We analyze the bending response to light or heat of a solid nematic disk with a director twisted from being radial on the upper surface to be azimuthal on the lower. We find a number of curl lobes determined purely by the geometry of the mechanical frustration that arises during the response.

Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski et al. [Phys. Rev. Lett. 109, 024101 (2012)] introduced a method based on dynamical Bayesian inference that facilitates the simultaneous detection of time-varying synchronization, directionality of influence, and coupling functions. It can distinguish unsynchronized dynamics from noise-induced phase slips. The method is based on phase dynamics, with Bayesian inference of the time-evolving parameters being achieved by shaping the prior densities to incorporate knowledge of previous samples. We now present the method in detail using numerically generated data, data from an analog electronic circuit, and cardiorespiratory data. We also generalize the method to encompass networks of interacting oscillators and thus demonstrate its applicability to small-scale networks.

We analyze the critical behavior of a class of discrete opinion models in the presence of disorder. Within this class, each agent opinion takes a discrete value ($\pm 1$ or 0) and its time evolution is ruled by two terms, one representing agent-agent interactions and the other the degree of conviction or persuasion (a self-interaction). The mean-field limit, where each agent can interact evenly with any other, is considered. Disorder is introduced in the strength of both interactions, with either quenched or annealed random variables. With probability $p$ $(1-p)$, a pairwise interaction reflects a negative (positive) coupling, while the degree of conviction also follows a binary probability distribution (two different discrete probability distributions are considered). Numerical simulations show that a nonequilibrium continuous phase transition, from a disordered state to a state with a prevailing opinion, occurs at a critical point $p_c$ that depends on the distribution of the convictions, with the transition being spoiled in some cases. We also show how the critical line, for each model, is affected by the update scheme (either parallel or sequential) as well as by the kind of disorder (either quenched or annealed).

We study a nonequilibrium equation of states of an ideal quantum gas confined in the cavity under a moving piston with a small but finite velocity in the case in which the cavity wall suddenly begins to move at the time origin. Confining ourselves to the thermally isolated process, the quantum nonadiabatic (QNA) contribution to Poisson's adiabatic equations and to Bernoulli's formula which bridges the pressure and internal energy is elucidated. We carry out a statistical mean of the nonadiabatic (time-reversal-symmetric) force operator found in our preceding paper [Nakamura et al., Phys. Rev. E 83, 041133 (2011)] in both the low-temperature quantum-mechanical and high-temperature quasiclassical regimes. The QNA contribution, which is proportional to the square of the piston's velocity and to the inverse of the longitudinal size of the cavity, has a coefficient that is dependent on the temperature, gas density, and dimensionality of the cavity. The investigation is done for a unidirectionally expanding three-dimensional (3D) rectangular parallelepiped cavity as well as its 1D version. Its relevance in a realistic nanoscale heat engine is discussed.

We use state-of-the-art molecular dynamics simulations to study hydrodynamic effects on aging during kinetics of phase separation in a fluid mixture. The domain growth law shows a crossover from a diffusive regime to a viscous hydrodynamic regime. There is a corresponding crossover in the autocorrelation function from a power-law behavior to an exponential decay. While the former is consistent with theories for diffusive domain growth, the latter results as a consequence of faster advective transport in fluids for which an analytical justification has been provided.

Axial dispersion rates of particles within horizontal rotating cylinders have been calculated for a decade of cylinder diameters. Throughout the range studied the rate of axial dispersion was found to be independent of the cylinder diameter. This phenomenon has been investigated further by spatially resolving the local contribution to the axial dispersion coefficient. This analysis demonstrates that, although the highest rates of axial dispersion occur at the free surface of the bed, there is a significant contribution to axial dispersion throughout the flowing region of the bed. Finally, based on an analogy with a Galton board, a linear relationship is proposed between the local rate of axial dispersion within a horizontal rotating cylinder and the product of the local particle concentration and the local shear rate in a plane perpendicular to the cylinder axis.

The distributions of the size of islands and of the capture zones are discussed comparatively, both experimentally and numerically, for the case of a sudden nucleation process with and without coarsening. The experiments were performed by growing InAs islands on GaAs(001) and the coarsening was altered by varying the temperature. In the two-dimensional kinetic Monte Carlo simulations a single-species diffusing adatom was taken into account, and the coarsening was altered in this case by modifying the binding energy between adatoms and islands. The results show that size and capture zone distributions overlap only when coarsening can be disregarded.

