We illustrate through theory and numerical simulations that redundant coupled dynamical systems can be extremely robust against local noise in comparison to uncoupled dynamical systems evolving in the same noisy environment. Previous studies have shown that the noise robustness of redundant coupled dynamical systems is linearly scalable and deviations due to noise can be minimized by increasing the number of coupled units. Here, we demonstrate that the noise robustness can actually be scaled superlinearly if some conditions are met and very high noise robustness can be realized with very few coupled units. We discuss these conditions and show that this superlinear scalability depends on the nonlinearity of the individual dynamical units. The phenomenon is demonstrated in discrete as well as continuous dynamical systems. This superlinear scalability not only provides us an opportunity to exploit the nonlinearity of physical systems without being bogged down by noise but may also help us in understanding the functional role of coupled redundancy found in many biological systems. Moreover, engineers can exploit superlinear noise suppression by starting a coupled system near (not necessarily at) the appropriate initial condition.

The effect of time-periodic forces on matter has been a topic of growing interest since the advent of lasers. It is known that dynamical systems with 2.5 or more degrees of freedom are intrinsically unstable. As a consequence, time-periodic driven systems can experience large excursions in energy. We analyze the classical and quantum dynamics of rubidium atoms confined to a time-periodic optical lattice with 2.5 degrees of freedom. When the laser polarizations are orthogonal, the system consists of two 1.5 uncoupled dynamical systems. When laser polarizations are turned away from orthogonal, an Arnold web forms and the dynamics undergoes a fundamental change. For parallel polarizations, we find huge random excursions in the rubidium atom energies and significant entanglement of energies in the quantum dynamics.

Structural holes are channels or paths spanned by a group of indirectly connected nodes and their intermediary in a network. In this work we emphasize the interesting role of structural holes as brokers for information propagation. Based on the distribution of the structural hole numbers associated with each node, we propose a simple yet effective approach for choosing the most influential nodes to immunize in containing the spreading processes. Using a wide spectrum of large real-world networks, we demonstrate that the proposed approach outperforms conventional methods in a remarkable way. In particular, we find that the performance gains of our approach are particularly prominent for networks with high transitivity and assortativity, which verifies the vital role of structural holes in information diffusion on networked systems.

In the present work, we study morphologies arising due to competing substrate interaction, electric field, and confinement effects on a symmetric diblock copolymer. We employ a coarse-grained nonlocal Cahn-Hilliard phenomenological model taking into account the appropriate contributions of substrate interaction and electrostatic field. The proposed model couples the Ohta-Kawasaki functional with Maxwell equation of electrostatics, thus alleviating the need for any approximate solution used in previous studies. We calculate the phase diagram in electric-field-substrate strength space for different film thicknesses. In addition to identifying the presence of parallel, perpendicular, and mixed lamellae phases similar to analytical calculations, we also find a region in the phase diagram where hybrid morphologies (combination of two phases) coexist. These hybrid morphologies arise either solely due to substrate affinity and confinement or are induced due to the applied electric field. The dependence of the critical fields for transition between the various phases on substrate strength, film thickness, and dielectric contrast is discussed. Some preliminary 3D results are also presented to corroborate the presence of hybrid morphologies.

The combinations of particle aspect ratio and enthalpic-barrier templates that lead to translational and orientational ordering of monolayers of rectangular particles are determined using Monte Carlo simulations and density functional theory. For sufficiently high enthalpic barriers, we find that only specific combinations of particle sizes and template spacings lead to ordered arrays. The pattern multiplication factor provided by the template extends to approximately ten times the smallest dimension of the particle.

