We have investigated dynamical heterogeneity in a highly supercooled liquid using molecular-dynamics simulations in three dimensions. Dynamical heterogeneity can be characterized by three quantities: correlation length ${\xi }_4$, intensity ${\chi }_4$, and lifetime ${\tau }_{\mathrm{hetero}}$. We evaluated all three quantities consistently from a single order parameter. In a previous study [H. Mizuno and R. Yamamoto, Phys. Rev. E 82, 030501(R) (2010)], we examined the lifetime ${\tau }_{\mathrm{hetero}}\left(t\right)$ in two time intervals $t={\tau }_{\alpha }$ and ${\tau }_{\mathrm{ngp}}$, where ${\tau }_{\alpha }$ is the $\alpha$-relaxation time and ${\tau }_{\mathrm{ngp}}$ is the time at which the non-Gaussian parameter of the Van Hove self-correlation function is maximized. In the present study, in addition to the lifetime ${\tau }_{\mathrm{hetero}}\left(t\right)$, we evaluated the correlation length ${\xi }_4\left(t\right)$ and the intensity ${\chi }_4\left(t\right)$ from the same order parameter used for the lifetime ${\tau }_{\mathrm{hetero}}\left(t\right)$. We found that as the temperature decreases, the lifetime ${\tau }_{\mathrm{hetero}}\left(t\right)$ grows dramatically, whereas the correlation length ${\xi }_4\left(t\right)$ and the intensity ${\chi }_4\left(t\right)$ increase slowly compared to ${\tau }_{\mathrm{hetero}}\left(t\right)$ or plateaus. Furthermore, we investigated the lifetime ${\tau }_{\mathrm{hetero}}\left(t\right)$ in more detail. We examined the time-interval dependence of the lifetime ${\tau }_{\mathrm{hetero}}\left(t\right)$ and found that as the time interval $t$ increases, ${\tau }_{\mathrm{hetero}}\left(t\right)$ monotonically becomes longer and plateaus at the relaxation time of the two-point density correlation function. At the large time intervals for which ${\tau }_{\mathrm{hetero}}\left(t\right)$ plateaus, the heterogeneous dynamics migrate in space with a diffusion mechanism, such as the particle density.

The biaxial smectic-$A^{*}$ (Sm-$A_B^{*}$) phase, appearing in the phase sequence Sm-$A^{*}$–Sm-$A_B^{*}$–Sm-$C^{*}$, is analyzed using Landau theory. It is found to possess a helical superstructure with a pitch that is significantly shorter than the pitch of the Sm-$C^{*}$ helical superstructure. The Sm-$A_B^{*}$–Sm-$C^{*}$ transition can be either first or second order, and correspondingly there will be either a jump or continuous variation in the pitch. The behaviors of the birefringence and electroclinic effect are analyzed and found to be similar to those of a Sm-$C_{\alpha }^{*}$ phase. As such, it is possible that the Sm-$A_B^{*}$ phase could be misidentified as a Sm-$C_{\alpha }^{*}$ phase. Ways to distinguish the two phases are discussed.

When beneficial mutations are relatively common, competition between multiple unfixed mutations can reduce the rate of fixation in well-mixed asexual populations. We introduce a one-dimensional model with a steady accumulation of beneficial mutations. We find a transition between periodic selection and multiple-mutation regimes. In the multiple-mutation regime, the increase of fitness along the lattice bears a striking similarity to surface growth phenomena, with power-law growth and saturation of the interface width. We also find significant differences compared to the well-mixed model. In our lattice model, the transition between regimes happens at a much lower mutation rate due to slower fixation times in one dimension. Also, the rate of fixation is reduced with increasing mutation rate due to the more intense competition, and it saturates with large population size.

We present a stability analysis of an interacting two-species Bose-Einstein condensate driven by a quantized field in the semiclassical limit. Transitions from Rabi to Josephson dynamics are identified depending on both the interatomic interaction to field-condensate coupling ratio and the ratio between the total excitation number and the condensate size. The quantized field is found to produce asymmetric dynamics for symmetric initial conditions for both Rabi and Josephson oscillations.

We study the dynamics of oscillators that are coupled in relay; namely, through an intermediary oscillator. From previous studies it is known that the oscillators show a transition from in-phase to out-of-phase oscillations or vice versa when the interactions involve a time delay. Here we show that, in the absence of time delay, relay coupling through conjugate variables has the same effect. However, this phase-flip transition does not occur abruptly at a certain critical value of the coupling parameter. Instead we find a parameter region around the phase-flip transition where bistability occurs. In this parameter interval in-phase and out-of-phase oscillations coexist with changing sizes of their basins of attraction. Further increase of the coupling strength leads to amplitude death and subsequently to the stabilization of a fixed point. These transitions are characterized through various quantities such as the average phase difference and crossings in the spectrum of Lyapunov exponents. Numerical results are presented for a specific case of coupled Rössler-like oscillators.

