In this paper, two important factors which affect the pedestrian outflow at a bottleneck significantly are studied in detail to analyze the effect of an obstacle setup in front of an exit. One is a conflict at an exit when pedestrians evacuate from a room. We use floor field model for simulating such behavior, which is a well-studied pedestrian model using cellular automata. The conflicts have been taken into account by the friction parameter. However, the friction parameter so far is a constant and does not depend on the number of the pedestrians conflicting at the same time. Thus, we have improved the friction parameter by the frictional function, which is a function of the number of the pedestrians involved in the conflict. Second, we have presented the cost of turning of pedestrians at the exit. Since pedestrians have inertia, their walking speeds decrease when they turn and the pedestrian outflow decreases. The validity of the extended model, which includes the frictional function and the turning function, is supported by the comparison of a mean-field theory and real experiments. We have observed that the pedestrian flow increases when we put an obstacle in front of an exit in our real experiments. The analytical results clearly explains the mechanism of the effect of the obstacle, i.e., the obstacle blocks pedestrians moving to the exit and decreases the average number of pedestrians involved in the conflict. We have also found that an obstacle works more effectively when we shift it from the center since pedestrians go through the exit with less turning.

Master-stability functions (MSFs) are fundamental to the study of synchronization in complex dynamical systems. For example, for a coupled oscillator network, a necessary condition for synchronization to occur is that the MSF at the corresponding normalized coupling parameters be negative. To understand the typical behaviors of the MSF for various chaotic oscillators is key to predicting the collective dynamics of a network of these oscillators. We address this issue by examining, systematically, MSFs for known chaotic oscillators. Our computations and analysis indicate that it is generic for MSFs being negative in a finite interval of a normalized coupling parameter. A general scheme is proposed to classify the typical behaviors of MSFs into four categories. These results are verified by direct simulations of synchronous dynamics on networks of actual coupled oscillators.

We report on experimental studies of steady-state two-phase flow in a quasi-two-dimensional porous medium. The wetting and the nonwetting phases are injected simultaneously from alternating inlet points into a Hele-Shaw cell containing one layer of randomly distributed glass beads, initially saturated with wetting fluid. The high viscous wetting phase and the low viscous nonwetting phase give a low viscosity ratio $M={10}^{-4}$. Transient behavior of this system is observed in time and space. However, we find that at a certain distance behind the initial front a “local” steady-state develops, sharing the same properties as the later “global“ steady state. In this state the nonwetting phase is fragmented into clusters, whose size distribution is shown to obey a scaling law, and the cutoff cluster size is found to be inversely proportional to the capillary number. The steady state is dominated by bubble dynamics, and we measure a power-law relationship between the pressure gradient and the capillary number. In fact, we demonstrate that there is a characteristic length scale in the system, depending on the capillary number through the pressure gradient that controls the steady-state dynamics.

The oscillation-center Hamiltonian is derived for a relativistic electron injected with an arbitrary momentum in a linearly polarized laser pulse propagating in tenuous plasma, assuming that the pulse length is smaller than the plasma wavelength. For hot electrons generated by collisions with ions under an intense laser drive, multiple regimes of ponderomotive acceleration are identified, and the laser dispersion is shown to affect the process at plasma densities down to ${10}^{17}{\text{cm}}^{-3}$. We consider the regime when the cold plasma is not accelerated, requiring $a/{\gamma }_g⪡1$, where $a$ is the laser parameter, proportional to the field amplitude, and ${\gamma }_g$ is the group-velocity Lorentz factor. In this case, the Lorentz factor $\gamma$ of hot electrons does not exceed $\Gamma \equiv a{\gamma }_g$ after acceleration, assuming its initial value also satisfies ${\gamma }_0\lesssim \Gamma$. Yet $\gamma \sim \Gamma$ is attained within a wide range of initial conditions; hence, a cutoff in the hot-electron distribution is predicted.

Stochastic Bloch equations which model the fluorescence of two-level molecules and atoms, NMR experiments, and Josephson junctions are investigated to illustrate the profound effect of multiplicative noise on the critical frequency of a dynamical system. Using exact solutions and the cumulant expansion we find two main effects: (i) even very weak noise may double or triple the number of critical frequencies, which is related to an instability of the system, and (ii) strong multiplicative noise may induce a nontrivial zero critical frequency thus wiping out the overdamped phase.

We report on the dynamical and statistical behavior of flowing collections of granular chains confined two-dimensionally (2D) within a rotating tumbler. Experiments are conducted with systems of chains of fixed length, but various lengths are considered. The dynamics are punctuated by cascades of chains along a free-surface cascades, which drive the development of mixed porous/laminar packing arrangements in bulk. We investigate the conformation of the system, as characterized by the porosity of the flow region occupied by the chains and the mean-square end-to-end distance of the chains during flow. Both of these measures show crossover transitions from a 2D self-avoiding walk to a 2D random walk when the chain length becomes long enough to allow self-contact.

