Complex networks emerge under different conditions including design (i.e., top-down decisions) through simple rules of growth and evolution. Such rules are typically local when dealing with biological systems and most social webs. An important deviation from such a scenario is provided by groups, collectives of agents engaged in technology development, such as open-source communities. Here we analyze their network structure, showing that it defines a complex weighted network with scaling laws at different levels, as measured by looking at e-mail exchanges. We also present a simple model of network growth involving nonlocal rules based on betweenness centrality. Our weighted network analysis suggests that a well-defined interplay between the overall goals of the community and the underlying hierarchical organization play a key role in shaping its dynamics.

A two dimensional amorphous material is modeled as an assembly of mesoscopic elemental pieces coupled together to form an elastically coherent structure. Plasticity is introduced as the existence of different minima in the energy landscape of the elemental constituents. Upon the application of an external strain rate, the material shears through the appearance of elemental slip events with quadrupolar symmetry. When the energy landscape of the elemental constituents is kept fixed, the slip events distribute uniformly throughout the sample, producing on average a uniform deformation. However, when the energy landscape at different spatial positions can be rearranged dynamically to account for structural relaxation, the system develops inhomogeneous deformation in the form of shear bands at low shear rates, and stick-slip-like motion at the shear bands for the lowest shear rates. The origin of strain localization is traced back to a region of negative correlation between strain rate and stress, which appears only if structural relaxation is present. The model also reproduces other well known effects in the rheology of amorphous materials, as a stress peak in a strain rate controlled experiment staring from rest, and the increase of the maximum of this peak with sample age.

We investigate the decoherence properties of a central system composed of two spins $1∕2$ in contact with a spin bath. The dynamical regime of the bath ranges from a fully integrable limit to complete chaoticity. We show that the dynamical regime of the bath determines the efficiency of the decoherence process. For perturbative regimes, the integrable limit provides stronger decoherence, while in the strong coupling regime the chaotic limit becomes more efficient. We also show that the decoherence time behaves in a similar way. On the contrary, the rate of decay of magnitudes like linear entropy or fidelity does not depend on the dynamical regime of the bath. We interpret the latter results as due to a comparable complexity of the Hamiltonian for both the integrable and the fully chaotic limits.

It is shown that, in a three-coupled-mode approximation, exact analytical solution of a system of equations, that describes a steady-state parametric frequency conversion, can be obtained as a solution of three closed nonlinear Schrödinger equations, coupled only through their boundary conditions. A reason for such a possibility lies in the description of the competition of two simultaneous second-order nonlinear processes in terms of an effective cascade cubic nonlinearity. Specific features and nontrivial asymptotes of complex self-consistent periodic solutions of the nonlinear Schrödinger equation are discussed.

By using projection superoperators, we present a new derivation of the quantum master equation first obtained by the authors in Phys. Rev. E 68, 066112 (2003). We show that this equation describes the dynamics of a subsystem weakly interacting with an environment of finite heat capacity and initially described by a microcanonical distribution. After applying the rotating wave approximation to the equation, we show that the subsystem dynamics preserves the energy of the total system (subsystem plus environment) and tends towards an equilibrium state which corresponds to equipartition inside the energy shell of the total system. For infinite heat capacity environments, this equation reduces to the Redfield master equation for a subsystem interacting with a thermostat. These results should be of particular interest to describe relaxation and decoherence in nanosystems where the environment can have a finite number of degrees of freedom and the equivalence between the microcanonical and the canonical ensembles is thus not always guaranteed.

A fast computer algorithm, the pebble game, has been used successfully to analyze the rigidity of two-dimensional (2D) elastic networks, as well as of a special class of 3D networks, the bond-bending networks, and enabled significant progress in studies of rigidity percolation on such networks. Application of the pebble game approach to general 3D networks has been hindered by the fact that the underlying mathematical theory is, strictly speaking, invalid in this case. We construct an approximate pebble game algorithm for general 3D networks, as well as a slower but exact algorithm, the relaxation algorithm, that we use for testing the new pebble game. Based on the results of these tests and additional considerations, we argue that in the particular case of randomly diluted central-force networks on bcc and fcc lattices, the pebble game is essentially exact. Using the pebble game, we observe an extremely sharp jump in the largest rigid cluster size in bond-diluted central-force networks in 3D, with the percolating cluster appearing and taking up most of the network after a single bond addition. This strongly suggests a first-order rigidity percolation transition, which is in contrast to the second-order transitions found previously for the 2D central-force and 3D bond-bending networks. While a first order rigidity transition has been observed previously for Bethe lattices and networks with “chemical order,” here it is in a regular randomly diluted network. In the case of site dilution, the transition is also first order for bcc lattices, but results for fcc lattices suggest a second-order transition. Even in bond-diluted lattices, while the transition appears massively first order in the order parameter (the percolating cluster size), it is continuous in the elastic moduli. This, and the apparent nonuniversality, make this phase transition highly unusual.

