Revealing Actual Viscoelastic Relaxation Times in Capillary Breakup.

We use experiments and theory to elucidate the size effect in capillary breakup rheometry, where prestretching in the viscocapillary stage causes the apparent relaxation time to be consistently smaller than the actual value. We propose a method accounting for both the experimental size and the finite extensibility of polymers to extract the actual relaxation time. A phase diagram characterizes the expected measurement variability and delineates scaling law conditions.

Low-dimensional behavior of a Kuramoto model with inertia and Hebbian learning.

We study low-dimensional dynamics in a Kuramoto model with inertia and Hebbian learning. In this model, the coupling strength between oscillators depends on the phase differences between the oscillators and changes according to a Hebbian learning rule. We analyze the special case of two coupled oscillators, which yields a five-dimensional dynamical system that decouples into a two-dimensional longitudinal system and a three-dimensional transverse system.