Fredrickson-Andersen model on Bethe lattice with random pinning

We study the effects of random pinning on the Fredrickson-Andersen model on the Bethe lattice. We find that the nonergodic transition temperature rises as the fraction of the pinned spins increases and the transition line terminates at a critical point. The freezing behavior of the spins is analogous to that of a randomly pinned p-spin mean-field spin glass model which has been recently reported. The diverging behavior of correlation lengths in the vicinity of the terminal critical point is found to be identical to the prediction of the inhomogeneous mode-coupling theory at the A3 singularity point for the glass transition.Comment: 6 pages, 7 figure

Cadherin-7 enhances Sonic Hedgehog signalling by preventing Gli3 repressor formation during neural tube patterning

Sonic Hedgehog (Shh) is a ventrally enriched morphogen controlling dorsoventral patterning of the neural tube. In the dorsal spinal cord, Gli3 protein bound to suppressor-of-fused (Sufu) is converted into Gli3 repressor (Gli3R), which inhibits Shh-target genes. Activation of Shh signalling prevents Gli3R formation, promoting neural tube ventralization. We show that cadherin-7 (Cdh7) expression in the intermediate spinal cord region is required to delimit the boundary between the ventral and the dorsal spinal cord. We demonstrate that Cdh7 functions as a receptor for Shh and enhances Shh signalling. Binding of Shh to Cdh7 promotes its aggregation on the cell membrane and association of Cdh7 with Gli3 and Sufu. These interactions prevent Gli3R formation and cause Gli3 protein degradation. We propose that Shh can act through Cdh7 to limit intracellular movement of Gli3 protein and production of Gli3R, thus eliciting more efficient activation of Gli-dependent signalling

The Fredrickson-Andersen model with random pinning on Bethe lattices and its MCT transitions

We investigate the dynamics of the randomly pinned Fredrickson-Andersen model on the Bethe lattice. We find a line of random pinning dynamical transitions whose dynamical critical properties are in the same universality class of the $A_2$ and $A_3$ transitions of Mode Coupling Theory. The $A_3$ behavior appears at the terminal point, where the relaxation becomes logarithmic and the relaxation time diverges exponentially. We explain the critical behavior in terms of self-induced disorder and avalanches, strengthening the relationship discussed in recent works between glassy dynamics and Random Field Ising Model.Comment: 8 pages, 7 figure

Supercooled Liquids Under Shear: Theory and Simulation

We analyze the behavior of supercooled fluids under shear both theoretically and numerically. Theoretically, we generalize the mode-coupling theory of supercooled fluids to systems under stationary shear flow. Our starting point is the set of generalized fluctuating hydrodynamic equations with a convection term. A nonlinear integro-differential equation for the intermediate scattering function is constructed. This theory is applied to a two-dimensional colloidal suspension. The shear rate dependence of the intermediate scattering function and the shear viscosity is analyzed. We have also performed extensive numerical simulations of a two-dimensional binary liquid with soft-core interactions near, but above, the glass transition temperature. Both theoretical and numerical results show: (i) A drastic reduction of the structural relaxation time and the shear viscosity due to shear. Both the structural relaxation time and the viscosity decrease as $\dot{\gamma}^{-\nu}$ with an exponent $\nu \leq 1$, where $\dot{\gamma}$ is the shear rate. (ii) Almost isotropic dynamics regardless of the strength of the anisotropic shear flow.Comment: 14 pages, 14 figure