Contrast-variation small-angle neutron scattering (CV-SANS) was applied to investigate the deformation mechanism of high-performance nanocomposite polymer hydrogels (NC gels) consisting of polymer chains and inorganic clay platelets. Anisotropic SANS functions were obtained at various stretching ratios, $\lambda$'s up to $\lambda =9$ and were decomposed to three partial structure factors, $S_{ij}\left(Q_{\parallel },Q_{\perp }\right)$. Here, the subscripts $i$ and $j$ denote the polymer $\left(P\right)$ or clay $\left(C\right)$ and $Q_{\parallel }$ and $Q_{\perp }$ are the magnitude of the scattering vectors along and perpendicular to the stretching directions, respectively. $S_{CC}\left(Q_{\parallel },Q_{\perp }\right)$ and $S_{PP}\left(Q_{\parallel },Q_{\perp }\right)$ suggested that the orientation of clay platelets saturated by $\lambda \approx 3$, while the polymer chain stretching continued by further stretching. On the other hand, $S_{CP}\left(Q_{\parallel },Q_{\perp }\right)$, only available by CV-SANS, indicated the presence of a polymer-enriched layer adsorbed to clay surface, which are responsible for large extensibility of NC gels over 1000% strain and large toughness exceeding 780 kPa.

We extend the model of a $2d$ solid to include a line of defects. Neighboring atoms on the defect line are connected by springs of different strength and different cohesive energy with respect to the rest of the system. Using the Migdal-Kadanoff renormalization group we show that the elastic energy is an irrelevant field at the bulk critical point. For zero elastic energy this model reduces to the Potts model. By using Monte Carlo simulations of the three- and four-state Potts model on a square lattice with a line of defects, we confirm the renormalization-group prediction that for a defect interaction larger than the bulk interaction the order parameter of the defect line changes discontinuously while the defect energy varies continuously as a function of temperature at the bulk critical temperature.

The effect of an ultrasonic wave on the nematic texture has long been known, but its interpretation in terms of a coherent dynamical theory has not yet been achieved. A proposal for such a theory is made in this paper. The diverse theoretical approaches attempted in the past to describe the interaction between sound and nematic molecular orientation are briefly summarized. A theory for second-grade fluids, which provides the appropriate theoretical background for nematoacoustics, is also revived. An explicit application of the proposed theory to a simple computable case is given, which yields predictions that are qualitatively confirmed by a number of experimental results.

We report a general technique to study a given experimental time series with superstatistics. Crucial for the applicability of the superstatistics concept is the existence of a parameter $\beta$ that fluctuates on a large time scale as compared to the other time scales of the complex system under consideration. The proposed method extracts the main superstatistical parameters out of a given data set and examines the validity of the superstatistical model assumptions. We test the method thoroughly with surrogate data sets. Then the applicability of the superstatistical approach is illustrated using real experimental data. We study two examples, velocity time series measured in turbulent Taylor-Couette flows and time series of log returns of the closing prices of some stock market indices.

In the study of cascading failures on complex networks, a key issue is to define capacities of edges and nodes as realistically as possible. This leads to the consideration of intrinsic edge capacity associated with laws governing flows on networks, which goes beyond the existing definitions of capacity based on the initial load as quantified by the betweenness centrality. Limited edge capacity (or bandwidth) and high flux or attack can trigger cascading processes, which we find as characteristically different from those reported in the literature. In particular, there can be an abnormal parameter regime where incrementally augmenting the edge capacity can counterintuitively increase the severeness of the cascading process. Another striking finding is that heterogeneous flow distribution tends to suppress the cascading process, in contrast to the current understanding that heterogeneity can make the network more vulnerable to cascading. We provide numerical computations and analysis to substantiate these findings.

We introduce a real-time method for the identification of time-varying interaction delays in coupled systems with and without unknown structural parameters and analyze the convergence of the delay identification process. The identification method can be applied to monitor the change in interaction delays, as well as to decode the encoding of interaction delays. Several examples are presented to illustrate the reliability and robustness of the suggested strategy.

Network models that represent the void space of a rock by a lattice of pores connected by throats can predict relative permeability once the pore geometry and wettability are known. Micro-computerized-tomography scanning provides a three-dimensional image of the pore space. However, these images cannot be directly input into network models. In this paper a modified maximal ball algorithm, extending the work of Silin and Patzek [D. Silin and T. Patzek, Physica A 371, 336 (2006)], is developed to extract simplified networks of pores and throats with parametrized geometry and interconnectivity from images of the pore space. The parameters of the pore networks, such as coordination number, and pore and throat size distributions are computed and compared to benchmark data from networks extracted by other methods, experimental data, and direct computation of permeability and formation factor on the underlying images. Good agreement is reached in most cases allowing networks derived from a wide variety of rock types to be used for predictive modeling.

