Fractal Heterogeneous Media

A method is proposed for generating compact fractal disordered media, by generalizing the random midpoint displacement algorithm. The obtained structures are invasive stochastic fractals, with the Hurst exponent varying as a continuous parameter, as opposed to lacunar deterministic fractals, such as the Menger sponge. By employing the Detrending Moving Average algorithm [Phys. Rev. E 76, 056703 (2007)], the Hurst exponent of the generated structure can be subsequently checked. The fractality of such a structure is referred to a property defined over a three dimensional topology rather than to the topology itself. Consequently, in this framework, the Hurst exponent should be intended as an estimator of compactness rather than of roughness. Applications can be envisaged for simulating and quantifying complex systems characterized by self-similar heterogeneity across space. For example, exploitation areas range from the design and control of multifunctional self-assembled artificial nano and micro structures, to the analysis and modelling of complex pattern formation in biology, environmental sciences, geomorphological sciences, etc

Optimization of Stone Cutting Techniques for the Seismic Protection of Archaeological Sites

Since the beginning of civilization, history tells of the movement of art pieces, monuments and manufacts from site to site. The causes are multiple: the displacements due to the "spoils of war", ordered by kings and emperors, the movements caused by the need for reuse, especially in the early Christian period, and so forth. Considerations about the events of the past, yield a possible strategy to transform this concept into a technique for earthquake prevention of archaeological sites. The seismic safety retrofits have often proven to be scarcely effective, because of the difficulties involved in complex sites. The aim of this study is to analyze an "alternative" method of preventing natural disaster like floods, eruption and earthquakes, through the movimentation of the most representative structural elements of archaeological sites by decomposition of the masonry and marbles [1]. The procedure considers a process of "cutting optimization," calibrated on the characteristics of the specific material that has to be cut and then displaced in safer places (i.e., MEP, "manufact evacuation plan"). This process should not create excessive problems to the structure, and aims to reassembly the manufact in contexts able to guarantee safety through advanced earthquake-resistant expedients. From these considerations, the work develops a procedure to safeguard the archaeological site of Pompei (Naples), through an appropriate analysis of representative portions of the site, aimed to a careful handling and to a proper reconstruction in a safe location, from the seismic point of vie

Progressive collapse of structures: A discussion on annotated nomenclature

The study of progressive collapse and structural robustness has advanced significantly after 9/11 event. There is a growing interest in the phenomenon, as well as in the development of numerical and experimental techniques that have led to great progress in understanding the structural robustness and integrity. However, the general ideas, concepts and definitions have been merely changed over the past twenty years. These concepts and definitions are first developed in the framework of a threat-independent methodology, implicitly focused on blast-induced progressive collapse (or other short-term extreme events) in framed structures, and then, generalized to other structural types, mechanisms and triggering events, without scrutinization. In this paper, the current definitions of the terms progressive collapse, initial (local) damage and progressive collapse analysis are challenged, their insufficiency is discussed and possible improvements are provided. The suggested definitions and discussions provide a deeper and more general nomenclature for progressive collapse and related topics

Snow metamorphism: a fractal approach

Snow is a porous disordered medium consisting of air and three water phases: ice, vapour and liquid. The ice phase consists of an assemblage of grains, ice matrix, initially arranged over a random load bearing skeleton. The quantitative relationship between density and morphological characteristics of different snow microstructures is still an open issue. In this work, a three-dimensional fractal description of density corresponding to different snow microstructure is put forward. First, snow density is simulated in terms of a generalized Menger sponge model. Then, a fully three-dimensional compact stochastic fractal model is adopted. The latter approach yields a quantitative map of the randomness of the snow texture, which is described as a three-dimensional fractional Brownian field with the Hurst exponent H varying as continuous parameter. The Hurst exponent is found to be strongly dependent on snow morphology and density. The approach might be applied to all those cases where the morphological evolution of snow cover or ice sheets should be conveniently described at a quantitative level

Series solution of beams with variable cross-section

Abstract In structural engineering beams with non-constant cross-section or beams with variable cross-section represent a class of slender bodies, aim of practitioners' interest due to the possibility of optimizing their geometry with respect to specific needs. Despite the advantages that engineers can obtain from their applications, non-trivial difficulties occurring in the non-prismatic beam modeling often lead to inaccurate predictions that vanish the gain of the optimization process. As a consequence, an effective non-prismatic beam modeling still represents a branch of the structural engineering of interest for the community, especially for advanced design applications in large spans elements. A straight beam of length l with variable inertia J(z) is provided in figure, subject to a generic live load condition q(z). The vertical displacement y(z) can be obtained from the solution of the differential equation of the elastic line, i.e., taking into consideration the inertia variability and neglecting, as first approximation, any shear contribution. Even if this solution is an approximate one, it is able to deal with the problem in its basic formulation. In this paper a solution for the problem stated is formulated using a series expansion of solutions, in a general load and cross section variability condition. Solution is thus obtained for a generic rectangular cross section beam with a variable height. Analytical solution is presented and evaluated using numerical evaluation of some cases of practical interest

Multi-scale analysis of contact between fractal surfaces

CMIS-2001, 3rd Contact Mechanics International Symposium, Peniche, Portuga