We present theoretical and numerical results for the one-dimensional stochastically forced Burgers equation decimated on a fractal Fourier set of dimension $D$. We investigate the robustness of the energy transfer mechanism and of the small-scale statistical fluctuations by changing $D$. We find that a very small percentage of mode-reduction $\left(D\lesssim 1\right)$ is enough to destroy most of the characteristics of the original nondecimated equation. In particular, we observe a suppression of intermittent fluctuations for $D<1$ and a quasisingular transition from the fully intermittent $(D=1)$ to the nonintermittent case for $D\lesssim 1$. Our results indicate that the existence of strong localized structures (shocks) in the one-dimensional Burgers equation is the result of highly entangled correlations amongst all Fourier modes.

Several continuum theories for shock waves give rise to a set of differential equations in which the analysis of the underlying vector field can be done using the tools of the theory of dynamical systems. We illustrate the importance of the divergences associated with the vector field by considering the ideas by Maxwell and Cattaneo and apply them to study shock waves in dilute gases. By comparing the predictions of the Maxwell-Cattaneo equations with shock wave experiments we are lead to the following conclusions: (a) For low compressions (low Mach numbers: $M$) the results from the Maxwell-Cattaneo equations provide profiles that are in fair agreement with the experiments, (b) as the Mach number is increased we find a range of Mach numbers ($1.27\approx M_1<M<M_2\approx 1.90$) such that numerical shock wave solutions to the Maxwell-Cattaneo equations cannot be found, and (c) for greater Mach numbers $(M>M_2)$ shock wave solutions can be found though they differ significantly from experiments.

We present a ternary free-energy lattice Boltzmann model. The distinguishing feature of our model is that we are able to analytically derive and independently vary all fluid-fluid surface tensions and the solid surface contact angles. We carry out a number of benchmark tests: (i) double emulsions and liquid lenses to validate the surface tensions, (ii) ternary fluids in contact with a square well to compare the contact angles against analytical predictions, and (iii) ternary phase separation to verify that the multicomponent fluid dynamics is accurately captured. Additionally we also describe how the model presented here can be extended to include an arbitrary number of fluid components.

We investigate the behavior of quantum correlations of paradigmatic quenched disordered quantum spin models, viz., the $XY$ spin glass and random-field $XY$ models. We show that quenched averaged quantum correlations can exhibit the order-from-disorder phenomenon for finite-size systems as well as in the thermodynamic limit. Moreover, we find that the order-from-disorder can become more pronounced in the presence of temperature by suitable tuning of the system parameters. The effects are found for entanglement measures as well as for information-theoretic quantum correlation ones, although the former show them more prominently. We also observe that the equivalence between the quenched averages and their self-averaged cousins—for classical and quantum correlations—is related to the quantum critical point in the corresponding ordered system.

We investigate two-variable reaction-diffusion systems of the hyperbolic type. A linear stability analysis is performed, and the conditions for diffusion-driven instabilities are derived. Two basic types of eigenvalues, real and complex, are described. Dispersion curves for both types of eigenvalues are plotted and their behavior is analyzed. The real case is related to the Turing instability, and the complex one corresponds to the wave instability. We emphasize the interesting feature that the wave instability in the hyperbolic equations occurs in two-variable systems, whereas in the parabolic case one needs three reaction-diffusion equations.

We analyze vector localized solutions of two-component Bose-Einstein condensates (BECs) with variable nonlinearity parameters and external trap potentials through a similarity transformation technique which transforms the two coupled Gross-Pitaevskii equations into a pair of coupled nonlinear Schrödinger equations with constant coefficients under a specific integrability condition. In this analysis we consider three different types of external trap potentials: a time-independent trap, a time-dependent monotonic trap, and a time-dependent periodic trap. We point out the existence of different interesting localized structures; namely, rogue waves, dark- and bright-soliton rogue waves, and rogue-wave breatherlike structures for the above three cases of trap potentials. We show how the vector localized density profiles in a constant background get deformed when we tune the strength of the trap parameter. Furthermore, we investigate the nature of the trajectories of the nonautonomous rogue waves. We also construct the dark-dark rogue wave solution for the repulsive-repulsive interaction of two-component BECs and analyze the associated characteristics for the three different kinds of traps. We then deduce single-, two-, and three-composite rogue waves for three-component BECs and discuss the correlated characteristics when we tune the strength of the trap parameter for different trap potentials.