The dynamics of particles interacting by key-lock binding of attached biomolecules are studied theoretically. Experimental realizations of such systems include colloids grafted with complementary single-stranded DNA (ssDNA), and particles grafted with antibodies to cell-membrane proteins. Depending on the coverage of the functional groups, we predict two distinct regimes. In the low coverage localized regime, there is an exponential distribution of departure times. As the coverage is increased the system enters a diffusive regime resulting from the interplay of particle desorption and diffusion. This interplay leads to much longer bound state lifetimes, a phenomenon qualitatively similar to aging in glassy systems. The diffusion behavior is analogous to dispersive transport in disordered semiconductors: depending on the interaction parameters it may range from a finite renormalization of the diffusion coefficient to anomalous, subdiffusive behavior. We make connections to recent experiments and discuss the implications for future studies.

The dynamics of two spatially discrete one-dimensional single-step model interfaces with a noncrossing constraint is studied in both nonsymmetric propagating and symmetric relaxing cases. We consider possible scaling scenarios and study a few special cases by using continuous-time Monte Carlo simulations. The roughness of the interfaces is observed to be nonmonotonic as a function of time, and in the stationary state it is nonmonotonic also as a function of the strength of the effective force driving the interfaces against each other. This is related on the one hand to the reduction of the available configuration space and on the other hand to the ability of the interfaces to conform to each other.

Using classical density functional theory, the structure of a molecular fluid around a cylindrical nanoparticle near a solid substrate is studied. The solvent-mediated force between the nanoparticle and the substrate is calculated in both the nematic and isotropic phases of the solvent. In the nematic phase, the force is short ranged and arises due to interaction between high-density regions near the substrate and nanoparticle. In the isotropic phase, the formation of a nematic bridge between the substrate and nanoparticle gives rise to an attractive force between them. The potential between the nanoparticle and substrate as a function of separation calculated numerically is compared to that calculated from the Derjaguin approximation. In the isotropic phase these are found to be in reasonable agreement at low separations, while the agreement is poorer in the nematic phase.

Drastic change in dynamics and statistics in a chemical reaction system, induced by smallness in the molecule number, is reported. Through stochastic simulations for random catalytic reaction networks, transition to a state is observed with the decrease in the total molecule number $N$, characterized by (i) large fluctuations in chemical concentrations as a result of intermittent switching over several states with extinction of some molecule species and (ii) strong deviation of time averaged distribution of chemical concentrations from that expected in the continuum limit, i.e., $N\to \infty$. The origin of transition is explained by the deficiency of the molecule leading to termination of some reactions. The critical number of molecules for the transition is obtained as a function of the number of molecule species $M$ and that of reaction paths $K$, while total reaction rates, scaled properly, are shown to follow a universal form as a function of $NK∕M$.

We propose a method for estimating nonlinear interdependences between time series using cellular nonlinear networks. Our approach is based on the nonlinear dynamics of interacting nonlinear elements. We apply it to time series of coupled nonlinear model systems and to electroencephalographic time series from an epilepsy patient, and we show that an accurate approximation of symmetric and asymmetric realizations of a nonlinear interdependence measure can be achieved, thus allowing one to detect the strength and direction of couplings.

Experimental studies have linked alternans, an abnormal beat-to-beat alternation of cardiac action potential duration, to the genesis of lethal arrhythmias such as ventricular fibrillation. Prior studies have considered various closed-loop feedback control algorithms for perturbing interstimulus intervals in such a way that alternans is suppressed. However, some experimental cases are restricted in that the controller’s stimuli must preempt those of the existing waves that are propagating in the tissue, and therefore only shortening perturbations to the underlying pacing are allowed. We present results demonstrating that a technique known as extended time-delay autosynchronization (ETDAS) can effectively control alternans locally while operating within the above constraints. We show that ETDAS, which has already been used to control chaos in physical systems, has numerous advantages over previously proposed alternans control schemes.

