FtsZ is a bacterial protein that forms filaments that play an essential role in midcell constriction during the process of cell division. The shape of individual filaments of different lengths imaged with atomic force microscopy was modeled considering the protein monomers as beads in a chain and a few parameters to represent their effective interactions. The flexural rigidity and persistence length of the filaments were estimated. This latter value was comparable to the filament length, implying that these biological polymers are halfway between the perfectly stiff linear aggregate whose shapes are fully controlled by the angle between the monomers and highly flexible polymers whose shapes follow a random walk model. The lateral interactions between adjacent filaments, also estimated in the modeling, were found to play an essential role in determining the final shape and kinetics of the coiled structures found in longer polymers. The estimated parameters were used to model the behavior of the polymers also on a cylindrical surface. This analysis points to the formation of helical structures that suggest a mechanism for force generation and amplification through the development of FtsZ spirals at the midcell division point.

In this paper, we present a stochastic model for the mixed-feedback loop (MFL), a motif found in integrated cellular networks of transcription regulation and protein-protein interaction. Previous bifurcation analysis indicates that this motif can serve as a bistable switch or a clock. We investigate how extrinsic and intrinsic noise affects its dynamic behaviors systematically. We find that this motif can exploit noise to enrich its dynamical performance. When the MFL is in the bistable region, under fluctuation of extrinsic noise, the MFL system can switch from one steady state to the other and meanwhile one protein’s production is amplified for more than three orders of magnitude. Further, from an engineering perspective, this noise-based switch and amplifier for gene expression is very easy to control. Without extrinsic noise, spontaneous transition between states occurs as the consequence of intrinsic noise. Such a switch is controlled by the parameters and system size. On the other hand, intrinsic noise can induce sustained stochastic oscillation when the corresponding deterministic system does not oscillate. Such stochastic oscillation shows the best performance at an optimal noise level, indicating the occurrence of intrinsic noise stochastic resonance which can contribute to the robustness of this oscillator. When considering the effects of extrinsic noise near bifurcation points, a similar phenomenon of extrinsic noise stochastic resonance is unveiled.

We derive exact asymptotic results for a stochastic queueing model in which tasks are executed according to a continuous-valued priority. The distribution $P\left(\tau \right)$ of the waiting times $\tau$ of executed tasks for this model is shown to behave asymptotically as a power law, $P\left(\tau \right)\sim {\tau }^{-3∕2}$, when the average rates of task arrival $\lambda$ and execution $\mu$ satisfy $\mu \le \lambda$ (as was earlier noted empirically). For $\mu >\lambda$, $P\left(\tau \right)\sim {\tau }^{-5∕2}\exp [-(\sqrt{\mu }-\sqrt{\lambda }{)}^2\tau ]$.

Forest-fire waiting times, defined as the time between successive fires above a certain size in a given region, are obtained for Italy. The probability densities of the waiting times are found to verify a scaling law, despite that fact that the distribution of fire sizes is not a power law. The meaning of such behavior in terms of the possible self-similarity of the process in a nonstationary system is discussed. We find that the scaling law arises as a consequence of the stationarity of fire sizes and the existence of a nontrivial “instantaneous” scaling law, sustained by the correlations of the process; as a consequence, the nonstationary Poisson process model does not account for all the complexity of the structure of fire occurrence.

Chaos control methods for the Ginzburg-Landau equation are presented using homogeneously, inhomogeneously, and locally applied multiple delayed feedback signals. In particular, it is shown that a small number of control cells is sufficient for stabilizing plane waves or for trapping spiral waves, and that successful control is closely connected to synchronization of the dynamics in regions close to the control cells.

This paper provides a temporal model for the propagation of transient ultrasonic waves in a layered isotropic porous material having a rigid frame. A temporal equivalent fluid model is considered, in which the acoustic wave propagates only in the fluid saturating the material. In this model, the inertial effects are described by the layered tortuosity and the viscous and thermal losses of the medium are described by two layered susceptibility kernels which depend on the viscous and thermal characteristic lengths. The medium is one dimensional and its physical parameters (porosity, tortuosity, and characteristics lengths) are depth dependent. A generalized hyperbolic fractional equation for transient sound wave propagation in layered material is established.