A method for automated coarse-graining of bulk polymers is presented, using the data-mining tool of local feature analysis. Most existing methods for polymer coarse-graining define superatoms based on their covalent bonding topology along the polymer backbone, but here superatoms are defined based only on their correlated motions, as observed in molecular dynamics simulations. Correlated atomic motions are identified in the simulation data using local feature analysis, between atoms in the same or in different polymer chains. Groups of highly correlated atoms constitute the superatoms in the coarse-graining scheme, and the positions of their seed coordinates are then projected forward in time. Based on only the seed positions, local feature analysis enables the full reconstruction of all atomic positions. This reconstruction suggests an iterative scheme to reduce the computation of the simulations to initialize another short molecular dynamic simulation, identify new superatoms, and again project forward in time.

A quantized chaotic map exhibiting localization of wave function intensity is opened. We investigate how such patterns as scars in the Husimi distributions are influenced by the losses through a number of numerical experiments. We find the scars to relocate on the stable or unstable manifolds depending on the position of the opening, and provide a classical argument to explain the observations. For asymmetrically introduced openings mode interaction contributes to determine the localization patterns. We finally show examples of similar localization in a simulated dielectric microcavity.

We develop an approach to understanding long chaotic transients in networks of excitatory pulse-coupled oscillators. Our idea is to identify a class of attractors, sequentially active firing (SAF) attractors, in terms of the temporal event structure of firing and receipt of pulses. Then all attractors can be classified into two groups: SAF attractors and non-SAF attractors. We establish that long transients typically arise in the transitional region of the parameter space where the SAF attractors are collectively destabilized. Bifurcation behavior of the SAF attractors is analyzed to provide a detailed understanding of the long irregular transients. Although demonstrated using pulse-coupled oscillator networks, our general methodology may be useful in understanding the origin of transient chaos in other types of networked systems, an extremely challenging problem in nonlinear dynamics and complex systems.

We present a phase-field-crystal model for driven systems which describes competing effects between thermally activated diffusional processes and those driven by externally imposed ballistic events. The model demonstrates how the mesoscopic Enrique and Bellon [Phys. Rev. Lett. 84, 2885 (2000)] model of externally induced ballistic mixing can be incorporated into the atomistic phase-field-crystal formalism. The combination of the two approaches results in a model capable of describing the microstructural and compositional evolution of a driven system while incorporating elastoplastic effects. The model is applied to the study of grain growth in nanocrystalline materials subjected to an external driving.

This hybrid method [finite-element discrete variable representation (FE-DVR)], introduced by Resigno and McCurdy [Phys. Rev. A 62, 032706 (2000)], uses Lagrange polynomials in each partition, rather than “hat” functions or Gaussian functions. These polynomials are discrete variable representation functions, and they are orthogonal under the Gauss-Lobatto quadrature discretization approximation. Accuracy analyses of this method are performed for the case of a one-dimensional Schrödinger equation with various types of local and nonlocal potentials for scattering boundary conditions. The accuracy is ascertained by a comparison with a spectral Chebyshev integral equation method, accurate to $1:{10}^{-11}$. For an accuracy of the phase shift of $1:{10}^{-8}$, the FE-DVR method is found to be 100 times faster than a sixth-order finite-difference method (Numerov), it is easy to program, and it can routinely achieve an accuracy of better than $1:{10}^{-8}$ for the numerical examples studied.

Experimental methods based on single particle tracking (SPT) are being increasingly employed in the physical and biological sciences, where nanoscale objects are visualized with high temporal and spatial resolution. SPT can probe interactions between a particle and its environment but the price to be paid is the absence of ensemble averaging and a consequent lack of statistics. Here we address the benchmark question of how to accurately extract the diffusion constant of one single Brownian trajectory. We analyze a class of estimators based on weighted functionals of the square displacement. For a certain choice of the weight function these functionals provide the true ensemble averaged diffusion coefficient, with a precision that increases with the trajectory resolution.

