Voltage-activated ion channels vary randomly between open and closed states, influenced by the membrane potential and other factors. Signal transduction is enhanced by noise in a simple ion channel model. The enhancement occurs in a finite range of signals; the range can be extended using populations of channels. The range increases more rapidly in multiple-threshold channel populations than in single-threshold populations. The diversity of ion channels may thus be present as a strategy to reduce the metabolic costs of handling a broad class of electrochemical signals.

We present a study of transport on complex networks with routing based on local information. Particles hop from one node of the network to another according to a set of routing rules with different degrees of congestion awareness, ranging from random diffusion to rigid congestion-gradient driven flow. Each node can be either source or destination for particles and all nodes have the same routing capacity, which are features of ad hoc wireless networks. It is shown that the transport capacity increases when a small amount of congestion awareness is present in the routing rules, and that it then decreases as the routing rules become too rigid when the flow becomes strictly congestion-gradient driven. Therefore, an optimum value of the congestion awareness exists in the routing rules. It is also shown that, in the limit of a large number of nodes, networks using routing based on local information jam at any nonzero load. Finally, we study the correlation between congestion at node level and a betweenness centrality measure.

We present experimental measurements near the onset of electroconvection (EC) of homeotropically aligned nematic liquid crystals Phase 5A and MBBA. A voltage of amplitude $\sqrt{2}{V}_0$ and frequency $f$ was applied. With increasing $V_0$, EC occurred after the bend Freedericksz transition. We found supercritical bifurcations to EC that were either stationary bifurcations or Hopf bifurcations to traveling convection rolls, depending on the sample conductances. Results for the onset voltages $V_c$, the critical wave numbers $k_c$, the obliqueness angles ${\theta }_c$, and the traveling-wave (Hopf) frequencies at onset ${\omega }_c$ over a range of sample conductances and driving frequencies are presented and compared, to the extent possible, with theoretical predictions. For the most part good agreement was found. However, the experiment revealed some unusual results for the orientations of the convection rolls relative to the direction selected by the Freedericksz domain.

We present patterns of electroconvection (EC) for the homeotropically aligned nematic liquid crystal MBBA. A voltage $V=\sqrt{2}{V}_0\sin \left(2\pi ft\right)$ was applied. With increasing $V_0$, the bend Freedericksz transition at $V_F$ was followed by the onset of EC at $V_c>V_F$. We found four distinct pattern types. First, a primary supercritical Hopf bifurcation to traveling waves (TW’s) of convection rolls occurred. The structure factor $S\left(\mathbf{k}\right)$ of this state reflected the azimuthal anisotropy of the underlying Freedericksz state. For $f<f_L\simeq 75\mathrm{Hz}$ there was a superposition of two oblique-roll modes (pattern I). These patterns were chaotic in space and time. For larger $f$ the patterns consisted of chaotic TW normal rolls (pattern II). Here the chaos was attributable to the motion of dislocations and domain walls between left- and right-traveling waves. A secondary bifurcation yielded pattern III; it had no dominant TW frequency but had broadband chaotic dynamics dominated by the motion of dislocations. This pattern type had been referred to by others as a “chevron pattern;” its structure factor still revealed azimuthal anisotropy. Finally, at somewhat larger $ϵ\equiv V^2∕V_c^2-1$ a highly disordered pattern IV with defect dynamics was found. This state had been studied before by Kai and co-workers and was referred to by them as “phase turbulence.” It had a structure factor that was (within our resolution) invariant under rotation. For patterns I, II, and III, $S\left(\mathbf{k}\right)$ contained crescent-shaped peaks. The peak shape was qualitatively different from the case of planar EC where the structure factor has an elliptical cross section. We present measurements of the widths $1∕{\xi }_k$ and $1∕{\xi }_{\theta }$ in the radial $\left(k\right)$ and the azimuthal $\left(\theta \right)$ directions. For small $ϵ$ (patterns I and II) we found that ${\xi }_k$ was consistent with the usual Ginzburg-Landau scaling ${\xi }_k\sim {ϵ}^{-{\nu }_k}$ with ${\nu }_k\simeq 1∕2$. However, for ${\xi }_{\theta }$ we found ${\xi }_{\theta }\sim {ϵ}^{-{\nu }_{\theta }}$ with ${\nu }_{\theta }\simeq 3∕4$. Presumably this anomalous scaling of ${\xi }_{\theta }$ is associated with the Goldstone mode of homeotropic EC. We also show data for the height $S_0$ of the structure factor that are consistent with $S_0\sim {ϵ}^{\beta }$ with $\beta \simeq -0.5$, implying that $S_0$ diverges at onset. This differs from the case of domain chaos in rotating Rayleigh-Bénard convection where experiment is consistent with $\beta =1∕2$ and thus with a vanishing $S_0$. The difference between the shape of the structure-factor cross section and between the exponents, for the present case, for planar EC, and for domain chaos suggests that there are different universality classes for spatiotemporal chaos.

