Library: Nexus-Soliton (NS)

last time edited @3rd. Dec. 2022

The NS project was started five years ago during my PhD time. The outputs have generated two major publications for 2D system. One of them is published on Nature Communication.

When two continuous symmetry breaking phase transitions happen consecutively in superfluid system, there is a chance that new phase is made out by fribration of vacua of the first and the second phase transitions. (ref1)(ref2 w/ more mathematics)

This results in composite defects described by relative homotopy groups. Moreoever, the isomorphic relationship of these relative homotopy make composite objects even more compilcate — they form nexus. 1D nexus has been observed expermentally, with remarkable agreements with NS simulations. read more in paper

Libaray NS was developed with BFGS nonlinear optimization algorithm and Galekin method of eigen problem. Finite element Discretization is used for numerical system.

The codes was implemented with Matlab and c++ languages. c++ programs should be complied to be dynamic object files (.so files) with suitbale interfaces before Matlab scripts could call them. However, same functions could be implemented and run without c++ parts, witha a bit slower. Matlab parfor is used for parallelism, and then addtional shell scripts are necessary for running on cluster.

There are still few open implements waiting for more work, for example:

Random lattices for solitions and HQVs — soliton glass;
3-Dimensional finite element mesh for system without translation symmetry along z-direction;
Adaptive mesh.

If you wanna discuss or have interesting to contribute, plz sent me email: samuel.thecurvature01@gmail.com

Link of repo: nexus-soliton

Open-access data of simulations: google-drive