Two essential elements required to generate a glass transition within phase-field-crystal (PFC) models are outlined based on observed freezing behaviors in various models of this class. The central dynamic features of glass formation in simple binary liquids are qualitatively reproduced across 12 orders of magnitude in time by applying a physically motivated time scaling to previous PFC simulation results. New aspects of the equilibrium phase behavior of the same binary model system are also outlined, aging behavior is explored in the moderate and deeply supercooled regimes, and aging exponents are extracted. General features of the elastic and plastic responses of amorphous and crystalline PFC solids under deformation are also compared and contrasted.

The entropy of network ensembles characterizes the amount of information encoded in the network structure and can be used to quantify network complexity and the relevance of given structural properties observed in real network datasets with respect to a random hypothesis. In many real networks the degrees of individual nodes are not fixed but change in time, while their statistical properties, such as the degree distribution, are preserved. Here we characterize the distribution of entropy of random networks with given degree sequences, where each degree sequence is drawn randomly from a given degree distribution. We show that the leading term of the entropy of scale-free network ensembles depends only on the network size and average degree and that entropy is self-averaging, meaning that its relative variance vanishes in the thermodynamic limit. We also characterize large fluctuations of entropy that are fully determined by the average degree in the network. Finally, above a certain threshold, large fluctuations of the average degree in the ensemble can lead to condensation, meaning that a single node in a network of size $N$ can attract $O\left(N\right)$ links.

We propose a method to recover from time series the parameters of coupled time-delay systems and the architecture of couplings between them. The method is based on a reconstruction of model delay-differential equations and estimation of statistical significance of couplings. It can be applied to networks composed of nonidentical nodes with an arbitrary number of unidirectional and bidirectional couplings. We test our method on chaotic and periodic time series produced by model equations of ensembles of diffusively coupled time-delay systems in the presence of noise, and apply it to experimental time series obtained from electronic oscillators with delayed feedback coupled by resistors.

Optomechanical systems are based on the nonlinear coupling between the electromagnetic (EM) field in a resonator and one or more bulk mechanical resonators such that the frequency of the EM field resonator depends on the displacement coordinates of each of the mechanical resonators. In this paper we consider the case of multiple mechanical resonators interacting with a common field for which the frequency of the EM resonance is tuned to depend quadratically (to lowest order) on the displacement of the resonators. By using the method of amplitude equations around a critical point, it is shown that groups of near-identical bulk mechanical resonators with low driving fail to synchronize unless their natural frequencies are identical, in which case the resulting system can exhibit multistability.

In this paper, we develop a mass-conserved volumetric lattice Boltzmann method (MCVLBM) for numerically solving fluid dynamics with willfully moving arbitrary boundaries. In MCVLBM, fluid particles are uniformly distributed in lattice cells and the lattice Boltzmann equations deal with the time evolution of the particle distribution function. By introducing a volumetric parameter $\mathcal{P}(x,y,z,t)$ defined as the occupation of solid volume in the cell, we distinguish three types of lattice cells in the simulation domain: solid cell (pure solid occupation, $\mathcal{P}=1$), fluid cell (pure fluid occupation, $\mathcal{P}=0$), and boundary cell (partial solid and partial fluid, $0<\mathcal{P}<1$). The formulation of volumetric lattice Boltzmann equations are self-regularized through $\mathcal{P}$ and consist of three parts: (1) collision taking into account the momentum exchange between the willfully moving boundary and the flow; (2) streaming accompanying a volumetric bounce-back procedure in boundary cells; and (3) boundary-induced volumetric fluid migration moving the residual fluid particles into the flow domain when the boundary swipes over a boundary cell toward a solid cell. The MCVLBM strictly satisfies mass conservation and can handle irregular boundary orientation and motion with respect to the mesh. Validation studies are carried out in four cases. The first is to simulate fluid dynamics in syringes focusing on how MCVLBM captures the underlying physics of flow driven by a willfully moving piston. The second and third cases are two-dimensional (2D) peristaltic flow and three-dimensional (3D) pipe flow, respectively. In each case, we compare the MCVLBM simulation result with the analytical solution and achieve quantitatively good agreements. The fourth case is to simulate blood flow in human aortic arteries with a very complicated irregular boundary. We study steady flow in two dimensions and unsteady flow via the pulsation of the cardiac cycle in three dimensions. In the 2D case, both vector (velocity) and scalar (pressure) fields are compared to computation results from a well-established Navier-Stokes solver and reasonably good agreements are obtained. In the 3D case, the unsteady flow pattern and wall shear stress are well captured at the representative time instants during the pulsation. The validations demonstrate that the MCVLBM is a relatively simple but reliable computation scheme to deal with static or moving irregular boundaries.

