lecture 5 uses and applications - uclucess21/18 lect 5 uses, applics, as given pd… · chaos in...
TRANSCRIPT
![Page 1: Lecture 5 Uses and Applications - UCLucess21/18 Lect 5 Uses, applics, as given PD… · CHAOS IN ENGINEERING Solids (spatial chaos) and Fluids (turbulence) Chemical Reactions Telecommunications](https://reader033.vdocuments.mx/reader033/viewer/2022050308/5f700f0b3613103b7a0355c4/html5/thumbnails/1.jpg)
Lecture 5 Uses and Applications
CHAOS IN ENGINEERING
Solids (spatial chaos) and Fluids (turbulence)
Chemical Reactions
Telecommunications and Mathematical methods
FRACTALS
Hearts and Lungs
Crystals, Snowflakes and the Fractal Dimension
IMPACTS AND FRICTION
Mooring towers and bouncing balls
Shimmy, chatter and time delays
HEALTH
Chaos in your heart and brain may be good for you
![Page 2: Lecture 5 Uses and Applications - UCLucess21/18 Lect 5 Uses, applics, as given PD… · CHAOS IN ENGINEERING Solids (spatial chaos) and Fluids (turbulence) Chemical Reactions Telecommunications](https://reader033.vdocuments.mx/reader033/viewer/2022050308/5f700f0b3613103b7a0355c4/html5/thumbnails/2.jpg)
Rig and Rod
![Page 3: Lecture 5 Uses and Applications - UCLucess21/18 Lect 5 Uses, applics, as given PD… · CHAOS IN ENGINEERING Solids (spatial chaos) and Fluids (turbulence) Chemical Reactions Telecommunications](https://reader033.vdocuments.mx/reader033/viewer/2022050308/5f700f0b3613103b7a0355c4/html5/thumbnails/3.jpg)
![Page 4: Lecture 5 Uses and Applications - UCLucess21/18 Lect 5 Uses, applics, as given PD… · CHAOS IN ENGINEERING Solids (spatial chaos) and Fluids (turbulence) Chemical Reactions Telecommunications](https://reader033.vdocuments.mx/reader033/viewer/2022050308/5f700f0b3613103b7a0355c4/html5/thumbnails/4.jpg)
Turbulence in fluid flow
![Page 6: Lecture 5 Uses and Applications - UCLucess21/18 Lect 5 Uses, applics, as given PD… · CHAOS IN ENGINEERING Solids (spatial chaos) and Fluids (turbulence) Chemical Reactions Telecommunications](https://reader033.vdocuments.mx/reader033/viewer/2022050308/5f700f0b3613103b7a0355c4/html5/thumbnails/6.jpg)
![Page 8: Lecture 5 Uses and Applications - UCLucess21/18 Lect 5 Uses, applics, as given PD… · CHAOS IN ENGINEERING Solids (spatial chaos) and Fluids (turbulence) Chemical Reactions Telecommunications](https://reader033.vdocuments.mx/reader033/viewer/2022050308/5f700f0b3613103b7a0355c4/html5/thumbnails/8.jpg)
![Page 9: Lecture 5 Uses and Applications - UCLucess21/18 Lect 5 Uses, applics, as given PD… · CHAOS IN ENGINEERING Solids (spatial chaos) and Fluids (turbulence) Chemical Reactions Telecommunications](https://reader033.vdocuments.mx/reader033/viewer/2022050308/5f700f0b3613103b7a0355c4/html5/thumbnails/9.jpg)
![Page 10: Lecture 5 Uses and Applications - UCLucess21/18 Lect 5 Uses, applics, as given PD… · CHAOS IN ENGINEERING Solids (spatial chaos) and Fluids (turbulence) Chemical Reactions Telecommunications](https://reader033.vdocuments.mx/reader033/viewer/2022050308/5f700f0b3613103b7a0355c4/html5/thumbnails/10.jpg)
Fractal-like structures emerge
naturally in plants and animals
