Ab-initio reconstruction of complex Euclidean networks in two dimensions.

Reconstruction of complex structures is an inverse problem arising in virtually all areas of science and technology, from protein structure determination to bulk heterostructure solar cells and the structure of nanoparticles. We cast this problem as a complex network problem where the edges in a network have weights equal to the Euclidean distance between their endpoints. We present a method for reconstruction of the locations of the nodes of the network given only the edge weights of the Euclidean network. The theoretical foundations of the method are based on rigidity theory, which enables derivation of a polynomial bound on its efficiency. An efficient implementation of the method is discussed and timing results indicate that the run time of the algorithm is polynomial in the number of nodes in the network. We have reconstructed Euclidean networks of about 1000 nodes in approximately 24 h on a desktop computer using this implementation. We also reconstruct Euclidean networks corresponding to polymer chains in two dimensions and planar graphene nanoparticles. We have also modified our base algorithm so that it can successfully solve random point sets when the input data are less precise.

PDFfit2 and PDFgui: computer programs for studying nanostructure in crystals.

PDFfit2 is a program as well as a library for real-space refinement of crystal structures. It is capable of fitting a theoretical three-dimensional (3D) structure to atomic pair distribution function data and is ideal for nanoscale investigations. The fit system accounts for lattice constants, atomic positions and anisotropic atomic displacement parameters, correlated atomic motion, and experimental factors that may affect the data. The atomic positions and thermal coefficients can be constrained to follow the symmetry requirements of an arbitrary space group. The PDFfit2 engine is written in C++ and is accessible via Python, allowing it to inter-operate with other Python programs. PDFgui is a graphical interface built on the PDFfit2 engine. PDFgui organizes fits and simplifies many data analysis tasks, such as configuring and plotting multiple fits. PDFfit2 and PDFgui are freely available via the Internet.