Synchronization, diversity, and topology of networks of integrate and fire oscillators

We study synchronization dynamics of a population of pulse-coupled oscillators. In particular, we focus our attention on the interplay between topological disorder and synchronization features of networks. First, we analyze synchronization time T in random networks, and find a scaling law which relates T to network connectivity. Then, we compare synchronization time for several other topological configurations, characterized by a different degree of randomness. The analysis shows that regular lattices perform better than a disordered network. This fact can be understood by considering the variability in the number of links between two adjacent neighbors. This phenomenon is equivalent to having a nonrandom topology with a distribution of interactions and it can be removed by an adequate local normalization of the couplings.

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.

Statistics of depth probed by cw measurement of photons in a turbid medium

Photon migration in a turbid medium has been modeled in many different ways. The motivation for such modeling is based on technology that can be used to probe potentially diagnostic optical properties of biological tissue. Surprisingly, one of the more effective models is also one of the simplest. It is based on statistical properties of a nearest-neighbor lattice random walk. Here we develop a theory allowing one to calculate the number of visits by a photon to a given depth, if it is eventually detected at an absorbing surface. This mimics cw measurements made on biological tissue and is directed towards characterizing the depth reached by photons injected at the surface. Our development of the theory uses formalism based on the theory of a continuous-time random walk (CTRW). Formally exact results are given in the Fourier-Laplace domain, which, in turn, are used to generate approximations for parameters of physical interest.

Stochastic resonance in nonpotential systems

We propose a method to analytically show the possibility for the appearance of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our results to the FitzHugh-Nagumo model under a periodic external forcing, showing that the model exhibits stochastic resonance. The procedure that we follow is based on the reduction to a one-dimensional dynamics in the adiabatic limit and in the topology of the phase space of the systems under study. Its application to other nonpotential systems is also discussed.

The Nonequilibrium thermodynamics of small systems

The interactions of tiny objects with their environments are dominated by thermal fluctuations. Guided by theory and assisted by new micromanipulation tools, scientists have begun to study such interactions in detail.

Noise-enhanced excitability in bistable activator-inhibitor media

We show that external fluctuations induce excitable behavior in a bistable spatially extended system with activator-inhibitor dynamics of the FitzHugh-Nagumo type. This can be understood as a mechanism for sustained signal propagation in bistable media. The phase diagram of the stochastic system is analytically obtained and numerically verified. For small-noise intensities, front propagation becomes unstable, and excitable pulses arise as the only possible spatiotemporal behavior of the system. For large-noise intensities, on the other hand, the system enters an effective regime of oscillatory behavior, where it exhibits spontaneous nucleation of pulses and synchronized firing.

Influence of ohmic heating on the flow field in thin-layer electrodeposition

In thin-layer electrodeposition the dissipated electrical energy leads to a substantial heating of the ion solution. We measured the resulting temperature field by means of an infrared camera. The properties of the temperature field correspond closely with the development of the concentration field. In particular, we find that the thermal gradients at the electrodes act similar to a weak additional driving force to the convection rolls driven by concentration gradients.

Actively maintained lipid nanodomains in biomembranes

Lipid rafts, defined as domains rich in cholesterol and sphingolipids, are involved in many important plasma membrane functions. Recent studies suggest that the way cells handle membrane cholesterol is fundamental in the formation of such lateral heterogeneities. We propose to model the plasma membrane as a nonequilibrium phase-separating system where cholesterol is dynamically incorporated and released. The model shows how cellular regulation of membrane cholesterol may determine the nanoscale lipid organization when the lipid mixture is close to a phase separation boundary, providing a plausible mechanism for raft formation in vivo.

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.

