In a recent paper [S. El Boustani, P. R. Buenzli, and P. A. Martin, Phys. Rev. E 73, 036113 (2006)] about quantum charges in equilibrium with radiation, among other things the asymptotic form of the electric-field correlation has been obtained by a microscopic calculation. It has been found that this correlation has a long-range algebraic decay of the form $1∕r^3$ (except in the classical limit). The macroscopic approach, in the Course of Theoretical Physics of Landau and Lifshitz, gives no such decay. In this Brief Report we revisit and complete the macroscopic approach of Landau and Lifshitz and suggest that, perhaps, the use of a classical electromagnetic field by El Boustani et al. was not justified.

Mushroom billiards have the remarkable property to show one or more clear cut integrable islands in one or several chaotic seas, without any fractal boundaries. The islands correspond to orbits confined to the hats of the mushrooms, which they share with the chaotic orbits. It is thus interesting to ask how long a chaotic orbit will remain in the hat before returning to the stem. This question is equivalent to the inquiry about delay times for scattering from the hat of the mushroom into an opening where the stem should be. For fixed angular momentum we find that no more than three different delay times are possible. This induces striking nonperiodic structures in the delay times that may be of importance for mesoscopic devices and should be accessible to microwave experiments.

We extend a previous analysis of spatial correlation functions for classical electromagnetic vector fields near a perfectly conducting boundary [Arnaut, Phys. Rev. E, 73, 036604 (2006)] to the case of an isotropic semi-infinite medium with planar interface and characterized by a first-order impedance boundary condition. The analytical results are illustrated with calculations for the case of point separations in the direction perpendicular to the interface. For the incident plus reflected field, the dependence of the complex-valued and inhomogeneous spatial correlation function on the permittivity, permeability, and conductivity of the medium is determined. For the refracted field, the spatial correlation is again complex valued but homogeneous and highly sensitive to the value of the refractive index. Based on the derived dependencies, nonlocal measurement methods for precision characterization of electromagnetic material properties are suggested. The influence of the directionality of incidence for electromagnetic beams is investigated. Narrowing the beam width results in a slower decrease of the amplitude of the correlation function as a function of point separation. Previously obtained asymptotic results for statistically homogeneous random free fields are retrieved as special cases.

A lattice Boltzman model for the simulation of binary mixtures is presented. Contrary to previous models, the present formulation is able to simulate mixtures with different Schmidt numbers and arbitrary molecular mass ratio of the components. In the hydrodynamic limit, the Navier-Stokes and the Stefan-Maxwell binary diffusion equations are recovered. The model is used for the simulation of binary diffusion and mixing layers. The results are found to be in good agreement with a derived similarity solution and with the predictions of a transient spectral element code.

We present an approximation scheme to solve the nonperturbative renormalization group equations and obtain the full momentum dependence of the $n$-point functions. It is based on an iterative procedure where, in a first step, an initial ansatz for the $n$-point functions is constructed by solving approximate flow equations derived from well motivated approximations. These approximations exploit the derivative expansion and the decoupling of high momentum modes. The method is applied to the $\mathrm{O}\left(N\right)$ model. In leading order, the self-energy is already accurate both in the perturbative and the scaling regimes. A stringent test is provided by the calculation of the shift $\mathrm{\Delta }{T}_c$ in the transition temperature of the weakly repulsive Bose gas, a quantity which is particularly sensitive to all momentum scales. The leading order result is in agreement with lattice calculations, albeit with a theoretical uncertainty of about 25%.

