The formation of self-organized structures in poly(9,9-di-$n$-alkylfluorene)s ∼1 vol % methylcyclohexane (MCH) and deuterated MCH (MCH-$d_{14}$) solutions was studied at room temperature using neutron and x-ray scattering (with the overall $q$ range of 0.000 58–4.29 Å${}^{-1}$) and optical spectroscopy. The number of side chain carbons $(N)$ ranged from 6 to 10. The phase behavior was rationalized in terms of polymer overlap, cross-link density, and blending rules. For $N=6-9$, the system contains isotropic areas and lyotropic areas where sheetlike assemblies (lateral size of >400 Å) and free polymer chains form ribbonlike agglomerates (characteristic dimension of >1500 Å) leading to a gel-like appearance of the solutions. The ribbons are largely packed together with surface fractal characteristics for $N=6-7$ but become open networklike structures with mass fractal characteristics for $N=8-9$, until the system goes through a transition to an isotropic phase of overlapping rodlike polymers for $N=10$. The polymer order within sheets varies allowing classification for loose membranes and ordered sheets, including the so-called β phase. The polymers within the ordered sheets have restricted motion for $N=6-7$ but more freedom to vibrate for $N=8-9$. The nodes in the ribbon network are suggested to contain ordered sheets cross-linking the ribbons together, while the nodes in the isotropic phase appear as weak density fluctuations cross-linking individual chains together. The tendencies for macrophase separation and the formation of non beta sheets decrease while the proportion of free chains increases with increasing $N$. The fraction of β phase varies nonlinearly, reaching its maximum at $N$ $=$ 8.

Functional networks of complex systems are obtained from the analysis of the temporal activity of their components, and are often used to infer their unknown underlying connectivity. We obtain the equations relating topology and function in a system of diffusively delay-coupled elements in complex networks. We solve exactly the resulting equations in motifs (directed structures of three nodes) and in directed networks. The mean-field solution for directed uncorrelated networks shows that the clusterization of the activity is dominated by the in-degree of the nodes, and that the locking frequency decreases with increasing average degree. We find that the exponent of a power law degree distribution of the structural topology $\gamma$ is related to the exponent of the associated functional network as $\alpha =(2-\gamma ){}^{-1}$ for $\gamma <2$.

We discuss how inference can be performed when data are sampled from the nonergodic phase of systems with multiple attractors. We take as a model system the finite connectivity Hopfield model in the memory phase and suggest a cavity method approach to reconstruct the couplings when the data are separately sampled from few attractor states. We also show how the inference results can be converted into a learning protocol for neural networks in which patterns are presented through weak external fields. The protocol is simple and fully local, and is able to store patterns with a finite overlap with the input patterns without ever reaching a spin-glass phase where all memories are lost.

The effect of shortcuts on the task completion landscape in parallel discrete-event simulation (PDES) is investigated. The morphology of the task completion landscape in PDES is known to be described well by the Langevin-type equation for nonequillibrium interface growth phenomena, such as the Kardar-Parisi-Zhang equation. From the numerical simulations, we find that the root-mean-squared fluctuation of task completion landscape, $W(t,N)$, scales as $W(t\to \infty ,N)~N$ when the number of shortcuts, $\ell$, is finite. Here $N$ is the number of nodes. This behavior can be understood from the mean-field type argument with effective defects when $\ell$ is finite. We also study the behavior of $W(t,N)$ when $\ell$ increases as $N$ increases and provide a criterion to design an optimal topology to achieve a better synchronizability in PDES.

Broken symmetry of vortices due to induced-charge electro-osmosis (ICEO) around stacking structures is important for the generation of a large net flow in a microchannel. Following theoretical predictions in our previous study, we herein report experimental observations of asymmetrical reverse vortex flows around stacking structures of carbon posts with a large height ($~$110 $\mu$m) in water, prepared by the pyrolysis of a photoresist film in a reducing gas. Further, by the use of a coupled calculation method that considers boundary effects precisely, the experimental results, except for the problem of anomalous flow reversal, are successfully explained. That is, unlike previous predictions, the precise calculations here show that stacking structures accelerate a reverse flow rather than suppressing it for a microfluidic channel because of the deformation of electric fields near the stacking portions; these structures can also generate a large net flow theoretically in the direction opposite that of a previous prediction for a standard vortex flow. Furthermore, by solving the one-dimensional Poisson-Nernst-Plank (PNP) equations in the presence of ac electric fields, we find that the anomalous flow reversal occurs by the phase retardation between the induced diffuse charge and the tangential electric field. In addition, we successfully explain the nonlinearity of the flow velocity on the applied voltage by the PNP analysis. In the future, we expect to improve the pumping performance significantly by using stacking structures of conductive posts along with a low-cost process.

