Vicinal surfaces are known to exhibit morphological instabilities during step-flow growth. Through a linear stability analysis of step meandering instabilities, we investigate two effects that are important in many heteroepitaxial systems: elastic monopole-monopole interactions arising from bulk stress and the Ehrlich-Schwoebel (ES) barriers due to the asymmetric adatom incorporation rates. The analysis shows that the effects of the ES barriers increase as the average terrace width increases, whereas the effects of elastic monopole-monopole interactions decrease. The ES barriers favor an in-phase step pattern with a zero phase shift between consecutive steps, while elastic stress favors an out-of-phase pattern with a phase shift of $\pi$. However, our analysis shows that the instability growth rate becomes nearly independent of the phase shift when either the ES-barrier effect or the stress effect is large. In particular, for ES-barrier-driven instability, the in-phase step pattern develops only within an intermediate range of terrace widths when bulk stress exists. Similarly, for the elastic-interaction-driven instability, an out-of-phase pattern only forms within a certain range of monopole strength; if the strength is too small, the ES barrier effect dominates, and if it is too large, the peak in the instability growth rate becomes delocalized in the phase shift and no patterns form. This transition between patterned and random step morphologies depends on the monopole strength, but is independent of the terrace width. A phase diagram that describes the regions of the ES-barrier-dominant instability and the elastic-interaction-dominant instability is established, along with the morphological phase diagrams that predict the step configurations as a function of the controlling parameters for the two types of instabilities.

The main focus of the present paper is studying dipolar frustration within smectic-$A_d$ layers as induced by dipole-dipole interactions. Our reference point is the Gay-Berne system with $\kappa =4$, ${\kappa }^{\prime }=5$, $\mu =2$ and $\nu =1$, which in the phase diagram shows a stable “island” of smectic-$A$ phase with a short-range hexagonal order within each layer [Phys. Rev. E 57, 6685 (1998)]. We carry out isothermal-isobaric Monte Carlo simulations for a dipolar version of this model, where the Gay-Berne interaction is supplemented by interaction between longitudinal dipole moments. For a fixed off-center position of the dipoles we increase value of the dipole moment and follow evolution of the liquid-crystalline part of the phase diagram focusing on changes of the nematic-smectic-$A$ phase boundaries and on structural response of the smectic-$A$ layers. For weak dipoles only the classical smectic-$A$ phase is stabilized, which then transforms into smectic-$A_d$ with layers being formed by two ferroelectrically polarized sublayers of opposite polarization. Average positions of dipoles that contribute to the polarization of a sublayer are located in a common plane, referred to as a dipolar plane. For not too strong dipole-dipole interactions increasing magnitude of the dipole moment causes stabilization of nematic at the expense of smectic-$A_d$. Under the same conditions the layer spacing increases and the distance between the dipolar planes within layers decreases. Each smectic sublayer is characterized by a short-range hexagonal order of the molecular centers of mass. With the dipole moment exceeding the threshold value, the polarization planes that built up the layers start to merge, which sets in the dipolar frustration. This, in turn, forces the system to develop a competition between frustrated hexagonal- and frustration-free tetragonal local order within each layer. When the local hexagonal order is transformed into the tetragonal one the stability range of smectic-$A_d$ increases with increasing dipole moment at the expense of the nematic phase. Similar competition is observed in crystalline phases. For small dipole moment only crystalline structures with long-range hexagonal order appear stable. They evolve with dipolar strength into monoclinic and tetragonal lattices.

In colloidal suspensions of nanosized ferroelectric particles and nematic liquid crystals a large increase in the isotropic-nematic transition temperature has been observed recently. By dynamic light scattering we measured the relaxation rate of the nematic director fluctuations in colloidal systems with $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ and ${\mathrm{Sn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ particles. A substantial increase in the bend-mode relaxation rate, attributed to an increase in the bend elastic constant, is observed. A mode with relaxation rate around $200000{\mathrm{s}}^{-1}$, independent of the scattering vector, is also observed. We propose that it represents the out-of-phase motion of the nematic director and average direction of the spontaneous polarization of the ferroelectric particles. No translation motion is observed, indicating that the particles may form chains.

In spite of the large mean bending moduli observed for phospholipid bilayers, stable vesicle phases were recently observed for dilute solutions of charged phospholipids. A correspondingly large negative Gaussian bending modulus associated with charged membranes results in an overall curvature energy that is so low that entropic stabilization is possible. The mean bending modulus determines the membrane persistence length and therefore it is reasonable that there is a correlation between the membrane rigidity and the size of the lipid vesicles. Here we show that in mixtures of the anionic phospholipid dioleoylphosphatidylglycerol and the zwitterionic phospholipid dioleoylphosphatidylcholine the radius of vesicles produced by repetitive freeze-thaw cycles is considerably smaller than expected from the rigidities of the corresponding pure lipid bilayers. Self-consistent field calculations indicate that the changes in the equilibrium radius of mixed bilayers can be attributed to the dependences of the mean bending modulus $k_c$ on lipid mixing and the average surface charge density.

