Three-dimensional hydrodynamic turbulence is investigated under the assumptions of homogeneity and weak axisymmetry. Following the kinematics developed by E. Lindborg [J. Fluid Mech. 302, 179 (1995)] we rewrite the von Kármán–Howarth equation in terms of measurable correlations and derive the exact relation associated with the flux conservation. This relation is then analyzed in the particular case of turbulence subject to solid-body rotation. We make the ansatz that the development of anisotropy implies an algebraic relation between the axial and the radial components of the separation vector $\mathbf{r}$ and we derive an exact vectorial law which is parametrized by the intensity of anisotropy. A simple dimensional analysis allows us to fix this parameter and find a unique expression.

The suprachiasmatic nucleus (SCN) pacemaker shows a free-running period ranging from 20 to 28 h for different species, which was usually explained from the angle of coupling strength. Based on the assumption of nonidentical coupling strengths in SCN, we find an alternative mechanism that the diversity of free-running period can be also caused by the distribution of coupling strengths. The free-running period is proportional to the average coupling strength and inverse proportional to the dispersion of couplings. Moreover, we present an analytic phase model to confirm our finding, which shows a solid foundation of our finding and opens a window to study the collective behaviors of SCN oscillators.

Search problems at various scales involve a searcher, be it a molecule before reaction or a foraging animal, which performs an intermittent motion. Here we analyze a generic model based on such type of intermittent motion, in which the searcher alternates phases of slow motion allowing detection and phases of fast motion without detection. We present full and systematic results for different modeling hypotheses of the detection mechanism in space in one, two, and three dimensions. Our study completes and extends the results of our recent letter [Loverdo et al., Nat. Phys. 4, 134 (2008)] and gives the necessary calculation details. In addition, another modeling of the detection case is presented. We show that the mean target detection time can be minimized as a function of the mean duration of each phase in one, two, and three dimensions. Importantly, this optimal strategy does not depend on the details of the modeling of the slow detection phase, which shows the robustness of our results. We believe that this systematic analysis can be used as a basis to study quantitatively various real search problems involving intermittent behaviors.

The effect of noise is studied in one-dimensional maps undergoing transcritical, tangent, and pitchfork bifurcations. The attractors of the noiseless map become metastable states in the presence of noise. In the weak-noise limit, a symplectic two-dimensional map is associated with the original one-dimensional map. The consequences of their noninvertibility on the phase-space structures are discussed. Heteroclinic orbits are identified which play a key role in the determination of the escape rates from the metastable states. Near bifurcations, the critical slowing down justifies the use of a continuous-time approximation replacing maps by flows, which allows the analytic calculation of the escape rates. This method provides the universal scaling behavior of the escape rates at the bifurcations.

The paper presents a multidimensional model for nonlinear Markovian random walks that generalizes the one we developed previously [I. Lubashevsky, R. Friedrich, and A. Heuer, Phys. Rev. E 79, 011110 (2009)] in order to describe the Lévy-type stochastic processes in terms of continuous trajectories of walker motion. This approach may open a way to treat Lévy flights or Lévy random walks in inhomogeneous media or systems with boundaries in the future. The proposed model assumes the velocity of a wandering particle to be affected by a linear friction and a nonlinear Langevin force whose intensity is proportional to the magnitude of the velocity for its large values. Based on the singular perturbation technique, the corresponding Fokker-Planck equation is analyzed and the relationship between the system parameters and the Lévy exponent is found. Following actually the previous paper we demonstrate also that anomalously long displacements of the wandering particle are caused by extremely large fluctuations in the particle velocity whose duration is determined by the system parameters rather than the duration of the observation interval. In this way we overcome the problem of ascribing to Lévy random-walk non-Markov properties.

According to the conventional approach neural ensembles are modeled with fixed ionic concentrations in the extracellular environment. However, in some cases the extracellular concentration of potassium ions cannot be regarded as constant. Such cases represent specific chemical pathway for neurons to interact and can influence strongly the behavior of single neurons and of large ensembles. The released chemical agent diffuses in the external medium and lowers thresholds of individual excitable units. We address this problem by studying simplified excitable units given by a modified FitzHugh-Nagumo dynamics. In our model the neurons interact only chemically via the released and diffusing potassium in the surrounding nonactive medium and are permanently affected by noise. First, we study the dynamics of a single excitable unit embedded in the extracellular matter. That leads to a number of noise-induced effects such as self-modulation of firing rate in an individual neuron. After the consideration of two coupled neurons we consider the spatially extended situation. By holding parameters of the neuron fixed, various patterns appear ranging from spirals and traveling waves to oscillons and inverted structures depending on the parameters of the medium.

