Quantum vortex structures and energy cascades are examined for two-dimensional quantum turbulence (2D QT) at zero temperature. A special unitary evolution algorithm, the quantum lattice algorithm, is employed to simulate the Bose-Einstein condensate governed by the Gross-Pitaevskii (GP) equation. A parameter regime is uncovered in which, as in 3D QT, there is a short Poincaré recurrence time. It is demonstrated that such short recurrence times are destroyed by stronger nonlinear interaction. The similar loss of Poincaré recurrence is also seen in the 3D GP equation. Various initial conditions are considered in an attempt to discern if 2D QT exhibits inverse cascades as is seen in 2D classical turbulence (CT). In our simulation parameter regimes, no dual cascade spectra were observed for 2D QT—unlike that seen in 2D CT.

For a class of nonequilibrium systems, called driven lattice gases, we study what happens when two systems are kept in contact and allowed to exchange particles with the total number of particles conserved. For both attractive and repulsive nearest-neighbor interactions among particles and for a wide range of parameter values, we find that, to a good approximation, one could define an intensive thermodynamic variable, such as the equilibrium chemical potential, that determines the final steady state for two initially separated driven lattice gases brought into contact. However, due to nontrivial contact dynamics, there are also observable deviations from this simple thermodynamic law. To illustrate the role of the contact dynamics, we study a variant of the zero-range process and discuss how the deviations could be explained by a modified large-deviation principle. We identify an additional contribution to the large-deviation function, which we call the excess chemical potential, for the variant of the zero-range process as well as the driven lattice gases. The excess chemical potential depends on the specifics of the contact dynamics and is in general a priori unknown. A contact dependence implies that, even though an intensive variable may equalize, the zeroth law could still be violated.

This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential delay equation and then numerically investigate the probabilistic properties of chaotic solutions of the same equation. Our results show that solutions of the deterministic equation with randomly selected initial conditions display a Gaussian-like density for long time, but the densities are supported on an interval of finite measure. Using these chaotic solutions as velocities, we are able to produce Brownian-like motions, which show statistical properties akin to those of a classical Brownian motion over both short and long time scales. Several conjectures are formulated for the probabilistic properties of the solution of the differential delay equation. Numerical studies suggest that these conjectures could be “universal” for similar types of “chaotic” dynamics, but we have been unable to prove this.

Communities are not static; they evolve, split and merge, appear and disappear, i.e., they are the product of dynamical processes that govern the evolution of a network. A good algorithm for community detection should not only quantify the topology of the network but incorporate the dynamical processes that take place on the network. We present an algorithm for community detection that combines network structure with processes that support the creation and/or evolution of communities. The algorithm does not embrace the universal approach but instead tries to focus on social networks and model dynamic social interactions that occur on those networks. It identifies leaders and communities that form around those leaders. It naturally supports overlapping communities by associating each node with a membership vector that describes the node's involvement in each community. This way, in addition to the overlapping communities, we can identify nodes that are good followers of their leader and also nodes with no clear community involvement that serve as proxies between several communities and that are equally as important. We run the algorithm for several real social networks which we believe represent a good fraction of the wide body of social networks and discuss the results, including other possible applications.

We show how to estimate the Kolmogorov-Sinai entropy rate for chaotic systems using the mutual information function, easily obtainable from experimental time series. We state the conditions under which the relationship is exact, and explore the usefulness of the approach for both maps and flows. We also explore refinements of the method, and study its convergence properties as a function of time series length.

The transition to turbulence in Rayleigh-Bénard convection with phase changes and the resulting convective patterns are studied in a three-dimensional Galerkin model. Our study is focused on the conditionally unstable regime of moist convection in which the stratification is stable for unsaturated air parcels and unstable for saturated parcels. We perform a comprehensive statistical analysis of the transition to convection that samples the dependence of attractors (or fixed points) in the phase space of the model on the dimensionless parameters. Conditionally unstable convection can be initiated either from a fully unsaturated linearly stable equilibrium or a fully saturated linearly unstable equilibrium. Highly localized moist convection can be found in a steady state, in an oscillating recharge-discharge regime, or turbulent in dependence of the aspect ratio and the degree of stable stratification of the unsaturated air. Our phase-space analysis predicts parameter ranges for which self-sustained convective regimes in the case of subcritical conditional instability can be observed. The observed regime transitions for moist convection bear some similarities to transitions to turbulence in simple shear flows.

The nonlinear wave propagation in a Bose-Einstein gravitationally condensate gas is investigated using a gravitating quantum fluid model. The small-amplitude dynamics is shown to be governed by a Korteweg–de Vries equation with a nonlocal term. The quantum effect provides the necessary dispersion, and the gravitational effect is responsible for the nonlocal term. This novel equation is solved analytically. The implications of such a soliton-like solution are outlined.

