Restricted solid-on-solid (RSOS) growth models are studied on two different decagonal quasicrystal lattices, namely the Penrose tiling lattice and the random tiling lattice. There exist two types of growth blocks—fat and skinny tiles—which may have different sticking probabilities. We found that the RSOS growths on both lattices belong to the Kardar-Parisi-Zhang universality class when they have the same sticking probabilities in spite of the lack of periodicity in the substrates. However, when they have tile-type dependent sticking probabilities, the RSOS models on two lattices may produce different scaling behaviors. Growth on Penrose tiling shows that the roughness exponent is around 0.4 while that on random tiling is around 0.49. Our observation may provide an effective way to investigate the bulk structures of decagonal quasicrystals.

It has been recently shown numerically that the transition from integrability to chaos in quantum systems and the corresponding spectral fluctuations are characterized by $1/f^{\alpha }$ noise with $1\le \alpha \le 2$. The system of interacting trapped bosons is inhomogeneous and complex. The presence of an external harmonic trap makes it more interesting as, in the atomic trap, the bosons occupy partly degenerate single-particle states. Earlier theoretical and experimental results show that at zero temperature the low-lying levels are of a collective nature and high-lying excitations are of a single-particle nature. We observe that for few bosons, the $P\left(s\right)$ distribution shows the Shnirelman peak, which exhibits a large number of quasidegenerate states. For a large number of bosons the low-lying levels are strongly affected by the interatomic interaction, and the corresponding level fluctuation shows a transition to a Wigner distribution with an increase in particle number. It does not follow Gaussian orthogonal ensemble random matrix predictions. For high-lying levels we observe the uncorrelated Poisson distribution. Thus it may be a very realistic system to prove that $1/f^{\alpha }$ noise is ubiquitous in nature.

A principle of hierarchical entropy maximization is proposed for generalized superstatistical systems, which are characterized by the existence of three levels of dynamics. If a generalized superstatistical system comprises a set of superstatistical subsystems, each made up of a set of cells, then the Boltzmann-Gibbs-Shannon entropy should be maximized first for each cell, second for each subsystem, and finally for the whole system. Hierarchical entropy maximization naturally reflects the sufficient time-scale separation between different dynamical levels and allows one to find the distribution of both the intensive parameter and the control parameter for the corresponding superstatistics. The hierarchical maximum entropy principle is applied to fluctuations of the photon Bose-Einstein condensate in a dye microcavity. This principle provides an alternative to the master equation approach recently applied to this problem. The possibility of constructing generalized superstatistics based on a statistics different from the Boltzmann-Gibbs statistics is pointed out.

Recent analysis of empirical data [Radicchi, Baronchelli, and Amaral, PloS ONE 7, e029910 (2012)] showed that humans adopt Lévy-flight strategies when exploring the bid space in online auctions. A game theoretical model proved that the observed Lévy exponents are nearly optimal, being close to the exponent value that guarantees the maximal economical return to players. Here, we rationalize these findings by adopting an evolutionary perspective. We show that a simple evolutionary process is able to account for the empirical measurements with the only assumption that the reproductive fitness of the players is proportional to their search ability. Contrary to previous modeling, our approach describes the emergence of the observed exponent without resorting to any strong assumptions on the initial searching strategies. Our results generalize earlier research, and open novel questions in cognitive, behavioral, and evolutionary sciences.

We present a study on connectivity percolation in suspensions of hard platelets by means of Monte Carlo simulation. We interpret our results using a contact-volume argument based on an effective single-particle cell model. It is commonly assumed that the percolation threshold of anisotropic objects scales as their inverse aspect ratio. While this rule has been shown to hold for rodlike particles, we find that for hard platelike particles the percolation threshold is nonmonotonic in the aspect ratio. It exhibits a shallow minimum at intermediate aspect ratios and then saturates to a constant value. This effect is caused by the isotropic-nematic transition preempting the percolation transition. Hence the common strategy to use highly anisotropic, conductive particles as fillers in composite materials in order to produce conduction at low filler concentration is expected to fail for platelike fillers such as graphene and graphite nanoplatelets.

