Generalized Onsager symmetry

Onsager's symmetry theorem for transport near equilibrium is extended in two directions. A corresponding symmetry is obtained for linear transport near nonequilibrium stationary states, and the class of transport laws is extended to include nonlocality in both space and time. The results are formally exact and independent of any specific model for the nonequilibrium state.

Noise suppression by noise

We have analyzed the interplay between an externally added noise and the intrinsic noise of systems that relax fast towards a stationary state, and found that increasing the intensity of the external noise can reduce the total noise of the system. We have established a general criterion for the appearance of this phenomenon and discussed two examples in detail.

Fluctuations in finite systems: fluctuations in fluids in thermocapillary motion

We compute nonequilibrium correlation functions about the stationary state in which the fluid moves as a consequence of tangential stresses on the liquid surface, related to a varying surface tension (thermocapillary motion). The nature of the stationary state makes it necessary to take into account that the system is finite. We then extend a previous analysis on fluctuations about simple stationary states to include some effects related to the finite size of the sample.

Modelling diffusion of innovations in a social network

A simple model of diffusion of innovations in a social network with upgrading costs is introduced. Agents are characterized by a single real variable, their technological level. According to local information, agents decide whether to upgrade their level or not, balancing their possible benefit with the upgrading cost. A critical point where technological avalanches display a power-law behavior is also found. This critical point is characterized by a macroscopic observable that turns out to optimize technological growth in the stationary state. Analytical results supporting our findings are found for the globally coupled case.

Self-organized evolution in a socio-economic environment

We propose a general scenario to analyze technological changes in socio-economic environments. We illustrate the ideas with a model that incorporating the main trends is simple enough to extract analytical results and, at the same time, sufficiently complex to display a rich dynamic behavior. Our study shows that there exists a macroscopic observable that is maximized in a regime where the system is critical, in the sense that the distribution of events follow power laws. Computer simulations show that, in addition, the system always self-organizes to achieve the optimal performance in the stationary state.

Onsager symmetry principle for a particle moving through a fluid not in equilibrium

We have shown that the mobility tensor for a particle moving through an arbitrary homogeneous stationary flow satisfies generalized Onsager symmetry relations in which the time-reversal transformation should also be applied to the external forces that keep the system in the stationary state. It is then found that the lift forces, responsible for the motion of the particle in a direction perpendicular to its velocity, have different parity than the drag forces.

Mean first-passage times for systems driven by equilibrium persistent-periodic dichotomous noise

In a recent paper, [J. M. Porrà, J. Masoliver, and K. Lindenberg, Phys. Rev. E 48, 951 (1993)], we derived the equations for the mean first-passage time for systems driven by the coin-toss square wave, a particular type of dichotomous noisy signal, to reach either one of two boundaries. The coin-toss square wave, which we here call periodic-persistent dichotomous noise, is a random signal that can only change its value at specified time points, where it changes its value with probability q or retains its previous value with probability p=1-q. These time points occur periodically at time intervals t. Here we consider the stationary version of this signal, that is, equilibrium periodic-persistent noise. We show that the mean first-passage time for systems driven by this stationary noise does not show either the discontinuities or the oscillations found in the case of nonstationary noise. We also discuss the existence of discontinuities in the mean first-passage time for random one-dimensional stochastic maps.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

Exact long-time behavior of a network of oscillators under random fields

We present an exact solution for the order parameters that characterize the stationary behavior of a population of Kuramotos phase oscillators under random external fields [Y. Kuramoto, in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, Vol. 39 (Springer, Berlin, 1975), p. 420]. From these results it is possible to generate the phase diagram of models with an arbitrary distribution of random frequencies and random fields.

New horizons for black holes and branes

We initiate a systematic scan of the landscape of black holes in any spacetime dimension using the recently proposed blackfold effective worldvolume theory. We focus primarily on asymptotically flat stationary vacuum solutions, where we uncover large classes of new black holes. These include helical black strings and black rings, black odd-spheres, for which the horizon is a product of a large and a small sphere, and non-uniform black cylinders. More exotic possibilities are also outlined. The blackfold description recovers correctly the ultraspinning Myers-Perry black holes as ellipsoidal even-ball configurations where the velocity field approaches the speed of light at the boundary of the ball. Helical black ring solutions provide the first instance of asymptotically flat black holes in more than four dimensions with a single spatial U(1) isometry. They also imply infinite rational non-uniqueness in ultraspinning regimes, where they maximize the entropy among all stationary single-horizon solutions. Moreover, static blackfolds are possible with the geometry of minimal surfaces. The absence of compact embedded minimal surfaces in Euclidean space is consistent with the uniqueness theorem of static black holes

Dynamics of Fréedericksz transition in a fluctuating magnetic field

Fréedericksz transition under twist deformation in a nematic layer is discussed when the magnetic field has a random component. A dynamical model which includes the thermal fluctuations of the system is presented. The randomness of the field produces a shift of the instability point. Beyond this instability point the time constant characteristic of the approach to the stationary stable state decreases because of the field fluctuations. The opposite happens for fields smaller than the critical one. The decay time of an unstable state, calculated as a mean first-passage time, is also decreased by the field fluctuations.

Inertial effects on reactive particles advected by turbulence

We study the problem of the advection of passive particles with inertia in a two-dimensional, synthetic, and stationary turbulent flow. The asymptotic analytical result and numerical simulations show the importance of inertial bias in collecting the particles preferentially in certain regions of the flow, depending on their density relative to that of the flow. We also study how these aggregates are affected when a simple chemical reaction mechanism is introduced through a Eulerian scheme. We find that inertia can be responsible for maintaining a stationary concentration pattern even under nonfavorable reactive conditions or destroying it under favorable ones.

Wave competition in excitable modulated media.

The propagation of an initially planar front is studied within the framework of the photosensitive Belousov-Zhabotinsky reaction modulated by a smooth spatial variation of the local front velocity in the direction perpendicular to front propagation. Under this modulation, the wave front develops several fingers corresponding to the local maxima of the modulation function. After a transient, the wave front achieves a stationary shape that does not necessarily coincide with the one externally imposed by the modulation. Theoretical predictions for the selection criteria of fingers and steady-state velocity are experimentally validated.

Nonequilibrium orientational patterns in two-component Langmuir monolayers

A model of a phase-separating two-component Langmuir monolayer in the presence of a photoinduced reaction interconverting two components is formulated. An interplay between phase separation, orientational ordering, and reaction is found to lead to a variety of nonequilibrium self-organized patterns, both stationary and traveling. Examples of the patterns, observed in numerical simulations, include flowing droplets, traveling stripes, wave sources, and vortex defects.

Nonequilibrium patterns and shape fluctuations in reactive membranes

A simple kinetic model of a two-component deformable and reactive bilayer is presented. The two differently shaped components are interconverted by a nonequilibrium reaction, and a phenomenological coupling between local composition and curvature is proposed. When the two components are not miscible, linear stability analysis predicts, and numerical simulations show, the formation of stationary nonequilibrium composition/curvature patterns whose typical size is determined by the reactive process. For miscible components, a linearization of the dynamic equations is performed in order to evaluate the correlation function for shape fluctuations from which the behavior of these systems in micropipet aspiration experiments can be predicted.