In this paper we evaluate the enhancement of nonequilibrium concentration fluctuations induced by the Soret effect when a binary fluid layer is subjected to a stationary temperature gradient. Starting from the fluctuating Boussinesq equations for a binary fluid in the large-Lewis-number approximation, we show how one can obtain an exact expression for the nonequilibrium structure factor in the long-wavelength limit for a fluid layer with realistic impermeable and no-slip boundary conditions. A numerical calculation of the wave-number dependence of the nonequilibrium enhancement and of the corresponding decay rate of the concentration fluctuations is also presented. Some physical consequences of our results are briefly discussed.

We show that optical light bullets can coexist with double bullet complexes in nonlinear dissipative systems. Coexistence occurs for a relatively large range of the system parameters, and is associated with either marginal stability or bistable existence of the two dissipative soliton species. In the case of marginal stability, spontaneous transformations of single bullets into double bullet complexes are observed. Among the bistable cases, we show how both clockwise and anticlockwise rotating double bullet complexes can be formed out of the phase-controlled interaction of two single bullets. The internal dynamics of pulsating double bullet complexes, with oscillations in both the spatial separation between the two bullets and the bullet shape in time domain is also detailed.

Omnidirectional light propagation in a realistic superlattice is investigated. This work complements two previous articles [Phys. Rev. E 59, 3624 (1999); 61, 5802 (2000)] that analyzed the cases of transverse electric (TE) and transverse magnetic (TM) polarization modes, respectively, of the dielectric superlattice modeled by means of Dirac $\delta$ functions. We present a quantitative analysis of the transmission functions, the band structures, the equifrequency surfaces, and the photon density of states (PDOS) for both TE and TM modes of the real superlattice without any approximations on the given dielectric function profiles. One of the advantages is that the Brewster effect can be manifested via our approach. In addition, the modes corresponding to TM evanescent waves that are absent from the Dirac comb model can be predicted. Finally, the exact PDOS of the realistic superlattice for the TE and TM modes can be obtained, respectively. These results are relevant to the spontaneous emission by an atom or to dipole radiation in one-dimensional periodic structures.

We develop a spectral formulation and a stationary WKB approximation for calculating the probabilities of rare events (large deviations from the mean) in systems of reacting particles with infinite-range interaction, describable by a master equation. We compare the stationary WKB approximation to a recent time-dependent semiclassical approximation developed, for the same class of problems, by Elgart and Kamenev [Phys. Rev. E 70, 41106 (2004)]. As a benchmark we use an exactly solvable problem of the binary annihilation reaction $2A\to \stackrel{̸}{0}$.

The structure of nearly static planar interfaces is studied within the framework of the Landau–de Gennes model with the dynamics governed by the time-dependent Ginzburg-Landau equation. To account for the full elastic anisotropy the free energy expansion is extended to include a third order gradient term. The solutions corresponding to the in-plane or homeotropic director alignment at the interface are sought. For this purpose a consistent perturbative scheme is constructed which enables one to calculate successive corrections to the velocity and the order parameter of the interface. The implications of the solutions are discussed. The elastic anisotropy introduces asymmetry into the order parameter and free energy profiles, even for the high symmetry homeotropic configuration. The velocity of the interface with the homeotropic or in-plane alignment is enhanced or reduced, respectively. There is no reorientation of the optical axis in the boundary layer. For the class of nematogens with approximate splay-bend degeneracy the temperature dependence of the interface velocity is weakly affected by the remaining twist anisotropy.

We have developed a multiscale approach for simulating the concentration fluctuations in a miscible blend subject to complex flow dynamics. We first simulate the hydrodynamics of a fluid as it flows through porous media. In particular, we monitor the velocity gradients as a function of time for a fluid “particle” as it follows a tortuous path through the system. Next, we evolve the structure factor of the spatial concentration fluctuations subject to this flow environment. The velocity gradients experienced by this fluid particle can result in elongation and rotation of the concentration fluctuations. In this manner, we couple the macroscopic flow fields in porous media with the microscopic concentration fluctuations in the polymer blend. We find a close correlation between the tortuous pathways, the velocity gradients in the fluid, and the perturbance of the structure factor from it quiescent state. Furthermore, we find that the concentrations tend to elongate towards the flow direction or at an acute angle with the flow direction.

