Scaling limit of domino tilings on a pentagonal domain.

We consider the six-vertex model at its free-fermion point with domain wall boundary conditions, which is equivalent to random domino tilings of the Aztec diamond. We compute the scaling limit of a particular nonlocal correlation function, essentially equivalent to the partition function for the domino tilings of a pentagon-shaped domain, obtained by cutting away a triangular region from a corner of the initial Aztec diamond. We observe a third-order phase transition when the geometric parameters of the obtained pentagonal domain are tuned to have the fifth side exactly tangent to the arctic ellipse of the corresponding initial model.

Third-order phase transition in random tilings.

We consider the domino tilings of an Aztec diamond with a cut-off corner of macroscopic square shape and given size and address the bulk properties of tilings as the size is varied. We observe that the free energy exhibits a third-order phase transition when the cut-off square, increasing in size, reaches the arctic ellipse-the phase separation curve of the original (unmodified) Aztec diamond. We obtain this result by studying the thermodynamic limit of a certain nonlocal correlation function of the underlying six-vertex model with domain wall boundary conditions, the so-called emptiness formation probability (EFP).

Relaxation kinetics following sudden Ca(2+) reduction in single myofibrils from skeletal muscle.

To investigate the roles of cross-bridge dissociation and cross-bridge-induced thin filament activation in the time course of muscle relaxation, we initiated force relaxation in single myofibrils from skeletal muscles by rapidly (approximately 10 ms) switching from high to low [Ca(2+)] solutions. Full force decay from maximal activation occurs in two phases: a slow one followed by a rapid one. The latter is initiated by sarcomere "give" and dominated by inter-sarcomere dynamics (see the companion paper, Stehle, R.