In a companion paper [Blaizot et al., Phys. Rev. E 74, 051116 (2006)], we have presented an approximation scheme to solve the nonperturbative renormalization group equations that allows the calculation of the $n$-point functions for arbitrary values of the external momenta. The method was applied in its leading order to the calculation of the self-energy of the $\mathrm{O}\left(N\right)$ model in the critical regime. The purpose of the present paper is to extend this study to the next-to-leading order of the approximation scheme. This involves the calculation of the four-point function at leading order, where interesting features arise, related to the occurrence of exceptional configurations of momenta in the flow equations. These require a special treatment, inviting us to improve the straightforward iteration scheme that we originally proposed. The final result for the self-energy at next-to-leading order exhibits a remarkable improvement as compared to the leading order calculation. This is demonstrated by the calculation of the shift $\mathrm{\Delta }{T}_c$, caused by weak interactions, in the temperature of Bose-Einstein condensation. This quantity depends on the self-energy at all momentum scales and can be used as a benchmark of the approximation. The improved next-to-leading order calculation of the self-energy presented in this paper leads to excellent agreement with lattice data and is within 4% of the exact large $N$ result.

In this paper, we use quantum-mechanical formalism to describe the time evolution of a classical dynamical system with fluctuating parameters. By appropriate choice of “interaction picture representation,” and the use of the Baker-Campbell-Hausdorff formula in the chronological time ordered evolution, we have obtained analytical expressions for the Lyapunov exponent of the energy evolution of the dynamical system. Our approach proved to be very powerful in handling either stochastic or highly correlated processes. The approach lends itself to generalizations for use in a wide field of applications.

The anomalous diffusion of a single file of Brownian particles moving on a circle at a given temperature is characterized in terms of nearest-neighbor collisions. The time and the distance a particle diffuses (normally) between two successive collisions are computed numerically; their means, distributions, and correlation functions are determined for different values of the file parameters and reproduced analytically by means of simple phenomenological arguments. Most notably, the jump autocorrelation functions develop slow power-law tails. The ensuing impact representation of the single file dynamics suggests an alternate description of the single file diffusion as a geometrically constrained fluctuation mechanism.

For sufficiently slow rates of strain, flowing foam can exhibit inhomogeneous flows. The nature of these flows is an area of active study in both two-dimensional model foams and three dimensional foam. Recent work in three-dimensional foam has identified three distinct regimes of flow [S. Rodts, J. C. Baudez, and P. Coussot, Europhys. Lett. 69, 636 (2005)]. Two of these regimes are identified with continuum behavior (full flow and shear banding), and the third regime is identified as a discrete regime exhibiting extreme localization. In this paper, the discrete regime is studied in more detail using a model two-dimensional foam: a bubble raft. We characterize the behavior of the bubble raft subjected to a constant rate of strain as a function of time, system size, and applied rate of strain. We observe localized flow that is consistent with the coexistence of a power-law fluid with rigid-body rotation. As a function of applied rate of strain, there is a transition from a continuum description of the flow to discrete flow when the thickness of the flow region is approximately ten bubbles. This occurs at an applied rotation rate of approximately $0.07{\mathrm{s}}^{-1}$.

We consider a lattice polymer model (random walk), in which the walk is allowed to visit lattice bonds at most twice. Such a model might have some relevance to describe statistical properties of RNA molecules. In order to mimic base pairing, we assign an attractive energy term to each doubly visited bond, and a further contribution to each pair of consecutive doubly visited bonds. The latter term is expected to mimic the stacking effect, whereas no effect of sequence, that is, of chemical specificity, is taken into account. The phase diagram is worked out exactly on a Bethe lattice, in a grand-canonical formulation. In the single molecule limit, the system undergoes two different phase transitions upon decreasing temperature: a $\Theta$-like collapse from a swollen “coil” state to a “molten” state, with a low fraction of doubly visited bonds, and subsequently to a “paired” state, with empty or doubly visited bonds only. The stacking effect drives the latter transition from second to first order.