We propose an exchange-driven aggregation growth model of population and assets with mutually catalyzed birth to study the interaction between the population and assets in their exchange-driven processes. In this model, monomer (or equivalently, individual) exchange occurs between any pair of aggregates of the same species (population or assets). The rate kernels of the exchanges of population and assets are $K(k,l)=Kkl$ and $L(k,l)=Lkl$, respectively, at which one monomer migrates from an aggregate of size $k$ to another of size $l$. Meanwhile, an aggregate of one species can yield a new monomer by the catalysis of an arbitrary aggregate of the other species. The rate kernel of asset-catalyzed population birth is $I(k,l)=Ik{l}^{\mu }$ [and that of population-catalyzed asset birth is $J(k,l)=Jk{l}^{\nu }$], at which an aggregate of size $k$ gains a monomer birth when it meets a catalyst aggregate of size $l$. The kinetic behaviors of the population and asset aggregates are solved based on the rate equations. The evolution of the aggregate size distributions of population and assets is found to fall into one of three categories for different parameters $\mu$ and $\nu$: (i) population (asset) aggregates evolve according to the conventional scaling form in the case of $\mu ⩽0$ $(\nu ⩽0)$, (ii) population (asset) aggregates evolve according to a modified scaling form in the case of $\nu =0$ and $\mu >0$ ($\mu =0$ and $\nu >0$), and (iii) both population and asset aggregates undergo gelation transitions at a finite time in the case of $\mu =\nu >0$.

A nonlinear optical phenomenon, relativistic cross-phase modulation, is reported. A relativistically intense light beam ($I=1.3\times {10}^{18}\mathrm{W}{\mathrm{cm}}^{-2}$, $\lambda =1.05\mathrm{\mu }\mathrm{m}$) is experimentally observed to cause phase modulation of a lower intensity, copropagating light beam in a plasma. The latter beam is generated when the former undergoes the stimulated Raman forward scattering instability. The bandwidth of the Raman satellite is found to be broadened from $3.8–100\mathrm{nm}$ when the pump laser power is increased from $0.45–2.4\mathrm{TW}$. A signature of relativistic cross-phase modulation, namely, asymmetric spectral broadening of the Raman signal, is observed at a pump power of $2.4\mathrm{TW}$. The experimental cross-phase modulated spectra compared well with theoretical calculations. Applications to generation of high-power single-cycle pulses are also discussed.

Particle simulations on a flat-topped somewhat underdense (typically $n_0∕n_c=0.6$) plasma slab by Nikolic et al. [Phys. Rev. E 66, 036404 (2002)] were seen to give transient stimulated scattering behavior with frequency shift $[{\omega }_0-{\omega }_s(\approx {\omega }_p)]$ considerably less than the plasma frequency ${\omega }_p$. This has been linked to the electron acoustic wave (EAW) and the scattering was thus seen as another example of stimulated electron acoustic scattering inferred by Montgomery et al. [Phys. Rev. Lett. 87, 155001 (2001)] from experiments on low-density plasmas. Montgomery et al. had noted the difficulty of how one could have a very narrow observed scattering from a wave whose damping was at least initially very high. Our Vlasov-Maxwell simulations for such somewhat underdense $(n_0∕n_c⩾0.25)$ plasmas show that the simulation resonance was in fact determined by the beating of the pump with a new “radiating pseudocavity” electromagnetic mode for the slab at a frequency close to ${\omega }_p$ with relatively low loss. This allows the initial narrow-band excitation of the kinetic electrostatic electron nonlinear (KEEN) waves (the nonlinear “cousins” of EAWs) at a well-defined frequency $({\omega }_K\approx {\omega }_0-{\omega }_p<{\omega }_p)$ which is not necessarily the value given by the EAW dispersion relation. (The KEEN wave characteristics have been discussed by Afeyan et al. [33rd AAAC (2003), #238, IFSA 2003].) The consideration of such a mechanism is relevant to moderately underdense hot plasmas.

