An approach aiming to quantify the dynamics of information within a population is developed based on the mapping of the processes underlying the system’s evolution into a birth and death type stochastic process and the derivation of a balance equation for the information entropy. Information entropy flux and information entropy production are identified and their time-dependent properties, as well as their dependence on the parameters present in the problem, are analyzed. States of minimum information entropy production are shown to exist for appropriate parameter values. Furthermore, uncertainty and information production are transiently intensified when the population traverses the inflexion point stage of the logisticlike growth process.

We study the solutions of the Smoluchowski coagulation equation with a regularization term which removes clusters from the system when their mass exceeds a specified cutoff size, $M$. We focus primarily on collision kernels which would exhibit an instantaneous gelation transition in the absence of any regularization. Numerical simulations demonstrate that for such kernels with monodisperse initial data, the regularized gelation time decreases as $M$ increases, consistent with the expectation that the gelation time is zero in the unregularized system. This decrease appears to be a logarithmically slow function of $M$, indicating that instantaneously gelling kernels may still be justifiable as physical models despite the fact that they are highly singular in the absence of a cutoff. We also study the case when a source of monomers is introduced in the regularized system. In this case a stationary state is reached. We present a complete analytic description of this regularized stationary state for the model kernel, $K(m_1,m_2)=max{\{m_1,m_2\}}^{\nu }$, which gels instantaneously when $M\to \infty$ if $\nu >1$. The stationary cluster size distribution decays as a stretched exponential for small cluster sizes and crosses over to a power law decay with exponent $\nu$ for large cluster sizes. The total particle density in the stationary state slowly vanishes as $[(\nu -1)\log M]{}^{-1/2}$ when $M\to \infty$. The approach to the stationary state is nontrivial: Oscillations about the stationary state emerge from the interplay between the monomer injection and the cutoff, $M$, which decay very slowly when $M$ is large. A quantitative analysis of these oscillations is provided for the addition model which describes the situation in which clusters can only grow by absorbing monomers.

Models of diffusion-driven pattern formation that rely on the Turing mechanism are utilized in many areas of science. However, many such models suffer from the defect of requiring fine tuning of parameters or an unrealistic separation of scales in the diffusivities of the constituents of the system in order to predict the formation of spatial patterns. In the context of a very generic model of ecological pattern formation, we show that the inclusion of intrinsic noise in Turing models leads to the formation of “quasipatterns” that form in generic regions of parameter space and are experimentally distinguishable from standard Turing patterns. The existence of quasipatterns removes the need for unphysical fine tuning or separation of scales in the application of Turing models to real systems.

Within the scope of a thermodynamic description using the maximum entropy production principle, transitions from one nonequilibrium (kinetic) regime to another are considered. It is shown that in the case when power-law dependencies of thermodynamic flux on force are similar for two regimes, only a transition accompanied by a positive jump of thermodynamic flux is possible between them. It is found that the difference in powers of the dependencies of thermodynamic fluxes on forces results in a number of interesting nonequilibrium transitions between kinetic regimes, including the reentrant one with a negative jump of thermodynamic flux.

The ground state and the spectral structure of lower-lying excited states of a dissipative two-level system coupled to a sub-Ohmic bath ($s=1/2$) with nonzero bias have been studied using the unitary transformation method. By calculating the ground-state entanglement entropy, the ground-state average of $\langle {\sigma }_z\rangle {}_G$, and the static susceptibility of the two-level system, we explore the nature of the transition (crossover) between the delocalized and localized state of the two-level system. Furthermore, we calculate the time-dependent expectation $\langle {\sigma }_z(t)\rangle$ and the time evolution of the entanglement entropy to show that, when the system undergoes a transition (crossover) from the delocalized to the localized state, the time evolution of the two-level system changes from coherent to decoherent dynamics.

We probe the limits of nonlinear wave spreading in disordered chains which are known to localize linear waves. We particularly extend recent studies on the regimes of strong and weak chaos during subdiffusive spreading of wave packets [Europhys. Lett. 91, 30001 (2010)] and consider strong disorder, which favors Anderson localization. We probe the limit of infinite disorder strength and study Fröhlich-Spencer-Wayne models. We find that the assumption of chaotic wave packet dynamics and its impact on spreading is in accord with all studied cases. Spreading appears to be asymptotic, without any observable slowing down. We also consider chains with spatially inhomogeneous nonlinearity, which give further support to our findings and conclusions.

We study the time evolution of correlation functions, spin current, and local magnetization in an isolated spin-1$/$2 chain initially prepared in a sharp domain wall state. The results are compared with the level of spatial delocalization of the eigenstates of the system which is measured using the inverse participation ratio. Both integrable and nonintegrable regimes are considered. Nonintegrability is introduced to the integrable Hamiltonian with nearest-neighbor couplings by adding a single-site impurity field or by adding next-nearest-neighbor couplings. A monotonic correspondence between the enhancement of the level of delocalization, spin current, and magnetization dynamics occurs in the integrable domain. This correspondence is, however, lost for chaotic models with weak Ising interactions.

