We study phase ordering dynamics of spatially periodic striped patterns on the small-world network that is derived from a two-dimensional regular lattice with distance-dependent random connections. It is demonstrated numerically that addition of spatial disorder in the form of shortcuts makes the growth of domains much slower or even frozen at late times.

Recently, waves propagating with negative phase velocity [simply called antiwaves (AWs)] have attracted great attention in the area of nonlinear oscillatory systems. In the present work we investigate the parameter conditions for AWs. So far AWs have been revealed from systems slightly beyond Hopf bifurcation or some other instabilities, and from some wave sources with certain restricted frequencies. Here we study general oscillatory media (including generalized complex Ginzburg-Landau systems and Brusselator model) and specify the parameter conditions of AWs by certain characteristic behaviors of the dispersion relation of the systems. Moreover, we predict that AWs and NWs (normal waves with positive phase velocity) can be realized at a same intrinsic parameter values but different pacing frequencies in parameter regions where the dispersion relation exhibits a maximum or minimum. All numerical simulations are perfectly consistent with these theoretical predictions where the oscillatory systems are driven by external periodic pacings with 1:1 frequency locking responses.

In recent years non-normality and transient growths have attracted much interest in fluid mechanics. Here, we investigate these topics with reference to the problem of interfacial instability in superposed Newtonian and non-Newtonian fluid layers. Under the hypothesis of the lubrication theory, we demonstrate the existence of significant transient growths in the parameter space region where the dynamical system is asymptotically stable, and show how they depend on the main physical parameters. In particular, the key role of the density ratio is highlighted.

In this work, the generalized Bautista-Manero-Puig (BMP) model derived from extended irreversible thermodynamics (EIT) is used to analyze the coupling of stress with concentration in complex fluids. It is shown that this model is consistent with previous analyses that predict mechanical and thermodynamic instabilities in the shear-banding regime. In particular, for simple shear flows, the model presented here predicts the structure factor in the plane of shear and the onset of instabilities in the gradient-vorticity plane. Furthermore, the model predicts distinctive features of the models of Brochard–de Gennes and Schmitt et al. as particular cases. For finite stress relaxation time, the generalized BMP model allows the prediction of transient structures normal to the vorticity axis. Instabilities are predicted in the regions of high viscosity, which suggest that the induction of a more viscous phase in a shear-thickening solution can lead the system to instability, in this case, the layering is predicted perpendicular to the vorticity direction. These transient structural patterns within the shear-thickening region correspond to spinodal phase separation. When the mechanical and thermodynamic instabilities are uncoupled, the model predictions agree with experiments and with the transient-gel model of Brochard and de Gennes.

The local-mean-energy approximation (LMEA) and the local-field approximation (LFA) are commonly applied to include the electron properties like transport and rate coefficients into a hydrodynamic description of gas discharge plasmas. Both the approaches base on the solution of the stationary spatially homogeneous Boltzmann equation for the electron component, but the consequences of these approaches differ drastically. These consequences of using both the approaches are studied and discussed on a kinetic level and by comparison of results of hydrodynamic investigations of low-pressure glow discharge plasmas. It is found that the LMEA is to be strongly recommended for the application to a hydrodynamic description of dc as well as rf discharge plasmas, while the LFA is conditionally suitable to describe dc glow discharges with rough reaction kinetics only and its application to rf discharge plasmas is inappropriate.

Reciprocity theorems for perturbed acoustic media are provided in the form of convolution- and correlation-type theorems. These reciprocity relations are particularly useful in the general treatment of both forward and inverse-scattering problems. Using Green’s functions to describe perturbed and unperturbed waves in two distinct wave states, representation theorems for scattered waves are derived from the reciprocity relations. While the convolution-type theorems can be manipulated to obtain scattering integrals that are analogous to the Lippmann-Schwinger equation, the correlation-type theorems can be used to retrieve the scattering response of the medium by cross correlations. Unlike previous formulations of Green’s function retrieval, the extraction of scattered-wave responses by cross correlations does not require energy equipartitioning. Allowing for uneven energy radiation brings experimental advantages to the retrieval of fields scattered by remote lossless and/or attenuative scatterers. These concepts are illustrated with a number of examples, including analytic solutions to a one-dimensional scattering problem, and a numerical example in the context of seismic waves recorded on the ocean bottom.

The aim of this paper is to compare results from lattice Boltzmann and Brownian-dynamics simulations of linear chain molecules. We have systematically varied the parameters that may affect the accuracy of the lattice Boltzmann simulations including grid resolution, temperature, polymer mass, and fluid viscosity. The effects of the periodic boundary conditions are minimized by an analytic correction for the different long-range interactions in periodic and unbounded systems. Lattice Boltzmann results for the diffusion coefficient and Rouse mode relaxation times were found to be insensitive to temperature, which suggests that effects of hydrodynamic retardation are small. By increasing the resolution of the lattice Boltzmann grid with respect to the polymer size, convergent results for the diffusion coefficient and relaxation times were obtained; these results agree with Brownian dynamics to within 1%–2%.