This paper concerns a basic electrostatic problem: how to calculate generalized Coulomb and self-polarization potentials in heterogeneous dielectric media. In particular, with simulations of ellipsoidal semiconductor quantum dots and elongated biomacromolecules being its target applications, this paper extends the so-called three-layer dielectric models for generalized Coulomb and self-polarization potential calculation from the spherical and the spheroidal geometries to the triaxial ellipsoidal geometry. Compared to the simple steplike dielectric model, these three-layer dielectric models can overcome the mathematical divergence in the self-polarization energy by employing continuous radial dielectric functions. More specifically, in this paper, the quasiharmonic three-layer dielectric model for the ellipsoidal geometry is discussed, and the explicit analytical series solutions of the corresponding electrostatic problem are obtained in terms of the ellipsoidal harmonics. Then a robust numerical procedure working for general three-layer dielectric models is developed. The key component of the numerical method is to subdivide the transition layer of the underlying three-layer model into multiple sublayers and then in each one of them approximate the select dielectric function of the transition layer by one of the quasiharmonic functional form rather than simply by a constant value as one would normally do. As a result, the numerical method has no numerical divergence.

The nonconsensus opinion model (NCO) introduced recently by Shao et al. [Phys. Rev. Lett. 103, 018701 (2009)] is solved exactly on the line. Although, as expected, the model exhibits no phase transition in one dimension, its study is interesting because of the possible connection with invasion percolation with trapping. The system evolves exponentially fast to the steady state, rapidly developing long-range correlations: The average cluster size in the steady state scales as the square of the initial cluster size, of the (uncorrelated) initial state. We also discuss briefly the NCO model on Bethe lattices, arguing that its phase transition diagram is different than that of regular percolation.

A Brownian motor is considered which operates due to asymmetric dichotomic fluctuations of the spatially periodic asymmetric potential energy. As shown, the motion direction and stopping points of this motor are dictated by the competition between the spatial and temporal asymmetry of the potential energy (or solely by temporal asymmetry in the case that the potential energy sign fluctuates). For an asymmetric sawtooth potential, the Brownian-particle average velocity is calculated numerically as a function of certain parameters of the model, whereas the low-frequency and low-energy approximations allow the corresponding analytical relationships to be derived for an arbitrarily shaped potential profile. It is shown that temporal asymmetry is not necessary for stopping point occurrence provided that the potential profile fluctuates not only in amplitude but in shape as well. This inference is illustrated by photoinduced fluctuations of the potential energy for a number of substituted arylpyrene molecules on a substrate with symmetrically distributed charge density.

A hydrodynamic model for dense granular flows, previously developed for confined flows, has been extended to address free surface flow down an inclined chute. Results show that the model can predict the existence of two critical inclination angles, namely, the avalanche starting angle ${\theta }_{\text{start}}$ above which the granular bed begins flowing from an initially jammed configuration, and an avalanche stopping angle ${\theta }_{\text{stop}}$, which is the minimum to maintain flowing conditions, in agreement with experiments and numerical simulations available from the literature. The dependence of these critical angles on the bed depth is also analytically formulated, reflecting the expected qualitative behavior. Such a hysteretic behavior is specific of granular flow and its prediction provides indications of consistence of the modeling approach. The improved model also captures the scaling of the velocity profiles down the bed depth.

It is well known that the metal-like strong reflection observed in the elytra of some kinds of beetles is produced by multilayer thin-film interference. For the quantitative analyses of the structural colors in these elytra, it is necessary to know accurate values of the refractive indices of the materials that comprise the multilayer structure. However, index determination is not an easy task: The elytron surface is not flat but curved and usually contains many irregular bumps, which cause scattering loss. These structural characteristics prevent us from directly applying conventional optical techniques for index determination, such as ellipsometry, since these techniques require a perfectly specular surface. In this paper, we report a new experimental procedure that can directly determine the refractive indices of individual layers in natural multilayer systems. This procedure involves semi-frontal thin-sectioning of the sample and subsequent optical examinations using a microspectrophotometer. We demonstrate that the complex refractive index and its wavelength dependence can be successfully determined for one kind of beetle.

In this paper, a time substitution as used by Duru and Kleinert in their treatment of the hydrogen atom with path integrals is performed to price timer options under stochastic volatility models. We present general pricing formulas for both the perpetual timer call options and the finite time-horizon timer call options. These general results allow us to find closed-form pricing formulas for both the perpetual and the finite time-horizon timer options under the 3/2 stochastic volatility model as well as under the Heston stochastic volatility model. For the treatment of timer options under the 3/2 model we will rely on the path integral for the Morse potential, with the Heston model we will rely on the Kratzer potential.

We study the synchronization properties of the delay dynamics of two identical semiconductor lasers coupled through a semitransparent mirror. Via an analytical and numerical approach, we investigate the influence of asymmetries, in particular mismatches of self- and cross-coupling strength and differences in self- and cross-coupling delay. We show that the former mismatch affects the stability of the zero-lag state but not the dynamics within the synchronization manifold, while the latter mismatch does not affect the quality of synchronization but alters the dynamics significantly. Our results are extended to different unidirectional coupling schemes. This is highly relevant for communication schemes utilizing chaotic dynamics. Finally, the influence of nonlinear gain saturation on the dynamics and stability of synchronization is discussed.