The kinetic equation governing a strongly magnetized transverse plasma flow past a convex ion-collecting object is solved numerically for arbitrary ion to electron temperature ratio $\tau$. The approximation of isothermal ions adopted in a recent fluid treatment of the same plasma model [I. H. Hutchinson, Phys. Rev. Lett. 101, 035004 (2008)] is shown to have no more than a small quantitative effect on the solution. In particular, the ion flux density to an elementary portion of the object still only depends on the local surface orientation. We rigorously show that the solution can be condensed in a single “calibration factor” $M_c$, function of $\tau$ only, enabling Mach probe measurements of parallel and perpendicular flows by probing flux ratios at two different angles in the plane of flow and magnetic field.

We investigate the interaction between breathers in sine-Gordon systems using a collective coordinate approach. Focusing on the in-phase or out-of-phase oscillation mode of two identical breathers, we derive a simple ordinary differential equation for the collective coordinate: the separation between the centers of mass of the two breathers $R$. Analytic solutions of this equation can reproduce quantitatively the results of a direct numerical simulation of the sine-Gordon equation over the whole parameter range. The interaction between the two breathers is attractive (repulsive) for the in-phase (out-of-phase) oscillation mode with an asymptotic exponential dependence on $R$. We find that the interaction within the innermost kink-antikink (kink-kink) pair for the in-phase (out-of-phase) case plays the most significant role in determining the sign and the strength of the effective breather-breather interaction. We also find an internal oscillation mode of the in-phase oscillating breather pair and obtain an analytic expression for the angular frequency of the mode.

We study nonlinear dynamics of classical electromagnetic wave propagation in a one-dimensional nonlinear periodic photonic structure. It is found that the period of Rabi oscillations can be modulated by the relatively weak nonlinearity $\left(2V_0/\gamma >1\right)$. When nonlinearity is relatively strong compared to the strength of resonant coupling $\left(2V_0/\gamma <1\right)$, Rabi oscillations is suppressed and the system shows a dynamical behavior, i.e., energy localizes in one mode rather than full oscillation between two degenerated modes. Phase plane analysis is applied to explain these dynamical phenomena.

We propose a model of the evolution of the networks of scientific citations. The model takes an out-degree distribution (distribution of number of citations) and two parameters as input. The parameters capture the two main ingredients of the model: the aging of the relevance of papers and the formation of triangles when new papers cite old. We compare our model to three network structural quantities of an empirical citation network. We find that unique point in parameter space optimizing the match between the real and model data for all quantities. The optimal parameter values suggest that the impact of scientific papers, at least in the empirical data set we model, is proportional to the inverse of the number of papers since they were published.

Spatiotemporal correlations in start-up flows of attractive colloids are explored by numerical simulations as a function of their volume fraction and shear rate. The suspension is first allowed to flocculate during a time $t_w$, then the stress necessary to induce its flow is computed. We find that, at low volume fractions, the stress is a universal function of the strain. On the contrary, at high volume fractions, this scaling behavior is no longer observed and a supplementary stress becomes necessary to induce flow. To better understand the physical origin of the supplementary stress, we examine the creation, disruption, and orientation of contacts between the particles and the corresponding contribution to stress as a function of strain. Our simulations show that the onset of flow is dominated by the creation of contacts between the particles at low shear rates and by their disruption at high shear rates. However, neither the evolution of the number of contacts with strain nor their orientation can fully account for the nonscaling behavior of the stress at high volume fractions. At small strains, the relative importance of forcing in the compression quadrant increases with volume fraction and with flocculation time. This mechanism of stress transmission through the compression quadrant is not accounted for in the usual description of yield stress, which considers the breaking of bonds oriented in the extension quadrant.

The slow dynamics of a single particle in multicomponent glass-forming systems including fragile and strong glasses is studied from a unified point of view. The simulation results on two different systems, bulk glass-forming ${\text{Cu}}_{60}{\text{Ti}}_{20}{\text{Zr}}_{20}$ melt and network-forming ${\text{SiO}}_2$, melt are analyzed by the mean-field theory (MFT) recently proposed and are compared with other systems near the glass transition. It is shown that the simulation results for the mean-square displacement are all collapsed into a master curve given by MFT if a long-time self-diffusion coefficient has the same value in each system. It is also shown that each long-time self-diffusion coefficient is described well by a singular function predicted recently from first principles. Thus, we conclude that there exists a simple universal mechanism near the glass transition even among any diversely different glass-forming systems.

Microtubules are a major component of the cytoskeleton distinguished by highly dynamic behavior both in vitro and in vivo referred to as dynamic instability. We propose a general mathematical model that accounts for the growth, catastrophe, rescue, and nucleation processes in the polymerization of microtubules from tubulin dimers. Our model is an extension of various mathematical models developed earlier formulated in order to capture and unify the various aspects of tubulin polymerization. While attempting to use a minimal number of adjustable parameters, the proposed model covers a broad range of behaviors and has predictive features discussed in the paper. We have analyzed the range of resultant dynamical behavior of the microtubules by changing each of the parameter values at a time and observing the emergence of various dynamical regimes that agree well with the previously reported experimental data and behavior.