We investigate the different regimes that emerge when a periodic driving force, the rocking force, acts on a collective feedback flashing ratchet. The interplay of the rocking and the feedback control gives a rich dynamics with different regimes presenting several unexpected features. In particular, we show that for both the one-particle ratchet and the collective version of the ratchet an appropriate rocking increases the flux. This mechanism gives the maximum flux that has been achieved in a ratchet device without an a priori bias.

The kinetics of isotropic-nematic (I-N) and nematic-isotropic (N-I) phase transitions in dispersions of rodlike fd viruses are studied. Concentration quenches were applied using pressure jumps in combination with polarization microscopy, birefringence, and turbidity measurements. The full biphasic region could be accessed, resulting in the construction of an experimental analog of the bifurcation diagram. The N-I spinodal points for dispersions of rods with varying concentrations of depletion agent (dextran) were obtained from orientation quenches using cessation of shear flow in combination with small-angle light scattering. We found that the location of the N-I spinodal point is independent of the attraction, which was confirmed by theory. Surprisingly, the experiments showed that also the absolute induction time, the critical nucleus, and the growth rate are insensitive of the attraction if the concentration is scaled to the distance to the phase boundaries.

We describe the use of a bright-field microscope for dynamic light scattering experiments on weakly scattering samples. The method is based on collecting a time sequence of microscope images and analyzing them in the Fourier space to extract the characteristic time constants as a function of the scattering wave vector. We derive a theoretical model for microscope imaging that accounts for (a) the three-dimensional nature of the sample, (b) the arbitrary coherence properties of the light source, and (c) the effect of the finite numerical aperture of the microscope objective. The model is tested successfully against experiments performed on a colloidal dispersion of small spheres in water, by means of the recently introduced differential dynamic microscopy technique [R. Cerbino and V. Trappe, Phys. Rev. Lett. 100, 188102 (2008)]. Finally, we extend our model to the class of microscopy techniques that can be described by a linear space-invariant imaging of the density of the scattering centers, which includes, for example, dynamic fluorescence microscopy.

Layered phases are a common pattern of self-organization for several soft materials. These phases undergo buckling instability when subjected to dilatative strain: beyond a critical threshold, layers, initially flat, exhibit a periodical undulation. By using a continuum model, in a finite deformation framework, an expression for the critical threshold is provided, which differs from that predicted by the Helfrich-Hurault theory and yet it reverts to it in a thick specimen limit. With respect to the relevant literature, an analogous disagreement is found in the undulation amplitude expression as well. The obtained results appear particularly relevant when dealing with layered materials whose intrinsic coherence length is comparable to the cell thickness.

Spherical lipid vesicles obtained by the extrusion method are nonequilibrium membrane structures more curved than the zero spontaneous curvature equilibrium state of the bilayer. Furthermore, these structures are quite rigid as compared to spontaneous vesicles or microemulsion droplets made of soluble surfactants. The dynamical description of the shape fluctuations derived by Milner and Safran (MS) [Phys. Rev. A 36, 4371 (1987)], which is based on the elastic Helfrich energy referred to the equilibrium state, could be misleading in these cases. In the present contribution, shape fluctuations of unilamellar palmitoyl-oleyl-phosphocholine (POPC) vesicles (radius $R_h\le 100\text{nm}$) prepared by extrusion are studied by means of neutron spin echo (NSE) in combination with dynamic light scattering (DLS). The relaxation of the fluctuation modes is inferred from the DLS autocorrelation functions and from the intermediate NSE scattering functions measured for several different values of the wave vector. The observed relaxations are compatible with a stretched-exponential decay rather than the single-exponential behavior. Dynamical frustration of the bulk dissipation mechanism in the way described by Zilman and Granek (ZG) for weak amplitude fluctuations [Phys. Rev. Lett. 77, 4788 (1996)] is invoked as a plausible scenario for explaining the subdiffusive nonexponential relaxations experimentally observed. The combined analysis of NSE and DLS data allows a calculation of the bending elastic constant of POPC vesicles $\kappa =19\pm 2k_{B}T$, in excellent agreement with literature data. The ZG approach is revealed as the adequate extension of the MS theory to describe fluctuation dynamics of rigid membranes.

