We report experimental evidence of the fact that, in an emerging Rayleigh-Bénard structure, the density of defects which appear scales as a power law in the rate of change of the control parameter. The scaling exponents agree with those calculated from the Kibble-Zurek mechanism. This is the first evidence to our knowledge that this mechanism works in a hydrodynamical system.

We show that the quadratic $\left({\chi }^{\left(2\right)}\right)$ interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-focusing cubic $\left({\chi }^{\left(3\right)}\right)$ nonlinearity, give rise to stable three-dimensional spatiotemporal solitons (STSs), despite the possibility of the supercritical collapse, induced by the ${\chi }^{\left(3\right)}$ nonlinearity. At exact phase matching $(\beta =0)$, the STSs are stable for energies from zero up to a certain maximum value, while for $\beta \ne 0$ the solitons are stable in energy intervals between finite limits.

We study the reaction-diffusion process $A+B\to \varnothing$ on uncorrelated scale-free networks analytically. By a mean-field ansatz we derive analytical expressions for the particle pair correlations and the particle density. Expressing the time evolution of the particle density in terms of the instantaneous particle pair correlations, we determine analytically the “jamming” effect which arises in the case of multicomponent, pairwise reactions. Comparing the relevant terms within the differential equation for the particle density, we find that the “jamming” effect diminishes in the long-time, low-density limit. This even holds true for the hubs of the network, despite that the hubs dynamically attract the particles.

In this paper we study an evolving email network model first introduced by Wang and De Wilde, to the best of our knowledge. The model is analyzed by formulating the network topology as a random process and studying the dynamics of the process. Our analytical results show a number of steady state properties about the email traffic between different nodes and the aggregate networking behavior (i.e., degree distribution, clustering coefficient, average path length, and phase transition), and also confirm the empirical results obtained by Wang and De Wilde. We also conducted simulations confirming the analytical results. Extensive simulations were run to evaluate email traffic behavior at the link and network levels, phase transition phenomena, and also studying the behavior of email traffic in a hierarchical network. The methods established here are also applicable to many other practical networks including sensor networks and social networks.

A simple model for the forces acting on a single fiber as it is withdrawn from a tangled fiber assembly is proposed. Particular emphasis is placed on understanding the dynamics of the reptating fiber with respect to the entanglement of fibers within the tuft. The resulting two-parameter model captures the qualitative features of experimental simulation. The model is extended to describe the breakup of a tuft. The results show good agreement with experiment and indicate where a tuft is most likely to fracture based on the density of fiber endpoints.

The critical behavior of the contact process (CP) in heterogeneous periodic and weakly disordered environments is investigated using the supercritical series expansion and Monte Carlo (MC) simulations. Phase-separation lines and critical exponents $\beta$ (from series expansion) and $\eta$ (from MC simulations) are calculated. A general analytical expression for the locus of critical points is suggested for the weak-disorder limit and confirmed by the series expansion analysis and the MC simulations. Our results for the critical exponents show that the CP in heterogeneous environments remains in the directed percolation universality class, while for environments with quenched disorder, the data are compatible with the scenario of continuously changing critical exponents.

We study the orientational relaxation of a spiral pattern around a central defect with topological strength $S=+1$ in free-standing smectic films. Instead of a continuous unwinding, a characteristic stick-slip relaxation is observed, where the elastic anisotropy plays the dominant role for the director anchoring in the vicinity of the defect. A model derived from nematic continuum theory is used to interpret the experimental observations.

The effect of shear on crystalline order is interesting fundamentally, as well as technologically, for producing long-range alignment of micron- and nanoscale structures. We study the influence of shear on a sphere-forming diblock copolymer thin film consisting of a stack of two to six hexagonal layers, using a stress-controlled rheometer to transmit the stress through a viscous fluid layer. Above a threshold stress, the hexagonal layers align macroscopically in the “easy shear” direction. A simple phenomenological model with an orientation-dependent order-disorder temperature, $T_{\mathrm{ODT}}^{*}\left(\delta \theta \right)=T_{\mathrm{ODT}}[1-(\sigma ∕{\sigma }_c){\sin }^2\left(3\delta \theta \right)]$ and recrystallization describes the influence of stress level, temperature, and shearing time remarkably well.

Nuclear magnetic resonance imaging measurements of liquid water ingress in a large number of nonactivated Y-type (Na) zeolite samples prepared under different conditions are reported on. Using an experimental arrangement that permits the application of Boltzmann’s transformation of the 1D (one-dimensional) diffusion equation, the spatiotemporal scaling variables required for a collapse of the measured profiles into universal curves revealed subdiffusive behavior in all cases. It is shown that the one-dimensional fractal time diffusion equation constitutes a powerful tool to analyze the data and provides a connection between the moisture dependence of the effective transport diffusivities and the shapes of the universal curves. Thus, even for anomalous diffusion, the relationship between the universal curves and structural characteristics of the system; such as porosity, tortuosity of the pore space and, in some cases, the interplay between mesopores and nanopores can be addressed.

We study the threshold control protocol for a collective flashing ratchet. In particular, we analyze the dependence of the current on the values of the thresholds. We have found analytical expressions for the small threshold dependence both for the few and for the many particle cases. For few particles the current is a decreasing function of the thresholds, thus, the maximum current is reached for zero thresholds. In contrast, for many particles the optimal thresholds have a nonzero finite value. We have numerically checked the relation that allows to obtain the optimal thresholds for an infinite number of particles from the optimal period of the periodic protocol. These optimal thresholds for an infinite number of particles give good results for many particles. In addition, they also give good results for few particles due to the smooth dependence of the current up to these threshold values.