We investigate patterns of collective phase synchronization in brain activity in awake, resting humans with eyes closed. The alpha range of human electroencephalographic activity is characterized by ever-changing patterns, with strong fluctuations in both time and overall level of phase synchronization. The correlations of these patterns are reflected in power-law scaling of these properties. We present evidence that the dynamics underlying this fluctuation is type-I intermittency. We present a model study illustrating that the scaling property and the collective intermittent dynamics are emergent features of globally coupled phase oscillators near the critical point of entering global frequency locking.

Ion channels are distributed in clusters in squid giant axons, rat retinal nerve fiber layers, pyramidal cell dendrites of Apteronotus, etc. Ion channel clusters along the unmyelinated axon generate spontaneous spiking due to ion channel noise. Ion channel clusters are coupled by the axonal cable, and spontaneous spiking of each ion channel cluster can be synchronized. This paper considers the spiking synchronization of two ion channel clusters coupled by an axon. It is shown that axonal parameters affect the spiking synchronization exponentially and ion channel clusters have maximal spiking synchronization when they have the same size. It is further shown that there is an optimal length of the ion channel clusters with maximal spiking synchronization and the optimal length accords with the length of the node of Ranvier in the myelinated axon.

A theoretical framework for predicting low frequency Raman vibrational spectra of viral capsids is presented and applied to the M13 bacteriophage. The method uses a continuum elastic theory for the vibrational modes and a bond-charge polarizability model of an amorphous material to roughly predict the Raman intensities. Comparison is made to experimental results for the M13 bacteriophage virus.

We introduce a stochastic approach for self-assembly in systems far from equilibrium. The building blocks are represented by a lattice of discrete variables (Potts-like spins), and physically meaningful mechanisms are obtained by restricting transitions through spatially local rules based on experimental data. We use the method to study nucleation of filopodia-like bundles in a system consisting of purified actin, fascin, actin-related protein $2∕3$, and beads coated with Wiskott-Aldrich syndrome protein. Consistent with previous speculation based on static experimental images, we find that bundles derive from $\Lambda$-precursor-like patterns of spins on the lattice. The ratcheting of the actin network relative to the surface that represents beads plays an important role in determining the number and orientation of bundles due to the fact that branching is the primary means for generating barbed ends pointed in directions that allow rapid filament growth. By enabling the de novo formation of coexisting morphologies without the computational cost of explicit representation of proteins, the approach introduced complements earlier models of cytoskeletal behavior in vitro and in vivo.

Synchronization in complex networks has attracted lots of interest in various fields. We consider synchronization in time-varying networks, in which the weights of links are time varying. We propose a useful approach—i.e., the matrix measure approach—to derive some analytically sufficient conditions for synchronization in time-varying networks. These conditions are less conservative than many existing synchronization conditions. Theoretical analysis and numerical simulations of different networks verify our main results.

A method is proposed to estimate system parameters by optimizing synchronization with a genetic algorithm. This method can effectively find the parameter values of a chaotic system with a rugged parameter landscape. Furthermore, even the parameters of a 200-dimensional coupled-map-lattice spatiotemporal chaotic system can be extracted from a scalar time series. Finally, a Chua’s circuit experiment shows the capacity of this method to estimate multiple parameters of real systems.

The finite-size Lyapunov exponent (FSLE) is the exponential rate at which two particles separate from a distance of $r$ to $a\times r$ $(a>1)$ and provides a measure of dispersive mixing in chaotic systems. It is shown analytically that for particle trajectories governed by symmetric $\alpha$-stable Levy motion, the FSLE is proportional to the diffusion coefficient and inversely proportional to $r^{\alpha }$. This power law provides an easy method to determine the parameters for Levy processes and hence has applications to superdiffusion in the atmospheric, oceanic, and terrestrial sciences.

A lattice of coupled chaotic dynamical systems may exhibit a completely synchronized state, which defines a low-dimensional invariant manifold in phase space. However, the high dimensionality of the latter typically yields a complex dynamics with many features like chaos suppression, quasiperiodicity, multistability, and intermittency. Such phenomena are described by considering the transversal dynamics to the synchronization manifold for a coupled logistic map lattice with a long-range coupling prescription.

We analytically address disease outbreaks in large, random networks with heterogeneous infectivity and susceptibility. The transmissibility $T_{uv}$ (the probability that infection of $u$ causes infection of $v$) depends on the infectivity of $u$ and the susceptibility of $v$. Initially, a single node is infected, following which a large-scale epidemic may or may not occur. We use a generating function approach to study how heterogeneity affects the probability that an epidemic occurs and, if one occurs, its attack rate (the fraction infected). For fixed average transmissibility, we find upper and lower bounds on these. An epidemic is most likely if infectivity is homogeneous and least likely if the variance of infectivity is maximized. Similarly, the attack rate is largest if susceptibility is homogeneous and smallest if the variance is maximized. We further show that heterogeneity in the infectious period is important, contrary to assumptions of previous studies. We confirm our theoretical predictions by simulation. Our results have implications for control strategy design and identification of populations at higher risk from an epidemic.

