Chaos in NaturePub Date : 2019-05-01DOI: 10.1142/9789814374439_0008
C. Letellier
{"title":"From Mathematics to Electronic Circuits","authors":"C. Letellier","doi":"10.1142/9789814374439_0008","DOIUrl":"https://doi.org/10.1142/9789814374439_0008","url":null,"abstract":"","PeriodicalId":215879,"journal":{"name":"Chaos in Nature","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126814173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chaos in NaturePub Date : 2019-05-01DOI: 10.1142/9789814374439_0009
C. Letellier
{"title":"From Meteorology to Chaos: The Second Wave","authors":"C. Letellier","doi":"10.1142/9789814374439_0009","DOIUrl":"https://doi.org/10.1142/9789814374439_0009","url":null,"abstract":"","PeriodicalId":215879,"journal":{"name":"Chaos in Nature","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114935821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chaos in NaturePub Date : 2019-05-01DOI: 10.1142/9789814374439_0007
C. Letellier
{"title":"Periodic and Chaotic Oscillators","authors":"C. Letellier","doi":"10.1142/9789814374439_0007","DOIUrl":"https://doi.org/10.1142/9789814374439_0007","url":null,"abstract":"","PeriodicalId":215879,"journal":{"name":"Chaos in Nature","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123156204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chaos in NaturePub Date : 2019-05-01DOI: 10.1142/9789814374439_0010
C. Letellier
{"title":"The Architecture of Chaotic Attractors","authors":"C. Letellier","doi":"10.1142/9789814374439_0010","DOIUrl":"https://doi.org/10.1142/9789814374439_0010","url":null,"abstract":"","PeriodicalId":215879,"journal":{"name":"Chaos in Nature","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121611858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chaos in NaturePub Date : 2019-05-01DOI: 10.1142/9789814374439_0001
C. Letellier
{"title":"The Laws of Dynamics","authors":"C. Letellier","doi":"10.1142/9789814374439_0001","DOIUrl":"https://doi.org/10.1142/9789814374439_0001","url":null,"abstract":"Newton's law linking force and acceleration is at the origin of modern physics. Applied to each plot of fluid, it is at the heart of weather and climate prediction models. The intuitive notion of force has been used since antiquity to understand static equilibria. It allows to design the vaults in architecture, to use a lever, to describe the fluid balance under the effect of Archimedes' thrust. It was the principle of inertia discovered by Galileo that paved the way for the laws of Newtonian dynamics, whose great success was in explaining the movement of planets and satellites, as well as the tides. This has required a great deal of mathematical expertise, which has its limits for more complex systems such as the atmosphere or the ocean. The resolution of the equations of dynamics has only been possible since the advent of computer calculation. However, the laws of conservation, quantity of movement, energy, kinetic moment, bring global constraints allowing a more direct understanding of certain phenomena.","PeriodicalId":215879,"journal":{"name":"Chaos in Nature","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124529881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chaos in NaturePub Date : 2019-05-01DOI: 10.1142/9789811201202_0002
Dylan Oelmann, Andrew MacDiarmid, May
{"title":"The Three-Body Problem","authors":"Dylan Oelmann, Andrew MacDiarmid, May","doi":"10.1142/9789811201202_0002","DOIUrl":"https://doi.org/10.1142/9789811201202_0002","url":null,"abstract":"The three-body problem studies the motion of three mutually attracting gravitational bodies, given their positions and initial velocities. The chaotic nature of the model due to its high sensitivity to initial conditions renders it impossible to use in the prediction of real world phenomena. Some of the most influential mathematicians studied the problem, including Newton, Euler, Lagrange, Jacobi, and Poincaré. This paper uses the Newtonian law of gravity to model the motion of three bodies. Using python, simulations were run using three different sets of initial conditions: The conditions for the Earth-Sun-Moon system, the Lemniscate solution, and Burrau’s solution. Case studies were done on each to analyze the results they produced, and we discuss the solver error of the models. The solutions all differ from their true, analytic solutions due to this error. The three-body problem can be expanded to the n-body problem, which has various applications in the real world, such as providing models of the orbits of the outer planets, the planets in the solar system, and even all the stars in the milky way galaxy. These models cannot be used to make predictions however, since the highly chaotic dependence on unmodelled variables can cause great variation in comparison to the model. The nonexistent general analytic solution to the problem could be used to make accurate predictions of phenomena in our solar system and universe, which would further develop the human understanding of the world.","PeriodicalId":215879,"journal":{"name":"Chaos in Nature","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129606171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chaos in NaturePub Date : 2019-05-01DOI: 10.1142/9789814374439_0013
C. Letellier
{"title":"Chaos in Biology and Biomedicine","authors":"C. Letellier","doi":"10.1142/9789814374439_0013","DOIUrl":"https://doi.org/10.1142/9789814374439_0013","url":null,"abstract":"","PeriodicalId":215879,"journal":{"name":"Chaos in Nature","volume":"43 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120975382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
求助内容：
应助结果提醒方式：