Protein aggregation in the form of amyloid fibrils has important biological and technological implications. Although the self-assembly process is highly efficient, aggregates not in the fibrillar form would also occur and it is important to include these disordered species when discussing the thermodynamic equilibrium behavior of the system. Here, we initiate such a task by considering a mixture of monomeric proteins and the corresponding aggregates in the disordered form (micelles) and in the fibrillar form (amyloid fibrils). Starting with a model on the respective binding free energies for these species, we calculate their concentrations at thermal equilibrium. We then discuss how the incorporation of the disordered structure furthers our understanding on the various amyloid promoting factors observed empirically, and on the kinetics of fibrilization.

We calculate the optimality score of a doublet precursor to the canonical genetic code with respect to mitigating the effects of point mutations and compare our results to corresponding ones for the canonical genetic code. We find that the proposed precursor is much less optimal than that of the canonical code. Our results render unlikely the notion that the doublet precursor was an intermediate state in the evolution of the canonical genetic code. These findings support the notion that code optimality reflects evolutionary dynamics, and that if such a doublet code originally had a biochemical significance, it arose before the emergence of translation.

Highly resolved profiles of the mean velocity in turbulent Rayleigh-Bénard convection in air are presented and discussed. The present work extends our recently performed experiments at constant aspect ratio [Phys. Rev. Lett. 99, 234504 (2007)] to variable aspect ratios. The experiments cover a range of Rayleigh numbers ${10}^9<\text{Ra}<{10}^{12}$ and aspect ratios $1.13<\Gamma <11.3$ whereas the Prandtl number is fixed at $\text{Pr}=0.7$. The major finding of the present work is that the profiles of the mean horizontal velocity and its fluctuations are virtually invariant against the variation in Ra or $\Gamma$ if the wall distance is scaled by the displacement thickness of the boundary layer. Furthermore we have studied typical length scales of the boundary layer and their scaling with Ra and $\Gamma$. Regarding a potential transition of the heat transport toward the ultimate regime we found that the boundary layer Reynolds number remains below ${\text{Re}}_{\delta }=250$ which is significantly lower than the predicted limit.

A fully relativistic treatment of Bernstein waves in an electron-positron pair plasma has remained too formidable a task, owing to the very complex nature of the problem. In this paper, we perform contour integration of the dielectric-response function and numerically compute the dispersion curves for a uniform magnetized relativistic electron-positron pair plasma. The behavior of the dispersion solution for several cases with different plasma temperatures is highlighted. In particular, we find two wave modes that exist only for large wavelengths and frequencies similar to the cyclotron frequency in a moderately relativistic pair plasma. The results presented here have important implications for the study of those objects where a hot magnetized electron-positron plasma plays a fundamental role in generating the observed radiation.

A magnetic deflection-energy analyzer and Faraday trap diagnostic have been used to make measurements of divergent deuterium anion flow in the inertial electrostatic confinement experiment at the University of Wisconsin–Madison (UW-IEC) [J. F. Santarius, G. L. Kulcinski, R. P. Ashley, D. R. Boris, B. B. Cipiti, S. K. Murali, G. R. Piefer, R. F. Radel, I. E. Radel, and A. L. Wehmeyer, Fusion Sci. Technol. 47, 1238 (2005)], a device to confine high-energy light ions in a spherically symmetric electrostatic potential well. Deuterium anion current densities as high as $8.5\mu \text{A}/{\text{cm}}^2$ have been measured at the wall of the UW-IEC device, 40 cm from the surface of the device cathode with a detector assembly of admittance area $0.7{\text{cm}}^2$. Energy spectra obtained using a magnetic deflection-energy analyzer diagnostic indicate the presence of ${\text{D}}_2^{-}$, and ${\text{D}}^{-}$ ions produced through thermal electron attachment near the device cathode, as well as ${\text{D}}^{-}$ ions produced via charge-transfer processes between the anode and cathode of the device.

The self-induced gap solitons in nonlinear magnetic metamaterials is investigated. It is shown that the self-induced gap solitons may exist due to the interaction of the discreteness and nonlinearity. The evolution of these localized structures is studied in the phase plane and analytical and numerical expressions are obtained.

