Morphological transition between diffusion-limited and ballistic aggregation growth patterns

In this work, the transition between diffusion-limited and ballistic aggregation models was revisited using a model in which biased random walks simulate the particle trajectories. The bias is controlled by a parameter $\lambda$, which assumes the value $\lambda=0$ (1) for ballistic (diffusion-limited) aggregation model. Patterns growing from a single seed were considered. In order to simulate large clusters, a new efficient algorithm was developed. For $\lambda \ne 0$, the patterns are fractal on the small length scales, but homogeneous on the large ones. We evaluated the mean density of particles $\bar{\rho}$ in the region defined by a circle of radius $r$ centered at the initial seed. As a function of $r$, $\bar{\rho}$ reaches the asymptotic value $\rho_0(\lambda)$ following a power law $\bar{\rho}=\rho_0+Ar^{-\gamma}$ with a universal exponent $\gamma=0.46(2)$, independent of $\lambda$. The asymptotic value has the behavior $\rho_0\sim|1-\lambda|^\beta$, where $\beta= 0.26(1)$. The characteristic crossover length that determines the transition from DLA- to BA-like scaling regimes is given by $\xi\sim|1-\lambda|^{-\nu}$, where $\nu=0.61(1)$, while the cluster mass at the crossover follows a power law $M_\xi\sim|1 -\lambda|^{-\alpha}$, where $\alpha=0.97(2)$. We deduce the scaling relations \beta=\n u\gamma and $\beta=2\nu-\alpha$ between these exponents.Comment: 7 pages, 8 figure

Some Properties of Domain Wall Solution in the Randall-Sundrum Model

Properties of the domain wall (kink) solution in the 5 dimensional Randall-Sundrum model are examined both {\it analytically} and {\it numerically}. The configuration is derived by the bulk Higgs mechanism. We focus on 1) the convergence property of the solution, 2) the stableness of the solution, 3) the non-singular property of the Riemann curvature, 4) the behaviours of the warp factor and the Higgs field. It is found that the bulk curvature changes the sign around the surface of the wall. We also present some {\it exact} solutions for two simple cases: a) the no potential case, b) the cosmological term dominated case. Both solutions have the (naked) curvature singularity. We can regard the domain wall solution as a singularity resolution of the exact solutions.Comment: Typographical error correction for publication. 16 pages, 4 figure

Heterogeneous Dynamics, Marginal Stability and Soft Modes in Hard Sphere Glasses

In a recent publication we established an analogy between the free energy of a hard sphere system and the energy of an elastic network [1]. This result enables one to study the free energy landscape of hard spheres, in particular to define normal modes. In this Letter we use these tools to analyze the activated transitions between meta-bassins, both in the aging regime deep in the glass phase and near the glass transition. We observe numerically that structural relaxation occurs mostly along a very small number of nearly-unstable extended modes. This number decays for denser packing and is significantly lowered as the system undergoes the glass transition. This observation supports that structural relaxation and marginal modes share common properties. In particular theoretical results [2, 3] show that these modes extend at least on some length scale $l^*\sim (\phi_c-\phi)^{-1/2}$ where $\phi_c$ corresponds to the maximum packing fraction, i.e. the jamming transition. This prediction is consistent with very recent numerical observations of sheared systems near the jamming threshold [4], where a similar exponent is found, and with the commonly observed growth of the rearranging regions with compression near the glass transition.Comment: 6 pages, improved versio

Black hole formation in bidimensional dilaton gravity coupled to scalar matter systems

This work deals with the formation of black hole in bidimensional dilaton gravity coupled to scalar matter fields. We investigate two scalar matter systems, one described by a sixth power potential and the other defined with two scalar fields containing up to the fourth power in the fields. The topological solutions that appear in these cases allow the formation of black holes in the corresponding dilaton gravity models.Comment: Latex, 9 pages. Published in Mod. Phys. Lett. A14 (1999) 268