Explicit formulas for the steady-state distribution of species in two interconnected communities of arbitrary sizes are derived in the framework of Hubbell’s neutral model of biodiversity. Migrations of seeds from both communities as well as mutations in both of them are taken into account. These results generalize those previously obtained for the “island-continent” model and they allow an analysis of the influence of the ratio of the sizes of the two communities on the dominance/diversity equilibrium. Exact expressions for species abundance distributions are deduced from a master equation for the joint probability distribution of species in the two communities. Moreover, an approximate self-consistent solution is derived. It corresponds to a generalization of previous results and it proves to be accurate over a broad range of parameters. The dynamical correlations between the abundances of a species in both communities are also discussed.

The Penna model of evolutionary ageing is an influential model of mutation accumulation and selection, where an individual’s genomic information is represented by a binary bit string. One key parameter of the model is the death threshold, $T$, the number of diseases any particular individual is able to endure. We show, by combined computer simulations and analytical formulation, that certain anomalies emerge in the asexual Penna model for $T>1$, which may lead to the so-called Eve effect. We characterize these anomalies and their associated demographic distributions. We argue that this anomaly is similar in nature to the well known first-passage problem.

The effect of rotation on turbulent convective flow between parallel plates has been assessed with direct numerical simulations. With increasing rotation-rate an interesting transition is observed in the vertical-velocity skewness. This transition indicates a localization of motion directed away from the wall and correlates well with changes observed in the heat flux, as well as in the thermal and viscous boundary layer thicknesses. The formation of localized intense vortical structures provides for intensified vertical heat transport through Ekman pumping. At higher rotation-rates this is counteracted by the inhibition of vertical motion by rotation as expressed in the geostrophic thermal-wind balance.

We use the “isoconfigurational ensemble” [Phys. Rev. Lett. 93, 135701 (2004)] to analyze both dynamical and structural properties in simulations of a glass-forming molecular liquid. We show that spatially correlated clusters of low-potential-energy molecules are observable on the time scale of structural relaxation, despite the absence of spatial correlations of potential energy in the instantaneous structure of the system. We find that these structural heterogeneities correlate with dynamical heterogeneities in the form of clusters of low molecular mobility.

Nonmagnetic particles in suspension in a ferrofluid act as magnetic holes when an external magnetic field is exerted: They acquire an effective dipolar moment opposing the surrounding one, which induces dipolar magnetic interactions. For a large enough imposed field and particle size, the induced interactions dominate the thermal forces, dipolar chains form. At equilibrium, these chains fluctuate under the effect of brownian noise. When the imposed magnetic field is suddenly decreased, these chains roughen dynamically. We study the time and size scaling of these fluctuations and roughening, and the relationships between the equilibrium and out of equilibrium behavior. We compare the experimental data both to Brownian dynamics simulations, and to a simple theory of semiflexible polymer chains, a generalization of the Rouse model. The scaling behavior of the experiments agree with the predictions of both theory and simulations over 5 orders of magnitudes. The roughening follows three successive regimes: The root mean square width of the chain initially evolves as $W\sim t^{1∕2}$, then it enters a subdiffusive regime where $W\sim t^{1∕4}$ and eventually it saturates to a level $W\sim N$, where $N$ is the number of particles in the chain. The exact prefactors as a function of the applied field, particle diameter, and temperature are also derived analytically. We also show that this phenomenon can be described equivalently as a non-Markovian diffusion process for a particle in an environment with memory effects. Within this framework, our system is shown to confirm the predictions of theories for anomalous diffusion in systems with memory.

One of the major challenges in electrochemistry is to properly account for polarization of the electrical double layer that forms at an electrode-electrolyte interface, especially when interpreting the impedance spectra of biological molecules, electrolytes, or live cell suspensions. This double layer, which affects the measured impedance, is also known as the electrode polarization effect. Various methods of correcting for its effects on impedance data have been reported, including varying the spacing between electrodes, four-electrode techniques, and electrodeless methods. Here we discuss the use of a constant phase element in a recently proposed circuit model, which can be thought of as a measure of the fractal nature of the interface. We also report on the conductivity spectra of several saline solutions over the frequency range $1\mathrm{Hz}–1\mathrm{MHz}$, in which we observe Debye-like relaxation behavior that changes with ion concentration and type. Good agreement is obtained with an alternative model that treats the cations and anions as overdamped oscillators in harmonic restoring potentials.