By characterizing the dynamics of idealized lattice models with a tunable kinetic constraint, we explore the different ways in which dynamical facilitation manifests itself within the local dynamics of glassy materials. Dynamical facilitation is characterized both by a mobility transfer function, the propensity for highly mobile regions to arise near regions that were previously mobile, and by a facilitation volume, the effect of an initial dynamical event on subsequent dynamics within a region surrounding it. Sustained bursts of dynamical activity—avalanches—are shown to occur in kinetically constrained models, but, contrary to recent claims, we find that the decreasing spatiotemporal extent of avalanches with increased supercooling previously observed in granular experiments does not imply diminishing facilitation. Viewed within the context of existing simulation and experimental evidence, our findings show that dynamical facilitation plays a significant role in the dynamics of systems investigated over the range of state points accessible to molecular simulations and granular experiments.

The static correlations and diffusive dynamics of hard ellipses are investigated in the isotropic and nematic phases by Monte Carlo simulation. In particular, an enhancement of the translational diffusion with respect to the rotational diffusion is observed at an onset concentration ${\phi }_{\mathrm{on}}$ within the isotropic phase, which is explained in terms of the formation of unstable nematic-like regions with a mean lifetime that exceeds the characteristic time of diffusion at ${\phi }_{\mathrm{on}}$. The relevance to the onset of spatially heterogeneous dynamics in supercooled glass-forming liquids is discussed.

We demonstrate the strong dependency of the isotropic-nematic (I-N) transition of discotic suspensions on the aspect ratio (ξ $=$ thickness/diameter) via control of the sizes of pristine ZrP crystals and subsequent exfoliation to monolayers. The size fractionation of the I-N transition facilitates the analysis of the effect of polydispersity. A systematic variation in the aspect ratio in the low aspect ratio region (0.001 $<$ ξ $<$ 0.01) showed that the I-N transition volume fraction increases with the aspect ratio in agreement with computer simulations. It was found that the transition volume fractions scale with aspect ratio ${\phi }_{\mathrm{I},\mathrm{N}}$ $=$ $m{\xi }^{1.36\pm 0.07}$, where the prefactor $m$ strongly depends on size polydispersity for ${\phi }_{\mathrm{N}}$ but does not depend on size polydispersity for ${\phi }_{\mathrm{I}}$ with ${\phi }_{\mathrm{I}}$ and ${\phi }_{\mathrm{N}}$ being the volume fractions of the isotropic and the nematic phases on the cloud curves, respectively.

A wealth of new research has highlighted the critical roles of small noncoding RNAs (sRNAs) in diverse processes, such as quorum sensing and cellular responses to stress. The pathways controlling these processes often have a central motif composed of a master regulator protein whose expression is controlled by multiple sRNAs. However, the stochastic gene expression of a single target gene regulated by multiple sRNAs is currently not well understood. To address this issue, we analyze a stochastic model of regulation of gene expression by multiple sRNAs. For this model, we derive exact analytic results for the regulated protein distribution, including compact expressions for its mean and variance. The derived results provide insights into the roles of multiple sRNAs in fine-tuning the noise in gene expression. In particular, we show that, in contrast to regulation by a single sRNA, multiple sRNAs provide a mechanism for independently controlling the mean and variance of the regulated protein distribution.

We present a nonlinear theory for relativistic x-ray free-electron lasers in the quantum regime, using a collective Klein-Gordon (KG) equation (for relativistic electrons), which is coupled with the Maxwell-Poisson equations for the electromagnetic and electrostatic fields. In our model, an intense electromagnetic wave is used as a wiggler which interacts with a relativistic electron beam to produce coherent tunable radiation. The KG-Maxwell-Poisson model is used to derive a general nonlinear dispersion relation for parametric instabilities in three space dimensions, including an arbitrarily large amplitude electromagnetic wiggler field. The nonlinear dispersion relation reveals the importance of quantum recoil effects and oblique scattering of the radiation that can be tuned by varying the beam energy.