Using molecular-dynamics simulation, we have calculated the interfacial free energy $\gamma$ between a hard-sphere fluid and hard spherical and cylindrical colloidal particles, as functions of the particle radius $R$ and the fluid packing fraction $\eta =\rho {\sigma }^3/6$, where $\rho$ and $\sigma$ are the number density and hard-sphere diameter, respectively. These results verify that Hadwiger's theorem from integral geometry, which predicts that $\gamma$ for a fluid at a surface, with certain restrictions, should be a linear combination of the average mean and Gaussian surface curvatures, is valid within the precision of the calculation for spherical and cylindrical surfaces up to $\eta \approx 0.42$. In addition, earlier results for $\gamma$ for this system [Bryk et al., Phys. Rev. E 68, 031602 (2003)] using a geometrically based classical density functional theory are in excellent agreement with the current simulation results for packing fractions in the range where Hadwiger's theorem is valid. However, above $\eta \approx 0.42$, $\gamma \left(R\right)$ shows significant deviations from the Hadwiger form indicating limitations to its use for high-density hard-sphere fluids. Using the results of this study together with Hadwiger's theorem allows one, in principle, to determine $\gamma$ for any sufficiently smooth surface immersed in a hard-sphere fluid.

The translational dynamics of hydration water confined in calcium-silicate-hydrate (C-S-H) gel was studied by quasielastic neutron scattering spectroscopy in the temperature range from 280 to 230 K. The stretch exponent β, the self-diffusion constant $D$, the average translational relaxation time $\langle \tau \rangle$, and the temperature dependence of confinement radius α extracted from the elastic fraction of immobile water molecules $p$($Q$) were obtained from the analyses of the low-$Q$ spectra according to the relaxing cage model. Measurements were made using C-S-H of three different water contents, 10$\%$, 17$\%$, and 30$\%$. Among the three samples of C-S-H gel with different water contents, the values of β decrease with increasing water contents, while α increases. The values of $D$ and $\langle \tau \rangle$ are insensitive to temperature for the two lower water contents, as opposed to the 30$\%$ case where a slight variation is observed. The trend for violation of the Stokes-Einstein relation is only visible in the case of 30$\%$ water content.

An important task in quantitative biology is to understand the role of stochasticity in biochemical regulation. Here, as an extension of our recent work [Phys. Rev. Lett. 107, 148101 (2011)], we study how input fluctuations affect the stochastic dynamics of a simple biological switch. In our model, the on transition rate of the switch is directly regulated by a noisy input signal, which is described as a non-negative mean-reverting diffusion process. This continuous process can be a good approximation of the discrete birth-death process and is much more analytically tractable. Within this setup, we apply the Feynman-Kac theorem to investigate the statistical features of the output switching dynamics. Consistent with our previous findings, the input noise is found to effectively suppress the input-dependent transitions. We show analytically that this effect becomes significant when the input signal fluctuates greatly in amplitude and reverts slowly to its mean.

We propose a formal expansion of the transfer entropy to put in evidence irreducible sets of variables which provide information for the future state of each assigned target. Multiplets characterized by a large contribution to the expansion are associated to the informational circuits present in the system, with an informational character which can be associated to the sign of the contribution. For the sake of computational complexity, we adopt the assumption of Gaussianity and use the corresponding exact formula for the conditional mutual information. We report the application of the proposed methodology on two electroencephalography (EEG) data sets.

We describe an approach to quantify the length scale of a chaotic element of a Rayleigh-Bénard convection layer exhibiting spatiotemporal chaos. The length scale of a chaotic element is determined by simultaneously evolving the dynamics of two convection layers with a unidirectional coupling that involves only the time-varying values of the fluid velocity and temperature on the lateral boundaries of the domain. In our results we numerically simulate the full Boussinesq equations for the precise conditions of experiment. By varying the size of the boundary used for the coupling we identify a length scale that describes the size of a chaotic element. The length scale of the chaotic element is of the same order of magnitude, and exhibits similar trends, as the natural chaotic length scale that is based upon the fractal dimension.

Experiments were conducted in order to study and characterize electrohydrodynamic atomization in the simple-jet mode for inviscid liquids. The operational window of this mode regarding the electric potential and liquid flow rate is presented. From the data it could be concluded that this mode can be divided by the characteristics of its breakup mechanism and that these characteristics are a function of the liquid Weber number and the electric Bond number for a given setup. Additionally we were also able to calculate the average charge per droplet and define the average size of primary and satellite droplets. The dispersion of the spray was also studied regarding its relation to the liquid Weber number and to the electric Bond number. We conclude that simple-jet mode electrosprays are a good option for applications which require monodisperse micrometer droplets with high throughput.