Universality has been a key concept for the classification of equilibrium critical phenomena, allowing associations among different physical processes and models. When dealing with nonequilibrium problems, however, the distinction in universality classes is not as clear and few are the examples, such as phase separation and kinetic roughening, for which universality has allowed to classify results in a general spirit. Here we focus on an out-of-equilibrium case, unstable crystal growth, lying in between phase ordering and pattern formation. We consider a well-established $2+1$-dimensional family of continuum nonlinear equations for the local height $h(\mathbf{x},t)$ of a crystal surface having the general form ${\partial }_{t}h(\mathbf{x},t)=-\nabla ·[\mathbf{j}\left(\nabla h\right)+\nabla \left({\nabla }^{2}h\right)]$: $\mathbf{j}\left(\nabla h\right)$ is an arbitrary function, which is linear for small $\nabla h$, and whose structure expresses instabilities which lead to the formation of pyramidlike structures of planar size $L$ and height $H$. Our task is the choice and calculation of the quantities that can operate as critical exponents, together with the discussion of what is relevant or not to the definition of our universality class. These aims are achieved by means of a perturbative, multiscale analysis of our model, leading to phase diffusion equations whose diffusion coefficients encapsulate all relevant information on dynamics. We identify two critical exponents: (i) the coarsening exponent, $n$, controlling the increase in time of the typical size of the pattern, $L\sim t^n$; (ii) the exponent $\beta$, controlling the increase in time of the typical slope of the pattern, $M\sim t^{\beta }$, where $M\approx H/L$. Our study reveals that there are only two different universality classes, according to the presence ($n=1/3$, $\beta =0$) or the absence ($n=1/4$, $\beta >0$) of faceting. The symmetry of the pattern, as well as the symmetry of the surface mass current $\mathbf{j}\left(\nabla h\right)$ and its precise functional form, is irrelevant. Our analysis seems to support the idea that also space dimensionality is irrelevant.

We numerically simulate the transport of elliptic Janus particles along narrow two-dimensional channels with reflecting walls. The self-propulsion velocity of the particle is oriented along either its major (prolate) or minor axis (oblate). In smooth channels, we observe long diffusion transients: ballistic for prolate particles and zero diffusion for oblate particles. Placed in a rough channel, prolate particles tend to drift against an applied drive by tumbling over the wall protrusions; for appropriate aspect ratios, the modulus of their negative mobility grows exceedingly large (giant negative mobility). This suggests that a small external drive suffices to efficiently direct self-propulsion of rod-like Janus particles in rough channels.

In this work we expose the role of environment, confinement, and external magnetic field $B$ in determining the low-temperature thermodynamic behavior in the context of cyclotron motion of a charged oscillator with anomalous dissipative coupling involving momentum instead of the much studied coordinate coupling. Explicit expressions for different quantum thermodynamic functions (QTFs) are obtained at low temperatures for different quantum heat baths characterized by the spectral density function $\mu \left(\omega \right)$. The power-law fall of different QTFs is in conformity with the third law of thermodynamics; however, the sensitivity of decay, i.e., the power of the power-law decay, explicitly depends on $\mu \left(\omega \right)$. We also discuss separately the influence of confinement and magnetic field on the low-temperature behavior of different QTFs. In this process we demonstrate how to control the low-temperature behavior of anomalous dissipative quantum systems by varying the confining length $a$, $B$, and the temperature $T$. Momentum dissipation reduces the effective mass of the system and we also discuss its effect on different QTFs at low temperatures.

We investigate numerically a density functional theory (DFT) for strongly confined ionic solutions in the canonical ensemble by comparing predictions of ionic concentration profiles and pressure for the double-layer configuration to those obtained with Monte Carlo (MC) simulations and the simpler Poisson-Boltzmann (PB) approach. The DFT consists of a bulk (ion-ion) and an ion-solid part. The bulk part includes nonideal terms accounting for long-range electrostatic and short-range steric correlations between ions and is evaluated with the mean spherical approximation and the local density approximation. The ion-solid part treats the ion-solid interactions at the mean-field level through the solution of a Poisson problem. The main findings are that ionic concentration profiles are generally better described by PB than by DFT, although DFT captures the nonmonotone co-ion profile missed by PB. Instead, DFT yields more accurate pressure predictions than PB, showing in particular that nonideal effects are important to describe highly confined ionic solutions. Finally, we present a numerical methodology capable of handling nonconvex minimization problems so as to explore DFT predictions when the reduced temperature falls below the critical temperature.

