3-D Evolution of Texture Collapse using Cactus

1. 3-D Evolution of Texture Collapse using Cactus Kim, Hee Il (CQUEST, Sogang Univ.) KPS meeting, 2006. 10. 20, Daegu EXCO

2. Texture? • Topological defect • No false vaccum core • Unstable to collapse • 3D simulations • Prokopec, Sornborger, & Brandenberger (`92) : 30x30x30 • Sornborger, Carroll, & Pyne (`97) : 64x64x64 • Not a current topic in Cosmology • Loser of war with inflation (in 1992, COBE era) • How about in condensed matter physics??? • Any other roles in cosmology and astrophysics??? • Anyway, it can be easily studied with your supercomputer of early `90 : ~200x200x200

3. What is Cactus? In Cactus Glossary “A green fleshy plant with lots of thorns, usuallyinflicting pain if touched.” Description in Homepage Cactus is an open source problem solving environment designed for scientists and engineers. Its modular structure easily enables parallel computation across different architectures and collaborative code development between different groups. Cactus originated in the academic research community, where it was developed and used over many years by a large international collaboration of physicists and computational scientists

4. Cactus Plug-In “Thorns” (modules) remote steering extensibleAPIs ANSI C driver Fortran/C/C++ parameters input/output scheduling equations of state interpolation Core “Flesh” errorhandling SOR solver Your Physics !! makesystem wave evolvers Your Computational Tools !! gridvariables multigrid boundaryconditions black holes coordinates

5. Cactus History Cactus originated in 1997 as a code for numerical relativity, following a long line of codes developed at the NCSA and then the AEI. • Cactus 1,2,3: Paul Walker, Joan Masso, John Shalf, Ed Seidel. • Cactus 4.0 beta 1, August 1999: Total rewrite and redesign of code, learning from experiences with previous versions (Tom Goodale): still developing v4.0 • In 2003, several members of the AEI Cactus group left Germany to help found the Center for Computation & Technology (CCT) at Louisiana State University with new director Ed Seidel. Cactus is now developed and supported by a close-knit team spanning AEI and CCT.

6. Supported Architectures

10. Carpet: Mesh refinement driver for Cactus Whisky: GR hydro code based on Cactus computational toolkit Taka: AMR driver for Cactus that uses the SAMRAI … Cactus Family(?) News on 2006-06-01 Parca: new AMR project using PARAMESH

11. Topological defect formation: Kibble mechanism Domain wall Cosmic string

12. Texture formations NO false vacuum core 1D 2D

13. Texture ~ hedgehog

14. Texture evolution Action Equations of Motion

15. Initial Conditions Winding number

16. Spherically symmetric texture (Kim & Lee, `94) Energy density & unwinding

17. Texture on Cactus • [khi@star ~]$ date • 2006. 09. 29. (금) 18:04:25 KST • [khi@star ~]$ cd Cactus/arrangements/ • [khi@star arrangements]$ ls • AEIThorns CactusConnect CactusExternal CactusTest CarpetAttic README CVS CactusEinstein CactusIO CactusUtils CarpetDev CactusBase CactusElliptic CactusPUGH CactusWave CarpetExtra CactusBench CactusExamples CactusPUGHIO Carpet KHIThorns • [khi@star arrangements]$ cd KHIThorns/ • [khi@star KHIThorns]$ ls • Texture TextureEnergy TextureID

18. Spherical textures (128^3) phi1 phi4

19. Gradient energy density: Cigar-shape textures (128^3) xz-plane xy-plane

20. Kinetic energy density: Cigar-shape textures (128^3) xz-plane xy-plane

21. Gradient energy density: Pancake-shape textures (128^3) xz-plane xy-plane

22. Kinetic energy density: Pancake-shape textures (128^3) xz-plane xy-plane

23. Potential energy density Cigar-shape Pancake-shape

24. Textures with subcritical winding number Gradient energy density in xz-plane

25. Concluding Remarks • Using Cactus, 3-D texture simulations reproduced nicely ! • Multi-texture evolution??? • Asymmetric texrure kick ??? • Gravitational waves??? • Cactus is not that difficult ^_^