This study focuses numerically on dynamics in two dimensions of vesicles in microcirculation. The method used is based on boundary integral formulation. This study is inspired by the behavior of red blood cells (RBCs) in the microvasculature. Red RBCs carry oxygen from the lungs and deliver it through the microvasculature. The shape adopted by RBCs can affect blood flow and influence oxygen delivery. Our simulation using vesicles (a simple model for RBC) reveals unexpected complexity as compared to the case where a purely unbounded Poiseuille flow is considered [Kaoui, Biros, and Misbah, Phys. Rev. Lett. 103, 188101 (2009)]. In sufficiently large channels (in the range of $100\mu \text{m}$; the vesicle size and its reduced volume are taken in the range of those of a human RBC), such as arterioles, a slipperlike (asymmetric) shape prevails. A parachutelike (symmetric) shape is adopted in smaller channels (in the range of $20\mu \text{m}$, as in venules), but this shape loses stability and again changes to a pronounced slipperlike morphology in channels having a size typical of capillaries (5–10 $\mu \text{m}$). Stiff membranes, mimicking malaria infection, for example, adopt a centered or off-centered snakelike locomotion instead (the denomination snaking is used for this regime). A general scenario of how and why vesicles adopt their morphologies and dynamics among several distinct possibilities is provided. This finding potentially points to nontrivial RBCs dynamics in the microvasculature.

Information theoretic quantities are useful tools to characterize symbolic sequences. In this paper, we use the Jensen-Shannon divergence to study symbolic binary sequences that represent the stationary state of a lattice-gas model describing the traffic of monomeric kinesin KIF1A. More specifically, the constructed binary sequences represent the state of a microtubule protofilament at different adenosine triphosphate (ATP) and KIF1A motor concentrations in the cytosol. The model presents some stationary regimes with phase coexistence. By using the Jensen-Shannon divergence, we develop a method of analysis that allows us to identify cases in which phase coexistence occurs and, for these cases, to locate the position of the interphase that separates the regions with different phase.

A wave train in an excitable reaction-diffusion medium shows a variety of spatiotemporal patterns as a result of interactions between the individual waves. In this paper, we report a novel spatiotemporal pattern in a wave train in a closed excitable medium. We carried out experiments using a photosensitive Belousov-Zhabotinsky reaction with Ru(bpy)${}_3$${}^{2+}$ as a catalyst and a numerical calculation using the FitzHugh-Nagumo equation. A wave train was locally distributed as an initial condition and the number of waves was systematically varied. In both the experiment and numerical calculation, density wave propagation was formed in a wave train during relaxation with a large number of waves. Our results suggest that density wave propagation originates from inhibitory interaction between the waves.

When two fluids of different densities move in a rotating Hele-Shaw cell, the interface between them becomes centrifugally unstable and deforms. Depending on the viscosity contrast of the system, distinct types of complex patterns arise at the fluid-fluid boundary. Deformations can also induce the emergence of interfacial singularities and topological changes such as droplet pinch-off and self-intersection. We present numerical simulations based on a diffuse-interface model for this particular two-phase displacement that capture a variety of pattern-forming behaviors. This is implemented by employing a Boussinesq Hele-Shaw-Cahn-Hilliard approach, considering the whole range of possible values for the viscosity contrast, and by including inertial effects due to the Coriolis force. The role played by these two physical contributions on the development of interface singularities is illustrated and discussed.

We present a systematic study of Au charge state distributions (CSDs) from low density, nonlocal thermodynamic equilibrium plasmas created in the Livermore electron beam ion traps (EBIT-I and EBIT-II). X-ray emission from Ni-like to Kr-like Au ions has been recorded from monoenergetic electron beam plasmas having $E_{\text{beam}}=2.66$, 2.92, 3.53, and 4.54 keV, and the CSDs of the beam plasmas have been inferred by fitting the collisionally excited line transitions and radiative recombination emission features with synthetic spectra. We have modeled the beam plasmas using a collisional-radiative code with various treatments of the atomic structure for the complex $M$- and $N$-shell ions and find that only models with extensive doubly excited states can properly account for the dielectronic recombination (DR) channels that control the CSDs. This finding would be unremarkable for plasmas with thermal electron distributions, where many such states are sampled, and the importance of DR is well established. But in an EBIT source, the beam is resonant with only a subset of such states having spectator electrons in orbitals with high principal quantum number $n$ ($8\le n\le 20$). The inclusion of such states in the model was also necessary to obtain agreement with observed stabilizing transitions in the x-ray spectra.

In nonequilibrium phase transitions of reaction-diffusion processes, the irrelevance of excluded volume interaction for the critical properties generally has been accepted due to the rare probability of multiple occupancy at criticality. Moreover, this belief is common sense in scale-free (SF) networks, which correspond to infinite dimensional irregular structures. However, the conventional belief is not satisfied in crowded environments in which the total number of particles is preserved in time. In this paper, we show, by investigating a typical process for epidemic spreading in crowded environments, that excluded volume interaction indeed changes critical behaviors in one dimension and surprisingly even mean-field behaviors in SF networks.