We formulate a single-cluster Monte Carlo algorithm for the simulation of the random-cluster model. This algorithm is a generalization of the Wolff single-cluster method for the $q$-state Potts model to noninteger values $q>1$. Its results for static quantities are in a satisfactory agreement with those of the existing Swendsen-Wang-Chayes-Machta (SWCM) algorithm, which involves a full-cluster decomposition of random-cluster configurations. We explore the critical dynamics of this algorithm for several two-dimensional Potts and random-cluster models. For integer $q$, the single-cluster algorithm can be reduced to the Wolff algorithm, for which case we find that the autocorrelation functions decay almost purely exponentially, with dynamic exponents $z_{\text{exp}}=0.07$ (1), 0.521 (7), and 1.007 (9) for $q=2$, 3, and 4, respectively. For noninteger $q$, the dynamical behavior of the single-cluster algorithm appears to be very dissimilar to that of the SWCM algorithm. For large critical systems, the autocorrelation function displays a range of power-law behavior as a function of time. The dynamic exponents are relatively large. We provide an explanation for this peculiar dynamic behavior.

We show and characterize numerically moving breathing pulses in the one-dimensional complex cubic-quintic Ginzburg-Landau equation. This class of stable moving breathing pulses has not been described before for this prototype envelope equation as it arises near the weakly hysteretic onset of traveling waves.

In recent years there are several reports showing that bent-core mesogenic molecules are able to form biaxial nematic phase in which molecular rotation around the long molecular axis is strongly hindered. The x-ray pattern with azimuthally split signals at low angle region of diffraction is usually given as evidence for the biaxial nematic phase. We show experimentally and theoretically that such x-ray pattern is due to the local smectic-$C$ fluctuations (“cybotactic” groups) in the uniaxial nematic phase.

A combination of analytical calculations and Monte Carlo simulations is used to find the ground state structures in monodisperse ferrofluid monolayers. Taking into account the magnetic dipole-dipole interaction between all particles in the system we observe different topological structures that are likely to exist at low temperatures. The most energetically favored structures we find are rings, embedded rings, and rings side by side, and we are able to derive analytical expressions for the total energy of these structures. A detailed analysis of embedded rings and rings side by side shows that the interring interactions are negligible. We furthermore find that a single ideal ring is the ground state structure for a ferrofluid monolayer. We compared our theoretical predictions to the results of simulated annealing data and found them to be in excellent agreement.

Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length $N_e$ which operate on results for a single chain length $N$ are shown to produce systematic $O\left(1/N\right)$ errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the $O\left(1/N\right)$ errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive, and test new estimators which eliminate these systematic errors using information obtainable from the variation in entanglement characteristics with chain length. The new estimators produce accurate results for $N_e$ from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.

In multicellular organisms, epithelial cells form layers separating compartments responsible for different physiological functions. At the early stage of epithelial layer formation, each cell of an aggregate defines an inner and an outer side by breaking the symmetry of its initial state, in a process known as epithelial polarization. By integrating recent biochemical and biophysical data with stochastic simulations of the relevant reaction-diffusion system, we provide evidence that epithelial cell polarization is a chemical phase-separation process induced by a local bistability in the signaling network at the level of the cell membrane. The early symmetry breaking event triggering phase separation is induced by adhesion-dependent mechanical forces localized in the point of convergence of cell surfaces when a threshold number of confluent cells is reached. The generality of the emerging phase-separation scenario is likely common to many processes of cell polarity formation.

In order to survive, reproduce, and (in multicellular organisms) differentiate, cells must control the concentrations of the myriad different proteins that are encoded in the genome. The precision of this control is limited by the inevitable randomness of individual molecular events. Here we explore how cells can maximize their control power in the presence of these physical limits; formally, we solve the theoretical problem of maximizing the information transferred from inputs to outputs when the number of available molecules is held fixed. We start with the simplest version of the problem, in which a single transcription factor protein controls the readout of one or more genes by binding to DNA. We further simplify by assuming that this regulatory network operates in steady state, that the noise is small relative to the available dynamic range, and that the target genes do not interact. Even in this simple limit, we find a surprisingly rich set of optimal solutions. Importantly, for each locally optimal regulatory network, all parameters are determined once the physical constraints on the number of available molecules are specified. Although we are solving an oversimplified version of the problem facing real cells, we see parallels between the structure of these optimal solutions and the behavior of actual genetic regulatory networks. Subsequent papers will discuss more complete versions of the problem.