![Page 12: Lecture 5 Uses and Applications - UCLucess21/18 Lect 5 Uses, applics, as given PD… · CHAOS IN ENGINEERING Solids (spatial chaos) and Fluids (turbulence) Chemical Reactions Telecommunications](https://reader033.vdocuments.mx/reader033/viewer/2022050308/5f700f0b3613103b7a0355c4/html5/thumbnails/12.jpg)
![Page 13: Lecture 5 Uses and Applications - UCLucess21/18 Lect 5 Uses, applics, as given PD… · CHAOS IN ENGINEERING Solids (spatial chaos) and Fluids (turbulence) Chemical Reactions Telecommunications](https://reader033.vdocuments.mx/reader033/viewer/2022050308/5f700f0b3613103b7a0355c4/html5/thumbnails/13.jpg)
![Page 14: Lecture 5 Uses and Applications - UCLucess21/18 Lect 5 Uses, applics, as given PD… · CHAOS IN ENGINEERING Solids (spatial chaos) and Fluids (turbulence) Chemical Reactions Telecommunications](https://reader033.vdocuments.mx/reader033/viewer/2022050308/5f700f0b3613103b7a0355c4/html5/thumbnails/14.jpg)
Articulated mooring towerOil tankers are moored to towers hinged at the base and held vertical by a buoyancy chamber. Waves drive these towers to oscillate, causing the hawser to the tanker to slacken and snatch in an ‘impact’. Subharmonics and chaos are generated.
m28 lv impct
![Page 17: Lecture 5 Uses and Applications - UCLucess21/18 Lect 5 Uses, applics, as given PD… · CHAOS IN ENGINEERING Solids (spatial chaos) and Fluids (turbulence) Chemical Reactions Telecommunications](https://reader033.vdocuments.mx/reader033/viewer/2022050308/5f700f0b3613103b7a0355c4/html5/thumbnails/17.jpg)
Chattering of machine cutting toolsAgain associated withsliding friction and timedelays
Surface milling
Stick-slip cutting and drill string buckling(in an under-sea drilling experiment)
m25 ab drill
![Page 18: Lecture 5 Uses and Applications - UCLucess21/18 Lect 5 Uses, applics, as given PD… · CHAOS IN ENGINEERING Solids (spatial chaos) and Fluids (turbulence) Chemical Reactions Telecommunications](https://reader033.vdocuments.mx/reader033/viewer/2022050308/5f700f0b3613103b7a0355c4/html5/thumbnails/18.jpg)
Sketch by Gabor Stepan to understand transient chaos in chatter (and shimmying)
![Page 19: Lecture 5 Uses and Applications - UCLucess21/18 Lect 5 Uses, applics, as given PD… · CHAOS IN ENGINEERING Solids (spatial chaos) and Fluids (turbulence) Chemical Reactions Telecommunications](https://reader033.vdocuments.mx/reader033/viewer/2022050308/5f700f0b3613103b7a0355c4/html5/thumbnails/19.jpg)
![Page 21: Lecture 5 Uses and Applications - UCLucess21/18 Lect 5 Uses, applics, as given PD… · CHAOS IN ENGINEERING Solids (spatial chaos) and Fluids (turbulence) Chemical Reactions Telecommunications](https://reader033.vdocuments.mx/reader033/viewer/2022050308/5f700f0b3613103b7a0355c4/html5/thumbnails/21.jpg)
CONCLUDING REMARKS
Chaos = random response of a precise deterministic system
It exhibits extreme sensitivity to initial conditions
Chaotic solutions are mathematically unsolvable
Numerical computations are prone to enormous errors
Detailed prediction is impossible
However there is order within chaos
FURTHER LECTURES AND INFORMATION
My homepage: http://www.ucl.ac.uk/~ucess21/
Norah Boyce Lecture, 10 May 2016, The butterfly effect
Same course of 5 lectures next year. Tell your friends!
Comments welcome on [email protected]