Abstract: In the paper the numerical simulation of heat diffusion in the fractal geometry of och snowflake is presented using multidomain mixed Boundary Element Method. he idea and motivation of work is to improve the cooling of small electronic devices sing fractal geometry of surface similar to cooling ribs. The heat diffusion is ssumed as the only principle of heat transfer. The results are compared to the heat lux of a flat surface. The limiting case of infinite small fractal element is computed sing Richardson extrapolation. Keywords:heat transfer, cooling of electronic devices, boundary element method, fractals Published: 10.07.2015; Views: 1123; Downloads: 265 Full text (313,63 KB) This document has many files! More...

Abstract: Quantum space time as given by topology and geometry of El Naschie's ▫$epsilon^(infty)$▫ theory must be regarded as fundamentally fuzzy. Itćs geometry and topology belong to the mathematical category of fuzzy logic and fuzzy set theory. All lines are fuzzy fractal lines in fuzzy spaces and all exact values are exact fuzzy expectation values. That way we remove many paradoxes and contradictions in the standard model of high energy particle physics. Keywords:matehmatics, fuzzy logic, fractals Published: 01.06.2012; Views: 877; Downloads: 22 Link to full text

Abstract: Encyclopedia of Complexity and Systems Science provides an authoritative single source for understanding and applying the concepts of complexity theory together with the tools and measures for analyzing complex systems in all fields of science and engineering. The science and tools of complexity and systems science include theories of self-organization, complex systems, synergetics, dynamical systems, turbulence, catastrophes, instabilities, nonlinearity, stochastic processes, chaos, neural networks, cellular automata, adaptive systems, and genetic algorithms. Examples of near-term problems and major unknowns that can be approached through complexity and systems science include: The structure, history and future of the universe; the biological basis of consciousness; the integration of genomics, proteomics and bioinformatics as systems biology; human longevity limits; the limits of computing; sustainability of life on earth; predictability, dynamics and extent of earthquakes, hurricanes, tsunamis, and other natural disasters; the dynamics of turbulent flows; lasers or fluids in physics, microprocessor design; macromolecular assembly in chemistry and biophysics; brain functions in cognitive neuroscience; climate change; ecosystem management; traffic management; and business cycles. All these seemingly quite different kinds of structure formation have a number of important features and underlying structures in common. These deep structural similarities can be exploited to transfer analytical methods and understanding from one field to another. This unique work will extend the influence of complexity and system science to a much wider audience than has been possible to date. Keywords:cellular automata, complex networks, computational nanoscience, ecological complexity, ergodic theory, fractals, game theory, granular computing, graph theory, intelligent systems, perturbation theory, quantum information science, system dynamics, traffic management, chaos, climate modelling, complex systems, dynamical sistems, fuzzy theory systems, nonlinear systems, soft computing, stochastic processes, synergetics, self-organization, systems biology, systems science Published: 01.06.2012; Views: 1995; Downloads: 99 Link to full text