We report on the low temperature behavior of the colloidal electrolyte by means of molecular dynamics simulations, where the electrostatic interactions were modeled using effective screened interactions. As in previous works, we have found a region of gas-liquid coexistence located in the low $T$–low $\rho$ region. At temperatures much lower than the critical one, the system cannot reach equilibrium, that is, the gas-liquid transition is arrested. Two different mechanisms have been identified to cause arrest: crowding at intermediate $T$ values, associated with the crossing point between the binodal and the glass line, and a gelationlike arrest at very low $T$. To test the latter, the dynamics of the colloidal electrolyte near this crossing point has been computed and compared to the universal predictions of the ideal mode-coupling theory. As in other glass-forming liquids, we found good agreement between this mean field theory and the dynamics of this complex system, although it fails just at the transition. Interestingly, in this region we found that the dynamics of this system is driven mainly by the steric interactions, showing all the typical properties of a repulsive colloidal glass. Finally, the isodiffusivity lines show that in this system with short-range attractions, there is no reentrant glass phenomenon as opposed to monocomponent attractive systems.

We report static and dynamic light-scattering measurements of aqueous glucose solutions near their glass transition. Photon correlation spectroscopy reveals two relaxation processes present in the supercooled liquid: a nonexponential and nonhydrodynamic, $\alpha$-relaxation occurring at short times and an exponential and hydrodynamic relaxation occurring at longer times. The slow relaxation is seen only in the polarized scattering geometry and is in many ways identical to the “ultraslow” mode recently observed by others in specially annealed molecular glass-forming liquids and attributed to the formation of long-range density correlations or “dynamic clusters.” Static light scattering confirms the existence of excess scattering in our glucose solutions that is consistent with clusters in a size range between 30 and $60\mathrm{nm}$. The size of the clusters varies with the water content and the clustering appears to be associated with the percolation of a hydrogen-bonded glucose network.

We solve the graph bipartitioning problem in dense graphs with arbitrary degree distribution using the replica method. We find the cut size to scale universally with $⟨\sqrt{k}⟩$. In contrast, earlier results studying the problem in graphs with a Poissonian degree distribution had found a scaling with $\sqrt{⟨k⟩}$ [Fu and Anderson, J. Phys. A 19, 1605 (1986)]. Our results also generalize to the problem of $q$ partitioning. They can be used to find the expected modularity $Q$ [Newman and Girvan, Phys. Rev. E 69, 026113 (2004)] of random graphs and allow for the assessment of the statistical significance of the output of community detection algorithms.

Excitable media show changes in their basic characteristics that reflect temporal changes in the environment. In the photosensitive Belousov-Zhabotinsky (BZ) reaction, excitability is decreased by illumination. We found that a traveling pulse failed to propagate when a certain level of light intensity was switched on abruptly, but the pulse continued propagating when the light intensity reached the same level gradually. We investigated the mechanism of adaptation of pulse propagation to the change in light intensity using two mathematical models, the Oregonator model (a specific model for the photosensitive BZ reaction), and the FitzHugh-Nagumo model (a generic model for excitable media). The appearance of a characteristic such as adaptation is shown to be a general feature for a traveling pulse in excitable media.

The dynamics of spiral waves in a pair of linearly coupled reaction-diffusion systems is investigated. We find that the spiral dynamics depends on the coupling strength between the two subsystems. When the coupling strength is weak, the frequency and wavelength of the spiral wave in each subsystem remain unchanged. The interaction between the two subsystems induces the drift of spiral waves. When the coupling strength is strong, synchronization between the two subsystems is established. The two subsystems play different roles in the collective dynamics: one subsystem is always dominant and enslaves the other.

We study the dynamics of an adaptive coupled array of phase oscillators. The adaptive law is designed in such a way that the coupling grows stronger for the pairs which have larger phase incoherence. The proposed scheme enhances the synchronization and achieves a more reasonable coupling dynamics for the network of oscillators with different intrinsic frequencies. The synchronization speed and the steady-state phase difference can be adjusted by the parameters of the adaptive law. Besides global coupling, nearest-neighbor ring coupling is also considered to demonstrate the generality of the method.

The effect of weak dissipation on chaotic scattering is relevant to situations of physical interest. We investigate how the fractal dimension of the set of singularities in a scattering function varies as the system becomes progressively more dissipative. A crossover phenomenon is uncovered where the dimension decreases relatively more rapidly as a dissipation parameter is increased from zero and then exhibits a much slower rate of decrease. We provide a heuristic theory and numerical support from both discrete-time and continuous-time scattering systems to establish the generality of this phenomenon. Our result is expected to be important for physical phenomena such as the advection of inertial particles in open chaotic flows, among others.