Networks and dynamical processes occurring on them have become a paradigmatic representation of complex systems. Studying the role of quenched disorder, both intrinsic to nodes and topological, is a key challenge. With this in mind, here we analyze the contact process (i.e., the simplest model for propagation phenomena) with node-dependent infection rates (i.e., intrinsic quenched disorder) on complex networks. We find Griffiths phases and other rare-region effects, leading rather generically to anomalously slow (algebraic, logarithmic, etc.) relaxation, on Erdős-Rényi networks. We predict similar effects to exist for other topologies as long as a nonvanishing percolation threshold exists. More strikingly, we find that Griffiths phases can also emerge—even with constant epidemic rates—as a consequence of mere topological heterogeneity. In particular, we find Griffiths phases in finite-dimensional networks as, for instance, a family of generalized small-world networks. These results have a broad spectrum of implications for propagation phenomena and other dynamical processes on networks, and are relevant for the analysis of both models and empirical data.

The model of scientific paradigms spreading throughout a community of agents with memory is analyzed using the master equation. The case of two competing ideas is considered for various networks of interactions, including agents placed at Erdős-Rényi graphs or complete graphs. The pace of adopting a new idea by the community is analyzed, along with the distribution of periods after which a new idea replaces the old one. The approach is extended for the chain topology to the more general case when more than two ideas compete. Our analytical results agree with the numerical simulations.

We introduce a family of new centralities, the $k$-spectral centralities. $k$-spectral centrality is a measurement of importance with respect to the deformation of the graph Laplacian associated with the graph. Due to this connection, $k$-spectral centralities have various interpretations in terms of spectrally determined information. We explore this centrality in the context of several examples. While for sparse unweighted networks 1-spectral centrality behaves similarly to other standard centralities, for dense weighted networks they show different properties. In summary, the $k$-spectral centralities provide a novel and useful measurement of relevance (for single network elements as well as whole subnetworks) distinct from other known measures.

We demonstrate that, in a two-dimensional dissipative medium described by the cubic-quintic (CQ) complex Ginzburg-Landau (CGL) equation with the viscous (spectral-filtering) term, necklace rings carrying a mixed radial-azimuthal phase modulation can evolve into polygonal or quasipolygonal stable soliton clusters, and into stable fundamental solitons. The outcome of the evolution is controlled by the depth and azimuthal anharmonicity of the phase-modulation profile, or by the radius and number of “beads” in the initial necklace ring. Threshold characteristics of the evolution of the patterns are identified and explained. Parameter regions for the formation of the stable polygonal and quasipolygonal soliton clusters, and of stable fundamental solitons, are identified. The model with the CQ terms replaced by the full saturable nonlinearity produces essentially the same set of basic dynamical scenarios; hence this set is a universal one for the CGL models.

We characterize the role of the impulse transmitted (time integral over a half-period) by resonant secondary excitations at controlling (suppressing and enhancing) escape from a potential well, which is induced by periodic primary excitations. By using the universal model of a dissipative Helmholtz oscillator, we demonstrate numerically that optimum control of escape occurs when the impulse transmitted by the chaos-controlling excitations is maximum while keeping their amplitude and period fixed. These findings are in complete agreement with analytical predictions from two independent methods: Melnikov analysis and energy-based analysis. Additional numerical results corresponding to other alternative escape-controlling excitations demonstrate the generality of the essential role of the excitation's impulse.