Spatiotemporal systems are commonly investigated in terms of spatiotemporal diagrams and, most often, the analysis is limited to the first instabilities. Due to the lack of a Takens-like theorem for spatiotemporal systems, the resulting dynamics is almost never interpreted using phase portraits reconstructed from one variable locally recorded. This work is an attempt to make an explicit link between reconstructed phase portraits and spatiotemporal diagrams. Defects distributions are interpreted in terms of a lack of phase coherence. The lack of a simple structure—as a torus characterized by a closed curve for Poincaré section when a quasiperiodic regime is identified—is tentatively interpreted in terms of observability. A first link is thus made between the defects distribution and the nature of the underlying dynamics.

We present an analytical linear model describing the interaction of a planar shock wave with an isotropic random pattern of density nonuniformities. This kind of interaction is important in inertial confinement fusion where shocks travel into weakly inhomogeneous cryogenic deuterium-wicked foams, and also in astrophysics, where shocks interact with interstellar density clumps. The model presented here is based on the exact theory of space and time evolution of the perturbed quantities generated by a corrugated shock wave traveling into a small-amplitude single-mode density field. Corresponding averages in both two and three dimensions are obtained as closed analytical expressions for the turbulent kinetic energy, acoustic energy flux, density amplification, and vorticity generation downstream. They are given as explicit functions of the two parameters (adiabatic exponent $\gamma$ and shock strength $M_1$) that govern the dynamics of the problem. In addition, these explicit formulas are simplified in the important asymptotic limits of weak and strong shocks and highly compressible fluids.

The propagation of surface electromagnetic waves along a uniform magnetic field is studied in a quantum electron-hole semiconductor plasma. A forward propagating mode is found by including the effect of quantum tunneling. In the classical limit ($\hslash \to 0$), one of the low-frequency modes found is similar to an experimentally observed one in $n$-type InSb at room temperature. The surface modes are shown to be significantly modified in the case of high-conductivity semiconductor plasmas where electrons and holes may be degenerate. The effects of the external magnetic field and the quantum tunneling on the surface wave modes are discussed.

In this paper we consider the Schelling social segregation model for two different populations. In Schelling’s model, segregation appears as a consequence of discrimination, measured by the local difference between two populations. For that, the model defines a tolerance criterion on the neighborhood of an individual, indicating wether the individual is able to move to a new place or not. Next, the model chooses which of the available unhappy individuals really moves. In our work, we study the patterns generated by the dynamical evolution of the Schelling model in terms of various parameters or the initial condition, such as the size of the neighborhood of an inhabitant, the tolerance, and the initial number of individuals. As a general rule we observe that segregation patterns minimize the interface of zones of different people. In this context we introduce an energy functional associated with the configuration which is a strictly decreasing function for the tolerant people case. Moreover, as far as we know, we are the first to notice that in the case of a non-strictly-decreasing energy functional, the system may segregate very efficiently.

Analytical multidomain solutions to the dynamical (Landau-Lifshitz-Gilbert) equation of a one-dimensional ferromagnet including an external magnetic field and spin-polarized electric current are found using the Hirota bilinearization method. A standard approach to solve the Landau-Lifshitz equation (without the Gilbert term) is modified in order to treat the dissipative dynamics. I establish the relations between the spin interaction parameters (the constants of exchange, anisotropy, dissipation, external-field intensity, and electric-current intensity) and the domain-wall parameters (width and velocity) and compare them to the results of the Walker approximation and micromagnetic simulations. The domain-wall motion driven by a longitudinal external field is analyzed with especial relevance to the field-induced collision of two domain walls. I determine the result of such a collision (which is found to be an elastic one) on the domain-wall parameters below and above the Walker breakdown (in weak- and strong-field regimes). Single-domain-wall dynamics in the presence of an external transverse field is studied with relevance to the challenge of increasing the domain-wall velocity below the breakdown.

Multidomain solutions to the time-dependent Ginzburg-Landau equation in the presence of an external field are analyzed using the Hirota bilinearization method. Domain-wall collisions are studied in detail considering different regimes of the critical parameter. I show the dynamics of the Ising and Bloch domain walls of the Ginzburg-Landau equation in the bistable regime to be similar to that of the Landau-Lifshitz domain walls. Domain-wall reflections lead to the appearance of bubble and pattern structures. Above the Bloch-Ising transition point, spatial structures are determined by the collisions of fronts propagating into an unstable state. Mutual annihilation of such fronts is described.

We present in this Rapid Communication experimental evidence of an acceleration of the zenithal easy-axis dynamics of a nematic liquid crystal (NLC) with the age of a NLC-polymer layer. The comparison with other hard alignment layers strongly indicates that the polymer softness and its ability to reorient in the nematic ordering field is at the origin of the measured dynamics. The unusual acceleration of the dynamics with the polymer age is discussed in terms of this unique coupling with the NLC order. The NLC behaves like a physical plasticizer as a result of the coupling between the NLC and the polymer orders.