Research on characteristics of noise-perturbed M–J sets based on equipotential point algorithm

AbstractAs the classical ones among the fractal sets, Julia set (abbreviated as J set) and Mandelbrot set (abbreviated as M set) have been explored widely in recent years. In this study, J set and M set under additive noise perturbation and multiplicative noise perturbation are created by equipotential point algorithm. Changes of the J set and M set under random noise perturbation as well as the close correlation between them are studied. Experimental results show that either additive noise perturbation or multiplicative noise perturbation may cause dramatic changes on J set. On the other hand, when the M set is perturbed by additive noise, it almost changes nothing but its position; when the M set is perturbed by multiplicative noise, its inner structures change with the stabilized areas shrinking, but it keeps the symmetry with respect to X axis. In addition, the J set and the M set still share the same stabilized periodic point in spite of noise perturbation

General Noise-Perturbed Superior Julia Sets

The aim of this paper is to offer an integrated approach to study the additive and multiplicative noises with respect to perturbations in superior Julia sets. External and internal perturbations in superior Julia sets are analyzed under the mixed effect of additive and multiplicative noises

Control of the Thermal Fractal Diffusion of Tightly Compressed Heterogeneous Layers of Thin Plates

As the thermal conductivity of thin plates composed of tightly compressed heterogeneous layers varies continuously in the form of an exponential function, we present a nonlinear dynamical model of the fractal growth of thermal diffusion. We also analyze the quantitative relationship between the probability of growth and the disturbance term, predict the control action of the environmental disturbance term on fractal growth, and use Matlab simulation to verify the control effectiveness of thermal fractal diffusion. The results facilitate the selection of appropriate control areas and control parameters for the thermal diffusion variable coefficients. In addition, variation in the fractal dimension reflects the influence of environmental disturbance on the complex process of thermal fractal diffusion

Developing a flexible and expressive realtime polyphonic wave terrain synthesis instrument based on a visual and multidimensional methodology

The Jitter extended library for Max/MSP is distributed with a gamut of tools for the generation, processing, storage, and visual display of multidimensional data structures. With additional support for a wide range of media types, and the interaction between these mediums, the environment presents a perfect working ground for Wave Terrain Synthesis. This research details the practical development of a realtime Wave Terrain Synthesis instrument within the Max/MSP programming environment utilizing the Jitter extended library. Various graphical processing routines are explored in relation to their potential use for Wave Terrain Synthesis

National Aeronautics and Space Administration (NASA)/American Society for Engineering Education (ASEE) Summer Faculty Fellowship Program, 1994, volume 1

The JSC NASA/ASEE Summer Faculty Fellowship Program was conducted by Texas A&M University and JSC. The objectives of the program, which began nationally in 1964 and at JSC in 1965 are to: (1) further the professional knowledge of qualified engineering and science faculty members, (2) stimulate an exchange of ideas between participants and NASA, (3) enrich and refresh the research and teaching activities of participants' institutions, and (4) contribute to the research objectives of the NASA centers. Each faculty fellow spent at least 10 weeks at JSC engaged in a research project in collaboration with a NASA JSC colleague. This document is a compilation of the final reports on the research projects completed by the faculty fellows during the summer of 1994

Emergent behavior in multiplicative critical processes and applications to economy

Tese de doutoramento, Física, Universidade de Lisboa, Faculdade de Ciências, 2014The main objective of this thesis is to develop a theoretical foundation for the study of economic phenomena based on methods of statistical physics applied to a system composed by set of multiplicative processes. An equivalent of equilibrium is established for such system and proved to behave statistically as in thermal equilibrium. An equivalent to canonical and microcanonical ensembles is realized and the relation with the theory of scale-free complex networks is made. The statistics of more than one century of US economy is studied in the light of these findings and an explanation for inflation and the resilience of wealth inequalities is found. The equivalent of Markov stochastic process on the set of multiplicative processes is established and the corresponding Fokker-Plank equation is derived. Moreover, a relation with self-organized criticality (SOC) is made. The study of market fluctuations is done using SOC models and yielding the same result as the Fokker-Planck approach. Based on these findings, we will argue that the distribution on the fluctuations of prices in organized market cannot follow Levy-stable distributions as stated by Mandelbrot.89 Finally, some applications to market and credit risk are made.O objectivo principal desta tese é o desenvolvimento de um novo equadramento teórico para o estudo dos fenómenos económicos baseado em métodos da física estatística aplicada a sistema composto por um agregado de processos multiplicativos. Num tal sistema, um estado equivalente ao estado de equil1íbrio emerge e demonstra-se que o seu comportamento estatístico é semelhante a um sistema em equilíbrio térmico. É realizado o estudo dos correspondentes ensembles canónico e microcanónico e feita a ligação com a teoria das redes complexas livres de escala. A estatística de mais de um século de economia dos EUA é estudada à luz destes desenvolvimentos é.dada uma explicação para os fenómenos da inflacção e da resiliência das desiguladades sociais. O equivalente ao processos estocásticos Markovianos no agregado de processos multiplicativos é establecido com o desenvolvimento da correspondente equação de Fokker-Planck e é feita a relacção com o fenómeno da criticalidade auto-organizada(SOC). O estudo das flutuações nos preços de mercado usando modelos SOC é feito levando ao mesmo resultado esperado pela abordagem equação de Fokker-Planck, o que nos vai permitir no futuro fazer a ligação com conjunto de ferramentas desenvolvidas pela matemática financeira. Baseado nestes resultados, argumentamos que as flutuações dos preços de mercado não podem seguir distribuições Lévy estáveis como propunha Mandelbrot89.Finalmente, algumas aplicações do enquadramento teórico são apresentadas.Fundação para a Ciência e a Tecnologia (FCT

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...