Estimating city evacuation time is a nontrivial problem due to the interaction between thousands of individual agents, giving rise to various collective phenomena, such as bottleneck formation, intermittent flow, and stop-and-go waves. We present a mean field approach to draw relationships between road network spatial attributes, the number of evacuees, and the resultant evacuation time estimate (ETE). Using volunteered geographic information, we divide 50 United Kingdom cities into a total of 704 catchment areas (CAs) which we define as an area where all agents share the same nearest exit node. 90% of the agents are within $\approx 6,847$ m of CA exit nodes with $\approx 13,778$ agents/CA. We establish a characteristic flow rate from catchment area attributes (population, distance to exit node, and exit node width) and a mean flow rate in a free-flow regime by simulating total evacuations using an agent based “queuing network” model. We use these variables to determine a relationship between catchment area attributes and resultant ETEs. This relationship could enable emergency planners to make a rapid appraisal of evacuation strategies and help support decisions in the run up to a crisis.

The nucleosome represents the basic unit of eukaryotic genome organization, and its conformational fluctuations play a crucial role in various cellular processes. Here we provide insights into the flipping transition of a nucleosome by computing its free-energy landscape as a function of the linking number and nucleosome orientation using the density-of-states Monte Carlo approach. To investigate how the energy landscape is affected by the presence of neighboring nucleosomes in a chromatin fiber, we also compute the free-energy landscape for a dinucleosome array. We find that the mononucleosome is bistable between conformations with negatively and positively crossed linkers while the conformation with open linkers appears as a transition state. The dinucleosome exhibits a markedly different energy landscape in which the conformation with open linkers populates not only the transition state but also the global minimum. This enhanced stability of the open state is attributed to increased rotational flexibility of nucleosomes arising from their mechanical coupling with neighboring nucleosomes. Our results provide a possible mechanism by which chromatin may enhance the accessibility of its DNA and facilitate the propagation and mitigation of DNA torsional stresses.

Classical chemical kinetics uses rate-equation models to describe how a reaction proceeds in time. Such models are sufficient for describing state transitions in a reaction where coherences between different states do not arise, in other words, a reaction that contains only incoherent transitions. A prominent example of a reaction containing coherent transitions is the radical-pair model. The kinetics of such reactions is defined by the so-called reaction operator that determines the radical-pair state as a function of intermediate transition rates. We argue that the well-known concept of quantum walks from quantum information theory is a natural and apt framework for describing multisite chemical reactions. By composing Kraus maps that act only on two sites at a time, we show how the quantum-walk formalism can be applied to derive a reaction operator for the standard avian radical-pair reaction. Our reaction operator predicts the same recombination dephasing rate as the conventional Haberkorn model, which is consistent with recent experiments [K. Maeda et al., J. Chem. Phys. 139, 234309 (2013)], in contrast to previous work by Jones and Hore [J. A. Jones and P. J. Hore, Chem. Phys. Lett. 488, 90 (2010)]. The standard radical-pair reaction has conventionally been described by either a normalized density operator incorporating both the radical pair and reaction products or a trace-decreasing density operator that considers only the radical pair. We demonstrate a density operator that is both normalized and refers only to radical-pair states. Generalizations to include additional dephasing processes and an arbitrary number of sites are also discussed.

We apply the quantum-walk approach proposed in the preceding paper [A. Chia et al., preceding paper, Phys. Rev. E 93, 032407 (2016)] to a radical-pair reaction where realistic estimates for the intermediate transition rates are available. The well-known average hitting time from quantum walks can be adopted as a measure of how quickly the reaction occurs and we calculate this for varying degrees of dephasing in the radical pair. The time for the radical pair to react to a product is found to be independent of the amount of dephasing introduced, even in the limit of no dephasing where the transient population dynamics exhibits strong coherent oscillations. This can be seen to arise from the existence of a rate-limiting step in the reaction and we argue that in such examples, a purely classical model based on rate equations can be used for estimating the time scale of the reaction but not necessarily its population dynamics.