Dynamic evolution of initial instability is investigated by an analytic model obtained by modifying the theory of Warren and Langer [Phys. Rev. E 47, 2702 (1993)] and the quantitative phase-field model in directional solidification under transient conditions for realistic parameters of a dilute alloy. The evolutions of tip velocity and concentration in the liquid side of the interface predicted by the analytic model agree very well with that from the phase-field simulation in the linear growth stage of the non-steady-state growth, indicating that the model could be used as a convenient method to study the initial instability during non-steady-state growth. The influences of non-steady-state conditions which include the increasing rate of pulling speed and temperature gradient at the onset of initial instability are investigated, and we find that, the initial instability seems to depend strongly on the non-steady-state conditions and the non-steady-state history, and thus, it should be primarily considered in the study of the transient growth.

A system of hard spheroplatelets near an impenetrable wall is studied in the low-density Onsager approximation. Spheroplatelets have optimal shape between rods and plates, and the direct transition from the isotropic to biaxial nematic phase is present. A simple local approximation for the one-particle distribution function is used. Analytical results for the surface tension and the entropy contributions are derived. The density and the order-parameter profiles near the wall are calculated. The preferred orientation of the short molecule axes is perpendicular to the wall. Biaxiality close to the wall can appear only if the phase is biaxial in the bulk.

Many cell types display random motility on two-dimensional substrates but crawl persistently in a single direction when confined in a microchannel or on an adhesive micropattern. Does this imply that the motility mechanism of confined cells is fundamentally different from that of unconfined cells? We argue that both free- and confined-cell migration may be described by a generic model of cells as “velocity-aligning” active Brownian particles previously proposed to solve a completely separate problem in collective cell migration. Our model can be mapped to a diffusive escape over a barrier and analytically solved to determine the cell's orientation distribution and repolarization rate. In quasi-one-dimensional confinement, velocity-aligning cells maintain their direction for times that can be exponentially larger than their persistence time in the absence of confinement. Our results suggest an important connection between single- and collective-cell migration: high persistence in confined cells corresponds with fast alignment of velocity to cell-cell forces.

A comprehensive coverage is crucial for communication, supply, and transportation networks, yet it is limited by the requirement of extensive infrastructure and heavy energy consumption. Here, we draw an analogy between spins in antiferromagnet and outlets in supply networks, and apply techniques from the studies of disordered systems to elucidate the effects of balancing the coverage and supply costs on the network behavior. A readily applicable, coverage optimization algorithm is derived. Simulation results show that magnetized and antiferromagnetic domains emerge and coexist to balance the need for coverage and energy saving. The scaling of parameters with system size agrees with the continuum approximation in two dimensions and the tree approximation in random graphs. Due to frustration caused by the competition between coverage and supply cost, a transition between easy and hard computation regimes is observed. We further suggest a local expansion approach to greatly simplify the message updates which shed light on simplifications in other problems.

Scale-free networks have been studied mostly as non-spatially embedded systems. However, in many realistic cases, they are spatially embedded and these constraints should be considered. Here, we study the structural and functional properties of a model of scale-free (SF) spatially embedded networks. In our model, both the degree and the length of links follow power law distributions as found in many real networks. We show that not all SF networks can be embedded in space and that the largest degree of a node in the network is usually smaller than in nonembedded SF networks. Moreover, the spatial constraints (each node has only few neighboring nodes) introduce degree-degree anticorrelations (disassortativity) since two high degree nodes cannot stay close in space. We also find significant effects of space embedding on the hopping distances (chemical distance) and the vulnerability of the networks.

A theoretical analysis is presented to show the general occurrence of phase clusters in weakly, globally coupled oscillators close to a Hopf bifurcation. Through a reductive perturbation method, we derive the amplitude equation with a higher-order correction term valid near a Hopf bifurcation point. This amplitude equation allows us to calculate analytically the phase coupling function from given limit-cycle oscillator models. Moreover, using the phase coupling function, the stability of phase clusters can be analyzed. We demonstrate our theory with the Brusselator model. Experiments are carried out to confirm the presence of phase clusters close to Hopf bifurcations with electrochemical oscillators.