Using the technique of pinning coupling in chaos control, we investigate how the two-dimensional drift-wave plasma turbulence described by the Hasegawa-Mima equation can be regulated into different spatiotemporal patterns. It is shown both analytically and numerically that, depending on the pattern structure of the target, the pinning strength necessary for regulating the turbulence could have a large variation. More specifically, with the increase of the wave number of the target, the critical pinning strength is found to be increased by a power-law scaling. Moreover, in both the transition and transient process of the pinning regulation, the modes of the turbulence are found to be suppressed in a hierarchical fashion, that is, by the sequence of mode wave number. The findings give insight into the dynamics of drift-wave turbulence, as well as indicative to the design of new control techniques for real-world turbulence.

Hybrid free-surface flows past disturbances in a two-dimensional channel are identified and studied. The fluid is assumed to be inviscid and incompressible, and the flow to be steady and irrotational. The disturbances consist of a step in the bottom of the channel and a flat object lying on the free-surface (e.g., a sluice gate). A weakly nonlinear one-dimensional analysis is used to classify the possible types of solutions, and nonlinear solutions are obtained numerically by a boundary integral equation method.

Similar to the classic three-dimensional Rosensweig instability, a ferrofluid confined in a vertical Hele-Shaw cell subjected to an in-plane normal magnetic field develops a periodic array of peaked interfacial structures. We perform a weakly nonlinear analysis that is able to reproduce the morphology of such pattern formation phenomenon at lowest nonlinear order. A mode-coupling theory is applied to compare the early nonlinear evolution of the interface with static shapes obtained when relevant forces equilibrate. Our nonlinear results indicate that the time-evolving shapes tend to approach stable stationary solutions.

It is well known that in a gas-filled duct or channel along which a temperature gradient is applied, a thermal creep flow is created. Here we show that a mass and momentum flux can also be induced in a gas confined between two parallel structured surfaces at different temperatures, i.e., orthogonal to the temperature gradient. We use both analytical and numerical methods to compute the resulting fluxes. The momentum flux assumes its maximum value in the free-molecular flow regime, the (normalized) mass flux in the transition flow regime. The discovered phenomena could find applications in methods for energy-conversion and thermal pumping of gases.

In the fast-ignition scheme, relativistic electrons transport energy from the laser deposition zone to the dense part of the target where the fusion reactions can be ignited. The magnetic fields and electron collisions play an important role in the collimation or defocusing of this electron beam. Detailed description of these effects requires large-scale kinetic calculations and is limited to short time intervals. In this paper, a reduced kinetic model of fast electron transport coupled to the radiation hydrodynamic code is presented. It opens the possibility to carry on hybrid simulations in a time scale of tens of picoseconds or more. It is shown with this code that plasma-generated magnetic fields induced by noncollinear temperature and density gradients may strongly modify electron transport in a time scale of a few picoseconds. These fields tend to defocus the electron beam, reducing the coupling efficiency to the target. This effect, that was not seen before in shorter time simulations, has to be accounted for in any ignition design using electrons as a driver.

We have performed a dynamic light-scattering (DLS) investigation of the effect of a water-soluble polymer, polyethylene glycol (PEG), on the bending elastic modulus κ of surfactant membranes. The polymer, in concentrations ranging from 0 to 8 $\mathrm{g}/$L (0 to 0.4 mM), was incorporated into the solvent of sponge phases of the sodium dodecyl sulfate (SDS)-hexanol-brine system. PEG adsorbs into the SDS membranes. The correlation functions of the polymer-doped sponge phases displayed a stretched-exponential decay, appropriately described by the Zilman-Granek (Z-G) theory for fluctuating membranes. The dynamics of the surfactant bilayers was slowed down by the addition of the polymer: Increasing PEG concentrations increase the DLS relaxation times. From the Z-G model we extracted the membrane-bending elastic modulus, as a function of polymer concentration, $C_{\mathrm{PEG}}=\kappa$ increases with $C_{\mathrm{PEG}}$, a behavior opposite to that expected from available models for the interaction between fluid membranes and adsorbing polymers. Our results suggest that the polymer penetrates to some extent the surfactant bilayers.

We consider here a classical model, consisting of $D_{2h}$ symmetric particles, whose centers of mass are associated with a three-dimensional simple-cubic lattice; the pair potential is isotropic in orientation space, and restricted to nearest neighbors. Two orthonormal triads define orientations of a pair of interacting particles; the simplest potential models proposed in the literature can be written as a linear combination involving the squares of the scalar products between corresponding unit vectors only, thus depending on three parameters, and making the interaction model rather versatile. A coupling constant with negative sign tends to keep the two interacting unit vectors parallel to each other, whereas a positive sign tends to keep them mutually orthogonal (antinematic coupling). We address here a special, extreme case of the above family, involving only antinematic couplings: more precisely, three antinematic terms whose coefficients are set to a common positive value (hence the name PPP model). The model under investigation produces a doubly degenerate pair ground state; the nearest-neighbor range of the interaction and the bipartite character of the lattice can propagate the pair ground state and increase the overall degeneracy, but without producing frustration. The model was investigated by a simplified molecular field treatment as well as by Monte Carlo simulation, whose results suggested a second-order transition to a low-temperature biaxially ordered phase; ground-state configurations producing orientational order have been selected by thermal fluctuations. The molecular field treatment also predicted a continuous transition, and was found to overestimate the transition temperature by a factor 2.