Using wide-line deuterium NMR, the effects of pressure on saturated-chain orientational order and gel–to–liquid-crystal phase transition temperature were observed in bilayers of 16:0-18:1 PC-$d_{31}$ (POPC-$d_{31}$) and 16:0-18:2 PC-$d_{31}$ (PLPC-$d_{31}$). Spectra were recorded for a range of pressures at selected temperatures and for a range of temperatures at selected pressures up to $193\mathrm{MPa}$. For 16:0-18:1 PC-$d_{31}$, the main transition temperature increased by $\sim 0.18\mathrm{K}∕\mathrm{MPa}$, a rate that is similar to what is found for bilayers of disaturated PC’s. For 16:0-18:2 PC-$d_{31}$, the increase in transition temperature with pressure was slightly smaller at $\sim 0.13\mathrm{K}∕\mathrm{MPa}$. To investigate the isothermal response of chain orientational order to pressure, spectra for each lipid were obtained for three pressures (ambient, $55\mathrm{MPa}$, and $110\mathrm{MPa}$) near room temperature $(\sim 25°\mathrm{C})$ and for three pressures (ambient, $110\mathrm{MPa}$, and $193\mathrm{MPa}$) at higher temperature $(\sim 40°\mathrm{C})$. These temperatures were chosen such that the difference between the higher observation temperature and the main transition of 16:0-18:1 PC-$d_{31}$ would be similar to the difference between the lower observation temperature and the main transition of 16:0-18:2 PC-$d_{31}$. Application of a given pressure was found to raise the orientational order for all methylene groups on the saturated chain of a particular lipid by roughly similar amounts. For comparable pressure differences, the pressure-induced ordering of the 16:0-18:1 PC-$d_{31}$ saturated chain at $\sim 40°\mathrm{C}$ was greater than that of the corresponding chain in 16:0-18:2 PC-$d_{31}$ at $\sim 25°\mathrm{C}$. These observations suggest that increasing levels of chain unsaturation may reduce the sensitivity of bilayer order to variations in pressure at corresponding temperatures relative to their ambient pressure transitions.

We address the problem of controlling the energy flow in lattice systems: we investigate, in an analytical approach, the properties of the heat conductivity of the harmonic crystal with self-consistent stochastic reservoirs, a single model with normal conductivity. For the case of weak interparticle interaction, in a perturbative analysis, we obtain an expression for the thermal conductivity and show how to decrease and/or increase the heat current inside the system by changing the masses of the particles and/or the on-site potentials. These results may be useful in the construction of devices controlling the heat conduction.

Through the last years, different strategies to enhance synchronization in complex networks have been proposed. In this work, we show that synchronization of nonidentical dynamical units that are attractively coupled in a small-world network is strongly improved by just making phase-repulsive a tiny fraction of the couplings. By a purely topological analysis that does not depend on the dynamical model, we link the emerging dynamical behavior with the structural properties of the sparsely coupled repulsive network.

We describe the evolution of a bistable chemical reaction in a closed two-dimensional chaotic laminar flow, from a localized initial disturbance. When the fluid mixing is sufficiently slow, the disturbance may spread and eventually occupy the entire fluid domain. By contrast, rapid mixing tends to dilute the initial state and so extinguish the disturbance. Such a dichotomy is well known. However, we report here a hitherto apparently unremarked intermediate case, a persistent highly localized disturbance. Such a localized state arises when the Damköhler number is great enough to sustain a “hot spot,” but not so great as to lead to global spread. We show that such a disturbance is located in the neighborhood of an unstable periodic orbit of the flow, and we describe some limited aspects of its behavior using a reduced, lamellar model.