Generation of dynamic structures in nonequilibrium reactive membranes

We present a nonequlibrium approach for the study of a flexible bilayer whose two components induce distinct curvatures. In turn, the two components are interconverted by an externally promoted reaction. Phase separation of the two species in the surface results in the growth of domains characterized by different local composition and curvature modulations. This domain growth is limited by the effective mixing due to the interconversion reaction, leading to a finite characteristic domain size. In addition to these effects, first introduced in our earlier work [ Phys. Rev. E 71 051906 (2005)], the important new feature is the assumption that the reactive process actively affects the local curvature of the bilayer. Specifically, we suggest that a force energetically activated by external sources causes a modification of the shape of the membrane at the reaction site. Our results show the appearance of a rich and robust dynamical phenomenology that includes the generation of traveling and/or oscillatory patterns. Linear stability analysis, amplitude equations, and numerical simulations of the model kinetic equations confirm the occurrence of these spatiotemporal behaviors in nonequilibrium reactive bilayers.

Periodic forcing of scroll rings and control of Winfree turbulence in excitable media

By simulations of the Barkley model, action of uniform periodic nonresonant forcing on scroll rings and wave turbulence in three-dimensional excitable media is investigated. Sufficiently strong rapid forcing converts expanding scroll rings into the collapsing ones and suppresses the Winfree turbulence caused by the negative tension of wave filaments. Slow strong forcing has an opposite effect, leading to expansion of scroll rings and induction of the turbulence. These effects are explained in the framework of the phenomenological kinematic theory of scroll waves.

Confined brownian ratchets

We analyze the dynamics of Brownian ratchets in a confined environment. The motion of the particles is described by a Fick-Jakobs kinetic equation in which the presence of boundaries is modeled by means of an entropic potential. The cases of a flashing ratchet, a two-state model, and a ratchet under the influence of a temperature gradient are analyzed in detail. We show the emergence of a strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may take place in situations where none of those mechanisms leads to rectification when acting individually. The combined rectification mechanisms may lead to bidirectional transport and to new routes to segregation phenomena. Confined Brownian ratchets could be used to control transport in mesostructures and to engineer new and more efficient devices for transport at the nanoscale.

Holographic optical tweezers combined with back-focal-plane displacement detection

A major problem with holographic optical tweezers (HOTs) is their incompatibility with laser-based position detection methods, such as back-focal-plane interferometry (BFPI). The alternatives generally used with HOTs, like high-speed video tracking, do not offer the same spatial and temporal bandwidths. This has limited the use of this technique in precise quantitative experiments. In this paper, we present an optical trap design that combines digital holography and back-focal-plane displacement detection. We show that, with a particularly simple setup, it is possible to generate a set of multiple holographic traps and an additional static non-holographic trap with orthogonal polarizations and that they can be, therefore, easily separated for measuring positions and forces with the high positional and temporal resolutions of laser-based detection. We prove that measurements from both polarizations contain less than 1% crosstalk and that traps in our setup are harmonic within the typical range. We further tested the instrument in a DNA stretching experiment and we discuss an interesting property of this configuration: the small drift of the differential signal between traps.

Elastic properties and secondary structure formation of single-stranded DNA at monovalent and divalent salt conditions

Single-stranded DNA (ssDNA) plays a major role in several biological processes. It is therefore of fundamental interest to understand how the elastic response and the formation of secondary structures are modulated by the interplay between base pairing and electrostatic interactions. Here we measure force-extension curves (FECs) of ssDNA molecules in optical tweezers set up over two orders of magnitude of monovalent and divalent salt conditions, and obtain its elastic parameters by fitting the FECs to semiflexible models of polymers. For both monovalent and divalent salts, we find that the electrostatic contribution to the persistence length is proportional to the Debye screening length, varying as the inverse of the square root of cation concentration. The intrinsic persistence length is equal to 0.7 nm for both types of salts, and the effectivity of divalent cations in screening electrostatic interactions appears to be 100-fold as compared with monovalent salt, in line with what has been recently reported for single-stranded RNA. Finally, we propose an analysis of the FECs using a model that accounts for the effective thickness of the filament at low salt condition and a simple phenomenological description that quantifies the formation of non-specific secondary structure at low forces.