Shape effects in the fluctuations of random isochrones on a square lattice.

We consider the isochrone curves in first-passage percolation on a 2D square lattice, i.e., the boundary of the set of points which can be reached in less than a given time from a certain origin.

Universal fluctuations of global geometrical measurements in planar clusters.

We characterize universal features of the sample-to-sample fluctuations of global geometrical observables, such as the area, width, length, and center-of-mass position, in random growing planar clusters. Our examples are taken from simulations of both continuous and discrete models of kinetically rough interfaces, including several universality classes, such as Kardar-Parisi-Zhang. We mostly focus on the scaling behavior with time of the sample-to-sample deviation for those global magnitudes, but we have also characterized their histograms and correlations.

Effects of confinement and vaccination on an epidemic outburst: A statistical mechanics approach.

This work describes a simple agent model for the spread of an epidemic outburst, with special emphasis on mobility and geographical considerations, which we characterize via statistical mechanics and numerical simulations. As the mobility is decreased, a percolation phase transition is found separating a free-propagation phase in which the outburst spreads without finding spatial barriers and a localized phase in which the outburst dies off. Interestingly, the number of infected agents is subject to maximal fluctuations at the transition point, building upon the unpredictability of the evolution of an epidemic outburst.

Nanowire reconstruction under external magnetic fields.

We consider the different structures that a magnetic nanowire adsorbed on a surface may adopt under the influence of external magnetic or electric fields. First, we propose a theoretical framework based on an Ising-like extension of the 1D Frenkel-Kontorova model, which is analyzed in detail using the transfer matrix formalism, determining a rich phase diagram displaying structural reconstructions at finite fields and an antiferromagnetic-paramagnetic phase transition of second order. Our conclusions are validated using ab initio calculations with density functional theory, paving the way for the search of actual materials where this complex phenomenon can be observed in the laboratory.

First-passage percolation under extreme disorder: From bond percolation to Kardar-Parisi-Zhang universality.

We consider the statistical properties of arrival times and balls on first-passage percolation (FPP) two-dimensional square lattices with strong disorder in the link times. A previous work showed a crossover in the weak disorder regime, between Gaussian and Kardar-Parisi-Zhang (KPZ) universality, with the crossover length decreasing as the noise amplitude grows. On the other hand, this work presents a very different behavior in the strong-disorder regime.

Power accretion in social systems.

We consider a model of power distribution in a social system where a set of agents plays a simple game on a graph: The probability of winning each round is proportional to the agent's current power, and the winner gets more power as a result. We show that when the agents are distributed on simple one-dimensional and two-dimensional networks, inequality grows naturally up to a certain stationary value characterized by a clear division between a higher and a lower class of agents. High class agents are separated by one or several lower class agents which serve as a geometrical barrier preventing further flow of power between them.

Nonuniversality of front fluctuations for compact colonies of nonmotile bacteria.

The front of a compact bacterial colony growing on a Petri dish is a paradigmatic instance of non-equilibrium fluctuations in the celebrated Eden, or Kardar-Parisi-Zhang (KPZ), universality class. While in many experiments the scaling exponents crucially differ from the expected KPZ values, the source of this disagreement has remained poorly understood. We have performed growth experiments with B.

Synchronization of fluctuating delay-coupled chaotic networks.

We study the synchronization of chaotic units connected through time-delayed fluctuating interactions. Focusing on small-world networks of Bernoulli and Logistic units with a fixed chiral backbone, we compare the synchronization properties of static and fluctuating networks in the regime of large delays. We find that random network switching may enhance the stability of synchronized states.

Circular Kardar-Parisi-Zhang equation as an inflating, self-avoiding ring polymer.

We consider the Kardar-Parisi-Zhang equation for a circular interface in two dimensions, unconstrained by the standard small-slope and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate the complete time evolution as a crossover between a short-time regime with the interface fluctuations of a self-avoiding ring or two-dimensional vesicle, and a long-time regime governed by the Tracy-Widom distribution expected for this geometry. For small-noise amplitudes, scaling behavior is only of the latter type.

Quantum manipulation via atomic-scale magnetoelectric effects.

Magnetoelectric effects at the atomic scale are demonstrated to afford unique functionality. This is shown explicitly for a quantum corral defined by a wall of magnetic atoms on a metal surface where spin-orbit coupling is observable. We show these magnetoelectric effects allow one to control the properties of systems placed inside the corral as well as their electronic signatures; they provide powerful alternative tools for probing electronic properties at the atomic scale.

H = xp model revisited and the Riemann zeros.

Berry and Keating conjectured that the classical Hamiltonian H = xp is related to the Riemann zeros. A regularization of this model yields semiclassical energies that behave, on average, as the nontrivial zeros of the Riemann zeta function. However, the classical trajectories are not closed, rendering the model incomplete.

Real-space renormalization-group approach to field evolution equations.

An operator formalism for the reduction of degrees of freedom in the evolution of discrete partial differential equations (PDE) via real-space renormalization group is introduced, in which cell overlapping is the key concept. Applications to (1+1)-dimensional PDEs are presented for linear and quadratic equations that are first order in time.