Chasnov [Phys. Fluids 10, 1191 (1998)] reviewed the results for passive scalar spectra in high-Schmidt-number stationary turbulence as derived by Kraichnan [J. Fluid Mech. 64, 737 (1974)] and generalized them to simple nonstationary flows. In two-dimensional turbulence, the Kraichnan spectra are usually fitted by numerically solving the spectral equation using the derived asymptotic behavior for small and large wave numbers. In this Brief Report, we show that the Kraichnan passive scalar spectrum over the entire range of $k$ is essentially a modified Bessel function of the second kind. We also present analytical forms of the spectra in three-dimensional nonstationary turbulence, where as shown by Chasnov, the nonstationarity can be responsible for different asymptotic behavior than the usual Kraichnan’s three-dimensional stationary form. Our results considerably simplify the “fitting” of passive scalar spectra from experimental and numerical data, with the simple analytical form valid for the whole range of $k$, instead of just the asymptotes, which are usually valid only for a small fraction of resolved wave numbers.

In a recent paper [Phys. Rev. E 75, 011506 (2007)] Hentschke et al. presented new results on the vapor-liquid transition in the Stockmayer fluid. In this Comment, we analyze the data further and demonstrate that at high dipole strength, the isotropic attractive part of the Stockmayer potential is negligible compared to the thermal energy at the vapor-liquid critical point. The results therefore suggest that the transition is largely driven by the dipolar interactions.

In their Comment, Ivanov, Kantorovich, and Camp [Phys. Rev. E. 77, 013501 (2008)] analyze molecular dynamics simulation data on the gas-liquid critical point of the Stockmayer fluid obtained recently by the authors. Based on this analysis they conclude that vapor-liquid phase separation may occur in purely dipolar systems. In this reply we argue that the existing data for the Stockmayer fluid as well as a related system are consistent with the nonexistence of vapor-liquid phase separation in purely dipolar systems.

We analyze the mixing properties of the microfluidic herringbone configuration introduced to mix scalar substances in a narrow channel at low Reynolds but large Péclet numbers. Because of the grooves sculpted on the channel floor, substantial transverse motions are superimposed onto the usual longitudinal Poiseuille dispersion along the channel, whose impact on both the mixing rate and mixture content is quantified. We demonstrate the direct link between the flow kinematics and the deformation rate of the mixture’s concentration distribution, whose overall shape is also determined.

Thin films of viscous fluids coating hydrophobic substrates are unstable to dewetting instabilities, and long-time evolution leads to the formation of an array of near-equilibrium droplets connected by ultrathin fluid layers. In the absence of gravity, previous use of lubrication theory has shown that coarsening dynamics will ensue—the system will evolve by successively eliminating small drops to yield fewer larger drops. While gravity has only a weak influence on the initial thin film, we show that it has a significant influence on the later stages of the coarsening dynamics, dramatically slowing the rate of coarsening for large drops. Small drops are relatively unaffected, but as coarsening progresses, these aggregate into larger drops whose shape and dynamics are dominated by gravity. The change in the mean drop shape causes a corresponding gradual transition from power-law coarsening to a logarithmic behavior.

The amount of mutual information contained in the time series of two elements gives a measure of how well their activities are coordinated. In a large, complex network of interacting elements, such as a genetic regulatory network within a cell, the average of the mutual information over all pairs, $⟨I⟩$, is a global measure of how well the system can coordinate its internal dynamics. We study this average pairwise mutual information in random Boolean networks (RBNs) as a function of the distribution of Boolean rules implemented at each element, assuming that the links in the network are randomly placed. Efficient numerical methods for calculating $⟨I⟩$ show that as the number of network nodes, $N$, approaches infinity, the quantity $N⟨I⟩$ exhibits a discontinuity at parameter values corresponding to critical RBNs. For finite systems it peaks near the critical value, but slightly in the disordered regime for typical parameter variations. The source of high values of $N⟨I⟩$ is the indirect correlations between pairs of elements from different long chains with a common starting point. The contribution from pairs that are directly linked approaches zero for critical networks and peaks deep in the disordered regime.

