Scaling properties of driven interfaces in disordered media

We perform a systematic study of several models that have been proposed for the purpose of understanding the motion of driven interfaces in disordered media. We identify two distinct universality classes: (i) One of these, referred to as directed percolation depinning (DPD), can be described by a Langevin equation similar to the Kardar-Parisi-Zhang equation, but with quenched disorder. (ii) The other, referred to as quenched Edwards-Wilkinson (QEW), can be described by a Langevin equation similar to the Edwards-Wilkinson equation but with quenched disorder. We find that for the DPD universality class the coefficient $\lambda$ of the nonlinear term diverges at the depinning transition, while for the QEW universality class either $\lambda = 0$ or $\lambda \to 0$ as the depinning transition is approached. The identification of the two universality classes allows us to better understand many of the results previously obtained experimentally and numerically. However, we find that some results cannot be understood in terms of the exponents obtained for the two universality classes {\it at\/} the depinning transition. In order to understand these remaining disagreements, we investigate the scaling properties of models in each of the two universality classes {\it above\/} the depinning transition. For the DPD universality class, we find for the roughness exponent $\alpha_P = 0.63 \pm 0.03$ for the pinned phase, and $\alpha_M = 0.75 \pm 0.05$ for the moving phase. For the growth exponent, we find $\beta_P = 0.67 \pm 0.05$ for the pinned phase, and $\beta_M = 0.74 \pm 0.06$ for the moving phase. Furthermore, we find an anomalous scaling of the prefactor of the width on the driving force. A new exponent $\varphi_M = -0.12 \pm 0.06$, characterizing the scaling of this prefactor, is shown to relate the values of the roughnessComment: Latex manuscript, Revtex 3.0, 15 pages, and 15 figures also available via anonymous ftp from ftp://jhilad.bu.edu/pub/abms/ (128.197.42.52

Stochastic Growth Equations and Reparametrization Invariance

It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach provides a particularly transparent way to obtain continuum growth equations for interfaces. It is straightforward to derive equations which describe the coarse grained evolution of discrete lattice models and analyze their small gradient expansion. In this way, the authors identify the basic mechanisms which lead to the most commonly used growth equations. The advantages of this formulation of growth processes is that it allows one to go beyond the frequently used no-overhang approximation. The reparametrization invariant form also displays explicitly the conservation laws for the specific process and all the symmetries with respect to space-time transformations which are usually lost in the small gradient expansion. Finally, it is observed, that the knowledge of the full equation of motion, beyond the lowest order gradient expansion, might be relevant in problems where the usual perturbative renormalization methods fail.Comment: 42 pages, Revtex, no figures. To appear in Rev. of Mod. Phy

Fasudil improves survival and promotes skeletal muscle development in a mouse model of spinal muscular atrophy

<p>Abstract</p> <p>Background</p> <p>Spinal muscular atrophy (SMA) is the leading genetic cause of infant death. It is caused by mutations/deletions of the survival motor neuron 1 (<it>SMN1</it>) gene and is typified by the loss of spinal cord motor neurons, muscular atrophy, and in severe cases, death. The SMN protein is ubiquitously expressed and various cellular- and tissue-specific functions have been investigated to explain the specific motor neuron loss in SMA. We have previously shown that the RhoA/Rho kinase (ROCK) pathway is misregulated in cellular and animal SMA models, and that inhibition of ROCK with the chemical Y-27632 significantly increased the lifespan of a mouse model of SMA. In the present study, we evaluated the therapeutic potential of the clinically approved ROCK inhibitor fasudil.</p> <p>Methods</p> <p>Fasudil was administered by oral gavage from post-natal day 3 to 21 at a concentration of 30 mg/kg twice daily. The effects of fasudil on lifespan and SMA pathological hallmarks of the SMA mice were assessed and compared to vehicle-treated mice. For the Kaplan-Meier survival analysis, the log-rank test was used and survival curves were considered significantly different at <it>P </it>< 0.05. For the remaining analyses, the Student's two-tail <it>t </it>test for paired variables and one-way analysis of variance (ANOVA) were used to test for differences between samples and data were considered significantly different at <it>P </it>< 0.05.</p> <p>Results</p> <p>Fasudil significantly improves survival of SMA mice. This dramatic phenotypic improvement is not mediated by an up-regulation of Smn protein or via preservation of motor neurons. However, fasudil administration results in a significant increase in muscle fiber and postsynaptic endplate size, and restores normal expression of markers of skeletal muscle development, suggesting that the beneficial effects of fasudil could be muscle-specific.</p> <p>Conclusions</p> <p>Our work underscores the importance of muscle as a therapeutic target in SMA and highlights the beneficial potential of ROCK inhibitors as a therapeutic strategy for SMA and for other degenerative diseases characterized by muscular atrophy and postsynaptic immaturity.</p