Stochastic integrate-and-fire (IF) neuron models have found widespread applications in computational neuroscience. Here we present results on the white-noise-driven perfect, leaky, and quadratic IF models, focusing on the spectral statistics (power spectra, cross spectra, and coherence functions) in different dynamical regimes (noise-induced and tonic firing regimes with low or moderate noise). We make the models comparable by tuning parameters such that the mean value and the coefficient of variation of the interspike interval (ISI) match for all of them. We find that, under these conditions, the power spectrum under white-noise stimulation is often very similar while the response characteristics, described by the cross spectrum between a fraction of the input noise and the output spike train, can differ drastically. We also investigate how the spike trains of two neurons of the same kind (e.g., two leaky IF neurons) correlate if they share a common noise input. We show that, depending on the dynamical regime, either two quadratic IF models or two leaky IFs are more strongly correlated. Our results suggest that, when choosing among simple IF models for network simulations, the details of the model have a strong effect on correlation and regularity of the output.

The blue scales on the cuticle of the male beetle Hoplia coerulea can absorb water, with the consequence that these scales, which have been shown to be responsible for the beetle’s bright blue coloration, reversibly turn to emerald green with increasing water contents. Optical measurements are shown, by analytic photonic-crystal models, to be compatible with the full filling of the scales structures with water. The natural mechanism shows the way to produce a very efficient hygrochromic material: a medium which significantly changes color when its water contents are modified.

Pattern formation induced by noise is a celebrated phenomenon in diverse reaction-diffusion systems. Here we report numerical simulations with the Lengyel-Epstein model for the chlorine dioxide-iodine-malonic acid reaction when perturbed with an external spatiotemporal stochastic forcing in the vicinity of the Hopf and Turing codimension-two bifurcation. Competition between Turing and Hopf modes gives rise to the generation of transient Turing patterns evolving to stationary global oscillations. This situation is reversed by the introduction of external fluctuations and Turing patterns become dominant in this case. The increase in the spatial coherence is found for intermediate noise intensity and small correlation length.

Detecting communities in complex networks accurately is a prime challenge, preceding further analyses of network characteristics and dynamics. Until now, community detection took into account only positively valued links, while many actual networks also feature negative links. We extend an existing Potts model to incorporate negative links as well, resulting in a method similar to the clustering of signed graphs, as dealt with in social balance theory, but more general. To illustrate our method, we applied it to a network of international alliances and disputes. Using data from 1993-2001, it turns out that the world can be divided into six power blocs similar to Huntington’s civilizations, with some notable exceptions.

Starch-water slurries are commonly used to study fracture dynamics. Drying starch cakes benefit from being simple, economical, and reproducible systems, and have been used to model desiccation fracture in soils, thin-film fracture in paint, and columnar joints in lava. In this paper, the physical properties of starch-water mixtures are studied, and used to interpret and develop a multiphase transport model of drying. Starch cakes are observed to have a nonlinear elastic modulus, and a desiccation strain that is comparable to that generated by their maximum achievable capillary pressure. It is shown that a large material porosity is divided between pore spaces between starch grains, and pores within starch grains. This division of pore space leads to two distinct drying regimes, controlled by liquid and vapor transport of water, respectively. The relatively unique ability for drying starch to generate columnar fracture patterns is shown to be linked to the unusually strong separation of these two transport mechanisms.

We develop a collective-phase description for a population of nonidentical limit-cycle oscillators with any network structure undergoing fully phase-locked collective oscillations. The whole network dynamics can be described by a single collective-phase variable. We derive a general formula for the collective-phase sensitivity, which quantifies the phase response of the whole network to weak external perturbations applied to the constituent oscillators. Moreover, we consider weakly interacting multiple networks and develop an effective phase coupling description for them. Several examples are given to illustrate our theory.

Scalar transport in closed potential flows is investigated for the specific case of a periodically reoriented dipole flow. Despite the irrotational nature of the flow, the periodic reorientations effectively create heteroclinic and/or homoclinic points arising from the joining of stable and unstable manifolds. For scalar advection, Lagrangian chaos can be achieved with breakdown of the regular Hamiltonian structure, which is governed by symmetry conditions imposed by the dipole flow. Instability envelopes associated with period-doubling bifurcations of fixed points govern which regions of the flow control parameter space admit global chaos. These regions are further refined via calculation of Lyapunov exponents. These results suggest significant scalar transport enhancement is possible within potential flows, given appropriate programming of stirring protocols.

The stability of dynamical states characterized by a uniform firing rate (splay states) is analyzed in a network of $N$ globally pulse-coupled rotators (neurons) subject to a generic velocity field. In particular, we analyze short-wavelength modes that were known to be marginally stable in the infinite $N$ limit and show that the corresponding Floquet exponent scale as $1/N^2$. Moreover, we find that the sign, and thereby the stability, of this spectral component is determined by the sign of the average derivative of the velocity field. For leaky-integrate-and-fire neurons, an analytic expression for the whole spectrum is obtained. In the intermediate case of continuous velocity fields, the Floquet exponents scale faster than $1/N^2$ (namely, as $1/N^4$) and we even find strictly neutral directions in a wider class than the sinusoidal velocity fields considered by Watanabe and Strogatz [Physica D 74, 197 (1994)].