity and invariance that give rise to our stochastic models. We illustrate the efficacy of the proposed schemes b...