No abstract

The propensity for synchronization of complex networks with directed and weighted links is considered. We show that a weighting procedure based upon the global structure of network pathways enhances complete synchronization of identical dynamical units in scale-free networks. Furthermore, we numerically show that very similar conditions hold also for phase synchronization of nonidentical chaotic oscillators.

We describe a 'reactor-diffusion' mechanism for precartilage condensation based on recent experiments on chondrogenesis in the early vertebrate limb and additional hypotheses. Cellular differentiation of mesenchymal cells into subtypes with different fibroblast growth factor (FGF) receptors occurs in the presence of spatio-temporal variations of FGFs and transforming growth factor-betas (TGF-βs). One class of differentiated cells produces elevated quantities of the extracellular matrix protein fibronectin, which initiates adhesion-mediated preskeletal mesenchymal condensation. The same class of cells also produces an FGFdependent laterally acting inhibitor that keeps condensations from expanding beyond a critical size. We show that this 'reactor-diffusion' mechanism leads naturally to patterning consistent with skeletal form, and describe simulations of spatio-temporal distribution of these differentiated cell types and the TGF-β and inhibitor concentrations in the developing limb bud.

We study the elastic theory of amorphous solids made of particles with finite range interactions in the thermodynamic limit. For the elastic theory to exist, one requires all the elastic coefficients, linear and nonlinear, to attain a finite thermodynamic limit. We show that for such systems the existence of nonaffine mechanical responses results in anomalous fluctuations of all the nonlinear coefficients of the elastic theory. While the shear modulus exists, the first nonlinear coefficient B(2) has anomalous fluctuations and the second nonlinear coefficient B(3) and all the higher order coefficients (which are nonzero by symmetry) diverge in the thermodynamic limit. These results call into question the existence of elasticity (or solidity) of amorphous solids at finite strains, even at zero temperature. We discuss the physical meaning of these results and propose that in these systems elasticity can never be decoupled from plasticity: the nonlinear response must be very substantially plastic.