Ground-state structures of finite, cylindrically confined two-dimensional Yukawa systems composed of charged superparamagnetic dust grains in an external magnetic field are investigated numerically, using molecular dynamic simulations and lattice summation methods. The ground-state configuration of the system is identified using, as an approximation, the experimentally obtained shape of the horizontal confinement potential in a classical single-layer dusty plasma experiment with nonmagnetic grains. Results are presented for the dependence of the number density and lattice parameters of the dust layer on (1) the ratio of the magnetic dipole-dipole force to electrostatic force between the grains and (2) the orientation of the grain magnetic moment with respect to the layer.

The dynamics of granular materials, particularly radial and axial segregation in horizontal rotating cylinders containing large and small particles, is studied by Magnetic Resonance Imaging (MRI). Stationary three-dimensional (3D) images and real-time two-dimensional (2D) structural images showing radial segregation, band formation, and band merging are reported. Quantitative local particle concentrations are measured in a noninvasive manner from the different magnetic resonance responses of the seeds throughout segregation. Data are acquired with sufficiently high temporal (300 ms for 2D images) and spatial resolutions (0.94 mm cubic voxels), to give insights into the underlying mechanisms of both radial and axial segregation. In particular, the increasing rate of the local particle concentration during radial segregation is quantified. Particle migration is observed in the bulk material of the 75% and 82% full cylinders during both radial and axial segregation, showing that this region beneath the avalanche layer does not behave as a solid body. We also provide direct experimental evidence to support recent numerical simulations of band merging.

The nonlinear dynamic behavior of superparamagnetic beads transported through a two-dimensional potential energy landscape is explored empirically and through numerical simulation. The beads are driven through a periodic array of micromagnets by an external rotating field oriented at an angle $\theta$ relative to the magnetization direction of the substrate. The bead's motion was highly sensitive to the angle of the driving field near critical angles and to various system parameters, including bead size, rotation frequency, and substrate pole density. Our results suggest the possibility of using this behavior in a highly discriminative colloidal separation system, in which two different bead types can be tuned to move in orthogonal directions.

In this study a Markov operator is introduced that represents the density evolution of an impulse-driven stochastic biological oscillator. The operator’s stochastic kernel is constructed using the asymptotic expansion of stochastic processes instead of solving the Fokker-Planck equation. The Markov operator is shown to successfully approximate the density evolution of the biological oscillator considered. The response of the oscillator to both periodic and time-varying impulses can be analyzed using the operator’s transient and stationary properties. Furthermore, an unreported stochastic dynamic bifurcation for the biological oscillator is obtained by using the eigenvalues of the product of the Markov operators.

In recent years, community structure has emerged as a key component of complex network analysis. As more data have been collected, researchers have begun investigating changing community structure across multiple networks. Several methods exist to analyze changing communities, but most of these are limited to evolution of a single network over time. In addition, most of the existing methods are more concerned with change at the community level than at the level of the individual node. In this paper, we introduce scaled inclusivity, which is a method to quantify the change in community structure across networks. Scaled inclusivity evaluates the consistency of the classification of every node in a network independently. In addition, the method can be applied cross sectionally as well as longitudinally. In this paper, we calculate the scaled inclusivity for a set of simulated networks of United States cities and a set of real networks consisting of teams that play in the top division of American college football. We found that scaled inclusivity yields reasonable results for the consistency of individual nodes in both sets of networks. We propose that scaled inclusivity may provide a useful way to quantify the change in a network’s community structure.

A major issue in biology is the understanding of the interactions between proteins. These interactions can be described by a network, where the proteins are modeled by nodes and the interactions by edges. The origin of these protein networks is not well understood yet. Here we present a two-step model, which generates clusters with the same topological properties as networks for protein-protein interactions, namely, the same degree distribution, cluster size distribution, clustering coefficient, and shortest path length. The biological and model networks are not scale-free but exhibit small-world features. The model allows the fitting of different biological systems by tuning a single parameter.

We present arguments which indicate that a transitional state in between two different regimes implies the occurrence of 1/$f$ time series and that this property is generic in both classical and quantum systems. Our study focuses on two particular examples: the one-dimensional module-1 logistic map and nuclear excitation spectra obtained with a schematic shell-model Hamiltonian. We suggest that a transitional point is characterized by the long-range correlations implied by 1/$f$ time series. We apply a Fourier spectral analysis and the detrended fluctuation analysis method to study the fluctuations to each system.

An extensive Monte Carlo simulation has been performed on a two-dimensional modified $XY$ model that behaves like a dense defect system. Topological defects are shown to introduce disorder in the system, which makes the helicity modulus jump nonuniversal. The results corroborate the experimental observation of a nonuniversal jump of the superconducting density in high-$T_c$ superconducting films.

