Robust Hund rule without Coulomb repulsion and exclusion principle in quantum antiferromagnetic chains of composite half spins.

Quantum spin chains with composite spins have been used to approximate conventional chains with higher spins. For instance, a spin 1 (or [Formula: see text]) chain was sometimes approximated by a chain with two (or three) spin [Formula: see text]'s per site. However, little examination has been given as to whether this approximation, effectively assuming the first Hund rule per site, is valid and why.

Improving series convergence: the simple pendulum and beyond.

A simple and easy to implement method for improving the convergence of a power series is presented. We observe that the most obvious or analytically convenient point about which to make a series expansion is not always the most computationally efficient. Series convergence can be dramatically improved by choosing the center of the series expansion to be at or near the average value at which the series is to be evaluated.

Modeling the nanoscratching of self-healing materials.

We use computational modeling to determine the mechanical response of crosslinked nanogels to an atomic force microscope (AFM) tip that is moved through the sample. We focus on two-dimensional systems where the nanogels are interconnected by both strong and labile bonds. To simulate this system, we modify the lattice spring model (LSM) to extend the applicability of this method to a broader range of elastic materials.