A parallel algorithm designed for widely used distributed computer clusters is developed for the real-space self-consistent-field theory for polymers. We adopt an efficient data partition method to ensure high performance of this parallel algorithm on clusters, which enables us to explore unknown phase structures of complex block polymers with high accuracy and efficiency. As a benchmark test, the algorithm is applied to an $ABC$ linear triblock copolymer, in which the volume fractions of the two end blocks of the polymer chain are equal $\left(f_A=f_C\right)$, to simplify the discussion. The three-dimensional microphases and phase diagram of this triblock copolymer are investigated in detail.

In the present work we introduce a methodology for solving a quantum billiard with Dirichlet boundary conditions. The procedure starts from the exactly known solutions for the particle in a circular disk, which are subsequently radially rescaled in such a way that they obey the new boundary conditions. In this way one constructs a complete basis set which can be used to obtain the eigenstates and eigenenergies of the corresponding quantum billiard to a high level of precision. Test calculations for several regular polygons show the efficiency of the method which often requires one or two basis functions to describe the lowest eigenstates with high accuracy.

The conventional periodic boundary conditions in two dimensions are extended to general boundary conditions, prescribed by primitive vector pairs that may not coincide with the coordinate axes. This extension is shown to be unambiguously specified by the twisting scheme. Equivalent relations between different twist settings are constructed explicitly. The classification of finite-size scaling functions is discussed based on the equivalent relations. A self-similar pattern for distinct classes of finite-size scaling functions is shown to appear on the plane that parametrizes the toroidal geometry.

On-lattice Monte Carlo simulations of colloidal random-stacking hard-sphere colloidal crystals are presented. The model yields close-packed crystals with random-stacking hexagonal structure. We find a significant amount of in-plane stacking disorder, which slowly anneals in the course of the simulation. The in-plane stacking disorder leads to lateral broadening of the stacking-disorder-induced Bragg rods. It is found that not only the scattering intensity, but also the width is modulated along the Bragg rods.

We revisit the scaling properties of a model for nonequilibrium wetting [Phys. Rev. Lett. 79, 2710 (1997)], correcting previous estimates of the critical exponents and providing a complete scaling scheme. Moreover, we investigate a special point in the phase diagram, where the model exhibits a roughening transition related to directed percolation. We argue that in the vicinity of this point evaporation from the middle of plateaus can be interpreted as an external field in the language of directed percolation. This analogy allows us to compute the crossover exponent and to predict the form of the phase transition line close to its terminal point.

We consider a two-dimensional $(d=2)$ kagomé lattice gas model with attractive three-particle interactions around each triangular face of the kagomé lattice. Exact solutions are obtained for multiparticle correlations along the liquid and vapor branches of the coexistence curve and at criticality. The correlation solutions are also determined along the continuation of the curvilinear diameter of the coexistence region into the disordered fluid region. The method generates a linear algebraic system of correlation identities with coefficients dependent only upon the interaction parameter. Using a priori knowledge of pertinent solutions for the density and elementary triplet correlation, one finds a closed and linearly independent set of correlation identities defined upon a spatially compact nine-site cluster of the kagomé lattice. Resulting exact solution curves of the correlations are plotted and discussed as functions of the temperature and are compared with corresponding results in a traditional kagomé lattice gas having nearest-neighbor pair interactions. An example of application for the multiparticle correlations is demonstrated in cavitation theory.

Using a time-averaging technique we obtain exactly the probability distribution for position and velocity of a Brownian particle under the influence of two heat baths at different temperatures. These baths are expressed by a white noise term, representing the fast dynamics, and a colored noise term, representing the slow dynamics. Our exact solution scheme accounts for inertial effects that are not present in approaches that assume the Brownian particle in the overdamped limit. We are also able to obtain the contributions associated with the fast noise that are usually neglected by other approaches.