We study the first-passage-time processes of the anomalous diffusion on the self-similar curves in two dimensions. The scaling properties of the mean-square displacement and mean first passage time of the fractional Brownian motion and subordinated walk on the different fractal curves (loop-erased random walk, harmonic explorer, and percolation front) are derived. We also define natural parametrized subordinated Schramm-Loewner evolution (NS-SLE) as a mathematical tool that can model diffusion on fractal curves. The scaling properties of the mean-square displacement and mean first passage time for NS-SLE are obtained by numerical means.

Dimensionality reduction is ubiquitous in the analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed low-dimensional space does not provide a complete and accurate description of the dynamics. Here I describe how to perform dimensionality reduction while preserving the essential properties of the dynamics. The approach is illustrated by analyzing the chess game—the archetype of complex dynamics. A variable that provides complete and accurate description of chess dynamics is constructed. The winning probability is predicted by describing the game as a random walk on the free-energy landscape associated with the variable. The approach suggests a possible way of obtaining a simple yet accurate description of many important complex phenomena. The analysis of the chess game shows that the approach can quantitatively describe the dynamics of processes where human decision-making plays a central role, e.g., financial and social dynamics.

The decay of current autocorrelation functions is investigated for quantum systems featuring strong interactions. Here the term “interaction” refers to that part of the Hamiltonian causing the (major) decay of the current. On the time scale before the (first) zero crossing of the current, its relaxation is shown to be well described by a suitable perturbation theory in the lowest orders of the interaction strength, particularly if interactions are strong. In this description the relaxation is found to be rather close to a Gaussian decay and the resulting diffusion coefficient approximately scales with the inverse interaction strength. These findings are confirmed by numerical results from exact diagonalization for several one-dimensional transport models including spin transport in the Heisenberg chain with respect to different spin quantum numbers, anisotropy, next-nearest-neighbor interaction, or alternating magnetic field; energy transport in the Ising chain with tilted magnetic field; and transport of excitations in a randomly coupled modular quantum system. The impact of these results for weak interactions is discussed.

The detection of weak signals through nonlinear relaxation times for a Brownian particle in an electromagnetic field is studied in the dynamical relaxation of the unstable state, characterized by a two-dimensional bistable potential. The detection process depends on a dimensionless quantity referred to as the receiver output, calculated as a function of the nonlinear relaxation time and being a characteristic time scale of our system. The latter characterizes the complete dynamical relaxation of the Brownian particle as it relaxes from the initial unstable state of the bistable potential to its corresponding steady state. The one-dimensional problem is also studied to complement the description.

We investigate the statistics of work performed on a noninteracting electron gas confined in a ring as a threaded magnetic field is turned on. For an electron gas initially prepared in a grand canonical state it is demonstrated that the Jarzynski equality continues to hold in this case, with the free energy replaced by the grand potential. The work distribution displays a marked dependence on the temperature. While in the classical (high-temperature) regime, the work probability density function follows a Gaussian distribution and the free energy difference entering the Jarzynski equality is null, the free energy difference is finite in the quantum regime, and the work probability distribution function becomes multimodal. We point out the dependence of the work statistics on the number of electrons composing the system.

We study quasistationary states (QSSs) resulting from violent relaxation in the one-dimensional self-gravitating “sheet model,” revisiting in particular the question of the adequacy of the theory of Lynden-Bell (LB) to describe them. For “waterbag” initial conditions characterized by a single phase-space density, the prediction of this theory is, in this model, a function of only one parameter, which can conveniently be chosen to be the ratio of the energy to that in the degenerate limit. Studying a class of such initial conditions in which the shape of the initial waterbag is varied, we find that the LB predictions are reasonably good always in the low-energy region, while at higher energies (i.e., in the nondegenerate limit) they are generally not even qualitatively correct, although certain initial conditions can still be found where they are as good as at low energy. We find notably that, in line with what has been observed by Levin et al. in some other models, when LB theory does not work, the QSSs are always characterized by the presence of a degenerate core, which these authors explain as the result of dynamical resonances. In short, LB theory appears to be a good approximation only when violent relaxation is sufficiently “gentle,” and otherwise a degenerate core-halo structure results.

We study a system of long rigid rods of fixed length $k$ with only excluded volume interaction. We show that, contrary to the general expectation, the self-consistent field equations of the Bethe approximation do not give the exact solution of the problem on the Bethe lattice in this case. We construct a new lattice, called the random locally treelike layered lattice, which allows a dense packing of rods, and we show that the Bethe self-consistent equations are exact for this lattice. For a four-coordinated lattice, $k$-mers with $k⩾4$ undergo a continuous isotropic-nematic phase transition. For even coordination number $q⩾6$, the transition exists only for $k⩾k_{\text{min}}\left(q\right)$, and is discontinuous.