We propose a test of stationarity based on the drift coefficients of the Langevin type and the associated Fokker-Planck equations. The test relies on the estimation of the drift coefficients of the underlying probability densities and posits that a time series is nonstationary if the estimated drift term is a nonlinear function of the random variable of the observed time series and the Markov property holds. We provide ample empirical evidence that demonstrates that well- known stationary systems give rise to linear estimates of the drift coefficients, whereas nonstationary time series exhibit nonlinear estimates of the drift term. This does not, indeed, imply that a nonlinear drift term in the Fokker-Planck equation of a dynamic stochastic process causes nonstationarity.

A method to identify distinct dynamical regimes and transitions between those regimes in a short univariate time series was recently introduced [N. Malik et al., Europhys. Lett. 97, 40009 (2012)], employing the computation of fluctuations in a measure of nonlinear similarity based on local recurrence properties. In this work, we describe the details of the analytical relationships between this newly introduced measure and the well-known concepts of attractor dimensions and Lyapunov exponents. We show that the new measure has linear dependence on the effective dimension of the attractor and it measures the variations in the sum of the Lyapunov spectrum. To illustrate the practical usefulness of the method, we identify various types of dynamical transitions in different nonlinear models. We present testbed examples for the new method's robustness against noise and missing values in the time series. We also use this method to analyze time series of social dynamics, specifically an analysis of the US crime record time series from 1975 to 1993. Using this method, we find that dynamical complexity in robberies was influenced by the unemployment rate until the late 1980s. We have also observed a dynamical transition in homicide and robbery rates in the late 1980s and early 1990s, leading to increase in the dynamical complexity of these rates.

Synchronization is a widespread phenomenon that occurs among interacting oscillatory systems. It facilitates their temporal coordination and can lead to the emergence of spontaneous order. The detection of synchronization from the time series of such systems is of great importance for the understanding and prediction of their dynamics, and several methods for doing so have been introduced. However, the common case where the interacting systems have time-variable characteristic frequencies and coupling parameters, and may also be subject to continuous external perturbation and noise, still presents a major challenge. Here we apply recent developments in dynamical Bayesian inference to tackle these problems. In particular, we discuss how to detect phase slips and the existence of deterministic coupling from measured data, and we unify the concepts of phase synchronization and general synchronization. Starting from phase or state observables, we present methods for the detection of both phase and generalized synchronization. The consistency and equivalence of phase and generalized synchronization are further demonstrated, by the analysis of time series from analog electronic simulations of coupled nonautonomous van der Pol oscillators. We demonstrate that the detection methods work equally well on numerically simulated chaotic systems. In all the cases considered, we show that dynamical Bayesian inference can clearly identify noise-induced phase slips and distinguish coherence from intrinsic coupling-induced synchronization.

A basic quantum-mechanical model for wave functions and current flow in open quantum dots or billiards is investigated. The model involves non-Hertmitian quantum mechanics, parity-time ($\mathcal{PT}$) symmetry, and $\mathcal{PT}$-symmetry breaking. Attached leads are represented by positive and negative imaginary potentials. Thus probability densities, currents flows, etc., for open quantum dots or billiards may be simulated in this way by solving the Schrödinger equation with a complex potential. Here we consider a nominally open ballistic quantum dot emulated by a planar microwave billiard. Results for probability distributions for densities, currents (Poynting vector), and stress tensor components are presented and compared with predictions based on Gaussian random wave theory. The results are also discussed in view of the corresponding measurements for the analogous microwave cavity. The model is of conceptual as well as of practical and educational interest.

Collision cross sections and transport coefficients are calculated for ${\mathrm{Ar}}^{+}$ ions, in the ground state ${}^2{P}_{3/2}$ and in the metastable state ${}^2{P}_{1/2}$, colliding with their parent gas. Differential and integral collision cross sections are obtained using a numerical integration of the nuclear Schrödinger equation for several published interaction potentials. The Cohen-Schneider semi-empirical model is used for the inclusion of the spin-orbit interaction. The corresponding differential collision cross sections are then used in an optimized Monte Carlo code to calculate the ion transport coefficients for each initial ion state over a wide range of reduced electric field. Ion swarm data results are then compared with available experimental data for different proportions of ions in each state. This allows us to identify the most reliable interaction potential which reproduces ion transport coefficients falling within the experimental error bars. Such ion transport data will be used in electrohydrodynamic and chemical kinetic models of the low temperature plasma jet to quantify and to tune the active species production for a better use in biomedical applications.