1 / 11

Symmetry

Symmetry. How do we define symmetry. An object invariant under a transformation Rotation Translation Time Lapse Reflection How many symmetries does a cube have?. 48. Curie’s Principle.

oihane
Download Presentation

Symmetry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Symmetry

  2. How do we define symmetry • An object invariant under a transformation • Rotation • Translation • Time Lapse • Reflection • How many symmetries does a cube have? 48

  3. Curie’s Principle • If certain causes produce certain effects, then the symmetries of the causes reappear in the effects produces • If certain effects reveal a certain asymmetry, then this asymmetry will be reflected in the causes that give rise to them

  4. An airplane • An airplane has bilateral symmetry • Does half a plane against a wall reproduce the flow past the airplane?

  5. Bifurcation • Symmetry “breaks” by creating an assortment of anti-symmetric states which sum to a symmetric state

  6. Airplane Flying • Has 2 steady states just off direct • Switches between the two due to turbulence or other “imperfections” • The overall “math” is symmetric, though there are anti-symmetric solutions

  7. Symmetry in Biology

  8. Start as spherically symmetric egg Lose symmetry with division Regain symmetry with blastula Lose symmetry as a sphere with a dimple Gastrulation

  9. Causes Difference of Pressure creates inward pressure Cell-Cell movement Location selection Breaking due to pressure will occur where walls are weaker Cell-Cell movement could be caused by selectively changing cell-cell adhesion Breaking of Symmetry

  10. What actually happens? • Cells change their adhesion properties and move via “random” motion • Axis is selected via signaling molecules established at the time of fertilization

  11. Conclusions • Small perturbations away from symmetry can cause substantial effects • Biology often just “pushes” an organism in the correct direction

More Related