Emergent spin excitations in a Bethe lattice at percolation.

We study the spin-1/2 quantum Heisenberg antiferromagnet on a Bethe lattice diluted to the percolation threshold. Dilution creates areas of even or odd sublattice imbalance resulting in "dangling spins" [L. Wang and A.

Self-consistent theory of reversible ligand binding to a spherical cell.

Ligand binding to receptors is the initial event in many signaling processes, and a quantitative understanding of this interaction is important for modeling cell behavior. In this paper, we study the kinetics of reversible ligand binding to receptors on a spherical cell surface using a self-consistent stochastic theory. Binding, dissociation, diffusion and rebinding of ligands are incorporated into the theory in a systematic manner.