The pressure exerted on a wall by a gas at equilibrium does not depend on the shape of the confining potential defining the walls. In contrast, it has been shown recently [A. P. Solon et al., Nat. Phys. 11, 673 (2015)] that a gas of overdamped active particles exerts on a wall a force that depends on the confining potential, resulting in a net force on an asymmetric wall between two chambers at equal densities. Here, considering a model of underdamped self-propelled dumbbells in two dimensions, we study how the behavior of the pressure depends on the damping coefficient of the dumbbells, thus exploring inertial effects. We find in particular that the force exerted on a moving wall between two chambers at equal density continuously vanishes at low damping coefficient, and exhibits a complex dependence on the damping coefficient at low density, when collisions are scarce. We further show that this behavior of the pressure can to a significant extent be understood in terms of the trajectories of individual particles close to and in contact with the wall.

We examine fluid flow through cross-slot devices with various depth to width ratios $\alpha$. At low Reynolds number, Re, flow is symmetric and a sharp boundary exists between the two incoming fluid streams. Above an $\alpha$-dependent critical value, $R{e}_c\left(\alpha \right)$, a steady symmetry-breaking bifurcation occurs and a spiral vortex structure develops. Order parameters characterizing the instability grow according to a sixth-order Landau potential, and show a progression from second- to first-order transitions as $\alpha$ increases beyond a tricritical value of $\alpha \approx 0.55$. Flow simulations indicate the instability is driven by vortex stretching at the stagnation point.

Community detection of network flows conventionally assumes one-step dynamics on the links. For sparse networks and interest in large-scale structures, longer timescales may be more appropriate. Oppositely, for large networks and interest in small-scale structures, shorter timescales may be better. However, current methods for analyzing networks at different timescales require expensive and often infeasible network reconstructions. To overcome this problem, we introduce a method that takes advantage of the inner workings of the map equation and evades the reconstruction step. This makes it possible to efficiently analyze large networks at different Markov times with no extra overhead cost. The method also evades the costly unipartite projection for identifying flow modules in bipartite networks.

We introduce and analyze a class of growing geometric random graphs that are invariant under rescaling of space and time. Directed connections between nodes are drawn according to influence zones that depend on node position in space and time, mimicking the heterogeneity and increased specialization found in growing networks. Through calculations and numerical simulations we explore the consequences of scale invariance for geometric random graphs generated this way. Our analysis reveals a dichotomy between scale-free and Poisson distributions of in- and out-degree, the existence of a random number of hub nodes, high clustering, and unusual percolation behavior. These properties are similar to those of empirically observed web graphs.

Considerable evidence suggests that anticipating sudden shifts from one state to another in bistable dynamical systems is a challenging task; examples include ecosystems, financial markets, and complex diseases. In this paper, we investigate the effects of additive, multiplicative, and cross-correlated stochastic perturbations on determining the regime shifts in a bistable gene regulatory system, which gives rise to two distinct states of low and high concentrations of protein. We obtain the stationary probability density and mean first-passage time of the system. We show that increasing the additive (multiplicative) noise intensity induces a regime shift from a low (high) to a high (low) protein concentration state. However, an increase in the cross-correlation intensity always induces regime shifts from a high to a low protein concentration state. For both bifurcation-induced (often called the tipping point) and noise-induced (called stochastic switching) regime shifts, we further explore the robustness of recently developed critical–down-based early warning signal (EWS) indicators (e.g., rising variance and lag-1 autocorrelation) on our simulated time-series data. We identify that using EWS indicators, prediction of an impending bifurcation-induced regime shift is relatively easier than that of a noise-induced regime shift in the considered system. Moreover, the success of EWS indicators also strongly depends upon the nature of the noise.