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Chaotic Motion
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas. Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorenz Attractor Yb
Lorenz is an originally German name derived from the Roman surname Laurentius, which means "from Laurentum". Given name People with the given name Lorenz include: * Prince Lorenz of Belgium (born 1955), member of the Belgian royal family by his marriage with Princess Astrid of Belgium * Lorenz Böhler (1885–1973), Austrian trauma surgeon * Lorenz Hart (1895–1943), American lyricist, half of the famed Broadway songwriting team Rodgers and Hart * Lorenz Lange (1690–1752), Russian official in Siberia * Lorenz Oken (1779–1851), German naturalist * Lorenz of Werle (1338/40–1393/94), Lord of Werle-Güstrow Surname People with the name surname Lorenz include: * Adolf Lorenz (1854–1946), Austrian surgeon * Alfred Lorenz (1868–1939), Austrian-German musical analyst * Angela Lorenz (born 1965), American artist * Barbara Lorenz, make-up artist * Carl Lorenz (1913–1993), German cyclist * Christian Lorenz (born 1966), German musician * Edward Norton Lorenz (1917–200 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tornado
A tornado is a violently rotating column of air that is in contact with both the surface of the Earth and a cumulonimbus cloud or, in rare cases, the base of a cumulus cloud. It is often referred to as a twister, whirlwind or cyclone, although the word cyclone is used in meteorology to name a weather system with a low-pressure area in the center around which, from an observer looking down toward the surface of the Earth, winds blow counterclockwise in the Northern Hemisphere and clockwise in the Southern. Tornadoes come in many shapes and sizes, and they are often visible in the form of a condensation funnel originating from the base of a cumulonimbus cloud, with a cloud of rotating debris and dust beneath it. Most tornadoes have wind speeds less than , are about across, and travel several kilometers (a few miles) before dissipating. The most extreme tornadoes can attain wind speeds of more than , are more than in diameter, and stay on the ground for more than 100 k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Environmental Science
Environmental science is an interdisciplinary academic field that integrates physics, biology, and geography (including ecology, chemistry, plant science, zoology, mineralogy, oceanography, limnology, soil science, geology and physical geography, and atmospheric science) to the study of the environment, and the solution of environmental problems. Environmental science emerged from the fields of natural history and medicine during the Enlightenment. Today it provides an integrated, quantitative, and interdisciplinary approach to the study of environmental systems. Environmental studies incorporates more of the social sciences for understanding human relationships, perceptions and policies towards the environment. Environmental engineering focuses on design and technology for improving environmental quality in every aspect. Environmental scientists seek to understand the earth’s physical, chemical, biological, and geological processes, and to use that knowledge to understan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sociology
Sociology is a social science that focuses on society, human social behavior, patterns of Interpersonal ties, social relationships, social interaction, and aspects of culture associated with everyday life. It uses various methods of Empirical research, empirical investigation and critical analysis to develop a body of knowledge about social order and social change. While some sociologists conduct research that may be applied directly to social policy and welfare, others focus primarily on refining the Theory, theoretical understanding of social processes and phenomenology (sociology), phenomenological method. Subject matter can range from Microsociology, micro-level analyses of society (i.e. of individual interaction and agency (sociology), agency) to Macrosociology, macro-level analyses (i.e. of social systems and social structure). Traditional focuses of sociology include social stratification, social class, social mobility, sociology of religion, religion, secularization, S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anthropology
Anthropology is the scientific study of humanity, concerned with human behavior, human biology, cultures, societies, and linguistics, in both the present and past, including past human species. Social anthropology studies patterns of behavior, while cultural anthropology studies cultural meaning, including norms and values. A portmanteau term sociocultural anthropology is commonly used today. Linguistic anthropology studies how language influences social life. Biological or physical anthropology studies the biological development of humans. Archaeological anthropology, often termed as 'anthropology of the past', studies human activity through investigation of physical evidence. It is considered a branch of anthropology in North America and Asia, while in Europe archaeology is viewed as a discipline in its own right or grouped under other related disciplines, such as history and palaeontology. Etymology The abstract noun ''anthropology'' is first attested in reference t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meteorology
Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not begin until the 18th century. The 19th century saw modest progress in the field after weather observation networks were formed across broad regions. Prior attempts at prediction of weather depended on historical data. It was not until after the elucidation of the laws of physics, and more particularly in the latter half of the 20th century the development of the computer (allowing for the automated solution of a great many modelling equations) that significant breakthroughs in weather forecasting were achieved. An important branch of weather forecasting is marine weather forecasting as it relates to maritime and coastal safety, in which weather effects also include atmospheric interactions with large bodies of water. Meteorological pheno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poincaré Map
In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensional subspace, called the Poincaré section, transversal to the flow of the system. More precisely, one considers a periodic orbit with initial conditions within a section of the space, which leaves that section afterwards, and observes the point at which this orbit first returns to the section. One then creates a map to send the first point to the second, hence the name ''first recurrence map''. The transversality of the Poincaré section means that periodic orbits starting on the subspace flow through it and not parallel to it. A Poincaré map can be interpreted as a discrete dynamical system with a state space that is one dimension smaller than the original continuous dynamical system. Because it preserves many properties of periodic and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recurrence Plot
In descriptive statistics and chaos theory, a recurrence plot (RP) is a plot showing, for each moment i in time, the times at which the state of a dynamical system returns to the previous state at i, i.e., when the phase space trajectory visits roughly the same area in the phase space as at time j. In other words, it is a plot of :\vec(i)\approx \vec(j), showing i on a horizontal axis and j on a vertical axis, where \vec is the state of the system (or its phase space trajectory). Background Natural processes can have a distinct recurrent behaviour, e.g. periodicities (as seasonal or Milankovich cycles), but also irregular cyclicities (as El Niño Southern Oscillation, heart beat intervals). Moreover, the recurrence of states, in the meaning that states are again arbitrarily close after some time of divergence, is a fundamental property of deterministic dynamical systems and is typical for nonlinear or chaotic systems (cf. Poincaré recurrence theorem). The recurrence of states ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, and to make predictions about behavior. Elements of a mathematical model Mathematical models can take many forms, including dynamical systems, statisti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Road Traffic
Traffic comprises pedestrians, vehicles, ridden or herded animals, trains, and other Public conveyance, conveyances that use public ways (roads) for travel and transportation. Traffic laws govern and regulate traffic, while rules of the road include traffic laws and Norm (sociology), informal rules that may have developed over time to facilitate the orderly and timely flow of traffic. Organized traffic generally has well-established priorities, lanes, Priority (right of way), right-of-way, and traffic control at intersection (road), intersections. Traffic is formally organized in many jurisdictions, with marked lanes, Junction (traffic), junctions, Intersection (road), intersections, interchange (road), interchanges, traffic signals, or traffic sign, signs. Traffic is often classified by type: heavy motor vehicle (e.g., car, truck), other vehicle (e.g., moped, bicycle), and pedestrian A pedestrian is a person traveling on foot, whether walking or running. In modern t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward Lorenz
Edward Norton Lorenz (May 23, 1917 – April 16, 2008) was an American mathematician and meteorologist who established the theoretical basis of weather and climate predictability, as well as the basis for computer-aided atmospheric physics and meteorology. He is best known as the founder of modern chaos theory, a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions. His discovery of deterministic chaos "profoundly influenced a wide range of basic sciences and brought about one of the most dramatic changes in mankind's view of nature since Sir Isaac Newton," according to the committee that awarded him the 1991 Kyoto Prize for basic sciences in the field of earth and planetary sciences. Biographical information Lorenz was born in 1917 in West Hartford, Connecticut. He acquired an early love of science from both sides of his family. His father, Edward Henry Lorenz (1882-1956), majored in mechanical engineering at the Mas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randomness
In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if the probability distribution is known, the frequency of different outcomes over repeated events (or "trials") is predictable.Strictly speaking, the frequency of an outcome will converge almost surely to a predictable value as the number of trials becomes arbitrarily large. Non-convergence or convergence to a different value is possible, but has probability zero. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4. In this view, randomness is not haphazardness; it is a measure of uncertainty of an outcome. Randomness applies to concepts of chance, probability, and information entropy. The fields of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