The biaxial nematic phase is generally taken, either explicitly or implicitly, to have $D_{2h}$ point group symmetry. However, it is possible for the biaxial phase to have a lower symmetry depending on that of its constituent molecules. Here we develop a molecular field theory for a nematogen composed of $C_{2h}$ molecules in terms of the nine independent second rank orientational order parameters defining the $C_{2h}$ biaxial nematic. In addition, there is a rank one order parameter constructed from two pseudovectors which is only nonzero in the $C_{2h}$ phase. The theory is simplified by removing all but the three dominant order parameters. The predicted phase behavior is found to be rich with three possible biaxial nematic phases and with the transitions involving a biaxial nematic phase exhibiting tricritical points.

An information-theoretic framework known as integrated information theory (IIT) has been introduced recently for the study of the emergence of consciousness in the brain [D. Balduzzi and G. Tononi, PLoS Comput. Biol. 4, e1000091 (2008)]. IIT purports that this phenomenon is to be equated with the generation of information by the brain surpassing the information that the brain’s constituents already generate independently of one another. IIT is not fully plausible in its modeling assumptions nor is it testable due to severe combinatorial growth embedded in its key definitions. Here we introduce an alternative to IIT which, while inspired in similar information-theoretic principles, seeks to address some of IIT’s shortcomings to some extent. Our alternative framework uses the same network-algorithmic cortical model we introduced earlier [A. Nathan and V. C. Barbosa, Phys. Rev. E 81, 021916 (2010)] and, to allow for somewhat improved testability relative to IIT, adopts the well-known notions of information gain and total correlation applied to a set of variables representing the reachability of neurons by messages in the model’s dynamics. We argue that these two quantities relate to each other in such a way that can be used to quantify the system’s efficiency in generating information beyond that which does not depend on integration. We give computational results on our cortical model and on variants thereof that are either structurally random in the sense of an Erdős-Rényi random directed graph or structurally deterministic. We have found that our cortical model stands out with respect to the others in the sense that many of its instances are capable of integrating information more efficiently than most of those others’ instances.

We derive the work performed in the Szilard engine (SZE) by using the dissipative work formula of nonequilibrium thermodynamics developed by Kawai et al. [Phys. Rev. Lett. 98, 080602 (2007)]. The work is described as the difference of probability distributions of measurement outcomes of the time-forward and the time-backward process.

Spatiotemporal chaos and turbulence are universal concepts for the explanation of irregular behavior in various physical systems. Recently, a remarkable new phenomenon, called “chimera states,” has been described, where in a spatially homogeneous system, regions of irregular incoherent motion coexist with regular synchronized motion, forming a self-organized pattern in a population of nonlocally coupled oscillators. Whereas most previous studies of chimera states focused their attention on the case of large numbers of oscillators employing the thermodynamic limit of infinitely many oscillators, here we investigate the properties of chimera states in populations of finite size using concepts from deterministic chaos. Our calculations of the Lyapunov spectrum show that the incoherent motion, which is described in the thermodynamic limit as a stationary behavior, in finite size systems appears as weak spatially extensive chaos. Moreover, for sufficiently small populations the chimera states reveal their transient nature: after a certain time span we observe a sudden collapse of the chimera pattern and a transition to the completely coherent state. Our results indicate that chimera states can be considered as chaotic transients, showing the same properties as type-II supertransients in coupled map lattices.

We obtain the degree distribution for a class of growing network models on flat and curved spaces. These models evolve by preferential attachment weighted by a function of the distance between nodes. The degree distribution of these models is similar to that of the fitness model of Bianconi and Barabási, with a fitness distribution dependent on the metric and the density of nodes. We show that curvature singularities in these spaces can give rise to asymptotic Bose-Einstein condensation, but transient condensation can be observed also in smooth hyperbolic spaces with strong curvature. We provide numerical results for spaces of constant curvature (sphere, flat, and hyperbolic space) and we discuss the conditions for the breakdown of this approach and the critical points of the transition to distance-dominated attachment. Finally, we discuss the distribution of link lengths.

A conserved noise restricted solid-on-solid model on both a Sierpinski gasket substrate and a checkerboard fractal substrate is studied. The interface width $W$ grows as $t^{\beta }$ at early time $t$ and becomes saturated at $L^{\alpha }$ for $t\gg L^z$, where $L$ is the system size. We obtain $\beta \approx 0.0788$, $\alpha \approx 0.377$ for a Sierpinski gasket, and $\beta \approx 0.100$, $\alpha \approx 0.516$ for a checkerboard fractal. The dynamic exponent $z\approx 4.79$ for a Sierpinski gasket and $z\approx 5.16$ for a checkerboard fractal are obtained by the relation $z=\alpha /\beta$. They satisfy the scaling relations $4\alpha +2d_f=z$ and $z=2z_{\mathrm{rw}}$, where $z_{\mathrm{rw}}$ is the random-walk exponent of the fractal substrate. A fractional Langevin equation is introduced to describe the model.