This paper presents an analysis of the Dudley-James two-vortex flow, which inspired several laboratory-scale liquid-metal experiments, in order to better demonstrate its relation to astrophysical dynamos. A coordinate transformation splits the flow into components that are axisymmetric and nonaxisymmetric relative to the induced magnetic dipole moment. The reformulation gives the flow the same dynamo ingredients as are present in more complicated convection-driven dynamo simulations. These ingredients are currents driven by the mean flow and currents driven by correlations between fluctuations in the flow and fluctuations in the magnetic field. The simple model allows us to isolate the dynamics of the growing eigenvector and trace them back to individual three-wave couplings between the magnetic field and the flow. This simple model demonstrates the necessity of poloidal advection in sustaining the dynamo and points to the effect of large-scale flow fluctuations in exciting a dynamo magnetic field.

In this paper an advective-dispersion equation with scale-dependent coefficients is proposed for describing transport through fractals. This equation is obtained by imposing scale invariance and assuming that the porosity, the dispersion coefficient, and the velocity follow fractional power laws on the scale. The model incorporates the empirically found trends in highly heterogeneous media, regarding the dependence of the dispersivity on the scale and the dispersion coefficient on the velocity. We conclude that the presence of nontrivial fractal parameters produces anomalous dispersion, as expected, and that the presence of convective processes induces a reescalation in the concentration and shifts the tracer velocity to different values with respect to the nonfractal case.

We determine the liquid-solid phase diagram for carbon-oxygen and oxygen-selenium plasma mixtures using two-phase molecular dynamics simulations. We identify liquid, solid, and interface regions using a bond angle metric. To study finite-size effects, we perform 27 648- and 55 296-ion simulations. To help monitor nonequilibrium effects, we calculate diffusion constants $D_i$. For the carbon-oxygen system we find that $D_{\text{O}}$ for oxygen ions in the solid is much smaller than $D_{\text{C}}$ for carbon ions and that both diffusion constants are 80 or more times smaller than diffusion constants in the liquid phase. There is excellent agreement between our carbon-oxygen phase diagram and that predicted by Medin and Cumming. This suggests that errors from finite-size and nonequilibrium effects are small and that the carbon-oxygen phase diagram is now accurately known. The oxygen-selenium system is a simple two-component model for more complex rapid proton capture nucleosynthesis ash compositions for an accreting neutron star. Diffusion of oxygen, in a predominantly selenium crystal, is remarkably fast, comparable to diffusion in the liquid phase. We find a somewhat lower melting temperature for the oxygen-selenium system than that predicted by Medin and Cumming. This is probably because of electron screening effects.

Understanding the in situ amplification of large-scale magnetic fields in turbulent astrophysical rotators has been a core subject of dynamo theory. When turbulent velocities are helical, large-scale dynamos that substantially amplify fields on scales that exceed the turbulent forcing scale arise, but the minimum sufficient fractional kinetic helicity $f_{h,C}$ has not been previously well quantified. Using direct numerical simulations for a simple helical dynamo, we show that $f_{h,C}$ decreases as the ratio of forcing to large-scale wave numbers $k_F/k_{\min }$ increases. From the condition that a large-scale helical dynamo must overcome the back reaction from any nonhelical field on the large scales, we develop a theory that can explain the simulations. For $k_F/k_{\min }⩾8$ we find $f_{h,C}\lesssim 3\%$, implying that very small helicity fractions strongly influence magnetic spectra for even moderate-scale separation.

Phase behavior of large three-dimensional (3D) complex plasma systems under microgravity conditions onboard the International Space Station is investigated. The neutral gas pressure is used as a control parameter to trigger phase changes. Detailed analysis of structural properties and evaluation of three different melting-freezing indicators reveal that complex plasmas can exhibit melting by increasing the gas pressure. Theoretical estimates of complex plasma parameters allow us to identify main factors responsible for the observed behavior. The location of phase states of the investigated systems on a relevant equilibrium phase diagram is estimated. Important differences between the melting process of 3D complex plasmas under microgravity conditions and that of flat 2D complex plasma crystals in ground based experiments are discussed.