Despite extensive work on traffic dynamics and epidemic spreading on complex networks, the interplay between these two types of dynamical processes has not received adequate attention. We study the effect of local-routing-based traffic dynamics on epidemic spreading. For the case of unbounded node-delivery capacity, where the traffic is free of congestion, we obtain analytic and numerical results indicating that the epidemic threshold can be maximized by an optimal routing protocol. This means that epidemic spreading can be effectively controlled by local traffic dynamics. For the case of bounded delivery capacity, numerical results and qualitative arguments suggest that traffic congestion can suppress epidemic spreading. Our results provide quantitative insight into the nontrivial role of traffic dynamics associated with a local-routing scheme in the epidemic spreading.

We obtain an initial-value representation for the quantum Loschmidt echo from the semiclassical theory of Wigner function evolution, together with the classical first-order perturbation theory. In the limit of small actions, the amplitude of each trajectory reduces to unity, just as in the dephasing representation introduced by Vaníček [Phys. Rev. E 70, 055201(R) (2004)], but these trajectories are generated here by the mean Hamiltonian for both the forward and the backward motion. This slight change of action may substantially alter the phase. The amplitude correction depends on the second derivative of the action. This improved dephasing approximation is verified to work even for quadratic Hamiltonians, for which the semiclassical evolution is exact, thus extending the range of application beyond its original scope in quantum chaos.

An experimental illustration of the transition between two basic transport regimes for wave-particle interaction is reported. A striking feature is that chaos, although present in both regimes, does not need to be invoked to explain the observed behavior. This experimental realization for a theoretical paradigm opens the possibility to check the validity of basic models, as is normally required in physics. Indeed, among seemingly simple problems exhibiting complex behavior is the classical interaction of an electron with electrostatic waves. Launching a low-intensity electron beam in a Traveling Wave Tube (TWT) recently allowed observing the real-world consequences of the richness of the electron trajectory. Here we show that self-consistent effects are nevertheless acting on a modulated test electron beam through the collective excitation of beam modes. The transition between two different particle transport regimes (stochastic diffusion in a set of waves and slow chaos associated to a pulsating separatrix) is directly measured by increasing the amplitude of the excitation.

Phase models are a powerful method to quantify the coupled dynamics of nonlinear oscillators from measured data. We use two phase modeling methods to quantify the dynamics of pairs of coupled electrochemical oscillators, based on the phases of the two oscillators independently and the phase difference, respectively. We discuss the benefits of the two-dimensional approach relative to the one-dimensional approach using phase difference. We quantify the dependence of the coupling functions on the coupling magnitude and coupling time delay. We show differences in synchronization predictions of the two models using a toy model. We show that the two-dimensional approach reveals behavior not detected by the one-dimensional model in a driven experimental oscillator. This approach is broadly applicable to quantify interactions between nonlinear oscillators, especially where intrinsic oscillator sensitivity and coupling evolve with time.

We consider a variant of the Kuramoto model in which all the oscillators are now assumed to have the same natural frequency, but some of them are negatively coupled to the mean field. These contrarian oscillators tend to align in antiphase with the mean field, whereas, the positively coupled conformist oscillators favor an in-phase relationship. The interplay between these effects can lead to rich dynamics. In addition to a splitting of the population into two diametrically opposed factions, the system can also display traveling waves, complete incoherence, and a blurred version of the two-faction state. Exact solutions for these states and their bifurcations are obtained by means of the Watanabe-Strogatz transformation and the Ott-Antonsen ansatz. Curiously, this system of oscillators with identical frequencies turns out to exhibit more complicated dynamics than its counterpart with heterogeneous natural frequencies.

We introduce and explore the asymmetric inclusion process (ASIP), an exactly solvable bosonic counterpart of the fermionic asymmetric exclusion process (ASEP). In both processes, random events cause particles to propagate unidirectionally along a one-dimensional lattice of $n$ sites. In the ASEP, particles are subject to exclusion interactions, whereas in the ASIP, particles are subject to inclusion interactions that coalesce them into inseparable clusters. We study the dynamics of the ASIP, derive evolution equations for the mean and probability generating function (PGF) of the sites’ occupancy vector, obtain explicit results for the above mean at steady state, and describe an iterative scheme for the computation of the PGF at steady state. We further obtain explicit results for the load distribution in steady state, with the load being the total number of particles present in all lattice sites. Finally, we address the problem of load optimization, and solve it under various criteria. The ASIP model establishes bridges between statistical physics and queueing theory as it represents a tandem array of queueing systems with (unlimited) batch service, and a tandem array of growth-collapse processes.

Steady-state properties of hard objects with exclusion interaction and a driven motion along a one-dimensional periodic lattice are investigated. The process is a generalization of the asymmetric simple exclusion process (ASEP) to particles of length $k$, and is called the $k$-ASEP. Here, we analyze both static and dynamic properties of the $k$-ASEP. Density correlations are found to display interesting features, such as pronounced oscillations in both space and time, as a consequence of the extended length of the particles. At long times, the density autocorrelation decays exponentially in time, except at a special $k$-dependent density when it decays as a power law. In the limit of large $k$ at a finite density of occupied sites, the appropriately scaled system reduces to a nonequilibrium generalization of the Tonks gas describing the motion of hard rods along a continuous line. This allows us to obtain in a simple way the known two-particle distribution for the Tonks gas. For large but finite $k$, we also obtain the leading-order correction to the Tonks result.