Based on recent work [L. Machura, M. Kostur, P. Talkner, J. Luczka, and P. Hanggi, Phys. Rev. Lett. 98, 040601 (2007)], we extend the study of inertial Brownian motors to the case of an asymmetric potential. It is found that some transport phenomena appear in the presence of an asymmetric potential. Within tailored parameter regimes, there exists two optimal values of the load at which the mean velocity takes its maximum, which means that a load can facilitate the transport in the two parameter regimes. In addition, the phenomenon of multiple current reversals can be observed when the load is increased.

One-mode projecting is extensively used to compress bipartite networks. Since one-mode projection is always less informative than the bipartite representation, a proper weighting method is required to better retain the original information. In this article, inspired by the network-based resource-allocation dynamics, we raise a weighting method which can be directly applied in extracting the hidden information of networks, with remarkably better performance than the widely used global ranking method as well as collaborative filtering. This work not only provides a creditable method for compressing bipartite networks, but also highlights a possible way for the better solution of a long-standing challenge in modern information science: How to do a personal recommendation.

To investigate the universality of the structure of interactions in different markets, we analyze the cross-correlation matrix $\mathbf{C}$ of stock price fluctuations in the National Stock Exchange (NSE) of India. We find that this emerging market exhibits strong correlations in the movement of stock prices compared to developed markets, such as the New York Stock Exchange (NYSE). This is shown to be due to the dominant influence of a common market mode on the stock prices. By comparison, interactions between related stocks, e.g., those belonging to the same business sector, are much weaker. This lack of distinct sector identity in emerging markets is explicitly shown by reconstructing the network of mutually interacting stocks. Spectral analysis of $\mathbf{C}$ for NSE reveals that, the few largest eigenvalues deviate from the bulk of the spectrum predicted by random matrix theory, but they are far fewer in number compared to, e.g., NYSE. We show this to be due to the relative weakness of intrasector interactions between stocks, compared to the market mode, by modeling stock price dynamics with a two-factor model. Our results suggest that the emergence of an internal structure comprising multiple groups of strongly coupled components is a signature of market development.

We investigate the effects of cross-diffusion on propagating waves in an activator-inhibitor system. The model consists of a piecewise linear approximation of FitzHugh-Nagumo kinetics and a cross-diffusion term for either the activator or the inhibitor. We obtain exact analytic solutions for traveling fronts and solitary pulses and discuss the corresponding speed diagrams. A detailed comparison with the corresponding Rinzel-Keller model for the usually studied case of self-diffusion is performed.

We show that chemical activity in hydrodynamical flows can be understood as the outcome of three basic effects: the stirring protocol of the flow, the local properties of the reaction, and the global folding dynamics which also depends on the geometry of the container. The essence of each of these components can be described by simple functional relations. In an ordinary differential equation approach, they determine a new chemical rate equation for the concentration, which turns out to be coupled to the dynamics of an effective fractal dimension. The theory predicts an exponential convergence to the asymptotic chemical state. This holds even in flows characterized by a linear stirring protocol where transient fractal patterns are shown to exist despite the lack of any chaotic set of the advection dynamics. In the exponential case the theory applies to flows of chaotic time dependence (chaotic flows) as well.

The temporal dynamics in the fluctuations of the plasma floating potentials from an undriven dc glow discharge argon plasma at an intermediate gas pressure of $250\mathrm{mTorr}$ and at the range of discharge currents $I=6–50\mathrm{mA}$ are investigated. In this study, the discharge current $I$ is used as the plasma system’s bifurcation parameter in analogy with the parameter space of a numerical dynamical system. Over several regions of the discharge current, the floating potential fluctuation time series data has been indicative of random noise, periodic oscillations, and irregular fluctuations. As the bifurcation parameter (discharge current) is increased, the Fourier spectrum of the data shows increased signs of period multiplication, quasiperiodicity, and instabilities. In addition, the computations of the correlation dimension provide some insight into the complex nature of the instabilities in the glow discharge plasma.

Analysis of the movement of particles in a nonuniform field requires accurate knowledge of the electric field distribution in the system. This paper describes a method for analytically solving the electric field distribution above interdigitated electrode arrays used for dielectrophoresis (DEP) and traveling wave dielectrophoresis (twDEP), using the Schwarz-Christoffel mapping method. The electric field solutions are used to calculate the dielectrophoretic force in both cases, and the traveling wave dielectrophoretic force and the electrorotational torque for the twDEP case. This method requires no approximations and can take into account the Neumann boundary condition used to represent an insulating lid and lower substrate. The analytical results of the electric field distributions are validated for different geometries by comparison with numerical simulations using the finite element method.