Microarray data analysis is useful for understanding biological processes. A number of clustering algorithms have been used to achieve this task. However, the performance of these methods can be significantly degraded due to the presence of nonsignificant conditions. In this paper, we propose a robust clustering algorithm based on a similarity measure. The key concept of the proposed similarity measure is to measure the similarity between two data points by their subdimensions. For example, assume that ${\mathbf{x}}_1$, ${\mathbf{x}}_2$, and ${\mathbf{x}}_3$ are ten-dimensional data vectors. The data point ${\mathbf{x}}_3$ is said to be closer to ${\mathbf{x}}_1$ than ${\mathbf{x}}_2$ if more than half of the dimensions of ${\mathbf{x}}_1$ and ${\mathbf{x}}_3$ are closer to ${\mathbf{x}}_1$ than ${\mathbf{x}}_2$. Thus, if two patterns are very similar except for a small amount of features, this measure will preserve the similarity. We have performed eight experiments to test the robustness of the proposed method, including three synthetic data sets, three real world data sets, and two microarray data sets. We also have compared the proposed method with four different clustering algorithms. Experimental results show that the proposed method yields better results than existing clustering algorithms.

Two three-dimensional $AB$ off-lattice protein models consisting of hydrophobic and hydrophilic monomers are studied in this paper. By incorporating an extra energy contribution into the original energy function, the protein folding is converted from a constraint optimization problem into an unconstrained one which can be solved by the well-known gradient method. From the initial configurations randomly generated by the heuristic strategy proposed in this paper, our algorithm can find better results than those by nPERM for the four Fibonacci sequences. Based on the initial configurations obtained by energy landscape paving (ELP) routine, some of our results for the lowest energies are better than the best values reported in the literature.

In this paper we present a model to describe the electrical properties of a confluent cell monolayer cultured on gold microelectrodes to be used with electric cell-substrate impedance sensing technique. This model was developed from microscopic considerations (distributed effects), and by assuming that the monolayer is an element with mean electrical characteristics (specific lumped parameters). No assumptions were made about cell morphology. The model has only three adjustable parameters. This model and other models currently used for data analysis are compared with data we obtained from electrical measurements of confluent monolayers of Madin-Darby Canine Kidney cells. One important parameter is the cell-substrate height and we found that estimates of this magnitude strongly differ depending on the model used for the analysis. We analyze the origin of the discrepancies, concluding that the estimates from the different models can be considered as limits for the true value of the cell-substrate height.

The responses of synapses in the neocortex show highly stochastic and nonlinear behavior. The microscopic dynamics underlying this behavior, and its computational consequences during natural patterns of synaptic input, are not explained by conventional macroscopic models of deterministic ensemble mean dynamics. Here, we introduce the correlation entropy of the synaptic input-output map as a measure of synaptic reliability which explicitly includes the microscopic dynamics. Applying this to experimental data, we find that cortical synapses show a low-dimensional chaos driven by the natural input pattern.

We study the structural stability of models of proteins for which the selected folds are unusually stable to mutation, that is, designable. A two-dimensional hydrophobic-polar lattice model was used to determine designable folds and these folds were investigated through Langevin dynamics. We find that the phase diagram of these proteins depends on their designability. In particular, highly designable folds are found to be weaker, i.e., easier to unfold, than low designable ones. We expect this to be related to protein flexibility.

Recent studies on complex systems have shown that the synchronization of oscillators, including neuronal ones, is faster, stronger, and more efficient in small-world networks than in regular or random networks. We show that the functional structures in the brain can be self-organized to both small-world and scale-free networks by synaptic reorganization via spike timing dependent synaptic plasticity instead of conventional Hebbian learning rules. We show that the balance between the excitatory and the inhibitory synaptic inputs is critical in the formation of the functional structure, which is found to lie in a self-organized critical state.

We study the synchronizability of weighted aging scale-free networks with non-normalized and asymmetrical coupling matrices. We found that the synchronizability of such networks is improved when the couplings from older to younger nodes become dominant, where the out degrees of the nodes are heterogeneous and their in degrees are homogeneous, and that the synchronizabilty of the networks is seriously weakened or even lost when the couplings from younger to older nodes become dominant, where the out degrees of the nodes are homogeneous and their in degrees are heterogeneous. We also found that both the heterogeneity of nodes and a smaller average degree can improve the synchronizability of the networks with some appropriately chosen weighting parameter values. We finally show an example of the coupled Lorenz systems for illustration and verification of the theoretical analysis.

An example of a flow system is presented with an attractor concentrated mostly at a surface of a two-dimensional torus, the dynamics on which is governed by the Arnold cat map. The system is composed of four coupled nonautonomous van der Pol oscillators. Three of them have equal characteristic frequencies, and in the other one the frequency is twice as large. The parameters controlling excitation of the two pairs of oscillators are forced to undergo a slow counterphase periodic modulation in time. At the end of the active stage for one pair of the oscillators, the excitation is passed to another pair, than back, and so on. In terms of a stroboscopic Poincaré section, the respective eight-dimensional (8D) mapping, due to strong phase volume compression, reduces approximately to a 2D map for the phases of one pair of the oscillators that corresponds approximately to the Arnold cat map. The largest two Lyapunov exponents (one positive and one negative) are close to those predicted with the cat map model. Estimates for the fractal dimension of the attractor of the Poincaré map are close to 2.