Study on acoustic field with fractal boundary using cellular automata

金沢大学理工研究域機械工学系In the present study, characteristics of the acoustic field in an enclosure bounded by fractal walls are investigated using Cellular Automata (CA). CA is a discrete system which consists of finite state variables arranged on uniform grid. The dynamics of CA is expressed by temporary updating the states of cells according to the local interaction rules, defined among a cell and its neighbors. In this paper, the effect of fractal shaped boundary structure to the reverberation and sound absorption characteristics of an enclosure is investigated for two dimensional acoustic wave propagation model described by CA. Local rules are provided for the construction of fractal patterns as well as representation of wave propagation phenomena. It is known by the numerical simulations that the damping enhancement and also frequency-selective absorbing behavior is seen for specific fractal patterns and stage numbers. © 2008 Springer-Verlag Berlin Heidelberg

Rupture by damage accumulation in rocks

The deformation of rocks is associated with microcracks nucleation and propagation, i.e. damage. The accumulation of damage and its spatial localization lead to the creation of a macroscale discontinuity, so-called "fault" in geological terms, and to the failure of the material, i.e. a dramatic decrease of the mechanical properties as strength and modulus. The damage process can be studied both statically by direct observation of thin sections and dynamically by recording acoustic waves emitted by crack propagation (acoustic emission). Here we first review such observations concerning geological objects over scales ranging from the laboratory sample scale (dm) to seismically active faults (km), including cliffs and rock masses (Dm, hm). These observations reveal complex patterns in both space (fractal properties of damage structures as roughness and gouge), time (clustering, particular trends when the failure approaches) and energy domains (power-law distributions of energy release bursts). We use a numerical model based on progressive damage within an elastic interaction framework which allows us to simulate these observations. This study shows that the failure in rocks can be the result of damage accumulation

Non-Standard Sound Synthesis with Dynamic Models

Full version unavailable due to 3rd party copyright restrictions.This Thesis proposes three main objectives: (i) to provide the concept of a new generalized non-standard synthesis model that would provide the framework for incorporating other non-standard synthesis approaches; (ii) to explore dynamic sound modeling through the application of new non-standard synthesis techniques and procedures; and (iii) to experiment with dynamic sound synthesis for the creation of novel sound objects. In order to achieve these objectives, this Thesis introduces a new paradigm for non-standard synthesis that is based in the algorithmic assemblage of minute wave segments to form sound waveforms. This paradigm is called Extended Waveform Segment Synthesis (EWSS) and incorporates a hierarchy of algorithmic models for the generation of microsound structures. The concepts of EWSS are illustrated with the development and presentation of a novel non-standard synthesis system, the Dynamic Waveform Segment Synthesis (DWSS). DWSS features and combines a variety of algorithmic models for direct synthesis generation: list generation and permutation, tendency masks, trigonometric functions, stochastic functions, chaotic functions and grammars. The core mechanism of DWSS is based in an extended application of Cellular Automata. The potential of the synthetic capabilities of DWSS is explored in a series of Case Studies where a number of sound object were generated revealing (i) the capabilities of the system to generate sound morphologies belonging to other non-standard synthesis approaches and, (ii) the capabilities of the system of generating novel sound objects with dynamic morphologies. The introduction of EWSS and DWSS is preceded by an extensive and critical overview on the concepts of microsound synthesis, algorithmic composition, the two cultures of computer music, the heretical approach in composition, non- standard synthesis and sonic emergence along with the thorough examination of algorithmic models and their application in sound synthesis and electroacoustic composition. This Thesis also proposes (i) a new definition for “algorithmic composition”, (ii) the term “totalistic algorithmic composition”, and (iii) four discrete aspects of non-standard synthesis

Effect of the dielectric inhomogeneity factor's range on the electrical tree evolution in solid dielectrics

The main contribution of the presented paper is to investigate the influence of the Dielectric Inhomogeneity Factor on the electrical tree evolution in solid dielectrics using cellular automata. We have a sample of the XLPE which is located between needle-to-plane electrodes under DC voltage. The electrical tree emanates from the end of the needle in which the electric stress attains a dielectric strength of the material. At every time step, Laplace's equation is solved to calculate the potential distribution which changes according to electrical tree development. Dynamic simulations clearly demonstrate the influence of the range of the Dielectric Inhomogeneity Factor on the electrical tree growth. Simulation results confirm the published technical literature

Anomalous diffusion: A basic mechanism for the evolution of inhomogeneous systems

In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be given to some methods applied in the analysis and characterization of diffusive regimes through the memory function, the mixing condition (or irreversibility), and ergodicity. Those methods can be used in the study of small-scale systems, ranging in size from single-molecule to particle clusters and including among others polymers, proteins, ion channels and biological cells, whose diffusive properties have received much attention lately.Comment: Review article, 20 pages, 7 figures. arXiv admin note: text overlap with arXiv:cond-mat/0201446 by other author

Discrete scale invariance and complex dimensions

We discuss the concept of discrete scale invariance and how it leads to complex critical exponents (or dimensions), i.e. to the log-periodic corrections to scaling. After their initial suggestion as formal solutions of renormalization group equations in the seventies, complex exponents have been studied in the eighties in relation to various problems of physics embedded in hierarchical systems. Only recently has it been realized that discrete scale invariance and its associated complex exponents may appear ``spontaneously'' in euclidean systems, i.e. without the need for a pre-existing hierarchy. Examples are diffusion-limited-aggregation clusters, rupture in heterogeneous systems, earthquakes, animals (a generalization of percolation) among many other systems. We review the known mechanisms for the spontaneous generation of discrete scale invariance and provide an extensive list of situations where complex exponents have been found. This is done in order to provide a basis for a better fundamental understanding of discrete scale invariance. The main motivation to study discrete scale invariance and its signatures is that it provides new insights in the underlying mechanisms of scale invariance. It may also be very interesting for prediction purposes.Comment: significantly extended version (Oct. 27, 1998) with new examples in several domains of the review paper with the same title published in Physics Reports 297, 239-270 (1998