Nonequilibrium Precursor Model for the Onset of Percolation in a Two-Phase System

Using a Boltzmann equation, we investigate the nonequilibrium dynamics of nonperturbative fluctuations within the context of Ginzburg-Landau models. As an illustration, we examine how a two-phase system initially prepared in a homogeneous, low-temperature phase becomes populated by precursors of the opposite phase as the temperature is increased. We compute the critical value of the order parameter for the onset of percolation, which signals the breakdown of the conventional dilute gas approximation.Comment: 4 pages, 4 eps figures (uses epsf), Revtex. Replaced with version in press Physical Review

Synchronization and structure in an adaptive oscillator network

We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance their mutual synchronization. We show that the evolving network reaches a small-world structure. Its clustering coefficient attains a maximum for an intermediate intensity of the coupling between oscillators, where a rich diversity of synchronized oscillator groups is observed. In the stationary state, these synchronized groups are directly associated with network clusters.Comment: 6 pages, 7 figure

Nonequilibrium dynamics of the three-dimensional Edwards-Anderson spin-glass model with Gaussian couplings: Strong heterogeneities and the backbone picture

We numerically study the three-dimensional Edwards-Anderson model with Gaussian couplings, focusing on the heterogeneities arising in its nonequilibrium dynamics. Results are analyzed in terms of the backbone picture, which links strong dynamical heterogeneities to spatial heterogeneities emerging from the correlation of local rigidity of the bond network. Different two-times quantities as the flipping time distribution and the correlation and response functions, are evaluated over the full system and over high- and low-rigidity regions. We find that the nonequilibrium dynamics of the model is highly correlated to spatial heterogeneities. Also, we observe a similar physical behavior to that previously found in the Edwards-Anderson model with a bimodal (discrete) bond distribution. Namely, the backbone behaves as the main structure that supports the spin-glass phase, within which a sort of domain-growth process develops, while the complement remains in a paramagnetic phase, even below the critical temperature

The initial value problem for linearized gravitational perturbations of the Schwarzschild naked singularity

The coupled equations for the scalar modes of the linearized Einstein equations around Schwarzschild's spacetime were reduced by Zerilli to a 1+1 wave equation with a potential $V$, on a field $\Psi_z$. For smooth metric perturbations $\Psi_z$ is singular at $r_s=-6M/(\ell-1)(\ell+2)$, $\ell$ the mode harmonic number, and $V$ has a second order pole at $r_s$. This is irrelevant to the black hole exterior stability problem, where $r>2M>0$, and $r_s <0$, but it introduces a non trivial problem in the naked singular case where $M0$, and the singularity appears in the relevant range of $r$. We solve this problem by developing a new approach to the evolution of the even mode, based on a {\em new gauge invariant function}, $\hat \Psi$ -related to $\Psi_z$ by an intertwiner operator- that is a regular function of the metric perturbation {\em for any value of $M$}. This allows to address the issue of evolution of gravitational perturbations in this non globally hyperbolic background, and to complete the proof of the linear instability of the Schwarzschild naked singularity, by showing that a previously found unstable mode is excitable by generic initial data. This is further illustrated by numerically solving the linearized equations for suitably chosen initial data.Comment: typos corrected, references adde

Drake Equation for the Multiverse: From the String Landscape to Complex Life

It is argued that selection criteria usually referred to as "anthropic conditions" for the existence of intelligent (typical) observers widely adopted in cosmology amount only to preconditions for primitive life. The existence of life does not imply in the existence of intelligent life. On the contrary, the transition from single-celled to complex, multi-cellular organisms is far from trivial, requiring stringent additional conditions on planetary platforms. An attempt is made to disentangle the necessary steps leading from a selection of universes out of a hypothetical multiverse to the existence of life and of complex life. It is suggested that what is currently called the "anthropic principle" should instead be named the "prebiotic principle."Comment: 6 pages, RevTeX, in press, Int. J. Mod. Phys.

Phase Transition in U(1) Configuration Space: Oscillons as Remnants of Vortex-Antivortex Annihilation

We show that the annihilation of vortex-antivortex pairs can lead to very long-lived oscillon states in 2d Abelian Higgs models. The emergence of oscillons is controlled by the ratio of scalar and vector field masses, β=(ms/mv)2 and can be described as a phase transition in field configuration space with critical value βc≃0.13(6)±2: only models with βO(β)∼|β−βc|o, where O is an order parameter indicating the presence of oscillons and o=0.2(2)±2 is the critical exponent

Information-Entropic Measure of Energy-Degenerate Kinks in Two-Field Models

We investigate the existence and properties of kink-like solitons in a class of models with two interacting scalar fields. In particular, we focus on models that display both double and single-kink solutions, treatable analytically using the Bogomol'nyi--Prasad--Sommerfield bound (BPS). Such models are of interest in applications that include Skyrmions and various superstring-motivated theories. Exploring a region of parameter space where the energy for very different spatially-bound configurations is degenerate, we show that a newly-proposed momentum-space entropic measure called Configurational Entropy (CE) can distinguish between such energy-degenerate spatial profiles. This information-theoretic measure of spatial complexity provides a complementary perspective to situations where strictly energy-based arguments are inconclusive