We demonstrate the existence of self-consistent Bloch modes in resonant nonlinear photonic crystals with a complex, intensity-dependent, and frequency-dependent dielectric function. Such a dielectric response may arise by “doping” the photonic crystal with resonant quantum dots, atomic impurities, or other two-level light emitters. These exact solutions of the nonlinear electromagnetic wave equation exhibit Bloch periodicity and describe fundamental eigenmodes of an active photonic crystal under incoherent pumping. In a simple model two-dimensional photonic crystal, doped with active two-level atoms, the optical field intensity of these waves shows a laserlike threshold behavior with pumping. This appears to be a universal property of active, nonlinear photonic crystals and photonic band gap materials, arising from multidirectional distributed feedback. We describe an iterative technique for computing the detailed properties of these exact, self-consistent nonlinear waves in strongly scattering photonic crystal architectures with regions of gain and loss.

In this paper we describe a variable stepsize integration method for the Hamiltonian dynamics of point vortices based on the explicit symplectic Zhang and Qin scheme. The adapted method is also explicit and preserves the reversible structure of the flow. In order to check the behavior of this adaptive method a numerical study of the exchange-scattering phenomenon in the three-vortex problem is made. The symmetry of the orbit and the energy evolution are discussed for the exchange-scattering model. A long-term integration of this and other models composed also of three vortices indicates that the adaptive Zhang-Qin method has good properties of efficiency and preservation of the first integrals associated with point vortex systems.

Several numerical algorithms for dynamic Monte Carlo simulations of surface chemistry have been proposed in the past. The variable step size method (VSSM) is commonly used for systems where the rate coefficients are constant in time, owing to its good efficiency. If rate coefficients vary in time, the first reaction method (FRM) has been shown to be more efficient. However, the cost of this algorithm to execute a reaction step depends on the considered lattice size, which can make this method inefficient for systems involving surface phenomena on different scales. Here we propose a general and efficient algorithm, the fast first reaction method (fFRM), which has the advantages of being applicable to systems with constant and time-varying rate coefficients, and of having a computational cost per reaction step that is independent of the lattice size. An additional feature of fFRM is that it is rejection-free, which means that once a reaction class is selected, a reaction of that type will be executed. A rejection-free variant of VSSM, called rVSSM, is also presented, which leads to an approximately 15% speedup compared with the VSSM algorithm for the considered example.

We present a theoretical discussion of a self-assembly scheme which makes it possible to use DNA to uniquely encode the composition and structure of microparticle and nanoparticle clusters. These anisotropic DNA-decorated clusters can be further used as building blocks for hierarchical self-assembly of larger structures. We address several important aspects of possible experimental implementation of the proposed scheme: the competition between different types of clusters in a solution, possible jamming in an unwanted configuration, and the degeneracy due to symmetry with respect to particle permutations.

We report on the observation of self-alignment of nematic liquid crystals into colloidal photonic crystals, over distances much larger than the typical size of the voids between the spheres. We observe that the infiltrated structure possesses a unique optical axis that is determined by an intrinsic structural anisotropy of photonic crystal opals. We develop a simple model to describe this self-alignment based on the connectivity of the pores. The resulting structure constitutes a polarization dependent photonic crystal that can be controlled electrically.

In order to check on a recent suggestion that local scale invariance [M. Henkel et al., Phys. Rev. Lett. 87, 265701 (2001)] might hold when the dynamics is of Gaussian nature, we have carried out the measurement of the response function in the kinetic Ising model with Glauber dynamics quenched to $T_C$ in $d=4$, where Gaussian behavior is expected to apply, and in the two other cases of the $d=2$ model quenched to $T_C$ and to below $T_C$, where instead deviations from Gaussian behavior are expected to appear. We find that in the $d=4$ case there is an excellent agreement between the numerical data, the local scale invariance prediction and the analytical Gaussian approximation. No logarithmic corrections are numerically detected. Conversely, in the $d=2$ cases, both in the quench to $T_C$ and to below $T_C$, sizable deviations of the local scale invariance behavior from the numerical data are observed. These results do support the idea that local scale invariance might miss to capture the non-Gaussian features of the dynamics. The considerable precision needed for the comparison has been achieved through the use of a fast new algorithm for the measurement of the response function without applying the external field. From these high quality data we obtain $a=0.27\pm 0.002$ for the scaling exponent of the response function in the $d=2$ Ising model quenched to below $T_C$, in agreement with previous results.

We describe a method for identifying correlation structures in irregular fluctuations (short-term variabilities) of multivariate time series, even if they exhibit long-term trends. This method is based on the previously proposed small shuffle surrogate method. The null hypothesis addressed by this method is that there is no short-term correlation structure among data or that the irregular fluctuations are independent. The method is demonstrated for numerical data generated by known systems and applied to several experimental time series.