Uncovering Topological Defects in Disordered Materials

<p dir="ltr">Topological defects are fundamental features of liquid crystalline materials that play crucial roles in determining their mechanical, optical, and rheological properties. Current computa tional techniques for identifying these defects in particle-based simulations rely primarily on Q-tensor theory and local order parameters, which do not fully exploit the underlying topological structure of the system. This work introduces a novel globally consistent vector field approach for identifying disclination cores in liquid crystalline materials that is inherently sensitive to the underlying topological structure. </p><p dir="ltr">Our method assigns a unique vector to each mesogen, effectively extending the concept of the liquid crystal director field down to individual mesogen scales while maintaining global consistency. In systems containing disclination cores, this consistent vector field approach identifies line segments in two-dimensional assemblies and quasi-two-dimensional surfaces in three-dimensional assemblies along which the assigned vector field exhibits discontinuities, with cores located at the interior termination points of these structures. By identifying discontinuities in an assigned vector field, the presence of defects can be detected by analyzing regions far from the defect cores themselves, making the method robust to local noise and data gaps. </p><p dir="ltr">We validate this approach by comparing our results to those obtained using the scalar order parameter for various liquid crystalline assemblies from molecular-dynamics simulations, including both synthetic defect geometries and realistic multiple-defect systems. Our analysis reveals several key advantages of the consistent vector field approach over existing methods: (1) earlier detection of defect core splitting in integer-charge defects, (2) ability to infer defect presence even when data near the core is unavailable, and (3) finer spatial resolution in defect identification. These capabilities demonstrate that our method truly captures the topological features of the data and provides a more robust framework for defect analysis in liquid crystalline materials. </p><p dir="ltr">Additionally, we extend our topological approach to amorphous glassy materials, which lack both positional and orientational order. We develop a continuum framework that iden tifies structural defects through the construction of local stress-free reference frames and the evolution of an inverse elastic distortion tensor. This approach captures persistent topo logical signatures of plasticity even in the absence of significant atomic motion, providing insights into the fundamental mechanisms of plastic deformation in disordered materials. </p><p dir="ltr">Our work establishes a unified framework for topological defect identification across both ordered and disordered materials, opening new avenues for understanding the relationship between microstructure and macroscopic material properties.</p>