A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study on materials with disclinations, limiting their size.
The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such systems and provide an alternate approach that correctly accounts for the intera…
Generalizes beam models to include curvature and torsion.
We study the topology of smectic defects in two and three dimensions. We give a topological classification of smectic point defects and disclination lines in three dimensions. In addition we describe the combination rules for smectic point defects in two and three dimensions, showing how the broken translational symmet…
Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a configuration of a body in classical elasticity is the sum of local contributions …
A new model for defective media using two scales.
Study of knotted defects in smectic liquid crystals using topological knot theory.